%------------------------------------------------------------------------------
% File     : ITP107_7 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : fmapal.ax [Gau19]
%          : HL4107_7.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  450 ( 149 unt; 209 typ;   0 def)
%            Number of atoms       :  568 ( 321 equ)
%            Maximal formula atoms :   14 (   1 avg)
%            Number of connectives :  342 (  15   ~;   4   |; 124   &)
%                                         (  46 <=>; 153  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   7 avg)
%            Maximal term depth    :   20 (   2 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :  220 ( 101   >; 119   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  206 ( 206 usr;   9 con; 0-7 aty)
%            Number of variables   : 1959 (1639   !;   1   ?;1959   :)
%                                         ( 319  !>;   0  ?*;   0  @-;   0  @+)
% SPC      : TF1_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Eenumeral_2Ebl,type,
    tyop_2Eenumeral_2Ebl: $tType > $tType ).

tff(tyop_2Eenumeral_2Ebt,type,
    tyop_2Eenumeral_2Ebt: $tType > $tType ).

tff(tyop_2Efinite__map_2Efmap,type,
    tyop_2Efinite__map_2Efmap: ( $tType * $tType ) > $tType ).

tff(tyop_2Elist_2Elist,type,
    tyop_2Elist_2Elist: $tType > $tType ).

tff(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: $tType ).

tff(tyop_2Emin_2Efun,type,
    tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).

tff(tyop_2Eoption_2Eoption,type,
    tyop_2Eoption_2Eoption: $tType > $tType ).

tff(tyop_2Epair_2Eprod,type,
    tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).

tff(tyop_2EternaryComparisons_2Eordering,type,
    tyop_2EternaryComparisons_2Eordering: $tType ).

tff(tyop_2Etoto_2Etoto,type,
    tyop_2Etoto_2Etoto: $tType > $tType ).

tff(app_2E2,type,
    app_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).

tff(p,type,
    p: tyop_2Emin_2Ebool > $o ).

tff(combin_i_2E0,type,
    combin_i_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).

tff(combin_k_2E0,type,
    combin_k_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).

tff(combin_s_2E0,type,
    combin_s_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))) ).

tff(c_2Ebool_2E_21_2E0,type,
    c_2Ebool_2E_21_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Ebool_2E_21_2E1,type,
    c_2Ebool_2E_21_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(c_2Epair_2E_2C_2E0,type,
    c_2Epair_2E_2C_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))) ).

tff(c_2Epair_2E_2C_2E2,type,
    c_2Epair_2E_2C_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > tyop_2Epair_2Eprod(A_27a,A_27b) ) ).

tff(c_2Ebool_2E_2F_5C_2E0,type,
    c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).

tff(c_2Ebool_2E_2F_5C_2E2,type,
    c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).

tff(c_2Emin_2E_3D_2E0,type,
    c_2Emin_2E_3D_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Emin_2E_3D_2E2,type,
    c_2Emin_2E_3D_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).

tff(c_2Emin_2E_3D_3D_3E_2E0,type,
    c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).

tff(c_2Emin_2E_3D_3D_3E_2E2,type,
    c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).

tff(c_2Ebool_2E_3F_2E0,type,
    c_2Ebool_2E_3F_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Ebool_2E_3F_2E1,type,
    c_2Ebool_2E_3F_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(c_2Emin_2E_40_2E0,type,
    c_2Emin_2E_40_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a) ).

tff(c_2Emin_2E_40_2E1,type,
    c_2Emin_2E_40_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > A_27a ) ).

tff(c_2Elist_2EAPPEND_2E0,type,
    c_2Elist_2EAPPEND_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).

tff(c_2Elist_2EAPPEND_2E2,type,
    c_2Elist_2EAPPEND_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Efmapal_2EAP__SND_2E0,type,
    c_2Efmapal_2EAP__SND_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c))) ).

tff(c_2Efmapal_2EAP__SND_2E1,type,
    c_2Efmapal_2EAP__SND_2E1: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( tyop_2Emin_2Efun(A_27b,A_27c) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)) ) ).

tff(c_2Efmapal_2EAP__SND_2E2,type,
    c_2Efmapal_2EAP__SND_2E2: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27b,A_27c) * tyop_2Epair_2Eprod(A_27a,A_27b) ) > tyop_2Epair_2Eprod(A_27a,A_27c) ) ).

tff(c_2Epred__set_2ECOMPL_2E0,type,
    c_2Epred__set_2ECOMPL_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Epred__set_2ECOMPL_2E1,type,
    c_2Epred__set_2ECOMPL_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Ebool_2ECOND_2E0,type,
    c_2Ebool_2ECOND_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))) ).

tff(c_2Ebool_2ECOND_2E3,type,
    c_2Ebool_2ECOND_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Ebool * A_27a * A_27a ) > A_27a ) ).

tff(c_2Elist_2ECONS_2E0,type,
    c_2Elist_2ECONS_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).

tff(c_2Elist_2ECONS_2E2,type,
    c_2Elist_2ECONS_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Efinite__map_2EDRESTRICT_2E0,type,
    c_2Efinite__map_2EDRESTRICT_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27a,A_27b))) ).

tff(c_2Efinite__map_2EDRESTRICT_2E2,type,
    c_2Efinite__map_2EDRESTRICT_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efinite__map_2Efmap(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) ).

tff(c_2Eenumeral_2EENUMERAL_2E0,type,
    c_2Eenumeral_2EENUMERAL_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).

tff(c_2Eenumeral_2EENUMERAL_2E2,type,
    c_2Eenumeral_2EENUMERAL_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Eenumeral_2Ebt(A_27a) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2EternaryComparisons_2EEQUAL_2E0,type,
    c_2EternaryComparisons_2EEQUAL_2E0: tyop_2EternaryComparisons_2Eordering ).

tff(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).

tff(c_2Efinite__map_2EFAPPLY_2E0,type,
    c_2Efinite__map_2EFAPPLY_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ).

tff(c_2Efinite__map_2EFAPPLY_2E2,type,
    c_2Efinite__map_2EFAPPLY_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efinite__map_2Efmap(A_27a,A_27b) * A_27a ) > A_27b ) ).

tff(c_2Efinite__map_2EFDOM_2E0,type,
    c_2Efinite__map_2EFDOM_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Efinite__map_2EFDOM_2E1,type,
    c_2Efinite__map_2EFDOM_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Efinite__map_2Efmap(A_27a,A_27b) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Efinite__map_2EFEMPTY_2E0,type,
    c_2Efinite__map_2EFEMPTY_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Efinite__map_2Efmap(A_27a,A_27b) ).

tff(c_2Efmapal_2EFMAPAL_2E0,type,
    c_2Efmapal_2EFMAPAL_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b))) ).

tff(c_2Efmapal_2EFMAPAL_2E2,type,
    c_2Efmapal_2EFMAPAL_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)) ) > tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) ).

tff(c_2Epair_2EFST_2E0,type,
    c_2Epair_2EFST_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a) ).

tff(c_2Efinite__map_2EFUNION_2E0,type,
    c_2Efinite__map_2EFUNION_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))) ).

tff(c_2Efinite__map_2EFUNION_2E2,type,
    c_2Efinite__map_2EFUNION_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efinite__map_2Efmap(A_27a,A_27b) * tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) > tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) ).

tff(c_2Efinite__map_2EFUN__FMAP_2E0,type,
    c_2Efinite__map_2EFUN__FMAP_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27a,A_27b))) ).

tff(c_2Efinite__map_2EFUN__FMAP_2E2,type,
    c_2Efinite__map_2EFUN__FMAP_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) ).

tff(c_2Efinite__map_2EFUPDATE_2E0,type,
    c_2Efinite__map_2EFUPDATE_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))) ).

tff(c_2Efinite__map_2EFUPDATE_2E2,type,
    c_2Efinite__map_2EFUPDATE_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efinite__map_2Efmap(A_27a,A_27b) * tyop_2Epair_2Eprod(A_27a,A_27b) ) > tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) ).

tff(c_2Efinite__map_2EFUPDATE__LIST_2E0,type,
    c_2Efinite__map_2EFUPDATE__LIST_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b))) ).

tff(c_2Efinite__map_2EFUPDATE__LIST_2E2,type,
    c_2Efinite__map_2EFUPDATE__LIST_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Efinite__map_2Efmap(A_27a,A_27b) * tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) > tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) ).

tff(c_2EternaryComparisons_2EGREATER_2E0,type,
    c_2EternaryComparisons_2EGREATER_2E0: tyop_2EternaryComparisons_2Eordering ).

tff(c_2Epred__set_2EGSPEC_2E0,type,
    c_2Epred__set_2EGSPEC_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Epred__set_2EGSPEC_2E1,type,
    c_2Epred__set_2EGSPEC_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Ecombin_2EI_2E0,type,
    c_2Ecombin_2EI_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).

tff(c_2Ecombin_2EI_2E1,type,
    c_2Ecombin_2EI_2E1: 
      !>[A_27a: $tType] : ( A_27a > A_27a ) ).

tff(c_2Ebool_2EIN_2E0,type,
    c_2Ebool_2EIN_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Ebool_2EIN_2E2,type,
    c_2Ebool_2EIN_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Eoption_2EIS__SOME_2E0,type,
    c_2Eoption_2EIS__SOME_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool) ).

tff(c_2EternaryComparisons_2ELESS_2E0,type,
    c_2EternaryComparisons_2ELESS_2E0: tyop_2EternaryComparisons_2Eordering ).

tff(c_2Eenumeral_2ELESS__ALL_2E0,type,
    c_2Eenumeral_2ELESS__ALL_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))) ).

tff(c_2Eenumeral_2ELESS__ALL_2E3,type,
    c_2Eenumeral_2ELESS__ALL_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Ebool_2ELET_2E0,type,
    c_2Ebool_2ELET_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ).

tff(c_2Ebool_2ELET_2E2,type,
    c_2Ebool_2ELET_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).

tff(c_2Elist_2ELIST__TO__SET_2E0,type,
    c_2Elist_2ELIST__TO__SET_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Elist_2ELIST__TO__SET_2E1,type,
    c_2Elist_2ELIST__TO__SET_2E1: 
      !>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Elist_2EMAP_2E0,type,
    c_2Elist_2EMAP_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))) ).

tff(c_2Elist_2EMAP_2E2,type,
    c_2Elist_2EMAP_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27b) ) ).

tff(c_2Elist_2ENIL_2E0,type,
    c_2Elist_2ENIL_2E0: 
      !>[A_27a: $tType] : tyop_2Elist_2Elist(A_27a) ).

tff(c_2Eoption_2ENONE_2E0,type,
    c_2Eoption_2ENONE_2E0: 
      !>[A_27a: $tType] : tyop_2Eoption_2Eoption(A_27a) ).

tff(c_2Efmapal_2EOFU_2E0,type,
    c_2Efmapal_2EOFU_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)))) ).

tff(c_2Efmapal_2EOFU_2E3,type,
    c_2Efmapal_2EOFU_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Efinite__map_2Efmap(A_27a,A_27b) * tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) > tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) ).

tff(c_2Eenumeral_2EOL_2E0,type,
    c_2Eenumeral_2EOL_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)) ).

tff(c_2Eenumeral_2EOL_2E2,type,
    c_2Eenumeral_2EOL_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Efmapal_2EOPTION__FLAT_2E0,type,
    c_2Efmapal_2EOPTION__FLAT_2E0: 
      !>[A_27z: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)) ).

tff(c_2Efmapal_2EOPTION__FLAT_2E1,type,
    c_2Efmapal_2EOPTION__FLAT_2E1: 
      !>[A_27z: $tType] : ( tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))) > tyop_2Elist_2Elist(A_27z) ) ).

tff(c_2Efmapal_2EOPTION__UPDATE_2E0,type,
    c_2Efmapal_2EOPTION__UPDATE_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))) ).

tff(c_2Efmapal_2EOPTION__UPDATE_2E3,type,
    c_2Efmapal_2EOPTION__UPDATE_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)) * tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)) * A_27a ) > tyop_2Eoption_2Eoption(A_27b) ) ).

tff(c_2Efmapal_2EORL_2E0,type,
    c_2Efmapal_2EORL_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)) ).

tff(c_2Efmapal_2EORL_2E2,type,
    c_2Efmapal_2EORL_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Efmapal_2EORL__bt_2E0,type,
    c_2Efmapal_2EORL__bt_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)) ).

tff(c_2Efmapal_2EORL__bt_2E2,type,
    c_2Efmapal_2EORL__bt_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Efmapal_2EORL__bt__lb_2E0,type,
    c_2Efmapal_2EORL__bt__lb_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))) ).

tff(c_2Efmapal_2EORL__bt__lb_2E3,type,
    c_2Efmapal_2EORL__bt__lb_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * A_27a * tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Efmapal_2EORL__bt__lb__ub_2E0,type,
    c_2Efmapal_2EORL__bt__lb__ub_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))) ).

tff(c_2Efmapal_2EORL__bt__lb__ub_2E4,type,
    c_2Efmapal_2EORL__bt__lb__ub_2E4: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * A_27a * tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)) * A_27a ) > tyop_2Emin_2Ebool ) ).

tff(c_2Efmapal_2EORL__bt__ub_2E0,type,
    c_2Efmapal_2EORL__bt__ub_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).

tff(c_2Efmapal_2EORL__bt__ub_2E3,type,
    c_2Efmapal_2EORL__bt__ub_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)) * A_27a ) > tyop_2Emin_2Ebool ) ).

tff(c_2Efmapal_2EORL__sublists_2E0,type,
    c_2Efmapal_2EORL__sublists_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)) ).

tff(c_2Efmapal_2EORL__sublists_2E2,type,
    c_2Efmapal_2EORL__sublists_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Efmapal_2EORWL_2E0,type,
    c_2Efmapal_2EORWL_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))) ).

tff(c_2Efmapal_2EORWL_2E3,type,
    c_2Efmapal_2EORWL_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Efinite__map_2Efmap(A_27a,A_27b) * tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Eenumeral_2EOWL_2E0,type,
    c_2Eenumeral_2EOWL_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))) ).

tff(c_2Eenumeral_2EOWL_2E3,type,
    c_2Eenumeral_2EOWL_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Elist_2EREVERSE_2E0,type,
    c_2Elist_2EREVERSE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)) ).

tff(c_2Elist_2EREVERSE_2E1,type,
    c_2Elist_2EREVERSE_2E1: 
      !>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Eoption_2ESOME_2E0,type,
    c_2Eoption_2ESOME_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)) ).

tff(c_2Eoption_2ESOME_2E1,type,
    c_2Eoption_2ESOME_2E1: 
      !>[A_27a: $tType] : ( A_27a > tyop_2Eoption_2Eoption(A_27a) ) ).

tff(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).

tff(c_2Eoption_2ETHE_2E0,type,
    c_2Eoption_2ETHE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),A_27a) ).

tff(c_2Efmapal_2EUFO_2E0,type,
    c_2Efmapal_2EUFO_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)))) ).

tff(c_2Efmapal_2EUFO_2E3,type,
    c_2Efmapal_2EUFO_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Efinite__map_2Efmap(A_27a,A_27b) * tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) > tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) ).

tff(c_2Erelation_2EWF_2E0,type,
    c_2Erelation_2EWF_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).

tff(c_2Erelation_2EWF_2E1,type,
    c_2Erelation_2EWF_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).

tff(c_2Erelation_2EWFREC_2E0,type,
    c_2Erelation_2EWFREC_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b))) ).

tff(c_2Erelation_2EWFREC_2E2,type,
    c_2Erelation_2EWFREC_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).

tff(c_2Ebool_2E_5C_2F_2E0,type,
    c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).

tff(c_2Ebool_2E_5C_2F_2E2,type,
    c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).

tff(c_2Etoto_2Eapto_2E0,type,
    c_2Etoto_2Eapto_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering))) ).

tff(c_2Etoto_2Eapto_2E3,type,
    c_2Etoto_2Eapto_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * A_27a * A_27a ) > tyop_2EternaryComparisons_2Eordering ) ).

tff(c_2Efmapal_2Eassocv_2E0,type,
    c_2Efmapal_2Eassocv_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))) ).

tff(c_2Efmapal_2Eassocv_2E2,type,
    c_2Efmapal_2Eassocv_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) * A_27a ) > tyop_2Eoption_2Eoption(A_27b) ) ).

tff(c_2Efmapal_2Ebl__to__fmap_2E0,type,
    c_2Efmapal_2Ebl__to__fmap_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b))) ).

tff(c_2Efmapal_2Ebl__to__fmap_2E2,type,
    c_2Efmapal_2Ebl__to__fmap_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)) ) > tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) ).

tff(c_2Eenumeral_2Ebt__CASE_2E0,type,
    c_2Eenumeral_2Ebt__CASE_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),A_27b))),A_27b))) ).

tff(c_2Eenumeral_2Ebt__CASE_2E3,type,
    c_2Eenumeral_2Ebt__CASE_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Eenumeral_2Ebt(A_27a) * A_27b * tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),A_27b))) ) > A_27b ) ).

tff(c_2Efmapal_2Ebt__map_2E0,type,
    c_2Efmapal_2Ebt__map_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Eenumeral_2Ebt(A_27b))) ).

tff(c_2Efmapal_2Ebt__map_2E2,type,
    c_2Efmapal_2Ebt__map_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Eenumeral_2Ebt(A_27a) ) > tyop_2Eenumeral_2Ebt(A_27b) ) ).

tff(c_2Efmapal_2Ebt__rplacv__cn_2E0,type,
    c_2Efmapal_2Ebt__rplacv__cn_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))))) ).

tff(c_2Efmapal_2Ebt__rplacv__cn_2E4,type,
    c_2Efmapal_2Ebt__rplacv__cn_2E4: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Epair_2Eprod(A_27a,A_27b) * tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)) * tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))) ) > tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)) ) ).

tff(c_2Efmapal_2Ebt__to__fmap__lb_2E0,type,
    c_2Efmapal_2Ebt__to__fmap__lb_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b)))) ).

tff(c_2Efmapal_2Ebt__to__fmap__lb_2E3,type,
    c_2Efmapal_2Ebt__to__fmap__lb_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * A_27a * tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)) ) > tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) ).

tff(c_2Efmapal_2Ebt__to__fmap__lb__ub_2E0,type,
    c_2Efmapal_2Ebt__to__fmap__lb__ub_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Efinite__map_2Efmap(A_27a,A_27b))))) ).

tff(c_2Efmapal_2Ebt__to__fmap__lb__ub_2E4,type,
    c_2Efmapal_2Ebt__to__fmap__lb__ub_2E4: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * A_27a * tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)) * A_27a ) > tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) ).

tff(c_2Efmapal_2Ebt__to__fmap__ub_2E0,type,
    c_2Efmapal_2Ebt__to__fmap__ub_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Efinite__map_2Efmap(A_27a,A_27b)))) ).

tff(c_2Efmapal_2Ebt__to__fmap__ub_2E3,type,
    c_2Efmapal_2Ebt__to__fmap__ub_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)) * A_27a ) > tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) ).

tff(c_2Eenumeral_2Ebt__to__list__ac_2E0,type,
    c_2Eenumeral_2Ebt__to__list__ac_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).

tff(c_2Eenumeral_2Ebt__to__list__ac_2E2,type,
    c_2Eenumeral_2Ebt__to__list__ac_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Eenumeral_2Ebt(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Efmapal_2Ebt__to__orl_2E0,type,
    c_2Efmapal_2Ebt__to__orl_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))) ).

tff(c_2Efmapal_2Ebt__to__orl_2E2,type,
    c_2Efmapal_2Ebt__to__orl_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)) ) > tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) ).

tff(c_2Efmapal_2Ebt__to__orl__ac_2E0,type,
    c_2Efmapal_2Ebt__to__orl__ac_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))) ).

tff(c_2Efmapal_2Ebt__to__orl__ac_2E3,type,
    c_2Efmapal_2Ebt__to__orl__ac_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)) * tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) > tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) ).

tff(c_2Efmapal_2Ebt__to__orl__lb_2E0,type,
    c_2Efmapal_2Ebt__to__orl__lb_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))) ).

