ITP001 Axioms: ITP068^4.ax
%------------------------------------------------------------------------------
% File : ITP068^4 : 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 : path.ax [Gau19]
% : HL4068^4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 759 ( 319 unt; 313 typ; 0 def)
% Number of atoms : 933 ( 496 equ; 16 cnn)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 20434 ( 16 ~; 11 |; 119 &;20135 @)
% ( 51 <=>; 102 =>; 0 <=; 0 <~>)
% Maximal formula depth : 42 ( 7 avg;20135 nst)
% Number of types : 7 ( 6 usr)
% Number of type conns : 754 ( 754 >; 0 *; 0 +; 0 <<)
% Number of symbols : 309 ( 307 usr; 101 con; 0-5 aty)
% Number of variables : 1730 ( 0 ^1688 !; 42 ?;1730 :)
% 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(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_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(tyop_2Epath_2Epath,type,
tyop_2Epath_2Epath: 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_2Epair_2E_23_23_2E3,type,
c_2Epair_2E_23_23_2E3: du > du > du > u ).
thf(c_2Earithmetic_2E_2B_2E0,type,
c_2Earithmetic_2E_2B_2E0: 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_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_2Elist_2EAPPEND_2E0,type,
c_2Elist_2EAPPEND_2E0: 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_2Ebool_2ECOND_2E0,type,
c_2Ebool_2ECOND_2E0: u ).
thf(c_2Ebool_2ECOND_2E3,type,
c_2Ebool_2ECOND_2E3: du > du > du > u ).
thf(c_2Elist_2ECONS_2E0,type,
c_2Elist_2ECONS_2E0: u ).
thf(c_2Elist_2ECONS_2E2,type,
c_2Elist_2ECONS_2E2: du > du > u ).
thf(c_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_2Epair_2EFST_2E1,type,
c_2Epair_2EFST_2E1: 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_2Epred__set_2EIMAGE_2E0,type,
c_2Epred__set_2EIMAGE_2E0: u ).
thf(c_2Epred__set_2EIMAGE_2E2,type,
c_2Epred__set_2EIMAGE_2E2: du > du > u ).
thf(c_2Ebool_2EIN_2E0,type,
c_2Ebool_2EIN_2E0: u ).
thf(c_2Ebool_2EIN_2E2,type,
c_2Ebool_2EIN_2E2: du > du > u ).
thf(c_2Epred__set_2EINSERT_2E0,type,
c_2Epred__set_2EINSERT_2E0: u ).
thf(c_2Epred__set_2EINSERT_2E2,type,
c_2Epred__set_2EINSERT_2E2: du > du > 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_2Elist_2ELENGTH_2E0,type,
c_2Elist_2ELENGTH_2E0: u ).
thf(c_2Elist_2ELENGTH_2E1,type,
c_2Elist_2ELENGTH_2E1: 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_2ELMAP_2E0,type,
c_2Ellist_2ELMAP_2E0: u ).
thf(c_2Ellist_2ELMAP_2E1,type,
c_2Ellist_2ELMAP_2E1: du > 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_2E2,type,
c_2Ellist_2ELNTH_2E2: du > 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_2ELUNFOLD_2E0,type,
c_2Ellist_2ELUNFOLD_2E0: u ).
thf(c_2Ellist_2ELUNFOLD_2E2,type,
c_2Ellist_2ELUNFOLD_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_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__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_2Epath_2EPL_2E0,type,
c_2Epath_2EPL_2E0: u ).
thf(c_2Epath_2EPL_2E1,type,
c_2Epath_2EPL_2E1: du > u ).
thf(c_2Epath_2ESN_2E0,type,
c_2Epath_2ESN_2E0: u ).
thf(c_2Epath_2ESN_2E1,type,
c_2Epath_2ESN_2E1: du > u ).
thf(c_2Epair_2ESND_2E0,type,
c_2Epair_2ESND_2E0: u ).
thf(c_2Epair_2ESND_2E1,type,
c_2Epair_2ESND_2E1: du > u ).
thf(c_2Eoption_2ESOME_2E0,type,
c_2Eoption_2ESOME_2E0: u ).
thf(c_2Eoption_2ESOME_2E1,type,
c_2Eoption_2ESOME_2E1: du > u ).
thf(c_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_2Eoption_2ETHE_2E0,type,
c_2Eoption_2ETHE_2E0: u ).
thf(c_2Eoption_2ETHE_2E1,type,
c_2Eoption_2ETHE_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_2Epred__set_2EUNIV_2E0,type,
c_2Epred__set_2EUNIV_2E0: u ).
thf(c_2Erelation_2EWF_2E0,type,
c_2Erelation_2EWF_2E0: u ).
thf(c_2Erelation_2EWF_2E1,type,
c_2Erelation_2EWF_2E1: du > u ).
thf(c_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_2Epath_2Edrop_2E0,type,
c_2Epath_2Edrop_2E0: u ).
thf(c_2Epath_2Edrop_2E2,type,
c_2Epath_2Edrop_2E2: du > du > u ).
thf(c_2Epath_2Eel_2E0,type,
c_2Epath_2Eel_2E0: u ).
thf(c_2Epath_2Eel_2E2,type,
c_2Epath_2Eel_2E2: du > du > u ).
thf(c_2Epath_2Eevery_2E0,type,
c_2Epath_2Eevery_2E0: u ).
thf(c_2Epath_2Eevery_2E2,type,
c_2Epath_2Eevery_2E2: du > du > u ).
thf(c_2Epath_2Eexists_2E0,type,
c_2Epath_2Eexists_2E0: u ).
thf(c_2Epath_2Eexists_2E2,type,
c_2Epath_2Eexists_2E2: du > du > u ).
thf(c_2Epath_2Efilter_2E0,type,
c_2Epath_2Efilter_2E0: u ).
thf(c_2Epath_2Efilter_2E2,type,
c_2Epath_2Efilter_2E2: du > du > u ).
thf(c_2Epath_2Efinite_2E0,type,
c_2Epath_2Efinite_2E0: u ).
thf(c_2Epath_2Efinite_2E1,type,
c_2Epath_2Efinite_2E1: du > u ).
thf(c_2Epath_2Efirst_2E0,type,
c_2Epath_2Efirst_2E0: u ).
thf(c_2Epath_2Efirst_2E1,type,
c_2Epath_2Efirst_2E1: du > u ).
thf(c_2Epath_2EfirstP__at_2E0,type,
c_2Epath_2EfirstP__at_2E0: u ).
thf(c_2Epath_2EfirstP__at_2E3,type,
c_2Epath_2EfirstP__at_2E3: du > du > du > u ).
thf(c_2Epath_2Efirst__label_2E0,type,
c_2Epath_2Efirst__label_2E0: u ).
thf(c_2Epath_2Efirst__label_2E1,type,
c_2Epath_2Efirst__label_2E1: du > u ).
thf(c_2Epath_2EfromPath_2E0,type,
c_2Epath_2EfromPath_2E0: u ).
thf(c_2Epath_2EfromPath_2E1,type,
c_2Epath_2EfromPath_2E1: du > u ).
thf(c_2EfixedPoint_2Egfp_2E0,type,
c_2EfixedPoint_2Egfp_2E0: u ).
thf(c_2EfixedPoint_2Egfp_2E1,type,
c_2EfixedPoint_2Egfp_2E1: du > u ).
thf(c_2Epath_2Eis__stopped_2E0,type,
c_2Epath_2Eis__stopped_2E0: u ).
thf(c_2Epath_2Eis__stopped_2E1,type,
c_2Epath_2Eis__stopped_2E1: du > u ).
thf(c_2Epath_2Elabels_2E0,type,
c_2Epath_2Elabels_2E0: u ).
thf(c_2Epath_2Elabels_2E1,type,
c_2Epath_2Elabels_2E1: du > u ).
thf(c_2Epath_2Elast_2E0,type,
c_2Epath_2Elast_2E0: u ).
thf(c_2Epath_2Elast_2E1,type,
c_2Epath_2Elast_2E1: du > u ).
thf(c_2Epath_2Elength_2E0,type,
c_2Epath_2Elength_2E0: u ).
thf(c_2Epath_2Elength_2E1,type,
c_2Epath_2Elength_2E1: du > u ).
thf(c_2Epath_2Emem_2E0,type,
c_2Epath_2Emem_2E0: u ).
thf(c_2Epath_2Emem_2E2,type,
c_2Epath_2Emem_2E2: du > du > u ).
thf(c_2EfixedPoint_2Emonotone_2E0,type,
c_2EfixedPoint_2Emonotone_2E0: u ).
thf(c_2EfixedPoint_2Emonotone_2E1,type,
c_2EfixedPoint_2Emonotone_2E1: du > u ).
thf(c_2Epath_2Enth__label_2E0,type,
c_2Epath_2Enth__label_2E0: u ).
thf(c_2Epath_2Enth__label_2E2,type,
c_2Epath_2Enth__label_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_2Epath_2Eokpath_2E0,type,
c_2Epath_2Eokpath_2E0: u ).
thf(c_2Epath_2Eokpath_2E1,type,
c_2Epath_2Eokpath_2E1: du > u ).
thf(c_2Epath_2Eokpath_2E2,type,
c_2Epath_2Eokpath_2E2: du > du > u ).
thf(c_2Epath_2Eokpath__f_2E0,type,
c_2Epath_2Eokpath__f_2E0: u ).
thf(c_2Epath_2Eokpath__f_2E1,type,
c_2Epath_2Eokpath__f_2E1: du > u ).
thf(c_2Epath_2Eokpath__f_2E2,type,
c_2Epath_2Eokpath__f_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_2Epath_2Eparallel__comp_2E0,type,
c_2Epath_2Eparallel__comp_2E0: u ).
thf(c_2Epath_2Eparallel__comp_2E2,type,
c_2Epath_2Eparallel__comp_2E2: du > du > u ).
thf(c_2Epath_2Eparallel__comp_2E5,type,
c_2Epath_2Eparallel__comp_2E5: du > du > du > du > du > u ).
thf(c_2Epath_2Epconcat_2E0,type,
c_2Epath_2Epconcat_2E0: u ).
thf(c_2Epath_2Epconcat_2E3,type,
c_2Epath_2Epconcat_2E3: du > du > du > u ).
thf(c_2Epath_2Epcons_2E0,type,
c_2Epath_2Epcons_2E0: u ).
thf(c_2Epath_2Epcons_2E3,type,
c_2Epath_2Epcons_2E3: du > du > du > u ).
thf(c_2Epath_2Epgenerate_2E0,type,
c_2Epath_2Epgenerate_2E0: u ).
thf(c_2Epath_2Epgenerate_2E2,type,
c_2Epath_2Epgenerate_2E2: du > du > u ).
