%------------------------------------------------------------------------------
% File     : ITP107^4 : TPTP v8.2.0. 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]
%          : HL4107^4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  495 ( 172 unt; 240 typ;   0 def)
%            Number of atoms       :  657 ( 340 equ;  13 cnn)
%            Maximal formula atoms :   16 (   1 avg)
%            Number of connectives : 33163 (  13   ~;   2   |; 123   &;32833   @)
%                                         (  41 <=>; 151  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   47 (  11 avg;32833 nst)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :  321 ( 321   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  238 ( 236 usr; 114 con; 0-5 aty)
%            Number of variables   : 1658 (   0   ^1657   !;   1   ?;1658   :)
% SPC      : TH0_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(u,type,
    u: $tType ).

thf(d,type,
    d: $tType ).

thf(du,type,
    du: $tType ).

thf(mono_2Etyop_2EternaryComparisons_2Eordering,type,
    mono_2Etyop_2EternaryComparisons_2Eordering: $tType ).

thf(tyop_2Eenumeral_2Ebl,type,
    tyop_2Eenumeral_2Ebl: d > d ).

thf(tyop_2Eenumeral_2Ebt,type,
    tyop_2Eenumeral_2Ebt: d > d ).

thf(tyop_2Efinite__map_2Efmap,type,
    tyop_2Efinite__map_2Efmap: d > d > d ).

thf(tyop_2Elist_2Elist,type,
    tyop_2Elist_2Elist: d > d ).

thf(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: d ).

thf(tyop_2Emin_2Efun,type,
    tyop_2Emin_2Efun: d > d > d ).

thf(tyop_2Eoption_2Eoption,type,
    tyop_2Eoption_2Eoption: d > d ).

thf(tyop_2Epair_2Eprod,type,
    tyop_2Epair_2Eprod: d > d > d ).

thf(tyop_2EternaryComparisons_2Eordering,type,
    tyop_2EternaryComparisons_2Eordering: d ).

thf(tyop_2Etoto_2Etoto,type,
    tyop_2Etoto_2Etoto: d > d ).

thf(s,type,
    s: d > u > du ).

thf(app_2E2,type,
    app_2E2: du > du > u ).

thf(combin_i_2E0,type,
    combin_i_2E0: u ).

thf(combin_k_2E0,type,
    combin_k_2E0: u ).

thf(combin_s_2E0,type,
    combin_s_2E0: u ).

thf(c_2Ebool_2E_21_2E0,type,
    c_2Ebool_2E_21_2E0: u ).

thf(c_2Ebool_2E_21_2E1,type,
    c_2Ebool_2E_21_2E1: du > u ).

thf(c_2Epair_2E_2C_2E0,type,
    c_2Epair_2E_2C_2E0: u ).

thf(c_2Epair_2E_2C_2E2,type,
    c_2Epair_2E_2C_2E2: du > du > u ).

thf(c_2Ebool_2E_2F_5C_2E0,type,
    c_2Ebool_2E_2F_5C_2E0: u ).

thf(c_2Ebool_2E_2F_5C_2E2,type,
    c_2Ebool_2E_2F_5C_2E2: du > du > u ).

thf(c_2Emin_2E_3D_2E0,type,
    c_2Emin_2E_3D_2E0: u ).

thf(c_2Emin_2E_3D_2E2,type,
    c_2Emin_2E_3D_2E2: du > du > u ).

thf(c_2Emin_2E_3D_3D_3E_2E0,type,
    c_2Emin_2E_3D_3D_3E_2E0: u ).

thf(c_2Emin_2E_3D_3D_3E_2E2,type,
    c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).

thf(c_2Ebool_2E_3F_2E0,type,
    c_2Ebool_2E_3F_2E0: u ).

thf(c_2Ebool_2E_3F_2E1,type,
    c_2Ebool_2E_3F_2E1: du > u ).

thf(c_2Emin_2E_40_2E0,type,
    c_2Emin_2E_40_2E0: u ).

thf(c_2Emin_2E_40_2E1,type,
    c_2Emin_2E_40_2E1: du > u ).

thf(c_2Elist_2EAPPEND_2E0,type,
    c_2Elist_2EAPPEND_2E0: u ).

thf(c_2Elist_2EAPPEND_2E2,type,
    c_2Elist_2EAPPEND_2E2: du > du > u ).

thf(c_2Efmapal_2EAP__SND_2E0,type,
    c_2Efmapal_2EAP__SND_2E0: u ).

thf(c_2Efmapal_2EAP__SND_2E1,type,
    c_2Efmapal_2EAP__SND_2E1: du > u ).

thf(c_2Efmapal_2EAP__SND_2E2,type,
    c_2Efmapal_2EAP__SND_2E2: du > du > u ).

thf(c_2Epred__set_2ECOMPL_2E0,type,
    c_2Epred__set_2ECOMPL_2E0: u ).

thf(c_2Epred__set_2ECOMPL_2E1,type,
    c_2Epred__set_2ECOMPL_2E1: du > u ).

thf(c_2Ebool_2ECOND_2E0,type,
    c_2Ebool_2ECOND_2E0: u ).

thf(c_2Ebool_2ECOND_2E3,type,
    c_2Ebool_2ECOND_2E3: du > du > du > u ).

thf(c_2Elist_2ECONS_2E0,type,
    c_2Elist_2ECONS_2E0: u ).

thf(c_2Elist_2ECONS_2E2,type,
    c_2Elist_2ECONS_2E2: du > du > u ).

thf(c_2Efinite__map_2EDRESTRICT_2E0,type,
    c_2Efinite__map_2EDRESTRICT_2E0: u ).

thf(c_2Efinite__map_2EDRESTRICT_2E2,type,
    c_2Efinite__map_2EDRESTRICT_2E2: du > du > u ).

thf(c_2Eenumeral_2EENUMERAL_2E0,type,
    c_2Eenumeral_2EENUMERAL_2E0: u ).

thf(c_2Eenumeral_2EENUMERAL_2E2,type,
    c_2Eenumeral_2EENUMERAL_2E2: du > du > u ).

thf(c_2EternaryComparisons_2EEQUAL_2E0,type,
    c_2EternaryComparisons_2EEQUAL_2E0: u ).

thf(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: u ).

thf(c_2Efinite__map_2EFAPPLY_2E0,type,
    c_2Efinite__map_2EFAPPLY_2E0: u ).

thf(c_2Efinite__map_2EFAPPLY_2E2,type,
    c_2Efinite__map_2EFAPPLY_2E2: du > du > u ).

thf(c_2Efinite__map_2EFDOM_2E0,type,
    c_2Efinite__map_2EFDOM_2E0: u ).

thf(c_2Efinite__map_2EFDOM_2E1,type,
    c_2Efinite__map_2EFDOM_2E1: du > u ).

thf(c_2Efinite__map_2EFEMPTY_2E0,type,
    c_2Efinite__map_2EFEMPTY_2E0: u ).

thf(c_2Efmapal_2EFMAPAL_2E0,type,
    c_2Efmapal_2EFMAPAL_2E0: u ).

thf(c_2Efmapal_2EFMAPAL_2E2,type,
    c_2Efmapal_2EFMAPAL_2E2: du > du > u ).

thf(c_2Epair_2EFST_2E0,type,
    c_2Epair_2EFST_2E0: u ).

thf(c_2Efinite__map_2EFUNION_2E0,type,
    c_2Efinite__map_2EFUNION_2E0: u ).

thf(c_2Efinite__map_2EFUNION_2E2,type,
    c_2Efinite__map_2EFUNION_2E2: du > du > u ).

thf(c_2Efinite__map_2EFUN__FMAP_2E0,type,
    c_2Efinite__map_2EFUN__FMAP_2E0: u ).

thf(c_2Efinite__map_2EFUN__FMAP_2E2,type,
    c_2Efinite__map_2EFUN__FMAP_2E2: du > du > u ).

thf(c_2Efinite__map_2EFUPDATE_2E0,type,
    c_2Efinite__map_2EFUPDATE_2E0: u ).

thf(c_2Efinite__map_2EFUPDATE_2E2,type,
    c_2Efinite__map_2EFUPDATE_2E2: du > du > u ).

thf(c_2Efinite__map_2EFUPDATE__LIST_2E0,type,
    c_2Efinite__map_2EFUPDATE__LIST_2E0: u ).

thf(c_2Efinite__map_2EFUPDATE__LIST_2E2,type,
    c_2Efinite__map_2EFUPDATE__LIST_2E2: du > du > u ).

thf(c_2EternaryComparisons_2EGREATER_2E0,type,
    c_2EternaryComparisons_2EGREATER_2E0: u ).

thf(c_2Epred__set_2EGSPEC_2E0,type,
    c_2Epred__set_2EGSPEC_2E0: u ).

thf(c_2Epred__set_2EGSPEC_2E1,type,
    c_2Epred__set_2EGSPEC_2E1: du > u ).

thf(c_2Ecombin_2EI_2E0,type,
    c_2Ecombin_2EI_2E0: u ).

thf(c_2Ecombin_2EI_2E1,type,
    c_2Ecombin_2EI_2E1: du > u ).

thf(c_2Ebool_2EIN_2E0,type,
    c_2Ebool_2EIN_2E0: u ).

thf(c_2Ebool_2EIN_2E2,type,
    c_2Ebool_2EIN_2E2: du > du > u ).

thf(c_2Eoption_2EIS__SOME_2E0,type,
    c_2Eoption_2EIS__SOME_2E0: u ).

thf(c_2EternaryComparisons_2ELESS_2E0,type,
    c_2EternaryComparisons_2ELESS_2E0: u ).

thf(c_2Eenumeral_2ELESS__ALL_2E0,type,
    c_2Eenumeral_2ELESS__ALL_2E0: u ).

thf(c_2Eenumeral_2ELESS__ALL_2E3,type,
    c_2Eenumeral_2ELESS__ALL_2E3: du > du > du > u ).

thf(c_2Ebool_2ELET_2E0,type,
    c_2Ebool_2ELET_2E0: u ).

thf(c_2Ebool_2ELET_2E2,type,
    c_2Ebool_2ELET_2E2: du > du > u ).

thf(c_2Elist_2ELIST__TO__SET_2E0,type,
    c_2Elist_2ELIST__TO__SET_2E0: u ).

thf(c_2Elist_2ELIST__TO__SET_2E1,type,
    c_2Elist_2ELIST__TO__SET_2E1: du > u ).

thf(c_2Elist_2EMAP_2E0,type,
    c_2Elist_2EMAP_2E0: u ).

thf(c_2Elist_2EMAP_2E2,type,
    c_2Elist_2EMAP_2E2: du > du > u ).

thf(c_2Elist_2ENIL_2E0,type,
    c_2Elist_2ENIL_2E0: u ).

thf(c_2Eoption_2ENONE_2E0,type,
    c_2Eoption_2ENONE_2E0: u ).

thf(c_2Efmapal_2EOFU_2E0,type,
    c_2Efmapal_2EOFU_2E0: u ).

thf(c_2Efmapal_2EOFU_2E3,type,
    c_2Efmapal_2EOFU_2E3: du > du > du > u ).

thf(c_2Eenumeral_2EOL_2E0,type,
    c_2Eenumeral_2EOL_2E0: u ).

thf(c_2Eenumeral_2EOL_2E2,type,
    c_2Eenumeral_2EOL_2E2: du > du > u ).

thf(c_2Efmapal_2EOPTION__FLAT_2E0,type,
    c_2Efmapal_2EOPTION__FLAT_2E0: u ).

thf(c_2Efmapal_2EOPTION__FLAT_2E1,type,
    c_2Efmapal_2EOPTION__FLAT_2E1: du > u ).

thf(c_2Efmapal_2EOPTION__UPDATE_2E0,type,
    c_2Efmapal_2EOPTION__UPDATE_2E0: u ).

thf(c_2Efmapal_2EOPTION__UPDATE_2E3,type,
    c_2Efmapal_2EOPTION__UPDATE_2E3: du > du > du > u ).

thf(c_2Efmapal_2EORL_2E0,type,
    c_2Efmapal_2EORL_2E0: u ).

thf(c_2Efmapal_2EORL_2E2,type,
    c_2Efmapal_2EORL_2E2: du > du > u ).

thf(c_2Efmapal_2EORL__bt_2E0,type,
    c_2Efmapal_2EORL__bt_2E0: u ).

thf(c_2Efmapal_2EORL__bt_2E2,type,
    c_2Efmapal_2EORL__bt_2E2: du > du > u ).

thf(c_2Efmapal_2EORL__bt__lb_2E0,type,
    c_2Efmapal_2EORL__bt__lb_2E0: u ).

thf(c_2Efmapal_2EORL__bt__lb_2E3,type,
    c_2Efmapal_2EORL__bt__lb_2E3: du > du > du > u ).

thf(c_2Efmapal_2EORL__bt__lb__ub_2E0,type,
    c_2Efmapal_2EORL__bt__lb__ub_2E0: u ).

thf(c_2Efmapal_2EORL__bt__lb__ub_2E4,type,
    c_2Efmapal_2EORL__bt__lb__ub_2E4: du > du > du > du > u ).

thf(c_2Efmapal_2EORL__bt__ub_2E0,type,
    c_2Efmapal_2EORL__bt__ub_2E0: u ).

thf(c_2Efmapal_2EORL__bt__ub_2E3,type,
    c_2Efmapal_2EORL__bt__ub_2E3: du > du > du > u ).

thf(c_2Efmapal_2EORL__sublists_2E0,type,
    c_2Efmapal_2EORL__sublists_2E0: u ).

thf(c_2Efmapal_2EORL__sublists_2E2,type,
    c_2Efmapal_2EORL__sublists_2E2: du > du > u ).

thf(c_2Efmapal_2EORWL_2E0,type,
    c_2Efmapal_2EORWL_2E0: u ).

thf(c_2Efmapal_2EORWL_2E3,type,
    c_2Efmapal_2EORWL_2E3: du > du > du > u ).

thf(c_2Eenumeral_2EOWL_2E0,type,
    c_2Eenumeral_2EOWL_2E0: u ).

thf(c_2Eenumeral_2EOWL_2E3,type,
    c_2Eenumeral_2EOWL_2E3: du > du > du > u ).

thf(c_2Elist_2EREVERSE_2E0,type,
    c_2Elist_2EREVERSE_2E0: u ).

thf(c_2Elist_2EREVERSE_2E1,type,
    c_2Elist_2EREVERSE_2E1: du > u ).

thf(c_2Eoption_2ESOME_2E0,type,
    c_2Eoption_2ESOME_2E0: u ).

thf(c_2Eoption_2ESOME_2E1,type,
    c_2Eoption_2ESOME_2E1: du > u ).

thf(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: u ).

thf(c_2Eoption_2ETHE_2E0,type,
    c_2Eoption_2ETHE_2E0: u ).

thf(c_2Efmapal_2EUFO_2E0,type,
    c_2Efmapal_2EUFO_2E0: u ).

thf(c_2Efmapal_2EUFO_2E3,type,
    c_2Efmapal_2EUFO_2E3: du > du > du > u ).

thf(c_2Erelation_2EWF_2E0,type,
    c_2Erelation_2EWF_2E0: u ).

thf(c_2Erelation_2EWF_2E1,type,
    c_2Erelation_2EWF_2E1: du > u ).

thf(c_2Erelation_2EWFREC_2E0,type,
    c_2Erelation_2EWFREC_2E0: u ).

thf(c_2Erelation_2EWFREC_2E2,type,
    c_2Erelation_2EWFREC_2E2: du > du > u ).

thf(c_2Ebool_2E_5C_2F_2E0,type,
    c_2Ebool_2E_5C_2F_2E0: u ).

thf(c_2Ebool_2E_5C_2F_2E2,type,
    c_2Ebool_2E_5C_2F_2E2: du > du > u ).

thf(c_2Etoto_2Eapto_2E0,type,
    c_2Etoto_2Eapto_2E0: u ).

thf(c_2Etoto_2Eapto_2E3,type,
    c_2Etoto_2Eapto_2E3: du > du > du > u ).

thf(c_2Efmapal_2Eassocv_2E0,type,
    c_2Efmapal_2Eassocv_2E0: u ).

thf(c_2Efmapal_2Eassocv_2E2,type,
    c_2Efmapal_2Eassocv_2E2: du > du > u ).

thf(c_2Efmapal_2Ebl__to__fmap_2E0,type,
    c_2Efmapal_2Ebl__to__fmap_2E0: u ).

thf(c_2Efmapal_2Ebl__to__fmap_2E2,type,
    c_2Efmapal_2Ebl__to__fmap_2E2: du > du > u ).

thf(c_2Eenumeral_2Ebt__CASE_2E0,type,
    c_2Eenumeral_2Ebt__CASE_2E0: u ).

thf(c_2Eenumeral_2Ebt__CASE_2E3,type,
    c_2Eenumeral_2Ebt__CASE_2E3: du > du > du > u ).

thf(c_2Efmapal_2Ebt__map_2E0,type,
    c_2Efmapal_2Ebt__map_2E0: u ).

thf(c_2Efmapal_2Ebt__map_2E2,type,
    c_2Efmapal_2Ebt__map_2E2: du > du > u ).

thf(c_2Efmapal_2Ebt__rplacv__cn_2E0,type,
    c_2Efmapal_2Ebt__rplacv__cn_2E0: u ).