tff(c_2Efmapal_2Ebt__to__orl__lb_2E3,type,
    c_2Efmapal_2Ebt__to__orl__lb_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * A_27a * tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)) ) > tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) ).

tff(c_2Efmapal_2Ebt__to__orl__lb__ac_2E0,type,
    c_2Efmapal_2Ebt__to__orl__lb__ac_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))) ).

tff(c_2Efmapal_2Ebt__to__orl__lb__ac_2E4,type,
    c_2Efmapal_2Ebt__to__orl__lb__ac_2E4: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * A_27a * tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)) * tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) > tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) ).

tff(c_2Efmapal_2Ebt__to__orl__lb__ub_2E0,type,
    c_2Efmapal_2Ebt__to__orl__lb__ub_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))) ).

tff(c_2Efmapal_2Ebt__to__orl__lb__ub_2E4,type,
    c_2Efmapal_2Ebt__to__orl__lb__ub_2E4: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * A_27a * tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)) * A_27a ) > tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) ).

tff(c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E0,type,
    c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))) ).

tff(c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5,type,
    c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * A_27a * tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)) * A_27a * tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) > tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) ).

tff(c_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__aux_2E0,type,
    c_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__aux_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))) ).

tff(c_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__aux_2E1,type,
    c_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__aux_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))) ) ).

tff(c_2Efmapal_2Ebt__to__orl__ub_2E0,type,
    c_2Efmapal_2Ebt__to__orl__ub_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))) ).

tff(c_2Efmapal_2Ebt__to__orl__ub_2E3,type,
    c_2Efmapal_2Ebt__to__orl__ub_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)) * A_27a ) > tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) ).

tff(c_2Efmapal_2Ebt__to__orl__ub__ac_2E0,type,
    c_2Efmapal_2Ebt__to__orl__ub__ac_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))) ).

tff(c_2Efmapal_2Ebt__to__orl__ub__ac_2E4,type,
    c_2Efmapal_2Ebt__to__orl__ub__ac_2E4: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)) * A_27a * tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) > tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) ).

tff(c_2Efmapal_2Ediff__merge_2E0,type,
    c_2Efmapal_2Ediff__merge_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))) ).

tff(c_2Efmapal_2Ediff__merge_2E3,type,
    c_2Efmapal_2Ediff__merge_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) ).

tff(c_2Efmapal_2Efmap_2E0,type,
    c_2Efmapal_2Efmap_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b)) ).

tff(c_2Efmapal_2Efmap_2E1,type,
    c_2Efmapal_2Efmap_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) > tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) ).

tff(c_2Efmapal_2Eincr__build_2E0,type,
    c_2Efmapal_2Eincr__build_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))) ).

tff(c_2Efmapal_2Eincr__build_2E2,type,
    c_2Efmapal_2Eincr__build_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) > tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))) ) ).

tff(c_2Efmapal_2Eincr__flat_2E0,type,
    c_2Efmapal_2Eincr__flat_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))) ).

tff(c_2Efmapal_2Eincr__flat_2E2,type,
    c_2Efmapal_2Eincr__flat_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))) ) > tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) ).

tff(c_2Efmapal_2Eincr__merge_2E0,type,
    c_2Efmapal_2Eincr__merge_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))) ).

tff(c_2Efmapal_2Eincr__merge_2E3,type,
    c_2Efmapal_2Eincr__merge_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) * tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))) ) > tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))) ) ).

tff(c_2Efmapal_2Eincr__sort_2E0,type,
    c_2Efmapal_2Eincr__sort_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))) ).

tff(c_2Efmapal_2Eincr__sort_2E2,type,
    c_2Efmapal_2Eincr__sort_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) > tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) ).

tff(c_2Efmapal_2Einter__merge_2E0,type,
    c_2Efmapal_2Einter__merge_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))) ).

tff(c_2Efmapal_2Einter__merge_2E3,type,
    c_2Efmapal_2Einter__merge_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) ).

tff(c_2Elist_2Elist__CASE_2E0,type,
    c_2Elist_2Elist__CASE_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),A_27b))) ).

tff(c_2Elist_2Elist__CASE_2E3,type,
    c_2Elist_2Elist__CASE_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * A_27b * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)) ) > A_27b ) ).

tff(c_2Efmapal_2Elist__rplacv__cn_2E0,type,
    c_2Efmapal_2Elist__rplacv__cn_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))) ).

tff(c_2Efmapal_2Elist__rplacv__cn_2E3,type,
    c_2Efmapal_2Elist__rplacv__cn_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epair_2Eprod(A_27a,A_27b) * tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) * tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))) ) > tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) ).

tff(c_2Eenumeral_2Elist__to__bt_2E0,type,
    c_2Eenumeral_2Elist__to__bt_2E0: 
      !>[A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Eenumeral_2Ebt(A_27c)) ).

tff(c_2Eenumeral_2Elist__to__bt_2E1,type,
    c_2Eenumeral_2Elist__to__bt_2E1: 
      !>[A_27c: $tType] : ( tyop_2Elist_2Elist(A_27c) > tyop_2Eenumeral_2Ebt(A_27c) ) ).

tff(c_2Efmapal_2Emerge_2E0,type,
    c_2Efmapal_2Emerge_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))) ).

tff(c_2Efmapal_2Emerge_2E3,type,
    c_2Efmapal_2Emerge_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) * tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) > tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) ).

tff(c_2Efmapal_2Emerge__out_2E0,type,
    c_2Efmapal_2Emerge__out_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))) ).

tff(c_2Efmapal_2Emerge__out_2E3,type,
    c_2Efmapal_2Emerge__out_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Etoto_2Etoto(A_27a) * tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) * tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))) ) > tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) ).

tff(c_2Eenumeral_2Enbl_2E0,type,
    c_2Eenumeral_2Enbl_2E0: 
      !>[A_27a: $tType] : tyop_2Eenumeral_2Ebl(A_27a) ).

tff(c_2Eenumeral_2Enode_2E0,type,
    c_2Eenumeral_2Enode_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Eenumeral_2Ebt(A_27a)))) ).

tff(c_2Eenumeral_2Enode_2E3,type,
    c_2Eenumeral_2Enode_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Eenumeral_2Ebt(A_27a) * A_27a * tyop_2Eenumeral_2Ebt(A_27a) ) > tyop_2Eenumeral_2Ebt(A_27a) ) ).

tff(c_2Eenumeral_2Ent_2E0,type,
    c_2Eenumeral_2Ent_2E0: 
      !>[A_27a: $tType] : tyop_2Eenumeral_2Ebt(A_27a) ).

tff(c_2Ecombin_2Eo_2E0,type,
    c_2Ecombin_2Eo_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b))) ).

tff(c_2Ecombin_2Eo_2E2,type,
    c_2Ecombin_2Eo_2E2: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27c,A_27b) * tyop_2Emin_2Efun(A_27a,A_27c) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).

tff(c_2Efinite__map_2Eo__f_2E0,type,
    c_2Efinite__map_2Eo__f_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27c))) ).

tff(c_2Efinite__map_2Eo__f_2E2,type,
    c_2Efinite__map_2Eo__f_2E2: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27b,A_27c) * tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) > tyop_2Efinite__map_2Efmap(A_27a,A_27c) ) ).

tff(c_2Eenumeral_2Eonebl_2E0,type,
    c_2Eenumeral_2Eonebl_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a)))) ).

tff(c_2Eenumeral_2Eonebl_2E3,type,
    c_2Eenumeral_2Eonebl_2E3: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Eenumeral_2Ebt(A_27a) * tyop_2Eenumeral_2Ebl(A_27a) ) > tyop_2Eenumeral_2Ebl(A_27a) ) ).

tff(c_2Eoption_2Eoption__CASE_2E0,type,
    c_2Eoption_2Eoption__CASE_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b))) ).

tff(c_2Eoption_2Eoption__CASE_2E3,type,
    c_2Eoption_2Eoption__CASE_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Eoption_2Eoption(A_27a) * A_27b * tyop_2Emin_2Efun(A_27a,A_27b) ) > A_27b ) ).

tff(c_2Efmapal_2Eoptry_2E0,type,
    c_2Efmapal_2Eoptry_2E0: 
      !>[A_27z: $tType] : tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27z),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27z),tyop_2Eoption_2Eoption(A_27z))) ).

tff(c_2Efmapal_2Eoptry_2E2,type,
    c_2Efmapal_2Eoptry_2E2: 
      !>[A_27z: $tType] : ( ( tyop_2Eoption_2Eoption(A_27z) * tyop_2Eoption_2Eoption(A_27z) ) > tyop_2Eoption_2Eoption(A_27z) ) ).

tff(c_2Efmapal_2Eoptry__list_2E0,type,
    c_2Efmapal_2Eoptry__list_2E0: 
      !>[A_27g: $tType,A_27z: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Eoption_2Eoption(A_27g))) ).

tff(c_2Efmapal_2Eoptry__list_2E2,type,
    c_2Efmapal_2Eoptry__list_2E2: 
      !>[A_27g: $tType,A_27z: $tType] : ( ( tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)) * tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)) ) > tyop_2Eoption_2Eoption(A_27g) ) ).

tff(c_2EternaryComparisons_2Eordering__CASE_2E0,type,
    c_2EternaryComparisons_2Eordering__CASE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)))) ).

tff(c_2EternaryComparisons_2Eordering__CASE_2E4,type,
    c_2EternaryComparisons_2Eordering__CASE_2E4: 
      !>[A_27a: $tType] : ( ( tyop_2EternaryComparisons_2Eordering * A_27a * A_27a * A_27a ) > A_27a ) ).

tff(c_2Epair_2Epair__CASE_2E0,type,
    c_2Epair_2Epair__CASE_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),A_27a)) ).

tff(c_2Epair_2Epair__CASE_2E2,type,
    c_2Epair_2Epair__CASE_2E2: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Epair_2Eprod(A_27b,A_27c) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)) ) > A_27a ) ).

tff(c_2Efmapal_2Eunlookup_2E0,type,
    c_2Efmapal_2Eunlookup_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b)) ).

tff(c_2Efmapal_2Eunlookup_2E1,type,
    c_2Efmapal_2Eunlookup_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)) > tyop_2Efinite__map_2Efmap(A_27a,A_27b) ) ).

tff(c_2Efmapal_2Evcossa_2E0,type,
    c_2Efmapal_2Evcossa_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eoption_2Eoption(A_27b))) ).

tff(c_2Efmapal_2Evcossa_2E2,type,
    c_2Efmapal_2Evcossa_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)) ) > tyop_2Eoption_2Eoption(A_27b) ) ).

tff(c_2Eenumeral_2Ezerbl_2E0,type,
    c_2Eenumeral_2Ezerbl_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(A_27a),tyop_2Eenumeral_2Ebl(A_27a)) ).

tff(c_2Eenumeral_2Ezerbl_2E1,type,
    c_2Eenumeral_2Ezerbl_2E1: 
      !>[A_27a: $tType] : ( tyop_2Eenumeral_2Ebl(A_27a) > tyop_2Eenumeral_2Ebl(A_27a) ) ).

tff(c_2Ebool_2E_7E_2E0,type,
    c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).

tff(c_2Ebool_2E_7E_2E1,type,
    c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).

tff(thm_2Eextra_2Dho_2Eeq__ext,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) )
     => ( V0f_2E0 = V1g_2E0 ) ) ).

tff(thm_2Eextra_2Dho_2Eboolext,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
      ( ( p(V0_2E0)
      <=> p(V1_2E0) )
     => ( V0_2E0 = V1_2E0 ) ) ).

tff(thm_2Eextra_2Dho_2Etruth,axiom,
    p(c_2Ebool_2ET_2E0) ).

tff(thm_2Eextra_2Dho_2Enotfalse,axiom,
    ~ p(c_2Ebool_2EF_2E0) ).

tff(thm_2Eextra_2Dho_2Ebool__cases__ax,axiom,
    ! [V0t_2E0: tyop_2Emin_2Ebool] :
      ( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
      | ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).

tff(thm_2Eextra_2Dho_2Ei__thm,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,combin_i_2E0(A_27a),V0x_2E0) = V0x_2E0 ) ).

tff(thm_2Eextra_2Dho_2Ek__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),combin_k_2E0(A_27a,A_27b),V0x_2E0),V1y_2E0) = V0x_2E0 ) ).

tff(thm_2Eextra_2Dho_2Es__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),combin_s_2E0(A_27a,A_27b,A_27c),V0f_2E0),V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ) ).

tff(logicdef_2E_2F_5C,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
        & p(V1_2E0) ) ) ).

tff(logicdef_2E_5C_2F,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
        | p(V1_2E0) ) ) ).

tff(logicdef_2E_7E,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2E_7E_2E1(V0_2E0))
    <=> ~ p(V0_2E0) ) ).

tff(logicdef_2E_3D_3D_3E,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
      ( p(c_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
       => p(V1_2E0) ) ) ).

tff(logicdef_2E_3D,axiom,
    ! [A_27a: $tType,V0_2E0: A_27a,V1_2E0: A_27a] :
      ( p(c_2Emin_2E_3D_2E2(A_27a,V0_2E0,V1_2E0))
    <=> ( V0_2E0 = V1_2E0 ) ) ).

tff(quantdef_2E_21,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2E_21_2E1(A_27a,V0f_2E0))
    <=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).

tff(quantdef_2E_3F,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2E_3F_2E1(A_27a,V0f_2E0))
    <=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).

tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: A_27b] : ( c_2Epair_2E_2C_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Epair_2E_2C_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: A_27a,X1_2E0: A_27c] : ( c_2Epair_2E_2C_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c),app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c)),c_2Epair_2E_2C_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(A_27a,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Epair_2E_2C_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Epair_2E_2C_2E0(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28tyop_2Eenumeral_2Ebt_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_2Ctyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))] : ( c_2Epair_2E_2C_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),c_2Epair_2E_2C_2E0(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eenumeral_2Ebt_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))] : ( c_2Epair_2E_2C_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Epair_2E_2C_2E0(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Etoto_2Etoto_28A_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Eenumeral_2Ebt_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_2Ctyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))] : ( c_2Epair_2E_2C_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))),c_2Epair_2E_2C_2E0(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
        & p(X1_2E0) )
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
      ( ( X0_2E0 = X1_2E0 )
    <=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).

tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
       => p(X1_2E0) )
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27z_29_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27z_29_29_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [A_27z: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E0(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool))),X0_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27z,axiom,
    ! [A_27z: $tType,X0_2E0: tyop_2Elist_2Elist(A_27z),X1_2E0: tyop_2Elist_2Elist(A_27z)] : ( c_2Elist_2EAPPEND_2E2(A_27z,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z),app_2E2(tyop_2Elist_2Elist(A_27z),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z)),c_2Elist_2EAPPEND_2E0(A_27z),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EAPPEND_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2EAPPEND_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Efmapal_2EAP__SND_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27c)] : ( c_2Efmapal_2EAP__SND_2E1(A_27a,A_27b,A_27c,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),c_2Efmapal_2EAP__SND_2E0(A_27a,A_27b,A_27c),X0_2E0) ) ).

tff(arityeq2_2Ec_2Efmapal_2EAP__SND_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2Efmapal_2EAP__SND_2E2(A_27a,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),c_2Efmapal_2EAP__SND_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2ECOMPL_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECOMPL_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E0(A_27a),X0_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: A_27b,X2_2E0: A_27b] : ( c_2Ebool_2ECOND_2E3(A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27b,A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),c_2Ebool_2ECOND_2E0(A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool,X2_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2ECOND_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Ebool_2ECOND_2E0(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(A_27b),X2_2E0: tyop_2Eoption_2Eoption(A_27b)] : ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27b),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(A_27b)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ECONS_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ECONS_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27z_29,axiom,
    ! [A_27z: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27z),X1_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z))] : ( c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(A_27z),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),app_2E2(tyop_2Eoption_2Eoption(A_27z),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z))),c_2Elist_2ECONS_2E0(tyop_2Eoption_2Eoption(A_27z)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27z_29_29,axiom,
    ! [A_27z: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),X1_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)))] : ( c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)))),c_2Elist_2ECONS_2E0(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),X1_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))] : ( c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Elist_2ECONS_2E0(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2ECONS_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Efinite__map_2EDRESTRICT_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),c_2Efinite__map_2EDRESTRICT_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eenumeral_2EENUMERAL_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Eenumeral_2EENUMERAL_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eenumeral_2EENUMERAL_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Efinite__map_2EFAPPLY_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0: A_27a] : ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27a,A_27b,app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b),c_2Efinite__map_2EFAPPLY_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Efinite__map_2EFDOM_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq2_2Ec_2Efmapal_2EFMAPAL_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2EFMAPAL_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),c_2Efmapal_2EFMAPAL_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Efmapal_2EFMAPAL_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27c))] : ( c_2Efmapal_2EFMAPAL_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Efinite__map_2Efmap(A_27a,A_27c),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Efinite__map_2Efmap(A_27a,A_27c)),c_2Efmapal_2EFMAPAL_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Efinite__map_2EFUNION_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),c_2Efinite__map_2EFUNION_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Efinite__map_2EFUN__FMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Efinite__map_2EFUN__FMAP_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),c_2Efinite__map_2EFUN__FMAP_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Efinite__map_2EFUPDATE_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0: tyop_2Epair_2Eprod(A_27a,A_27b)] : ( c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),c_2Efinite__map_2EFUPDATE_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Efinite__map_2EFUPDATE__LIST_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),c_2Efinite__map_2EFUPDATE__LIST_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(A_27a,A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27z_29,axiom,
    ! [A_27z: $tType,X0_2E0: tyop_2Elist_2Elist(A_27z)] : ( c_2Ecombin_2EI_2E1(tyop_2Elist_2Elist(A_27z),X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z),c_2Ecombin_2EI_2E0(tyop_2Elist_2Elist(A_27z)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Ecombin_2EI_2E1(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ecombin_2EI_2E0(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Eenumeral_2ELESS__ALL_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: A_27a,X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Eenumeral_2ELESS__ALL_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eenumeral_2ELESS__ALL_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Eenumeral_2Ebt_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Ebool_2ELET_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),c_2Ebool_2ELET_2E0(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Ebool_2ELET_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),c_2Ebool_2ELET_2E0(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EMAP_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2EMAP_2E0(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27c)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27c))),c_2Elist_2EMAP_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Efmapal_2EOFU_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efmapal_2EOFU_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),c_2Efmapal_2EOFU_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Eenumeral_2EOL_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2EOL_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Eenumeral_2EOL_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Efmapal_2EOPTION__FLAT_2E1_2Emono_2EA_27z,axiom,
    ! [A_27z: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)))] : ( c_2Efmapal_2EOPTION__FLAT_2E1(A_27z,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z),c_2Efmapal_2EOPTION__FLAT_2E0(A_27z),X0_2E0) ) ).

tff(arityeq3_2Ec_2Efmapal_2EOPTION__UPDATE_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X2_2E0: A_27a] : ( c_2Efmapal_2EOPTION__UPDATE_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Efmapal_2EOPTION__UPDATE_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Efmapal_2EORL_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2EORL_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),c_2Efmapal_2EORL_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Efmapal_2EORL__bt_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2EORL__bt_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),c_2Efmapal_2EORL__bt_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Efmapal_2EORL__bt__lb_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: A_27a,X2_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2EORL__bt__lb_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),c_2Efmapal_2EORL__bt__lb_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq4_2Ec_2Efmapal_2EORL__bt__lb__ub_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: A_27a,X2_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X3_2E0: A_27a] : ( c_2Efmapal_2EORL__bt__lb__ub_2E4(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Efmapal_2EORL__bt__lb__ub_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).

