ITP001 Axioms: ITP049^4.ax
%------------------------------------------------------------------------------
% File : ITP049^4 : 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 : llist.ax [Gau19]
% : HL4049^4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 777 ( 319 unt; 281 typ; 0 def)
% Number of atoms : 1064 ( 693 equ; 16 cnn)
% Maximal formula atoms : 15 ( 1 avg)
% Number of connectives : 27446 ( 16 ~; 23 |; 157 &;26966 @)
% ( 90 <=>; 194 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 7 avg;26966 nst)
% Number of types : 6 ( 5 usr)
% Number of type conns : 431 ( 431 >; 0 *; 0 +; 0 <<)
% Number of symbols : 278 ( 276 usr; 108 con; 0-4 aty)
% Number of variables : 1881 ( 0 ^1798 !; 83 ?;1881 :)
% 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_2Enum_2Enum,type,
mono_2Etyop_2Enum_2Enum: $tType ).
thf(mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: $tType ).
thf(tyop_2Elist_2Elist,type,
tyop_2Elist_2Elist: d > d ).
thf(tyop_2Ellist_2Ellist,type,
tyop_2Ellist_2Ellist: d > d ).
thf(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: d ).
thf(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: d > d > d ).
thf(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: d ).
thf(tyop_2Eoption_2Eoption,type,
tyop_2Eoption_2Eoption: d > d ).
thf(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: d > 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_23_23_2E0,type,
c_2Epair_2E_23_23_2E0: u ).
thf(c_2Epair_2E_23_23_2E2,type,
c_2Epair_2E_23_23_2E2: du > du > u ).
thf(c_2Earithmetic_2E_2B_2E0,type,
c_2Earithmetic_2E_2B_2E0: u ).
thf(c_2Earithmetic_2E_2B_2E1,type,
c_2Earithmetic_2E_2B_2E1: du > u ).
thf(c_2Earithmetic_2E_2B_2E2,type,
c_2Earithmetic_2E_2B_2E2: du > 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_2Earithmetic_2E_2D_2E0,type,
c_2Earithmetic_2E_2D_2E0: u ).
thf(c_2Earithmetic_2E_2D_2E2,type,
c_2Earithmetic_2E_2D_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_2Enum_2E0_2E0,type,
c_2Enum_2E0_2E0: u ).
thf(c_2Eprim__rec_2E_3C_2E0,type,
c_2Eprim__rec_2E_3C_2E0: u ).
thf(c_2Eprim__rec_2E_3C_2E2,type,
c_2Eprim__rec_2E_3C_2E2: du > du > u ).
thf(c_2Earithmetic_2E_3C_3D_2E0,type,
c_2Earithmetic_2E_3C_3D_2E0: u ).
thf(c_2Earithmetic_2E_3C_3D_2E2,type,
c_2Earithmetic_2E_3C_3D_2E2: du > du > u ).
thf(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0: u ).
thf(c_2Emin_2E_3D_2E1,type,
c_2Emin_2E_3D_2E1: du > 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_2Ebool_2E_3F_21_2E0,type,
c_2Ebool_2E_3F_21_2E0: u ).
thf(c_2Ebool_2E_3F_21_2E1,type,
c_2Ebool_2E_3F_21_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_2E1,type,
c_2Elist_2EAPPEND_2E1: du > u ).
thf(c_2Elist_2EAPPEND_2E2,type,
c_2Elist_2EAPPEND_2E2: du > du > u ).
thf(c_2Earithmetic_2EBIT1_2E0,type,
c_2Earithmetic_2EBIT1_2E0: u ).
thf(c_2Earithmetic_2EBIT1_2E1,type,
c_2Earithmetic_2EBIT1_2E1: du > u ).
thf(c_2Earithmetic_2EBIT2_2E0,type,
c_2Earithmetic_2EBIT2_2E0: u ).
thf(c_2Earithmetic_2EBIT2_2E1,type,
c_2Earithmetic_2EBIT2_2E1: du > u ).
thf(c_2Epred__set_2ECHOICE_2E0,type,
c_2Epred__set_2ECHOICE_2E0: u ).
thf(c_2Epred__set_2ECHOICE_2E1,type,
c_2Epred__set_2ECHOICE_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_2E1,type,
c_2Elist_2ECONS_2E1: du > u ).
thf(c_2Elist_2ECONS_2E2,type,
c_2Elist_2ECONS_2E2: du > du > u ).
thf(c_2Epred__set_2EDIFF_2E0,type,
c_2Epred__set_2EDIFF_2E0: u ).
thf(c_2Epred__set_2EDIFF_2E2,type,
c_2Epred__set_2EDIFF_2E2: du > du > u ).
thf(c_2Elist_2EDROP_2E0,type,
c_2Elist_2EDROP_2E0: u ).
thf(c_2Elist_2EDROP_2E2,type,
c_2Elist_2EDROP_2E2: du > du > u ).
thf(c_2Elist_2EEL_2E0,type,
c_2Elist_2EEL_2E0: u ).
thf(c_2Elist_2EEL_2E2,type,
c_2Elist_2EEL_2E2: du > du > u ).
thf(c_2Epred__set_2EEMPTY_2E0,type,
c_2Epred__set_2EEMPTY_2E0: u ).
thf(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: u ).
thf(c_2Epair_2EFST_2E0,type,
c_2Epair_2EFST_2E0: u ).
thf(c_2Earithmetic_2EFUNPOW_2E0,type,
c_2Earithmetic_2EFUNPOW_2E0: u ).
thf(c_2Earithmetic_2EFUNPOW_2E3,type,
c_2Earithmetic_2EFUNPOW_2E3: du > du > du > u ).
thf(c_2Elist_2EGENLIST_2E0,type,
c_2Elist_2EGENLIST_2E0: u ).
thf(c_2Elist_2EGENLIST_2E2,type,
c_2Elist_2EGENLIST_2E2: du > du > 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_2Elist_2EHD_2E0,type,
c_2Elist_2EHD_2E0: u ).
thf(c_2Elist_2EHD_2E1,type,
c_2Elist_2EHD_2E1: du > u ).
thf(c_2Ecombin_2EI_2E0,type,
c_2Ecombin_2EI_2E0: u ).
thf(c_2Eoption_2EIS__SOME_2E0,type,
c_2Eoption_2EIS__SOME_2E0: u ).
thf(c_2Eoption_2EIS__SOME_2E1,type,
c_2Eoption_2EIS__SOME_2E1: du > u ).
thf(c_2Ecombin_2EK_2E0,type,
c_2Ecombin_2EK_2E0: u ).
thf(c_2Ellist_2ELAPPEND_2E0,type,
c_2Ellist_2ELAPPEND_2E0: u ).
thf(c_2Ellist_2ELAPPEND_2E2,type,
c_2Ellist_2ELAPPEND_2E2: du > du > u ).
thf(c_2Ellist_2ELCONS_2E0,type,
c_2Ellist_2ELCONS_2E0: u ).
thf(c_2Ellist_2ELCONS_2E2,type,
c_2Ellist_2ELCONS_2E2: du > du > u ).
thf(c_2Ellist_2ELDROP_2E0,type,
c_2Ellist_2ELDROP_2E0: u ).
thf(c_2Ellist_2ELDROP_2E1,type,
c_2Ellist_2ELDROP_2E1: du > u ).
thf(c_2Ellist_2ELDROP_2E2,type,
c_2Ellist_2ELDROP_2E2: du > du > u ).
thf(c_2Elist_2ELENGTH_2E0,type,
c_2Elist_2ELENGTH_2E0: u ).
thf(c_2Elist_2ELENGTH_2E1,type,
c_2Elist_2ELENGTH_2E1: 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_2Ellist_2ELFILTER_2E0,type,
c_2Ellist_2ELFILTER_2E0: u ).
thf(c_2Ellist_2ELFILTER_2E2,type,
c_2Ellist_2ELFILTER_2E2: du > du > u ).
thf(c_2Ellist_2ELFINITE_2E0,type,
c_2Ellist_2ELFINITE_2E0: u ).
thf(c_2Ellist_2ELFINITE_2E1,type,
c_2Ellist_2ELFINITE_2E1: du > u ).
thf(c_2Ellist_2ELFLATTEN_2E0,type,
c_2Ellist_2ELFLATTEN_2E0: u ).
thf(c_2Ellist_2ELFLATTEN_2E1,type,
c_2Ellist_2ELFLATTEN_2E1: du > u ).
thf(c_2Ellist_2ELGENLIST_2E0,type,
c_2Ellist_2ELGENLIST_2E0: u ).
thf(c_2Ellist_2ELGENLIST_2E2,type,
c_2Ellist_2ELGENLIST_2E2: du > du > u ).
thf(c_2Ellist_2ELHD_2E0,type,
c_2Ellist_2ELHD_2E0: u ).
thf(c_2Ellist_2ELHD_2E1,type,
c_2Ellist_2ELHD_2E1: du > u ).
thf(c_2Ellist_2ELLENGTH_2E0,type,
c_2Ellist_2ELLENGTH_2E0: u ).
thf(c_2Ellist_2ELLENGTH_2E1,type,
c_2Ellist_2ELLENGTH_2E1: du > u ).
thf(c_2Ellist_2ELMAP_2E0,type,
c_2Ellist_2ELMAP_2E0: u ).
thf(c_2Ellist_2ELMAP_2E2,type,
c_2Ellist_2ELMAP_2E2: du > du > u ).
thf(c_2Ellist_2ELNIL_2E0,type,
c_2Ellist_2ELNIL_2E0: u ).
thf(c_2Ellist_2ELNTH_2E0,type,
c_2Ellist_2ELNTH_2E0: u ).
thf(c_2Ellist_2ELNTH_2E1,type,
c_2Ellist_2ELNTH_2E1: du > u ).
thf(c_2Ellist_2ELNTH_2E2,type,
c_2Ellist_2ELNTH_2E2: du > du > u ).
thf(c_2Ellist_2ELPREFIX_2E0,type,
c_2Ellist_2ELPREFIX_2E0: u ).
thf(c_2Ellist_2ELPREFIX_2E2,type,
c_2Ellist_2ELPREFIX_2E2: du > du > u ).
thf(c_2Ellist_2ELREPEAT_2E0,type,
c_2Ellist_2ELREPEAT_2E0: u ).
thf(c_2Ellist_2ELREPEAT_2E1,type,
c_2Ellist_2ELREPEAT_2E1: du > u ).
thf(c_2Ellist_2ELTAKE_2E0,type,
c_2Ellist_2ELTAKE_2E0: u ).
thf(c_2Ellist_2ELTAKE_2E2,type,
c_2Ellist_2ELTAKE_2E2: du > du > u ).
thf(c_2Ellist_2ELTL_2E0,type,
c_2Ellist_2ELTL_2E0: u ).
thf(c_2Ellist_2ELTL_2E1,type,
c_2Ellist_2ELTL_2E1: du > u ).
thf(c_2Ellist_2ELTL__HD_2E0,type,
c_2Ellist_2ELTL__HD_2E0: u ).
thf(c_2Ellist_2ELTL__HD_2E1,type,
c_2Ellist_2ELTL__HD_2E1: du > u ).
thf(c_2Ellist_2ELUNFOLD_2E0,type,
c_2Ellist_2ELUNFOLD_2E0: u ).
thf(c_2Ellist_2ELUNFOLD_2E1,type,
c_2Ellist_2ELUNFOLD_2E1: du > u ).
thf(c_2Ellist_2ELUNFOLD_2E2,type,
c_2Ellist_2ELUNFOLD_2E2: du > du > u ).
thf(c_2Ellist_2ELUNZIP_2E0,type,
c_2Ellist_2ELUNZIP_2E0: u ).
thf(c_2Ellist_2ELUNZIP_2E1,type,
c_2Ellist_2ELUNZIP_2E1: du > u ).
thf(c_2Ellist_2ELZIP_2E0,type,
c_2Ellist_2ELZIP_2E0: u ).
thf(c_2Ellist_2ELZIP_2E1,type,
c_2Ellist_2ELZIP_2E1: du > u ).
thf(c_2Earithmetic_2EMOD_2E0,type,
c_2Earithmetic_2EMOD_2E0: u ).
thf(c_2Earithmetic_2EMOD_2E2,type,
c_2Earithmetic_2EMOD_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_2Elist_2ENULL_2E0,type,
c_2Elist_2ENULL_2E0: u ).
thf(c_2Elist_2ENULL_2E1,type,
c_2Elist_2ENULL_2E1: du > u ).
thf(c_2Earithmetic_2ENUMERAL_2E0,type,
c_2Earithmetic_2ENUMERAL_2E0: u ).
thf(c_2Earithmetic_2ENUMERAL_2E1,type,
c_2Earithmetic_2ENUMERAL_2E1: du > u ).
thf(c_2Eoption_2EOPTION__BIND_2E0,type,
c_2Eoption_2EOPTION__BIND_2E0: u ).
thf(c_2Eoption_2EOPTION__BIND_2E2,type,
c_2Eoption_2EOPTION__BIND_2E2: du > du > u ).
thf(c_2Eoption_2EOPTION__JOIN_2E0,type,
c_2Eoption_2EOPTION__JOIN_2E0: u ).
thf(c_2Eoption_2EOPTION__JOIN_2E1,type,
c_2Eoption_2EOPTION__JOIN_2E1: du > u ).
thf(c_2Eoption_2EOPTION__MAP_2E0,type,
c_2Eoption_2EOPTION__MAP_2E0: u ).
thf(c_2Eoption_2EOPTION__MAP_2E2,type,
c_2Eoption_2EOPTION__MAP_2E2: du > du > u ).
thf(c_2Eprim__rec_2EPRE_2E0,type,
c_2Eprim__rec_2EPRE_2E0: u ).
thf(c_2Epair_2ESND_2E0,type,
c_2Epair_2ESND_2E0: 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_2Epred__set_2ESUBSET_2E0,type,
c_2Epred__set_2ESUBSET_2E0: u ).
thf(c_2Epred__set_2ESUBSET_2E2,type,
c_2Epred__set_2ESUBSET_2E2: du > du > u ).
thf(c_2Enum_2ESUC_2E0,type,
c_2Enum_2ESUC_2E0: u ).
thf(c_2Enum_2ESUC_2E1,type,
c_2Enum_2ESUC_2E1: du > u ).
thf(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: u ).
thf(c_2Elist_2ETAKE_2E0,type,
c_2Elist_2ETAKE_2E0: u ).
thf(c_2Elist_2ETAKE_2E2,type,
c_2Elist_2ETAKE_2E2: du > du > u ).
thf(c_2Eoption_2ETHE_2E0,type,
c_2Eoption_2ETHE_2E0: u ).
thf(c_2Eoption_2ETHE_2E1,type,
c_2Eoption_2ETHE_2E1: du > u ).
thf(c_2Elist_2ETL_2E0,type,
c_2Elist_2ETL_2E0: u ).
thf(c_2Elist_2ETL_2E1,type,
c_2Elist_2ETL_2E1: du > u ).
thf(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
c_2Ebool_2ETYPE__DEFINITION_2E0: u ).
thf(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
c_2Ebool_2ETYPE__DEFINITION_2E2: du > du > u ).