thf(c_2Efmapal_2Ebt__rplacv__cn_2E4,type,
    c_2Efmapal_2Ebt__rplacv__cn_2E4: du > du > du > du > u ).

thf(c_2Efmapal_2Ebt__to__fmap__lb_2E0,type,
    c_2Efmapal_2Ebt__to__fmap__lb_2E0: u ).

thf(c_2Efmapal_2Ebt__to__fmap__lb_2E3,type,
    c_2Efmapal_2Ebt__to__fmap__lb_2E3: du > du > du > u ).

thf(c_2Efmapal_2Ebt__to__fmap__lb__ub_2E0,type,
    c_2Efmapal_2Ebt__to__fmap__lb__ub_2E0: u ).

thf(c_2Efmapal_2Ebt__to__fmap__lb__ub_2E4,type,
    c_2Efmapal_2Ebt__to__fmap__lb__ub_2E4: du > du > du > du > u ).

thf(c_2Efmapal_2Ebt__to__fmap__ub_2E0,type,
    c_2Efmapal_2Ebt__to__fmap__ub_2E0: u ).

thf(c_2Efmapal_2Ebt__to__fmap__ub_2E3,type,
    c_2Efmapal_2Ebt__to__fmap__ub_2E3: du > du > du > u ).

thf(c_2Eenumeral_2Ebt__to__list__ac_2E0,type,
    c_2Eenumeral_2Ebt__to__list__ac_2E0: u ).

thf(c_2Eenumeral_2Ebt__to__list__ac_2E2,type,
    c_2Eenumeral_2Ebt__to__list__ac_2E2: du > du > u ).

thf(c_2Efmapal_2Ebt__to__orl_2E0,type,
    c_2Efmapal_2Ebt__to__orl_2E0: u ).

thf(c_2Efmapal_2Ebt__to__orl_2E2,type,
    c_2Efmapal_2Ebt__to__orl_2E2: du > du > u ).

thf(c_2Efmapal_2Ebt__to__orl__ac_2E0,type,
    c_2Efmapal_2Ebt__to__orl__ac_2E0: u ).

thf(c_2Efmapal_2Ebt__to__orl__ac_2E3,type,
    c_2Efmapal_2Ebt__to__orl__ac_2E3: du > du > du > u ).

thf(c_2Efmapal_2Ebt__to__orl__lb_2E0,type,
    c_2Efmapal_2Ebt__to__orl__lb_2E0: u ).

thf(c_2Efmapal_2Ebt__to__orl__lb_2E3,type,
    c_2Efmapal_2Ebt__to__orl__lb_2E3: du > du > du > u ).

thf(c_2Efmapal_2Ebt__to__orl__lb__ac_2E0,type,
    c_2Efmapal_2Ebt__to__orl__lb__ac_2E0: u ).

thf(c_2Efmapal_2Ebt__to__orl__lb__ac_2E4,type,
    c_2Efmapal_2Ebt__to__orl__lb__ac_2E4: du > du > du > du > u ).

thf(c_2Efmapal_2Ebt__to__orl__lb__ub_2E0,type,
    c_2Efmapal_2Ebt__to__orl__lb__ub_2E0: u ).

thf(c_2Efmapal_2Ebt__to__orl__lb__ub_2E4,type,
    c_2Efmapal_2Ebt__to__orl__lb__ub_2E4: du > du > du > du > u ).

thf(c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E0,type,
    c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E0: u ).

thf(c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5,type,
    c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5: du > du > du > du > du > u ).

thf(c_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__aux_2E0,type,
    c_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__aux_2E0: u ).

thf(c_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__aux_2E1,type,
    c_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__aux_2E1: du > u ).

thf(c_2Efmapal_2Ebt__to__orl__ub_2E0,type,
    c_2Efmapal_2Ebt__to__orl__ub_2E0: u ).

thf(c_2Efmapal_2Ebt__to__orl__ub_2E3,type,
    c_2Efmapal_2Ebt__to__orl__ub_2E3: du > du > du > u ).

thf(c_2Efmapal_2Ebt__to__orl__ub__ac_2E0,type,
    c_2Efmapal_2Ebt__to__orl__ub__ac_2E0: u ).

thf(c_2Efmapal_2Ebt__to__orl__ub__ac_2E4,type,
    c_2Efmapal_2Ebt__to__orl__ub__ac_2E4: du > du > du > du > u ).

thf(c_2Efmapal_2Ediff__merge_2E0,type,
    c_2Efmapal_2Ediff__merge_2E0: u ).

thf(c_2Efmapal_2Ediff__merge_2E3,type,
    c_2Efmapal_2Ediff__merge_2E3: du > du > du > u ).

thf(c_2Efmapal_2Efmap_2E0,type,
    c_2Efmapal_2Efmap_2E0: u ).

thf(c_2Efmapal_2Efmap_2E1,type,
    c_2Efmapal_2Efmap_2E1: du > u ).

thf(c_2Efmapal_2Eincr__build_2E0,type,
    c_2Efmapal_2Eincr__build_2E0: u ).

thf(c_2Efmapal_2Eincr__build_2E2,type,
    c_2Efmapal_2Eincr__build_2E2: du > du > u ).

thf(c_2Efmapal_2Eincr__flat_2E0,type,
    c_2Efmapal_2Eincr__flat_2E0: u ).

thf(c_2Efmapal_2Eincr__flat_2E2,type,
    c_2Efmapal_2Eincr__flat_2E2: du > du > u ).

thf(c_2Efmapal_2Eincr__merge_2E0,type,
    c_2Efmapal_2Eincr__merge_2E0: u ).

thf(c_2Efmapal_2Eincr__merge_2E3,type,
    c_2Efmapal_2Eincr__merge_2E3: du > du > du > u ).

thf(c_2Efmapal_2Eincr__sort_2E0,type,
    c_2Efmapal_2Eincr__sort_2E0: u ).

thf(c_2Efmapal_2Eincr__sort_2E2,type,
    c_2Efmapal_2Eincr__sort_2E2: du > du > u ).

thf(c_2Efmapal_2Einter__merge_2E0,type,
    c_2Efmapal_2Einter__merge_2E0: u ).

thf(c_2Efmapal_2Einter__merge_2E3,type,
    c_2Efmapal_2Einter__merge_2E3: du > du > du > u ).

thf(c_2Elist_2Elist__CASE_2E0,type,
    c_2Elist_2Elist__CASE_2E0: u ).

thf(c_2Elist_2Elist__CASE_2E3,type,
    c_2Elist_2Elist__CASE_2E3: du > du > du > u ).

thf(c_2Efmapal_2Elist__rplacv__cn_2E0,type,
    c_2Efmapal_2Elist__rplacv__cn_2E0: u ).

thf(c_2Efmapal_2Elist__rplacv__cn_2E3,type,
    c_2Efmapal_2Elist__rplacv__cn_2E3: du > du > du > u ).

thf(c_2Eenumeral_2Elist__to__bt_2E0,type,
    c_2Eenumeral_2Elist__to__bt_2E0: u ).

thf(c_2Eenumeral_2Elist__to__bt_2E1,type,
    c_2Eenumeral_2Elist__to__bt_2E1: du > u ).

thf(c_2Efmapal_2Emerge_2E0,type,
    c_2Efmapal_2Emerge_2E0: u ).

thf(c_2Efmapal_2Emerge_2E3,type,
    c_2Efmapal_2Emerge_2E3: du > du > du > u ).

thf(c_2Efmapal_2Emerge__out_2E0,type,
    c_2Efmapal_2Emerge__out_2E0: u ).

thf(c_2Efmapal_2Emerge__out_2E3,type,
    c_2Efmapal_2Emerge__out_2E3: du > du > du > u ).

thf(c_2Eenumeral_2Enbl_2E0,type,
    c_2Eenumeral_2Enbl_2E0: u ).

thf(c_2Eenumeral_2Enode_2E0,type,
    c_2Eenumeral_2Enode_2E0: u ).

thf(c_2Eenumeral_2Enode_2E3,type,
    c_2Eenumeral_2Enode_2E3: du > du > du > u ).

thf(c_2Eenumeral_2Ent_2E0,type,
    c_2Eenumeral_2Ent_2E0: u ).

thf(c_2Ecombin_2Eo_2E0,type,
    c_2Ecombin_2Eo_2E0: u ).

thf(c_2Ecombin_2Eo_2E2,type,
    c_2Ecombin_2Eo_2E2: du > du > u ).

thf(c_2Efinite__map_2Eo__f_2E0,type,
    c_2Efinite__map_2Eo__f_2E0: u ).

thf(c_2Efinite__map_2Eo__f_2E2,type,
    c_2Efinite__map_2Eo__f_2E2: du > du > u ).

thf(c_2Eenumeral_2Eonebl_2E0,type,
    c_2Eenumeral_2Eonebl_2E0: u ).

thf(c_2Eenumeral_2Eonebl_2E3,type,
    c_2Eenumeral_2Eonebl_2E3: du > du > du > u ).

thf(c_2Eoption_2Eoption__CASE_2E0,type,
    c_2Eoption_2Eoption__CASE_2E0: u ).

thf(c_2Eoption_2Eoption__CASE_2E3,type,
    c_2Eoption_2Eoption__CASE_2E3: du > du > du > u ).

thf(c_2Efmapal_2Eoptry_2E0,type,
    c_2Efmapal_2Eoptry_2E0: u ).

thf(c_2Efmapal_2Eoptry_2E2,type,
    c_2Efmapal_2Eoptry_2E2: du > du > u ).

thf(c_2Efmapal_2Eoptry__list_2E0,type,
    c_2Efmapal_2Eoptry__list_2E0: u ).

thf(c_2Efmapal_2Eoptry__list_2E2,type,
    c_2Efmapal_2Eoptry__list_2E2: du > du > u ).

thf(c_2EternaryComparisons_2Eordering__CASE_2E0,type,
    c_2EternaryComparisons_2Eordering__CASE_2E0: u ).

thf(c_2EternaryComparisons_2Eordering__CASE_2E4,type,
    c_2EternaryComparisons_2Eordering__CASE_2E4: du > du > du > du > u ).

thf(c_2Epair_2Epair__CASE_2E0,type,
    c_2Epair_2Epair__CASE_2E0: u ).

thf(c_2Epair_2Epair__CASE_2E2,type,
    c_2Epair_2Epair__CASE_2E2: du > du > u ).

thf(c_2Efmapal_2Eunlookup_2E0,type,
    c_2Efmapal_2Eunlookup_2E0: u ).

thf(c_2Efmapal_2Eunlookup_2E1,type,
    c_2Efmapal_2Eunlookup_2E1: du > u ).

thf(c_2Efmapal_2Evcossa_2E0,type,
    c_2Efmapal_2Evcossa_2E0: u ).

thf(c_2Efmapal_2Evcossa_2E2,type,
    c_2Efmapal_2Evcossa_2E2: du > du > u ).

thf(c_2Eenumeral_2Ezerbl_2E0,type,
    c_2Eenumeral_2Ezerbl_2E0: u ).

thf(c_2Eenumeral_2Ezerbl_2E1,type,
    c_2Eenumeral_2Ezerbl_2E1: du > u ).

thf(c_2Ebool_2E_7E_2E0,type,
    c_2Ebool_2E_7E_2E0: u ).

thf(c_2Ebool_2E_7E_2E1,type,
    c_2Ebool_2E_7E_2E1: du > u ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o > $o ) > $o > $o > $o > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29: ( mono_2Etyop_2EternaryComparisons_2Eordering > $o > $o > $o > $o ) > mono_2Etyop_2EternaryComparisons_2Eordering > $o > $o > $o > $o ).

thf(mono_2Ec_2Ebool_2E_2F_5C,type,
    mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).

thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
    mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).

thf(mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool,type,
    mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool: $o > $o > $o > $o ).

thf(mono_2Ec_2EternaryComparisons_2EEQUAL,type,
    mono_2Ec_2EternaryComparisons_2EEQUAL: mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Ec_2Ebool_2EF,type,
    mono_2Ec_2Ebool_2EF: $o ).

thf(mono_2Ec_2EternaryComparisons_2EGREATER,type,
    mono_2Ec_2EternaryComparisons_2EGREATER: mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Ec_2EternaryComparisons_2ELESS,type,
    mono_2Ec_2EternaryComparisons_2ELESS: mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(mono_2Ec_2Ebool_2ET,type,
    mono_2Ec_2Ebool_2ET: $o ).

thf(mono_2Ec_2Ebool_2E_5C_2F,type,
    mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).

thf(mono_2Ec_2EternaryComparisons_2Eordering__CASE_2Emono_2Etyop_2Emin_2Ebool,type,
    mono_2Ec_2EternaryComparisons_2Eordering__CASE_2Emono_2Etyop_2Emin_2Ebool: mono_2Etyop_2EternaryComparisons_2Eordering > $o > $o > $o > $o ).

thf(mono_2Ec_2Ebool_2E_7E,type,
    mono_2Ec_2Ebool_2E_7E: $o > $o ).

thf(i_mono_2Etyop_2Emin_2Ebool,type,
    i_mono_2Etyop_2Emin_2Ebool: $o > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29: ( $o > $o > $o > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29: ( mono_2Etyop_2EternaryComparisons_2Eordering > $o > $o > $o > $o ) > u ).

thf(i_mono_2Etyop_2EternaryComparisons_2Eordering,type,
    i_mono_2Etyop_2EternaryComparisons_2Eordering: mono_2Etyop_2EternaryComparisons_2Eordering > u ).

thf(j_mono_2Etyop_2Emin_2Ebool,type,
    j_mono_2Etyop_2Emin_2Ebool: du > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29: du > $o > $o > $o > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29: du > mono_2Etyop_2EternaryComparisons_2Eordering > $o > $o > $o > $o ).

thf(j_mono_2Etyop_2EternaryComparisons_2Eordering,type,
    j_mono_2Etyop_2EternaryComparisons_2Eordering: du > mono_2Etyop_2EternaryComparisons_2Eordering ).

thf(reserved_2Eho_2Eeq__ext,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
      ( ! [V2x_2E0: u] :
          ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
          = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
        = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).

thf(reserved_2Eho_2Ei__thm,axiom,
    ! [A_27a: d,V0x_2E0: u] :
      ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
      = ( s @ A_27a @ V0x_2E0 ) ) ).

thf(reserved_2Eho_2Ek__thm,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
      ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ combin_k_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) )
      = ( s @ A_27a @ V0x_2E0 ) ) ).

thf(reserved_2Eho_2Es__thm,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
      ( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
      = ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ).

thf(reserved_2Elogic_2E_2F_5C,axiom,
    ! [V0: $o,V1: $o] :
      ( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
    <=> ( V0
        & V1 ) ) ).

thf(reserved_2Elogic_2E_5C_2F,axiom,
    ! [V0: $o,V1: $o] :
      ( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
    <=> ( V0
        | V1 ) ) ).

thf(reserved_2Elogic_2E_7E,axiom,
    ! [V0: $o] :
      ( ( mono_2Ec_2Ebool_2E_7E @ V0 )
    <=> ( (~) @ V0 ) ) ).

thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
    ! [V0: $o,V1: $o] :
      ( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
    <=> ( V0
       => V1 ) ) ).

thf(reserved_2Elogic_2E_3D,axiom,
    ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
    <=> ( ( s @ A_27a @ V0_2E0 )
        = ( s @ A_27a @ V1_2E0 ) ) ) ).

thf(reserved_2Equant_2E_21,axiom,
    ! [A_27a: d,V0f_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
    <=> ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).

thf(reserved_2Equant_2E_3F,axiom,
    ! [A_27a: d,V0f_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
    <=> ? [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: u] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
      = ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2EternaryComparisons_2Eordering,axiom,
    ! [V0_2E0: u] :
      ( ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ V0_2E0 ) ) ) )
      = ( s @ tyop_2EternaryComparisons_2Eordering @ V0_2E0 ) ) ).

thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: $o] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: $o > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: $o > $o > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0: $o > $o > $o > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > $o > $o > $o > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2EternaryComparisons_2Eordering,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V0 ) ) )
      = V0 ) ).

thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ A_27c @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27c @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,X0_2E0: u,X1: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) ) ) ).

thf(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: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ 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 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(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: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( 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 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( 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 ) ) )
      = ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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_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 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( 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 ) ) ) ) ).

thf(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: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( 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 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ X1_2E0 ) ) )
      = ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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_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 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ X1_2E0 ) ) ) ) ).

thf(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: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( 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_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( 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 ) ) )
      = ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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_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 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( 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 ) ) ) ) ).

thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( ( s @ A_27a @ X0_2E0 )
        = ( s @ A_27a @ X1_2E0 ) )
    <=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).