tff(arityeq3_2Ec_2Efmapal_2EORL__bt__ub_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0: A_27a] : ( c_2Efmapal_2EORL__bt__ub_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Efmapal_2EORL__bt__ub_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Efmapal_2EORL__sublists_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))] : ( c_2Efmapal_2EORL__sublists_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),c_2Efmapal_2EORL__sublists_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Efmapal_2EORWL_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2EORWL_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),c_2Efmapal_2EORWL_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Eenumeral_2EOWL_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eenumeral_2EOWL_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Eenumeral_2EOWL_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EREVERSE_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Elist_2EREVERSE_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EREVERSE_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: A_27b] : ( c_2Eoption_2ESOME_2E1(A_27b,X0_2E0) = app_2E2(A_27b,tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27z,axiom,
    ! [A_27z: $tType,X0_2E0: A_27z] : ( c_2Eoption_2ESOME_2E1(A_27z,X0_2E0) = app_2E2(A_27z,tyop_2Eoption_2Eoption(A_27z),c_2Eoption_2ESOME_2E0(A_27z),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27z_29,axiom,
    ! [A_27z: $tType,X0_2E0: tyop_2Elist_2Elist(A_27z)] : ( c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27z),X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27z),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),c_2Eoption_2ESOME_2E0(tyop_2Elist_2Elist(A_27z)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ESOME_2E0(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),X0_2E0) ) ).

tff(arityeq3_2Ec_2Efmapal_2EUFO_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),X2_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efmapal_2EUFO_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),c_2Efmapal_2EUFO_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27z_29_29_29,axiom,
    ! [A_27z: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWF_2E1(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E0(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)))),X0_2E0) ) ).

tff(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27z_29_29_29_20mono_2Etyop_2Elist_2Elist_28A_27z_29,axiom,
    ! [A_27z: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)))] : ( c_2Erelation_2EWFREC_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z))),c_2Erelation_2EWFREC_2E0(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Etoto_2Etoto_28A_27a_29_2Ctyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Eenumeral_2Ebt_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_2Ctyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_29_29_29_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))] : ( c_2Erelation_2EWFREC_2E2(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Erelation_2EWFREC_2E0(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
        | p(X1_2E0) )
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq3_2Ec_2Etoto_2Eapto_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: A_27a,X2_2E0: A_27a] : ( c_2Etoto_2Eapto_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2EternaryComparisons_2Eordering,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2EternaryComparisons_2Eordering)),c_2Etoto_2Eapto_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Efmapal_2Eassocv_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0: A_27a] : ( c_2Efmapal_2Eassocv_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Efmapal_2Eassocv_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Efmapal_2Ebl__to__fmap_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2Ebl__to__fmap_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),c_2Efmapal_2Ebl__to__fmap_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Eenumeral_2Ebt__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))] : ( c_2Eenumeral_2Ebt__CASE_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Eenumeral_2Ebt__CASE_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Efmapal_2Ebt__map_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Efmapal_2Ebt__map_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Eenumeral_2Ebt(A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Eenumeral_2Ebt(A_27b)),c_2Efmapal_2Ebt__map_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Efmapal_2Ebt__map_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),X1_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2Ebt__map_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(A_27a)),c_2Efmapal_2Ebt__map_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Efmapal_2Ebt__map_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),X1_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2Ebt__map_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27c)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27c))),c_2Efmapal_2Ebt__map_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),X0_2E0),X1_2E0) ) ).

tff(arityeq4_2Ec_2Efmapal_2Ebt__rplacv__cn_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),X2_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X3_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))] : ( c_2Efmapal_2Ebt__rplacv__cn_2E4(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Efmapal_2Ebt__rplacv__cn_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).

tff(arityeq3_2Ec_2Efmapal_2Ebt__to__fmap__lb_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: A_27a,X2_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2Ebt__to__fmap__lb_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),c_2Efmapal_2Ebt__to__fmap__lb_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq4_2Ec_2Efmapal_2Ebt__to__fmap__lb__ub_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: A_27a,X2_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X3_2E0: A_27a] : ( c_2Efmapal_2Ebt__to__fmap__lb__ub_2E4(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27a,tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Efinite__map_2Efmap(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Efinite__map_2Efmap(A_27a,A_27b))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Efinite__map_2Efmap(A_27a,A_27b)))),c_2Efmapal_2Ebt__to__fmap__lb__ub_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).

tff(arityeq3_2Ec_2Efmapal_2Ebt__to__fmap__ub_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0: A_27a] : ( c_2Efmapal_2Ebt__to__fmap__ub_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Efinite__map_2Efmap(A_27a,A_27b)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Efinite__map_2Efmap(A_27a,A_27b))),c_2Efmapal_2Ebt__to__fmap__ub_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Eenumeral_2Ebt__to__list__ac_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Eenumeral_2Ebt__to__list__ac_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eenumeral_2Ebt__to__list__ac_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Efmapal_2Ebt__to__orl_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2Ebt__to__orl_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Efmapal_2Ebt__to__orl_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Efmapal_2Ebt__to__orl__ac_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2Ebt__to__orl__ac_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Efmapal_2Ebt__to__orl__ac_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Efmapal_2Ebt__to__orl__lb_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: A_27a,X2_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2Ebt__to__orl__lb_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Efmapal_2Ebt__to__orl__lb_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq4_2Ec_2Efmapal_2Ebt__to__orl__lb__ac_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: A_27a,X2_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X3_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2Ebt__to__orl__lb__ac_2E4(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Efmapal_2Ebt__to__orl__lb__ac_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).

tff(arityeq4_2Ec_2Efmapal_2Ebt__to__orl__lb__ub_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: A_27a,X2_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X3_2E0: A_27a] : ( c_2Efmapal_2Ebt__to__orl__lb__ub_2E4(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Efmapal_2Ebt__to__orl__lb__ub_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).

tff(arityeq5_2Ec_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: A_27a,X2_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X3_2E0: A_27a,X4_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0,X4_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0),X4_2E0) ) ).

tff(arityeq1_2Ec_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__aux_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Ebool))] : ( c_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__aux_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__aux_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq3_2Ec_2Efmapal_2Ebt__to__orl__ub_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0: A_27a] : ( c_2Efmapal_2Ebt__to__orl__ub_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Efmapal_2Ebt__to__orl__ub_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq4_2Ec_2Efmapal_2Ebt__to__orl__ub__ac_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0: A_27a,X3_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2Ebt__to__orl__ub__ac_2E4(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Efmapal_2Ebt__to__orl__ub__ac_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).

tff(arityeq3_2Ec_2Efmapal_2Ediff__merge_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Efmapal_2Ediff__merge_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Efmapal_2Ediff__merge_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Efmapal_2Efmap_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2Efmap_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Efmap_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Efmapal_2Efmap_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27c))] : ( c_2Efmapal_2Efmap_2E1(A_27a,A_27c,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Efinite__map_2Efmap(A_27a,A_27c),c_2Efmapal_2Efmap_2E0(A_27a,A_27c),X0_2E0) ) ).

tff(arityeq2_2Ec_2Efmapal_2Eincr__build_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2Eincr__build_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2Efmapal_2Eincr__build_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Efmapal_2Eincr__flat_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))] : ( c_2Efmapal_2Eincr__flat_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Efmapal_2Eincr__flat_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Efmapal_2Eincr__merge_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))] : ( c_2Efmapal_2Eincr__merge_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),c_2Efmapal_2Eincr__merge_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Efmapal_2Eincr__sort_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2Eincr__sort_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Efmapal_2Eincr__sort_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Efmapal_2Einter__merge_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Efmapal_2Einter__merge_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Efmapal_2Einter__merge_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27z_29_29_20mono_2Etyop_2Elist_2Elist_28A_27z_29,axiom,
    ! [A_27z: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),X1_2E0: tyop_2Elist_2Elist(A_27z),X2_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)))] : ( c_2Elist_2Elist__CASE_2E3(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),tyop_2Elist_2Elist(A_27z),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z),app_2E2(tyop_2Elist_2Elist(A_27z),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z))),c_2Elist_2Elist__CASE_2E0(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),tyop_2Elist_2Elist(A_27z)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Efmapal_2Elist__rplacv__cn_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))] : ( c_2Efmapal_2Elist__rplacv__cn_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Efmapal_2Elist__rplacv__cn_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Eenumeral_2Elist__to__bt_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Eenumeral_2Elist__to__bt_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Elist__to__bt_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ) ).

tff(arityeq3_2Ec_2Efmapal_2Emerge_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2Emerge_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Efmapal_2Emerge_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Efmapal_2Emerge__out_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Etoto_2Etoto(A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))] : ( c_2Efmapal_2Emerge__out_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Efmapal_2Emerge__out_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Eenumeral_2Enode_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Eenumeral_2Ebt(A_27a),X1_2E0: A_27a,X2_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Eenumeral_2Enode_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Eenumeral_2Ebt(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Eenumeral_2Ebt(A_27a)),app_2E2(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27a),tyop_2Eenumeral_2Ebt(A_27a))),c_2Eenumeral_2Enode_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Eenumeral_2Enode_2E3_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Eenumeral_2Ebt(A_27b),X1_2E0: A_27b,X2_2E0: tyop_2Eenumeral_2Ebt(A_27b)] : ( c_2Eenumeral_2Enode_2E3(A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(A_27b),tyop_2Eenumeral_2Ebt(A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27b),tyop_2Eenumeral_2Ebt(A_27b)),app_2E2(tyop_2Eenumeral_2Ebt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(A_27b),tyop_2Eenumeral_2Ebt(A_27b))),c_2Eenumeral_2Enode_2E0(A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Eenumeral_2Enode_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),X2_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Eenumeral_2Enode_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))] : ( c_2Ecombin_2Eo_2E2(A_27a,A_27b,tyop_2Eoption_2Eoption(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2Eo_2E0(A_27a,A_27b,tyop_2Eoption_2Eoption(A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))] : ( c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E0(A_27a,tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Efinite__map_2Eo__f_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efinite__map_2Eo__f_2E2(A_27a,A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27c)),c_2Efinite__map_2Eo__f_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Eenumeral_2Eonebl_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0: tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Eenumeral_2Eonebl_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Eenumeral_2Eonebl_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27z_29_20mono_2Etyop_2Elist_2Elist_28A_27z_29,axiom,
    ! [A_27z: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),X1_2E0: tyop_2Elist_2Elist(A_27z),X2_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z))] : ( c_2Eoption_2Eoption__CASE_2E3(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z)),tyop_2Elist_2Elist(A_27z),app_2E2(tyop_2Elist_2Elist(A_27z),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z)),tyop_2Elist_2Elist(A_27z)),app_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z)),tyop_2Elist_2Elist(A_27z))),c_2Eoption_2Eoption__CASE_2E0(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Efmapal_2Eoptry_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27b),X1_2E0: tyop_2Eoption_2Eoption(A_27b)] : ( c_2Efmapal_2Eoptry_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b)),c_2Efmapal_2Eoptry_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Efmapal_2Eoptry_2E2_2Emono_2EA_27g,axiom,
    ! [A_27g: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27g),X1_2E0: tyop_2Eoption_2Eoption(A_27g)] : ( c_2Efmapal_2Eoptry_2E2(A_27g,X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27g),tyop_2Eoption_2Eoption(A_27g),app_2E2(tyop_2Eoption_2Eoption(A_27g),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27g),tyop_2Eoption_2Eoption(A_27g)),c_2Efmapal_2Eoptry_2E0(A_27g),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Efmapal_2Eoptry_2E2_2Emono_2EA_27z,axiom,
    ! [A_27z: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27z),X1_2E0: tyop_2Eoption_2Eoption(A_27z)] : ( c_2Efmapal_2Eoptry_2E2(A_27z,X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27z),tyop_2Eoption_2Eoption(A_27z),app_2E2(tyop_2Eoption_2Eoption(A_27z),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27z),tyop_2Eoption_2Eoption(A_27z)),c_2Efmapal_2Eoptry_2E0(A_27z),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Efmapal_2Eoptry__list_2E2_2Emono_2EA_27g_20mono_2EA_27z,axiom,
    ! [A_27g: $tType,A_27z: $tType,X0_2E0: tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),X1_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z))] : ( c_2Efmapal_2Eoptry__list_2E2(A_27g,A_27z,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Eoption_2Eoption(A_27g),app_2E2(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Eoption_2Eoption(A_27g)),c_2Efmapal_2Eoptry__list_2E0(A_27g,A_27z),X0_2E0),X1_2E0) ) ).

tff(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2EternaryComparisons_2Eordering,X1_2E0: A_27b,X2_2E0: A_27b,X3_2E0: A_27b] : ( c_2EternaryComparisons_2Eordering__CASE_2E4(A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(A_27b,A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),c_2EternaryComparisons_2Eordering__CASE_2E0(A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).

tff(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2EternaryComparisons_2Eordering,X1_2E0: tyop_2Emin_2Ebool,X2_2E0: tyop_2Emin_2Ebool,X3_2E0: tyop_2Emin_2Ebool] : ( c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Emin_2Ebool,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),app_2E2(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))),c_2EternaryComparisons_2Eordering__CASE_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).

tff(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2Etyop_2Eenumeral_2Ebt_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2EternaryComparisons_2Eordering,X1_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X3_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2EternaryComparisons_2Eordering__CASE_2E0(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).

tff(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2EternaryComparisons_2Eordering,X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X3_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(tyop_2EternaryComparisons_2Eordering,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),c_2EternaryComparisons_2Eordering__CASE_2E0(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_20mono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2Epair__CASE_2E0(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_20mono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2Epair__CASE_2E0(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28tyop_2Eenumeral_2Ebt_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_2Ctyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2Epair__CASE_2E0(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_20mono_2Etyop_2Eenumeral_2Ebt_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X1_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2Epair__CASE_2E0(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_20mono_2Etyop_2Etoto_2Etoto_28A_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Eenumeral_2Ebt_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_2Ctyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),X1_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2Epair__CASE_2E0(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Efmapal_2Eunlookup_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))] : ( c_2Efmapal_2Eunlookup_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efmapal_2Eunlookup_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq2_2Ec_2Efmapal_2Evcossa_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2Evcossa_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eoption_2Eoption(A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eoption_2Eoption(A_27b)),c_2Efmapal_2Evcossa_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Eenumeral_2Ezerbl_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Eenumeral_2Ezerbl_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eenumeral_2Ezerbl_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool] :
      ( ~ p(X0_2E0)
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0_2E0)) ) ).

tff(thm_2Efmapal_2Eoptry,axiom,
    ! [A_27z: $tType] :
      ( ! [V0p_2E0: A_27z,V1q_2E0: tyop_2Eoption_2Eoption(A_27z)] : ( c_2Efmapal_2Eoptry_2E2(A_27z,c_2Eoption_2ESOME_2E1(A_27z,V0p_2E0),V1q_2E0) = c_2Eoption_2ESOME_2E1(A_27z,V0p_2E0) )
      & ! [V2q_2E0: tyop_2Eoption_2Eoption(A_27z)] : ( c_2Efmapal_2Eoptry_2E2(A_27z,c_2Eoption_2ENONE_2E0(A_27z),V2q_2E0) = V2q_2E0 ) ) ).

tff(thm_2Efmapal_2Evcossa,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0a_2E0: A_27a,V1l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2Evcossa_2E2(A_27a,A_27b,V0a_2E0,V1l_2E0) = c_2Efmapal_2Eassocv_2E2(A_27a,A_27b,V1l_2E0,V0a_2E0) ) ).

tff(thm_2Efmapal_2EOPTION__UPDATE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2x_2E0: A_27a] : ( c_2Efmapal_2EOPTION__UPDATE_2E3(A_27a,A_27b,V0f_2E0,V1g_2E0,V2x_2E0) = c_2Efmapal_2Eoptry_2E2(A_27b,app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27b),V0f_2E0,V2x_2E0),app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27b),V1g_2E0,V2x_2E0)) ) ).

tff(thm_2Efmapal_2Eincr__build,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2Eincr__build_2E2(A_27a,A_27b,V0cmp_2E0,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))) = c_2Elist_2ENIL_2E0(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))) )
      & ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2ab_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),V3l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2Eincr__build_2E2(A_27a,A_27b,V1cmp_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V2ab_2E0,V3l_2E0)) = c_2Efmapal_2Eincr__merge_2E3(A_27a,A_27b,V1cmp_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V2ab_2E0,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Efmapal_2Eincr__build_2E2(A_27a,A_27b,V1cmp_2E0,V3l_2E0)) ) ) ).

tff(thm_2Efmapal_2Eincr__flat,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))] : ( c_2Efmapal_2Eincr__flat_2E2(A_27a,A_27b,V0cmp_2E0,V1lol_2E0) = c_2Efmapal_2Emerge__out_2E3(A_27a,A_27b,V0cmp_2E0,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),V1lol_2E0) ) ).

tff(thm_2Efmapal_2Eincr__sort,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2Eincr__sort_2E2(A_27a,A_27b,V0cmp_2E0,V1l_2E0) = c_2Efmapal_2Emerge__out_2E3(A_27a,A_27b,V0cmp_2E0,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2Eincr__build_2E2(A_27a,A_27b,V0cmp_2E0,V1l_2E0)) ) ).

tff(thm_2Efmapal_2EOPTION__FLAT__primitive,axiom,
    ! [A_27z: $tType,F3_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z)))),F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] :
      ( ! [V4OPTION__FLAT_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),V7l_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),V8a_2E0: tyop_2Elist_2Elist(A_27z)] : ( app_2E2(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z),app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z))),F3_2E0,V4OPTION__FLAT_2E0),V7l_2E0),V8a_2E0) = c_2Ecombin_2EI_2E1(tyop_2Elist_2Elist(A_27z),c_2Elist_2EAPPEND_2E2(A_27z,V8a_2E0,app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z),V4OPTION__FLAT_2E0,V7l_2E0))) )
     => ( ! [V4OPTION__FLAT_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),V6v_2E0: tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),V7l_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)))] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z),app_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z))),F2_2E0,V4OPTION__FLAT_2E0),V6v_2E0),V7l_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z),V6v_2E0,c_2Ecombin_2EI_2E1(tyop_2Elist_2Elist(A_27z),app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z),V4OPTION__FLAT_2E0,V7l_2E0)),app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27z),tyop_2Elist_2Elist(A_27z))),F3_2E0,V4OPTION__FLAT_2E0),V7l_2E0)) )
       => ( ! [V4OPTION__FLAT_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),V5a_27_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)))] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),F1_2E0,V4OPTION__FLAT_2E0),V5a_27_2E0) = c_2Elist_2Elist__CASE_2E3(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),tyop_2Elist_2Elist(A_27z),V5a_27_2E0,c_2Ecombin_2EI_2E1(tyop_2Elist_2Elist(A_27z),c_2Elist_2ENIL_2E0(A_27z)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z))),F2_2E0,V4OPTION__FLAT_2E0)) )
         => ( ! [V0R_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool))] :
                ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,F0_2E0,V0R_2E0))
              <=> ( p(c_2Erelation_2EWF_2E1(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),V0R_2E0))
                  & ! [V1l_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool),V0R_2E0,V1l_2E0),c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(A_27z)),V1l_2E0)))
                  & ! [V2a_2E0: tyop_2Elist_2Elist(A_27z),V3l_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool),V0R_2E0,V3l_2E0),c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27z),V2a_2E0),V3l_2E0))) ) )
           => ( c_2Efmapal_2EOPTION__FLAT_2E0(A_27z) = c_2Erelation_2EWFREC_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Elist_2Elist(A_27z),c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)),F0_2E0),F1_2E0) ) ) ) ) ) ).

tff(thm_2Efmapal_2Eunlookup,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))] : ( c_2Efmapal_2Eunlookup_2E1(A_27a,A_27b,V0f_2E0) = c_2Efinite__map_2EFUN__FMAP_2E2(A_27a,A_27b,c_2Ecombin_2Eo_2E2(A_27a,A_27b,tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ETHE_2E0(A_27b),V0f_2E0),c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EIS__SOME_2E0(A_27b),V0f_2E0)) ) ).

tff(thm_2Efmapal_2Ebt__to__fmap__lb,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1lb_2E0: A_27a,V3x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V0cmp_2E0),V1lb_2E0),V3x_2E0))
        <=> ( c_2Etoto_2Eapto_2E3(A_27a,V0cmp_2E0,V1lb_2E0,V3x_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
     => ( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1lb_2E0: A_27a,V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0cmp_2E0),V1lb_2E0),V3x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V3x_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V0cmp_2E0),V1lb_2E0),V3x_2E0)) )
       => ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1lb_2E0: A_27a,V2t_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2Ebt__to__fmap__lb_2E3(A_27a,A_27b,V0cmp_2E0,V1lb_2E0,V2t_2E0) = c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,c_2Efmapal_2EFMAPAL_2E2(A_27a,A_27b,V0cmp_2E0,V2t_2E0),c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0cmp_2E0),V1lb_2E0))) ) ) ) ).