thf(c_2Epair_2EUNCURRY_2E0,type,
c_2Epair_2EUNCURRY_2E0: u ).
thf(c_2Epair_2EUNCURRY_2E1,type,
c_2Epair_2EUNCURRY_2E1: du > u ).
thf(c_2Epred__set_2EUNION_2E0,type,
c_2Epred__set_2EUNION_2E0: u ).
thf(c_2Epred__set_2EUNION_2E2,type,
c_2Epred__set_2EUNION_2E2: du > du > u ).
thf(c_2Earithmetic_2EZERO_2E0,type,
c_2Earithmetic_2EZERO_2E0: 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_2Eset__relation_2Edomain_2E0,type,
c_2Eset__relation_2Edomain_2E0: u ).
thf(c_2Eset__relation_2Edomain_2E1,type,
c_2Eset__relation_2Edomain_2E1: du > u ).
thf(c_2Ellist_2Eevery_2E0,type,
c_2Ellist_2Eevery_2E0: u ).
thf(c_2Ellist_2Eevery_2E2,type,
c_2Ellist_2Eevery_2E2: du > du > u ).
thf(c_2Ellist_2Eexists_2E0,type,
c_2Ellist_2Eexists_2E0: u ).
thf(c_2Ellist_2Eexists_2E2,type,
c_2Ellist_2Eexists_2E2: du > du > u ).
thf(c_2Eset__relation_2Efinite__prefixes_2E0,type,
c_2Eset__relation_2Efinite__prefixes_2E0: u ).
thf(c_2Eset__relation_2Efinite__prefixes_2E2,type,
c_2Eset__relation_2Efinite__prefixes_2E2: du > du > u ).
thf(c_2Ellist_2EfromList_2E0,type,
c_2Ellist_2EfromList_2E0: u ).
thf(c_2Ellist_2EfromList_2E1,type,
c_2Ellist_2EfromList_2E1: du > u ).
thf(c_2Elist_2EisPREFIX_2E0,type,
c_2Elist_2EisPREFIX_2E0: u ).
thf(c_2Elist_2EisPREFIX_2E2,type,
c_2Elist_2EisPREFIX_2E2: du > du > u ).
thf(c_2Eset__relation_2Elinear__order_2E0,type,
c_2Eset__relation_2Elinear__order_2E0: u ).
thf(c_2Eset__relation_2Elinear__order_2E2,type,
c_2Eset__relation_2Elinear__order_2E2: du > du > u ).
thf(c_2Ellist_2Elinear__order__to__list__f_2E0,type,
c_2Ellist_2Elinear__order__to__list__f_2E0: u ).
thf(c_2Ellist_2Elinear__order__to__list__f_2E1,type,
c_2Ellist_2Elinear__order__to__list__f_2E1: du > u ).
thf(c_2Ellist_2Ellength__rel_2E0,type,
c_2Ellist_2Ellength__rel_2E0: u ).
thf(c_2Ellist_2Ellength__rel_2E2,type,
c_2Ellist_2Ellength__rel_2E2: du > du > u ).
thf(c_2Ellist_2Ellist__abs_2E0,type,
c_2Ellist_2Ellist__abs_2E0: u ).
thf(c_2Ellist_2Ellist__abs_2E1,type,
c_2Ellist_2Ellist__abs_2E1: du > u ).
thf(c_2Ellist_2Ellist__rep_2E0,type,
c_2Ellist_2Ellist__rep_2E0: u ).
thf(c_2Ellist_2Ellist__rep_2E1,type,
c_2Ellist_2Ellist__rep_2E1: du > u ).
thf(c_2Ellist_2Ellist__rep_2E2,type,
c_2Ellist_2Ellist__rep_2E2: du > du > u ).
thf(c_2Ellist_2Elrep__ok_2E0,type,
c_2Ellist_2Elrep__ok_2E0: u ).
thf(c_2Ellist_2Elrep__ok_2E1,type,
c_2Ellist_2Elrep__ok_2E1: du > u ).
thf(c_2Eset__relation_2Eminimal__elements_2E0,type,
c_2Eset__relation_2Eminimal__elements_2E0: u ).
thf(c_2Eset__relation_2Eminimal__elements_2E2,type,
c_2Eset__relation_2Eminimal__elements_2E2: du > du > 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_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_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_2Eset__relation_2Erange_2E0,type,
c_2Eset__relation_2Erange_2E0: u ).
thf(c_2Eset__relation_2Erange_2E1,type,
c_2Eset__relation_2Erange_2E1: du > u ).
thf(c_2Eset__relation_2Errestrict_2E0,type,
c_2Eset__relation_2Errestrict_2E0: u ).
thf(c_2Eset__relation_2Errestrict_2E2,type,
c_2Eset__relation_2Errestrict_2E2: du > du > u ).
thf(c_2Ellist_2EtoList_2E0,type,
c_2Ellist_2EtoList_2E0: u ).
thf(c_2Ellist_2EtoList_2E1,type,
c_2Ellist_2EtoList_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_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29: ( $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum,type,
mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).
thf(mono_2Ec_2Earithmetic_2E_2B,type,
mono_2Ec_2Earithmetic_2E_2B: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2E_2D,type,
mono_2Ec_2Earithmetic_2E_2D: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2E_2F_5C,type,
mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(mono_2Ec_2Enum_2E0,type,
mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Eprim__rec_2E_3C,type,
mono_2Ec_2Eprim__rec_2E_3C: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Earithmetic_2E_3C_3D,type,
mono_2Ec_2Earithmetic_2E_3C_3D: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(mono_2Ec_2Emin_2E_40_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Emin_2E_40_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2EBIT1,type,
mono_2Ec_2Earithmetic_2EBIT1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2EBIT2,type,
mono_2Ec_2Earithmetic_2EBIT2: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).
thf(mono_2Ec_2Ebool_2EF,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(mono_2Ec_2Earithmetic_2EMOD,type,
mono_2Ec_2Earithmetic_2EMOD: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).
thf(mono_2Ec_2Earithmetic_2ENUMERAL,type,
mono_2Ec_2Earithmetic_2ENUMERAL: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Eoption_2EOPTION__MAP_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Eoption_2EOPTION__MAP_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).
thf(mono_2Ec_2Eprim__rec_2EPRE,type,
mono_2Ec_2Eprim__rec_2EPRE: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).
thf(mono_2Ec_2Enum_2ESUC,type,
mono_2Ec_2Enum_2ESUC: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2ET,type,
mono_2Ec_2Ebool_2ET: $o ).
thf(mono_2Ec_2Eoption_2ETHE_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Eoption_2ETHE_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2EZERO,type,
mono_2Ec_2Earithmetic_2EZERO: mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2E_5C_2F,type,
mono_2Ec_2Ebool_2E_5C_2F: $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_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29: ( $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > u ).
thf(i_mono_2Etyop_2Enum_2Enum,type,
i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).
thf(i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > 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_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29: du > $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29: du > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29: du > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Enum_2Enum > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29: du > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).
thf(j_mono_2Etyop_2Enum_2Enum,type,
j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).
thf(j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: du > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).
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_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0_2E0: u] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ) )
= ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ 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_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29,axiom,
! [V0: $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ 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_23_23_2E2_2Emono_2EA_27b_20mono_2EA_27a_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( c_2Epair_2E_23_23_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) ) @ c_2Epair_2E_23_23_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_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_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_27c_20mono_2EA_27b,axiom,
! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27c @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2Etyop_2Ellist_2Ellist_28A_27b_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ A_27a @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: d,X0_2E0: u,X1: $o] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ X0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) ) ) ).
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_2Emin_2E_3D_2E1_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Emin_2E_3D_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_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_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Ellist_2Ellist_28A_27b_29_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Elist_2EAPPEND_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2EAPPEND_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2EAPPEND_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ 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 @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2EAPPEND_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epred__set_2ECHOICE_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ A_27a @ ( c_2Epred__set_2ECHOICE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ A_27a ) @ c_2Epred__set_2ECHOICE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
! [A_27a: d,X0: $o,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Ellist_2Ellist_28A_27b_29,axiom,
! [A_27b: d,X0: $o,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: d,X0: $o,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29,axiom,
! [A_27a: d,X0: $o,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Ellist_2Ellist_28A_27a_29_29,axiom,
! [A_27a: d,X0: $o,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29_2CA_27a_29_29,axiom,
! [A_27a: d,X0: $o,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29,axiom,
! [A_27a: d,X0: $o,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ X2_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Elist_2ECONS_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2ECONS_2E1 @ ( s @ A_27a @ X0_2E0 ) ) )
= ( 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 ) ) ) ) ).
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(arityeq1_2Ec_2Elist_2ECONS_2E1_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( c_2Elist_2ECONS_2E1 @ ( s @ A_27b @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27b ) ) ) @ c_2Elist_2ECONS_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Elist_2ECONS_2E1_2Emono_2EA_27c,axiom,
! [A_27c: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Elist_2Elist @ A_27c ) ) @ ( c_2Elist_2ECONS_2E1 @ ( s @ A_27c @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Elist_2Elist @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Elist_2Elist @ A_27c ) ) ) @ c_2Elist_2ECONS_2E0 ) @ ( s @ A_27c @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDIFF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_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 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EDIFF_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Elist_2EDROP_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( 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 @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2EDROP_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ A_27a @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27a ) ) @ c_2Elist_2EEL_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Earithmetic_2EFUNPOW_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum,X2_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Earithmetic_2EFUNPOW_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ c_2Earithmetic_2EFUNPOW_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Earithmetic_2EFUNPOW_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Ellist_2Ellist_28A_27a_29_29,axiom,
! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum,X2_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Earithmetic_2EFUNPOW_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ X0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) ) ) @ c_2Earithmetic_2EFUNPOW_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Earithmetic_2EFUNPOW_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum,X2_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( c_2Earithmetic_2EFUNPOW_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ X0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) ) @ c_2Earithmetic_2EFUNPOW_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X2_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ X0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) )
= ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2EGENLIST_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) ) ).
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_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2EGSPEC_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Elist_2EHD_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ A_27a @ ( c_2Elist_2EHD_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27a ) @ c_2Elist_2EHD_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Eoption_2EIS__SOME_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ c_2Eoption_2EIS__SOME_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELAPPEND_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ c_2Ellist_2ELAPPEND_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELAPPEND_2E2_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ c_2Ellist_2ELAPPEND_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ c_2Ellist_2ELCONS_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27b @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ c_2Ellist_2ELCONS_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2EA_27c,axiom,
! [A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27c @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( tyop_2Ellist_2Ellist @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( tyop_2Ellist_2Ellist @ A_27c ) ) ) @ c_2Ellist_2ELCONS_2E0 ) @ ( s @ A_27c @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2EA_27d,axiom,
! [A_27d: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27d ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27d @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27d ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27d ) @ ( tyop_2Ellist_2Ellist @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27d ) @ ( tyop_2Ellist_2Ellist @ A_27d ) ) ) @ c_2Ellist_2ELCONS_2E0 ) @ ( s @ A_27d @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27d ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) ) @ c_2Ellist_2ELCONS_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27c_29,axiom,
! [A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27c ) ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27c ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27c ) ) @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27c ) ) @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27c ) ) ) ) @ c_2Ellist_2ELCONS_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27c ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27d_29,axiom,
! [A_27d: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27d ) ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27d ) @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27d ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27d ) ) @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27d ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27d ) ) @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27d ) ) ) ) @ c_2Ellist_2ELCONS_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27d ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27d ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELCONS_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_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ c_2Ellist_2ELCONS_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Ellist_2ELDROP_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( c_2Ellist_2ELDROP_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) ) @ c_2Ellist_2ELDROP_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELDROP_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) ) @ c_2Ellist_2ELDROP_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELDROP_2E2_2Emono_2EA_27b,axiom,
! [A_27b: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) ) @ c_2Ellist_2ELDROP_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELDROP_2E2_2Emono_2EA_27c,axiom,
! [A_27c: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27c ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27c ) ) ) ) @ c_2Ellist_2ELDROP_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Enum_2Enum ) @ c_2Elist_2ELENGTH_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29_2CA_27a_29_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) @ ( c_2Ebool_2ELET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) ) ) @ c_2Ebool_2ELET_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2Ctyop_2Ellist_2Ellist_28A_27b_29_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2Ctyop_2Ellist_2Ellist_28A_27b_29_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Ebool_2ELET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) ) @ c_2Ebool_2ELET_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELFILTER_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELFILTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ c_2Ellist_2ELFILTER_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELFILTER_2E2_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELFILTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ c_2Ellist_2ELFILTER_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Ellist_2ELFINITE_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Ellist_2ELFINITE_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ellist_2ELFINITE_2E1_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ tyop_2Emin_2Ebool ) @ c_2Ellist_2ELFINITE_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ellist_2ELFLATTEN_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELFLATTEN_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ c_2Ellist_2ELFLATTEN_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Ellist_2ELFLATTEN_2E1_2Emono_2EA_27c,axiom,
! [A_27c: d,X0_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( c_2Ellist_2ELFLATTEN_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27c ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27c ) ) @ ( tyop_2Ellist_2Ellist @ A_27c ) ) @ c_2Ellist_2ELFLATTEN_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27c ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Ellist_2ELFLATTEN_2E1_2Emono_2EA_27d,axiom,
! [A_27d: d,X0_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27d ) @ ( c_2Ellist_2ELFLATTEN_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27d ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27d ) ) @ ( tyop_2Ellist_2Ellist @ A_27d ) ) @ c_2Ellist_2ELFLATTEN_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27d ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELGENLIST_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ X1 ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ c_2Ellist_2ELGENLIST_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ X1 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELGENLIST_2E2_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u,X1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ X1 ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ c_2Ellist_2ELGENLIST_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ X1 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ellist_2ELHD_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Ellist_2ELHD_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Ellist_2ELHD_2E1_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ c_2Ellist_2ELHD_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Ellist_2ELHD_2E1_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ c_2Ellist_2ELHD_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Ellist_2ELLENGTH_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ c_2Ellist_2ELLENGTH_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ellist_2ELLENGTH_2E1_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ c_2Ellist_2ELLENGTH_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ c_2Ellist_2ELMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELMAP_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ c_2Ellist_2ELMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELMAP_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ c_2Ellist_2ELMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELMAP_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ c_2Ellist_2ELMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Ellist_2ELNTH_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Ellist_2ELNTH_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ c_2Ellist_2ELNTH_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELNTH_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ c_2Ellist_2ELNTH_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELNTH_2E2_2Emono_2EA_27b,axiom,
! [A_27b: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ c_2Ellist_2ELNTH_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELNTH_2E2_2Emono_2EA_27c,axiom,
! [A_27c: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( tyop_2Eoption_2Eoption @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( tyop_2Eoption_2Eoption @ A_27c ) ) ) @ c_2Ellist_2ELNTH_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELPREFIX_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELPREFIX_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Ellist_2ELPREFIX_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELPREFIX_2E2_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELPREFIX_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2Ellist_2ELPREFIX_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ellist_2ELREPEAT_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELREPEAT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ c_2Ellist_2ELREPEAT_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELTAKE_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ c_2Ellist_2ELTAKE_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELTAKE_2E2_2Emono_2EA_27b,axiom,
! [A_27b: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) ) ) @ c_2Ellist_2ELTAKE_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELTAKE_2E2_2Emono_2EA_27c,axiom,
! [A_27c: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27c ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27c ) ) ) ) @ c_2Ellist_2ELTAKE_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Ellist_2ELTL_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ c_2Ellist_2ELTL_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Ellist_2ELTL_2E1_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ c_2Ellist_2ELTL_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Ellist_2ELTL_2E1_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) ) @ c_2Ellist_2ELTL_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Ellist_2ELTL__HD_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( c_2Ellist_2ELTL__HD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ c_2Ellist_2ELTL__HD_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELUNFOLD_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ c_2Ellist_2ELUNFOLD_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Ellist_2ELUNFOLD_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELUNFOLD_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ c_2Ellist_2ELUNFOLD_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELUNFOLD_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ c_2Ellist_2ELUNFOLD_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELUNFOLD_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) ) @ X0_2E0 ) @ ( s @ A_27c @ X1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ c_2Ellist_2ELUNFOLD_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) ) @ X0_2E0 ) ) ) @ ( s @ A_27c @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELUNFOLD_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ X0_2E0 ) @ ( s @ A_27c @ X1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ c_2Ellist_2ELUNFOLD_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ X0_2E0 ) ) ) @ ( s @ A_27c @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELUNFOLD_2E2_2Emono_2EA_27a_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ c_2Ellist_2ELUNFOLD_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELUNFOLD_2E2_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ X0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ c_2Ellist_2ELUNFOLD_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ellist_2ELUNZIP_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Ellist_2ELUNZIP_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ c_2Ellist_2ELUNZIP_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Ellist_2ELZIP_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ellist_2ELZIP_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ c_2Ellist_2ELZIP_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Elist_2ENULL_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2ENULL_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Elist_2ENULL_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2EOPTION__BIND_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ c_2Eoption_2EOPTION__BIND_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2CA_27a_29_20mono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( c_2Eoption_2EOPTION__BIND_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) ) @ c_2Eoption_2EOPTION__BIND_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2EA_27a_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2EOPTION__BIND_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ c_2Eoption_2EOPTION__BIND_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2EOPTION__BIND_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) ) @ c_2Eoption_2EOPTION__BIND_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2CA_27a_29_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( c_2Eoption_2EOPTION__BIND_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) ) @ c_2Eoption_2EOPTION__BIND_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( c_2Eoption_2EOPTION__BIND_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ c_2Eoption_2EOPTION__BIND_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Eoption_2EOPTION__JOIN_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Eoption_2EOPTION__JOIN_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Eoption_2EOPTION__JOIN_2E1_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ c_2Eoption_2EOPTION__JOIN_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Eoption_2EOPTION__MAP_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_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