thf(c_2Epath_2Eplink_2E0,type,
c_2Epath_2Eplink_2E0: u ).
thf(c_2Epath_2Eplink_2E2,type,
c_2Epath_2Eplink_2E2: du > du > u ).
thf(c_2Epath_2Epmap_2E0,type,
c_2Epath_2Epmap_2E0: u ).
thf(c_2Epath_2Epmap_2E3,type,
c_2Epath_2Epmap_2E3: du > du > du > u ).
thf(c_2Epath_2Eseg_2E0,type,
c_2Epath_2Eseg_2E0: u ).
thf(c_2Epath_2Eseg_2E3,type,
c_2Epath_2Eseg_2E3: du > du > du > u ).
thf(c_2Epath_2Estopped__at_2E0,type,
c_2Epath_2Estopped__at_2E0: u ).
thf(c_2Epath_2Estopped__at_2E1,type,
c_2Epath_2Estopped__at_2E1: du > u ).
thf(c_2Epath_2Etail_2E0,type,
c_2Epath_2Etail_2E0: u ).
thf(c_2Epath_2Etail_2E1,type,
c_2Epath_2Etail_2E1: du > u ).
thf(c_2Epath_2Etake_2E0,type,
c_2Epath_2Etake_2E0: u ).
thf(c_2Epath_2Etake_2E2,type,
c_2Epath_2Etake_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_2Epath_2EtoPath_2E0,type,
c_2Epath_2EtoPath_2E0: u ).
thf(c_2Epath_2EtoPath_2E1,type,
c_2Epath_2EtoPath_2E1: du > u ).
thf(c_2Epath_2Etrace__machine_2E0,type,
c_2Epath_2Etrace__machine_2E0: u ).
thf(c_2Epath_2Etrace__machine_2E1,type,
c_2Epath_2Etrace__machine_2E1: du > u ).
thf(c_2Epath_2Etrace__machine_2E4,type,
c_2Epath_2Etrace__machine_2E4: du > du > du > du > u ).
thf(c_2Epath_2Eunfold_2E0,type,
c_2Epath_2Eunfold_2E0: u ).
thf(c_2Epath_2Eunfold_2E3,type,
c_2Epath_2Eunfold_2E3: du > du > 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_2Ebool_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( $o > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > $o > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool: ( ( mono_2Etyop_2Enum_2Enum > $o ) > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: ( ( 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_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_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Enum_2Enum > $o ).
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_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Enum_2Enum > $o > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Enum_2Enum > $o > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ) > mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > ( 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).
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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_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_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).
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_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > ( mono_2Etyop_2Enum_2Enum > 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_2Enum_2Enum > 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_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_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_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_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_2Enum_2Enum > 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_2Enum_2Enum > 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_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_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Enum_2Enum > $o > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).
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_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_2Epred__set_2EEMPTY_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Ebool_2EF,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(mono_2Ec_2Epred__set_2EGSPEC_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Epred__set_2EGSPEC_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Epred__set_2EIMAGE_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Epred__set_2EIMAGE_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).
thf(mono_2Ec_2Epred__set_2EINSERT_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Epred__set_2EINSERT_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
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_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_2Eoption_2Eoption__CASE_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
mono_2Ec_2Eoption_2Eoption__CASE_2Emono_2Etyop_2Enum_2Enum_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_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).
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_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( $o > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ) > 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: ( ( 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Enum_2Enum > $o ) > 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_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: ( mono_2Etyop_2Enum_2Enum > $o > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: ( mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_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 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > 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_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > ( 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_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_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_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29: ( mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > ( 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_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(i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_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_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > $o > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: du > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: du > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: du > ( 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Enum_2Enum > $o ).
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_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: du > mono_2Etyop_2Enum_2Enum > $o > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: du > mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).
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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_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 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).
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_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29: du > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > ( 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_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_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_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29: du > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > ( 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_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(j_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_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_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( 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_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_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ 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_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ 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_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_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_2Emin_2Efun @ tyop_2Enum_2Enum @ ( 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( 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_2Emin_2Efun @ tyop_2Enum_2Enum @ ( 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_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_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_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( 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_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_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_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( 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_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( 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_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(ij_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ 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_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: $o > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
! [V0: ( 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_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_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_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_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_2Emin_2Efun_28tyop_2Enum_2Enum_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] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_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_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > ( 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_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_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_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > ( 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_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( 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_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_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(ji_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
( ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_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(arityeq3_2Ec_2Epair_2E_23_23_2E3_2Emono_2EA_27a_20mono_2Etyop_2Ellist_2Ellist_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2EA_27c_20mono_2Etyop_2Ellist_2Ellist_28tyop_2Epair_2Eprod_28A_27d_2CA_27c_29_29,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27d @ A_27c ) ) ) @ ( c_2Epair_2E_23_23_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27d @ A_27c ) ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27d @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27d @ A_27c ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27d @ A_27c ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27d @ A_27c ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27d @ A_27c ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27d @ A_27c ) ) ) ) ) ) @ c_2Epair_2E_23_23_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27d @ A_27c ) ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ X2_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_23_23_2E2_2Emono_2EA_27b_20mono_2EA_27a_20mono_2EA_27d_20mono_2EA_27c,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Epair_2Eprod @ A_27d @ A_27c ) ) @ ( c_2Epair_2E_23_23_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Epair_2Eprod @ A_27d @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Epair_2Eprod @ A_27d @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Epair_2Eprod @ A_27d @ A_27c ) ) ) ) @ c_2Epair_2E_23_23_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ A_27c @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27c @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27d,axiom,
! [A_27a: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27d ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ A_27d @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Epair_2Eprod @ A_27a @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Epair_2Eprod @ A_27a @ A_27d ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27d @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Ellist_2Ellist_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27e,axiom,
! [A_27c: d,A_27e: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27e ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ X0_2E0 ) @ ( s @ A_27e @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27e ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27e @ ( tyop_2Epair_2Eprod @ A_27c @ A_27e ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27e @ ( tyop_2Epair_2Eprod @ A_27c @ A_27e ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27c @ X0_2E0 ) ) ) @ ( s @ A_27e @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27c @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epath_2Epath_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1: $o] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ 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_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(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(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Epath_2Epath_28A_27a_2CA_27b_29,axiom,
! [A_27a: d,A_27b: d,X0: $o,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X2_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2ECONS_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27b,axiom,
! [A_27b: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ A_27b @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X1_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ A_27b ) ) @ c_2Elist_2EEL_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27a_20mono_2Etyop_2Ellist_2Ellist_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ A_27a @ ( c_2Epair_2EFST_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ X0_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epath_2Epath_28A_27a_2CA_27b_29_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2EGSPEC_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epath_2Epath_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2Ctyop_2Epath_2Epath_28A_27a_2CA_27b_29_29_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2EGSPEC_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epath_2Epath_28A_27a_2CA_27b_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ 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_2ELAPPEND_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ c_2Ellist_2ELAPPEND_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ 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_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ c_2Ellist_2ELCONS_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27b,axiom,
! [A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Enum_2Enum ) @ c_2Elist_2ELENGTH_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ tyop_2Enum_2Enum ) @ c_2Elist_2ELENGTH_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ 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_2ELFINITE_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ c_2Ellist_2ELFINITE_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_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 @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) ) @ c_2Ellist_2ELMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Ellist_2ELMAP_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27d_2CA_27c_29,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27d @ A_27c ) ) ) @ ( c_2Ellist_2ELMAP_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Epair_2Eprod @ A_27d @ A_27c ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27d @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Epair_2Eprod @ A_27d @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27d @ A_27c ) ) ) ) @ c_2Ellist_2ELMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Epair_2Eprod @ A_27d @ A_27c ) ) @ X0_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_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_2ELUNFOLD_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_27c ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Ellist_2Ellist @ A_27c ) ) ) @ c_2Ellist_2ELUNFOLD_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ellist_2ELUNFOLD_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2EA_27c,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ X0_2E0 ) @ ( s @ A_27c @ X1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ c_2Ellist_2ELUNFOLD_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ X0_2E0 ) ) ) @ ( s @ A_27c @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27c_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_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 @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2EPL_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X0_2E0 ) ) ) )
= ( 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_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ c_2Epath_2EPL_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2EPL_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: d,A_27d: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ X0_2E0 ) ) ) )
= ( 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_2Epath_2Epath @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ c_2Epath_2EPL_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2ESN_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2ESN_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( 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_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ tyop_2Emin_2Ebool ) @ c_2Epath_2ESN_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27a_20mono_2Etyop_2Ellist_2Ellist_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ c_2Epair_2ESND_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ 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_2Elist_2Elist_28A_27b_29,axiom,
! [A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29,axiom,
! [A_27a: d,A_27c: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ c_2Eoption_2ETHE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Ellist_2Ellist_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_29_20mono_2Etyop_2Epath_2Epath_28A_27a_2CA_27b_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ETYPE__DEFINITION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2ETYPE__DEFINITION_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2Ctyop_2Epath_2Epath_28A_27a_2CA_27b_29_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epath_2Epath_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2EUNCURRY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27b_20mono_2Etyop_2Epath_2Epath_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epath_2Epath_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2EUNCURRY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27c_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27c_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ c_2Epair_2EUNCURRY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Epath_2Epath_28A_27a_2CA_27b_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EUNION_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2EWF_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( 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_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2Erelation_2EWF_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epath_2Edrop_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Edrop_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) ) @ c_2Epath_2Edrop_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epath_2Eel_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ A_27a @ ( c_2Epath_2Eel_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X1_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ A_27a ) ) @ c_2Epath_2Eel_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epath_2Eel_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: d,A_27d: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ A_27c @ ( c_2Epath_2Eel_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ X1_2E0 ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ A_27c ) ) @ c_2Epath_2Eel_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epath_2Eevery_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eevery_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2Epath_2Eevery_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epath_2Eevery_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eevery_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ c_2Epath_2Eevery_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epath_2Eexists_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2Epath_2Eexists_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epath_2Eexists_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ c_2Epath_2Eexists_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epath_2Efilter_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Efilter_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) ) @ c_2Epath_2Efilter_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Efinite_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ c_2Epath_2Efinite_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Efinite_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: d,A_27d: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ tyop_2Emin_2Ebool ) @ c_2Epath_2Efinite_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Efirst_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X0_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ A_27a ) @ c_2Epath_2Efirst_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Efirst_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: d,A_27c: d,X0_2E0: u] :
( ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ X0_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ A_27a ) @ c_2Epath_2Efirst_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Efirst_2E1_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: d,A_27c: d,X0_2E0: u] :
( ( s @ A_27b @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ X0_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ A_27b ) @ c_2Epath_2Efirst_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Efirst_2E1_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: d,A_27c: d,X0_2E0: u] :
( ( s @ A_27c @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27b ) @ X0_2E0 ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27c @ A_27b ) @ A_27c ) @ c_2Epath_2Efirst_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27b ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Efirst_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: d,A_27d: d,X0_2E0: u] :
( ( s @ A_27c @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ X0_2E0 ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ A_27c ) @ c_2Epath_2Efirst_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Efirst_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27a ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ c_2Epath_2Efirst_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Efirst_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ c_2Epath_2Efirst_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ X0_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Epath_2EfirstP__at_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2EfirstP__at_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X2 ) ) ) ) )
= ( 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_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ c_2Epath_2EfirstP__at_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X1_2E0 ) ) ) @ X2 ) ) ).