tff(thm_2Efmapal_2Ebt__to__fmap__ub,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3x_2E0: A_27a,V2ub_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V0cmp_2E0),V3x_2E0),V2ub_2E0))
        <=> ( c_2Etoto_2Eapto_2E3(A_27a,V0cmp_2E0,V3x_2E0,V2ub_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
     => ( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2ub_2E0: A_27a,V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0cmp_2E0),V2ub_2E0),V3x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V3x_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V0cmp_2E0),V3x_2E0),V2ub_2E0)) )
       => ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1t_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V2ub_2E0: A_27a] : ( c_2Efmapal_2Ebt__to__fmap__ub_2E3(A_27a,A_27b,V0cmp_2E0,V1t_2E0,V2ub_2E0) = c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,c_2Efmapal_2EFMAPAL_2E2(A_27a,A_27b,V0cmp_2E0,V1t_2E0),c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0cmp_2E0),V2ub_2E0))) ) ) ) ).

tff(thm_2Efmapal_2Ebt__to__fmap__lb__ub,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))))] :
      ( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1lb_2E0: A_27a,V4x_2E0: A_27a,V3ub_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0,V0cmp_2E0),V1lb_2E0),V4x_2E0),V3ub_2E0))
        <=> ( ( c_2Etoto_2Eapto_2E3(A_27a,V0cmp_2E0,V1lb_2E0,V4x_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
            & ( c_2Etoto_2Eapto_2E3(A_27a,V0cmp_2E0,V4x_2E0,V3ub_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) )
     => ( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1lb_2E0: A_27a,V3ub_2E0: A_27a,V4x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V0cmp_2E0),V1lb_2E0),V3ub_2E0),V4x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V4x_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0,V0cmp_2E0),V1lb_2E0),V4x_2E0),V3ub_2E0)) )
       => ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1lb_2E0: A_27a,V2t_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V3ub_2E0: A_27a] : ( c_2Efmapal_2Ebt__to__fmap__lb__ub_2E4(A_27a,A_27b,V0cmp_2E0,V1lb_2E0,V2t_2E0,V3ub_2E0) = c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,c_2Efmapal_2EFMAPAL_2E2(A_27a,A_27b,V0cmp_2E0,V2t_2E0),c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V0cmp_2E0),V1lb_2E0),V3ub_2E0))) ) ) ) ).

tff(thm_2Efmapal_2Ebt__map,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Efmapal_2Ebt__map_2E2(A_27a,A_27b,V0f_2E0,c_2Eenumeral_2Ent_2E0(A_27a)) = c_2Eenumeral_2Ent_2E0(A_27b) )
      & ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2l_2E0: tyop_2Eenumeral_2Ebt(A_27a),V3x_2E0: A_27a,V4r_2E0: tyop_2Eenumeral_2Ebt(A_27a)] : ( c_2Efmapal_2Ebt__map_2E2(A_27a,A_27b,V1f_2E0,c_2Eenumeral_2Enode_2E3(A_27a,V2l_2E0,V3x_2E0,V4r_2E0)) = c_2Eenumeral_2Enode_2E3(A_27b,c_2Efmapal_2Ebt__map_2E2(A_27a,A_27b,V1f_2E0,V2l_2E0),app_2E2(A_27a,A_27b,V1f_2E0,V3x_2E0),c_2Efmapal_2Ebt__map_2E2(A_27a,A_27b,V1f_2E0,V4r_2E0)) ) ) ).

tff(thm_2Efmapal_2Efmap,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2Efmap_2E1(A_27a,A_27b,V0l_2E0) = c_2Efinite__map_2EFUPDATE__LIST_2E2(A_27a,A_27b,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b),c_2Elist_2EREVERSE_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),V0l_2E0)) ) ).

tff(thm_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__AUX,axiom,
    ! [A_27a: $tType,A_27b: $tType,F7_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F6_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))))))),F5_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))))))),F4_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))))),F3_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))),F2_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))] :
      ( ! [V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V5lb_2E0: A_27a,V14x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F7_2E0,V3cmp_2E0),V5lb_2E0),V14x_2E0))
        <=> ( c_2Etoto_2Eapto_2E3(A_27a,V3cmp_2E0,V5lb_2E0,V14x_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
     => ( ! [V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V5lb_2E0: A_27a,V9ub_2E0: A_27a,V1bt__to__orl__lb__ub__ac__tupled_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V11l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V13r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V10m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V14x_2E0: A_27a,V15y_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))))))),F6_2E0,V3cmp_2E0),V5lb_2E0),V9ub_2E0),V1bt__to__orl__lb__ub__ac__tupled_2E0),V11l_2E0),V13r_2E0),V10m_2E0),V14x_2E0),V15y_2E0) = c_2Ecombin_2EI_2E1(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F7_2E0,V3cmp_2E0),V5lb_2E0),V14x_2E0),c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F7_2E0,V3cmp_2E0),V14x_2E0),V9ub_2E0),app_2E2(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1bt__to__orl__lb__ub__ac__tupled_2E0,c_2Epair_2E_2C_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),V3cmp_2E0,c_2Epair_2E_2C_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V5lb_2E0,c_2Epair_2E_2C_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V11l_2E0,c_2Epair_2E_2C_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V14x_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V14x_2E0,V15y_2E0),app_2E2(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1bt__to__orl__lb__ub__ac__tupled_2E0,c_2Epair_2E_2C_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),V3cmp_2E0,c_2Epair_2E_2C_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V14x_2E0,c_2Epair_2E_2C_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V13r_2E0,c_2Epair_2E_2C_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V9ub_2E0,V10m_2E0))))))))))),app_2E2(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1bt__to__orl__lb__ub__ac__tupled_2E0,c_2Epair_2E_2C_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),V3cmp_2E0,c_2Epair_2E_2C_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V5lb_2E0,c_2Epair_2E_2C_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V11l_2E0,c_2Epair_2E_2C_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V9ub_2E0,V10m_2E0)))))),app_2E2(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1bt__to__orl__lb__ub__ac__tupled_2E0,c_2Epair_2E_2C_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),V3cmp_2E0,c_2Epair_2E_2C_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V5lb_2E0,c_2Epair_2E_2C_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V13r_2E0,c_2Epair_2E_2C_2E2(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V9ub_2E0,V10m_2E0))))))) )
       => ( ! [V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V5lb_2E0: A_27a,V9ub_2E0: A_27a,V1bt__to__orl__lb__ub__ac__tupled_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V10m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V11l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V12v9_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),V13r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))))),F5_2E0,V3cmp_2E0),V5lb_2E0),V9ub_2E0),V1bt__to__orl__lb__ub__ac__tupled_2E0),V10m_2E0),V11l_2E0),V12v9_2E0),V13r_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),A_27a,A_27b,V12v9_2E0,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))))))),F6_2E0,V3cmp_2E0),V5lb_2E0),V9ub_2E0),V1bt__to__orl__lb__ub__ac__tupled_2E0),V11l_2E0),V13r_2E0),V10m_2E0)) )
         => ( ! [V7v4_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V5lb_2E0: A_27a,V1bt__to__orl__lb__ub__ac__tupled_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V9ub_2E0: A_27a,V10m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))),F4_2E0,V7v4_2E0),V3cmp_2E0),V5lb_2E0),V1bt__to__orl__lb__ub__ac__tupled_2E0),V9ub_2E0),V10m_2E0) = c_2Eenumeral_2Ebt__CASE_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V7v4_2E0,c_2Ecombin_2EI_2E1(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V10m_2E0),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))))),F5_2E0,V3cmp_2E0),V5lb_2E0),V9ub_2E0),V1bt__to__orl__lb__ub__ac__tupled_2E0),V10m_2E0)) )
           => ( ! [V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V5lb_2E0: A_27a,V1bt__to__orl__lb__ub__ac__tupled_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V7v4_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8v5_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))] : ( app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),F3_2E0,V3cmp_2E0),V5lb_2E0),V1bt__to__orl__lb__ub__ac__tupled_2E0),V7v4_2E0),V8v5_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V8v5_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))),F4_2E0,V7v4_2E0),V3cmp_2E0),V5lb_2E0),V1bt__to__orl__lb__ub__ac__tupled_2E0)) )
             => ( ! [V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1bt__to__orl__lb__ub__ac__tupled_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V5lb_2E0: A_27a,V6v3_2E0: tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))] : ( app_2E2(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),F2_2E0,V3cmp_2E0),V1bt__to__orl__lb__ub__ac__tupled_2E0),V5lb_2E0),V6v3_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V6v3_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),F3_2E0,V3cmp_2E0),V5lb_2E0),V1bt__to__orl__lb__ub__ac__tupled_2E0)) )
               => ( ! [V1bt__to__orl__lb__ub__ac__tupled_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V4v1_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))] : ( app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),F1_2E0,V1bt__to__orl__lb__ub__ac__tupled_2E0),V3cmp_2E0),V4v1_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V4v1_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),F2_2E0,V3cmp_2E0),V1bt__to__orl__lb__ub__ac__tupled_2E0)) )
                 => ( ! [V1bt__to__orl__lb__ub__ac__tupled_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V2a_2E0: tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))] : ( app_2E2(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),F0_2E0,V1bt__to__orl__lb__ub__ac__tupled_2E0),V2a_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),V2a_2E0,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),F1_2E0,V1bt__to__orl__lb__ub__ac__tupled_2E0)) )
                   => ! [V0R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Emin_2Ebool))] : ( c_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__aux_2E1(A_27a,A_27b,V0R_2E0) = c_2Erelation_2EWFREC_2E2(tyop_2Epair_2Eprod(tyop_2Etoto_2Etoto(A_27a),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(A_27a,tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0R_2E0,F0_2E0) ) ) ) ) ) ) ) ) ) ).

tff(thm_2Efmapal_2EORWL,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
      ( p(c_2Efmapal_2EORWL_2E3(A_27a,A_27b,V0cmp_2E0,V1f_2E0,V2l_2E0))
    <=> ( ( V1f_2E0 = c_2Efmapal_2Efmap_2E1(A_27a,A_27b,V2l_2E0) )
        & p(c_2Efmapal_2EORL_2E2(A_27a,A_27b,V0cmp_2E0,V2l_2E0)) ) ) ).

tff(thm_2Efmapal_2EOFU,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0cmp_2E0),V2g_2E0),V3x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V3x_2E0,c_2Eenumeral_2ELESS__ALL_2E3(A_27a,V0cmp_2E0,V3x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V2g_2E0))) )
     => ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efmapal_2EOFU_2E3(A_27a,A_27b,V0cmp_2E0,V1f_2E0,V2g_2E0) = c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V1f_2E0,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0cmp_2E0),V2g_2E0))),V2g_2E0) ) ) ).

tff(thm_2Efmapal_2EUFO,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V1f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3y_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V1f_2E0),V0cmp_2E0),V3y_2E0))
        <=> ! [V4z_2E0: A_27a] :
              ( p(c_2Ebool_2EIN_2E2(A_27a,V4z_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,V1f_2E0)))
             => ( c_2Etoto_2Eapto_2E3(A_27a,V0cmp_2E0,V4z_2E0,V3y_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) )
     => ( ! [V1f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V1f_2E0),V0cmp_2E0),V3y_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V3y_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V1f_2E0),V0cmp_2E0),V3y_2E0)) )
       => ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1f_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2g_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b)] : ( c_2Efmapal_2EUFO_2E3(A_27a,A_27b,V0cmp_2E0,V1f_2E0,V2g_2E0) = c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V1f_2E0,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V2g_2E0,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V1f_2E0),V0cmp_2E0)))) ) ) ) ).

tff(thm_2Efmapal_2EAP__SND,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V1a_2E0: A_27a,V2b_2E0: A_27b] : ( c_2Efmapal_2EAP__SND_2E2(A_27a,A_27b,A_27c,V0f_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1a_2E0,V2b_2E0)) = c_2Epair_2E_2C_2E2(A_27a,A_27c,V1a_2E0,app_2E2(A_27b,A_27c,V0f_2E0,V2b_2E0)) ) ).

tff(thm_2Efmapal_2EORL__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))] :
      ( ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),V0P_2E0,V1cmp_2E0),c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))))
        & ! [V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3a_2E0: A_27a,V4b_2E0: A_27b,V5l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
            ( p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),V0P_2E0,V2cmp_2E0),V5l_2E0))
           => p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),V0P_2E0,V2cmp_2E0),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V3a_2E0,V4b_2E0),V5l_2E0))) ) )
     => ! [V6v_2E0: tyop_2Etoto_2Etoto(A_27a),V7v1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),V0P_2E0,V6v_2E0),V7v1_2E0)) ) ).

tff(thm_2Efmapal_2EORL,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2EORL_2E2(A_27a,A_27b,V0cmp_2E0,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))) = c_2Ebool_2ET_2E0 )
      & ! [V1l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3b_2E0: A_27b,V4a_2E0: A_27a] :
          ( p(c_2Efmapal_2EORL_2E2(A_27a,A_27b,V2cmp_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V4a_2E0,V3b_2E0),V1l_2E0)))
        <=> ( p(c_2Efmapal_2EORL_2E2(A_27a,A_27b,V2cmp_2E0,V1l_2E0))
            & ! [V5p_2E0: A_27a,V6q_2E0: A_27b] :
                ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V5p_2E0,V6q_2E0),c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),V1l_2E0)))
               => ( c_2Etoto_2Eapto_2E3(A_27a,V2cmp_2E0,V4a_2E0,V5p_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) ) ) ) ) ).

tff(thm_2Efmapal_2Eoptry__list__ind,axiom,
    ! [A_27g: $tType,A_27z: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Emin_2Ebool))] :
      ( ( ! [V1f_2E0: tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Emin_2Ebool),V0P_2E0,V1f_2E0),c_2Elist_2ENIL_2E0(tyop_2Eoption_2Eoption(A_27z))))
        & ! [V2f_2E0: tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),V3l_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z))] :
            ( p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Emin_2Ebool),V0P_2E0,V2f_2E0),V3l_2E0))
           => p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Emin_2Ebool),V0P_2E0,V2f_2E0),c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(A_27z),c_2Eoption_2ENONE_2E0(A_27z),V3l_2E0))) )
        & ! [V4f_2E0: tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),V5z_2E0: A_27z,V6l_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z))] :
            ( p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Emin_2Ebool),V0P_2E0,V4f_2E0),V6l_2E0))
           => p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Emin_2Ebool),V0P_2E0,V4f_2E0),c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(A_27z),c_2Eoption_2ESOME_2E1(A_27z,V5z_2E0),V6l_2E0))) ) )
     => ! [V7v_2E0: tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),V8v1_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),tyop_2Emin_2Ebool),V0P_2E0,V7v_2E0),V8v1_2E0)) ) ).

tff(thm_2Efmapal_2Eoptry__list,axiom,
    ! [A_27g: $tType,A_27z: $tType] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g))] : ( c_2Efmapal_2Eoptry__list_2E2(A_27g,A_27z,V0f_2E0,c_2Elist_2ENIL_2E0(tyop_2Eoption_2Eoption(A_27z))) = c_2Eoption_2ENONE_2E0(A_27g) )
      & ! [V1l_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),V2f_2E0: tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g))] : ( c_2Efmapal_2Eoptry__list_2E2(A_27g,A_27z,V2f_2E0,c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(A_27z),c_2Eoption_2ENONE_2E0(A_27z),V1l_2E0)) = c_2Efmapal_2Eoptry__list_2E2(A_27g,A_27z,V2f_2E0,V1l_2E0) )
      & ! [V3z_2E0: A_27z,V4l_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(A_27z)),V5f_2E0: tyop_2Emin_2Efun(A_27z,tyop_2Eoption_2Eoption(A_27g))] : ( c_2Efmapal_2Eoptry__list_2E2(A_27g,A_27z,V5f_2E0,c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(A_27z),c_2Eoption_2ESOME_2E1(A_27z,V3z_2E0),V4l_2E0)) = c_2Efmapal_2Eoptry_2E2(A_27g,app_2E2(A_27z,tyop_2Eoption_2Eoption(A_27g),V5f_2E0,V3z_2E0),c_2Efmapal_2Eoptry__list_2E2(A_27g,A_27z,V5f_2E0,V4l_2E0)) ) ) ).

tff(thm_2Efmapal_2Eassocv__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ( ! [V1a_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))),V1a_2E0))
        & ! [V2x_2E0: A_27a,V3y_2E0: A_27b,V4l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V5a_2E0: A_27a] :
            ( ( ( V5a_2E0 != V2x_2E0 )
             => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0,V4l_2E0),V5a_2E0)) )
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0),V4l_2E0)),V5a_2E0)) ) )
     => ! [V6v_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V7v1_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0,V6v_2E0),V7v1_2E0)) ) ).

tff(thm_2Efmapal_2Eassocv,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ! [V4a_2E0: A_27a,V2x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V4a_2E0),V2x_2E0))
        <=> ( V4a_2E0 = V2x_2E0 ) )
     => ( ! [V0a_2E0: A_27a] : ( c_2Efmapal_2Eassocv_2E2(A_27a,A_27b,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),V0a_2E0) = c_2Eoption_2ENONE_2E0(A_27b) )
        & ! [V1y_2E0: A_27b,V2x_2E0: A_27a,V3l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V4a_2E0: A_27a] : ( c_2Efmapal_2Eassocv_2E2(A_27a,A_27b,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V1y_2E0),V3l_2E0),V4a_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27b),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V4a_2E0),V2x_2E0),c_2Eoption_2ESOME_2E1(A_27b,V1y_2E0),c_2Efmapal_2Eassocv_2E2(A_27a,A_27b,V3l_2E0,V4a_2E0)) ) ) ) ).

tff(thm_2Efmapal_2Emerge__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))] :
      ( ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0,V1cmp_2E0),c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))),V2l_2E0))
        & ! [V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V4v4_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),V5v5_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0,V3cmp_2E0),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V4v4_2E0,V5v5_2E0)),c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))))
        & ! [V6cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V7a1_2E0: A_27a,V8b1_2E0: A_27b,V9l1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V10a2_2E0: A_27a,V11b2_2E0: A_27b,V12l2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
            ( ( ( ( c_2Etoto_2Eapto_2E3(A_27a,V6cmp_2E0,V7a1_2E0,V10a2_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
               => p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0,V6cmp_2E0),V9l1_2E0),V12l2_2E0)) )
              & ( ( c_2Etoto_2Eapto_2E3(A_27a,V6cmp_2E0,V7a1_2E0,V10a2_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
               => p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0,V6cmp_2E0),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V7a1_2E0,V8b1_2E0),V9l1_2E0)),V12l2_2E0)) )
              & ( ( c_2Etoto_2Eapto_2E3(A_27a,V6cmp_2E0,V7a1_2E0,V10a2_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
               => p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0,V6cmp_2E0),V9l1_2E0),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V10a2_2E0,V11b2_2E0),V12l2_2E0))) ) )
           => p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0,V6cmp_2E0),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V7a1_2E0,V8b1_2E0),V9l1_2E0)),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V10a2_2E0,V11b2_2E0),V12l2_2E0))) ) )
     => ! [V13v_2E0: tyop_2Etoto_2Etoto(A_27a),V14v1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V15v2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0,V13v_2E0),V14v1_2E0),V15v2_2E0)) ) ).