! [A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27c_29_20mono_2Etyop_2Elist_2Elist_28A_27c_29,axiom,
! [A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27c ) ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Elist_2Elist @ A_27c ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27c ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27c ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Elist_2Elist @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27c ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27c ) ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Elist_2Elist @ A_27c ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27c ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Ellist_2Ellist_28A_27a_29_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Ellist_2Ellist_28A_27b_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2CA_27a_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2CA_27a_29_20mono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2CA_27a_29_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A_27a @ 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_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Ellist_2Ellist_28A_27b_29,axiom,
! [A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29,axiom,
! [A_27b: d,A_27c: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29_2CA_27a_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2CA_27a_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ 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 @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2ESUBSET_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Elist_2ETAKE_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ETAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( 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 @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2ETAKE_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ A_27a @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ A_27a ) @ c_2Eoption_2ETHE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Eoption_2ETHE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ c_2Eoption_2ETHE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2Etyop_2Ellist_2Ellist_28tyop_2Ellist_2Ellist_28A_27a_29_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ c_2Eoption_2ETHE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Elist_2ETL_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ETL_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Elist_2ETL_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28A_27a_29_29_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ETYPE__DEFINITION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2ETYPE__DEFINITION_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2EUNCURRY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27b_20mono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ c_2Epair_2EUNCURRY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27c_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ c_2Epair_2EUNCURRY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2Etyop_2Ellist_2Ellist_28A_27b_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2Ctyop_2Ellist_2Ellist_28A_27b_29_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) ) @ c_2Epair_2EUNCURRY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_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 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EUNION_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Eset__relation_2Edomain_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Edomain_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ 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 @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Eset__relation_2Edomain_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2Eevery_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eevery_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Ellist_2Eevery_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2Eevery_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eevery_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Ellist_2Eevery_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2Eexists_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Ellist_2Eexists_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Eset__relation_2Efinite__prefixes_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eset__relation_2Efinite__prefixes_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ 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 @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Eset__relation_2Efinite__prefixes_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ellist_2EfromList_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ c_2Ellist_2EfromList_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Elist_2EisPREFIX_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EisPREFIX_2E2 @ ( s @ ( tyop_2Elist_2Elist @ 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_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Elist_2EisPREFIX_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Eset__relation_2Elinear__order_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eset__relation_2Elinear__order_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ 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 @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Eset__relation_2Elinear__order_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ellist_2Elinear__order__to__list__f_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) @ ( c_2Ellist_2Elinear__order__to__list__f_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) ) @ c_2Ellist_2Elinear__order__to__list__f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2Ellength__rel_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Ellength__rel_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ c_2Ellist_2Ellength__rel_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) ) ) @ X1 ) ) ).
thf(arityeq1_2Ec_2Ellist_2Ellist__abs_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2Ellist__abs_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ c_2Ellist_2Ellist__abs_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Ellist_2Ellist__rep_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Ellist_2Ellist__rep_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ c_2Ellist_2Ellist__rep_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2Ellist__rep_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2Ellist__rep_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ c_2Ellist_2Ellist__rep_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ellist_2Elrep__ok_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Elrep__ok_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ c_2Ellist_2Elrep__ok_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ellist_2Elrep__ok_2E1_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Elrep__ok_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ c_2Ellist_2Elrep__ok_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Eset__relation_2Eminimal__elements_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Eminimal__elements_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( 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 @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Eset__relation_2Eminimal__elements_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) ) ) @ c_2Ecombin_2Eo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Ellist_2Ellist_28A_27b_29_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) ) @ c_2Ecombin_2Eo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) ) @ c_2Ecombin_2Eo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27b ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) ) @ c_2Ecombin_2Eo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27b ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: d,X0: $o > $o,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ X0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_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 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Ecombin_2Eo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ X0 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ X1 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) ) @ c_2Ecombin_2Eo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ X1 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ X1 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ c_2Ecombin_2Eo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ X1 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) ) ) @ c_2Ecombin_2Eo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Ellist_2Ellist_28A_27a_29_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2CA_27a_29_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: d,X0_2E0: u,X1: $o,X2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ 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 @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ X2_2E0 ) ) ) ) ) ).
thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Ellist_2Ellist_28A_27a_29_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: d,X0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ X0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ X0 ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Ellist_2Ellist_28A_27b_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1: $o,X2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ 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 @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ X2_2E0 ) ) ) ) ) ).
thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ X2_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27b_29_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ 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_2Ellist_2Ellist @ A_27b ) ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ ( tyop_2Ellist_2Ellist @ 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_2Ellist_2Ellist @ A_27b ) ) ) @ ( tyop_2Ellist_2Ellist @ 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_2Ellist_2Ellist @ A_27b ) ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( 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_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29_20mono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Eset__relation_2Erange_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Erange_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ 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 @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Eset__relation_2Erange_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Eset__relation_2Errestrict_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Errestrict_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Eset__relation_2Errestrict_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Ellist_2EtoList_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2EtoList_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Ellist_2EtoList_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Ellist_2EtoList_2E1_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( c_2Ellist_2EtoList_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) ) @ c_2Ellist_2EtoList_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ 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_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,axiom,
! [V0: $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1: $o] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ V0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Emin_2E_40_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 @ mono_2Ec_2Emin_2E_40_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ c_2Emin_2E_40_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Emin_2E_40_2Emono_2Etyop_2Enum_2Enum @ V0 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( c_2Emin_2E_40_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29 @ mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
! [V0: $o,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V2: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V0 @ V1 @ V2 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V1 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V2 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ c_2Eoption_2ENONE_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Eoption_2EOPTION__MAP_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ mono_2Ec_2Eoption_2EOPTION__MAP_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( mono_2Ec_2Eoption_2EOPTION__MAP_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Eoption_2ESOME_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ c_2Eoption_2ESOME_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ V0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Eoption_2ETHE_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 @ mono_2Ec_2Eoption_2ETHE_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ c_2Eoption_2ETHE_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Eoption_2ETHE_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Eoption_2ETHE_2Emono_2Etyop_2Enum_2Enum @ V0 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V0 ) ) ) ) ) ).
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_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,axiom,
! [V0: $o > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1: $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(thm_2Ellist_2Elrep__ok__def,axiom,
! [A_27a: d,F0: mono_2Etyop_2Enum_2Enum > $o] :
( ! [V6x: mono_2Etyop_2Enum_2Enum] :
( ( F0 @ V6x )
<=> ( V6x = mono_2Ec_2Enum_2E0 ) )
=> ! [V0x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Elrep__ok_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V0x_2E0 ) ) ) )
<=> ? [V1lrep__ok_27_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V1lrep__ok_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V0x_2E0 ) ) ) )
& ! [V2a0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V1lrep__ok_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V2a0_2E0 ) ) ) )
=> ( ! [V3x: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V2a0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3x ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
| ? [V4h_2E0: u,V5t_2E0: u] :
( ! [V6x: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V2a0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6x ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F0 @ V6x ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V4h_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V5t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2D @ V6x @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V1lrep__ok_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V5t_2E0 ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2Ellist__TY__DEF,axiom,
! [A_27a: d] :
? [V0rep_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ETYPE__DEFINITION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ c_2Ellist_2Elrep__ok_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ V0rep_2E0 ) ) ) ) ).
thf(thm_2Ellist_2Ellist__absrep,axiom,
! [A_27a: d] :
( ! [V0a_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2Ellist__abs_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Ellist_2Ellist__rep_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0a_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0a_2E0 ) )
& ! [V1r_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Elrep__ok_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V1r_2E0 ) ) ) )
<=> ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Ellist_2Ellist__rep_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2Ellist__abs_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V1r_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V1r_2E0 ) ) ) ) ).
thf(thm_2Ellist_2ELNIL,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
=> ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2Ellist__abs_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ F0_2E0 ) ) ) ) ) ).
thf(thm_2Ellist_2ELCONS,axiom,
! [A_27a: d,F1: mono_2Etyop_2Enum_2Enum > $o,F0_2E0: u] :
( ! [V2n: mono_2Etyop_2Enum_2Enum] :
( ( F1 @ V2n )
<=> ( V2n = mono_2Ec_2Enum_2E0 ) )
=> ( ! [V0h_2E0: u,V1t_2E0: u,V2n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V0h_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1t_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F1 @ V2n ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0h_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2Ellist__rep_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2D @ V2n @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
=> ! [V0h_2E0: u,V1t_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V0h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1t_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2Ellist__abs_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V0h_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1t_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELTL__HD__def,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V0ll_2E0: u,V1h_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) @ ( s @ A_27a @ V1h_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2Ellist__abs_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Ellist_2Ellist__rep_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ mono_2Ec_2Enum_2ESUC ) ) ) ) ) ) @ ( s @ A_27a @ V1h_2E0 ) ) ) ) ) )
=> ! [V0ll_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( c_2Ellist_2ELTL__HD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2Ellist__rep_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELHD,axiom,
! [A_27a: d,V0ll_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2Ellist__rep_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ).
thf(thm_2Ellist_2ELTL,axiom,
! [A_27a: d,F1_2E0: u,F0_2E0: u] :
( ! [V0ll_2E0: u,V2n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2Ellist__rep_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V2n @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
=> ( ! [V0ll_2E0: u,V1v_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) @ ( s @ A_27a @ V1v_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2Ellist__abs_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) ) ) ) ) )
=> ! [V0ll_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELNTH,axiom,
! [A_27a: d] :
( ! [V0ll_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) )
& ! [V1n: mono_2Etyop_2Enum_2Enum,V2ll_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V1n ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Ellist_2ELNTH_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELUNFOLD__def,axiom,
! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
( ! [V0f_2E0: u,V3m_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V3m_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( c_2Eoption_2EOPTION__BIND_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V3m_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ c_2Ecombin_2EK_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V0f_2E0 ) ) ) ) ) ) ) )
=> ( ! [V0f_2E0: u,V1z_2E0: u,V2n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V0f_2E0 ) ) ) @ ( s @ A_27b @ V1z_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a ) @ c_2Epair_2ESND_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( c_2Earithmetic_2EFUNPOW_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V0f_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V0f_2E0 ) @ ( s @ A_27b @ V1z_2E0 ) ) ) ) ) ) ) )
=> ! [V0f_2E0: u,V1z_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V0f_2E0 ) @ ( s @ A_27b @ V1z_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2Ellist__abs_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V0f_2E0 ) ) ) @ ( s @ A_27b @ V1z_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELTAKE,axiom,
! [A_27a: d,F1_2E0: u,F0_2E0: u] :
( ! [V3hd_2E0: u,V4tl_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ F1_2E0 ) @ ( s @ A_27a @ V3hd_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4tl_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V3hd_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4tl_2E0 ) ) ) ) ) )
=> ( ! [V1n: mono_2Etyop_2Enum_2Enum,V2ll_2E0: u,V3hd_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) ) @ ( s @ A_27a @ V3hd_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ F1_2E0 ) @ ( s @ A_27a @ V3hd_2E0 ) ) ) ) ) )
=> ( ! [V0ll_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) )
& ! [V1n: mono_2Etyop_2Enum_2Enum,V2ll_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V1n ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELMAP,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0f_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ c_2Ellist_2ELNIL_2E0 ) )
& ! [V1f_2E0: u,V2h_2E0: u,V3t_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V2h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3t_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ A_27a @ V2h_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3t_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELAPPEND,axiom,
! [A_27a: d] :
( ! [V0x_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0x_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0x_2E0 ) )
& ! [V1h_2E0: u,V2t_2E0: u,V3x_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V1h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2t_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3x_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V1h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2t_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3x_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELFINITE__def,axiom,
! [A_27a: d,V0x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0x_2E0 ) ) ) )
<=> ! [V1LFINITE_27_2E0: u] :
( ! [V2a0_2E0: u] :
( ( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2a0_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) )
| ? [V3h_2E0: u,V4t_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2a0_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V3h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V4t_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1LFINITE_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V4t_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1LFINITE_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2a0_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1LFINITE_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0x_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2Ellength__rel__def,axiom,
! [A_27a: d,V0x_2E0: u,V1x_27: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Ellength__rel_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0x_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1x_27 ) ) ) ) )
<=> ! [V2llength__rel_27_2E0: u] :
( ! [V3a0_2E0: u,V4a1: mono_2Etyop_2Enum_2Enum] :
( ( ( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3a0_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) )
& ( V4a1 = mono_2Ec_2Enum_2E0 ) )
| ? [V5h_2E0: u,V6n: mono_2Etyop_2Enum_2Enum,V7t_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3a0_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V5h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V7t_2E0 ) ) ) )
& ( V4a1
= ( mono_2Ec_2Enum_2ESUC @ V6n ) )
& ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V2llength__rel_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V7t_2E0 ) ) ) @ V6n ) ) )
=> ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V2llength__rel_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3a0_2E0 ) ) ) @ V4a1 ) )
=> ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V2llength__rel_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0x_2E0 ) ) ) @ V1x_27 ) ) ) ).