thf(arityeq1_2Ec_2Epath_2Efirst__label_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ A_27b @ ( c_2Epath_2Efirst__label_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X0_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ A_27b ) @ c_2Epath_2Efirst__label_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Efirst__label_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ A_27a @ ( c_2Epath_2Efirst__label_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27a ) @ X0_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27b @ A_27a ) @ A_27a ) @ c_2Epath_2Efirst__label_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2EfromPath_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Epath_2EfromPath_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ c_2Epath_2EfromPath_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2EfixedPoint_2Egfp_2E1_2Emono_2Etyop_2Epath_2Epath_28A_27a_2CA_27b_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2EfixedPoint_2Egfp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2EfixedPoint_2Egfp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Eis__stopped_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eis__stopped_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ c_2Epath_2Eis__stopped_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Eis__stopped_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: d,A_27d: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eis__stopped_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ tyop_2Emin_2Ebool ) @ c_2Epath_2Eis__stopped_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Elabels_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Epath_2Elabels_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ c_2Epath_2Elabels_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Elabels_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: d,A_27c: d,X0_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( c_2Epath_2Elabels_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ ( tyop_2Ellist_2Ellist @ A_27c ) ) @ c_2Epath_2Elabels_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Elabels_2E1_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: d,A_27c: d,X0_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( c_2Epath_2Elabels_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( tyop_2Ellist_2Ellist @ A_27c ) ) @ c_2Epath_2Elabels_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Elabels_2E1_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: d,A_27c: d,X0_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Epath_2Elabels_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27b ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27c @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ c_2Epath_2Elabels_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27b ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Elabels_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Epath_2Elabels_2E1 @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27a ) @ ( tyop_2Ellist_2Ellist @ A_27a ) ) @ c_2Epath_2Elabels_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Elabels_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Epath_2Elabels_2E1 @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ ( tyop_2Ellist_2Ellist @ A_27b ) ) @ c_2Epath_2Elabels_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Elast_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ A_27a @ ( c_2Epath_2Elast_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X0_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ A_27a ) @ c_2Epath_2Elast_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Elast_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: d,A_27d: d,X0_2E0: u] :
( ( s @ A_27c @ ( c_2Epath_2Elast_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ X0_2E0 ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ A_27c ) @ c_2Epath_2Elast_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Elength_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Epath_2Elength_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ 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_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ c_2Epath_2Elength_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Elength_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: d,A_27c: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Epath_2Elength_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ 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_2Epath_2Epath @ A_27a @ A_27c ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ c_2Epath_2Elength_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Elength_2E1_2Emono_2EA_27b_20mono_2EA_27d,axiom,
! [A_27b: d,A_27d: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Epath_2Elength_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27d ) @ 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_2Epath_2Epath @ A_27b @ A_27d ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ c_2Epath_2Elength_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27d ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Elength_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: d,A_27d: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Epath_2Elength_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ 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_2Epath_2Epath @ A_27c @ A_27d ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ c_2Epath_2Elength_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epath_2Emem_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Emem_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2Epath_2Emem_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epath_2Emem_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Emem_2E2 @ ( s @ A_27c @ X0_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ tyop_2Emin_2Ebool ) ) @ c_2Epath_2Emem_2E0 ) @ ( s @ A_27c @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2EfixedPoint_2Emonotone_2E1_2Emono_2Etyop_2Epath_2Epath_28A_27a_2CA_27b_29_20mono_2Etyop_2Epath_2Epath_28A_27a_2CA_27b_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EfixedPoint_2Emonotone_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ 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 @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2EfixedPoint_2Emonotone_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epath_2Enth__label_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ A_27b @ ( c_2Epath_2Enth__label_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X1_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ A_27b ) ) @ c_2Epath_2Enth__label_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epath_2Enth__label_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ A_27a @ ( c_2Epath_2Enth__label_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27a ) @ X1_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27b @ A_27a ) @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27b @ A_27a ) @ A_27a ) ) @ c_2Epath_2Enth__label_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epath_2Enth__label_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: d,A_27d: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ A_27c @ ( c_2Epath_2Enth__label_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27d @ A_27c ) @ X1_2E0 ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27d @ A_27c ) @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27d @ A_27c ) @ A_27c ) ) @ c_2Epath_2Enth__label_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27d @ A_27c ) @ 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_2EA_27b_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27b: d,X0_2E0: u,X1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ 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_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) ) ) @ c_2Ecombin_2Eo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ 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(arityeq1_2Ec_2Epath_2Eokpath_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2Eokpath_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2Epath_2Eokpath_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epath_2Eokpath_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2Epath_2Eokpath_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epath_2Eokpath_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ c_2Epath_2Eokpath_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epath_2Eokpath_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ c_2Epath_2Eokpath_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epath_2Eokpath_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27b ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27c @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27c @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2Epath_2Eokpath_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27b ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epath_2Eokpath_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27a ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Epath_2Eokpath_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27a ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epath_2Eokpath_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27c,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ c_2Epath_2Eokpath_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epath_2Eokpath_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2Epath_2Eokpath_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Eokpath__f_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epath_2Eokpath__f_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epath_2Eokpath__f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epath_2Eokpath__f_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2Eokpath__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epath_2Eokpath__f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29_20mono_2Etyop_2Epath_2Epath_28A_27b_2CA_27c_29,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27a_29_20mono_2Etyop_2Epath_2Epath_28A_27b_2CA_27c_29,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ X2_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Epath_2Epath_28A_27b_2CA_27c_29_20mono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Epath_2Epath_28A_27b_2CA_27c_29_20mono_2EA_27b_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Epath_2Epath_28A_27b_2CA_27c_29_20mono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epath_2Eparallel__comp_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27a_20mono_2EA_27c_20mono_2EA_27c,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epath_2Eparallel__comp_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epath_2Eparallel__comp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq5_2Ec_2Epath_2Eparallel__comp_2E5_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d_20mono_2EA_27e,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,A_27e: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u,X4_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eparallel__comp_2E5 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27e @ tyop_2Emin_2Ebool ) ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27d ) @ X2_2E0 ) @ ( s @ A_27b @ X3_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27e ) @ X4_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27e ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27e ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27e ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27e @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27e ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27e @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27e ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epath_2Eparallel__comp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27e @ tyop_2Emin_2Ebool ) ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27d ) @ X2_2E0 ) ) ) @ ( s @ A_27b @ X3_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27e ) @ X4_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epath_2Eparallel__comp_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epath_2Eparallel__comp_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epath_2Eparallel__comp_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Epath_2Epconcat_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epconcat_2E3 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) ) ) @ c_2Epath_2Epconcat_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Epath_2Epconcat_2E3_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( c_2Epath_2Epconcat_2E3 @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ X0_2E0 ) @ ( s @ A_27d @ X1_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) ) ) ) @ c_2Epath_2Epconcat_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ X0_2E0 ) ) ) @ ( s @ A_27d @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Epath_2Epcons_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) ) ) @ c_2Epath_2Epcons_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Epath_2Epcons_2E3_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ A_27c @ X1_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) ) ) ) @ c_2Epath_2Epcons_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27c @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Epath_2Epcons_2E3_2Emono_2EA_27a_20mono_2EA_27d,axiom,
! [A_27a: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27d ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ A_27d @ X1_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27d ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27d ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27d ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27d ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27d ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27d ) ) ) ) @ c_2Epath_2Epcons_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27d @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27d ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Epath_2Epcons_2E3_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27b @ X0_2E0 ) @ ( s @ A_27c @ X1_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) ) @ c_2Epath_2Epcons_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) @ ( s @ A_27c @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Epath_2Epcons_2E3_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27c @ X0_2E0 ) @ ( s @ A_27d @ X1_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) ) ) ) @ c_2Epath_2Epcons_2E0 ) @ ( s @ A_27c @ X0_2E0 ) ) ) @ ( s @ A_27d @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ X2_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epath_2Epgenerate_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epgenerate_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) ) @ c_2Epath_2Epgenerate_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epath_2Eplink_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Eplink_2E2 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) ) @ c_2Epath_2Eplink_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Epath_2Epmap_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epmap_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) ) ) @ c_2Epath_2Epmap_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Epath_2Epmap_2E3_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b_20mono_2EA_27d,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27d ) @ ( c_2Epath_2Epmap_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ X1_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27d ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27d ) ) ) ) @ c_2Epath_2Epmap_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Epath_2Epmap_2E3_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epath_2Epmap_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27c ) @ X1_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27d ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27d ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27d ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27d ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) ) @ c_2Epath_2Epmap_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27c ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27d ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Epath_2Epmap_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( c_2Epath_2Epmap_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ X1_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) ) ) ) @ c_2Epath_2Epmap_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Epath_2Epmap_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27d_20mono_2EA_27c,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27d @ A_27c ) @ ( c_2Epath_2Epmap_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27d ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ X1_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27d @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27d @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27d @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27d @ A_27c ) ) ) ) @ c_2Epath_2Epmap_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27d ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Epath_2Epmap_2E3_2Emono_2EA_27c_20mono_2EA_27d_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epmap_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) ) ) @ c_2Epath_2Epmap_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Epath_2Epmap_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27c_20mono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ ( c_2Epath_2Epmap_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27c ) @ X1_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) ) ) ) @ c_2Epath_2Epmap_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27c ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Epath_2Epmap_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27c_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epath_2Epmap_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27c ) @ X1_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) ) @ c_2Epath_2Epmap_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27c ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Epath_2Eseg_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0: mono_2Etyop_2Enum_2Enum,X1: mono_2Etyop_2Enum_2Enum,X2_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Eseg_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) ) ) @ c_2Epath_2Eseg_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X1 ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X2_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Estopped__at_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ X0_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) @ c_2Epath_2Estopped__at_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Estopped__at_2E1_2Emono_2EA_27a_20mono_2EA_27d,axiom,
! [A_27a: d,A_27d: d,X0_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27d ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ X0_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27a @ A_27d ) ) @ c_2Epath_2Estopped__at_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Estopped__at_2E1_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: d,A_27c: d,X0_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27b @ X0_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ c_2Epath_2Estopped__at_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Etail_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etail_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) @ c_2Epath_2Etail_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Etail_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27a ) @ ( c_2Epath_2Etail_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27b @ A_27a ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27a ) ) @ c_2Epath_2Etail_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epath_2Etake_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etake_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) ) @ c_2Epath_2Etake_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ X1_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(arityeq1_2Ec_2Ellist_2EtoList_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Ellist_2EtoList_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ c_2Ellist_2EtoList_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2EtoPath_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2EtoPath_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) @ c_2Epath_2EtoPath_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2EtoPath_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: d,A_27d: d,X0_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( c_2Epath_2EtoPath_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27d @ A_27c ) ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27d @ A_27c ) ) ) @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) ) @ c_2Epath_2EtoPath_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27d @ A_27c ) ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Epath_2Etrace__machine_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epath_2Etrace__machine_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Epath_2Etrace__machine_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ).