tff(thm_2Efmapal_2Emerge,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2Emerge_2E3(A_27a,A_27b,V1cmp_2E0,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l_2E0) = V0l_2E0 )
      & ! [V2v5_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3v4_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),V4cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2Emerge_2E3(A_27a,A_27b,V4cmp_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V3v4_2E0,V2v5_2E0),c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))) = c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V3v4_2E0,V2v5_2E0) )
      & ! [V5l2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V6l1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V7cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V8b2_2E0: A_27b,V9b1_2E0: A_27b,V10a2_2E0: A_27a,V11a1_2E0: A_27a] : ( c_2Efmapal_2Emerge_2E3(A_27a,A_27b,V7cmp_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V11a1_2E0,V9b1_2E0),V6l1_2E0),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V10a2_2E0,V8b2_2E0),V5l2_2E0)) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Etoto_2Eapto_2E3(A_27a,V7cmp_2E0,V11a1_2E0,V10a2_2E0),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V11a1_2E0,V9b1_2E0),c_2Efmapal_2Emerge_2E3(A_27a,A_27b,V7cmp_2E0,V6l1_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V10a2_2E0,V8b2_2E0),V5l2_2E0))),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V11a1_2E0,V9b1_2E0),c_2Efmapal_2Emerge_2E3(A_27a,A_27b,V7cmp_2E0,V6l1_2E0,V5l2_2E0)),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V10a2_2E0,V8b2_2E0),c_2Efmapal_2Emerge_2E3(A_27a,A_27b,V7cmp_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V11a1_2E0,V9b1_2E0),V6l1_2E0),V5l2_2E0))) ) ) ).

tff(thm_2Efmapal_2Eincr__merge__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)))] :
      ( ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),V0P_2E0,V1cmp_2E0),V2l_2E0),c_2Elist_2ENIL_2E0(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))
        & ! [V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V4l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V5lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),V0P_2E0,V3cmp_2E0),V4l_2E0),c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V5lol_2E0)))
        & ! [V6cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V7l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V8m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V9lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))] :
            ( p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),V0P_2E0,V6cmp_2E0),c_2Efmapal_2Emerge_2E3(A_27a,A_27b,V6cmp_2E0,V7l_2E0,V8m_2E0)),V9lol_2E0))
           => p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),V0P_2E0,V6cmp_2E0),V7l_2E0),c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V8m_2E0),V9lol_2E0))) ) )
     => ! [V10v_2E0: tyop_2Etoto_2Etoto(A_27a),V11v1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V12v2_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),V0P_2E0,V10v_2E0),V11v1_2E0),V12v2_2E0)) ) ).

tff(thm_2Efmapal_2Eincr__merge,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2Eincr__merge_2E3(A_27a,A_27b,V1cmp_2E0,V0l_2E0,c_2Elist_2ENIL_2E0(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))) = c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0l_2E0),c_2Elist_2ENIL_2E0(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))) )
      & ! [V2lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V3l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V4cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2Eincr__merge_2E3(A_27a,A_27b,V4cmp_2E0,V3l_2E0,c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V2lol_2E0)) = c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3l_2E0),V2lol_2E0) )
      & ! [V5m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V6lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V7l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V8cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2Eincr__merge_2E3(A_27a,A_27b,V8cmp_2E0,V7l_2E0,c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V5m_2E0),V6lol_2E0)) = c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Efmapal_2Eincr__merge_2E3(A_27a,A_27b,V8cmp_2E0,c_2Efmapal_2Emerge_2E3(A_27a,A_27b,V8cmp_2E0,V7l_2E0,V5m_2E0),V6lol_2E0)) ) ) ).

tff(thm_2Efmapal_2EORL__sublists__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool))] :
      ( ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),V0P_2E0,V1cmp_2E0),c_2Elist_2ENIL_2E0(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))
        & ! [V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))] :
            ( p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),V0P_2E0,V2cmp_2E0),V3lol_2E0))
           => p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),V0P_2E0,V2cmp_2E0),c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V3lol_2E0))) )
        & ! [V4cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V5m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V6lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))] :
            ( p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),V0P_2E0,V4cmp_2E0),V6lol_2E0))
           => p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),V0P_2E0,V4cmp_2E0),c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V5m_2E0),V6lol_2E0))) ) )
     => ! [V7v_2E0: tyop_2Etoto_2Etoto(A_27a),V8v1_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),V0P_2E0,V7v_2E0),V8v1_2E0)) ) ).

tff(thm_2Efmapal_2EORL__sublists,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2EORL__sublists_2E2(A_27a,A_27b,V0cmp_2E0,c_2Elist_2ENIL_2E0(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))) = c_2Ebool_2ET_2E0 )
      & ! [V1lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2EORL__sublists_2E2(A_27a,A_27b,V2cmp_2E0,c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V1lol_2E0)) = c_2Efmapal_2EORL__sublists_2E2(A_27a,A_27b,V2cmp_2E0,V1lol_2E0) )
      & ! [V3m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V4lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V5cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] :
          ( p(c_2Efmapal_2EORL__sublists_2E2(A_27a,A_27b,V5cmp_2E0,c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3m_2E0),V4lol_2E0)))
        <=> ( p(c_2Efmapal_2EORL_2E2(A_27a,A_27b,V5cmp_2E0,V3m_2E0))
            & p(c_2Efmapal_2EORL__sublists_2E2(A_27a,A_27b,V5cmp_2E0,V4lol_2E0)) ) ) ) ).

tff(thm_2Efmapal_2Emerge__out__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)))] :
      ( ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),V0P_2E0,V1cmp_2E0),V2l_2E0),c_2Elist_2ENIL_2E0(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))
        & ! [V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V4l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V5lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))] :
            ( p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),V0P_2E0,V3cmp_2E0),V4l_2E0),V5lol_2E0))
           => p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),V0P_2E0,V3cmp_2E0),V4l_2E0),c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V5lol_2E0))) )
        & ! [V6cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V7l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V8m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V9lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))] :
            ( p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),V0P_2E0,V6cmp_2E0),c_2Efmapal_2Emerge_2E3(A_27a,A_27b,V6cmp_2E0,V7l_2E0,V8m_2E0)),V9lol_2E0))
           => p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),V0P_2E0,V6cmp_2E0),V7l_2E0),c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V8m_2E0),V9lol_2E0))) ) )
     => ! [V10v_2E0: tyop_2Etoto_2Etoto(A_27a),V11v1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V12v2_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),tyop_2Emin_2Ebool)),V0P_2E0,V10v_2E0),V11v1_2E0),V12v2_2E0)) ) ).

tff(thm_2Efmapal_2Emerge__out,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2Emerge__out_2E3(A_27a,A_27b,V1cmp_2E0,V0l_2E0,c_2Elist_2ENIL_2E0(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))) = V0l_2E0 )
      & ! [V2lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V3l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V4cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2Emerge__out_2E3(A_27a,A_27b,V4cmp_2E0,V3l_2E0,c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V2lol_2E0)) = c_2Efmapal_2Emerge__out_2E3(A_27a,A_27b,V4cmp_2E0,V3l_2E0,V2lol_2E0) )
      & ! [V5m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V6lol_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),V7l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V8cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2Emerge__out_2E3(A_27a,A_27b,V8cmp_2E0,V7l_2E0,c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V5m_2E0),V6lol_2E0)) = c_2Efmapal_2Emerge__out_2E3(A_27a,A_27b,V8cmp_2E0,c_2Efmapal_2Emerge_2E3(A_27a,A_27b,V8cmp_2E0,V7l_2E0,V5m_2E0),V6lol_2E0) ) ) ).

tff(thm_2Efmapal_2EOPTION__FLAT__ind,axiom,
    ! [A_27z: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool)] :
      ( ( p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ENIL_2E0(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)))))
        & ! [V1l_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)))] :
            ( p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool,V0P_2E0,V1l_2E0))
           => p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(A_27z)),V1l_2E0))) )
        & ! [V2a_2E0: tyop_2Elist_2Elist(A_27z),V3l_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)))] :
            ( p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool,V0P_2E0,V3l_2E0))
           => p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27z),V2a_2E0),V3l_2E0))) ) )
     => ! [V4v_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),tyop_2Emin_2Ebool,V0P_2E0,V4v_2E0)) ) ).

tff(thm_2Efmapal_2EOPTION__FLAT,axiom,
    ! [A_27z: $tType] :
      ( ( c_2Efmapal_2EOPTION__FLAT_2E1(A_27z,c_2Elist_2ENIL_2E0(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)))) = c_2Elist_2ENIL_2E0(A_27z) )
      & ! [V0l_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)))] : ( c_2Efmapal_2EOPTION__FLAT_2E1(A_27z,c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),c_2Eoption_2ENONE_2E0(tyop_2Elist_2Elist(A_27z)),V0l_2E0)) = c_2Efmapal_2EOPTION__FLAT_2E1(A_27z,V0l_2E0) )
      & ! [V1l_2E0: tyop_2Elist_2Elist(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z))),V2a_2E0: tyop_2Elist_2Elist(A_27z)] : ( c_2Efmapal_2EOPTION__FLAT_2E1(A_27z,c_2Elist_2ECONS_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27z)),c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27z),V2a_2E0),V1l_2E0)) = c_2Elist_2EAPPEND_2E2(A_27z,V2a_2E0,c_2Efmapal_2EOPTION__FLAT_2E1(A_27z,V1l_2E0)) ) ) ).

tff(thm_2Efmapal_2Ebt__to__fmap__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))] :
      ( ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : p(app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),V0P_2E0,V1cmp_2E0),c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))))
        & ! [V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V4x_2E0: A_27a,V5v_2E0: A_27b,V6r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] :
            ( ( p(app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),V0P_2E0,V2cmp_2E0),V3l_2E0))
              & p(app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),V0P_2E0,V2cmp_2E0),V6r_2E0)) )
           => p(app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),V0P_2E0,V2cmp_2E0),c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V3l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V4x_2E0,V5v_2E0),V6r_2E0))) ) )
     => ! [V7v_2E0: tyop_2Etoto_2Etoto(A_27a),V8v1_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),V0P_2E0,V7v_2E0),V8v1_2E0)) ) ).

tff(thm_2Efmapal_2Ebt__to__fmap,axiom,
    ! [A_27a: $tType,A_27b: $tType,F3_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F2_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V5cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1x_2E0: A_27a,V7z_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F3_2E0,V5cmp_2E0),V1x_2E0),V7z_2E0))
        <=> ( c_2Etoto_2Eapto_2E3(A_27a,V5cmp_2E0,V1x_2E0,V7z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
     => ( ! [V5cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1x_2E0: A_27a,V7z_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F1_2E0,V5cmp_2E0),V1x_2E0),V7z_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V7z_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F3_2E0,V5cmp_2E0),V1x_2E0),V7z_2E0)) )
       => ( ! [V5cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V6y_2E0: A_27a,V1x_2E0: A_27a] :
              ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0,V5cmp_2E0),V6y_2E0),V1x_2E0))
            <=> ( c_2Etoto_2Eapto_2E3(A_27a,V5cmp_2E0,V6y_2E0,V1x_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
         => ( ! [V5cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1x_2E0: A_27a,V6y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V5cmp_2E0),V1x_2E0),V6y_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V6y_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0,V5cmp_2E0),V6y_2E0),V1x_2E0)) )
           => ( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2EFMAPAL_2E2(A_27a,A_27b,V0cmp_2E0,c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))) = c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b) )
              & ! [V1x_2E0: A_27a,V2v_2E0: A_27b,V3r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V4l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V5cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2EFMAPAL_2E2(A_27a,A_27b,V5cmp_2E0,c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V4l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V2v_2E0),V3r_2E0)) = c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,c_2Efmapal_2EFMAPAL_2E2(A_27a,A_27b,V5cmp_2E0,V4l_2E0),c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V5cmp_2E0),V1x_2E0))),c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V2v_2E0))),c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,c_2Efmapal_2EFMAPAL_2E2(A_27a,A_27b,V5cmp_2E0,V3r_2E0),c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F1_2E0,V5cmp_2E0),V1x_2E0)))) ) ) ) ) ) ) ).

tff(thm_2Efmapal_2EFAPPLY__nt,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1x_2E0: A_27a] : ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efmapal_2EFMAPAL_2E2(A_27a,A_27b,V0cmp_2E0,c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))),V1x_2E0) = c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b),V1x_2E0) ) ).

tff(thm_2Efmapal_2EFAPPLY__node,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1x_2E0: A_27a,V2l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V3a_2E0: A_27a,V4b_2E0: A_27b,V5r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efmapal_2EFMAPAL_2E2(A_27a,A_27b,V0cmp_2E0,c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V2l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V3a_2E0,V4b_2E0),V5r_2E0)),V1x_2E0) = c_2EternaryComparisons_2Eordering__CASE_2E4(A_27b,c_2Etoto_2Eapto_2E3(A_27a,V0cmp_2E0,V1x_2E0,V3a_2E0),c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efmapal_2EFMAPAL_2E2(A_27a,A_27b,V0cmp_2E0,V2l_2E0),V1x_2E0),V4b_2E0,c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efmapal_2EFMAPAL_2E2(A_27a,A_27b,V0cmp_2E0,V5r_2E0),V1x_2E0)) ) ).

tff(thm_2Efmapal_2Ebt__FST__FDOM,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1t_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Efmapal_2EFMAPAL_2E2(A_27a,A_27b,V0cmp_2E0,V1t_2E0)) = c_2Eenumeral_2EENUMERAL_2E2(A_27a,V0cmp_2E0,c_2Efmapal_2Ebt__map_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V1t_2E0)) ) ).

tff(thm_2Efmapal_2Ebt__to__orl__lb__ub__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))))] :
      ( ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2lb_2E0: A_27a,V3ub_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0P_2E0,V1cmp_2E0),V2lb_2E0),c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))),V3ub_2E0))
        & ! [V4cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V5lb_2E0: A_27a,V6l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V7x_2E0: A_27a,V8y_2E0: A_27b,V9r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V10ub_2E0: A_27a] :
            ( ( ( ( c_2Etoto_2Eapto_2E3(A_27a,V4cmp_2E0,V5lb_2E0,V7x_2E0) != c_2EternaryComparisons_2ELESS_2E0 )
               => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0P_2E0,V4cmp_2E0),V5lb_2E0),V9r_2E0),V10ub_2E0)) )
              & ( ( ( c_2Etoto_2Eapto_2E3(A_27a,V4cmp_2E0,V5lb_2E0,V7x_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
                  & ( c_2Etoto_2Eapto_2E3(A_27a,V4cmp_2E0,V7x_2E0,V10ub_2E0) != c_2EternaryComparisons_2ELESS_2E0 ) )
               => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0P_2E0,V4cmp_2E0),V5lb_2E0),V6l_2E0),V10ub_2E0)) )
              & ( ( ( c_2Etoto_2Eapto_2E3(A_27a,V4cmp_2E0,V5lb_2E0,V7x_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
                  & ( c_2Etoto_2Eapto_2E3(A_27a,V4cmp_2E0,V7x_2E0,V10ub_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
               => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0P_2E0,V4cmp_2E0),V5lb_2E0),V6l_2E0),V7x_2E0)) )
              & ( ( ( c_2Etoto_2Eapto_2E3(A_27a,V4cmp_2E0,V5lb_2E0,V7x_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
                  & ( c_2Etoto_2Eapto_2E3(A_27a,V4cmp_2E0,V7x_2E0,V10ub_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
               => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0P_2E0,V4cmp_2E0),V7x_2E0),V9r_2E0),V10ub_2E0)) ) )
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0P_2E0,V4cmp_2E0),V5lb_2E0),c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V6l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V7x_2E0,V8y_2E0),V9r_2E0)),V10ub_2E0)) ) )
     => ! [V11v_2E0: tyop_2Etoto_2Etoto(A_27a),V12v1_2E0: A_27a,V13v2_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V14v3_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0P_2E0,V11v_2E0),V12v1_2E0),V13v2_2E0),V14v3_2E0)) ) ).

tff(thm_2Efmapal_2Ebt__to__orl__lb__ub,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
      ( ! [V9cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V7lb_2E0: A_27a,V4x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V9cmp_2E0),V7lb_2E0),V4x_2E0))
        <=> ( c_2Etoto_2Eapto_2E3(A_27a,V9cmp_2E0,V7lb_2E0,V4x_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
     => ( ! [V0ub_2E0: A_27a,V1lb_2E0: A_27a,V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2Ebt__to__orl__lb__ub_2E4(A_27a,A_27b,V2cmp_2E0,V1lb_2E0,c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),V0ub_2E0) = c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)) )
        & ! [V3y_2E0: A_27b,V4x_2E0: A_27a,V5ub_2E0: A_27a,V6r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V7lb_2E0: A_27a,V8l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V9cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2Ebt__to__orl__lb__ub_2E4(A_27a,A_27b,V9cmp_2E0,V7lb_2E0,c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V8l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V4x_2E0,V3y_2E0),V6r_2E0),V5ub_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V9cmp_2E0),V7lb_2E0),V4x_2E0),c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V9cmp_2E0),V4x_2E0),V5ub_2E0),c_2Elist_2EAPPEND_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Elist_2EAPPEND_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Efmapal_2Ebt__to__orl__lb__ub_2E4(A_27a,A_27b,V9cmp_2E0,V7lb_2E0,V8l_2E0,V4x_2E0),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V4x_2E0,V3y_2E0),c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Efmapal_2Ebt__to__orl__lb__ub_2E4(A_27a,A_27b,V9cmp_2E0,V4x_2E0,V6r_2E0,V5ub_2E0)),c_2Efmapal_2Ebt__to__orl__lb__ub_2E4(A_27a,A_27b,V9cmp_2E0,V7lb_2E0,V8l_2E0,V5ub_2E0)),c_2Efmapal_2Ebt__to__orl__lb__ub_2E4(A_27a,A_27b,V9cmp_2E0,V7lb_2E0,V6r_2E0,V5ub_2E0)) ) ) ) ).

tff(thm_2Efmapal_2Ebt__to__orl__lb__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))] :
      ( ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2lb_2E0: A_27a] : p(app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0,V1cmp_2E0),V2lb_2E0),c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))))
        & ! [V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V4lb_2E0: A_27a,V5l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6x_2E0: A_27a,V7y_2E0: A_27b,V8r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] :
            ( ( ( ( c_2Etoto_2Eapto_2E3(A_27a,V3cmp_2E0,V4lb_2E0,V6x_2E0) != c_2EternaryComparisons_2ELESS_2E0 )
               => p(app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0,V3cmp_2E0),V4lb_2E0),V8r_2E0)) )
              & ( ( c_2Etoto_2Eapto_2E3(A_27a,V3cmp_2E0,V4lb_2E0,V6x_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
               => p(app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0,V3cmp_2E0),V6x_2E0),V8r_2E0)) ) )
           => p(app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0,V3cmp_2E0),V4lb_2E0),c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V5l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V6x_2E0,V7y_2E0),V8r_2E0))) ) )
     => ! [V9v_2E0: tyop_2Etoto_2Etoto(A_27a),V10v1_2E0: A_27a,V11v2_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0,V9v_2E0),V10v1_2E0),V11v2_2E0)) ) ).

tff(thm_2Efmapal_2Ebt__to__orl__lb,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
      ( ! [V7cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V5lb_2E0: A_27a,V3x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V7cmp_2E0),V5lb_2E0),V3x_2E0))
        <=> ( c_2Etoto_2Eapto_2E3(A_27a,V7cmp_2E0,V5lb_2E0,V3x_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
     => ( ! [V0lb_2E0: A_27a,V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2Ebt__to__orl__lb_2E3(A_27a,A_27b,V1cmp_2E0,V0lb_2E0,c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))) = c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)) )
        & ! [V2y_2E0: A_27b,V3x_2E0: A_27a,V4r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V5lb_2E0: A_27a,V6l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V7cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2Ebt__to__orl__lb_2E3(A_27a,A_27b,V7cmp_2E0,V5lb_2E0,c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V6l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V3x_2E0,V2y_2E0),V4r_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V7cmp_2E0),V5lb_2E0),V3x_2E0),c_2Elist_2EAPPEND_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Elist_2EAPPEND_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Efmapal_2Ebt__to__orl__lb__ub_2E4(A_27a,A_27b,V7cmp_2E0,V5lb_2E0,V6l_2E0,V3x_2E0),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V3x_2E0,V2y_2E0),c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Efmapal_2Ebt__to__orl__lb_2E3(A_27a,A_27b,V7cmp_2E0,V3x_2E0,V4r_2E0)),c_2Efmapal_2Ebt__to__orl__lb_2E3(A_27a,A_27b,V7cmp_2E0,V5lb_2E0,V4r_2E0)) ) ) ) ).