thf(thm_2Ellist_2ELLENGTH,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V0ll_2E0: u,V1n: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) @ V1n )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Ellength__rel_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) ) ) ) )
=> ! [V0ll_2E0: u] :
( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) ) @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Emin_2E_40_2Emono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) ) ) ) @ mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum ) ) ) ).
thf(thm_2Ellist_2EtoList,axiom,
! [A_27a: d,V0ll_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2EtoList_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Eoption_2ETHE_2Emono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ).
thf(thm_2Ellist_2EfromList__def,axiom,
! [A_27a: d] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) )
& ! [V0h_2E0: u,V1t_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V0h_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1t_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V0h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1t_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELDROP,axiom,
! [A_27a: d] :
( ! [V0ll_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) )
& ! [V1n: mono_2Etyop_2Enum_2Enum,V2ll_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V1n ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( c_2Ellist_2ELDROP_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2Eexists__def,axiom,
! [A_27a: d,V0x_2E0: u,V1x_27_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0x_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1x_27_2E0 ) ) ) )
<=> ! [V2exists_27_2E0: u] :
( ! [V3a0_2E0: u] :
( ( ? [V4h_2E0: u,V5t_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3a0_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V4h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V5t_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0x_2E0 ) @ ( s @ A_27a @ V4h_2E0 ) ) ) ) )
| ? [V6h_2E0: u,V7t_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3a0_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V6h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V7t_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V2exists_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V7t_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V2exists_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3a0_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V2exists_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1x_27_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2Eevery__def,axiom,
! [A_27a: d,V0P_2E0: u,V1ll_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eevery_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) )
<=> ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ebool_2E_7E ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELFILTER,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V0P_2E0: u,V1ll_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) )
<=> ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) ) ) )
=> ! [V0P_2E0: u,V1ll_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELFILTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELFILTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELFILTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELFLATTEN,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V0ll_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ V0ll_2E0 ) ) ) )
<=> ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ V0ll_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) )
=> ! [V0ll_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELFLATTEN_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ V0ll_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eevery_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Emin_2E_3D_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ V0ll_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ V0ll_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELFLATTEN_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ V0ll_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ V0ll_2E0 ) ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELFLATTEN_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ V0ll_2E0 ) ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ V0ll_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELZIP__THM,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0l1_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ellist_2ELZIP_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ c_2Ellist_2ELNIL_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Ellist_2ELNIL_2E0 ) )
& ! [V1l2_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ellist_2ELZIP_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V1l2_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Ellist_2ELNIL_2E0 ) )
& ! [V2h1_2E0: u,V3h2_2E0: u,V4t1_2E0: u,V5t2_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ellist_2ELZIP_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V2h1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V4t1_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27b @ V3h2_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V5t2_2E0 ) ) ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2h1_2E0 ) @ ( s @ A_27b @ V3h2_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ellist_2ELZIP_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V4t1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V5t2_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELUNZIP__THM,axiom,
! [A_27a: d,A_27b: d,F0_2E0: u] :
( ! [V0x_2E0: u,V1y_2E0: u,V3ll1_2E0: u,V4ll2_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3ll1_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V4ll2_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3ll1_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27b @ V1y_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V4ll2_2E0 ) ) ) ) ) )
=> ( ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Ellist_2ELUNZIP_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Ellist_2ELNIL_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ c_2Ellist_2ELNIL_2E0 ) ) ) )
& ! [V0x_2E0: u,V1y_2E0: u,V2t_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Ellist_2ELUNZIP_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ellist_2ELCONS_2E2 @ ( 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_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2t_2E0 ) ) ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Ebool_2ELET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Ellist_2ELUNZIP_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2t_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2Elinear__order__to__list__f__def,axiom,
! [A_27a: d,F1_2E0: u,F0_2E0: u] :
( ! [V1min_2E0: u] :
( ( 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 ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1min_2E0 ) ) ) )
<=> ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1min_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) )
=> ( ! [V0lo_2E0: u,V1min_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0lo_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1min_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1min_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Errestrict_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0lo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDIFF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Edomain_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0lo_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Erange_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0lo_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1min_2E0 ) ) ) ) ) @ ( s @ A_27a @ ( c_2Epred__set_2ECHOICE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1min_2E0 ) ) ) ) ) ) ) ) ) )
=> ! [V0lo_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) @ ( c_2Ellist_2Elinear__order__to__list__f_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0lo_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) @ ( c_2Ebool_2ELET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0lo_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Eminimal__elements_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Edomain_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0lo_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Erange_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0lo_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0lo_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELPREFIX__def,axiom,
! [A_27a: d,F0_2E0: u,F2_2E0: u,F3_2E0: u,F1_2E0: u] :
( ! [V0l1_2E0: u,V1l2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l1_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l2_2E0 ) ) ) )
<=> ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l1_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l2_2E0 ) ) )
=> ( ! [V2xs_2E0: u,V1l2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2xs_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l2_2E0 ) ) ) )
<=> ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2xs_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l2_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2xs_2E0 ) ) ) ) )
=> ( ! [V2xs_2E0: u,V3ys_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 @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2xs_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3ys_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EisPREFIX_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2xs_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3ys_2E0 ) ) ) ) )
=> ( ! [V1l2_2E0: u,V2xs_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_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2xs_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2EtoList_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l2_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2xs_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2xs_2E0 ) ) ) ) ) ) )
=> ! [V0l1_2E0: u,V1l2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELPREFIX_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l2_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2EtoList_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l1_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l1_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l2_2E0 ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELGENLIST__def,axiom,
! [A_27a: d,F1_2E0: u,F0_2E0: u] :
( ! [V3lim: mono_2Etyop_2Enum_2Enum,V2f_2E0: u,V4n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) ) @ F1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3lim ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2f_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4n ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Eprim__rec_2E_3C @ V4n @ V3lim ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V4n @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4n ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
=> ( ! [V0f_2E0: u,V1n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V0f_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V1n @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V0f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) ) ) ) ) ) ) )
=> ( ! [V0f_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V0f_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V0f_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) )
& ! [V2f_2E0: u,V3lim: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2f_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ V3lim ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ A_27a ) ) ) ) ) @ F1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3lim ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2f_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELREPEAT__def,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V0l_2E0: u,V1n: mono_2Etyop_2Enum_2Enum] :
( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) ) )
= ( s @ A_27a @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2EMOD @ V1n @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) )
=> ! [V0l_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELREPEAT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2ENULL_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2Elrep__ok__rules,axiom,
! [A_27a: d,F0_2E0: u,F2: mono_2Etyop_2Enum_2Enum > $o,F1_2E0: u] :
( ! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
=> ( ! [V3n: mono_2Etyop_2Enum_2Enum] :
( ( F2 @ V3n )
<=> ( V3n = mono_2Ec_2Enum_2E0 ) )
=> ( ! [V1h_2E0: u,V2t_2E0: u,V3n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ F1_2E0 ) @ ( s @ A_27a @ V1h_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V2t_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F2 @ V3n ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V1h_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V2t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2D @ V3n @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Elrep__ok_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ F0_2E0 ) ) ) )
& ! [V1h_2E0: u,V2t_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Elrep__ok_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V2t_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Elrep__ok_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ F1_2E0 ) @ ( s @ A_27a @ V1h_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V2t_2E0 ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2Elrep__ok__coind,axiom,
! [A_27a: d,F0: mono_2Etyop_2Enum_2Enum > $o] :
( ! [V5x: mono_2Etyop_2Enum_2Enum] :
( ( F0 @ V5x )
<=> ( V5x = mono_2Ec_2Enum_2E0 ) )
=> ! [V0lrep__ok_27_2E0: u] :
( ! [V1a0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V0lrep__ok_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V1a0_2E0 ) ) ) )
=> ( ! [V2x: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V1a0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2x ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
| ? [V3h_2E0: u,V4t_2E0: u] :
( ! [V5x: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V1a0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5x ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F0 @ V5x ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V3h_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V4t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2D @ V5x @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V0lrep__ok_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V4t_2E0 ) ) ) ) ) ) )
=> ! [V6a0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V0lrep__ok_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V6a0_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Elrep__ok_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V6a0_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2Elrep__ok__cases,axiom,
! [A_27a: d,F0: mono_2Etyop_2Enum_2Enum > $o] :
( ! [V4x: mono_2Etyop_2Enum_2Enum] :
( ( F0 @ V4x )
<=> ( V4x = mono_2Ec_2Enum_2E0 ) )
=> ! [V0a0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Elrep__ok_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V0a0_2E0 ) ) ) )
<=> ( ! [V1x: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V0a0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1x ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
| ? [V2h_2E0: u,V3t_2E0: u] :
( ! [V4x: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V0a0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4x ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F0 @ V4x ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V2h_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V3t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2D @ V4x @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Elrep__ok_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V3t_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2Elrep__ok__alt,axiom,
! [A_27a: d,V0f_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Elrep__ok_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V0f_2E0 ) ) ) )
<=> ! [V1n: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V0f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V1n ) ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V0f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2Elrep__ok__MAP,axiom,
! [A_27a: d,A_27b: d,F0_2E0: u] :
( ! [V1f_2E0: u,V0g_2E0: u,V2n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V1f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ V0g_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V1f_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ V0g_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) ) ) ) ) )
=> ! [V0g_2E0: u,V1f_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Elrep__ok_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V1f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ V0g_2E0 ) ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Elrep__ok_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ V0g_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2Elrep__ok__FUNPOW__BIND,axiom,
! [A_27a: d,F1_2E0: u,F0_2E0: u] :
( ! [V0g_2E0: u,V3m_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V0g_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V3m_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2EOPTION__BIND_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V3m_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V0g_2E0 ) ) ) )
=> ( ! [V0g_2E0: u,V1fz_2E0: u,V2n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V0g_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1fz_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Earithmetic_2EFUNPOW_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V0g_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1fz_2E0 ) ) ) )
=> ! [V0g_2E0: u,V1fz_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Elrep__ok_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ V0g_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ V1fz_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2Ellist__rep__LCONS,axiom,
! [A_27a: d,F0: mono_2Etyop_2Enum_2Enum > $o] :
( ! [V2x: mono_2Etyop_2Enum_2Enum] :
( ( F0 @ V2x )
<=> ( V2x = mono_2Ec_2Enum_2E0 ) )
=> ! [V0t_2E0: u,V1h_2E0: u,V2x: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2Ellist__rep_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V1h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0t_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2x ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F0 @ V2x ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V1h_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2Ellist__rep_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2D @ V2x @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2Ellist__rep__LNIL,axiom,
! [A_27a: d,V0x: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2Ellist__rep_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0x ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ).
thf(thm_2Ellist_2ELTL__HD__LNIL,axiom,
! [A_27a: d] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( c_2Ellist_2ELTL__HD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) ).
thf(thm_2Ellist_2ELTL__HD__LCONS,axiom,
! [A_27a: d,V0t_2E0: u,V1h_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( c_2Ellist_2ELTL__HD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V1h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0t_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0t_2E0 ) @ ( s @ A_27a @ V1h_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELTL__HD__HD,axiom,
! [A_27a: d,V0ll_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) @ A_27a ) @ c_2Epair_2ESND_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( c_2Ellist_2ELTL__HD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELTL__HD__TL,axiom,
! [A_27a: d,V0ll_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( c_2Ellist_2ELTL__HD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELHD__LCONS,axiom,
! [A_27a: d,V0t_2E0: u,V1h_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V1h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0t_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V1h_2E0 ) ) ) ) ).
thf(thm_2Ellist_2ELTL__LCONS,axiom,
! [A_27a: d,V0t_2E0: u,V1h_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V1h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0t_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0t_2E0 ) ) ) ) ).
thf(thm_2Ellist_2ELHDTL__CONS__THM,axiom,
! [A_27a: d,V0h_2E0: u,V1t_2E0: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V0h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1t_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0h_2E0 ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V0h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1t_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1t_2E0 ) ) ) ) ) ).
thf(thm_2Ellist_2Ellist__CASES,axiom,
! [A_27a: d,V0l_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) )
| ? [V1h_2E0: u,V2t_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V1h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2t_2E0 ) ) ) ) ) ).
thf(thm_2Ellist_2ELTL__HD__11,axiom,
! [A_27a: d,V0ll2_2E0: u,V1ll1_2E0: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( c_2Ellist_2ELTL__HD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( c_2Ellist_2ELTL__HD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll2_2E0 ) ) ) )
=> ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll1_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll2_2E0 ) ) ) ).
thf(thm_2Ellist_2ELHD__THM,axiom,
! [A_27a: d,A_27b: d] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
& ! [V0h_2E0: u,V1t_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27b @ V0h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V1t_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V0h_2E0 ) ) ) ) ) ).
thf(thm_2Ellist_2ELTL__THM,axiom,
! [A_27a: d,A_27b: d] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) )
& ! [V0h_2E0: u,V1t_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27b @ V0h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V1t_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V1t_2E0 ) ) ) ) ) ).
thf(thm_2Ellist_2ELCONS__NOT__NIL,axiom,
! [A_27a: d,V0h_2E0: u,V1t_2E0: u] :
( ( (~)
@ ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V0h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1t_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) )
& ( (~)
@ ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V0h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1t_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELCONS__11,axiom,
! [A_27a: d,V0h1_2E0: u,V1t1_2E0: u,V2h2_2E0: u,V3t2_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V0h1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1t1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V2h2_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3t2_2E0 ) ) ) )
<=> ( ( ( s @ A_27a @ V0h1_2E0 )
= ( s @ A_27a @ V2h2_2E0 ) )
& ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1t1_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3t2_2E0 ) ) ) ) ).
thf(thm_2Ellist_2ELTL__HD__iff,axiom,
! [A_27a: d,V0x_2E0: u,V1t_2E0: u,V2h_2E0: u] :
( ( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( c_2Ellist_2ELTL__HD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0x_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1t_2E0 ) @ ( s @ A_27a @ V2h_2E0 ) ) ) ) ) )
<=> ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0x_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V2h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1t_2E0 ) ) ) ) )
& ( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( c_2Ellist_2ELTL__HD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0x_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) )
<=> ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0x_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) ) ) ).
thf(thm_2Ellist_2ELHD__EQ__NONE,axiom,
! [A_27a: d,V0ll_2E0: u] :
( ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
<=> ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) )
& ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) )
<=> ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) ) ) ).
thf(thm_2Ellist_2ELTL__EQ__NONE,axiom,
! [A_27a: d,V0ll_2E0: u] :
( ( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) )
<=> ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) )
& ( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) )
<=> ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) ) ) ).