thf(arityeq4_2Ec_2Epath_2Etrace__machine_2E4_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Etrace__machine_2E4 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) @ ( s @ A_27a @ X2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X3_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 @ A_27a @ ( 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 @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Epath_2Etrace__machine_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X3_2E0 ) ) ) ) ) ).
thf(arityeq3_2Ec_2Epath_2Eunfold_2E3_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epath_2Eunfold_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ X1_2E0 ) @ ( s @ A_27a @ X2_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) ) @ c_2Epath_2Eunfold_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Epath_2Eunfold_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Eunfold_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ X1_2E0 ) @ ( s @ A_27c @ X2_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epath_2Epath @ A_27a @ 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_2Epath_2Epath @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) ) ) @ c_2Epath_2Eunfold_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ X1_2E0 ) ) ) @ ( s @ A_27c @ X2_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_2Ebool_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: $o > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,V1: $o] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_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_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_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_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( 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_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_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_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
! [V0: ( 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_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_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ V0 ) ) @ ( 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 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_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 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_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_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_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_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_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_2Emin_2Efun_28tyop_2Enum_2Enum_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,V1: mono_2Etyop_2Enum_2Enum] :
( ( 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 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_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_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_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_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_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_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > ( mono_2Etyop_2Enum_2Enum > 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_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( 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_2Emin_2Efun @ tyop_2Enum_2Enum @ ( 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_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_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_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_2Enum_2Enum > 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_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_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_2Emin_2Efun @ tyop_2Enum_2Enum @ ( 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_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( 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_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_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_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_2Epair_2E_2C_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Enum_2Enum,V1: $o] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool @ V0 @ V1 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
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_2Epred__set_2EEMPTY_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Epred__set_2EGSPEC_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ mono_2Ec_2Epred__set_2EGSPEC_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2EGSPEC_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_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 @ ( mono_2Ec_2Epred__set_2EGSPEC_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ V0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Epred__set_2EIMAGE_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_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ mono_2Ec_2Epred__set_2EIMAGE_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_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EIMAGE_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( mono_2Ec_2Epred__set_2EIMAGE_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_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_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2EIN_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ 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_2Ec_2Epred__set_2EINSERT_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ mono_2Ec_2Epred__set_2EINSERT_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EINSERT_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( mono_2Ec_2Epred__set_2EINSERT_2Emono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ 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_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(monoeq_2Emono_2Ec_2Eoption_2Eoption__CASE_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( 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_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29 @ mono_2Ec_2Eoption_2Eoption__CASE_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V2: mono_2Etyop_2Enum_2Enum > 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__CASE_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V0 @ V1 @ V2 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ V1 ) ) @ ( 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 @ V2 ) ) ) ) ) ).
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_2Ebool_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: $o > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,V1: $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o,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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ( 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
! [V0: ( 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_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
( ( 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_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > ( mono_2Etyop_2Enum_2Enum > $o ) > 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,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_2Emin_2Efun_28tyop_2Enum_2Enum_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,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_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,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_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_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_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > ( mono_2Etyop_2Enum_2Enum > 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_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_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_2Enum_2Enum > 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_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_2Epath_2Epath__TY__DEF,axiom,
! [A_27a: d,A_27b: d,F0_2E0: u] :
( ! [V1x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1x_2E0 ) ) ) )
= mono_2Ec_2Ebool_2ET )
=> ? [V0rep_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ETYPE__DEFINITION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ V0rep_2E0 ) ) ) ) ) ).
thf(thm_2Epath_2Epath__absrep__bijections,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0a_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2EtoPath_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Epath_2EfromPath_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0a_2E0 ) ) ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0a_2E0 ) )
& ! [V1r_2E0: u] :
( mono_2Ec_2Ebool_2ET
<=> ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Epath_2EfromPath_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2EtoPath_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1r_2E0 ) ) ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1r_2E0 ) ) ) ) ).
thf(thm_2Epath_2Efirst__def,axiom,
! [A_27a: d,A_27b: d,V0p_2E0: u] :
( ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) )
= ( s @ A_27a @ ( c_2Epair_2EFST_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Epath_2EfromPath_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) ) ) ).
thf(thm_2Epath_2Estopped__at__def,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2EtoPath_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ c_2Ellist_2ELNIL_2E0 ) ) ) ) ) ) ).
thf(thm_2Epath_2Epcons__def,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1r_2E0: u,V2p_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ A_27b @ V1r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2EtoPath_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ V1r_2E0 ) @ ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Epath_2EfromPath_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Efinite__def,axiom,
! [A_27a: d,A_27b: d,V0sigma_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0sigma_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Epath_2EfromPath_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0sigma_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Elast__thm,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0x_2E0: u] :
( ( s @ A_27a @ ( c_2Epath_2Elast_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) ) )
= ( s @ A_27a @ V0x_2E0 ) )
& ! [V1x_2E0: u,V2r_2E0: u,V3p_2E0: u] :
( ( s @ A_27a @ ( c_2Epath_2Elast_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V2r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3p_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Epath_2Elast_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3p_2E0 ) ) ) ) ) ).
thf(thm_2Epath_2Epmap__def,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0f_2E0: u,V1g_2E0: u,V2p_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( c_2Epath_2Epmap_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ V1g_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( c_2Epath_2EtoPath_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27d @ A_27c ) ) ) @ ( c_2Epair_2E_23_23_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27d @ A_27c ) ) ) @ ( c_2Ellist_2ELMAP_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Epair_2Eprod @ A_27d @ A_27c ) ) @ ( c_2Epair_2E_23_23_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ V1g_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V0f_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Epath_2EfromPath_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Etail__def,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1r_2E0: u,V2p_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etail_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ A_27b @ V1r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ).
thf(thm_2Epath_2Efirst__label__def,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1r_2E0: u,V2p_2E0: u] :
( ( s @ A_27b @ ( c_2Epath_2Efirst__label_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ A_27b @ V1r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) )
= ( s @ A_27b @ V1r_2E0 ) ) ).
thf(thm_2Epath_2Elength__def,axiom,
! [A_27a: d,A_27b: d,V0p_2E0: u] :
( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Epath_2Elength_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) @ ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Ellist_2EtoList_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Epath_2EfromPath_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) ) ) ) ) ) ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) @ mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum ) ) ).
thf(thm_2Epath_2Eel__def,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0p_2E0: u] :
( ( s @ A_27a @ ( c_2Epath_2Eel_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) )
= ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) )
& ! [V1n: mono_2Etyop_2Enum_2Enum,V2p_2E0: u] :
( ( s @ A_27a @ ( c_2Epath_2Eel_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V1n ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) )
= ( s @ A_27a @ ( c_2Epath_2Eel_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etail_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Enth__label__def,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0p_2E0: u] :
( ( s @ A_27a @ ( c_2Epath_2Enth__label_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27a ) @ V0p_2E0 ) ) )
= ( s @ A_27a @ ( c_2Epath_2Efirst__label_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27a ) @ V0p_2E0 ) ) ) )
& ! [V1n: mono_2Etyop_2Enum_2Enum,V2p_2E0: u] :
( ( s @ A_27a @ ( c_2Epath_2Enth__label_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V1n ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27a ) @ V2p_2E0 ) ) )
= ( s @ A_27a @ ( c_2Epath_2Enth__label_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27a ) @ ( c_2Epath_2Etail_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27a ) @ V2p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Epconcat__def,axiom,
! [A_27a: d,A_27b: d,V0p1_2E0: u,V1lab_2E0: u,V2p2_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epconcat_2E3 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p1_2E0 ) @ ( s @ A_27b @ V1lab_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p2_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2EtoPath_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p1_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Epath_2EfromPath_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p1_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ V1lab_2E0 ) @ ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p2_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Epath_2EfromPath_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p2_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2EPL__def,axiom,
! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
( ! [V0p_2E0: u,V1i: 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_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) @ V1i )
<=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ V1i @ ( 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_2Epath_2Elength_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) ) ) ) )
=> ( ! [V0p_2E0: u,V1i: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) @ V1i )
= ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool @ V1i @ ( 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_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) @ V1i ) ) )
=> ! [V0p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) )
= ( mono_2Ec_2Epred__set_2EGSPEC_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2EfirstP__at__def,axiom,
! [A_27a: d,A_27b: d,V0P_2E0: u,V1p_2E0: u,V2i: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2EfirstP__at_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2i ) ) ) ) )
<=> ( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V2i @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_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 @ ( c_2Epath_2Eel_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) ) )
& ! [V3j: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V3j @ V2i )
=> ( (~) @ ( 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 @ ( c_2Epath_2Eel_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3j ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Eexists__def,axiom,
! [A_27a: d,A_27b: d,V0P_2E0: u,V1p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) )
<=> ? [V2i: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2EfirstP__at_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2i ) ) ) ) ) ) ).
thf(thm_2Epath_2Eevery__def,axiom,
! [A_27a: d,A_27b: d,V0P_2E0: u,V1p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eevery_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) )
<=> ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_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_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) ) ) ).
thf(thm_2Epath_2Emem__def,axiom,
! [A_27a: d,A_27b: d,V0s_2E0: u,V1p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Emem_2E2 @ ( s @ A_27a @ V0s_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) )
<=> ? [V2i: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V2i @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) )
& ( ( s @ A_27a @ V0s_2E0 )
= ( s @ A_27a @ ( c_2Epath_2Eel_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) ) ) ).
thf(thm_2Epath_2Edrop__def,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0p_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Edrop_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) )
& ! [V1n: mono_2Etyop_2Enum_2Enum,V2p_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Edrop_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V1n ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Edrop_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etail_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Etake__def,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0p_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etake_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) ) )
& ! [V1n: mono_2Etyop_2Enum_2Enum,V2p_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etake_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V1n ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) @ ( s @ A_27b @ ( c_2Epath_2Efirst__label_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etake_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etail_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Eseg__def,axiom,
! [A_27a: d,A_27b: d,V0i: mono_2Etyop_2Enum_2Enum,V1j: mono_2Etyop_2Enum_2Enum,V2p_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Eseg_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0i ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1j ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etake_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2D @ V1j @ V0i ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Edrop_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) ) ) ).