tff(thm_2Efmapal_2Ebt__to__orl__ub__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
      ( ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2ub_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0P_2E0,V1cmp_2E0),c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))),V2ub_2E0))
        & ! [V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V4l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V5x_2E0: A_27a,V6y_2E0: A_27b,V7r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8ub_2E0: A_27a] :
            ( ( ( ( c_2Etoto_2Eapto_2E3(A_27a,V3cmp_2E0,V5x_2E0,V8ub_2E0) != c_2EternaryComparisons_2ELESS_2E0 )
               => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0P_2E0,V3cmp_2E0),V4l_2E0),V8ub_2E0)) )
              & ( ( c_2Etoto_2Eapto_2E3(A_27a,V3cmp_2E0,V5x_2E0,V8ub_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
               => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0P_2E0,V3cmp_2E0),V4l_2E0),V5x_2E0)) ) )
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0P_2E0,V3cmp_2E0),c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V4l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V5x_2E0,V6y_2E0),V7r_2E0)),V8ub_2E0)) ) )
     => ! [V9v_2E0: tyop_2Etoto_2Etoto(A_27a),V10v1_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V11v2_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0P_2E0,V9v_2E0),V10v1_2E0),V11v2_2E0)) ) ).

tff(thm_2Efmapal_2Ebt__to__orl__ub,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
      ( ! [V7cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3x_2E0: A_27a,V4ub_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V7cmp_2E0),V3x_2E0),V4ub_2E0))
        <=> ( c_2Etoto_2Eapto_2E3(A_27a,V7cmp_2E0,V3x_2E0,V4ub_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
     => ( ! [V0ub_2E0: A_27a,V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2Ebt__to__orl__ub_2E3(A_27a,A_27b,V1cmp_2E0,c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),V0ub_2E0) = c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)) )
        & ! [V2y_2E0: A_27b,V3x_2E0: A_27a,V4ub_2E0: A_27a,V5r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V7cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2Ebt__to__orl__ub_2E3(A_27a,A_27b,V7cmp_2E0,c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V6l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V3x_2E0,V2y_2E0),V5r_2E0),V4ub_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V7cmp_2E0),V3x_2E0),V4ub_2E0),c_2Elist_2EAPPEND_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Elist_2EAPPEND_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Efmapal_2Ebt__to__orl__ub_2E3(A_27a,A_27b,V7cmp_2E0,V6l_2E0,V3x_2E0),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V3x_2E0,V2y_2E0),c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Efmapal_2Ebt__to__orl__lb__ub_2E4(A_27a,A_27b,V7cmp_2E0,V3x_2E0,V5r_2E0,V4ub_2E0)),c_2Efmapal_2Ebt__to__orl__ub_2E3(A_27a,A_27b,V7cmp_2E0,V6l_2E0,V4ub_2E0)) ) ) ) ).

tff(thm_2Efmapal_2Ebt__to__orl__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))] :
      ( ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : p(app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),V0P_2E0,V1cmp_2E0),c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))))
        & ! [V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V4x_2E0: A_27a,V5y_2E0: A_27b,V6r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),V0P_2E0,V2cmp_2E0),c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V3l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V4x_2E0,V5y_2E0),V6r_2E0))) )
     => ! [V7v_2E0: tyop_2Etoto_2Etoto(A_27a),V8v1_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),V0P_2E0,V7v_2E0),V8v1_2E0)) ) ).

tff(thm_2Efmapal_2Ebt__to__orl,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0y_2E0: A_27b,V1x_2E0: A_27a,V2r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V3l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V4cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] :
      ( ( c_2Efmapal_2Ebt__to__orl_2E2(A_27a,A_27b,V4cmp_2E0,c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))) = c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)) )
      & ( c_2Efmapal_2Ebt__to__orl_2E2(A_27a,A_27b,V4cmp_2E0,c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V3l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V0y_2E0),V2r_2E0)) = c_2Elist_2EAPPEND_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Elist_2EAPPEND_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Efmapal_2Ebt__to__orl__ub_2E3(A_27a,A_27b,V4cmp_2E0,V3l_2E0,V1x_2E0),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V0y_2E0),c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Efmapal_2Ebt__to__orl__lb_2E3(A_27a,A_27b,V4cmp_2E0,V1x_2E0,V2r_2E0)) ) ) ).

tff(thm_2Efmapal_2Ebt__to__orl__lb__ub__ac__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))))] :
      ( ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2lb_2E0: A_27a,V3ub_2E0: A_27a,V4m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),V0P_2E0,V1cmp_2E0),V2lb_2E0),c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))),V3ub_2E0),V4m_2E0))
        & ! [V5cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V6lb_2E0: A_27a,V7l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8x_2E0: A_27a,V9y_2E0: A_27b,V10r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V11ub_2E0: A_27a,V12m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
            ( ( ( ( c_2Etoto_2Eapto_2E3(A_27a,V5cmp_2E0,V6lb_2E0,V8x_2E0) != c_2EternaryComparisons_2ELESS_2E0 )
               => p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),V0P_2E0,V5cmp_2E0),V6lb_2E0),V10r_2E0),V11ub_2E0),V12m_2E0)) )
              & ( ( ( c_2Etoto_2Eapto_2E3(A_27a,V5cmp_2E0,V6lb_2E0,V8x_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
                  & ( c_2Etoto_2Eapto_2E3(A_27a,V5cmp_2E0,V8x_2E0,V11ub_2E0) != c_2EternaryComparisons_2ELESS_2E0 ) )
               => p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),V0P_2E0,V5cmp_2E0),V6lb_2E0),V7l_2E0),V11ub_2E0),V12m_2E0)) )
              & ( ( ( c_2Etoto_2Eapto_2E3(A_27a,V5cmp_2E0,V6lb_2E0,V8x_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
                  & ( c_2Etoto_2Eapto_2E3(A_27a,V5cmp_2E0,V8x_2E0,V11ub_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
               => p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),V0P_2E0,V5cmp_2E0),V6lb_2E0),V7l_2E0),V8x_2E0),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V8x_2E0,V9y_2E0),c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5(A_27a,A_27b,V5cmp_2E0,V8x_2E0,V10r_2E0,V11ub_2E0,V12m_2E0)))) )
              & ( ( ( c_2Etoto_2Eapto_2E3(A_27a,V5cmp_2E0,V6lb_2E0,V8x_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
                  & ( c_2Etoto_2Eapto_2E3(A_27a,V5cmp_2E0,V8x_2E0,V11ub_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
               => p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),V0P_2E0,V5cmp_2E0),V8x_2E0),V10r_2E0),V11ub_2E0),V12m_2E0)) ) )
           => p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),V0P_2E0,V5cmp_2E0),V6lb_2E0),c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V7l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V8x_2E0,V9y_2E0),V10r_2E0)),V11ub_2E0),V12m_2E0)) ) )
     => ! [V13v_2E0: tyop_2Etoto_2Etoto(A_27a),V14v1_2E0: A_27a,V15v2_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V16v3_2E0: A_27a,V17v4_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),V0P_2E0,V13v_2E0),V14v1_2E0),V15v2_2E0),V16v3_2E0),V17v4_2E0)) ) ).

tff(thm_2Efmapal_2Ebt__to__orl__lb__ub__ac,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
      ( ! [V11cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V9lb_2E0: A_27a,V5x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V11cmp_2E0),V9lb_2E0),V5x_2E0))
        <=> ( c_2Etoto_2Eapto_2E3(A_27a,V11cmp_2E0,V9lb_2E0,V5x_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
     => ( ! [V0ub_2E0: A_27a,V1m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2lb_2E0: A_27a,V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5(A_27a,A_27b,V3cmp_2E0,V2lb_2E0,c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),V0ub_2E0,V1m_2E0) = V1m_2E0 )
        & ! [V4y_2E0: A_27b,V5x_2E0: A_27a,V6ub_2E0: A_27a,V7r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V9lb_2E0: A_27a,V10l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V11cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5(A_27a,A_27b,V11cmp_2E0,V9lb_2E0,c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V10l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V5x_2E0,V4y_2E0),V7r_2E0),V6ub_2E0,V8m_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V11cmp_2E0),V9lb_2E0),V5x_2E0),c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V11cmp_2E0),V5x_2E0),V6ub_2E0),c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5(A_27a,A_27b,V11cmp_2E0,V9lb_2E0,V10l_2E0,V5x_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V5x_2E0,V4y_2E0),c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5(A_27a,A_27b,V11cmp_2E0,V5x_2E0,V7r_2E0,V6ub_2E0,V8m_2E0))),c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5(A_27a,A_27b,V11cmp_2E0,V9lb_2E0,V10l_2E0,V6ub_2E0,V8m_2E0)),c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5(A_27a,A_27b,V11cmp_2E0,V9lb_2E0,V7r_2E0,V6ub_2E0,V8m_2E0)) ) ) ) ).

tff(thm_2Efmapal_2Ebt__to__orl__lb__ac__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))))] :
      ( ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2lb_2E0: A_27a,V3m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0,V1cmp_2E0),V2lb_2E0),c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))),V3m_2E0))
        & ! [V4cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V5lb_2E0: A_27a,V6l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V7x_2E0: A_27a,V8y_2E0: A_27b,V9r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V10m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
            ( ( ( ( c_2Etoto_2Eapto_2E3(A_27a,V4cmp_2E0,V5lb_2E0,V7x_2E0) != c_2EternaryComparisons_2ELESS_2E0 )
               => p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0,V4cmp_2E0),V5lb_2E0),V9r_2E0),V10m_2E0)) )
              & ( ( c_2Etoto_2Eapto_2E3(A_27a,V4cmp_2E0,V5lb_2E0,V7x_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
               => p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0,V4cmp_2E0),V7x_2E0),V9r_2E0),V10m_2E0)) ) )
           => p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0,V4cmp_2E0),V5lb_2E0),c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V6l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V7x_2E0,V8y_2E0),V9r_2E0)),V10m_2E0)) ) )
     => ! [V11v_2E0: tyop_2Etoto_2Etoto(A_27a),V12v1_2E0: A_27a,V13v2_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V14v3_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0,V11v_2E0),V12v1_2E0),V13v2_2E0),V14v3_2E0)) ) ).

tff(thm_2Efmapal_2Ebt__to__orl__lb__ac,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
      ( ! [V9cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V7lb_2E0: A_27a,V4x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V9cmp_2E0),V7lb_2E0),V4x_2E0))
        <=> ( c_2Etoto_2Eapto_2E3(A_27a,V9cmp_2E0,V7lb_2E0,V4x_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
     => ( ! [V0m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1lb_2E0: A_27a,V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2Ebt__to__orl__lb__ac_2E4(A_27a,A_27b,V2cmp_2E0,V1lb_2E0,c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),V0m_2E0) = V0m_2E0 )
        & ! [V3y_2E0: A_27b,V4x_2E0: A_27a,V5r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V7lb_2E0: A_27a,V8l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V9cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2Ebt__to__orl__lb__ac_2E4(A_27a,A_27b,V9cmp_2E0,V7lb_2E0,c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V8l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V4x_2E0,V3y_2E0),V5r_2E0),V6m_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V9cmp_2E0),V7lb_2E0),V4x_2E0),c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5(A_27a,A_27b,V9cmp_2E0,V7lb_2E0,V8l_2E0,V4x_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V4x_2E0,V3y_2E0),c_2Efmapal_2Ebt__to__orl__lb__ac_2E4(A_27a,A_27b,V9cmp_2E0,V4x_2E0,V5r_2E0,V6m_2E0))),c_2Efmapal_2Ebt__to__orl__lb__ac_2E4(A_27a,A_27b,V9cmp_2E0,V7lb_2E0,V5r_2E0,V6m_2E0)) ) ) ) ).

tff(thm_2Efmapal_2Ebt__to__orl__ub__ac__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))))] :
      ( ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2ub_2E0: A_27a,V3m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0,V1cmp_2E0),c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))),V2ub_2E0),V3m_2E0))
        & ! [V4cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V5l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6x_2E0: A_27a,V7y_2E0: A_27b,V8r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V9ub_2E0: A_27a,V10m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
            ( ( ( ( c_2Etoto_2Eapto_2E3(A_27a,V4cmp_2E0,V6x_2E0,V9ub_2E0) != c_2EternaryComparisons_2ELESS_2E0 )
               => p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0,V4cmp_2E0),V5l_2E0),V9ub_2E0),V10m_2E0)) )
              & ( ( c_2Etoto_2Eapto_2E3(A_27a,V4cmp_2E0,V6x_2E0,V9ub_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
               => p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0,V4cmp_2E0),V5l_2E0),V6x_2E0),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V6x_2E0,V7y_2E0),c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5(A_27a,A_27b,V4cmp_2E0,V6x_2E0,V8r_2E0,V9ub_2E0,V10m_2E0)))) ) )
           => p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0,V4cmp_2E0),c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V5l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V6x_2E0,V7y_2E0),V8r_2E0)),V9ub_2E0),V10m_2E0)) ) )
     => ! [V11v_2E0: tyop_2Etoto_2Etoto(A_27a),V12v1_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V13v2_2E0: A_27a,V14v3_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),V0P_2E0,V11v_2E0),V12v1_2E0),V13v2_2E0),V14v3_2E0)) ) ).

tff(thm_2Efmapal_2Ebt__to__orl__ub__ac,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
      ( ! [V9cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V4x_2E0: A_27a,V5ub_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V9cmp_2E0),V4x_2E0),V5ub_2E0))
        <=> ( c_2Etoto_2Eapto_2E3(A_27a,V9cmp_2E0,V4x_2E0,V5ub_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
     => ( ! [V0ub_2E0: A_27a,V1m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2Ebt__to__orl__ub__ac_2E4(A_27a,A_27b,V2cmp_2E0,c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),V0ub_2E0,V1m_2E0) = V1m_2E0 )
        & ! [V3y_2E0: A_27b,V4x_2E0: A_27a,V5ub_2E0: A_27a,V6r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V7m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V8l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V9cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2Ebt__to__orl__ub__ac_2E4(A_27a,A_27b,V9cmp_2E0,c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V8l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V4x_2E0,V3y_2E0),V6r_2E0),V5ub_2E0,V7m_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V9cmp_2E0),V4x_2E0),V5ub_2E0),c_2Efmapal_2Ebt__to__orl__ub__ac_2E4(A_27a,A_27b,V9cmp_2E0,V8l_2E0,V4x_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V4x_2E0,V3y_2E0),c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5(A_27a,A_27b,V9cmp_2E0,V4x_2E0,V6r_2E0,V5ub_2E0,V7m_2E0))),c_2Efmapal_2Ebt__to__orl__ub__ac_2E4(A_27a,A_27b,V9cmp_2E0,V8l_2E0,V5ub_2E0,V7m_2E0)) ) ) ) ).

tff(thm_2Efmapal_2Ebt__to__orl__ac__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))] :
      ( ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0,V1cmp_2E0),c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))),V2m_2E0))
        & ! [V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V4l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V5x_2E0: A_27a,V6y_2E0: A_27b,V7r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0,V3cmp_2E0),c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V4l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V5x_2E0,V6y_2E0),V7r_2E0)),V8m_2E0)) )
     => ! [V9v_2E0: tyop_2Etoto_2Etoto(A_27a),V10v1_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V11v2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0,V9v_2E0),V10v1_2E0),V11v2_2E0)) ) ).

tff(thm_2Efmapal_2Ebt__to__orl__ac,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0y_2E0: A_27b,V1x_2E0: A_27a,V2r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V3m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V4l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V5cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] :
      ( ( c_2Efmapal_2Ebt__to__orl__ac_2E3(A_27a,A_27b,V5cmp_2E0,c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),V3m_2E0) = V3m_2E0 )
      & ( c_2Efmapal_2Ebt__to__orl__ac_2E3(A_27a,A_27b,V5cmp_2E0,c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V4l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V0y_2E0),V2r_2E0),V3m_2E0) = c_2Efmapal_2Ebt__to__orl__ub__ac_2E4(A_27a,A_27b,V5cmp_2E0,V4l_2E0,V1x_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V0y_2E0),c_2Efmapal_2Ebt__to__orl__lb__ac_2E4(A_27a,A_27b,V5cmp_2E0,V1x_2E0,V2r_2E0,V3m_2E0))) ) ) ).

tff(thm_2Efmapal_2EORWL__bt__to__orl,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1t_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(c_2Efmapal_2EORWL_2E3(A_27a,A_27b,V0cmp_2E0,c_2Efmapal_2EFMAPAL_2E2(A_27a,A_27b,V0cmp_2E0,V1t_2E0),c_2Efmapal_2Ebt__to__orl_2E2(A_27a,A_27b,V0cmp_2E0,V1t_2E0))) ).

tff(thm_2Efmapal_2Ebl__to__fmap__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))] :
      ( ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : p(app_2E2(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),V0P_2E0,V1cmp_2E0),c_2Eenumeral_2Enbl_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))))
        & ! [V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3b_2E0: tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b))] :
            ( p(app_2E2(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),V0P_2E0,V2cmp_2E0),V3b_2E0))
           => p(app_2E2(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),V0P_2E0,V2cmp_2E0),c_2Eenumeral_2Ezerbl_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),V3b_2E0))) )
        & ! [V4cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V5x_2E0: A_27a,V6y_2E0: A_27b,V7t_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8b_2E0: tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b))] :
            ( p(app_2E2(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),V0P_2E0,V4cmp_2E0),V8b_2E0))
           => p(app_2E2(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),V0P_2E0,V4cmp_2E0),c_2Eenumeral_2Eonebl_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V5x_2E0,V6y_2E0),V7t_2E0,V8b_2E0))) ) )
     => ! [V9v_2E0: tyop_2Etoto_2Etoto(A_27a),V10v1_2E0: tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(app_2E2(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),V0P_2E0,V9v_2E0),V10v1_2E0)) ) ).

tff(thm_2Efmapal_2Ebl__to__fmap,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V6cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V4x_2E0: A_27a,V8z_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V6cmp_2E0),V4x_2E0),V8z_2E0))
        <=> ( c_2Etoto_2Eapto_2E3(A_27a,V6cmp_2E0,V4x_2E0,V8z_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
     => ( ! [V6cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V4x_2E0: A_27a,V8z_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V6cmp_2E0),V4x_2E0),V8z_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V8z_2E0,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V6cmp_2E0),V4x_2E0),V8z_2E0)) )
       => ( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2Ebl__to__fmap_2E2(A_27a,A_27b,V0cmp_2E0,c_2Eenumeral_2Enbl_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))) = c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b) )
          & ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2b_2E0: tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2Ebl__to__fmap_2E2(A_27a,A_27b,V1cmp_2E0,c_2Eenumeral_2Ezerbl_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),V2b_2E0)) = c_2Efmapal_2Ebl__to__fmap_2E2(A_27a,A_27b,V1cmp_2E0,V2b_2E0) )
          & ! [V3y_2E0: A_27b,V4x_2E0: A_27a,V5t_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V7b_2E0: tyop_2Eenumeral_2Ebl(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2Ebl__to__fmap_2E2(A_27a,A_27b,V6cmp_2E0,c_2Eenumeral_2Eonebl_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V4x_2E0,V3y_2E0),V5t_2E0,V7b_2E0)) = c_2Efmapal_2EOFU_2E3(A_27a,A_27b,V6cmp_2E0,c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V4x_2E0,V3y_2E0)),c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,c_2Efmapal_2EFMAPAL_2E2(A_27a,A_27b,V6cmp_2E0,V5t_2E0),c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V6cmp_2E0),V4x_2E0)))),c_2Efmapal_2Ebl__to__fmap_2E2(A_27a,A_27b,V6cmp_2E0,V7b_2E0)) ) ) ) ) ).

tff(thm_2Efmapal_2Ebt__to__orl__ID__IMP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
      ( p(c_2Efmapal_2EORL_2E2(A_27a,A_27b,V0cmp_2E0,V1l_2E0))
     => ( c_2Efmapal_2Ebt__to__orl_2E2(A_27a,A_27b,V0cmp_2E0,c_2Eenumeral_2Elist__to__bt_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),V1l_2E0)) = V1l_2E0 ) ) ).

tff(thm_2Efmapal_2Efmap__FDOM,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Efmapal_2Efmap_2E1(A_27a,A_27b,V0l_2E0)) = c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a,c_2Epair_2EFST_2E0(A_27a,A_27b),V0l_2E0)) ) ).