thf(thm_2Ellist_2ELHDTL__EQ__SOME,axiom,
! [A_27a: d,V0h_2E0: u,V1t_2E0: u,V2ll_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V0h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1t_2E0 ) ) ) )
<=> ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0h_2E0 ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1t_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELNTH__THM,axiom,
! [A_27a: d,A_27b: d,A_27c: d] :
( ! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
& ! [V1h_2E0: u,V2t_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27b @ V1h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V2t_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V1h_2E0 ) ) ) )
& ! [V3n: mono_2Etyop_2Enum_2Enum,V4h_2E0: u,V5t_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V3n ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27c @ V4h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ V5t_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ V5t_2E0 ) ) ) ) ) ).
thf(thm_2Ellist_2ELNTH__rep,axiom,
! [A_27a: d,V0i: mono_2Etyop_2Enum_2Enum,V1ll_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0i ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2Ellist__rep_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0i ) ) ) ) ) ).
thf(thm_2Ellist_2ELNTH__EQ,axiom,
! [A_27a: d,V0ll1_2E0: u,V1ll2_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll1_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll2_2E0 ) )
<=> ! [V2n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll2_2E0 ) ) ) ) ) ).
thf(thm_2Ellist_2ELUNFOLD,axiom,
! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
( ! [V0f_2E0: u,V3v1_2E0: u,V4v2_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V0f_2E0 ) ) ) @ ( s @ A_27a @ V3v1_2E0 ) ) ) @ ( s @ A_27b @ V4v2_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27b @ V4v2_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V3v1_2E0 ) ) ) ) ) )
=> ( ! [V0f_2E0: u,V2v_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V2v_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V2v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V0f_2E0 ) ) ) ) ) )
=> ! [V0f_2E0: u,V1x_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ c_2Ellist_2ELNIL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V0f_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELUNFOLD__UNIQUE,axiom,
! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
( ! [V1g_2E0: u,V4v1_2E0: u,V5v2_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V4v1_2E0 ) ) ) @ ( s @ A_27b @ V5v2_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27b @ V5v2_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) @ ( s @ A_27a @ V4v1_2E0 ) ) ) ) ) )
=> ( ! [V1g_2E0: u,V3v_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V3v_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V3v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) ) ) ) ) )
=> ! [V0f_2E0: u,V1g_2E0: u] :
( ! [V2x_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ c_2Ellist_2ELNIL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) ) ) ) ) )
=> ! [V6y_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) @ ( s @ A_27a @ V6y_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V6y_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELUNFOLD__LTL__HD,axiom,
! [A_27a: d,V0ll_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ c_2Ellist_2ELTL__HD_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ).
thf(thm_2Ellist_2ELTL__HD__LUNFOLD,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1f_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( c_2Ellist_2ELTL__HD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1f_2E0 ) @ ( s @ A_27b @ V0x_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( c_2Epair_2E_23_23_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELUNFOLD_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ c_2Ecombin_2EI_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1f_2E0 ) @ ( s @ A_27b @ V0x_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELNTH__LUNFOLD,axiom,
! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
( ! [V1n: mono_2Etyop_2Enum_2Enum,V2f_2E0: u,V4tx_2E0: u,V5hx_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) ) @ F1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V2f_2E0 ) ) ) @ ( s @ A_27b @ V4tx_2E0 ) ) ) @ ( s @ A_27a @ V5hx_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V2f_2E0 ) @ ( s @ A_27b @ V4tx_2E0 ) ) ) ) ) )
=> ( ! [V1n: mono_2Etyop_2Enum_2Enum,V2f_2E0: u,V3v_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V2f_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ V3v_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ V3v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) ) @ F1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V2f_2E0 ) ) ) ) ) )
=> ! [V0x_2E0: u,V1n: mono_2Etyop_2Enum_2Enum,V2f_2E0: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V2f_2E0 ) @ ( s @ A_27b @ V0x_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a ) @ c_2Epair_2ESND_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V2f_2E0 ) @ ( s @ A_27b @ V0x_2E0 ) ) ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V1n ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V2f_2E0 ) @ ( s @ A_27b @ V0x_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V2f_2E0 ) @ ( s @ A_27b @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V2f_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELNTH__LUNFOLD__compute,axiom,
! [A_27a: d,A_27b: d,F3_2E0: u,F0_2E0: u,F2_2E0: u,F1_2E0: u] :
( ! [V2n: mono_2Etyop_2Enum_2Enum,V1f_2E0: u,V4tx_2E0: u,V5hx_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) ) @ F3_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1f_2E0 ) ) ) @ ( s @ A_27b @ V4tx_2E0 ) ) ) @ ( s @ A_27a @ V5hx_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2D @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V2n ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1f_2E0 ) @ ( s @ A_27b @ V4tx_2E0 ) ) ) ) ) )
=> ( ! [V2n: mono_2Etyop_2Enum_2Enum,V1f_2E0: u,V3v_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1f_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ V3v_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ V3v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) ) @ F3_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1f_2E0 ) ) ) ) ) )
=> ( ! [V6n: mono_2Etyop_2Enum_2Enum,V1f_2E0: u,V8tx_2E0: u,V9hx_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) ) @ F2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6n ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1f_2E0 ) ) ) @ ( s @ A_27b @ V8tx_2E0 ) ) ) @ ( s @ A_27a @ V9hx_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V6n ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1f_2E0 ) @ ( s @ A_27b @ V8tx_2E0 ) ) ) ) ) )
=> ( ! [V6n: mono_2Etyop_2Enum_2Enum,V1f_2E0: u,V7v_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ F1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6n ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1f_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ V7v_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ V7v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) ) @ F2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6n ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1f_2E0 ) ) ) ) ) )
=> ! [V0x_2E0: u,V1f_2E0: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1f_2E0 ) @ ( s @ A_27b @ V0x_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a ) @ c_2Epair_2ESND_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1f_2E0 ) @ ( s @ A_27b @ V0x_2E0 ) ) ) ) ) )
& ! [V2n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V2n ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1f_2E0 ) @ ( s @ A_27b @ V0x_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1f_2E0 ) @ ( s @ A_27b @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1f_2E0 ) ) ) ) ) )
& ! [V6n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V6n ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1f_2E0 ) @ ( s @ A_27b @ V0x_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1f_2E0 ) @ ( s @ A_27b @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ F1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6n ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1f_2E0 ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELHD__LUNFOLD,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1f_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1f_2E0 ) @ ( s @ A_27b @ V0x_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a ) @ c_2Epair_2ESND_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1f_2E0 ) @ ( s @ A_27b @ V0x_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELTL__LUNFOLD,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1f_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1f_2E0 ) @ ( s @ A_27b @ V0x_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELUNFOLD_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27b ) @ c_2Epair_2EFST_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1f_2E0 ) @ ( s @ A_27b @ V0x_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2Ellist__Axiom__1,axiom,
! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
( ! [V1g_2E0: u,V4a_2E0: u,V5b_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V4a_2E0 ) ) ) @ ( s @ A_27b @ V5b_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27b @ V5b_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) ) ) ) ) )
=> ( ! [V1g_2E0: u,V3v_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V3v_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V3v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) ) ) ) ) )
=> ! [V0f_2E0: u] :
? [V1g_2E0: u] :
! [V2x_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ c_2Ellist_2ELNIL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2Ellist__Axiom__1ue,axiom,
! [A_27a: d,A_27b: d,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
( ! [V1g_2E0: u,V4a_2E0: u,V5b_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V4a_2E0 ) ) ) @ ( s @ A_27b @ V5b_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27b @ V5b_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) @ ( s @ A_27a @ V4a_2E0 ) ) ) ) ) )
=> ( ! [V1g_2E0: u,V3v_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V3v_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V3v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) ) ) ) ) )
=> ( ! [V0f_2E0: u,V1g_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) ) ) )
<=> ! [V2x_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ c_2Ellist_2ELNIL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) ) ) ) ) ) )
=> ! [V0f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V0f_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2Ellist__ue__Axiom,axiom,
! [A_27a: d,A_27b: d,F0_2E0: u] :
( ! [V0f_2E0: u,V1g_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) ) ) )
<=> ( ! [V2x_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27b ) @ c_2Epair_2ESND_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) )
& ! [V3x_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) ) ) ) )
=> ! [V0f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V0f_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2Ellist__Axiom,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u] :
? [V1g_2E0: u] :
( ! [V2x_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27b ) @ c_2Epair_2ESND_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) )
& ! [V3x_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELUNFOLD__BISIMULATION,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0f1_2E0: u,V1f2_2E0: u,V2x1_2E0: u,V3x2_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V0f1_2E0 ) @ ( s @ A_27a @ V2x1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ V1f2_2E0 ) @ ( s @ A_27c @ V3x2_2E0 ) ) ) )
<=> ? [V4R_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V4R_2E0 ) @ ( s @ A_27a @ V2x1_2E0 ) ) ) @ ( s @ A_27c @ V3x2_2E0 ) ) ) )
& ! [V5y1_2E0: u,V6y2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V4R_2E0 ) @ ( s @ A_27a @ V5y1_2E0 ) ) ) @ ( s @ A_27c @ V6y2_2E0 ) ) ) )
=> ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V0f1_2E0 ) @ ( s @ A_27a @ V5y1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eoption_2ENONE_2E0 ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ V1f2_2E0 ) @ ( s @ A_27c @ V6y2_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
| ? [V7h_2E0: u,V8t1_2E0: u,V9t2_2E0: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V0f1_2E0 ) @ ( s @ A_27a @ V5y1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V8t1_2E0 ) @ ( s @ A_27b @ V7h_2E0 ) ) ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ V1f2_2E0 ) @ ( s @ A_27c @ V6y2_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ V9t2_2E0 ) @ ( s @ A_27b @ V7h_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V4R_2E0 ) @ ( s @ A_27a @ V8t1_2E0 ) ) ) @ ( s @ A_27c @ V9t2_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELLIST__BISIMULATION0,axiom,
! [A_27a: d,V0ll1_2E0: u,V1ll2_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll1_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll2_2E0 ) )
<=> ? [V2R_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll1_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll2_2E0 ) ) ) )
& ! [V3ll3_2E0: u,V4ll4_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3ll3_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V4ll4_2E0 ) ) ) )
=> ( ( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3ll3_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) )
& ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V4ll4_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) )
| ? [V5h_2E0: u,V6t1_2E0: u,V7t2_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3ll3_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V5h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V6t1_2E0 ) ) ) )
& ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V4ll4_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V5h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V7t2_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V6t1_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V7t2_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELLIST__BISIMULATION,axiom,
! [A_27a: d,V0ll1_2E0: u,V1ll2_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll1_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll2_2E0 ) )
<=> ? [V2R_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll1_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll2_2E0 ) ) ) )
& ! [V3ll3_2E0: u,V4ll4_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3ll3_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V4ll4_2E0 ) ) ) )
=> ( ( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3ll3_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) )
& ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V4ll4_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) )
| ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3ll3_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V4ll4_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3ll3_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V4ll4_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELLIST__STRONG__BISIMULATION,axiom,
! [A_27a: d,V0ll1_2E0: u,V1ll2_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll1_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll2_2E0 ) )
<=> ? [V2R_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll1_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll2_2E0 ) ) ) )
& ! [V3ll3_2E0: u,V4ll4_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3ll3_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V4ll4_2E0 ) ) ) )
=> ( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3ll3_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V4ll4_2E0 ) )
| ? [V5h_2E0: u,V6t1_2E0: u,V7t2_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3ll3_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V5h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V6t1_2E0 ) ) ) )
& ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V4ll4_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V5h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V7t2_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V6t1_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V7t2_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELTAKE__LUNFOLD,axiom,
! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
( ! [V1n: mono_2Etyop_2Enum_2Enum,V2f_2E0: u,V4tx_2E0: u,V5hx_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ) ) @ F1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V2f_2E0 ) ) ) @ ( s @ A_27b @ V4tx_2E0 ) ) ) @ ( s @ A_27a @ V5hx_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2ECONS_2E1 @ ( s @ A_27a @ V5hx_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V2f_2E0 ) @ ( s @ A_27b @ V4tx_2E0 ) ) ) ) ) ) ) )
=> ( ! [V1n: mono_2Etyop_2Enum_2Enum,V2f_2E0: u,V3v_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V2f_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ V3v_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ V3v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ) ) @ F1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V2f_2E0 ) ) ) ) ) )
=> ! [V0x_2E0: u,V1n: mono_2Etyop_2Enum_2Enum,V2f_2E0: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V2f_2E0 ) @ ( s @ A_27b @ V0x_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V1n ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V2f_2E0 ) @ ( s @ A_27b @ V0x_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V2f_2E0 ) @ ( s @ A_27b @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V2f_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELTAKE__THM,axiom,
! [A_27a: d,A_27b: d,A_27c: d] :
( ! [V0l_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) )
& ! [V1n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V1n ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ c_2Ellist_2ELNIL_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) @ c_2Eoption_2ENONE_2E0 ) )
& ! [V2n: mono_2Etyop_2Enum_2Enum,V3h_2E0: u,V4t_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27c ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V2n ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27c @ V3h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ V4t_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27c ) ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Elist_2Elist @ A_27c ) ) @ ( c_2Elist_2ECONS_2E1 @ ( s @ A_27c @ V3h_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27c ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ V4t_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELTAKE__SNOC__LNTH,axiom,
! [A_27a: d,F1_2E0: u,F0_2E0: u] :
( ! [V2l_2E0: u,V3e_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l_2E0 ) ) ) @ ( s @ A_27a @ V3e_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V3e_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ) ) ) )
=> ( ! [V0n: mono_2Etyop_2Enum_2Enum,V1ll_2E0: u,V2l_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l_2E0 ) ) ) ) ) )
=> ! [V0n: mono_2Etyop_2Enum_2Enum,V1ll_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V0n ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELTAKE__EQ__NONE__LNTH,axiom,
! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1ll_2E0: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) ).
thf(thm_2Ellist_2ELTAKE__NIL__EQ__SOME,axiom,
! [A_27a: d,V0l_2E0: u,V1m: mono_2Etyop_2Enum_2Enum] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1m ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) )
<=> ( ( V1m = mono_2Ec_2Enum_2E0 )
& ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 )
= ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ).
thf(thm_2Ellist_2ELTAKE__NIL__EQ__NONE,axiom,
! [A_27a: d,V0m: mono_2Etyop_2Enum_2Enum] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0m ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) )
<=> ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V0m ) ) ).
thf(thm_2Ellist_2ELTAKE__EQ,axiom,
! [A_27a: d,V0ll1_2E0: u,V1ll2_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll1_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll2_2E0 ) )
<=> ! [V2n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll2_2E0 ) ) ) ) ) ).
thf(thm_2Ellist_2ELTAKE__CONS__EQ__NONE,axiom,
! [A_27a: d,V0m: mono_2Etyop_2Enum_2Enum,V1h_2E0: u,V2t_2E0: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0m ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V1h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2t_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) )
<=> ? [V3n: mono_2Etyop_2Enum_2Enum] :
( ( V0m
= ( mono_2Ec_2Enum_2ESUC @ V3n ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2t_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ).