thf(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: d,X0_2E0: u] :
      ( ( s @ ( 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_2E1 @ ( s @ ( 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 ) @ X0_2E0 ) ) )
      = ( s @ ( 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 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( 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 ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27z,axiom,
    ! [A_27z: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27z ) @ ( tyop_2Elist_2Elist @ A_27z ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27z ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27z ) @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ c_2Elist_2EAPPEND_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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_2Elist_2EAPPEND_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Efmapal_2EAP__SND_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( c_2Efmapal_2EAP__SND_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ c_2Efmapal_2EAP__SND_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efmapal_2EAP__SND_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( c_2Efmapal_2EAP__SND_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ c_2Efmapal_2EAP__SND_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epred__set_2ECOMPL_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2ECOMPL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2ECOMPL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0: $o,X1_2E0: u,X2_2E0: u] :
      ( ( s @ A_27b @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ A_27b @ X1_2E0 ) @ ( s @ A_27b @ X2_2E0 ) ) )
      = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) @ ( s @ A_27b @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
    ! [A_27a: d,A_27b: d,X0: $o,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( tyop_2Emin_2Efun @ 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 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
    ! [A_27b: d,X0: $o,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ 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 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2ECONS_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27z_29,axiom,
    ! [A_27z: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27z ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27z ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27z_29_29,axiom,
    ! [A_27z: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) ) ) @ c_2Elist_2ECONS_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ X1_2E0 ) ) ) ) ).

thf(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: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EDRESTRICT_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ c_2Efinite__map_2EDRESTRICT_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Eenumeral_2EENUMERAL_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EENUMERAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFAPPLY_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
      = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ c_2Efinite__map_2EFAPPLY_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Efinite__map_2EFDOM_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Efinite__map_2EFDOM_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efmapal_2EFMAPAL_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EFMAPAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ c_2Efmapal_2EFMAPAL_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efmapal_2EFMAPAL_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efmapal_2EFMAPAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUNION_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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_2Efinite__map_2EFUNION_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUN__FMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUN__FMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ c_2Efinite__map_2EFUN__FMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUPDATE_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ c_2Efinite__map_2EFUPDATE_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUPDATE__LIST_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ c_2Efinite__map_2EFUPDATE__LIST_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27z_29,axiom,
    ! [A_27z: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ ( c_2Ecombin_2EI_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27z ) @ ( tyop_2Elist_2Elist @ A_27z ) ) @ c_2Ecombin_2EI_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ecombin_2EI_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ c_2Ecombin_2EI_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq3_2Ec_2Eenumeral_2ELESS__ALL_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2ELESS__ALL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X2_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ c_2Eenumeral_2ELESS__ALL_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X2_2E0 ) ) ) ) ) ).

thf(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: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ELET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ) ).

thf(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: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ELET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Elist_2ELIST__TO__SET_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(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: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Efmapal_2EOFU_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EOFU_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ c_2Efmapal_2EOFU_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Eenumeral_2EOL_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Eenumeral_2EOL_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Efmapal_2EOPTION__FLAT_2E1_2Emono_2EA_27z,axiom,
    ! [A_27z: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ ( c_2Efmapal_2EOPTION__FLAT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ ( tyop_2Elist_2Elist @ A_27z ) ) @ c_2Efmapal_2EOPTION__FLAT_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Efmapal_2EOPTION__UPDATE_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efmapal_2EOPTION__UPDATE_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ X1_2E0 ) @ ( s @ A_27a @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ c_2Efmapal_2EOPTION__UPDATE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efmapal_2EORL_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Efmapal_2EORL__bt_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL__bt_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq3_2Ec_2Efmapal_2EORL__bt__lb_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL__bt__lb_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ c_2Efmapal_2EORL__bt__lb_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) ) ) ) ).

thf(arityeq4_2Ec_2Efmapal_2EORL__bt__lb__ub_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL__bt__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) @ ( s @ A_27a @ X3_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ c_2Efmapal_2EORL__bt__lb__ub_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) ) @ ( s @ A_27a @ X3_2E0 ) ) ) ) ) ).

thf(arityeq3_2Ec_2Efmapal_2EORL__bt__ub_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL__bt__ub_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) @ ( s @ A_27a @ X2_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ c_2Efmapal_2EORL__bt__ub_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Efmapal_2EORL__sublists_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL__sublists_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ c_2Efmapal_2EORL__sublists_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq3_2Ec_2Efmapal_2EORWL_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORWL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ c_2Efmapal_2EORWL_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) ) ) ) ).

thf(arityeq3_2Ec_2Eenumeral_2EOWL_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOWL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ c_2Eenumeral_2EOWL_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2EREVERSE_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EREVERSE_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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_2EREVERSE_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27z,axiom,
    ! [A_27z: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27z ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27z @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27z ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27z @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A_27z @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27z_29,axiom,
    ! [A_27z: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27z ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Efmapal_2EUFO_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EUFO_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ c_2Efmapal_2EUFO_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X2_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27z_29_29_29,axiom,
    ! [A_27z: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2EWF_2E1 @ ( s @ ( 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 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( 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_2Erelation_2EWF_2E0 ) @ ( s @ ( 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 ) ) ) ) ) ).

thf(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: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ ( tyop_2Elist_2Elist @ A_27z ) ) @ ( c_2Erelation_2EWFREC_2E2 @ ( s @ ( 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 ) @ ( s @ ( 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 ) ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ ( tyop_2Elist_2Elist @ A_27z ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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_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 ) @ ( s @ ( 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 ) ) ) @ ( s @ ( 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 ) ) ) @ X1_2E0 ) ) ) ) ).

thf(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: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( 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 @ ( s @ ( 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 ) ) @ X0_2E0 ) @ ( s @ ( 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 ) ) ) ) @ X1_2E0 ) ) )
      = ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ ( app_2E2 @ ( s @ ( 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_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 ) @ ( s @ ( 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 ) ) @ X0_2E0 ) ) ) @ ( s @ ( 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 ) ) ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Etoto_2Eapto_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ A_27a @ X2_2E0 ) ) ) )
      = ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2EternaryComparisons_2Eordering ) ) ) @ c_2Etoto_2Eapto_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Efmapal_2Eassocv_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efmapal_2Eassocv_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ c_2Efmapal_2Eassocv_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efmapal_2Ebl__to__fmap_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Ebl__to__fmap_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ c_2Efmapal_2Ebl__to__fmap_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(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: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Ebt__CASE_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) @ ( s @ ( 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 ) ) ) ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( 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 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) @ ( s @ ( 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 ) ) ) ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efmapal_2Ebt__map_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eenumeral_2Ebt @ A_27b ) @ ( c_2Efmapal_2Ebt__map_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eenumeral_2Ebt @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Eenumeral_2Ebt @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efmapal_2Ebt__map_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Efmapal_2Ebt__map_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(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: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( c_2Efmapal_2Ebt__map_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2Efmapal_2Ebt__rplacv__cn_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
      ( ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__rplacv__cn_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ X3_2E0 ) ) )
      = ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) ) @ c_2Efmapal_2Ebt__rplacv__cn_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ X3_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Efmapal_2Ebt__to__fmap__lb_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Ebt__to__fmap__lb_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ c_2Efmapal_2Ebt__to__fmap__lb_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2Efmapal_2Ebt__to__fmap__lb__ub_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Ebt__to__fmap__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) @ ( s @ A_27a @ X3_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) @ c_2Efmapal_2Ebt__to__fmap__lb__ub_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) ) @ ( s @ A_27a @ X3_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Efmapal_2Ebt__to__fmap__ub_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Ebt__to__fmap__ub_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) @ ( s @ A_27a @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ c_2Efmapal_2Ebt__to__fmap__ub_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Eenumeral_2Ebt__to__list__ac_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Ebt__to__list__ac_2E2 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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_2Eenumeral_2Ebt__to__list__ac_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efmapal_2Ebt__to__orl_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ c_2Efmapal_2Ebt__to__orl_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Efmapal_2Ebt__to__orl__ac_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__ac_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) @ c_2Efmapal_2Ebt__to__orl__ac_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Efmapal_2Ebt__to__orl__lb_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) @ c_2Efmapal_2Ebt__to__orl__lb_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2Efmapal_2Ebt__to__orl__lb__ac_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb__ac_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X3_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) ) @ c_2Efmapal_2Ebt__to__orl__lb__ac_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X3_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2Efmapal_2Ebt__to__orl__lb__ub_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) @ ( s @ A_27a @ X3_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) ) @ c_2Efmapal_2Ebt__to__orl__lb__ub_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) ) @ ( s @ A_27a @ X3_2E0 ) ) ) ) ).

thf(arityeq5_2Ec_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u,X4_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) @ ( s @ A_27a @ X3_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X4_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) ) ) @ c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) ) @ ( s @ A_27a @ X3_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X4_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__aux_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( 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_2E1 @ ( s @ ( 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 ) ) @ X0_2E0 ) ) )
      = ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ c_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__aux_2E0 ) @ ( s @ ( 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 ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Efmapal_2Ebt__to__orl__ub_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__ub_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) @ ( s @ A_27a @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) @ c_2Efmapal_2Ebt__to__orl__ub_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2Efmapal_2Ebt__to__orl__ub__ac_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__ub__ac_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) @ ( s @ A_27a @ X2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X3_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) ) @ c_2Efmapal_2Ebt__to__orl__ub__ac_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X3_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Efmapal_2Ediff__merge_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ediff__merge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) @ c_2Efmapal_2Ediff__merge_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Efmapal_2Efmap_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Efmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ c_2Efmapal_2Efmap_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Efmapal_2Efmap_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efmapal_2Efmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) ) @ c_2Efmapal_2Efmap_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efmapal_2Eincr__build_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ ( c_2Efmapal_2Eincr__build_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) ) @ c_2Efmapal_2Eincr__build_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efmapal_2Eincr__flat_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Eincr__flat_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ c_2Efmapal_2Eincr__flat_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Efmapal_2Eincr__merge_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ ( c_2Efmapal_2Eincr__merge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) ) ) @ c_2Efmapal_2Eincr__merge_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efmapal_2Eincr__sort_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Eincr__sort_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ c_2Efmapal_2Eincr__sort_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Efmapal_2Einter__merge_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Einter__merge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) @ c_2Efmapal_2Einter__merge_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(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: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ ( c_2Elist_2Elist__CASE_2E3 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ X1_2E0 ) @ ( s @ ( 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 ) ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ X1_2E0 ) ) ) @ ( s @ ( 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 ) ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Efmapal_2Elist__rplacv__cn_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Elist__rplacv__cn_2E3 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) @ c_2Efmapal_2Elist__rplacv__cn_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eenumeral_2Elist__to__bt_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Elist__to__bt_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Efmapal_2Emerge_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Emerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) @ c_2Efmapal_2Emerge_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Efmapal_2Emerge__out_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Emerge__out_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) @ c_2Efmapal_2Emerge__out_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eenumeral_2Enode_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( tyop_2Eenumeral_2Ebt @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ c_2Eenumeral_2Enode_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eenumeral_2Enode_2E3_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Eenumeral_2Ebt @ A_27b ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27b ) @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27b ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Eenumeral_2Ebt @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27b ) @ ( tyop_2Eenumeral_2Ebt @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ A_27b ) @ ( tyop_2Eenumeral_2Ebt @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27b ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eenumeral_2Enode_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ ( app_2E2 @ ( s @ ( 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_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) ) @ c_2Eenumeral_2Enode_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2Eo__f_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ c_2Efinite__map_2Eo__f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eenumeral_2Eonebl_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Eonebl_2E3 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ ( app_2E2 @ ( s @ ( 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_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) ) @ c_2Eenumeral_2Eonebl_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27z_29_20mono_2Etyop_2Elist_2Elist_28A_27z_29,axiom,
    ! [A_27z: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27z ) @ ( tyop_2Elist_2Elist @ A_27z ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27z ) @ ( tyop_2Elist_2Elist @ A_27z ) ) @ ( tyop_2Elist_2Elist @ A_27z ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27z ) @ ( tyop_2Elist_2Elist @ A_27z ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efmapal_2Eoptry_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efmapal_2Eoptry_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ c_2Efmapal_2Eoptry_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efmapal_2Eoptry_2E2_2Emono_2EA_27g,axiom,
    ! [A_27g: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27g ) @ ( c_2Efmapal_2Eoptry_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27g ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27g ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27g ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27g ) @ ( tyop_2Eoption_2Eoption @ A_27g ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27g ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27g ) @ ( tyop_2Eoption_2Eoption @ A_27g ) ) ) @ c_2Efmapal_2Eoptry_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27g ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27g ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efmapal_2Eoptry_2E2_2Emono_2EA_27z,axiom,
    ! [A_27z: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27z ) @ ( c_2Efmapal_2Eoptry_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27z ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27z ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27z ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27z ) @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27z ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27z ) @ ( tyop_2Eoption_2Eoption @ A_27z ) ) ) @ c_2Efmapal_2Eoptry_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27z ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27z ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efmapal_2Eoptry__list_2E2_2Emono_2EA_27g_20mono_2EA_27z,axiom,
    ! [A_27g: d,A_27z: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27g ) @ ( c_2Efmapal_2Eoptry__list_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27z @ ( tyop_2Eoption_2Eoption @ A_27g ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27g ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ ( tyop_2Eoption_2Eoption @ A_27g ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ c_2Efmapal_2Eoptry__list_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27z @ ( tyop_2Eoption_2Eoption @ A_27g ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0: mono_2Etyop_2EternaryComparisons_2Eordering,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
      ( ( s @ A_27b @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ X0 ) ) @ ( s @ A_27b @ X1_2E0 ) @ ( s @ A_27b @ X2_2E0 ) @ ( s @ A_27b @ X3_2E0 ) ) )
      = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ 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 ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ X0 ) ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) @ ( s @ A_27b @ X2_2E0 ) ) ) @ ( s @ A_27b @ X3_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2Etyop_2Eenumeral_2Ebt_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
    ! [A_27a: d,A_27b: d,X0: mono_2Etyop_2EternaryComparisons_2Eordering,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
      ( ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ X0 ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X3_2E0 ) ) )
      = ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ 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 ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ X0 ) ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X3_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29,axiom,
    ! [A_27a: d,A_27b: d,X0: mono_2Etyop_2EternaryComparisons_2Eordering,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ X0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X3_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ 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 ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ X0 ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X3_2E0 ) ) ) ) ).

thf(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: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ X1_2E0 ) ) ) ) ).

thf(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: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ X0_2E0 ) @ ( s @ ( 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 ) ) ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( 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 ) ) ) ) @ X1_2E0 ) ) ) ) ).

thf(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: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( 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 ) @ ( s @ ( 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 ) ) ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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_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 ) @ ( s @ ( 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 ) ) ) @ ( s @ ( 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 ) ) ) ) @ X1_2E0 ) ) ) ) ).

thf(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: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( 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 ) @ ( s @ ( 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 ) ) ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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_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 ) @ ( s @ ( 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 ) ) ) @ ( s @ ( 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 ) ) ) ) @ X1_2E0 ) ) ) ) ).

thf(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: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( 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 ) ) ) ) ) ) @ X0_2E0 ) @ ( s @ ( 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 ) ) ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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_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 ) @ ( s @ ( 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 ) ) ) ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( 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 ) ) ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Efmapal_2Eunlookup_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Eunlookup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ c_2Efmapal_2Eunlookup_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efmapal_2Evcossa_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efmapal_2Evcossa_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ c_2Efmapal_2Evcossa_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eenumeral_2Ezerbl_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Ezerbl_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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_2Ezerbl_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: $o > $o,V1: $o] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: $o > $o > $o,V1: $o] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: $o > $o > $o > $o,V1: $o] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > $o > $o > $o > $o,V1: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29 @ V0 ) ) @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 @ mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) @ c_2Ebool_2ECOND_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: $o,V1: $o,V2: $o] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool @ V0 @ V1 @ V2 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V2 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2EternaryComparisons_2Eordering__CASE_2E0_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2EternaryComparisons_2Eordering @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2EternaryComparisons_2Eordering_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29 @ mono_2Ec_2EternaryComparisons_2Eordering__CASE_2Emono_2Etyop_2Emin_2Ebool ) )
    = ( s @ ( tyop_2Emin_2Efun @ 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 ) ) ).

thf(monoeq_2Emono_2Ec_2EternaryComparisons_2Eordering__CASE_2E4_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering,V1: $o,V2: $o,V3: $o] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2EternaryComparisons_2Eordering__CASE_2Emono_2Etyop_2Emin_2Ebool @ V0 @ V1 @ V2 @ V3 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( i_mono_2Etyop_2EternaryComparisons_2Eordering @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V2 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V3 ) ) ) ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: $o > $o,V1: $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: $o > $o > $o,V1: $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: $o > $o > $o > $o,V1: $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2EternaryComparisons_2Eordering_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0: mono_2Etyop_2EternaryComparisons_2Eordering > $o > $o > $o > $o,V1: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(thm_2Efmapal_2Eoptry,axiom,
    ! [A_27z: d] :
      ( ! [V0p_2E0: u,V1q_2E0: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27z ) @ ( c_2Efmapal_2Eoptry_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27z ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27z @ V0p_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27z ) @ V1q_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27z ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27z @ V0p_2E0 ) ) ) )
      & ! [V2q_2E0: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27z ) @ ( c_2Efmapal_2Eoptry_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27z ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27z ) @ V2q_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27z ) @ V2q_2E0 ) ) ) ).

thf(thm_2Efmapal_2Evcossa,axiom,
    ! [A_27a: d,A_27b: d,V0a_2E0: u,V1l_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efmapal_2Evcossa_2E2 @ ( s @ A_27a @ V0a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efmapal_2Eassocv_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) @ ( s @ A_27a @ V0a_2E0 ) ) ) ) ).