thf(thm_2Epath_2Elabels__def,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0x_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Epath_2Elabels_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ c_2Ellist_2ELNIL_2E0 ) )
& ! [V1x_2E0: u,V2r_2E0: u,V3p_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Epath_2Elabels_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V2r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3p_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELCONS_2E2 @ ( s @ A_27b @ V2r_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Epath_2Elabels_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Eis__stopped__def,axiom,
! [A_27a: d,A_27b: d,V0p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eis__stopped_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) )
<=> ? [V1x_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
thf(thm_2Epath_2Efilter__def,axiom,
! [A_27a: d,A_27b: d,V0P_2E0: u] :
( ! [V1x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) )
=> ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Efilter_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) ) )
& ! [V2x_2E0: u,V3r_2E0: u,V4p_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Efilter_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V4p_2E0 ) ) ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V4p_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Efilter_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V4p_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Efilter_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V4p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Epgenerate__def,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epgenerate_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V1g_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( 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 @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V1g_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epgenerate_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_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V1g_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 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Eokpath__f__def,axiom,
! [A_27a: d,A_27b: d,F3_2E0: u,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
( ! [V0R_2E0: u,V3x_2E0: u,V4r_2E0: u,V5p_2E0: u,V1X_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ A_27b @ V4r_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1X_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_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ A_27b @ V4r_2E0 ) ) ) @ ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1X_2E0 ) ) ) ) ) )
=> ( ! [V3x_2E0: u,V0R_2E0: u,V1X_2E0: u,V4r_2E0: u,V5p_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ F2_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1X_2E0 ) ) ) @ ( s @ A_27b @ V4r_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ A_27b @ V4r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ A_27b @ V4r_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1X_2E0 ) ) ) ) ) )
=> ( ! [V0R_2E0: u,V1X_2E0: u,V3x_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1X_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ F2_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1X_2E0 ) ) ) ) ) )
=> ( ! [V2x_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) ) ) )
=> ! [V0R_2E0: u,V1X_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2Eokpath__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1X_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1X_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Eokpath__def,axiom,
! [A_27a: d,A_27b: d,V0R_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2Eokpath_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2EfixedPoint_2Egfp_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epath_2Eokpath__f_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) ) ) ) ) ) ).
thf(thm_2Epath_2Eplink__def,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0x_2E0: u,V1p_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Eplink_2E2 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) )
& ! [V2x_2E0: u,V3r_2E0: u,V4p1_2E0: u,V5p2_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Eplink_2E2 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V4p1_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p2_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Eplink_2E2 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V4p1_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p2_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2ESN__def,axiom,
! [A_27a: d,A_27b: d,F0_2E0: u] :
( ! [V0R_2E0: u,V1x_2E0: u,V2y_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_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) ) ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ A_27a @ V2y_2E0 ) ) ) )
<=> ? [V3l_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 @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) @ ( s @ A_27a @ V2y_2E0 ) ) ) @ ( s @ A_27b @ V3l_2E0 ) ) ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) )
=> ! [V0R_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2ESN_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Erelation_2EWF_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Eunfold__def,axiom,
! [A_27a: d,A_27b: d,A_27c: d,F1_2E0: u,F0_2E0: u] :
( ! [V0proj_2E0: u,V4next__s_2E0: u,V5lbl_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V0proj_2E0 ) ) ) @ ( s @ A_27c @ V4next__s_2E0 ) ) ) @ ( s @ A_27b @ V5lbl_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ V4next__s_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ V5lbl_2E0 ) @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V0proj_2E0 ) @ ( s @ A_27c @ V4next__s_2E0 ) ) ) ) ) ) ) )
=> ( ! [V0proj_2E0: u,V1f_2E0: u,V3s_2E0: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ ( 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_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V0proj_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ V1f_2E0 ) ) ) @ ( s @ A_27c @ V3s_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V0proj_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 ) ) ) @ V1f_2E0 ) @ ( s @ A_27c @ V3s_2E0 ) ) ) ) ) )
=> ! [V0proj_2E0: u,V1f_2E0: u,V2s_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Eunfold_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V0proj_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ V1f_2E0 ) @ ( s @ A_27c @ V2s_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2EtoPath_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V0proj_2E0 ) @ ( s @ A_27c @ V2s_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) @ ( 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_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V0proj_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ V1f_2E0 ) ) ) @ ( s @ A_27c @ V2s_2E0 ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Etrace__machine__def,axiom,
! [A_27a: d,V0P_2E0: u,V1s_2E0: u,V2l_2E0: u,V3s_27_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Etrace__machine_2E4 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1s_2E0 ) @ ( s @ A_27a @ V2l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3s_27_2E0 ) ) ) )
<=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1s_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V2l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ) ) ) )
& ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3s_27_2E0 )
= ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1s_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ A_27a @ V2l_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Eparallel__comp__def,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,A_27e: d,V0m1_2E0: u,V1m2_2E0: u,V2s1_2E0: u,V3s2_2E0: u,V4l_2E0: u,V5s1_27_2E0: u,V6s2_27_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eparallel__comp_2E5 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) ) @ V0m1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27e @ tyop_2Emin_2Ebool ) ) ) @ V1m2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27d ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2s1_2E0 ) @ ( s @ A_27d @ V3s2_2E0 ) ) ) @ ( s @ A_27b @ V4l_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27e ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ V5s1_27_2E0 ) @ ( s @ A_27e @ V6s2_27_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_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) ) @ V0m1_2E0 ) @ ( s @ A_27a @ V2s1_2E0 ) ) ) @ ( s @ A_27b @ V4l_2E0 ) ) ) @ ( s @ A_27c @ V5s1_27_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27e @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27e @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27e @ tyop_2Emin_2Ebool ) ) ) @ V1m2_2E0 ) @ ( s @ A_27d @ V3s2_2E0 ) ) ) @ ( s @ A_27b @ V4l_2E0 ) ) ) @ ( s @ A_27e @ V6s2_27_2E0 ) ) ) ) ) ) ).
thf(thm_2Epath_2Epath__rep__bijections__thm,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0a_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2EtoPath_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Epath_2EfromPath_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0a_2E0 ) ) ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0a_2E0 ) )
& ! [V1r_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Epath_2EfromPath_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2EtoPath_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1r_2E0 ) ) ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1r_2E0 ) ) ) ).
thf(thm_2Epath_2EtoPath__11,axiom,
! [A_27a: d,A_27b: d,V0r_2E0: u,V1r_27_2E0: u] :
( ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2EtoPath_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V0r_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2EtoPath_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1r_27_2E0 ) ) ) )
<=> ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V0r_2E0 )
= ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1r_27_2E0 ) ) ) ).
thf(thm_2Epath_2EfromPath__11,axiom,
! [A_27a: d,A_27b: d,V0a_2E0: u,V1a_27_2E0: u] :
( ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Epath_2EfromPath_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0a_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Epath_2EfromPath_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1a_27_2E0 ) ) ) )
<=> ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0a_2E0 )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1a_27_2E0 ) ) ) ).
thf(thm_2Epath_2EfromPath__onto,axiom,
! [A_27a: d,A_27b: d,V0r_2E0: u] :
? [V1a_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V0r_2E0 )
= ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Epath_2EfromPath_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1a_2E0 ) ) ) ) ).
thf(thm_2Epath_2EtoPath__onto,axiom,
! [A_27a: d,A_27b: d,V0a_2E0: u] :
? [V1r_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0a_2E0 )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2EtoPath_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ V1r_2E0 ) ) ) ) ).
thf(thm_2Epath_2Estopped__at__11,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
( ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V1y_2E0 ) ) ) )
<=> ( ( s @ A_27a @ V0x_2E0 )
= ( s @ A_27a @ V1y_2E0 ) ) ) ).
thf(thm_2Epath_2Epcons__11,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1r_2E0: u,V2p_2E0: u,V3y_2E0: u,V4s_2E0: u,V5q_2E0: u] :
( ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ A_27b @ V1r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V3y_2E0 ) @ ( s @ A_27b @ V4s_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5q_2E0 ) ) ) )
<=> ( ( ( s @ A_27a @ V0x_2E0 )
= ( s @ A_27a @ V3y_2E0 ) )
& ( ( s @ A_27b @ V1r_2E0 )
= ( s @ A_27b @ V4s_2E0 ) )
& ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5q_2E0 ) ) ) ) ).
thf(thm_2Epath_2Estopped__at__not__pcons,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u,V2r_2E0: u,V3p_2E0: u] :
( ( (~)
@ ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V1y_2E0 ) @ ( s @ A_27b @ V2r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3p_2E0 ) ) ) ) )
& ( (~)
@ ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V1y_2E0 ) @ ( s @ A_27b @ V2r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3p_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) ) ) ) ).
thf(thm_2Epath_2Epath__cases,axiom,
! [A_27a: d,A_27b: d,V0p_2E0: u] :
( ? [V1x_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) )
| ? [V2x_2E0: u,V3r_2E0: u,V4q_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V4q_2E0 ) ) ) ) ) ).
thf(thm_2Epath_2EFORALL__path,axiom,
! [A_27a: d,A_27b: d,V0P_2E0: u] :
( ! [V1p_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) )
<=> ( ! [V2x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) )
& ! [V3x_2E0: u,V4r_2E0: u,V5p_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ A_27b @ V4r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2EEXISTS__path,axiom,
! [A_27a: d,A_27b: d,V0P_2E0: u] :
( ? [V1p_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) )
<=> ( ? [V2x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) )
| ? [V3x_2E0: u,V4r_2E0: u,V5p_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ A_27b @ V4r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Efirst__thm,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0x_2E0: u] :
( ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) ) )
= ( s @ A_27a @ V0x_2E0 ) )
& ! [V1x_2E0: u,V2r_2E0: u,V3p_2E0: u] :
( ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V2r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3p_2E0 ) ) ) ) )
= ( s @ A_27a @ V1x_2E0 ) ) ) ).
thf(thm_2Epath_2Efinite__thm,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) ) ) )
= mono_2Ec_2Ebool_2ET )
& ! [V1x_2E0: u,V2r_2E0: u,V3p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V2r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3p_2E0 ) ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3p_2E0 ) ) ) ) ) ) ).