thf(thm_2Ellist_2ELTAKE__CONS__EQ__SOME,axiom,
! [A_27a: d,V0m: mono_2Etyop_2Enum_2Enum,V1h_2E0: u,V2t_2E0: u,V3l_2E0: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0m ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V1h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2t_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3l_2E0 ) ) ) )
<=> ( ( ( V0m = mono_2Ec_2Enum_2E0 )
& ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3l_2E0 )
= ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) )
| ? [V4n: mono_2Etyop_2Enum_2Enum,V5l_27_2E0: u] :
( ( V0m
= ( mono_2Ec_2Enum_2ESUC @ V4n ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2t_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V5l_27_2E0 ) ) ) )
& ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3l_2E0 )
= ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V1h_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V5l_27_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELTAKE__EQ__SOME__CONS,axiom,
! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1l_2E0: u,V2x_2E0: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2x_2E0 ) ) ) )
=> ! [V3h_2E0: u] :
? [V4y_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V3h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V4y_2E0 ) ) ) ) ) ).
thf(thm_2Ellist_2ELMAP__APPEND,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u,V1ll1_2E0: u,V2ll2_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll2_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll1_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll2_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELAPPEND__EQ__LNIL,axiom,
! [A_27a: d,V0l2_2E0: u,V1l1_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l2_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) )
<=> ( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l1_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) )
& ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l2_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) ) ) ).
thf(thm_2Ellist_2ELAPPEND__ASSOC,axiom,
! [A_27a: d,V0ll1_2E0: u,V1ll2_2E0: u,V2ll3_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll2_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll3_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll2_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll3_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELMAP__MAP,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2ll_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V1g_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ V2ll_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V1g_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ V2ll_2E0 ) ) ) ) ).
thf(thm_2Ellist_2ELAPPEND__NIL__2ND,axiom,
! [A_27a: d,V0ll_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ).
thf(thm_2Ellist_2ELHD__LAPPEND,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V1l1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l1_2E0 ) ) ) )
<=> ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l1_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) )
=> ! [V0l2_2E0: u,V1l1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l2_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l2_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l1_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELTL__LAPPEND,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V1l1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l1_2E0 ) ) ) )
<=> ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l1_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) )
=> ! [V0l2_2E0: u,V1l1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l2_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l2_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l1_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l2_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELTAKE__LAPPEND1,axiom,
! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1l1_2E0: u,V2l2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l1_2E0 ) ) ) ) ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2l2_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l1_2E0 ) ) ) ) ) ).
thf(thm_2Ellist_2ELFINITE__rules,axiom,
! [A_27a: d] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) ) )
& ! [V0h_2E0: u,V1t_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1t_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V0h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1t_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELFINITE__ind,axiom,
! [A_27a: d,V0LFINITE_27_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0LFINITE_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) ) )
& ! [V1h_2E0: u,V2t_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0LFINITE_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2t_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0LFINITE_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V1h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2t_2E0 ) ) ) ) ) ) ) )
=> ! [V3a0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3a0_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0LFINITE_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3a0_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELFINITE__strongind,axiom,
! [A_27a: d,V0LFINITE_27_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0LFINITE_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) ) )
& ! [V1h_2E0: u,V2t_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2t_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0LFINITE_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2t_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0LFINITE_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V1h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2t_2E0 ) ) ) ) ) ) ) )
=> ! [V3a0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3a0_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0LFINITE_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3a0_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELFINITE__cases,axiom,
! [A_27a: d,V0a0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0a0_2E0 ) ) ) )
<=> ( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0a0_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) )
| ? [V1h_2E0: u,V2t_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0a0_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V1h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2t_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2t_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELFINITE__THM,axiom,
! [A_27a: d,A_27b: d] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) ) )
= mono_2Ec_2Ebool_2ET )
& ! [V0h_2E0: u,V1t_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27b @ V0h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V1t_2E0 ) ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V1t_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELFINITE,axiom,
! [A_27a: d,V0ll_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) )
<=> ? [V1n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) ) ).
thf(thm_2Ellist_2Ellength__rel__rules,axiom,
! [A_27a: d] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Ellength__rel_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) )
& ! [V0h_2E0: u,V1n: mono_2Etyop_2Enum_2Enum,V2t_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Ellength__rel_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Ellength__rel_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V0h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2t_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V1n ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2Ellength__rel__ind,axiom,
! [A_27a: d,V0llength__rel_27_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0llength__rel_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) ) @ mono_2Ec_2Enum_2E0 )
& ! [V1h_2E0: u,V2n: mono_2Etyop_2Enum_2Enum,V3t_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0llength__rel_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3t_2E0 ) ) ) @ V2n )
=> ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0llength__rel_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V1h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3t_2E0 ) ) ) ) ) @ ( mono_2Ec_2Enum_2ESUC @ V2n ) ) ) )
=> ! [V4a0_2E0: u,V5a1: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Ellength__rel_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V4a0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5a1 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0llength__rel_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V4a0_2E0 ) ) ) @ V5a1 ) ) ) ).
thf(thm_2Ellist_2Ellength__rel__strongind,axiom,
! [A_27a: d,V0llength__rel_27_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0llength__rel_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) ) @ mono_2Ec_2Enum_2E0 )
& ! [V1h_2E0: u,V2n: mono_2Etyop_2Enum_2Enum,V3t_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Ellength__rel_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0llength__rel_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3t_2E0 ) ) ) @ V2n ) )
=> ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0llength__rel_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V1h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3t_2E0 ) ) ) ) ) @ ( mono_2Ec_2Enum_2ESUC @ V2n ) ) ) )
=> ! [V4a0_2E0: u,V5a1: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Ellength__rel_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V4a0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5a1 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0llength__rel_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V4a0_2E0 ) ) ) @ V5a1 ) ) ) ).
thf(thm_2Ellist_2Ellength__rel__cases,axiom,
! [A_27a: d,V0a0_2E0: u,V1a1: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Ellength__rel_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0a0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1a1 ) ) ) ) )
<=> ( ( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0a0_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) )
& ( V1a1 = mono_2Ec_2Enum_2E0 ) )
| ? [V2h_2E0: u,V3n: mono_2Etyop_2Enum_2Enum,V4t_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0a0_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V2h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V4t_2E0 ) ) ) )
& ( V1a1
= ( mono_2Ec_2Enum_2ESUC @ V3n ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Ellength__rel_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V4t_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELLENGTH__THM,axiom,
! [A_27a: d,A_27b: d] :
( ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) ) )
= ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) )
& ! [V0h_2E0: u,V1t_2E0: u] :
( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27b @ V0h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V1t_2E0 ) ) ) ) ) )
= ( mono_2Ec_2Eoption_2EOPTION__MAP_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2ESUC @ ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V1t_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELLENGTH__0,axiom,
! [A_27a: d,V0x_2E0: u] :
( ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0x_2E0 ) ) ) )
= ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) )
<=> ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0x_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) ) ).
thf(thm_2Ellist_2ELFINITE__HAS__LENGTH,axiom,
! [A_27a: d,V0ll_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) )
=> ? [V1n: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) )
= ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ V1n ) ) ) ).
thf(thm_2Ellist_2ENOT__LFINITE__NO__LENGTH,axiom,
! [A_27a: d,V0ll_2E0: u] :
( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) ) )
=> ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) )
= mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum ) ) ).
thf(thm_2Ellist_2ELFINITE__LLENGTH,axiom,
! [A_27a: d,V0ll_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) )
<=> ? [V1n: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) )
= ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ V1n ) ) ) ).
thf(thm_2Ellist_2ELFINITE__INDUCTION,axiom,
! [A_27a: d,V0LFINITE_27_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0LFINITE_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) ) )
& ! [V1h_2E0: u,V2t_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0LFINITE_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2t_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0LFINITE_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V1h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2t_2E0 ) ) ) ) ) ) ) )
=> ! [V3a0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3a0_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0LFINITE_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3a0_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELFINITE__STRONG__INDUCTION,axiom,
! [A_27a: d,V0LFINITE_27_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0LFINITE_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) ) )
& ! [V1h_2E0: u,V2t_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2t_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0LFINITE_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2t_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0LFINITE_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V1h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2t_2E0 ) ) ) ) ) ) ) )
=> ! [V3a0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3a0_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0LFINITE_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3a0_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELFINITE__MAP,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u,V1ll_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) ) ) ).
thf(thm_2Ellist_2ELFINITE__APPEND,axiom,
! [A_27a: d,V0ll1_2E0: u,V1ll2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll2_2E0 ) ) ) ) ) )
<=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll1_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll2_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELTAKE__LNTH__EL,axiom,
! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1ll_2E0: u,V2m: mono_2Etyop_2Enum_2Enum,V3l_2E0: u] :
( ( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3l_2E0 ) ) ) )
& ( mono_2Ec_2Eprim__rec_2E_3C @ V2m @ V0n ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2m ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2m ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3l_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ENOT__LFINITE__APPEND,axiom,
! [A_27a: d,V0ll1_2E0: u,V1ll2_2E0: u] :
( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll1_2E0 ) ) ) ) )
=> ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll2_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll1_2E0 ) ) ) ).
thf(thm_2Ellist_2ELFINITE__LAPPEND__IMP__NIL,axiom,
! [A_27a: d,V0ll_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) )
=> ! [V1l2_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l2_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) )
=> ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l2_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) ) ) ).
thf(thm_2Ellist_2ELLENGTH__MAP,axiom,
! [A_27a: d,A_27b: d,V0ll_2E0: u,V1f_2E0: u] :
( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) ) ) )
= ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) ) ) ).
thf(thm_2Ellist_2ELLENGTH__APPEND,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V0ll1_2E0: u,V1ll2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll1_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll2_2E0 ) ) ) )
<=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll1_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll2_2E0 ) ) ) ) ) )
=> ! [V0ll1_2E0: u,V1ll2_2E0: u] :
( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll2_2E0 ) ) ) ) ) )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll1_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll2_2E0 ) ) ) ) @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Eoption_2ETHE_2Emono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll1_2E0 ) ) ) ) ) @ ( mono_2Ec_2Eoption_2ETHE_2Emono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll2_2E0 ) ) ) ) ) ) ) @ mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum ) ) ) ).
thf(thm_2Ellist_2EtoList__THM,axiom,
! [A_27a: d,A_27b: d] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2EtoList_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) )
& ! [V0h_2E0: u,V1t_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( c_2Ellist_2EtoList_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27b @ V0h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V1t_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( c_2Elist_2ECONS_2E1 @ ( s @ A_27b @ V0h_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( c_2Ellist_2EtoList_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V1t_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2EfromList__EQ__LNIL,axiom,
! [A_27a: d,V0l_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) )
<=> ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 )
= ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) ).
thf(thm_2Ellist_2ELHD__fromList,axiom,
! [A_27a: d,V0l_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2ENULL_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ ( c_2Elist_2EHD_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELTL__fromList,axiom,
! [A_27a: d,V0l_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2ENULL_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ETL_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELFINITE__fromList,axiom,
! [A_27a: d,V0l_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELLENGTH__fromList,axiom,
! [A_27a: d,V0l_2E0: u] :
( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) ) ) )
= ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELTAKE__fromList,axiom,
! [A_27a: d,V0l_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) ) ).
thf(thm_2Ellist_2Efrom__toList,axiom,
! [A_27a: d,V0l_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2EtoList_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) ) ).
thf(thm_2Ellist_2ELFINITE__toList,axiom,
! [A_27a: d,V0ll_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) )
=> ? [V1l_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2EtoList_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) ) ).
thf(thm_2Ellist_2ELFINITE__toList__SOME,axiom,
! [A_27a: d,V0ll_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2EtoList_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2Eto__fromList,axiom,
! [A_27a: d,V0ll_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) )
=> ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2EtoList_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) ).
thf(thm_2Ellist_2ELTAKE__LAPPEND2,axiom,
! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1l1_2E0: u,V2l2_2E0: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2l2_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Elist_2EAPPEND_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2EtoList_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l1_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2D @ V0n @ ( mono_2Ec_2Eoption_2ETHE_2Emono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l1_2E0 ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2l2_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELNTH__fromList,axiom,
! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1l_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Eprim__rec_2E_3C @ V0n @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ).
thf(thm_2Ellist_2Elnth__fromList__some,axiom,
! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1l_2E0: u] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V0n @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) )
<=> ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELDROP__FUNPOW,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V2m_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ V2m_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2EOPTION__BIND_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ V2m_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ c_2Ellist_2ELTL_2E0 ) ) ) )
=> ! [V0n: mono_2Etyop_2Enum_2Enum,V1ll_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Earithmetic_2EFUNPOW_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELDROP__THM,axiom,
! [A_27a: d,A_27b: d,A_27c: d] :
( ! [V0ll_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) )
& ! [V1n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V1n ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ c_2Ellist_2ELNIL_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ c_2Eoption_2ENONE_2E0 ) )
& ! [V2n: mono_2Etyop_2Enum_2Enum,V3h_2E0: u,V4t_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27c ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V2n ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27c @ V3h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ V4t_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27c ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ V4t_2E0 ) ) ) ) ) ).
thf(thm_2Ellist_2ELDROP1__THM,axiom,
! [A_27a: d] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( c_2Ellist_2ELDROP_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ c_2Ellist_2ELTL_2E0 ) ) ).
thf(thm_2Ellist_2ELNTH__HD__LDROP,axiom,
! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1ll_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2EOPTION__BIND_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Ellist_2ELHD_2E0 ) ) ) ) ).
thf(thm_2Ellist_2ENOT__LFINITE__TAKE,axiom,
! [A_27a: d,V0ll_2E0: u] :
( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) ) )
=> ! [V1n: mono_2Etyop_2Enum_2Enum] :
? [V2y_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2y_2E0 ) ) ) ) ) ).
thf(thm_2Ellist_2ELFINITE__TAKE,axiom,
! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1ll_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) )
& ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0n @ ( mono_2Ec_2Eoption_2ETHE_2Emono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) ) ) ) )
=> ? [V2y_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2y_2E0 ) ) ) ) ) ).
thf(thm_2Ellist_2ENOT__LFINITE__DROP,axiom,
! [A_27a: d,V0ll_2E0: u] :
( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) ) )
=> ! [V1n: mono_2Etyop_2Enum_2Enum] :
? [V2y_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2y_2E0 ) ) ) ) ) ).
thf(thm_2Ellist_2ELFINITE__DROP,axiom,
! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1ll_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) )
& ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0n @ ( mono_2Ec_2Eoption_2ETHE_2Emono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) ) ) ) )
=> ? [V2y_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2y_2E0 ) ) ) ) ) ).
thf(thm_2Ellist_2ELTAKE__DROP,axiom,
! [A_27a: d] :
( ! [V0n: mono_2Etyop_2Enum_2Enum,V1ll_2E0: u] :
( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) ) )
=> ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) )
& ! [V2n: mono_2Etyop_2Enum_2Enum,V3ll_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3ll_2E0 ) ) ) )
& ( mono_2Ec_2Earithmetic_2E_3C_3D @ V2n @ ( mono_2Ec_2Eoption_2ETHE_2Emono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3ll_2E0 ) ) ) ) ) ) )
=> ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3ll_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3ll_2E0 ) ) ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3ll_2E0 ) ) ) ) ).