thf(thm_2Efmapal_2EOPTION__UPDATE,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efmapal_2EOPTION__UPDATE_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efmapal_2Eoptry_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Eincr__build,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0cmp_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ ( c_2Efmapal_2Eincr__build_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ c_2Elist_2ENIL_2E0 ) )
      & ! [V1cmp_2E0: u,V2ab_2E0: u,V3l_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ ( c_2Efmapal_2Eincr__build_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V2ab_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3l_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ ( c_2Efmapal_2Eincr__merge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V2ab_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ ( c_2Efmapal_2Eincr__build_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3l_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Eincr__flat,axiom,
    ! [A_27a: d,A_27b: d,V0cmp_2E0: u,V1lol_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Eincr__flat_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ V1lol_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Emerge__out_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ V1lol_2E0 ) ) ) ) ).

thf(thm_2Efmapal_2Eincr__sort,axiom,
    ! [A_27a: d,A_27b: d,V0cmp_2E0: u,V1l_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Eincr__sort_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Emerge__out_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ ( c_2Efmapal_2Eincr__build_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) ) ) ) ) ).

thf(thm_2Efmapal_2EOPTION__FLAT__primitive,axiom,
    ! [A_27z: d,F3_2E0: u,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
      ( ! [V4OPTION__FLAT_2E0: u,V7l_2E0: u,V8a_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27z ) @ ( tyop_2Elist_2Elist @ A_27z ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ ( tyop_2Elist_2Elist @ A_27z ) ) @ V4OPTION__FLAT_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ V7l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ V8a_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ ( c_2Ecombin_2EI_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ V8a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ ( tyop_2Elist_2Elist @ A_27z ) ) @ V4OPTION__FLAT_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ V7l_2E0 ) ) ) ) ) ) ) )
     => ( ! [V4OPTION__FLAT_2E0: u,V6v_2E0: u,V7l_2E0: u] :
            ( ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ ( tyop_2Elist_2Elist @ A_27z ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ ( tyop_2Elist_2Elist @ A_27z ) ) @ V4OPTION__FLAT_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) @ V6v_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ V7l_2E0 ) ) )
            = ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) @ V6v_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ ( c_2Ecombin_2EI_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ ( tyop_2Elist_2Elist @ A_27z ) ) @ V4OPTION__FLAT_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ V7l_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27z ) @ ( tyop_2Elist_2Elist @ A_27z ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ ( tyop_2Elist_2Elist @ A_27z ) ) @ V4OPTION__FLAT_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ V7l_2E0 ) ) ) ) ) )
       => ( ! [V4OPTION__FLAT_2E0: u,V5a_27_2E0: u] :
              ( ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ ( tyop_2Elist_2Elist @ A_27z ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ ( tyop_2Elist_2Elist @ A_27z ) ) @ V4OPTION__FLAT_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ V5a_27_2E0 ) ) )
              = ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ ( c_2Elist_2Elist__CASE_2E3 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ V5a_27_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ ( c_2Ecombin_2EI_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ c_2Elist_2ENIL_2E0 ) ) ) @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ ( tyop_2Elist_2Elist @ A_27z ) ) @ V4OPTION__FLAT_2E0 ) ) ) ) ) )
         => ( ! [V0R_2E0: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( 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 ) @ F0_2E0 ) @ ( s @ ( 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 ) ) @ V0R_2E0 ) ) ) )
              <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2EWF_2E1 @ ( s @ ( 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 ) ) @ V0R_2E0 ) ) ) )
                  & ! [V1l_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ V1l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ V1l_2E0 ) ) ) ) ) )
                  & ! [V2a_2E0: u,V3l_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ V3l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ V2a_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ V3l_2E0 ) ) ) ) ) ) ) )
           => ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ ( tyop_2Elist_2Elist @ A_27z ) ) @ c_2Efmapal_2EOPTION__FLAT_2E0 )
              = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ ( tyop_2Elist_2Elist @ A_27z ) ) @ ( c_2Erelation_2EWFREC_2E2 @ ( s @ ( 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_2E1 @ ( s @ ( 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 ) @ F0_2E0 ) ) ) @ ( s @ ( 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 ) ) ) @ F1_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Eunlookup,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Eunlookup_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ V0f_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUN__FMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ A_27b ) @ c_2Eoption_2ETHE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) @ c_2Eoption_2EIS__SOME_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ V0f_2E0 ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebt__to__fmap__lb,axiom,
    ! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V0cmp_2E0: u,V1lb_2E0: u,V3x_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ A_27a @ V1lb_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1lb_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) )
            = mono_2Ec_2EternaryComparisons_2ELESS ) )
     => ( ! [V0cmp_2E0: u,V1lb_2E0: u,V3x_2E0: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ A_27a @ V1lb_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ A_27a @ V1lb_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) ) )
       => ! [V0cmp_2E0: u,V1lb_2E0: u,V2t_2E0: u] :
            ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Ebt__to__fmap__lb_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2t_2E0 ) ) )
            = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EFMAPAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2t_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ A_27a @ V1lb_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebt__to__fmap__ub,axiom,
    ! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V0cmp_2E0: u,V3x_2E0: u,V2ub_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ A_27a @ V2ub_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ A_27a @ V2ub_2E0 ) ) ) )
            = mono_2Ec_2EternaryComparisons_2ELESS ) )
     => ( ! [V0cmp_2E0: u,V2ub_2E0: u,V3x_2E0: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ A_27a @ V2ub_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ A_27a @ V2ub_2E0 ) ) ) ) ) )
       => ! [V0cmp_2E0: u,V1t_2E0: u,V2ub_2E0: u] :
            ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Ebt__to__fmap__ub_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1t_2E0 ) @ ( s @ A_27a @ V2ub_2E0 ) ) )
            = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EFMAPAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1t_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ A_27a @ V2ub_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebt__to__fmap__lb__ub,axiom,
    ! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V0cmp_2E0: u,V1lb_2E0: u,V4x_2E0: u,V3ub_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ A_27a @ V1lb_2E0 ) ) ) @ ( s @ A_27a @ V4x_2E0 ) ) ) @ ( s @ A_27a @ V3ub_2E0 ) ) ) )
        <=> ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1lb_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) ) ) )
              = mono_2Ec_2EternaryComparisons_2ELESS )
            & ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ A_27a @ V3ub_2E0 ) ) ) )
              = mono_2Ec_2EternaryComparisons_2ELESS ) ) )
     => ( ! [V0cmp_2E0: u,V1lb_2E0: u,V3ub_2E0: u,V4x_2E0: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ A_27a @ V1lb_2E0 ) ) ) @ ( s @ A_27a @ V3ub_2E0 ) ) ) @ ( s @ A_27a @ V4x_2E0 ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ A_27a @ V1lb_2E0 ) ) ) @ ( s @ A_27a @ V4x_2E0 ) ) ) @ ( s @ A_27a @ V3ub_2E0 ) ) ) ) ) )
       => ! [V0cmp_2E0: u,V1lb_2E0: u,V2t_2E0: u,V3ub_2E0: u] :
            ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Ebt__to__fmap__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2t_2E0 ) @ ( s @ A_27a @ V3ub_2E0 ) ) )
            = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EFMAPAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2t_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ A_27a @ V1lb_2E0 ) ) ) @ ( s @ A_27a @ V3ub_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebt__map,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0f_2E0: u] :
          ( ( s @ ( tyop_2Eenumeral_2Ebt @ A_27b ) @ ( c_2Efmapal_2Ebt__map_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ c_2Eenumeral_2Ent_2E0 ) ) )
          = ( s @ ( tyop_2Eenumeral_2Ebt @ A_27b ) @ c_2Eenumeral_2Ent_2E0 ) )
      & ! [V1f_2E0: u,V2l_2E0: u,V3x_2E0: u,V4r_2E0: u] :
          ( ( s @ ( tyop_2Eenumeral_2Ebt @ A_27b ) @ ( c_2Efmapal_2Ebt__map_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2l_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V4r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eenumeral_2Ebt @ A_27b ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27b ) @ ( c_2Efmapal_2Ebt__map_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V2l_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27b ) @ ( c_2Efmapal_2Ebt__map_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ V4r_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Efmap,axiom,
    ! [A_27a: d,A_27b: d,V0l_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Efmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EREVERSE_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l_2E0 ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebt__to__orl__lb__ub__ac__tupled__AUX,axiom,
    ! [A_27a: d,A_27b: d,F7_2E0: u,F6_2E0: u,F5_2E0: u,F4_2E0: u,F3_2E0: u,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
      ( ! [V3cmp_2E0: u,V5lb_2E0: u,V14x_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F7_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ A_27a @ V5lb_2E0 ) ) ) @ ( s @ A_27a @ V14x_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ A_27a @ V5lb_2E0 ) @ ( s @ A_27a @ V14x_2E0 ) ) ) )
            = mono_2Ec_2EternaryComparisons_2ELESS ) )
     => ( ! [V3cmp_2E0: u,V5lb_2E0: u,V9ub_2E0: u,V1bt__to__orl__lb__ub__ac__tupled_2E0: u,V11l_2E0: u,V13r_2E0: u,V10m_2E0: u,V14x_2E0: u,V15y_2E0: u] :
            ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) ) ) ) ) ) ) @ F6_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ A_27a @ V5lb_2E0 ) ) ) @ ( s @ A_27a @ V9ub_2E0 ) ) ) @ ( s @ ( 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 ) ) ) @ V1bt__to__orl__lb__ub__ac__tupled_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V11l_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V13r_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10m_2E0 ) ) ) @ ( s @ A_27a @ V14x_2E0 ) ) ) @ ( s @ A_27b @ V15y_2E0 ) ) )
            = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ecombin_2EI_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F7_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ A_27a @ V5lb_2E0 ) ) ) @ ( s @ A_27a @ V14x_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F7_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ A_27a @ V14x_2E0 ) ) ) @ ( s @ A_27a @ V9ub_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V1bt__to__orl__lb__ub__ac__tupled_2E0 ) @ ( s @ ( 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_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ ( 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 @ ( s @ A_27a @ V5lb_2E0 ) @ ( s @ ( 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 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V11l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V14x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V14x_2E0 ) @ ( s @ A_27b @ V15y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V1bt__to__orl__lb__ub__ac__tupled_2E0 ) @ ( s @ ( 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_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ ( 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 @ ( s @ A_27a @ V14x_2E0 ) @ ( s @ ( 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 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V13r_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V9ub_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10m_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V1bt__to__orl__lb__ub__ac__tupled_2E0 ) @ ( s @ ( 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_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ ( 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 @ ( s @ A_27a @ V5lb_2E0 ) @ ( s @ ( 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 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V11l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V9ub_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10m_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V1bt__to__orl__lb__ub__ac__tupled_2E0 ) @ ( s @ ( 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_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ ( 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 @ ( s @ A_27a @ V5lb_2E0 ) @ ( s @ ( 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 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V13r_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V9ub_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10m_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
       => ( ! [V3cmp_2E0: u,V5lb_2E0: u,V9ub_2E0: u,V1bt__to__orl__lb__ub__ac__tupled_2E0: u,V10m_2E0: u,V11l_2E0: u,V12v9_2E0: u,V13r_2E0: u] :
              ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) ) ) ) ) ) @ F5_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ A_27a @ V5lb_2E0 ) ) ) @ ( s @ A_27a @ V9ub_2E0 ) ) ) @ ( s @ ( 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 ) ) ) @ V1bt__to__orl__lb__ub__ac__tupled_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10m_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V11l_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V12v9_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V13r_2E0 ) ) )
              = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V12v9_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) ) ) ) ) ) ) @ F6_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ A_27a @ V5lb_2E0 ) ) ) @ ( s @ A_27a @ V9ub_2E0 ) ) ) @ ( s @ ( 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 ) ) ) @ V1bt__to__orl__lb__ub__ac__tupled_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V11l_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V13r_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10m_2E0 ) ) ) ) ) )
         => ( ! [V7v4_2E0: u,V3cmp_2E0: u,V5lb_2E0: u,V1bt__to__orl__lb__ub__ac__tupled_2E0: u,V9ub_2E0: u,V10m_2E0: u] :
                ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) ) ) ) @ F4_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7v4_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ A_27a @ V5lb_2E0 ) ) ) @ ( s @ ( 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 ) ) ) @ V1bt__to__orl__lb__ub__ac__tupled_2E0 ) ) ) @ ( s @ A_27a @ V9ub_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10m_2E0 ) ) )
                = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Ebt__CASE_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7v4_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ecombin_2EI_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10m_2E0 ) ) ) @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) ) ) ) ) ) @ F5_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ A_27a @ V5lb_2E0 ) ) ) @ ( s @ A_27a @ V9ub_2E0 ) ) ) @ ( s @ ( 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 ) ) ) @ V1bt__to__orl__lb__ub__ac__tupled_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10m_2E0 ) ) ) ) ) )
           => ( ! [V3cmp_2E0: u,V5lb_2E0: u,V1bt__to__orl__lb__ub__ac__tupled_2E0: u,V7v4_2E0: u,V8v5_2E0: u] :
                  ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ A_27a @ V5lb_2E0 ) ) ) @ ( s @ ( 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 ) ) ) @ V1bt__to__orl__lb__ub__ac__tupled_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7v4_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V8v5_2E0 ) ) )
                  = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V8v5_2E0 ) @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) ) ) ) @ F4_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7v4_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ A_27a @ V5lb_2E0 ) ) ) @ ( s @ ( 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 ) ) ) @ V1bt__to__orl__lb__ub__ac__tupled_2E0 ) ) ) ) ) )
             => ( ! [V3cmp_2E0: u,V1bt__to__orl__lb__ub__ac__tupled_2E0: u,V5lb_2E0: u,V6v3_2E0: u] :
                    ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ ( 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 ) ) ) @ V1bt__to__orl__lb__ub__ac__tupled_2E0 ) ) ) @ ( s @ A_27a @ V5lb_2E0 ) ) ) @ ( s @ ( 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 ) ) ) ) @ V6v3_2E0 ) ) )
                    = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( 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 ) ) ) ) @ V6v3_2E0 ) @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ A_27a @ V5lb_2E0 ) ) ) @ ( s @ ( 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 ) ) ) @ V1bt__to__orl__lb__ub__ac__tupled_2E0 ) ) ) ) ) )
               => ( ! [V1bt__to__orl__lb__ub__ac__tupled_2E0: u,V3cmp_2E0: u,V4v1_2E0: u] :
                      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) @ F1_2E0 ) @ ( s @ ( 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 ) ) ) @ V1bt__to__orl__lb__ub__ac__tupled_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ ( 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 ) ) ) ) ) @ V4v1_2E0 ) ) )
                      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( 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 ) ) ) ) ) @ V4v1_2E0 ) @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ ( 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 ) ) ) @ V1bt__to__orl__lb__ub__ac__tupled_2E0 ) ) ) ) ) )
                 => ( ! [V1bt__to__orl__lb__ub__ac__tupled_2E0: u,V2a_2E0: u] :
                        ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ F0_2E0 ) @ ( s @ ( 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 ) ) ) @ V1bt__to__orl__lb__ub__ac__tupled_2E0 ) ) ) @ ( s @ ( 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 ) ) ) ) ) ) @ V2a_2E0 ) ) )
                        = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( 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 ) ) ) ) ) ) @ V2a_2E0 ) @ ( s @ ( 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 ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) @ F1_2E0 ) @ ( s @ ( 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 ) ) ) @ V1bt__to__orl__lb__ub__ac__tupled_2E0 ) ) ) ) ) )
                   => ! [V0R_2E0: u] :
                        ( ( s @ ( 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_2E1 @ ( s @ ( 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 ) ) @ V0R_2E0 ) ) )
                        = ( s @ ( 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 @ ( s @ ( 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 ) ) @ V0R_2E0 ) @ ( s @ ( 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 ) ) ) ) @ F0_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2EORWL,axiom,
    ! [A_27a: d,A_27b: d,V0cmp_2E0: u,V1f_2E0: u,V2l_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORWL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) ) ) )
    <=> ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Efmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) ) ) ) ) ) ).