thf(thm_2Epath_2Epath__bisimulation,axiom,
! [A_27a: d,A_27b: d,V0p1_2E0: u,V1p2_2E0: u] :
( ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p1_2E0 )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p2_2E0 ) )
<=> ? [V2R_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p1_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p2_2E0 ) ) ) )
& ! [V3q1_2E0: u,V4q2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3q1_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V4q2_2E0 ) ) ) )
=> ( ? [V5x_2E0: u] :
( ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3q1_2E0 )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V5x_2E0 ) ) ) )
& ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V4q2_2E0 )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V5x_2E0 ) ) ) ) )
| ? [V6x_2E0: u,V7r_2E0: u,V8q1_27_2E0: u,V9q2_27_2E0: u] :
( ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3q1_2E0 )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ A_27b @ V7r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V8q1_27_2E0 ) ) ) )
& ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V4q2_2E0 )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ A_27b @ V7r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V9q2_27_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V8q1_27_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V9q2_27_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Efinite__path__ind,axiom,
! [A_27a: d,A_27b: d,V0P_2E0: u] :
( ( ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) )
& ! [V2x_2E0: u,V3r_2E0: u,V4p_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V4p_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V4p_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V4p_2E0 ) ) ) ) ) ) ) )
=> ! [V5q_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5q_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5q_2E0 ) ) ) ) ) ) ).
thf(thm_2Epath_2Epmap__thm,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0g_2E0: u,V1f_2E0: u] :
( ! [V2x_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epath_2Epmap_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27c ) @ V0g_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27d ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V2x_2E0 ) ) ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) )
& ! [V3x_2E0: u,V4r_2E0: u,V5p_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epath_2Epmap_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27c ) @ V0g_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27d ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ A_27d @ V4r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27d ) @ V5p_2E0 ) ) ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27c ) @ V0g_2E0 ) @ ( s @ A_27d @ V4r_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epath_2Epmap_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27c ) @ V0g_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27d ) @ V5p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Efirst__pmap,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0g_2E0: u,V1f_2E0: u,V2p_2E0: u] :
( ( s @ A_27c @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( c_2Epath_2Epmap_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ V0g_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V1f_2E0 ) @ ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) ) ) ).
thf(thm_2Epath_2Elast__pmap,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0g_2E0: u,V1f_2E0: u,V2p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) )
=> ( ( s @ A_27c @ ( c_2Epath_2Elast_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( c_2Epath_2Epmap_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ V0g_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V1f_2E0 ) @ ( s @ A_27a @ ( c_2Epath_2Elast_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Efinite__pmap,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0f_2E0: u,V1g_2E0: u,V2p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( c_2Epath_2Epmap_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ V1g_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) ) ).
thf(thm_2Epath_2Elength__thm,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d] :
( ! [V0x_2E0: u] :
( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Epath_2Elength_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) ) ) )
= ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
& ! [V1x_2E0: u,V2r_2E0: u,V3p_2E0: u] :
( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Epath_2Elength_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27c @ V1x_2E0 ) @ ( s @ A_27d @ V2r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ V3p_2E0 ) ) ) ) ) )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ V3p_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_2Epath_2Elength_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ V3p_2E0 ) ) ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) @ mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum ) ) ) ).
thf(thm_2Epath_2Ealt__length__thm,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d] :
( ! [V0x_2E0: u] :
( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Epath_2Elength_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) ) ) )
= ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
& ! [V1x_2E0: u,V2r_2E0: u,V3p_2E0: u] :
( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Epath_2Elength_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27c @ V1x_2E0 ) @ ( s @ A_27d @ V2r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ V3p_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_2Epath_2Elength_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ V3p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Elength__never__zero,axiom,
! [A_27a: d,A_27b: d,V0p_2E0: u] :
( (~)
@ ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Epath_2Elength_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) )
= ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Epath_2Efinite__length,axiom,
! [A_27a: d,A_27b: d,V0p_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) )
<=> ? [V1n: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Epath_2Elength_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) )
= ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ V1n ) ) )
& ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) )
<=> ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Epath_2Elength_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) )
= mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum ) ) ) ).
thf(thm_2Epath_2Elength__pmap,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0f_2E0: u,V1g_2E0: u,V2p_2E0: u] :
( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Epath_2Elength_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27d ) @ ( c_2Epath_2Epmap_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ V1g_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ V2p_2E0 ) ) ) ) ) )
= ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Epath_2Elength_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ V2p_2E0 ) ) ) ) ) ).
thf(thm_2Epath_2Eel__def__compute,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0p_2E0: u] :
( ( s @ A_27a @ ( c_2Epath_2Eel_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) )
= ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) )
& ! [V1n: mono_2Etyop_2Enum_2Enum,V2p_2E0: u] :
( ( s @ A_27a @ ( c_2Epath_2Eel_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) )
= ( s @ A_27a @ ( c_2Epath_2Eel_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_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 ) ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etail_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) ) )
& ! [V3n: mono_2Etyop_2Enum_2Enum,V4p_2E0: u] :
( ( s @ A_27a @ ( c_2Epath_2Eel_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V3n ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V4p_2E0 ) ) )
= ( s @ A_27a @ ( c_2Epath_2Eel_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V3n ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etail_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V4p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Enth__label__def__compute,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0p_2E0: u] :
( ( s @ A_27a @ ( c_2Epath_2Enth__label_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27a ) @ V0p_2E0 ) ) )
= ( s @ A_27a @ ( c_2Epath_2Efirst__label_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27a ) @ V0p_2E0 ) ) ) )
& ! [V1n: mono_2Etyop_2Enum_2Enum,V2p_2E0: u] :
( ( s @ A_27a @ ( c_2Epath_2Enth__label_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27a ) @ V2p_2E0 ) ) )
= ( s @ A_27a @ ( c_2Epath_2Enth__label_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_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 ) ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27a ) @ ( c_2Epath_2Etail_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27a ) @ V2p_2E0 ) ) ) ) ) )
& ! [V3n: mono_2Etyop_2Enum_2Enum,V4p_2E0: u] :
( ( s @ A_27a @ ( c_2Epath_2Enth__label_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V3n ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27a ) @ V4p_2E0 ) ) )
= ( s @ A_27a @ ( c_2Epath_2Enth__label_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V3n ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27a ) @ ( c_2Epath_2Etail_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27a ) @ V4p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Epath__Axiom,axiom,
! [A_27a: d,A_27b: d,A_27c: d,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
( ! [V3y_2E0: u,V1g_2E0: u,V6l_2E0: u,V7v_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) ) ) @ F2_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ V1g_2E0 ) ) ) @ ( s @ A_27c @ V6l_2E0 ) ) ) @ ( s @ A_27a @ V7v_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27b @ V3y_2E0 ) @ ( s @ A_27c @ V6l_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ V1g_2E0 ) @ ( s @ A_27a @ V7v_2E0 ) ) ) ) ) )
=> ( ! [V3y_2E0: u,V1g_2E0: u,V5v3_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) ) @ F1_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ V1g_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ V5v3_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ V5v3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) ) ) @ F2_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ V1g_2E0 ) ) ) ) ) )
=> ( ! [V1g_2E0: u,V3y_2E0: u,V4v2_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ V1g_2E0 ) ) ) @ ( s @ A_27b @ V3y_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ V4v2_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ V4v2_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27b @ V3y_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) ) @ F1_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ V1g_2E0 ) ) ) ) ) )
=> ! [V0f_2E0: u] :
? [V1g_2E0: u] :
! [V2x_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ V1g_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Epconcat__thm,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d] :
( ! [V0x_2E0: u,V1lab_2E0: u,V2p2_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epconcat_2E3 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1lab_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p2_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ A_27b @ V1lab_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p2_2E0 ) ) ) )
& ! [V3x_2E0: u,V4r_2E0: u,V5p_2E0: u,V6lab_2E0: u,V7p2_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( c_2Epath_2Epconcat_2E3 @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27c @ V3x_2E0 ) @ ( s @ A_27d @ V4r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ V5p_2E0 ) ) ) @ ( s @ A_27d @ V6lab_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ V7p2_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27c @ V3x_2E0 ) @ ( s @ A_27d @ V4r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( c_2Epath_2Epconcat_2E3 @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ V5p_2E0 ) @ ( s @ A_27d @ V6lab_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ V7p2_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Epconcat__eq__stopped,axiom,
! [A_27a: d,A_27b: d,V0p1_2E0: u,V1lab_2E0: u,V2p2_2E0: u,V3x_2E0: u] :
( ( (~)
@ ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epconcat_2E3 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p1_2E0 ) @ ( s @ A_27b @ V1lab_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p2_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V3x_2E0 ) ) ) ) )
& ( (~)
@ ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V3x_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epconcat_2E3 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p1_2E0 ) @ ( s @ A_27b @ V1lab_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p2_2E0 ) ) ) ) ) ) ).
thf(thm_2Epath_2Epconcat__eq__pcons,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1r_2E0: u,V2p_2E0: u,V3p1_2E0: u,V4lab_2E0: u,V5p2_2E0: u] :
( ( ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epconcat_2E3 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3p1_2E0 ) @ ( s @ A_27b @ V4lab_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p2_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ A_27b @ V1r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) )
<=> ( ( ( ( s @ A_27b @ V4lab_2E0 )
= ( s @ A_27b @ V1r_2E0 ) )
& ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3p1_2E0 )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) )
& ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p2_2E0 ) ) )
| ? [V6p1_27_2E0: u] :
( ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3p1_2E0 )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ A_27b @ V1r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V6p1_27_2E0 ) ) ) )
& ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epconcat_2E3 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V6p1_27_2E0 ) @ ( s @ A_27b @ V4lab_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p2_2E0 ) ) ) ) ) ) )
& ( ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ A_27b @ V1r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epconcat_2E3 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3p1_2E0 ) @ ( s @ A_27b @ V4lab_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p2_2E0 ) ) ) )
<=> ( ( ( ( s @ A_27b @ V4lab_2E0 )
= ( s @ A_27b @ V1r_2E0 ) )
& ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3p1_2E0 )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) )
& ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p2_2E0 ) ) )
| ? [V7p1_27_2E0: u] :
( ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3p1_2E0 )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ A_27b @ V1r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V7p1_27_2E0 ) ) ) )
& ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epconcat_2E3 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V7p1_27_2E0 ) @ ( s @ A_27b @ V4lab_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p2_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Efinite__pconcat,axiom,
! [A_27a: d,A_27b: d,V0p1_2E0: u,V1lab_2E0: u,V2p2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epconcat_2E3 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p1_2E0 ) @ ( s @ A_27b @ V1lab_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p2_2E0 ) ) ) ) ) )
<=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p1_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p2_2E0 ) ) ) ) ) ) ).
thf(thm_2Epath_2Einfinite__PL,axiom,
! [A_27a: d,A_27b: d,V0p_2E0: u] :
( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) )
=> ! [V1i: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1i @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) ) ) ).
thf(thm_2Epath_2EPL__pcons,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1r_2E0: u,V2q_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ A_27b @ V1r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2q_2E0 ) ) ) ) ) )
= ( mono_2Ec_2Epred__set_2EINSERT_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Epred__set_2EIMAGE_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2ESUC @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2q_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2EPL__stopped__at,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) ) ) )
= ( mono_2Ec_2Epred__set_2EINSERT_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 @ mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Enum_2Enum ) ) ).