thf(thm_2Ellist_2ELDROP__ADD,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V1k2: mono_2Etyop_2Enum_2Enum,V3ll_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k2 ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k2 ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3ll_2E0 ) ) ) )
=> ! [V0k1: mono_2Etyop_2Enum_2Enum,V1k2: mono_2Etyop_2Enum_2Enum,V2x_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V0k1 @ V1k2 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2x_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0k1 ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2x_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1k2 ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELDROP__SOME__LLENGTH,axiom,
! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum,V2ll_2E0: u,V3l_2E0: u] :
( ( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3l_2E0 ) ) ) )
& ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) ) )
= ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ V1m ) ) )
=> ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0n @ V1m )
& ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3l_2E0 ) ) ) )
= ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2D @ V1m @ V0n ) ) ) ) ) ).
thf(thm_2Ellist_2ELFINITE__LNTH__NONE,axiom,
! [A_27a: d,V0ll_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) )
<=> ? [V1n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) ).
thf(thm_2Ellist_2Einfinite__lnth__some,axiom,
! [A_27a: d,V0ll_2E0: u] :
( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) ) )
<=> ! [V1n: mono_2Etyop_2Enum_2Enum] :
? [V2x_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ).
thf(thm_2Ellist_2ELNTH__LAPPEND,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V0n: mono_2Etyop_2Enum_2Enum,V2l1_2E0: u,V1l2_2E0: u,V3m: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2l1_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l2_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3m ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Eprim__rec_2E_3C @ V0n @ V3m ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2l1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2D @ V0n @ V3m ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l2_2E0 ) ) ) ) ) )
=> ! [V0n: mono_2Etyop_2Enum_2Enum,V1l2_2E0: u,V2l1_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2l1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l2_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2l1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2l1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2l1_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l2_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELNTH__ADD,axiom,
! [A_27a: d,V0a: mono_2Etyop_2Enum_2Enum,V1b: mono_2Etyop_2Enum_2Enum,V2ll_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V0a @ V1b ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2EOPTION__BIND_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0a ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( c_2Ellist_2ELNTH_2E1 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1b ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2Elnth__some__down__closed,axiom,
! [A_27a: d,V0ll_2E0: u,V1x_2E0: u,V2n1: mono_2Etyop_2Enum_2Enum,V3n2: mono_2Etyop_2Enum_2Enum] :
( ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n1 ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) )
& ( mono_2Ec_2Earithmetic_2E_3C_3D @ V3n2 @ V2n1 ) )
=> ? [V4y_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3n2 ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V4y_2E0 ) ) ) ) ) ).
thf(thm_2Ellist_2Eexists__rules,axiom,
! [A_27a: d,V0P_2E0: u] :
( ! [V1h_2E0: u,V2t_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ V1h_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V1h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2t_2E0 ) ) ) ) ) ) )
& ! [V3h_2E0: u,V4t_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V4t_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V3h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V4t_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2Eexists__ind,axiom,
! [A_27a: d,V0P_2E0: u,V1exists_27_2E0: u] :
( ( ! [V2h_2E0: u,V3t_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ V2h_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1exists_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V2h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3t_2E0 ) ) ) ) ) ) )
& ! [V4h_2E0: u,V5t_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1exists_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V5t_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1exists_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V4h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V5t_2E0 ) ) ) ) ) ) ) )
=> ! [V6a0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V6a0_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1exists_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V6a0_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2Eexists__strongind,axiom,
! [A_27a: d,V0P_2E0: u,V1exists_27_2E0: u] :
( ( ! [V2h_2E0: u,V3t_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ V2h_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1exists_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V2h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3t_2E0 ) ) ) ) ) ) )
& ! [V4h_2E0: u,V5t_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V5t_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1exists_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V5t_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1exists_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V4h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V5t_2E0 ) ) ) ) ) ) ) )
=> ! [V6a0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V6a0_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1exists_27_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V6a0_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2Eexists__cases,axiom,
! [A_27a: d,V0P_2E0: u,V1a0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1a0_2E0 ) ) ) )
<=> ( ? [V2h_2E0: u,V3t_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1a0_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V2h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3t_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ V2h_2E0 ) ) ) ) )
| ? [V4h_2E0: u,V5t_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1a0_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V4h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V5t_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V5t_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2Eexists__thm,axiom,
! [A_27a: d,V0t_2E0: u,V1h_2E0: u,V2P_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) ) )
= mono_2Ec_2Ebool_2EF )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V1h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0t_2E0 ) ) ) ) ) )
<=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ A_27a @ V1h_2E0 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0t_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2Eexists__LNTH,axiom,
! [A_27a: d,V0P_2E0: u,V1l_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l_2E0 ) ) ) )
<=> ? [V2n: mono_2Etyop_2Enum_2Enum,V3e_2E0: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V3e_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ V3e_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2EMONO__exists,axiom,
! [A_27a: d,V0l_2E0: u,V1Q_2E0: u,V2P_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 ) @ V2P_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1Q_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1Q_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2Eexists__strong__ind,axiom,
! [A_27a: d,V0P_2E0: u,V1Q_2E0: u] :
( ( ! [V2h_2E0: u,V3t_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ V2h_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1Q_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V2h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3t_2E0 ) ) ) ) ) ) )
& ! [V4h_2E0: u,V5t_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1Q_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V5t_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V5t_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1Q_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V4h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V5t_2E0 ) ) ) ) ) ) ) )
=> ! [V6a0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V6a0_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1Q_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V6a0_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2Eexists__LDROP,axiom,
! [A_27a: d,V0ll_2E0: u,V1P_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) )
<=> ? [V2n: mono_2Etyop_2Enum_2Enum,V3a_2E0: u,V4t_2E0: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V3a_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V4t_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ A_27a @ V3a_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2Eevery__coind,axiom,
! [A_27a: d,V0P_2E0: u,V1Q_2E0: u] :
( ! [V2h_2E0: u,V3t_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1Q_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V2h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3t_2E0 ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ V2h_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1Q_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3t_2E0 ) ) ) ) ) )
=> ! [V4ll_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1Q_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V4ll_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eevery_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V4ll_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2Eevery__thm,axiom,
! [A_27a: d,V0t_2E0: u,V1h_2E0: u,V2P_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eevery_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) ) )
= mono_2Ec_2Ebool_2ET )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eevery_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V1h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0t_2E0 ) ) ) ) ) )
<=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ A_27a @ V1h_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eevery_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0t_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELL__ALL__THM,axiom,
! [A_27a: d,V0t_2E0: u,V1h_2E0: u,V2P_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eevery_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) ) )
= mono_2Ec_2Ebool_2ET )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eevery_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V1h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0t_2E0 ) ) ) ) ) )
<=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ A_27a @ V1h_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eevery_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0t_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2EMONO__every,axiom,
! [A_27a: d,V0l_2E0: u,V1Q_2E0: u,V2P_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 ) @ V2P_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1Q_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eevery_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eevery_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1Q_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2Eevery__strong__coind,axiom,
! [A_27a: d,V0P_2E0: u,V1Q_2E0: u] :
( ( ! [V2h_2E0: u,V3t_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1Q_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V2h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3t_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ V2h_2E0 ) ) ) ) )
& ! [V4h_2E0: u,V5t_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1Q_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V4h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V5t_2E0 ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1Q_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V5t_2E0 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eevery_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V5t_2E0 ) ) ) ) ) ) )
=> ! [V6ll_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V1Q_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V6ll_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eevery_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V6ll_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELFILTER__THM,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0P_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELFILTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) )
& ! [V1P_2E0: u,V2h_2E0: u,V3t_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELFILTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27b @ V2h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V3t_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ A_27b @ V2h_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27b @ V2h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELFILTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V3t_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELFILTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V3t_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELFILTER__NIL,axiom,
! [A_27a: d,V0P_2E0: u,V1ll_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eevery_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ebool_2E_7E ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) )
=> ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELFILTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) ) ).
thf(thm_2Ellist_2ELFILTER__EQ__NIL,axiom,
! [A_27a: d,V0P_2E0: u,V1ll_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELFILTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) )
<=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eevery_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ebool_2E_7E ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) ) ) ).
thf(thm_2Ellist_2ELFILTER__APPEND,axiom,
! [A_27a: d,V0P_2E0: u,V1ll1_2E0: u,V2ll2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll1_2E0 ) ) ) )
=> ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELFILTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll2_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELFILTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll1_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELFILTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll2_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELFLATTEN__THM,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0t_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELFLATTEN_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ c_2Ellist_2ELNIL_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) )
& ! [V1tl_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( c_2Ellist_2ELFLATTEN_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27c ) ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ c_2Ellist_2ELNIL_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27c ) ) @ V0t_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( c_2Ellist_2ELFLATTEN_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27c ) ) @ V0t_2E0 ) ) ) )
& ! [V2h_2E0: u,V3t_2E0: u,V4tl_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27d ) @ ( c_2Ellist_2ELFLATTEN_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27d ) ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27d ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27d @ V2h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27d ) @ V3t_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27d ) ) @ V4tl_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27d ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27d @ V2h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27d ) @ ( c_2Ellist_2ELFLATTEN_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27d ) ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27d ) @ V3t_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27d ) ) @ V4tl_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELFLATTEN__APPEND,axiom,
! [A_27a: d,V0h_2E0: u,V1t_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELFLATTEN_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ V1t_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELFLATTEN_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ V1t_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELFLATTEN__EQ__NIL,axiom,
! [A_27a: d,V0ll_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELFLATTEN_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ V0ll_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) )
<=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2Eevery_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Emin_2E_3D_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ V0ll_2E0 ) ) ) ) ) ).
thf(thm_2Ellist_2ELFLATTEN__SINGLETON,axiom,
! [A_27a: d,V0h_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELFLATTEN_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ c_2Ellist_2ELNIL_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0h_2E0 ) ) ).
thf(thm_2Ellist_2ELZIP__LUNZIP,axiom,
! [A_27a: d,A_27b: d,V0ll_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Ellist_2ELZIP_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Ellist_2ELUNZIP_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ll_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ll_2E0 ) ) ).
thf(thm_2Ellist_2ELUNFOLD__THM,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u,V1x_2E0: u,V2v1_2E0: u,V3v2_2E0: u] :
( ( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eoption_2ENONE_2E0 ) )
=> ( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ c_2Ellist_2ELNIL_2E0 ) ) )
& ( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2v1_2E0 ) @ ( s @ A_27b @ V3v2_2E0 ) ) ) ) ) )
=> ( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27b @ V3v2_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2v1_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELLIST__EQ,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
( ! [V2x_2E0: u] :
( ( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ c_2Ellist_2ELNIL_2E0 ) )
& ( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ c_2Ellist_2ELNIL_2E0 ) ) )
| ? [V3h_2E0: u,V4y_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27b @ V3h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V4y_2E0 ) ) ) ) ) )
& ( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27b @ V3h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) @ ( s @ A_27a @ V4y_2E0 ) ) ) ) ) ) ) )
=> ! [V5x_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ V1g_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) ) ) ) ).
thf(thm_2Ellist_2ELUNFOLD__EQ,axiom,
! [A_27a: d,A_27b: d,V0R_2E0: u,V1f_2E0: u,V2s_2E0: u,V3ll_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ A_27a @ V2s_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V3ll_2E0 ) ) ) )
& ! [V4s_2E0: u,V5ll_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ A_27a @ V4s_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V5ll_2E0 ) ) ) )
=> ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V1f_2E0 ) @ ( s @ A_27a @ V4s_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Eoption_2ENONE_2E0 ) )
& ( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V5ll_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ c_2Ellist_2ELNIL_2E0 ) ) )
| ? [V6s_27_2E0: u,V7x_2E0: u,V8ll_27_2E0: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V1f_2E0 ) @ ( s @ A_27a @ V4s_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V6s_27_2E0 ) @ ( s @ A_27b @ V7x_2E0 ) ) ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V5ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V7x_2E0 ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V5ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V8ll_27_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ A_27a @ V6s_27_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V8ll_27_2E0 ) ) ) ) ) ) ) )
=> ( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ V1f_2E0 ) @ ( s @ A_27a @ V2s_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V3ll_2E0 ) ) ) ).
thf(thm_2Ellist_2ELMAP__LUNFOLD,axiom,
! [A_27a: d,A_27b: d,A_27c: d,F1_2E0: u,F0_2E0: u] :
( ! [V0f_2E0: u,V4x_2E0: u,V5y_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ A_27c @ V4x_2E0 ) ) ) @ ( s @ A_27a @ V5y_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ V4x_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V5y_2E0 ) ) ) ) ) )
=> ( ! [V0f_2E0: u,V1g_2E0: u,V3s_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) ) @ V1g_2E0 ) ) ) @ ( s @ A_27c @ V3s_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) ) @ V1g_2E0 ) @ ( s @ A_27c @ V3s_2E0 ) ) ) ) ) )
=> ! [V0f_2E0: u,V1g_2E0: u,V2s_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) ) @ V1g_2E0 ) @ ( s @ A_27c @ V2s_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) ) @ V1g_2E0 ) ) ) @ ( s @ A_27c @ V2s_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELNTH__LDROP,axiom,
! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1l_2E0: u,V2x_2E0: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V2x_2E0 ) ) ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l_2E0 ) ) ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ).
thf(thm_2Ellist_2ELAPPEND__fromList,axiom,
! [A_27a: d,V0l1_2E0: u,V1l2_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l1_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l2_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l2_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELTAKE__LENGTH,axiom,
! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1ll_2E0: u,V2l_2E0: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l_2E0 ) ) ) )
=> ( V0n
= ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELTAKE__TAKE__LESS,axiom,
! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum,V2ll_2E0: u,V3l_2E0: u] :
( ( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3l_2E0 ) ) ) )
& ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1m @ V0n ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1m ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ETAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1m ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3l_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELTAKE__LLENGTH__NONE,axiom,
! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum,V2ll_2E0: u] :
( ( ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) ) )
= ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ V0n ) )
& ( mono_2Ec_2Eprim__rec_2E_3C @ V0n @ V1m ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1m ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) ) ).
thf(thm_2Ellist_2ELTAKE__LLENGTH__SOME,axiom,
! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1ll_2E0: u] :
( ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) )
= ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ V0n ) )
=> ? [V2l_2E0: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l_2E0 ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2EtoList_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2EtoList__LAPPEND__APPEND,axiom,
! [A_27a: d,V0x_2E0: u,V1l2_2E0: u,V2l1_2E0: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2EtoList_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2l1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l2_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0x_2E0 ) ) ) )
=> ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0x_2E0 )
= ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2EtoList_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2l1_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2EtoList_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l2_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELNTH__LLENGTH__NONE,axiom,
! [A_27a: d,V0x: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2l_2E0: u] :
( ( ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2l_2E0 ) ) ) )
= ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ V0x ) )
& ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0x @ V1n ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2l_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) ).
thf(thm_2Ellist_2ELNTH__NONE__MONO,axiom,
! [A_27a: d,V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2l_2E0: u] :
( ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0m ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2l_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
& ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ V1n ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2l_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) ).