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

thf(thm_2Efmapal_2EUFO,axiom,
    ! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V1f_2E0: u,V0cmp_2E0: u,V3y_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ A_27a @ V3y_2E0 ) ) ) )
        <=> ! [V4z_2E0: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V4z_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) ) ) ) ) )
             => ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V4z_2E0 ) @ ( s @ A_27a @ V3y_2E0 ) ) ) )
                = mono_2Ec_2EternaryComparisons_2ELESS ) ) )
     => ( ! [V1f_2E0: u,V0cmp_2E0: u,V3y_2E0: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ A_27a @ V3y_2E0 ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3y_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ A_27a @ V3y_2E0 ) ) ) ) ) )
       => ! [V0cmp_2E0: u,V1f_2E0: u,V2g_2E0: u] :
            ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EUFO_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2g_2E0 ) ) )
            = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2g_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2EAP__SND,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1a_2E0: u,V2b_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( c_2Efmapal_2EAP__SND_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ A_27b @ V2b_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V0f_2E0 ) @ ( s @ A_27b @ V2b_2E0 ) ) ) ) ) ) ).

thf(thm_2Efmapal_2EORL__ind,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ! [V1cmp_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) ) ) )
        & ! [V2cmp_2E0: u,V3a_2E0: u,V4b_2E0: u,V5l_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V5l_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3a_2E0 ) @ ( s @ A_27b @ V4b_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V5l_2E0 ) ) ) ) ) ) ) )
     => ! [V6v_2E0: u,V7v1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6v_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7v1_2E0 ) ) ) ) ) ).

thf(thm_2Efmapal_2EORL,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0cmp_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) ) ) )
          = mono_2Ec_2Ebool_2ET )
      & ! [V1l_2E0: u,V2cmp_2E0: u,V3b_2E0: u,V4a_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ A_27b @ V3b_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) ) ) ) )
        <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) ) )
            & ! [V5p_2E0: u,V6q_2E0: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V5p_2E0 ) @ ( s @ A_27b @ V6q_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) ) ) ) )
               => ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ A_27a @ V5p_2E0 ) ) ) )
                  = mono_2Ec_2EternaryComparisons_2ELESS ) ) ) ) ) ).

thf(thm_2Efmapal_2Eoptry__list__ind,axiom,
    ! [A_27g: d,A_27z: d,V0P_2E0: u] :
      ( ( ! [V1f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27z @ ( tyop_2Eoption_2Eoption @ A_27g ) ) @ V1f_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ c_2Elist_2ENIL_2E0 ) ) ) )
        & ! [V2f_2E0: u,V3l_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27z @ ( tyop_2Eoption_2Eoption @ A_27g ) ) @ V2f_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ V3l_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27z @ ( tyop_2Eoption_2Eoption @ A_27g ) ) @ V2f_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27z ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ V3l_2E0 ) ) ) ) ) ) )
        & ! [V4f_2E0: u,V5z_2E0: u,V6l_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27z @ ( tyop_2Eoption_2Eoption @ A_27g ) ) @ V4f_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ V6l_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27z @ ( tyop_2Eoption_2Eoption @ A_27g ) ) @ V4f_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27z ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27z @ V5z_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ V6l_2E0 ) ) ) ) ) ) ) )
     => ! [V7v_2E0: u,V8v1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27z @ ( tyop_2Eoption_2Eoption @ A_27g ) ) @ V7v_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ V8v1_2E0 ) ) ) ) ) ).

thf(thm_2Efmapal_2Eoptry__list,axiom,
    ! [A_27g: d,A_27z: d] :
      ( ! [V0f_2E0: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27g ) @ ( c_2Efmapal_2Eoptry__list_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27z @ ( tyop_2Eoption_2Eoption @ A_27g ) ) @ V0f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ c_2Elist_2ENIL_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27g ) @ c_2Eoption_2ENONE_2E0 ) )
      & ! [V1l_2E0: u,V2f_2E0: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27g ) @ ( c_2Efmapal_2Eoptry__list_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27z @ ( tyop_2Eoption_2Eoption @ A_27g ) ) @ V2f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27z ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ V1l_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27g ) @ ( c_2Efmapal_2Eoptry__list_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27z @ ( tyop_2Eoption_2Eoption @ A_27g ) ) @ V2f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ V1l_2E0 ) ) ) )
      & ! [V3z_2E0: u,V4l_2E0: u,V5f_2E0: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27g ) @ ( c_2Efmapal_2Eoptry__list_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27z @ ( tyop_2Eoption_2Eoption @ A_27g ) ) @ V5f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27z ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27z @ V3z_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ V4l_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27g ) @ ( c_2Efmapal_2Eoptry_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27g ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27z @ ( tyop_2Eoption_2Eoption @ A_27g ) ) @ V5f_2E0 ) @ ( s @ A_27z @ V3z_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27g ) @ ( c_2Efmapal_2Eoptry__list_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27z @ ( tyop_2Eoption_2Eoption @ A_27g ) ) @ V5f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ A_27z ) ) @ V4l_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Eassocv__ind,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ! [V1a_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) ) ) @ ( s @ A_27a @ V1a_2E0 ) ) ) )
        & ! [V2x_2E0: u,V3y_2E0: u,V4l_2E0: u,V5a_2E0: u] :
            ( ( ( (~)
                @ ( ( s @ A_27a @ V5a_2E0 )
                  = ( s @ A_27a @ V2x_2E0 ) ) )
             => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4l_2E0 ) ) ) @ ( s @ A_27a @ V5a_2E0 ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4l_2E0 ) ) ) ) ) @ ( s @ A_27a @ V5a_2E0 ) ) ) ) ) )
     => ! [V6v_2E0: u,V7v1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6v_2E0 ) ) ) @ ( s @ A_27a @ V7v1_2E0 ) ) ) ) ) ).

thf(thm_2Efmapal_2Eassocv,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V4a_2E0: u,V2x_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
        <=> ( ( s @ A_27a @ V4a_2E0 )
            = ( s @ A_27a @ V2x_2E0 ) ) )
     => ( ! [V0a_2E0: u] :
            ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efmapal_2Eassocv_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ A_27a @ V0a_2E0 ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) )
        & ! [V1y_2E0: u,V2x_2E0: u,V3l_2E0: u,V4a_2E0: u] :
            ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efmapal_2Eassocv_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V1y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3l_2E0 ) ) ) @ ( s @ A_27a @ V4a_2E0 ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V1y_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efmapal_2Eassocv_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3l_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Emerge__ind,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ! [V1cmp_2E0: u,V2l_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) ) ) )
        & ! [V3cmp_2E0: u,V4v4_2E0: u,V5v5_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V4v4_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V5v5_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) ) ) )
        & ! [V6cmp_2E0: u,V7a1_2E0: u,V8b1_2E0: u,V9l1_2E0: u,V10a2_2E0: u,V11b2_2E0: u,V12l2_2E0: u] :
            ( ( ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) @ ( s @ A_27a @ V7a1_2E0 ) @ ( s @ A_27a @ V10a2_2E0 ) ) ) )
                  = mono_2Ec_2EternaryComparisons_2EEQUAL )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V9l1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V12l2_2E0 ) ) ) ) )
              & ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) @ ( s @ A_27a @ V7a1_2E0 ) @ ( s @ A_27a @ V10a2_2E0 ) ) ) )
                  = mono_2Ec_2EternaryComparisons_2EGREATER )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V7a1_2E0 ) @ ( s @ A_27b @ V8b1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V9l1_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V12l2_2E0 ) ) ) ) )
              & ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) @ ( s @ A_27a @ V7a1_2E0 ) @ ( s @ A_27a @ V10a2_2E0 ) ) ) )
                  = mono_2Ec_2EternaryComparisons_2ELESS )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V9l1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V10a2_2E0 ) @ ( s @ A_27b @ V11b2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V12l2_2E0 ) ) ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V7a1_2E0 ) @ ( s @ A_27b @ V8b1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V9l1_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V10a2_2E0 ) @ ( s @ A_27b @ V11b2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V12l2_2E0 ) ) ) ) ) ) ) )
     => ! [V13v_2E0: u,V14v1_2E0: u,V15v2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V13v_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V14v1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V15v2_2E0 ) ) ) ) ) ).

thf(thm_2Efmapal_2Emerge,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0l_2E0: u,V1cmp_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Emerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l_2E0 ) )
      & ! [V2v5_2E0: u,V3v4_2E0: u,V4cmp_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Emerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V3v4_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2v5_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V3v4_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2v5_2E0 ) ) ) )
      & ! [V5l2_2E0: u,V6l1_2E0: u,V7cmp_2E0: u,V8b2_2E0: u,V9b1_2E0: u,V10a2_2E0: u,V11a1_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Emerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V11a1_2E0 ) @ ( s @ A_27b @ V9b1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6l1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V10a2_2E0 ) @ ( s @ A_27b @ V8b2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V5l2_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7cmp_2E0 ) @ ( s @ A_27a @ V11a1_2E0 ) @ ( s @ A_27a @ V10a2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V11a1_2E0 ) @ ( s @ A_27b @ V9b1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Emerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6l1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V10a2_2E0 ) @ ( s @ A_27b @ V8b2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V5l2_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V11a1_2E0 ) @ ( s @ A_27b @ V9b1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Emerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6l1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V5l2_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V10a2_2E0 ) @ ( s @ A_27b @ V8b2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Emerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V11a1_2E0 ) @ ( s @ A_27b @ V9b1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6l1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V5l2_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Eincr__merge__ind,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ! [V1cmp_2E0: u,V2l_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ c_2Elist_2ENIL_2E0 ) ) ) )
        & ! [V3cmp_2E0: u,V4l_2E0: u,V5lol_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ V5lol_2E0 ) ) ) ) ) )
        & ! [V6cmp_2E0: u,V7l_2E0: u,V8m_2E0: u,V9lol_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Emerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8m_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ V9lol_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8m_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ V9lol_2E0 ) ) ) ) ) ) ) )
     => ! [V10v_2E0: u,V11v1_2E0: u,V12v2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V10v_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V11v1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ V12v2_2E0 ) ) ) ) ) ).

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

thf(thm_2Efmapal_2EORL__sublists__ind,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ! [V1cmp_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ c_2Elist_2ENIL_2E0 ) ) ) )
        & ! [V2cmp_2E0: u,V3lol_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ V3lol_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ V3lol_2E0 ) ) ) ) ) ) )
        & ! [V4cmp_2E0: u,V5m_2E0: u,V6lol_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ V6lol_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V5m_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ V6lol_2E0 ) ) ) ) ) ) ) )
     => ! [V7v_2E0: u,V8v1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7v_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ V8v1_2E0 ) ) ) ) ) ).

thf(thm_2Efmapal_2EORL__sublists,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0cmp_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL__sublists_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ c_2Elist_2ENIL_2E0 ) ) ) )
          = mono_2Ec_2Ebool_2ET )
      & ! [V1lol_2E0: u,V2cmp_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL__sublists_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ V1lol_2E0 ) ) ) ) ) )
          = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL__sublists_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ V1lol_2E0 ) ) ) ) )
      & ! [V3m_2E0: u,V4lol_2E0: u,V5cmp_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL__sublists_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3m_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ V4lol_2E0 ) ) ) ) ) )
        <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3m_2E0 ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL__sublists_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ V4lol_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Emerge__out__ind,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ! [V1cmp_2E0: u,V2l_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ c_2Elist_2ENIL_2E0 ) ) ) )
        & ! [V3cmp_2E0: u,V4l_2E0: u,V5lol_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ V5lol_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ V5lol_2E0 ) ) ) ) ) ) )
        & ! [V6cmp_2E0: u,V7l_2E0: u,V8m_2E0: u,V9lol_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Emerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8m_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ V9lol_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8m_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ V9lol_2E0 ) ) ) ) ) ) ) )
     => ! [V10v_2E0: u,V11v1_2E0: u,V12v2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V10v_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V11v1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ V12v2_2E0 ) ) ) ) ) ).

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

thf(thm_2Efmapal_2EOPTION__FLAT__ind,axiom,
    ! [A_27z: d,V0P_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ c_2Elist_2ENIL_2E0 ) ) ) )
        & ! [V1l_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ V1l_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ V1l_2E0 ) ) ) ) ) ) )
        & ! [V2a_2E0: u,V3l_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ V3l_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ V2a_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ V3l_2E0 ) ) ) ) ) ) ) )
     => ! [V4v_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ V4v_2E0 ) ) ) ) ) ).

thf(thm_2Efmapal_2EOPTION__FLAT,axiom,
    ! [A_27z: d] :
      ( ( ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ ( c_2Efmapal_2EOPTION__FLAT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ c_2Elist_2ENIL_2E0 ) ) )
        = ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ c_2Elist_2ENIL_2E0 ) )
      & ! [V0l_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ ( c_2Efmapal_2EOPTION__FLAT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ V0l_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ ( c_2Efmapal_2EOPTION__FLAT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ V0l_2E0 ) ) ) )
      & ! [V1l_2E0: u,V2a_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ ( c_2Efmapal_2EOPTION__FLAT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ V2a_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ V1l_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ V2a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27z ) @ ( c_2Efmapal_2EOPTION__FLAT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27z ) ) ) @ V1l_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebt__to__fmap__ind,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ! [V1cmp_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) ) ) )
        & ! [V2cmp_2E0: u,V3l_2E0: u,V4x_2E0: u,V5v_2E0: u,V6r_2E0: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3l_2E0 ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6r_2E0 ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ A_27b @ V5v_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6r_2E0 ) ) ) ) ) ) ) )
     => ! [V7v_2E0: u,V8v1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7v_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8v1_2E0 ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebt__to__fmap,axiom,
    ! [A_27a: d,A_27b: d,F3_2E0: u,F1_2E0: u,F2_2E0: u,F0_2E0: u] :
      ( ! [V5cmp_2E0: u,V1x_2E0: u,V7z_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) ) ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ A_27a @ V7z_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27a @ V7z_2E0 ) ) ) )
            = mono_2Ec_2EternaryComparisons_2ELESS ) )
     => ( ! [V5cmp_2E0: u,V1x_2E0: u,V7z_2E0: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) ) ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ A_27a @ V7z_2E0 ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V7z_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) ) ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ A_27a @ V7z_2E0 ) ) ) ) ) )
       => ( ! [V5cmp_2E0: u,V6y_2E0: u,V1x_2E0: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) ) ) @ ( s @ A_27a @ V6y_2E0 ) ) ) @ ( s @ A_27a @ V1x_2E0 ) ) ) )
            <=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) @ ( s @ A_27a @ V6y_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) )
                = mono_2Ec_2EternaryComparisons_2ELESS ) )
         => ( ! [V5cmp_2E0: u,V1x_2E0: u,V6y_2E0: u] :
                ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) ) ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ A_27a @ V6y_2E0 ) ) )
                = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V6y_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) ) ) @ ( s @ A_27a @ V6y_2E0 ) ) ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) )
           => ( ! [V0cmp_2E0: u] :
                  ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EFMAPAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) ) )
                  = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) )
              & ! [V1x_2E0: u,V2v_2E0: u,V3r_2E0: u,V4l_2E0: u,V5cmp_2E0: u] :
                  ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EFMAPAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V2v_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3r_2E0 ) ) ) ) )
                  = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EFMAPAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4l_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) ) ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V2v_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EFMAPAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3r_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) ) ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2EFAPPLY__nt,axiom,
    ! [A_27a: d,A_27b: d,V0cmp_2E0: u,V1x_2E0: u] :
      ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EFMAPAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) ) ) @ ( s @ A_27a @ V1x_2E0 ) ) )
      = ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ).