thf(thm_2Epath_2EPL__thm,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) ) ) )
= ( mono_2Ec_2Epred__set_2EINSERT_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 @ mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Enum_2Enum ) )
& ! [V1x_2E0: u,V2r_2E0: u,V3q_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V2r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3q_2E0 ) ) ) ) ) )
= ( mono_2Ec_2Epred__set_2EINSERT_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2Epred__set_2EIMAGE_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2ESUC @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3q_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2EPL__0,axiom,
! [A_27a: d,A_27b: d,V0p_2E0: u] : ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) ) ).
thf(thm_2Epath_2EPL__downward__closed,axiom,
! [A_27a: d,A_27b: d,V0i: mono_2Etyop_2Enum_2Enum,V1p_2E0: u] :
( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V0i @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) )
=> ! [V2j: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V2j @ V0i )
=> ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V2j @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2EPL__pmap,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0p_2E0: u,V1g_2E0: u,V2f_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epmap_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V2f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ V1g_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ V0p_2E0 ) ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ V0p_2E0 ) ) ) ) ) ).
thf(thm_2Epath_2Eel__pmap,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0g_2E0: u,V1f_2E0: u,V2i: mono_2Etyop_2Enum_2Enum,V3p_2E0: u] :
( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V2i @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3p_2E0 ) ) ) ) )
=> ( ( s @ A_27c @ ( c_2Epath_2Eel_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( c_2Epath_2Epmap_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ V0g_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3p_2E0 ) ) ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V1f_2E0 ) @ ( s @ A_27a @ ( c_2Epath_2Eel_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Enth__label__pmap,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0g_2E0: u,V1f_2E0: u,V2i: mono_2Etyop_2Enum_2Enum,V3p_2E0: u] :
( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ V2i ) @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3p_2E0 ) ) ) ) )
=> ( ( s @ A_27c @ ( c_2Epath_2Enth__label_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27d @ A_27c ) @ ( c_2Epath_2Epmap_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27d ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V0g_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3p_2E0 ) ) ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V0g_2E0 ) @ ( s @ A_27b @ ( c_2Epath_2Enth__label_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2EfirstP__at__thm,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0P_2E0: u,V1x_2E0: u,V2n: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2EfirstP__at_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) ) ) )
<=> ( ( V2n = mono_2Ec_2Enum_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 @ V1x_2E0 ) ) ) ) ) )
& ! [V3P_2E0: u,V4n: mono_2Etyop_2Enum_2Enum,V5x_2E0: u,V6r_2E0: u,V7p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2EfirstP__at_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V5x_2E0 ) @ ( s @ A_27b @ V6r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V7p_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4n ) ) ) ) )
<=> ( ( ( V4n = mono_2Ec_2Enum_2E0 )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3P_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) ) ) )
| ( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V4n )
& ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3P_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2EfirstP__at_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V7p_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2D @ V4n @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2EfirstP__at__zero,axiom,
! [A_27a: d,A_27b: d,V0P_2E0: u,V1p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2EfirstP__at_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_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 @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Eexists__thm,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0P_2E0: u] :
( ! [V1x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V1x_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 @ V1x_2E0 ) ) ) ) )
& ! [V2x_2E0: u,V3r_2E0: u,V4p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27c @ V3r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ V4p_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 @ V2x_2E0 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ V4p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Eevery__thm,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0P_2E0: u] :
( ! [V1x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eevery_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V1x_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 @ V1x_2E0 ) ) ) ) )
& ! [V2x_2E0: u,V3r_2E0: u,V4p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eevery_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27c @ V3r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ V4p_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 @ V2x_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eevery_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ V4p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Enot__every,axiom,
! [A_27a: d,A_27b: d,V0P_2E0: u,V1p_2E0: u] :
( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eevery_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) )
<=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_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_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) ) ).
thf(thm_2Epath_2Enot__exists,axiom,
! [A_27a: d,A_27b: d,V0P_2E0: u,V1p_2E0: u] :
( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) )
<=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_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_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) ) ).
thf(thm_2Epath_2Eexists__el,axiom,
! [A_27a: d,A_27b: d,V0P_2E0: u,V1p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) )
<=> ? [V2i: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V2i @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_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 @ ( c_2Epath_2Eel_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Eevery__el,axiom,
! [A_27a: d,A_27b: d,V0P_2E0: u,V1p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eevery_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) )
<=> ! [V2i: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V2i @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_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 @ ( c_2Epath_2Eel_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Eevery__coinduction,axiom,
! [A_27a: d,A_27b: d,V0P_2E0: u,V1Q_2E0: u] :
( ( ! [V2x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1Q_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) )
& ! [V3x_2E0: u,V4r_2E0: u,V5p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ A_27b @ V4r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p_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 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p_2E0 ) ) ) ) ) ) )
=> ! [V6p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V6p_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eevery_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1Q_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V6p_2E0 ) ) ) ) ) ) ).
thf(thm_2Epath_2Eexists__induction,axiom,
! [A_27a: d,A_27b: d,V0Q_2E0: u,V1P_2E0: u] :
( ( ! [V2x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0Q_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) )
& ! [V3x_2E0: u,V4r_2E0: u,V5p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0Q_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ A_27b @ V4r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p_2E0 ) ) ) ) ) ) )
& ! [V6x_2E0: u,V7r_2E0: u,V8p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V8p_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V6x_2E0 ) @ ( s @ A_27b @ V7r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V8p_2E0 ) ) ) ) ) ) ) )
=> ! [V9p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0Q_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V9p_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V9p_2E0 ) ) ) ) ) ) ).
thf(thm_2Epath_2Emem__thm,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d] :
( ! [V0x_2E0: u,V1s_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Emem_2E2 @ ( s @ A_27a @ V1s_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) ) ) )
<=> ( ( s @ A_27a @ V1s_2E0 )
= ( s @ A_27a @ V0x_2E0 ) ) )
& ! [V2x_2E0: u,V3r_2E0: u,V4p_2E0: u,V5s_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Emem_2E2 @ ( s @ A_27c @ V5s_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27c @ V2x_2E0 ) @ ( s @ A_27d @ V3r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ V4p_2E0 ) ) ) ) ) )
<=> ( ( ( s @ A_27c @ V5s_2E0 )
= ( s @ A_27c @ V2x_2E0 ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Emem_2E2 @ ( s @ A_27c @ V5s_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ V4p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Edrop__def__compute,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0p_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Edrop_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) )
& ! [V1n: mono_2Etyop_2Enum_2Enum,V2p_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Edrop_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Edrop_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_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 ) ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etail_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) ) )
& ! [V3n: mono_2Etyop_2Enum_2Enum,V4p_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Edrop_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V3n ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V4p_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Edrop_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V3n ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etail_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V4p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Enumeral__drop,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0n: mono_2Etyop_2Enum_2Enum,V1p_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Edrop_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Edrop_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2D @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etail_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) ) )
& ! [V2n: mono_2Etyop_2Enum_2Enum,V3p_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Edrop_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V2n ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3p_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Edrop_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V2n ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etail_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Efinite__drop,axiom,
! [A_27a: d,A_27b: d,V0p_2E0: u,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1n @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Edrop_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) ) ) ).
thf(thm_2Epath_2Elength__drop,axiom,
! [A_27a: d,A_27b: d,F0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
( ! [V1n: mono_2Etyop_2Enum_2Enum,V2m: mono_2Etyop_2Enum_2Enum] :
( ( F0 @ V1n @ V2m )
= ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2D @ V2m @ V1n ) ) )
=> ! [V0p_2E0: u,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1n @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) )
=> ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Epath_2Elength_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Edrop_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) ) )
= ( mono_2Ec_2Eoption_2Eoption__CASE_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Epath_2Elength_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) @ mono_2Ec_2Eoption_2ENONE_2Emono_2Etyop_2Enum_2Enum @ ( F0 @ V1n ) ) ) ) ) ).
thf(thm_2Epath_2EPL__drop,axiom,
! [A_27a: d,A_27b: d,F0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ! [V1i: mono_2Etyop_2Enum_2Enum,V2n: mono_2Etyop_2Enum_2Enum] :
( ( F0 @ V1i @ V2n )
= ( mono_2Ec_2Earithmetic_2E_2D @ V2n @ V1i ) )
=> ! [V0p_2E0: u,V1i: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1i @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Edrop_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) ) )
= ( mono_2Ec_2Epred__set_2EIMAGE_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ ( F0 @ V1i ) @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2EIN__PL__drop,axiom,
! [A_27a: d,A_27b: d,V0i: mono_2Etyop_2Enum_2Enum,V1j: mono_2Etyop_2Enum_2Enum,V2p_2E0: u] :
( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V0i @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) )
=> ( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1j @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Edrop_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) ) ) )
= ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V0i @ V1j ) @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Efirst__drop,axiom,
! [A_27a: d,A_27b: d,V0i: mono_2Etyop_2Enum_2Enum,V1p_2E0: u] :
( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V0i @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) )
=> ( ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Edrop_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Epath_2Eel_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) ) ).
thf(thm_2Epath_2Efirst__label__drop,axiom,
! [A_27a: d,A_27b: d,V0i: mono_2Etyop_2Enum_2Enum,V1p_2E0: u] :
( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V0i @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) )
=> ( ( s @ A_27b @ ( c_2Epath_2Efirst__label_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Edrop_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) )
= ( s @ A_27b @ ( c_2Epath_2Enth__label_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) ) ).
thf(thm_2Epath_2Etail__drop,axiom,
! [A_27a: d,A_27b: d,V0i: mono_2Etyop_2Enum_2Enum,V1p_2E0: u] :
( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V0i @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) )
=> ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etail_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Edrop_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Edrop_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V0i @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) ) ).
thf(thm_2Epath_2Eel__drop,axiom,
! [A_27a: d,A_27b: d,V0i: mono_2Etyop_2Enum_2Enum,V1j: mono_2Etyop_2Enum_2Enum,V2p_2E0: u] :
( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V0i @ V1j ) @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) )
=> ( ( s @ A_27a @ ( c_2Epath_2Eel_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Edrop_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1j ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Epath_2Eel_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V0i @ V1j ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) ) ).
thf(thm_2Epath_2Enth__label__drop,axiom,
! [A_27a: d,A_27b: d,V0i: mono_2Etyop_2Enum_2Enum,V1j: mono_2Etyop_2Enum_2Enum,V2p_2E0: u] :
( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2E_2B @ V0i @ V1j ) ) @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) )
=> ( ( s @ A_27b @ ( c_2Epath_2Enth__label_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Edrop_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1j ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) )
= ( s @ A_27b @ ( c_2Epath_2Enth__label_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V0i @ V1j ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) ) ).