tff(thm_2Efmapal_2EORL__FUNION__IMP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
      ( p(c_2Efmapal_2EORL_2E2(A_27a,A_27b,V0cmp_2E0,V1l_2E0))
     => ! [V2m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
          ( p(c_2Efmapal_2EORL_2E2(A_27a,A_27b,V0cmp_2E0,V2m_2E0))
         => ( p(c_2Efmapal_2EORL_2E2(A_27a,A_27b,V0cmp_2E0,c_2Efmapal_2Emerge_2E3(A_27a,A_27b,V0cmp_2E0,V1l_2E0,V2m_2E0)))
            & ( c_2Efmapal_2Efmap_2E1(A_27a,A_27b,c_2Efmapal_2Emerge_2E3(A_27a,A_27b,V0cmp_2E0,V1l_2E0,V2m_2E0)) = c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,c_2Efmapal_2Efmap_2E1(A_27a,A_27b,V1l_2E0),c_2Efmapal_2Efmap_2E1(A_27a,A_27b,V2m_2E0)) ) ) ) ) ).

tff(thm_2Efmapal_2EFMAPAL__FDOM__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1x_2E0: A_27a] : ( c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Efmapal_2EFMAPAL_2E2(A_27a,A_27b,V0cmp_2E0,c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))))) = c_2Ebool_2EF_2E0 )
      & ! [V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3x_2E0: A_27a,V4a_2E0: A_27a,V5b_2E0: A_27b,V6l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V7r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Efmapal_2EFMAPAL_2E2(A_27a,A_27b,V2cmp_2E0,c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V6l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V4a_2E0,V5b_2E0),V7r_2E0)))) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Emin_2Ebool,c_2Etoto_2Eapto_2E3(A_27a,V2cmp_2E0,V3x_2E0,V4a_2E0),c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Efmapal_2EFMAPAL_2E2(A_27a,A_27b,V2cmp_2E0,V6l_2E0))),c_2Ebool_2ET_2E0,c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Efmapal_2EFMAPAL_2E2(A_27a,A_27b,V2cmp_2E0,V7r_2E0)))) ) ) ).

tff(thm_2Efmapal_2Einter__merge__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))] :
      ( ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V1cmp_2E0),c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2ENIL_2E0(A_27a)))
        & ! [V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3a_2E0: A_27a,V4b_2E0: A_27b,V5l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V2cmp_2E0),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V3a_2E0,V4b_2E0),V5l_2E0)),c_2Elist_2ENIL_2E0(A_27a)))
        & ! [V6cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V7y_2E0: A_27a,V8m_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V6cmp_2E0),c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2ECONS_2E2(A_27a,V7y_2E0,V8m_2E0)))
        & ! [V9cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V10a_2E0: A_27a,V11b_2E0: A_27b,V12l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V13y_2E0: A_27a,V14m_2E0: tyop_2Elist_2Elist(A_27a)] :
            ( ( ( ( c_2Etoto_2Eapto_2E3(A_27a,V9cmp_2E0,V10a_2E0,V13y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
               => p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V9cmp_2E0),V12l_2E0),V14m_2E0)) )
              & ( ( c_2Etoto_2Eapto_2E3(A_27a,V9cmp_2E0,V10a_2E0,V13y_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
               => p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V9cmp_2E0),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V10a_2E0,V11b_2E0),V12l_2E0)),V14m_2E0)) )
              & ( ( c_2Etoto_2Eapto_2E3(A_27a,V9cmp_2E0,V10a_2E0,V13y_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
               => p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V9cmp_2E0),V12l_2E0),c_2Elist_2ECONS_2E2(A_27a,V13y_2E0,V14m_2E0))) ) )
           => p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V9cmp_2E0),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V10a_2E0,V11b_2E0),V12l_2E0)),c_2Elist_2ECONS_2E2(A_27a,V13y_2E0,V14m_2E0))) ) )
     => ! [V15v_2E0: tyop_2Etoto_2Etoto(A_27a),V16v1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V17v2_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V15v_2E0),V16v1_2E0),V17v2_2E0)) ) ).

tff(thm_2Efmapal_2Einter__merge,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2Einter__merge_2E3(A_27a,A_27b,V0cmp_2E0,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)) )
      & ! [V1l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3b_2E0: A_27b,V4a_2E0: A_27a] : ( c_2Efmapal_2Einter__merge_2E3(A_27a,A_27b,V2cmp_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V4a_2E0,V3b_2E0),V1l_2E0),c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)) )
      & ! [V5y_2E0: A_27a,V6m_2E0: tyop_2Elist_2Elist(A_27a),V7cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2Einter__merge_2E3(A_27a,A_27b,V7cmp_2E0,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(A_27a,V5y_2E0,V6m_2E0)) = c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)) )
      & ! [V8y_2E0: A_27a,V9m_2E0: tyop_2Elist_2Elist(A_27a),V10l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V11cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V12b_2E0: A_27b,V13a_2E0: A_27a] : ( c_2Efmapal_2Einter__merge_2E3(A_27a,A_27b,V11cmp_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V13a_2E0,V12b_2E0),V10l_2E0),c_2Elist_2ECONS_2E2(A_27a,V8y_2E0,V9m_2E0)) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Etoto_2Eapto_2E3(A_27a,V11cmp_2E0,V13a_2E0,V8y_2E0),c_2Efmapal_2Einter__merge_2E3(A_27a,A_27b,V11cmp_2E0,V10l_2E0,c_2Elist_2ECONS_2E2(A_27a,V8y_2E0,V9m_2E0)),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V13a_2E0,V12b_2E0),c_2Efmapal_2Einter__merge_2E3(A_27a,A_27b,V11cmp_2E0,V10l_2E0,V9m_2E0)),c_2Efmapal_2Einter__merge_2E3(A_27a,A_27b,V11cmp_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V13a_2E0,V12b_2E0),V10l_2E0),V9m_2E0)) ) ) ).

tff(thm_2Efmapal_2EORL__DRESTRICT__IMP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
      ( p(c_2Efmapal_2EORL_2E2(A_27a,A_27b,V0cmp_2E0,V1l_2E0))
     => ! [V2m_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( p(c_2Eenumeral_2EOL_2E2(A_27a,V0cmp_2E0,V2m_2E0))
         => ( p(c_2Efmapal_2EORL_2E2(A_27a,A_27b,V0cmp_2E0,c_2Efmapal_2Einter__merge_2E3(A_27a,A_27b,V0cmp_2E0,V1l_2E0,V2m_2E0)))
            & ( c_2Efmapal_2Efmap_2E1(A_27a,A_27b,c_2Efmapal_2Einter__merge_2E3(A_27a,A_27b,V0cmp_2E0,V1l_2E0,V2m_2E0)) = c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,c_2Efmapal_2Efmap_2E1(A_27a,A_27b,V1l_2E0),c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2m_2E0)) ) ) ) ) ).

tff(thm_2Efmapal_2Ediff__merge__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))] :
      ( ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V1cmp_2E0),c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2ENIL_2E0(A_27a)))
        & ! [V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3a_2E0: A_27a,V4b_2E0: A_27b,V5l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V2cmp_2E0),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V3a_2E0,V4b_2E0),V5l_2E0)),c_2Elist_2ENIL_2E0(A_27a)))
        & ! [V6cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V7y_2E0: A_27a,V8m_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V6cmp_2E0),c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Elist_2ECONS_2E2(A_27a,V7y_2E0,V8m_2E0)))
        & ! [V9cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V10a_2E0: A_27a,V11b_2E0: A_27b,V12l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V13y_2E0: A_27a,V14m_2E0: tyop_2Elist_2Elist(A_27a)] :
            ( ( ( ( c_2Etoto_2Eapto_2E3(A_27a,V9cmp_2E0,V10a_2E0,V13y_2E0) = c_2EternaryComparisons_2EEQUAL_2E0 )
               => p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V9cmp_2E0),V12l_2E0),V14m_2E0)) )
              & ( ( c_2Etoto_2Eapto_2E3(A_27a,V9cmp_2E0,V10a_2E0,V13y_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
               => p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V9cmp_2E0),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V10a_2E0,V11b_2E0),V12l_2E0)),V14m_2E0)) )
              & ( ( c_2Etoto_2Eapto_2E3(A_27a,V9cmp_2E0,V10a_2E0,V13y_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
               => p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V9cmp_2E0),V12l_2E0),c_2Elist_2ECONS_2E2(A_27a,V13y_2E0,V14m_2E0))) ) )
           => p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V9cmp_2E0),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V10a_2E0,V11b_2E0),V12l_2E0)),c_2Elist_2ECONS_2E2(A_27a,V13y_2E0,V14m_2E0))) ) )
     => ! [V15v_2E0: tyop_2Etoto_2Etoto(A_27a),V16v1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V17v2_2E0: tyop_2Elist_2Elist(A_27a)] : p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V15v_2E0),V16v1_2E0),V17v2_2E0)) ) ).

tff(thm_2Efmapal_2Ediff__merge,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2Ediff__merge_2E3(A_27a,A_27b,V0cmp_2E0,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)) )
      & ! [V1l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3b_2E0: A_27b,V4a_2E0: A_27a] : ( c_2Efmapal_2Ediff__merge_2E3(A_27a,A_27b,V2cmp_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V4a_2E0,V3b_2E0),V1l_2E0),c_2Elist_2ENIL_2E0(A_27a)) = c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V4a_2E0,V3b_2E0),V1l_2E0) )
      & ! [V5y_2E0: A_27a,V6m_2E0: tyop_2Elist_2Elist(A_27a),V7cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2Ediff__merge_2E3(A_27a,A_27b,V7cmp_2E0,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2ECONS_2E2(A_27a,V5y_2E0,V6m_2E0)) = c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)) )
      & ! [V8y_2E0: A_27a,V9m_2E0: tyop_2Elist_2Elist(A_27a),V10l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V11cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V12b_2E0: A_27b,V13a_2E0: A_27a] : ( c_2Efmapal_2Ediff__merge_2E3(A_27a,A_27b,V11cmp_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V13a_2E0,V12b_2E0),V10l_2E0),c_2Elist_2ECONS_2E2(A_27a,V8y_2E0,V9m_2E0)) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Etoto_2Eapto_2E3(A_27a,V11cmp_2E0,V13a_2E0,V8y_2E0),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V13a_2E0,V12b_2E0),c_2Efmapal_2Ediff__merge_2E3(A_27a,A_27b,V11cmp_2E0,V10l_2E0,c_2Elist_2ECONS_2E2(A_27a,V8y_2E0,V9m_2E0))),c_2Efmapal_2Ediff__merge_2E3(A_27a,A_27b,V11cmp_2E0,V10l_2E0,V9m_2E0),c_2Efmapal_2Ediff__merge_2E3(A_27a,A_27b,V11cmp_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V13a_2E0,V12b_2E0),V10l_2E0),V9m_2E0)) ) ) ).

tff(thm_2Efmapal_2EORL__DRESTRICT__COMPL__IMP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
      ( p(c_2Efmapal_2EORL_2E2(A_27a,A_27b,V0cmp_2E0,V1l_2E0))
     => ! [V2m_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( p(c_2Eenumeral_2EOL_2E2(A_27a,V0cmp_2E0,V2m_2E0))
         => ( p(c_2Efmapal_2EORL_2E2(A_27a,A_27b,V0cmp_2E0,c_2Efmapal_2Ediff__merge_2E3(A_27a,A_27b,V0cmp_2E0,V1l_2E0,V2m_2E0)))
            & ( c_2Efmapal_2Efmap_2E1(A_27a,A_27b,c_2Efmapal_2Ediff__merge_2E3(A_27a,A_27b,V0cmp_2E0,V1l_2E0,V2m_2E0)) = c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,c_2Efmapal_2Efmap_2E1(A_27a,A_27b,V1l_2E0),c_2Epred__set_2ECOMPL_2E1(A_27a,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2m_2E0))) ) ) ) ) ).

tff(thm_2Efmapal_2EFMAPAL__fmap,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2Efmap_2E1(A_27a,A_27b,V1l_2E0) = c_2Efmapal_2EFMAPAL_2E2(A_27a,A_27b,V0cmp_2E0,c_2Eenumeral_2Elist__to__bt_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Efmapal_2Eincr__sort_2E2(A_27a,A_27b,V0cmp_2E0,V1l_2E0))) ) ).

tff(thm_2Efmapal_2EORL__FMAPAL,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
      ( p(c_2Efmapal_2EORL_2E2(A_27a,A_27b,V0cmp_2E0,V1l_2E0))
     => ( c_2Efmapal_2Efmap_2E1(A_27a,A_27b,V1l_2E0) = c_2Efmapal_2EFMAPAL_2E2(A_27a,A_27b,V0cmp_2E0,c_2Eenumeral_2Elist__to__bt_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),V1l_2E0)) ) ) ).

tff(thm_2Efmapal_2EORWL__FUNION__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1s_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3t_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V4m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
      ( ( p(c_2Efmapal_2EORWL_2E3(A_27a,A_27b,V0cmp_2E0,V1s_2E0,V2l_2E0))
        & p(c_2Efmapal_2EORWL_2E3(A_27a,A_27b,V0cmp_2E0,V3t_2E0,V4m_2E0)) )
     => p(c_2Efmapal_2EORWL_2E3(A_27a,A_27b,V0cmp_2E0,c_2Efinite__map_2EFUNION_2E2(A_27a,A_27b,V1s_2E0,V3t_2E0),c_2Efmapal_2Emerge_2E3(A_27a,A_27b,V0cmp_2E0,V2l_2E0,V4m_2E0))) ) ).

tff(thm_2Efmapal_2EORWL__DRESTRICT__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1s_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4m_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( p(c_2Efmapal_2EORWL_2E3(A_27a,A_27b,V0cmp_2E0,V1s_2E0,V2l_2E0))
        & p(c_2Eenumeral_2EOWL_2E3(A_27a,V0cmp_2E0,V3t_2E0,V4m_2E0)) )
     => p(c_2Efmapal_2EORWL_2E3(A_27a,A_27b,V0cmp_2E0,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V1s_2E0,V3t_2E0),c_2Efmapal_2Einter__merge_2E3(A_27a,A_27b,V0cmp_2E0,V2l_2E0,V4m_2E0))) ) ).

tff(thm_2Efmapal_2EORWL__DRESTRICT__COMPL__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1s_2E0: tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V3t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4m_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( p(c_2Efmapal_2EORWL_2E3(A_27a,A_27b,V0cmp_2E0,V1s_2E0,V2l_2E0))
        & p(c_2Eenumeral_2EOWL_2E3(A_27a,V0cmp_2E0,V3t_2E0,V4m_2E0)) )
     => p(c_2Efmapal_2EORWL_2E3(A_27a,A_27b,V0cmp_2E0,c_2Efinite__map_2EDRESTRICT_2E2(A_27a,A_27b,V1s_2E0,c_2Epred__set_2ECOMPL_2E1(A_27a,V3t_2E0)),c_2Efmapal_2Ediff__merge_2E3(A_27a,A_27b,V0cmp_2E0,V2l_2E0,V4m_2E0))) ) ).

tff(thm_2Efmapal_2Eo__f__bt__map,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1f_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V2t_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efinite__map_2Eo__f_2E2(A_27a,A_27b,A_27c,V1f_2E0,c_2Efmapal_2EFMAPAL_2E2(A_27a,A_27b,V0cmp_2E0,V2t_2E0)) = c_2Efmapal_2EFMAPAL_2E2(A_27a,A_27c,V0cmp_2E0,c_2Efmapal_2Ebt__map_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c),c_2Efmapal_2EAP__SND_2E1(A_27a,A_27b,A_27c,V1f_2E0),V2t_2E0)) ) ).

tff(thm_2Efmapal_2EFAPPLY__fmap__NIL,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a] : ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efmapal_2Efmap_2E1(A_27a,A_27b,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))),V0x_2E0) = c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efinite__map_2EFEMPTY_2E0(A_27a,A_27b),V0x_2E0) ) ).

tff(thm_2Efmapal_2EFAPPLY__fmap__CONS,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ! [V0x_2E0: A_27a,V1y_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0x_2E0),V1y_2E0))
        <=> ( V0x_2E0 = V1y_2E0 ) )
     => ! [V0x_2E0: A_27a,V1y_2E0: A_27a,V2z_2E0: A_27b,V3l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efmapal_2Efmap_2E1(A_27a,A_27b,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V1y_2E0,V2z_2E0),V3l_2E0)),V0x_2E0) = c_2Ebool_2ECOND_2E3(A_27b,app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V0x_2E0),V1y_2E0),V2z_2E0,c_2Efinite__map_2EFAPPLY_2E2(A_27a,A_27b,c_2Efmapal_2Efmap_2E1(A_27a,A_27b,V3l_2E0),V0x_2E0)) ) ) ).

tff(thm_2Efmapal_2Eo__f__fmap,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V1l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efinite__map_2Eo__f_2E2(A_27a,A_27b,A_27c,V0f_2E0,c_2Efmapal_2Efmap_2E1(A_27a,A_27b,V1l_2E0)) = c_2Efmapal_2Efmap_2E1(A_27a,A_27c,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c),c_2Efmapal_2EAP__SND_2E1(A_27a,A_27b,A_27c,V0f_2E0),V1l_2E0)) ) ).

tff(thm_2Efmapal_2EORL__bt__lb__ub__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))))] :
      ( ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2lb_2E0: A_27a,V3ub_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0P_2E0,V1cmp_2E0),V2lb_2E0),c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))),V3ub_2E0))
        & ! [V4cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V5lb_2E0: A_27a,V6l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V7x_2E0: A_27a,V8y_2E0: A_27b,V9r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V10ub_2E0: A_27a] :
            ( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0P_2E0,V4cmp_2E0),V5lb_2E0),V6l_2E0),V7x_2E0))
              & p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0P_2E0,V4cmp_2E0),V7x_2E0),V9r_2E0),V10ub_2E0)) )
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0P_2E0,V4cmp_2E0),V5lb_2E0),c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V6l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V7x_2E0,V8y_2E0),V9r_2E0)),V10ub_2E0)) ) )
     => ! [V11v_2E0: tyop_2Etoto_2Etoto(A_27a),V12v1_2E0: A_27a,V13v2_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V14v3_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V0P_2E0,V11v_2E0),V12v1_2E0),V13v2_2E0),V14v3_2E0)) ) ).

tff(thm_2Efmapal_2EORL__bt__lb__ub,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0ub_2E0: A_27a,V1lb_2E0: A_27a,V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] :
          ( p(c_2Efmapal_2EORL__bt__lb__ub_2E4(A_27a,A_27b,V2cmp_2E0,V1lb_2E0,c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),V0ub_2E0))
        <=> ( c_2Etoto_2Eapto_2E3(A_27a,V2cmp_2E0,V1lb_2E0,V0ub_2E0) = c_2EternaryComparisons_2ELESS_2E0 ) )
      & ! [V3y_2E0: A_27b,V4x_2E0: A_27a,V5ub_2E0: A_27a,V6r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V7lb_2E0: A_27a,V8l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V9cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] :
          ( p(c_2Efmapal_2EORL__bt__lb__ub_2E4(A_27a,A_27b,V9cmp_2E0,V7lb_2E0,c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V8l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V4x_2E0,V3y_2E0),V6r_2E0),V5ub_2E0))
        <=> ( p(c_2Efmapal_2EORL__bt__lb__ub_2E4(A_27a,A_27b,V9cmp_2E0,V7lb_2E0,V8l_2E0,V4x_2E0))
            & p(c_2Efmapal_2EORL__bt__lb__ub_2E4(A_27a,A_27b,V9cmp_2E0,V4x_2E0,V6r_2E0,V5ub_2E0)) ) ) ) ).

tff(thm_2Efmapal_2EORL__bt__lb__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))] :
      ( ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2lb_2E0: A_27a] : p(app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0,V1cmp_2E0),V2lb_2E0),c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))))
        & ! [V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V4lb_2E0: A_27a,V5l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6x_2E0: A_27a,V7y_2E0: A_27b,V8r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] :
            ( p(app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0,V3cmp_2E0),V6x_2E0),V8r_2E0))
           => p(app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0,V3cmp_2E0),V4lb_2E0),c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V5l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V6x_2E0,V7y_2E0),V8r_2E0))) ) )
     => ! [V9v_2E0: tyop_2Etoto_2Etoto(A_27a),V10v1_2E0: A_27a,V11v2_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),V0P_2E0,V9v_2E0),V10v1_2E0),V11v2_2E0)) ) ).