thf(thm_2Efmapal_2EFAPPLY__node,axiom,
    ! [A_27a: d,A_27b: d,V0cmp_2E0: u,V1x_2E0: u,V2l_2E0: u,V3a_2E0: u,V4b_2E0: u,V5r_2E0: u] :
      ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EFMAPAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3a_2E0 ) @ ( s @ A_27b @ V4b_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V5r_2E0 ) ) ) ) ) @ ( s @ A_27a @ V1x_2E0 ) ) )
      = ( s @ A_27b @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27a @ V3a_2E0 ) ) ) @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EFMAPAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) ) ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ A_27b @ V4b_2E0 ) @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EFMAPAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V5r_2E0 ) ) ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebt__FST__FDOM,axiom,
    ! [A_27a: d,A_27b: d,V0cmp_2E0: u,V1t_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EFMAPAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1t_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eenumeral_2EENUMERAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ A_27a ) @ ( c_2Efmapal_2Ebt__map_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1t_2E0 ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebt__to__orl__lb__ub__ind,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ! [V1cmp_2E0: u,V2lb_2E0: u,V3ub_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ A_27a @ V2lb_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) ) ) @ ( s @ A_27a @ V3ub_2E0 ) ) ) )
        & ! [V4cmp_2E0: u,V5lb_2E0: u,V6l_2E0: u,V7x_2E0: u,V8y_2E0: u,V9r_2E0: u,V10ub_2E0: u] :
            ( ( ( ( (~)
                  @ ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ A_27a @ V5lb_2E0 ) @ ( s @ A_27a @ V7x_2E0 ) ) ) )
                    = mono_2Ec_2EternaryComparisons_2ELESS ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) ) ) @ ( s @ A_27a @ V5lb_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V9r_2E0 ) ) ) @ ( s @ A_27a @ V10ub_2E0 ) ) ) ) )
              & ( ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ A_27a @ V5lb_2E0 ) @ ( s @ A_27a @ V7x_2E0 ) ) ) )
                    = mono_2Ec_2EternaryComparisons_2ELESS )
                  & ( (~)
                    @ ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ A_27a @ V7x_2E0 ) @ ( s @ A_27a @ V10ub_2E0 ) ) ) )
                      = mono_2Ec_2EternaryComparisons_2ELESS ) ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) ) ) @ ( s @ A_27a @ V5lb_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6l_2E0 ) ) ) @ ( s @ A_27a @ V10ub_2E0 ) ) ) ) )
              & ( ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ A_27a @ V5lb_2E0 ) @ ( s @ A_27a @ V7x_2E0 ) ) ) )
                    = mono_2Ec_2EternaryComparisons_2ELESS )
                  & ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ A_27a @ V7x_2E0 ) @ ( s @ A_27a @ V10ub_2E0 ) ) ) )
                    = mono_2Ec_2EternaryComparisons_2ELESS ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) ) ) @ ( s @ A_27a @ V5lb_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6l_2E0 ) ) ) @ ( s @ A_27a @ V7x_2E0 ) ) ) ) )
              & ( ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ A_27a @ V5lb_2E0 ) @ ( s @ A_27a @ V7x_2E0 ) ) ) )
                    = mono_2Ec_2EternaryComparisons_2ELESS )
                  & ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ A_27a @ V7x_2E0 ) @ ( s @ A_27a @ V10ub_2E0 ) ) ) )
                    = mono_2Ec_2EternaryComparisons_2ELESS ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) ) ) @ ( s @ A_27a @ V7x_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V9r_2E0 ) ) ) @ ( s @ A_27a @ V10ub_2E0 ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) ) ) @ ( s @ A_27a @ V5lb_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V7x_2E0 ) @ ( s @ A_27b @ V8y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V9r_2E0 ) ) ) ) ) @ ( s @ A_27a @ V10ub_2E0 ) ) ) ) ) )
     => ! [V11v_2E0: u,V12v1_2E0: u,V13v2_2E0: u,V14v3_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11v_2E0 ) ) ) @ ( s @ A_27a @ V12v1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V13v2_2E0 ) ) ) @ ( s @ A_27a @ V14v3_2E0 ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebt__to__orl__lb__ub,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V9cmp_2E0: u,V7lb_2E0: u,V4x_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) ) ) @ ( s @ A_27a @ V7lb_2E0 ) ) ) @ ( s @ A_27a @ V4x_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) @ ( s @ A_27a @ V7lb_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) ) ) )
            = mono_2Ec_2EternaryComparisons_2ELESS ) )
     => ( ! [V0ub_2E0: u,V1lb_2E0: u,V2cmp_2E0: u] :
            ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ A_27a @ V1lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) @ ( s @ A_27a @ V0ub_2E0 ) ) )
            = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) )
        & ! [V3y_2E0: u,V4x_2E0: u,V5ub_2E0: u,V6r_2E0: u,V7lb_2E0: u,V8l_2E0: u,V9cmp_2E0: u] :
            ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) @ ( s @ A_27a @ V7lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6r_2E0 ) ) ) @ ( s @ A_27a @ V5ub_2E0 ) ) )
            = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) ) ) @ ( s @ A_27a @ V7lb_2E0 ) ) ) @ ( s @ A_27a @ V4x_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) ) ) @ ( s @ A_27a @ V4x_2E0 ) ) ) @ ( s @ A_27a @ V5ub_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) @ ( s @ A_27a @ V7lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8l_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6r_2E0 ) @ ( s @ A_27a @ V5ub_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) @ ( s @ A_27a @ V7lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8l_2E0 ) @ ( s @ A_27a @ V5ub_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) @ ( s @ A_27a @ V7lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6r_2E0 ) @ ( s @ A_27a @ V5ub_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebt__to__orl__lb__ind,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ! [V1cmp_2E0: u,V2lb_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ A_27a @ V2lb_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) ) ) )
        & ! [V3cmp_2E0: u,V4lb_2E0: u,V5l_2E0: u,V6x_2E0: u,V7y_2E0: u,V8r_2E0: u] :
            ( ( ( ( (~)
                  @ ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ A_27a @ V4lb_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) ) ) )
                    = mono_2Ec_2EternaryComparisons_2ELESS ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ A_27a @ V4lb_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8r_2E0 ) ) ) ) )
              & ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ A_27a @ V4lb_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) ) ) )
                  = mono_2Ec_2EternaryComparisons_2ELESS )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ A_27a @ V6x_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8r_2E0 ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ A_27a @ V4lb_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V5l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ A_27b @ V7y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8r_2E0 ) ) ) ) ) ) ) )
     => ! [V9v_2E0: u,V10v1_2E0: u,V11v2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9v_2E0 ) ) ) @ ( s @ A_27a @ V10v1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V11v2_2E0 ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebt__to__orl__lb,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V7cmp_2E0: u,V5lb_2E0: u,V3x_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7cmp_2E0 ) ) ) @ ( s @ A_27a @ V5lb_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7cmp_2E0 ) @ ( s @ A_27a @ V5lb_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) )
            = mono_2Ec_2EternaryComparisons_2ELESS ) )
     => ( ! [V0lb_2E0: u,V1cmp_2E0: u] :
            ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ A_27a @ V0lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) ) )
            = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) )
        & ! [V2y_2E0: u,V3x_2E0: u,V4r_2E0: u,V5lb_2E0: u,V6l_2E0: u,V7cmp_2E0: u] :
            ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7cmp_2E0 ) @ ( s @ A_27a @ V5lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ A_27b @ V2y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4r_2E0 ) ) ) ) )
            = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7cmp_2E0 ) ) ) @ ( s @ A_27a @ V5lb_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7cmp_2E0 ) @ ( s @ A_27a @ V5lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6l_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ A_27b @ V2y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7cmp_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4r_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7cmp_2E0 ) @ ( s @ A_27a @ V5lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4r_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebt__to__orl__ub__ind,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ! [V1cmp_2E0: u,V2ub_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) ) ) @ ( s @ A_27a @ V2ub_2E0 ) ) ) )
        & ! [V3cmp_2E0: u,V4l_2E0: u,V5x_2E0: u,V6y_2E0: u,V7r_2E0: u,V8ub_2E0: u] :
            ( ( ( ( (~)
                  @ ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ A_27a @ V8ub_2E0 ) ) ) )
                    = mono_2Ec_2EternaryComparisons_2ELESS ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4l_2E0 ) ) ) @ ( s @ A_27a @ V8ub_2E0 ) ) ) ) )
              & ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ A_27a @ V8ub_2E0 ) ) ) )
                  = mono_2Ec_2EternaryComparisons_2ELESS )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4l_2E0 ) ) ) @ ( s @ A_27a @ V5x_2E0 ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ A_27b @ V6y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7r_2E0 ) ) ) ) ) @ ( s @ A_27a @ V8ub_2E0 ) ) ) ) ) )
     => ! [V9v_2E0: u,V10v1_2E0: u,V11v2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9v_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10v1_2E0 ) ) ) @ ( s @ A_27a @ V11v2_2E0 ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebt__to__orl__ub,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V7cmp_2E0: u,V3x_2E0: u,V4ub_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7cmp_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ A_27a @ V4ub_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7cmp_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ A_27a @ V4ub_2E0 ) ) ) )
            = mono_2Ec_2EternaryComparisons_2ELESS ) )
     => ( ! [V0ub_2E0: u,V1cmp_2E0: u] :
            ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__ub_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) @ ( s @ A_27a @ V0ub_2E0 ) ) )
            = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) )
        & ! [V2y_2E0: u,V3x_2E0: u,V4ub_2E0: u,V5r_2E0: u,V6l_2E0: u,V7cmp_2E0: u] :
            ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__ub_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ A_27b @ V2y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V5r_2E0 ) ) ) @ ( s @ A_27a @ V4ub_2E0 ) ) )
            = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7cmp_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ A_27a @ V4ub_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__ub_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6l_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ A_27b @ V2y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7cmp_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V5r_2E0 ) @ ( s @ A_27a @ V4ub_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__ub_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6l_2E0 ) @ ( s @ A_27a @ V4ub_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebt__to__orl__ind,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ! [V1cmp_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) ) ) )
        & ! [V2cmp_2E0: u,V3l_2E0: u,V4x_2E0: u,V5y_2E0: u,V6r_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ A_27b @ V5y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6r_2E0 ) ) ) ) ) ) )
     => ! [V7v_2E0: u,V8v1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7v_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8v1_2E0 ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebt__to__orl,axiom,
    ! [A_27a: d,A_27b: d,V0y_2E0: u,V1x_2E0: u,V2r_2E0: u,V3l_2E0: u,V4cmp_2E0: u] :
      ( ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) ) )
        = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) )
      & ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V0y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2r_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__ub_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3l_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V0y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2r_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebt__to__orl__lb__ub__ac__ind,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ! [V1cmp_2E0: u,V2lb_2E0: u,V3ub_2E0: u,V4m_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ A_27a @ V2lb_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) ) ) @ ( s @ A_27a @ V3ub_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4m_2E0 ) ) ) )
        & ! [V5cmp_2E0: u,V6lb_2E0: u,V7l_2E0: u,V8x_2E0: u,V9y_2E0: u,V10r_2E0: u,V11ub_2E0: u,V12m_2E0: u] :
            ( ( ( ( (~)
                  @ ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) @ ( s @ A_27a @ V6lb_2E0 ) @ ( s @ A_27a @ V8x_2E0 ) ) ) )
                    = mono_2Ec_2EternaryComparisons_2ELESS ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) ) ) @ ( s @ A_27a @ V6lb_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10r_2E0 ) ) ) @ ( s @ A_27a @ V11ub_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V12m_2E0 ) ) ) ) )
              & ( ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) @ ( s @ A_27a @ V6lb_2E0 ) @ ( s @ A_27a @ V8x_2E0 ) ) ) )
                    = mono_2Ec_2EternaryComparisons_2ELESS )
                  & ( (~)
                    @ ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) @ ( s @ A_27a @ V8x_2E0 ) @ ( s @ A_27a @ V11ub_2E0 ) ) ) )
                      = mono_2Ec_2EternaryComparisons_2ELESS ) ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) ) ) @ ( s @ A_27a @ V6lb_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7l_2E0 ) ) ) @ ( s @ A_27a @ V11ub_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V12m_2E0 ) ) ) ) )
              & ( ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) @ ( s @ A_27a @ V6lb_2E0 ) @ ( s @ A_27a @ V8x_2E0 ) ) ) )
                    = mono_2Ec_2EternaryComparisons_2ELESS )
                  & ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) @ ( s @ A_27a @ V8x_2E0 ) @ ( s @ A_27a @ V11ub_2E0 ) ) ) )
                    = mono_2Ec_2EternaryComparisons_2ELESS ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) ) ) @ ( s @ A_27a @ V6lb_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7l_2E0 ) ) ) @ ( s @ A_27a @ V8x_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V8x_2E0 ) @ ( s @ A_27b @ V9y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) @ ( s @ A_27a @ V8x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10r_2E0 ) @ ( s @ A_27a @ V11ub_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V12m_2E0 ) ) ) ) ) ) ) ) )
              & ( ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) @ ( s @ A_27a @ V6lb_2E0 ) @ ( s @ A_27a @ V8x_2E0 ) ) ) )
                    = mono_2Ec_2EternaryComparisons_2ELESS )
                  & ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) @ ( s @ A_27a @ V8x_2E0 ) @ ( s @ A_27a @ V11ub_2E0 ) ) ) )
                    = mono_2Ec_2EternaryComparisons_2ELESS ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) ) ) @ ( s @ A_27a @ V8x_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10r_2E0 ) ) ) @ ( s @ A_27a @ V11ub_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V12m_2E0 ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) ) ) @ ( s @ A_27a @ V6lb_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V8x_2E0 ) @ ( s @ A_27b @ V9y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10r_2E0 ) ) ) ) ) @ ( s @ A_27a @ V11ub_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V12m_2E0 ) ) ) ) ) )
     => ! [V13v_2E0: u,V14v1_2E0: u,V15v2_2E0: u,V16v3_2E0: u,V17v4_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V13v_2E0 ) ) ) @ ( s @ A_27a @ V14v1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V15v2_2E0 ) ) ) @ ( s @ A_27a @ V16v3_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V17v4_2E0 ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebt__to__orl__lb__ub__ac,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V11cmp_2E0: u,V9lb_2E0: u,V5x_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) ) ) @ ( s @ A_27a @ V9lb_2E0 ) ) ) @ ( s @ A_27a @ V5x_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ A_27a @ V9lb_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) ) )
            = mono_2Ec_2EternaryComparisons_2ELESS ) )
     => ( ! [V0ub_2E0: u,V1m_2E0: u,V2lb_2E0: u,V3cmp_2E0: u] :
            ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ A_27a @ V2lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) @ ( s @ A_27a @ V0ub_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1m_2E0 ) ) )
            = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1m_2E0 ) )
        & ! [V4y_2E0: u,V5x_2E0: u,V6ub_2E0: u,V7r_2E0: u,V8m_2E0: u,V9lb_2E0: u,V10l_2E0: u,V11cmp_2E0: u] :
            ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ A_27a @ V9lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ A_27b @ V4y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7r_2E0 ) ) ) @ ( s @ A_27a @ V6ub_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8m_2E0 ) ) )
            = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) ) ) @ ( s @ A_27a @ V9lb_2E0 ) ) ) @ ( s @ A_27a @ V5x_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) ) ) @ ( s @ A_27a @ V5x_2E0 ) ) ) @ ( s @ A_27a @ V6ub_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ A_27a @ V9lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10l_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ A_27b @ V4y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7r_2E0 ) @ ( s @ A_27a @ V6ub_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8m_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ A_27a @ V9lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10l_2E0 ) @ ( s @ A_27a @ V6ub_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8m_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ A_27a @ V9lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7r_2E0 ) @ ( s @ A_27a @ V6ub_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8m_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebt__to__orl__lb__ac__ind,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ! [V1cmp_2E0: u,V2lb_2E0: u,V3m_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ A_27a @ V2lb_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3m_2E0 ) ) ) )
        & ! [V4cmp_2E0: u,V5lb_2E0: u,V6l_2E0: u,V7x_2E0: u,V8y_2E0: u,V9r_2E0: u,V10m_2E0: u] :
            ( ( ( ( (~)
                  @ ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ A_27a @ V5lb_2E0 ) @ ( s @ A_27a @ V7x_2E0 ) ) ) )
                    = mono_2Ec_2EternaryComparisons_2ELESS ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) ) ) @ ( s @ A_27a @ V5lb_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V9r_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10m_2E0 ) ) ) ) )
              & ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ A_27a @ V5lb_2E0 ) @ ( s @ A_27a @ V7x_2E0 ) ) ) )
                  = mono_2Ec_2EternaryComparisons_2ELESS )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) ) ) @ ( s @ A_27a @ V7x_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V9r_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10m_2E0 ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) ) ) @ ( s @ A_27a @ V5lb_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V7x_2E0 ) @ ( s @ A_27b @ V8y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V9r_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10m_2E0 ) ) ) ) ) )
     => ! [V11v_2E0: u,V12v1_2E0: u,V13v2_2E0: u,V14v3_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11v_2E0 ) ) ) @ ( s @ A_27a @ V12v1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V13v2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V14v3_2E0 ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebt__to__orl__lb__ac,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V9cmp_2E0: u,V7lb_2E0: u,V4x_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) ) ) @ ( s @ A_27a @ V7lb_2E0 ) ) ) @ ( s @ A_27a @ V4x_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) @ ( s @ A_27a @ V7lb_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) ) ) )
            = mono_2Ec_2EternaryComparisons_2ELESS ) )
     => ( ! [V0m_2E0: u,V1lb_2E0: u,V2cmp_2E0: u] :
            ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb__ac_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ A_27a @ V1lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0m_2E0 ) ) )
            = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0m_2E0 ) )
        & ! [V3y_2E0: u,V4x_2E0: u,V5r_2E0: u,V6m_2E0: u,V7lb_2E0: u,V8l_2E0: u,V9cmp_2E0: u] :
            ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb__ac_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) @ ( s @ A_27a @ V7lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V5r_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6m_2E0 ) ) )
            = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) ) ) @ ( s @ A_27a @ V7lb_2E0 ) ) ) @ ( s @ A_27a @ V4x_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) @ ( s @ A_27a @ V7lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8l_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb__ac_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V5r_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6m_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb__ac_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) @ ( s @ A_27a @ V7lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V5r_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6m_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebt__to__orl__ub__ac__ind,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ! [V1cmp_2E0: u,V2ub_2E0: u,V3m_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) ) ) @ ( s @ A_27a @ V2ub_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3m_2E0 ) ) ) )
        & ! [V4cmp_2E0: u,V5l_2E0: u,V6x_2E0: u,V7y_2E0: u,V8r_2E0: u,V9ub_2E0: u,V10m_2E0: u] :
            ( ( ( ( (~)
                  @ ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ A_27a @ V9ub_2E0 ) ) ) )
                    = mono_2Ec_2EternaryComparisons_2ELESS ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V5l_2E0 ) ) ) @ ( s @ A_27a @ V9ub_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10m_2E0 ) ) ) ) )
              & ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ A_27a @ V9ub_2E0 ) ) ) )
                  = mono_2Ec_2EternaryComparisons_2ELESS )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V5l_2E0 ) ) ) @ ( s @ A_27a @ V6x_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ A_27b @ V7y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8r_2E0 ) @ ( s @ A_27a @ V9ub_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10m_2E0 ) ) ) ) ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V5l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ A_27b @ V7y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8r_2E0 ) ) ) ) ) @ ( s @ A_27a @ V9ub_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10m_2E0 ) ) ) ) ) )
     => ! [V11v_2E0: u,V12v1_2E0: u,V13v2_2E0: u,V14v3_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11v_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V12v1_2E0 ) ) ) @ ( s @ A_27a @ V13v2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V14v3_2E0 ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebt__to__orl__ub__ac,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V9cmp_2E0: u,V4x_2E0: u,V5ub_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) ) ) @ ( s @ A_27a @ V4x_2E0 ) ) ) @ ( s @ A_27a @ V5ub_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ A_27a @ V5ub_2E0 ) ) ) )
            = mono_2Ec_2EternaryComparisons_2ELESS ) )
     => ( ! [V0ub_2E0: u,V1m_2E0: u,V2cmp_2E0: u] :
            ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__ub__ac_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) @ ( s @ A_27a @ V0ub_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1m_2E0 ) ) )
            = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1m_2E0 ) )
        & ! [V3y_2E0: u,V4x_2E0: u,V5ub_2E0: u,V6r_2E0: u,V7m_2E0: u,V8l_2E0: u,V9cmp_2E0: u] :
            ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__ub__ac_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6r_2E0 ) ) ) @ ( s @ A_27a @ V5ub_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7m_2E0 ) ) )
            = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) ) ) @ ( s @ A_27a @ V4x_2E0 ) ) ) @ ( s @ A_27a @ V5ub_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__ub__ac_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8l_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb__ub__ac_2E5 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6r_2E0 ) @ ( s @ A_27a @ V5ub_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7m_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__ub__ac_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8l_2E0 ) @ ( s @ A_27a @ V5ub_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7m_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebt__to__orl__ac__ind,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ! [V1cmp_2E0: u,V2m_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2m_2E0 ) ) ) )
        & ! [V3cmp_2E0: u,V4l_2E0: u,V5x_2E0: u,V6y_2E0: u,V7r_2E0: u,V8m_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ A_27b @ V6y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7r_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8m_2E0 ) ) ) ) )
     => ! [V9v_2E0: u,V10v1_2E0: u,V11v2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9v_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10v1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V11v2_2E0 ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebt__to__orl__ac,axiom,
    ! [A_27a: d,A_27b: d,V0y_2E0: u,V1x_2E0: u,V2r_2E0: u,V3m_2E0: u,V4l_2E0: u,V5cmp_2E0: u] :
      ( ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__ac_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3m_2E0 ) ) )
        = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3m_2E0 ) )
      & ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__ac_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V0y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2r_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3m_2E0 ) ) )
        = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__ub__ac_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4l_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V0y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__lb__ac_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2r_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3m_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2EORWL__bt__to__orl,axiom,
    ! [A_27a: d,A_27b: d,V0cmp_2E0: u,V1t_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORWL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EFMAPAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1t_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1t_2E0 ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebl__to__fmap__ind,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ! [V1cmp_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Enbl_2E0 ) ) ) )
        & ! [V2cmp_2E0: u,V3b_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3b_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Ezerbl_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3b_2E0 ) ) ) ) ) ) )
        & ! [V4cmp_2E0: u,V5x_2E0: u,V6y_2E0: u,V7t_2E0: u,V8b_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8b_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Eonebl_2E3 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ A_27b @ V6y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7t_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8b_2E0 ) ) ) ) ) ) ) )
     => ! [V9v_2E0: u,V10v1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9v_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10v1_2E0 ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebl__to__fmap,axiom,
    ! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V6cmp_2E0: u,V4x_2E0: u,V8z_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) ) ) @ ( s @ A_27a @ V4x_2E0 ) ) ) @ ( s @ A_27a @ V8z_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ A_27a @ V8z_2E0 ) ) ) )
            = mono_2Ec_2EternaryComparisons_2ELESS ) )
     => ( ! [V6cmp_2E0: u,V4x_2E0: u,V8z_2E0: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) ) ) @ ( s @ A_27a @ V4x_2E0 ) ) ) @ ( s @ A_27a @ V8z_2E0 ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V8z_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) ) ) @ ( s @ A_27a @ V4x_2E0 ) ) ) @ ( s @ A_27a @ V8z_2E0 ) ) ) ) ) )
       => ( ! [V0cmp_2E0: u] :
              ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Ebl__to__fmap_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Enbl_2E0 ) ) )
              = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) )
          & ! [V1cmp_2E0: u,V2b_2E0: u] :
              ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Ebl__to__fmap_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Ezerbl_2E1 @ ( s @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2b_2E0 ) ) ) ) )
              = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Ebl__to__fmap_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2b_2E0 ) ) ) )
          & ! [V3y_2E0: u,V4x_2E0: u,V5t_2E0: u,V6cmp_2E0: u,V7b_2E0: u] :
              ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Ebl__to__fmap_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Eonebl_2E3 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V5t_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7b_2E0 ) ) ) ) )
              = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EOFU_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EFMAPAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V5t_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) ) ) @ ( s @ A_27a @ V4x_2E0 ) ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Ebl__to__fmap_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebl @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7b_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebt__to__orl__ID__IMP,axiom,
    ! [A_27a: d,A_27b: d,V0cmp_2E0: u,V1l_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Elist__to__bt_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) ) ).