thf(thm_2Ellist_2Elinear__order__to__llist__eq,axiom,
! [A_27a: d,F3_2E0: u,F0_2E0: u,F2_2E0: u,F1_2E0: u] :
( ! [V2ll_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 @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) ) )
<=> ? [V4i: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4i ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V3x_2E0 ) ) ) ) )
=> ( ! [V2ll_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_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_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 @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) ) )
=> ( ! [V2ll_2E0: u,V5x_2E0: u,V6y_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_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) ) @ ( s @ A_27a @ V5x_2E0 ) ) ) @ ( s @ A_27a @ V6y_2E0 ) ) ) )
<=> ? [V7i: mono_2Etyop_2Enum_2Enum,V8j: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V7i @ V8j )
& ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7i ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V5x_2E0 ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8j ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V6y_2E0 ) ) ) ) ) )
=> ( ! [V2ll_2E0: u,V5x_2E0: u,V6y_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) ) @ ( s @ A_27a @ V5x_2E0 ) ) ) @ ( s @ A_27a @ V6y_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V5x_2E0 ) @ ( 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_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) ) @ ( s @ A_27a @ V5x_2E0 ) ) ) @ ( s @ A_27a @ V6y_2E0 ) ) ) ) ) )
=> ! [V0lo_2E0: u,V1X_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eset__relation_2Elinear__order_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0lo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1X_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eset__relation_2Efinite__prefixes_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0lo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1X_2E0 ) ) ) ) )
=> ? [V2ll_2E0: u] :
( ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1X_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_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) ) ) ) )
& ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0lo_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) ) ) ) ) ) )
& ! [V9i: mono_2Etyop_2Enum_2Enum,V10j: mono_2Etyop_2Enum_2Enum,V11x_2E0: u] :
( ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V9i ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V11x_2E0 ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V10j ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V11x_2E0 ) ) ) ) )
=> ( V9i = V10j ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2Elinear__order__to__llist,axiom,
! [A_27a: d,F3_2E0: u,F0_2E0: u,F2_2E0: u,F1_2E0: u] :
( ! [V2ll_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 @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) ) )
<=> ? [V4i: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4i ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V3x_2E0 ) ) ) ) )
=> ( ! [V2ll_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_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_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 @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) ) )
=> ( ! [V2ll_2E0: u,V5x_2E0: u,V6y_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_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) ) @ ( s @ A_27a @ V5x_2E0 ) ) ) @ ( s @ A_27a @ V6y_2E0 ) ) ) )
<=> ? [V7i: mono_2Etyop_2Enum_2Enum,V8j: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V7i @ V8j )
& ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7i ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V5x_2E0 ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8j ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V6y_2E0 ) ) ) ) ) )
=> ( ! [V2ll_2E0: u,V5x_2E0: u,V6y_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) ) @ ( s @ A_27a @ V5x_2E0 ) ) ) @ ( s @ A_27a @ V6y_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V5x_2E0 ) @ ( 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_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) ) @ ( s @ A_27a @ V5x_2E0 ) ) ) @ ( s @ A_27a @ V6y_2E0 ) ) ) ) ) )
=> ! [V0lo_2E0: u,V1X_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eset__relation_2Elinear__order_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0lo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1X_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eset__relation_2Efinite__prefixes_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0lo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1X_2E0 ) ) ) ) )
=> ? [V2ll_2E0: u] :
( ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1X_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_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0lo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) ) ) ) ) ) ) ) )
& ! [V9i: mono_2Etyop_2Enum_2Enum,V10j: mono_2Etyop_2Enum_2Enum,V11x_2E0: u] :
( ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V9i ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V11x_2E0 ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V10j ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V11x_2E0 ) ) ) ) )
=> ( V9i = V10j ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELPREFIX__LNIL,axiom,
! [A_27a: d,V0ll_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELPREFIX_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELPREFIX_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) ) )
<=> ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) ) ) ).
thf(thm_2Ellist_2ELPREFIX__LCONS,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0ll_2E0: u,V1h_2E0: u,V2t_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELPREFIX_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V1h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2t_2E0 ) ) ) ) ) )
<=> ( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) )
| ? [V3l_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V1h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3l_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELPREFIX_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3l_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2t_2E0 ) ) ) ) ) ) )
& ! [V4h_2E0: u,V5t_2E0: u,V6ll_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELPREFIX_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27b @ V4h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V5t_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V6ll_2E0 ) ) ) )
<=> ? [V7l_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V6ll_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27b @ V4h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V7l_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELPREFIX_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V5t_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ V7l_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELPREFIX__LUNFOLD,axiom,
! [A_27a: d,A_27b: d,F0_2E0: u,F2_2E0: u,F1_2E0: u] :
( ! [V1ll_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) )
<=> ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) )
=> ( ! [V1ll_2E0: u,V2f_2E0: u,V4n_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_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V2f_2E0 ) ) ) @ ( s @ A_27b @ V4n_2E0 ) ) ) @ ( s @ A_27a @ V5x_2E0 ) ) ) )
<=> ! [V6h_2E0: u,V7t_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V6h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V7t_2E0 ) ) ) )
=> ( ( ( s @ A_27a @ V6h_2E0 )
= ( s @ A_27a @ V5x_2E0 ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELPREFIX_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V7t_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V2f_2E0 ) @ ( s @ A_27b @ V4n_2E0 ) ) ) ) ) ) ) ) )
=> ( ! [V1ll_2E0: u,V2f_2E0: u,V3v_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V2f_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ V3v_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ V3v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V2f_2E0 ) ) ) ) ) ) )
=> ! [V0n_2E0: u,V1ll_2E0: u,V2f_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELPREFIX_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V2f_2E0 ) @ ( s @ A_27b @ V0n_2E0 ) ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V2f_2E0 ) @ ( s @ A_27b @ V0n_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V2f_2E0 ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELPREFIX__REFL,axiom,
! [A_27a: d,V0ll_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELPREFIX_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) ) ).
thf(thm_2Ellist_2ELPREFIX__ANTISYM,axiom,
! [A_27a: d,V0l2_2E0: u,V1l1_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELPREFIX_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l2_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELPREFIX_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l2_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l1_2E0 ) ) ) ) )
=> ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l1_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l2_2E0 ) ) ) ).
thf(thm_2Ellist_2ELPREFIX__TRANS,axiom,
! [A_27a: d,V0l3_2E0: u,V1l2_2E0: u,V2l1_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELPREFIX_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2l1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l2_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELPREFIX_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l2_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l3_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELPREFIX_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2l1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l3_2E0 ) ) ) ) ) ).
thf(thm_2Ellist_2ELPREFIX__fromList,axiom,
! [A_27a: d,F0_2E0: u,F1_2E0: u] :
( ! [V0l_2E0: u,V1ll_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) )
<=> ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) ) )
=> ( ! [V0l_2E0: u,V2ys_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 @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2ys_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EisPREFIX_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2ys_2E0 ) ) ) ) )
=> ! [V0l_2E0: u,V1ll_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELPREFIX_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2EtoList_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2Eprefixes__lprefix__total,axiom,
! [A_27a: d,V0ll_2E0: u,V1l1_2E0: u,V2l2_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELPREFIX_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELPREFIX_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2l2_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0ll_2E0 ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELPREFIX_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2l2_2E0 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELPREFIX_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2l2_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l1_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELTAKE__IMP__LDROP,axiom,
! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1ll_2E0: u,V2l1_2E0: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l1_2E0 ) ) ) )
=> ? [V3l2_2E0: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3l2_2E0 ) ) ) )
& ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2l1_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3l2_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) ) ).
thf(thm_2Ellist_2ELDROP__EQ__LNIL,axiom,
! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1ll_2E0: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) ) )
<=> ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ll_2E0 ) ) ) )
= ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ V0n ) ) ) ).
thf(thm_2Ellist_2ELPREFIX__APPEND,axiom,
! [A_27a: d,V0l2_2E0: u,V1l1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELPREFIX_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l2_2E0 ) ) ) )
<=> ? [V2ll_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l2_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2ll_2E0 ) ) ) ) ) ).
thf(thm_2Ellist_2ENOT__LFINITE__DROP__LFINITE,axiom,
! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1l_2E0: u,V2t_2E0: u] :
( ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l_2E0 ) ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2t_2E0 ) ) ) ) )
=> ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2t_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELDROP__APPEND1,axiom,
! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1l2_2E0: u,V2l1_2E0: u,V3l_2E0: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2l1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3l_2E0 ) ) ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2l1_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l2_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V3l_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1l2_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELDROP__fromList,axiom,
! [A_27a: d,V0ls_2E0: u,V1n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0ls_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0ls_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0ls_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ).
thf(thm_2Ellist_2ELDROP__SUC,axiom,
! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1ls_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V0n ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ls_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2EOPTION__BIND_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELDROP_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1ls_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ c_2Ellist_2ELTL_2E0 ) ) ) ) ).
thf(thm_2Ellist_2ELHD__LGENLIST,axiom,
! [A_27a: d,F0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o] :
( ! [V0limopt: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
( ( F0 @ V0limopt )
<=> ( V0limopt
= ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) )
=> ! [V0limopt: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1f_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1f_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V0limopt ) ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F0 @ V0limopt ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELTL__LGENLIST,axiom,
! [A_27a: d,F0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o] :
( ! [V0limopt: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
( ( F0 @ V0limopt )
<=> ( V0limopt
= ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) )
=> ! [V0limopt: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1f_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1f_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V0limopt ) ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F0 @ V0limopt ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ mono_2Ec_2Enum_2ESUC ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( mono_2Ec_2Eoption_2EOPTION__MAP_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Eprim__rec_2EPRE @ V0limopt ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2Enumopt__BISIMULATION,axiom,
! [V0mopt: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1nopt: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
( ( V0mopt = V1nopt )
<=> ? [V2R: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > $o] :
( ( V2R @ V0mopt @ V1nopt )
& ! [V3m: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V4n: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
( ( V2R @ V3m @ V4n )
=> ( ( ( V3m
= ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) )
& ( V4n
= ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) )
| ( ( (~)
@ ( V3m
= ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) )
& ( (~)
@ ( V4n
= ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) )
& ( V2R @ ( mono_2Ec_2Eoption_2EOPTION__MAP_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Eprim__rec_2EPRE @ V3m ) @ ( mono_2Ec_2Eoption_2EOPTION__MAP_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Eprim__rec_2EPRE @ V4n ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELGENLIST__EQ__LNIL,axiom,
! [A_27a: d,V0n: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1f_2E0: u] :
( ( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1f_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V0n ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) )
<=> ( V0n
= ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) )
& ( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1f_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V0n ) ) ) ) )
<=> ( V0n
= ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ).
thf(thm_2Ellist_2ELFINITE__LGENLIST,axiom,
! [A_27a: d,V0n: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1f_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1f_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V0n ) ) ) ) ) ) )
<=> ( (~) @ ( V0n = mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum ) ) ) ).
thf(thm_2Ellist_2ELTL__HD__LTL__LHD,axiom,
! [A_27a: d,F1_2E0: u,F0_2E0: u] :
( ! [V1h_2E0: u,V2t_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) ) @ F1_2E0 ) @ ( s @ A_27a @ V1h_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2t_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2t_2E0 ) @ ( s @ A_27a @ V1h_2E0 ) ) ) ) ) )
=> ( ! [V0l_2E0: u,V1h_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l_2E0 ) ) ) @ ( s @ A_27a @ V1h_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( c_2Eoption_2EOPTION__BIND_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) ) @ F1_2E0 ) @ ( s @ A_27a @ V1h_2E0 ) ) ) ) ) )
=> ! [V0l_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( c_2Ellist_2ELTL__HD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) @ ( c_2Eoption_2EOPTION__BIND_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Ellist_2Ellist @ A_27a ) @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0l_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELGENLIST__SOME,axiom,
! [A_27a: d,V0f_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V0f_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) )
& ! [V1n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V0f_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V1n ) ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V0f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ mono_2Ec_2Enum_2ESUC ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ V1n ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELGENLIST__SOME__compute,axiom,
! [A_27a: d,V0f_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V0f_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) )
& ! [V1n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V0f_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V0f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ mono_2Ec_2Enum_2ESUC ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2D @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) )
& ! [V2n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V0f_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V2n ) ) ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V0f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ mono_2Ec_2Enum_2ESUC ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V2n ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELNTH__LGENLIST,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V0n: mono_2Etyop_2Enum_2Enum,V1f_2E0: u,V3lim0: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1f_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3lim0 ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Eprim__rec_2E_3C @ V0n @ V3lim0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
=> ! [V0n: mono_2Etyop_2Enum_2Enum,V1f_2E0: u,V2lim: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1f_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V2lim ) ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V2lim ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ F0_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1f_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELNTH__LMAP,axiom,
! [A_27a: d,A_27b: d,V0n: mono_2Etyop_2Enum_2Enum,V1f_2E0: u,V2l_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2l_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELNTH_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V2l_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELLENGTH__LGENLIST,axiom,
! [A_27a: d,V0limopt: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1f_2E0: u] :
( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1f_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V0limopt ) ) ) ) ) ) )
= V0limopt ) ).
thf(thm_2Ellist_2ELMAP__LGENLIST,axiom,
! [A_27a: d,A_27b: d,V0limopt: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1g_2E0: u,V2f_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V2f_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V1g_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V0limopt ) ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ V2f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V0limopt ) ) ) ) ) ).
thf(thm_2Ellist_2ELGENLIST__EQ__CONS,axiom,
! [A_27a: d,V0t_2E0: u,V1h_2E0: u,V2f_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2f_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27a @ V1h_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0t_2E0 ) ) ) )
<=> ( ( ( s @ A_27a @ V1h_2E0 )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) )
& ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V0t_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELGENLIST__CHUNK__GENLIST,axiom,
! [A_27a: d,V0n: mono_2Etyop_2Enum_2Enum,V1f_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1f_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1f_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELGENLIST_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( mono_2Ec_2Earithmetic_2E_2B @ V0n ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELREPEAT__thm,axiom,
! [A_27a: d,V0l_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELREPEAT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELREPEAT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELREPEAT__NIL,axiom,
! [A_27a: d] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELREPEAT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) ) ).
thf(thm_2Ellist_2ELREPEAT__EQ__LNIL,axiom,
! [A_27a: d,V0l_2E0: u] :
( ( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELREPEAT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 ) )
<=> ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 )
= ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) )
& ( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ c_2Ellist_2ELNIL_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELREPEAT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) )
<=> ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 )
= ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ).
thf(thm_2Ellist_2ELHD__LREPEAT,axiom,
! [A_27a: d,V0l_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELREPEAT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ellist_2ELHD_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELTL__LREPEAT,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V0l_2E0: u,V1t_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1t_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1t_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELREPEAT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) ) ) )
=> ! [V0l_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELREPEAT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ ( c_2Ellist_2ELTL_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2EfromList_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Ellist_2ELLENGTH__LREPEAT,axiom,
! [A_27a: d,V0l_2E0: u] :
( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Ellist_2ELLENGTH_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Ellist_2ELREPEAT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) ) ) )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2ENULL_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0l_2E0 ) ) ) ) @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) @ mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum ) ) ).
%------------------------------------------------------------------------------