tff(thm_2Efmapal_2EORL__bt__lb,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0lb_2E0: A_27a,V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2EORL__bt__lb_2E3(A_27a,A_27b,V1cmp_2E0,V0lb_2E0,c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))) = c_2Ebool_2ET_2E0 )
      & ! [V2y_2E0: A_27b,V3x_2E0: A_27a,V4r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V5lb_2E0: A_27a,V6l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V7cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] :
          ( p(c_2Efmapal_2EORL__bt__lb_2E3(A_27a,A_27b,V7cmp_2E0,V5lb_2E0,c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V6l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V3x_2E0,V2y_2E0),V4r_2E0)))
        <=> ( p(c_2Efmapal_2EORL__bt__lb__ub_2E4(A_27a,A_27b,V7cmp_2E0,V5lb_2E0,V6l_2E0,V3x_2E0))
            & p(c_2Efmapal_2EORL__bt__lb_2E3(A_27a,A_27b,V7cmp_2E0,V3x_2E0,V4r_2E0)) ) ) ) ).

tff(thm_2Efmapal_2EORL__bt__ub__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
      ( ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2ub_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0P_2E0,V1cmp_2E0),c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))),V2ub_2E0))
        & ! [V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V4l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V5x_2E0: A_27a,V6y_2E0: A_27b,V7r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V8ub_2E0: A_27a] :
            ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0P_2E0,V3cmp_2E0),V4l_2E0),V5x_2E0))
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0P_2E0,V3cmp_2E0),c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V4l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V5x_2E0,V6y_2E0),V7r_2E0)),V8ub_2E0)) ) )
     => ! [V9v_2E0: tyop_2Etoto_2Etoto(A_27a),V10v1_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V11v2_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0P_2E0,V9v_2E0),V10v1_2E0),V11v2_2E0)) ) ).

tff(thm_2Efmapal_2EORL__bt__ub,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0ub_2E0: A_27a,V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2EORL__bt__ub_2E3(A_27a,A_27b,V1cmp_2E0,c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),V0ub_2E0) = c_2Ebool_2ET_2E0 )
      & ! [V2y_2E0: A_27b,V3x_2E0: A_27a,V4ub_2E0: A_27a,V5r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V6l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V7cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] :
          ( p(c_2Efmapal_2EORL__bt__ub_2E3(A_27a,A_27b,V7cmp_2E0,c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V6l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V3x_2E0,V2y_2E0),V5r_2E0),V4ub_2E0))
        <=> ( p(c_2Efmapal_2EORL__bt__ub_2E3(A_27a,A_27b,V7cmp_2E0,V6l_2E0,V3x_2E0))
            & p(c_2Efmapal_2EORL__bt__lb__ub_2E4(A_27a,A_27b,V7cmp_2E0,V3x_2E0,V5r_2E0,V4ub_2E0)) ) ) ) ).

tff(thm_2Efmapal_2EORL__bt__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))] :
      ( ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : p(app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),V0P_2E0,V1cmp_2E0),c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))))
        & ! [V2cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V4x_2E0: A_27a,V5y_2E0: A_27b,V6r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),V0P_2E0,V2cmp_2E0),c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V3l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V4x_2E0,V5y_2E0),V6r_2E0))) )
     => ! [V7v_2E0: tyop_2Etoto_2Etoto(A_27a),V8v1_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),V0P_2E0,V7v_2E0),V8v1_2E0)) ) ).

tff(thm_2Efmapal_2EORL__bt,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0y_2E0: A_27b,V1x_2E0: A_27a,V2r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V3l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V4cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] :
      ( ( c_2Efmapal_2EORL__bt_2E2(A_27a,A_27b,V4cmp_2E0,c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))) = c_2Ebool_2ET_2E0 )
      & ( p(c_2Efmapal_2EORL__bt_2E2(A_27a,A_27b,V4cmp_2E0,c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V3l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V0y_2E0),V2r_2E0)))
      <=> ( p(c_2Efmapal_2EORL__bt__ub_2E3(A_27a,A_27b,V4cmp_2E0,V3l_2E0,V1x_2E0))
          & p(c_2Efmapal_2EORL__bt__lb_2E3(A_27a,A_27b,V4cmp_2E0,V1x_2E0,V2r_2E0)) ) ) ) ).

tff(thm_2Efmapal_2Ebetter__bt__to__orl,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1t_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( c_2Efmapal_2Ebt__to__orl_2E2(A_27a,A_27b,V0cmp_2E0,V1t_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Efmapal_2EORL__bt_2E2(A_27a,A_27b,V0cmp_2E0,V1t_2E0),c_2Eenumeral_2Ebt__to__list__ac_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),V1t_2E0,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Efmapal_2Ebt__to__orl__ac_2E3(A_27a,A_27b,V0cmp_2E0,V1t_2E0,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)))) ) ).

tff(thm_2Efmapal_2Elist__rplacv__cn__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))))] :
      ( ! [V9cn_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V6w_2E0: A_27a,V7z_2E0: A_27b,V10m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),F0_2E0,V9cn_2E0),V6w_2E0),V7z_2E0),V10m_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V9cn_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V6w_2E0,V7z_2E0),V10m_2E0)) )
     => ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool)))] :
          ( ( ! [V1x_2E0: A_27a,V2y_2E0: A_27b,V3cn_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))] : p(app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool)),V0P_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V2y_2E0)),c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))),V3cn_2E0))
            & ! [V4x_2E0: A_27a,V5y_2E0: A_27b,V6w_2E0: A_27a,V7z_2E0: A_27b,V8l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V9cn_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))] :
                ( ( ( V4x_2E0 != V6w_2E0 )
                 => p(app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool)),V0P_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V4x_2E0,V5y_2E0)),V8l_2E0),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),F0_2E0,V9cn_2E0),V6w_2E0),V7z_2E0))) )
               => p(app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool)),V0P_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V4x_2E0,V5y_2E0)),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V6w_2E0,V7z_2E0),V8l_2E0)),V9cn_2E0)) ) )
         => ! [V11v_2E0: A_27a,V12v1_2E0: A_27b,V13v2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V14v3_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))] : p(app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool)),V0P_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V11v_2E0,V12v1_2E0)),V13v2_2E0),V14v3_2E0)) ) ) ).

tff(thm_2Efmapal_2Elist__rplacv__cn,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))))),F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
      ( ! [V8cn_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),V6w_2E0: A_27a,V3z_2E0: A_27b,V9m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),F1_2E0,V8cn_2E0),V6w_2E0),V3z_2E0),V9m_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V8cn_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V6w_2E0,V3z_2E0),V9m_2E0)) )
     => ( ! [V5x_2E0: A_27a,V6w_2E0: A_27a] :
            ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V5x_2E0),V6w_2E0))
          <=> ( V5x_2E0 = V6w_2E0 ) )
       => ( ! [V0y_2E0: A_27b,V1x_2E0: A_27a,V2cn_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))] : ( c_2Efmapal_2Elist__rplacv__cn_2E3(A_27a,A_27b,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V0y_2E0),c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),V2cn_2E0) = c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)) )
          & ! [V3z_2E0: A_27b,V4y_2E0: A_27b,V5x_2E0: A_27a,V6w_2E0: A_27a,V7l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V8cn_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))] : ( c_2Efmapal_2Elist__rplacv__cn_2E3(A_27a,A_27b,c_2Epair_2E_2C_2E2(A_27a,A_27b,V5x_2E0,V4y_2E0),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V6w_2E0,V3z_2E0),V7l_2E0),V8cn_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0,V5x_2E0),V6w_2E0),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V8cn_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V5x_2E0,V4y_2E0),V7l_2E0)),c_2Efmapal_2Elist__rplacv__cn_2E3(A_27a,A_27b,c_2Epair_2E_2C_2E2(A_27a,A_27b,V5x_2E0,V4y_2E0),V7l_2E0,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))))),F1_2E0,V8cn_2E0),V6w_2E0),V3z_2E0))) ) ) ) ) ).

tff(thm_2Efmapal_2Efmap__FDOM__rec,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0x_2E0: A_27a] : ( c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Efmapal_2Efmap_2E1(A_27a,A_27b,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))))) = c_2Ebool_2EF_2E0 )
      & ! [V1x_2E0: A_27a,V2w_2E0: A_27a,V3z_2E0: A_27b,V4l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
          ( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Efmapal_2Efmap_2E1(A_27a,A_27b,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V2w_2E0,V3z_2E0),V4l_2E0)))))
        <=> ( ( V1x_2E0 = V2w_2E0 )
            | p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Efmapal_2Efmap_2E1(A_27a,A_27b,V4l_2E0)))) ) ) ) ).

tff(thm_2Efmapal_2Elist__rplacv__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))),F2_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),F3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),F4_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))))] :
      ( ! [V4m_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),F1_2E0,V4m_2E0) = V4m_2E0 )
     => ( ! [V3ans_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
            ( p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,F2_2E0,V3ans_2E0))
          <=> ( V3ans_2E0 = c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)) ) )
       => ( ! [V0x_2E0: A_27a,V2l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
              ( p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),F3_2E0,V0x_2E0),V2l_2E0))
            <=> ~ p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Efmapal_2Efmap_2E1(A_27a,A_27b,V2l_2E0)))) )
         => ( ! [V0x_2E0: A_27a,V2l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1y_2E0: A_27b,V3ans_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] :
                ( p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),F4_2E0,V0x_2E0),V2l_2E0),V1y_2E0),V3ans_2E0))
              <=> ( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Efmapal_2Efmap_2E1(A_27a,A_27b,V2l_2E0))))
                  & ( c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,c_2Efmapal_2Efmap_2E1(A_27a,A_27b,V2l_2E0),c_2Epair_2E_2C_2E2(A_27a,A_27b,V0x_2E0,V1y_2E0)) = c_2Efmapal_2Efmap_2E1(A_27a,A_27b,V3ans_2E0) ) ) )
           => ( ! [V0x_2E0: A_27a,V2l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V1y_2E0: A_27b,V3ans_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),F0_2E0,V0x_2E0),V2l_2E0),V1y_2E0),V3ans_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,F2_2E0,V3ans_2E0),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),F3_2E0,V0x_2E0),V2l_2E0),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),F4_2E0,V0x_2E0),V2l_2E0),V1y_2E0),V3ans_2E0)) )
             => ! [V0x_2E0: A_27a,V1y_2E0: A_27b,V2l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(c_2Ebool_2ELET_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),F0_2E0,V0x_2E0),V2l_2E0),V1y_2E0),c_2Efmapal_2Elist__rplacv__cn_2E3(A_27a,A_27b,c_2Epair_2E_2C_2E2(A_27a,A_27b,V0x_2E0,V1y_2E0),V2l_2E0,F1_2E0))) ) ) ) ) ) ).

tff(thm_2Efmapal_2Ebt__rplacv__cn__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))))))] :
      ( ! [V12cn_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),V8l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V9w_2E0: A_27a,V10z_2E0: A_27b,V13m_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))))),F0_2E0,V12cn_2E0),V8l_2E0),V9w_2E0),V10z_2E0),V13m_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V12cn_2E0,c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V8l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V9w_2E0,V10z_2E0),V13m_2E0)) )
     => ( ! [V12cn_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),V9w_2E0: A_27a,V10z_2E0: A_27b,V11r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V14m_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))))),F1_2E0,V12cn_2E0),V9w_2E0),V10z_2E0),V11r_2E0),V14m_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V12cn_2E0,c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V14m_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V9w_2E0,V10z_2E0),V11r_2E0)) )
       => ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool))))] :
            ( ( ! [V1cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V2x_2E0: A_27a,V3y_2E0: A_27b,V4cn_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))] : p(app_2E2(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool))),V0P_2E0,V1cmp_2E0),c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0)),c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b))),V4cn_2E0))
              & ! [V5cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V6x_2E0: A_27a,V7y_2E0: A_27b,V8l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V9w_2E0: A_27a,V10z_2E0: A_27b,V11r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V12cn_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))] :
                  ( ( ( ( c_2Etoto_2Eapto_2E3(A_27a,V5cmp_2E0,V6x_2E0,V9w_2E0) = c_2EternaryComparisons_2EGREATER_2E0 )
                     => p(app_2E2(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool))),V0P_2E0,V5cmp_2E0),c_2Epair_2E_2C_2E2(A_27a,A_27b,V6x_2E0,V7y_2E0)),V11r_2E0),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))))),F0_2E0,V12cn_2E0),V8l_2E0),V9w_2E0),V10z_2E0))) )
                    & ( ( c_2Etoto_2Eapto_2E3(A_27a,V5cmp_2E0,V6x_2E0,V9w_2E0) = c_2EternaryComparisons_2ELESS_2E0 )
                     => p(app_2E2(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool))),V0P_2E0,V5cmp_2E0),c_2Epair_2E_2C_2E2(A_27a,A_27b,V6x_2E0,V7y_2E0)),V8l_2E0),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))))),F1_2E0,V12cn_2E0),V9w_2E0),V10z_2E0),V11r_2E0))) ) )
                 => p(app_2E2(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool))),V0P_2E0,V5cmp_2E0),c_2Epair_2E_2C_2E2(A_27a,A_27b,V6x_2E0,V7y_2E0)),c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V8l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V9w_2E0,V10z_2E0),V11r_2E0)),V12cn_2E0)) ) )
           => ! [V15v_2E0: tyop_2Etoto_2Etoto(A_27a),V16v1_2E0: A_27a,V17v2_2E0: A_27b,V18v3_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V19v4_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))] : p(app_2E2(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Ebool))),V0P_2E0,V15v_2E0),c_2Epair_2E_2C_2E2(A_27a,A_27b,V16v1_2E0,V17v2_2E0)),V18v3_2E0),V19v4_2E0)) ) ) ) ).

tff(thm_2Efmapal_2Ebt__rplacv__cn,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))))))] :
      ( ! [V10cn_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),V9l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V7w_2E0: A_27a,V4z_2E0: A_27b,V13m_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))))),F1_2E0,V10cn_2E0),V9l_2E0),V7w_2E0),V4z_2E0),V13m_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V10cn_2E0,c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V9l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V7w_2E0,V4z_2E0),V13m_2E0)) )
     => ( ! [V10cn_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),V7w_2E0: A_27a,V4z_2E0: A_27b,V8r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V12m_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))))),F0_2E0,V10cn_2E0),V7w_2E0),V4z_2E0),V8r_2E0),V12m_2E0) = app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V10cn_2E0,c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V12m_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V7w_2E0,V4z_2E0),V8r_2E0)) )
       => ( ! [V0y_2E0: A_27b,V1x_2E0: A_27a,V2cn_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),V3cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2Ebt__rplacv__cn_2E4(A_27a,A_27b,V3cmp_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V0y_2E0),c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),V2cn_2E0) = c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)) )
          & ! [V4z_2E0: A_27b,V5y_2E0: A_27b,V6x_2E0: A_27a,V7w_2E0: A_27a,V8r_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V9l_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V10cn_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),V11cmp_2E0: tyop_2Etoto_2Etoto(A_27a)] : ( c_2Efmapal_2Ebt__rplacv__cn_2E4(A_27a,A_27b,V11cmp_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V6x_2E0,V5y_2E0),c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V9l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V7w_2E0,V4z_2E0),V8r_2E0),V10cn_2E0) = c_2EternaryComparisons_2Eordering__CASE_2E4(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Etoto_2Eapto_2E3(A_27a,V11cmp_2E0,V6x_2E0,V7w_2E0),c_2Efmapal_2Ebt__rplacv__cn_2E4(A_27a,A_27b,V11cmp_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V6x_2E0,V5y_2E0),V9l_2E0,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))))),F0_2E0,V10cn_2E0),V7w_2E0),V4z_2E0),V8r_2E0)),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V10cn_2E0,c_2Eenumeral_2Enode_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),V9l_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V6x_2E0,V5y_2E0),V8r_2E0)),c_2Efmapal_2Ebt__rplacv__cn_2E4(A_27a,A_27b,V11cmp_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V6x_2E0,V5y_2E0),V8r_2E0,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))))),app_2E2(tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)))))),F1_2E0,V10cn_2E0),V9l_2E0),V7w_2E0),V4z_2E0))) ) ) ) ) ).

tff(thm_2Efmapal_2Ebt__rplacv__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))),F2_2E0: tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),F3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),F4_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))))),F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))))] :
      ( ! [V5m_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),F1_2E0,V5m_2E0) = V5m_2E0 )
     => ( ! [V4ans_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] :
            ( p(app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,F2_2E0,V4ans_2E0))
          <=> ( V4ans_2E0 = c_2Eenumeral_2Ent_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)) ) )
       => ( ! [V1x_2E0: A_27a,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3t_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] :
              ( p(app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),F3_2E0,V1x_2E0),V0cmp_2E0),V3t_2E0))
            <=> ~ p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Efmapal_2EFMAPAL_2E2(A_27a,A_27b,V0cmp_2E0,V3t_2E0)))) )
         => ( ! [V1x_2E0: A_27a,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3t_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V2y_2E0: A_27b,V4ans_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] :
                ( p(app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),F4_2E0,V1x_2E0),V0cmp_2E0),V3t_2E0),V2y_2E0),V4ans_2E0))
              <=> ( p(c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,c_2Efinite__map_2EFDOM_2E1(A_27a,A_27b,c_2Efmapal_2EFMAPAL_2E2(A_27a,A_27b,V0cmp_2E0,V3t_2E0))))
                  & ( c_2Efinite__map_2EFUPDATE_2E2(A_27a,A_27b,c_2Efmapal_2EFMAPAL_2E2(A_27a,A_27b,V0cmp_2E0,V3t_2E0),c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V2y_2E0)) = c_2Efmapal_2EFMAPAL_2E2(A_27a,A_27b,V0cmp_2E0,V4ans_2E0) ) ) )
           => ( ! [V1x_2E0: A_27a,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V3t_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),V2y_2E0: A_27b,V4ans_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : ( app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),F0_2E0,V1x_2E0),V0cmp_2E0),V3t_2E0),V2y_2E0),V4ans_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,F2_2E0,V4ans_2E0),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),F3_2E0,V1x_2E0),V0cmp_2E0),V3t_2E0),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),F4_2E0,V1x_2E0),V0cmp_2E0),V3t_2E0),V2y_2E0),V4ans_2E0)) )
             => ! [V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1x_2E0: A_27a,V2y_2E0: A_27b,V3t_2E0: tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(c_2Ebool_2ELET_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Etoto_2Etoto(A_27a),tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eenumeral_2Ebt(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)))),F0_2E0,V1x_2E0),V0cmp_2E0),V3t_2E0),V2y_2E0),c_2Efmapal_2Ebt__rplacv__cn_2E4(A_27a,A_27b,V0cmp_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V1x_2E0,V2y_2E0),V3t_2E0,F1_2E0))) ) ) ) ) ) ).

tff(thm_2Efmapal_2EFUN__fmap__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b)))] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b)),F0_2E0,V0f_2E0),V2x_2E0) = c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0)) )
     => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Efmapal_2Efmap_2E1(A_27a,A_27b,c_2Elist_2EMAP_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27b)),F0_2E0,V0f_2E0),V1l_2E0)) = c_2Efinite__map_2EFUN__FMAP_2E2(A_27a,A_27b,V0f_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0)) ) ) ).

tff(thm_2Efmapal_2Efmap__ORWL__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0cmp_2E0: tyop_2Etoto_2Etoto(A_27a),V1l_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b))] : p(c_2Efmapal_2EORWL_2E3(A_27a,A_27b,V0cmp_2E0,c_2Efmapal_2Efmap_2E1(A_27a,A_27b,V1l_2E0),c_2Efmapal_2Eincr__sort_2E2(A_27a,A_27b,V0cmp_2E0,V1l_2E0))) ).

%------------------------------------------------------------------------------