thf(thm_2Efmapal_2Efmap__FDOM,axiom,
    ! [A_27a: d,A_27b: d,V0l_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Efmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l_2E0 ) ) ) ) ) ) ).

thf(thm_2Efmapal_2EORL__FUNION__IMP,axiom,
    ! [A_27a: d,A_27b: d,V0cmp_2E0: u,V1l_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) ) )
     => ! [V2m_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2m_2E0 ) ) ) )
         => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Emerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2m_2E0 ) ) ) ) ) )
            & ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Efmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Emerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2m_2E0 ) ) ) ) )
              = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Efmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Efmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2m_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2EFMAPAL__FDOM__THM,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0cmp_2E0: u,V1x_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EFMAPAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) ) ) ) ) ) ) )
          = mono_2Ec_2Ebool_2EF )
      & ! [V2cmp_2E0: u,V3x_2E0: u,V4a_2E0: u,V5b_2E0: u,V6l_2E0: u,V7r_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EFMAPAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ A_27b @ V5b_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7r_2E0 ) ) ) ) ) ) ) ) ) )
          = ( mono_2Ec_2EternaryComparisons_2Eordering__CASE_2Emono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EFMAPAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6l_2E0 ) ) ) ) ) ) ) ) @ mono_2Ec_2Ebool_2ET @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EFMAPAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7r_2E0 ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Einter__merge__ind,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ! [V1cmp_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) )
        & ! [V2cmp_2E0: u,V3a_2E0: u,V4b_2E0: u,V5l_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3a_2E0 ) @ ( s @ A_27b @ V4b_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V5l_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) )
        & ! [V6cmp_2E0: u,V7y_2E0: u,V8m_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V7y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V8m_2E0 ) ) ) ) ) )
        & ! [V9cmp_2E0: u,V10a_2E0: u,V11b_2E0: u,V12l_2E0: u,V13y_2E0: u,V14m_2E0: u] :
            ( ( ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) @ ( s @ A_27a @ V10a_2E0 ) @ ( s @ A_27a @ V13y_2E0 ) ) ) )
                  = mono_2Ec_2EternaryComparisons_2EEQUAL )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V12l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V14m_2E0 ) ) ) ) )
              & ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) @ ( s @ A_27a @ V10a_2E0 ) @ ( s @ A_27a @ V13y_2E0 ) ) ) )
                  = mono_2Ec_2EternaryComparisons_2EGREATER )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V10a_2E0 ) @ ( s @ A_27b @ V11b_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V12l_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V14m_2E0 ) ) ) ) )
              & ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) @ ( s @ A_27a @ V10a_2E0 ) @ ( s @ A_27a @ V13y_2E0 ) ) ) )
                  = mono_2Ec_2EternaryComparisons_2ELESS )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V12l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V13y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V14m_2E0 ) ) ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V10a_2E0 ) @ ( s @ A_27b @ V11b_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V12l_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V13y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V14m_2E0 ) ) ) ) ) ) ) )
     => ! [V15v_2E0: u,V16v1_2E0: u,V17v2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V15v_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V16v1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V17v2_2E0 ) ) ) ) ) ).

thf(thm_2Efmapal_2Einter__merge,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0cmp_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Einter__merge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) )
      & ! [V1l_2E0: u,V2cmp_2E0: u,V3b_2E0: u,V4a_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Einter__merge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ A_27b @ V3b_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) )
      & ! [V5y_2E0: u,V6m_2E0: u,V7cmp_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Einter__merge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V5y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V6m_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) )
      & ! [V8y_2E0: u,V9m_2E0: u,V10l_2E0: u,V11cmp_2E0: u,V12b_2E0: u,V13a_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Einter__merge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V13a_2E0 ) @ ( s @ A_27b @ V12b_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V8y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V9m_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ A_27a @ V13a_2E0 ) @ ( s @ A_27a @ V8y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Einter__merge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V8y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V9m_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V13a_2E0 ) @ ( s @ A_27b @ V12b_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Einter__merge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V9m_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Einter__merge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V13a_2E0 ) @ ( s @ A_27b @ V12b_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V9m_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2EORL__DRESTRICT__IMP,axiom,
    ! [A_27a: d,A_27b: d,V0cmp_2E0: u,V1l_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) ) )
     => ! [V2m_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m_2E0 ) ) ) )
         => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Einter__merge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m_2E0 ) ) ) ) ) )
            & ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Efmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Einter__merge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m_2E0 ) ) ) ) )
              = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Efmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Ediff__merge__ind,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ! [V1cmp_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) )
        & ! [V2cmp_2E0: u,V3a_2E0: u,V4b_2E0: u,V5l_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3a_2E0 ) @ ( s @ A_27b @ V4b_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V5l_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) )
        & ! [V6cmp_2E0: u,V7y_2E0: u,V8m_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V6cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V7y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V8m_2E0 ) ) ) ) ) )
        & ! [V9cmp_2E0: u,V10a_2E0: u,V11b_2E0: u,V12l_2E0: u,V13y_2E0: u,V14m_2E0: u] :
            ( ( ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) @ ( s @ A_27a @ V10a_2E0 ) @ ( s @ A_27a @ V13y_2E0 ) ) ) )
                  = mono_2Ec_2EternaryComparisons_2EEQUAL )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V12l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V14m_2E0 ) ) ) ) )
              & ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) @ ( s @ A_27a @ V10a_2E0 ) @ ( s @ A_27a @ V13y_2E0 ) ) ) )
                  = mono_2Ec_2EternaryComparisons_2EGREATER )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V10a_2E0 ) @ ( s @ A_27b @ V11b_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V12l_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V14m_2E0 ) ) ) ) )
              & ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) @ ( s @ A_27a @ V10a_2E0 ) @ ( s @ A_27a @ V13y_2E0 ) ) ) )
                  = mono_2Ec_2EternaryComparisons_2ELESS )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V12l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V13y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V14m_2E0 ) ) ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V10a_2E0 ) @ ( s @ A_27b @ V11b_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V12l_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V13y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V14m_2E0 ) ) ) ) ) ) ) )
     => ! [V15v_2E0: u,V16v1_2E0: u,V17v2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V15v_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V16v1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V17v2_2E0 ) ) ) ) ) ).

thf(thm_2Efmapal_2Ediff__merge,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0cmp_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ediff__merge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) )
      & ! [V1l_2E0: u,V2cmp_2E0: u,V3b_2E0: u,V4a_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ediff__merge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ A_27b @ V3b_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ A_27b @ V3b_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) ) )
      & ! [V5y_2E0: u,V6m_2E0: u,V7cmp_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ediff__merge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V5y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V6m_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) )
      & ! [V8y_2E0: u,V9m_2E0: u,V10l_2E0: u,V11cmp_2E0: u,V12b_2E0: u,V13a_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ediff__merge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V13a_2E0 ) @ ( s @ A_27b @ V12b_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V8y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V9m_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ A_27a @ V13a_2E0 ) @ ( s @ A_27a @ V8y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V13a_2E0 ) @ ( s @ A_27b @ V12b_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ediff__merge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V8y_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V9m_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ediff__merge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V9m_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ediff__merge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V13a_2E0 ) @ ( s @ A_27b @ V12b_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V9m_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2EORL__DRESTRICT__COMPL__IMP,axiom,
    ! [A_27a: d,A_27b: d,V0cmp_2E0: u,V1l_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) ) )
     => ! [V2m_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m_2E0 ) ) ) )
         => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ediff__merge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m_2E0 ) ) ) ) ) )
            & ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Efmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ediff__merge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m_2E0 ) ) ) ) )
              = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Efmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2ECOMPL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2m_2E0 ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2EFMAPAL__fmap,axiom,
    ! [A_27a: d,A_27b: d,V0cmp_2E0: u,V1l_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Efmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EFMAPAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Elist__to__bt_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Eincr__sort_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2EORL__FMAPAL,axiom,
    ! [A_27a: d,A_27b: d,V0cmp_2E0: u,V1l_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Efmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EFMAPAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Elist__to__bt_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2EORWL__FUNION__THM,axiom,
    ! [A_27a: d,A_27b: d,V0cmp_2E0: u,V1s_2E0: u,V2l_2E0: u,V3t_2E0: u,V4m_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORWL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1s_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORWL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V3t_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4m_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORWL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1s_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V3t_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Emerge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4m_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2EORWL__DRESTRICT__THM,axiom,
    ! [A_27a: d,A_27b: d,V0cmp_2E0: u,V1s_2E0: u,V2l_2E0: u,V3t_2E0: u,V4m_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORWL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1s_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOWL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3t_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4m_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORWL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3t_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Einter__merge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4m_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2EORWL__DRESTRICT__COMPL__THM,axiom,
    ! [A_27a: d,A_27b: d,V0cmp_2E0: u,V1s_2E0: u,V2l_2E0: u,V3t_2E0: u,V4m_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORWL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1s_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eenumeral_2EOWL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3t_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4m_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORWL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2ECOMPL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3t_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ediff__merge_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4m_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Eo__f__bt__map,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0cmp_2E0: u,V1f_2E0: u,V2t_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V1f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EFMAPAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2t_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efmapal_2EFMAPAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( c_2Efmapal_2Ebt__map_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( c_2Efmapal_2EAP__SND_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V1f_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2t_2E0 ) ) ) ) ) ) ).

thf(thm_2Efmapal_2EFAPPLY__fmap__NIL,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u] :
      ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Efmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) ) ) @ ( s @ A_27a @ V0x_2E0 ) ) )
      = ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) ) ).

thf(thm_2Efmapal_2EFAPPLY__fmap__CONS,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V0x_2E0: u,V1y_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27a @ V1y_2E0 ) ) ) )
        <=> ( ( s @ A_27a @ V0x_2E0 )
            = ( s @ A_27a @ V1y_2E0 ) ) )
     => ! [V0x_2E0: u,V1y_2E0: u,V2z_2E0: u,V3l_2E0: u] :
          ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Efmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1y_2E0 ) @ ( s @ A_27b @ V2z_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3l_2E0 ) ) ) ) ) @ ( s @ A_27a @ V0x_2E0 ) ) )
          = ( s @ A_27b @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27a @ V1y_2E0 ) ) ) @ ( s @ A_27b @ V2z_2E0 ) @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Efmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3l_2E0 ) ) ) @ ( s @ A_27a @ V0x_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Eo__f__fmap,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1l_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Efmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efmapal_2Efmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( c_2Efmapal_2EAP__SND_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) ) ) ) ) ).

thf(thm_2Efmapal_2EORL__bt__lb__ub__ind,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ! [V1cmp_2E0: u,V2lb_2E0: u,V3ub_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ A_27a @ V2lb_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) ) ) @ ( s @ A_27a @ V3ub_2E0 ) ) ) )
        & ! [V4cmp_2E0: u,V5lb_2E0: u,V6l_2E0: u,V7x_2E0: u,V8y_2E0: u,V9r_2E0: u,V10ub_2E0: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) ) ) @ ( s @ A_27a @ V5lb_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6l_2E0 ) ) ) @ ( s @ A_27a @ V7x_2E0 ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) ) ) @ ( s @ A_27a @ V7x_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V9r_2E0 ) ) ) @ ( s @ A_27a @ V10ub_2E0 ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) ) ) @ ( s @ A_27a @ V5lb_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V7x_2E0 ) @ ( s @ A_27b @ V8y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V9r_2E0 ) ) ) ) ) @ ( s @ A_27a @ V10ub_2E0 ) ) ) ) ) )
     => ! [V11v_2E0: u,V12v1_2E0: u,V13v2_2E0: u,V14v3_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11v_2E0 ) ) ) @ ( s @ A_27a @ V12v1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V13v2_2E0 ) ) ) @ ( s @ A_27a @ V14v3_2E0 ) ) ) ) ) ).

thf(thm_2Efmapal_2EORL__bt__lb__ub,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0ub_2E0: u,V1lb_2E0: u,V2cmp_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL__bt__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ A_27a @ V1lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) @ ( s @ A_27a @ V0ub_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) @ ( s @ A_27a @ V1lb_2E0 ) @ ( s @ A_27a @ V0ub_2E0 ) ) ) )
            = mono_2Ec_2EternaryComparisons_2ELESS ) )
      & ! [V3y_2E0: u,V4x_2E0: u,V5ub_2E0: u,V6r_2E0: u,V7lb_2E0: u,V8l_2E0: u,V9cmp_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL__bt__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) @ ( s @ A_27a @ V7lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6r_2E0 ) ) ) @ ( s @ A_27a @ V5ub_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL__bt__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) @ ( s @ A_27a @ V7lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8l_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL__bt__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9cmp_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6r_2E0 ) @ ( s @ A_27a @ V5ub_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2EORL__bt__lb__ind,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ! [V1cmp_2E0: u,V2lb_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ A_27a @ V2lb_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) ) ) )
        & ! [V3cmp_2E0: u,V4lb_2E0: u,V5l_2E0: u,V6x_2E0: u,V7y_2E0: u,V8r_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ A_27a @ V6x_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8r_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ A_27a @ V4lb_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V5l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ A_27b @ V7y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8r_2E0 ) ) ) ) ) ) ) )
     => ! [V9v_2E0: u,V10v1_2E0: u,V11v2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9v_2E0 ) ) ) @ ( s @ A_27a @ V10v1_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V11v2_2E0 ) ) ) ) ) ).

thf(thm_2Efmapal_2EORL__bt__lb,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0lb_2E0: u,V1cmp_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL__bt__lb_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ A_27a @ V0lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) ) ) )
          = mono_2Ec_2Ebool_2ET )
      & ! [V2y_2E0: u,V3x_2E0: u,V4r_2E0: u,V5lb_2E0: u,V6l_2E0: u,V7cmp_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL__bt__lb_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7cmp_2E0 ) @ ( s @ A_27a @ V5lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ A_27b @ V2y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4r_2E0 ) ) ) ) ) )
        <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL__bt__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7cmp_2E0 ) @ ( s @ A_27a @ V5lb_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6l_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL__bt__lb_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7cmp_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4r_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2EORL__bt__ub__ind,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ! [V1cmp_2E0: u,V2ub_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) ) ) @ ( s @ A_27a @ V2ub_2E0 ) ) ) )
        & ! [V3cmp_2E0: u,V4l_2E0: u,V5x_2E0: u,V6y_2E0: u,V7r_2E0: u,V8ub_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4l_2E0 ) ) ) @ ( s @ A_27a @ V5x_2E0 ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ A_27b @ V6y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7r_2E0 ) ) ) ) ) @ ( s @ A_27a @ V8ub_2E0 ) ) ) ) ) )
     => ! [V9v_2E0: u,V10v1_2E0: u,V11v2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V9v_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10v1_2E0 ) ) ) @ ( s @ A_27a @ V11v2_2E0 ) ) ) ) ) ).

thf(thm_2Efmapal_2EORL__bt__ub,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0ub_2E0: u,V1cmp_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL__bt__ub_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) @ ( s @ A_27a @ V0ub_2E0 ) ) ) )
          = mono_2Ec_2Ebool_2ET )
      & ! [V2y_2E0: u,V3x_2E0: u,V4ub_2E0: u,V5r_2E0: u,V6l_2E0: u,V7cmp_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL__bt__ub_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ A_27b @ V2y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V5r_2E0 ) ) ) @ ( s @ A_27a @ V4ub_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL__bt__ub_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6l_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL__bt__lb__ub_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7cmp_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V5r_2E0 ) @ ( s @ A_27a @ V4ub_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2EORL__bt__ind,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ! [V1cmp_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) ) ) )
        & ! [V2cmp_2E0: u,V3l_2E0: u,V4x_2E0: u,V5y_2E0: u,V6r_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V2cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ A_27b @ V5y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V6r_2E0 ) ) ) ) ) ) )
     => ! [V7v_2E0: u,V8v1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V7v_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8v1_2E0 ) ) ) ) ) ).

thf(thm_2Efmapal_2EORL__bt,axiom,
    ! [A_27a: d,A_27b: d,V0y_2E0: u,V1x_2E0: u,V2r_2E0: u,V3l_2E0: u,V4cmp_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL__bt_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) ) ) )
        = mono_2Ec_2Ebool_2ET )
      & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL__bt_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V0y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2r_2E0 ) ) ) ) ) )
      <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL__bt__ub_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3l_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) )
          & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL__bt__lb_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V4cmp_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2r_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebetter__bt__to__orl,axiom,
    ! [A_27a: d,A_27b: d,V0cmp_2E0: u,V1t_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1t_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORL__bt_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1t_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Ebt__to__list__ac_2E2 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1t_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__to__orl__ac_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1t_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Elist__rplacv__cn__ind,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V9cn_2E0: u,V6w_2E0: u,V7z_2E0: u,V10m_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) @ ( s @ ( 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 ) ) ) @ ( s @ A_27a @ V6w_2E0 ) ) ) @ ( s @ A_27b @ V7z_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10m_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V6w_2E0 ) @ ( s @ A_27b @ V7z_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V10m_2E0 ) ) ) ) ) )
     => ! [V0P_2E0: u] :
          ( ( ! [V1x_2E0: u,V2y_2E0: u,V3cn_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V2y_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V3cn_2E0 ) ) ) )
            & ! [V4x_2E0: u,V5y_2E0: u,V6w_2E0: u,V7z_2E0: u,V8l_2E0: u,V9cn_2E0: u] :
                ( ( ( (~)
                    @ ( ( s @ A_27a @ V4x_2E0 )
                      = ( s @ A_27a @ V6w_2E0 ) ) )
                 => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ A_27b @ V5y_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8l_2E0 ) ) ) @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) @ ( s @ ( 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 ) ) ) @ ( s @ A_27a @ V6w_2E0 ) ) ) @ ( s @ A_27b @ V7z_2E0 ) ) ) ) ) ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ A_27b @ V5y_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V6w_2E0 ) @ ( s @ A_27b @ V7z_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8l_2E0 ) ) ) ) ) @ ( s @ ( 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 ) ) ) ) ) )
         => ! [V11v_2E0: u,V12v1_2E0: u,V13v2_2E0: u,V14v3_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V11v_2E0 ) @ ( s @ A_27b @ V12v1_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V13v2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V14v3_2E0 ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Elist__rplacv__cn,axiom,
    ! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V8cn_2E0: u,V6w_2E0: u,V3z_2E0: u,V9m_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V8cn_2E0 ) ) ) @ ( s @ A_27a @ V6w_2E0 ) ) ) @ ( s @ A_27b @ V3z_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V9m_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V8cn_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V6w_2E0 ) @ ( s @ A_27b @ V3z_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V9m_2E0 ) ) ) ) ) )
     => ( ! [V5x_2E0: u,V6w_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) ) @ ( s @ A_27a @ V6w_2E0 ) ) ) )
          <=> ( ( s @ A_27a @ V5x_2E0 )
              = ( s @ A_27a @ V6w_2E0 ) ) )
       => ( ! [V0y_2E0: u,V1x_2E0: u,V2cn_2E0: u] :
              ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Elist__rplacv__cn_2E3 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V0y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V2cn_2E0 ) ) )
              = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) )
          & ! [V3z_2E0: u,V4y_2E0: u,V5x_2E0: u,V6w_2E0: u,V7l_2E0: u,V8cn_2E0: u] :
              ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Elist__rplacv__cn_2E3 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ A_27b @ V4y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V6w_2E0 ) @ ( s @ A_27b @ V3z_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7l_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V8cn_2E0 ) ) )
              = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) ) @ ( s @ A_27a @ V6w_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V8cn_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ A_27b @ V4y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7l_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Elist__rplacv__cn_2E3 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ A_27b @ V4y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V7l_2E0 ) @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V8cn_2E0 ) ) ) @ ( s @ A_27a @ V6w_2E0 ) ) ) @ ( s @ A_27b @ V3z_2E0 ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Efmap__FDOM__rec,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0x_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Efmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ) ) ) )
          = mono_2Ec_2Ebool_2EF )
      & ! [V1x_2E0: u,V2w_2E0: u,V3z_2E0: u,V4l_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Efmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2w_2E0 ) @ ( s @ A_27b @ V3z_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4l_2E0 ) ) ) ) ) ) ) ) ) )
        <=> ( ( ( s @ A_27a @ V1x_2E0 )
              = ( s @ A_27a @ V2w_2E0 ) )
            | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Efmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4l_2E0 ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Elist__rplacv__thm,axiom,
    ! [A_27a: d,A_27b: d,F1_2E0: u,F2_2E0: u,F3_2E0: u,F4_2E0: u,F0_2E0: u] :
      ( ! [V4m_2E0: u] :
          ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4m_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4m_2E0 ) )
     => ( ! [V3ans_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ F2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3ans_2E0 ) ) ) )
          <=> ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3ans_2E0 )
              = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) ) )
       => ( ! [V0x_2E0: u,V2l_2E0: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ F3_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) ) ) )
            <=> ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Efmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) ) ) ) ) ) ) ) ) )
         => ( ! [V0x_2E0: u,V2l_2E0: u,V1y_2E0: u,V3ans_2E0: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ F4_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3ans_2E0 ) ) ) )
              <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Efmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) ) ) ) ) ) ) )
                  & ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Efmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ A_27b @ V1y_2E0 ) ) ) ) )
                    = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Efmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3ans_2E0 ) ) ) ) ) )
           => ( ! [V0x_2E0: u,V2l_2E0: u,V1y_2E0: u,V3ans_2E0: u] :
                  ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3ans_2E0 ) ) ) )
                  = ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ F2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3ans_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ F3_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ F4_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3ans_2E0 ) ) ) ) ) )
             => ! [V0x_2E0: u,V1y_2E0: u,V2l_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ELET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Elist__rplacv__cn_2E3 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ A_27b @ V1y_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2l_2E0 ) @ ( s @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebt__rplacv__cn__ind,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u,F1_2E0: u] :
      ( ! [V12cn_2E0: u,V8l_2E0: u,V9w_2E0: u,V10z_2E0: u,V13m_2E0: u] :
          ( ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) @ ( s @ ( 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 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8l_2E0 ) ) ) @ ( s @ A_27a @ V9w_2E0 ) ) ) @ ( s @ A_27b @ V10z_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V13m_2E0 ) ) )
          = ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V9w_2E0 ) @ ( s @ A_27b @ V10z_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V13m_2E0 ) ) ) ) ) )
     => ( ! [V12cn_2E0: u,V9w_2E0: u,V10z_2E0: u,V11r_2E0: u,V14m_2E0: u] :
            ( ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) ) ) @ F1_2E0 ) @ ( s @ ( 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 ) ) ) @ ( s @ A_27a @ V9w_2E0 ) ) ) @ ( s @ A_27b @ V10z_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V11r_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V14m_2E0 ) ) )
            = ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V14m_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V9w_2E0 ) @ ( s @ A_27b @ V10z_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V11r_2E0 ) ) ) ) ) )
       => ! [V0P_2E0: u] :
            ( ( ! [V1cmp_2E0: u,V2x_2E0: u,V3y_2E0: u,V4cn_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V1cmp_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V4cn_2E0 ) ) ) )
              & ! [V5cmp_2E0: u,V6x_2E0: u,V7y_2E0: u,V8l_2E0: u,V9w_2E0: u,V10z_2E0: u,V11r_2E0: u,V12cn_2E0: u] :
                  ( ( ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ A_27a @ V9w_2E0 ) ) ) )
                        = mono_2Ec_2EternaryComparisons_2EGREATER )
                     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ A_27b @ V7y_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V11r_2E0 ) ) ) @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) @ ( s @ ( 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 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8l_2E0 ) ) ) @ ( s @ A_27a @ V9w_2E0 ) ) ) @ ( s @ A_27b @ V10z_2E0 ) ) ) ) ) ) )
                    & ( ( ( j_mono_2Etyop_2EternaryComparisons_2Eordering @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ A_27a @ V9w_2E0 ) ) ) )
                        = mono_2Ec_2EternaryComparisons_2ELESS )
                     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ A_27b @ V7y_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8l_2E0 ) ) ) @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) ) ) @ F1_2E0 ) @ ( s @ ( 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 ) ) ) @ ( s @ A_27a @ V9w_2E0 ) ) ) @ ( s @ A_27b @ V10z_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V11r_2E0 ) ) ) ) ) ) ) )
                 => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V5cmp_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ A_27b @ V7y_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V9w_2E0 ) @ ( s @ A_27b @ V10z_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V11r_2E0 ) ) ) ) ) @ ( s @ ( 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 ) ) ) ) ) )
           => ! [V15v_2E0: u,V16v1_2E0: u,V17v2_2E0: u,V18v3_2E0: u,V19v4_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V15v_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V16v1_2E0 ) @ ( s @ A_27b @ V17v2_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V18v3_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V19v4_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebt__rplacv__cn,axiom,
    ! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V10cn_2E0: u,V9l_2E0: u,V7w_2E0: u,V4z_2E0: u,V13m_2E0: u] :
          ( ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) @ ( s @ ( 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 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V9l_2E0 ) ) ) @ ( s @ A_27a @ V7w_2E0 ) ) ) @ ( s @ A_27b @ V4z_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V13m_2E0 ) ) )
          = ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V9l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V7w_2E0 ) @ ( s @ A_27b @ V4z_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V13m_2E0 ) ) ) ) ) )
     => ( ! [V10cn_2E0: u,V7w_2E0: u,V4z_2E0: u,V8r_2E0: u,V12m_2E0: u] :
            ( ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( 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 ) ) ) @ ( s @ A_27a @ V7w_2E0 ) ) ) @ ( s @ A_27b @ V4z_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8r_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V12m_2E0 ) ) )
            = ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V12m_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V7w_2E0 ) @ ( s @ A_27b @ V4z_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8r_2E0 ) ) ) ) ) )
       => ( ! [V0y_2E0: u,V1x_2E0: u,V2cn_2E0: u,V3cmp_2E0: u] :
              ( ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__rplacv__cn_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V3cmp_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V0y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V2cn_2E0 ) ) )
              = ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) )
          & ! [V4z_2E0: u,V5y_2E0: u,V6x_2E0: u,V7w_2E0: u,V8r_2E0: u,V9l_2E0: u,V10cn_2E0: u,V11cmp_2E0: u] :
              ( ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__rplacv__cn_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ A_27b @ V5y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V9l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V7w_2E0 ) @ ( s @ A_27b @ V4z_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8r_2E0 ) ) ) @ ( s @ ( 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 ) ) )
              = ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2EternaryComparisons_2Eordering__CASE_2E4 @ ( s @ tyop_2EternaryComparisons_2Eordering @ ( c_2Etoto_2Eapto_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ A_27a @ V7w_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__rplacv__cn_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ A_27b @ V5y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V9l_2E0 ) @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( 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 ) ) ) @ ( s @ A_27a @ V7w_2E0 ) ) ) @ ( s @ A_27b @ V4z_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8r_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eenumeral_2Enode_2E3 @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V9l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ A_27b @ V5y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8r_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__rplacv__cn_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V11cmp_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ A_27b @ V5y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V8r_2E0 ) @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) @ ( s @ ( 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 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V9l_2E0 ) ) ) @ ( s @ A_27a @ V7w_2E0 ) ) ) @ ( s @ A_27b @ V4z_2E0 ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Ebt__rplacv__thm,axiom,
    ! [A_27a: d,A_27b: d,F1_2E0: u,F2_2E0: u,F3_2E0: u,F4_2E0: u,F0_2E0: u] :
      ( ! [V5m_2E0: u] :
          ( ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( 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 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V5m_2E0 ) ) )
          = ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V5m_2E0 ) )
     => ( ! [V4ans_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ F2_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4ans_2E0 ) ) ) )
          <=> ( ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4ans_2E0 )
              = ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eenumeral_2Ent_2E0 ) ) )
       => ( ! [V1x_2E0: u,V0cmp_2E0: u,V3t_2E0: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ F3_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3t_2E0 ) ) ) )
            <=> ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EFMAPAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3t_2E0 ) ) ) ) ) ) ) ) ) )
         => ( ! [V1x_2E0: u,V0cmp_2E0: u,V3t_2E0: u,V2y_2E0: u,V4ans_2E0: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) @ F4_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3t_2E0 ) ) ) @ ( s @ A_27b @ V2y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4ans_2E0 ) ) ) )
              <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EFMAPAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3t_2E0 ) ) ) ) ) ) ) )
                  & ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EFMAPAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3t_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V2y_2E0 ) ) ) ) )
                    = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2EFMAPAL_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4ans_2E0 ) ) ) ) ) )
           => ( ! [V1x_2E0: u,V0cmp_2E0: u,V3t_2E0: u,V2y_2E0: u,V4ans_2E0: u] :
                  ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3t_2E0 ) ) ) @ ( s @ A_27b @ V2y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4ans_2E0 ) ) ) )
                  = ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ F2_2E0 ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4ans_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Etoto_2Etoto @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) @ F3_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3t_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) ) ) ) ) @ F4_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3t_2E0 ) ) ) @ ( s @ A_27b @ V2y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4ans_2E0 ) ) ) ) ) )
             => ! [V0cmp_2E0: u,V1x_2E0: u,V2y_2E0: u,V3t_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ELET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( 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 @ ( s @ ( 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 ) ) ) ) @ ( app_2E2 @ ( s @ ( 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 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3t_2E0 ) ) ) @ ( s @ A_27b @ V2y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Ebt__rplacv__cn_2E4 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V2y_2E0 ) ) ) @ ( s @ ( tyop_2Eenumeral_2Ebt @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3t_2E0 ) @ ( s @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2EFUN__fmap__thm,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V0f_2E0: u,V2x_2E0: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) )
     => ! [V0f_2E0: u,V1l_2E0: u] :
          ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Efmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUN__FMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efmapal_2Efmap__ORWL__thm,axiom,
    ! [A_27a: d,A_27b: d,V0cmp_2E0: u,V1l_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efmapal_2EORWL_2E3 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efmapal_2Efmap_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Efmapal_2Eincr__sort_2E2 @ ( s @ ( tyop_2Etoto_2Etoto @ A_27a ) @ V0cmp_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) ) ) ) ) ).

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