thf(thm_2Epath_2Etake__def__compute,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0p_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etake_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) ) )
& ! [V1n: mono_2Etyop_2Enum_2Enum,V2p_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etake_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) @ ( s @ A_27b @ ( c_2Epath_2Efirst__label_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etake_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_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 ) ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etail_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) ) ) ) )
& ! [V3n: mono_2Etyop_2Enum_2Enum,V4p_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etake_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V3n ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V4p_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V4p_2E0 ) ) ) @ ( s @ A_27b @ ( c_2Epath_2Efirst__label_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V4p_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etake_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V3n ) ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etail_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V4p_2E0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Efirst__take,axiom,
! [A_27a: d,A_27b: d,V0p_2E0: u,V1i: mono_2Etyop_2Enum_2Enum] :
( ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etake_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) ).
thf(thm_2Epath_2Efinite__take,axiom,
! [A_27a: d,A_27b: d,V0p_2E0: u,V1i: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1i @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etake_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Elength__take,axiom,
! [A_27a: d,A_27b: d,V0p_2E0: u,V1i: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1i @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) )
=> ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Enum_2Enum ) @ ( c_2Epath_2Elength_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etake_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) ) )
= ( mono_2Ec_2Eoption_2ESOME_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V1i @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2Epath_2EPL__take,axiom,
! [A_27a: d,A_27b: d,F0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
( ! [V1i: mono_2Etyop_2Enum_2Enum,V2n: mono_2Etyop_2Enum_2Enum] :
( ( F0 @ V1i @ V2n )
= ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool @ V2n @ ( mono_2Ec_2Earithmetic_2E_3C_3D @ V2n @ V1i ) ) )
=> ! [V0p_2E0: u,V1i: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1i @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etake_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) ) )
= ( mono_2Ec_2Epred__set_2EGSPEC_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ ( F0 @ V1i ) ) ) ) ) ).
thf(thm_2Epath_2Elast__take,axiom,
! [A_27a: d,A_27b: d,V0i: mono_2Etyop_2Enum_2Enum,V1p_2E0: u] :
( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V0i @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) )
=> ( ( s @ A_27a @ ( c_2Epath_2Elast_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etake_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Epath_2Eel_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) ) ).
thf(thm_2Epath_2Enth__label__take,axiom,
! [A_27a: d,A_27b: d,V0n: mono_2Etyop_2Enum_2Enum,V1p_2E0: u,V2i: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ V2i @ V0n )
& ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V0n @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) ) )
=> ( ( s @ A_27b @ ( c_2Epath_2Enth__label_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etake_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) )
= ( s @ A_27b @ ( c_2Epath_2Enth__label_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) ) ).
thf(thm_2Epath_2Esingleton__seg,axiom,
! [A_27a: d,A_27b: d,V0i: mono_2Etyop_2Enum_2Enum,V1p_2E0: u] :
( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V0i @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) )
=> ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Eseg_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0i ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ ( c_2Epath_2Eel_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Erecursive__seg,axiom,
! [A_27a: d,A_27b: d,V0i: mono_2Etyop_2Enum_2Enum,V1j: mono_2Etyop_2Enum_2Enum,V2p_2E0: u] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ V0i @ V1j )
& ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1j @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) ) )
=> ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Eseg_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0i ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1j ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ ( c_2Epath_2Eel_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) @ ( s @ A_27b @ ( c_2Epath_2Enth__label_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Eseg_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V0i @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1j ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2EPL__seg,axiom,
! [A_27a: d,A_27b: d,F0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
( ! [V1j: mono_2Etyop_2Enum_2Enum,V0i: mono_2Etyop_2Enum_2Enum,V3n: mono_2Etyop_2Enum_2Enum] :
( ( F0 @ V1j @ V0i @ V3n )
= ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool @ V3n @ ( mono_2Ec_2Earithmetic_2E_3C_3D @ V3n @ ( mono_2Ec_2Earithmetic_2E_2D @ V1j @ V0i ) ) ) )
=> ! [V0i: mono_2Etyop_2Enum_2Enum,V1j: mono_2Etyop_2Enum_2Enum,V2p_2E0: u] :
( ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0i @ V1j )
& ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1j @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Eseg_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0i ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1j ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) ) )
= ( mono_2Ec_2Epred__set_2EGSPEC_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ ( F0 @ V1j @ V0i ) ) ) ) ) ).
thf(thm_2Epath_2Efinite__seg,axiom,
! [A_27a: d,A_27b: d,V0p_2E0: u,V1i: mono_2Etyop_2Enum_2Enum,V2j: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1i @ V2j )
& ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V2j @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Eseg_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1i ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2j ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Efirst__seg,axiom,
! [A_27a: d,A_27b: d,V0i: mono_2Etyop_2Enum_2Enum,V1j: mono_2Etyop_2Enum_2Enum,V2p_2E0: u] :
( ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0i @ V1j )
& ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1j @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) ) )
=> ( ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Eseg_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0i ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1j ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Epath_2Eel_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) ) ).
thf(thm_2Epath_2Elast__seg,axiom,
! [A_27a: d,A_27b: d,V0i: mono_2Etyop_2Enum_2Enum,V1j: mono_2Etyop_2Enum_2Enum,V2p_2E0: u] :
( ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0i @ V1j )
& ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V1j @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) ) )
=> ( ( s @ A_27a @ ( c_2Epath_2Elast_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Eseg_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0i ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1j ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Epath_2Eel_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1j ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_2E0 ) ) ) ) ) ).
thf(thm_2Epath_2EfirstP__at__unique,axiom,
! [A_27a: d,A_27b: d,V0P_2E0: u,V1p_2E0: u,V2n: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2EfirstP__at_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2n ) ) ) ) )
=> ! [V3m: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2EfirstP__at_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3m ) ) ) ) )
<=> ( V3m = V2n ) ) ) ).
thf(thm_2Epath_2Eis__stopped__thm,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d] :
( ! [V0x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eis__stopped_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) ) ) )
= mono_2Ec_2Ebool_2ET )
& ! [V1x_2E0: u,V2r_2E0: u,V3p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eis__stopped_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27c @ V1x_2E0 ) @ ( s @ A_27d @ V2r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27d ) @ V3p_2E0 ) ) ) ) ) )
= mono_2Ec_2Ebool_2EF ) ) ).
thf(thm_2Epath_2Efilter__every,axiom,
! [A_27a: d,A_27b: d,V0P_2E0: u,V1p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eexists_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eevery_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Efilter_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Epgenerate__infinite,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epgenerate_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V1g_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Epgenerate__not__stopped,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
( (~)
@ ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epgenerate_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V1g_2E0 ) ) ) ) ) ).
thf(thm_2Epath_2Eel__pgenerate,axiom,
! [A_27a: d,A_27b: d,V0n: mono_2Etyop_2Enum_2Enum,V1f_2E0: u,V2g_2E0: u] :
( ( s @ A_27a @ ( c_2Epath_2Eel_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epgenerate_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V2g_2E0 ) ) ) ) )
= ( 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 ) ) ) ) ) ).
thf(thm_2Epath_2Enth__label__pgenerate,axiom,
! [A_27a: d,A_27b: d,V0n: mono_2Etyop_2Enum_2Enum,V1f_2E0: u,V2g_2E0: u] :
( ( s @ A_27b @ ( c_2Epath_2Enth__label_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epgenerate_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V2g_2E0 ) ) ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V2g_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) ) ) ) ).
thf(thm_2Epath_2Epgenerate__11,axiom,
! [A_27a: d,A_27b: d,V0f1_2E0: u,V1g1_2E0: u,V2f2_2E0: u,V3g2_2E0: u] :
( ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epgenerate_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V1g1_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epgenerate_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V3g2_2E0 ) ) ) )
<=> ( ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V0f1_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2f2_2E0 ) )
& ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V1g1_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V3g2_2E0 ) ) ) ) ).
thf(thm_2Epath_2Epgenerate__onto,axiom,
! [A_27a: d,A_27b: d,V0p_2E0: u] :
( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) )
=> ? [V1f_2E0: u,V2g_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epgenerate_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V2g_2E0 ) ) ) ) ) ).
thf(thm_2Epath_2Eokpath__monotone,axiom,
! [A_27a: d,A_27b: d,V0R_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2EfixedPoint_2Emonotone_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epath_2Eokpath__f_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) ) ) ) ) ) ).
thf(thm_2Epath_2Eokpath__co__ind,axiom,
! [A_27a: d,A_27b: d,V0R_2E0: u,V1P_2E0: u] :
( ! [V2x_2E0: u,V3r_2E0: u,V4p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V4p_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_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ V3r_2E0 ) ) ) @ ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V4p_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V4p_2E0 ) ) ) ) ) )
=> ! [V5p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p_2E0 ) ) ) ) ) ) ).
thf(thm_2Epath_2Eokpath__cases,axiom,
! [A_27a: d,A_27b: d,V0R_2E0: u,V1x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1x_2E0 ) ) ) )
<=> ( ? [V2x_27_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1x_2E0 )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V2x_27_2E0 ) ) ) )
| ? [V3x_27_2E0: u,V4r_2E0: u,V5p_2E0: u] :
( ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1x_2E0 )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V3x_27_2E0 ) @ ( s @ A_27b @ V4r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p_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_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) @ ( s @ A_27a @ V3x_27_2E0 ) ) ) @ ( s @ A_27b @ V4r_2E0 ) ) ) @ ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Eokpath__thm,axiom,
! [A_27a: d,A_27b: d,V0R_2E0: u] :
( ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) )
& ! [V2x_2E0: u,V3r_2E0: u,V4p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V4p_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_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ V3r_2E0 ) ) ) @ ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V4p_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V4p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Efinite__okpath__ind,axiom,
! [A_27a: d,A_27b: d,V0P_2E0: u,V1R_2E0: u] :
( ( ! [V2x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) )
& ! [V3x_2E0: u,V4r_2E0: u,V5p_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V1R_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p_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_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V1R_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ A_27b @ V4r_2E0 ) ) ) @ ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ A_27b @ V4r_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V5p_2E0 ) ) ) ) ) ) ) )
=> ! [V6sigma_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V1R_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V6sigma_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V6sigma_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V6sigma_2E0 ) ) ) ) ) ) ).
thf(thm_2Epath_2Eokpath__pmap,axiom,
! [A_27a: d,A_27b: d,V0R_2E0: u,V1f_2E0: u,V2g_2E0: u,V3p_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3p_2E0 ) ) ) )
& ! [V4x_2E0: u,V5r_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_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) ) ) @ ( s @ A_27b @ V5r_2E0 ) ) ) @ ( s @ A_27a @ V6y_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_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V1f_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ V2g_2E0 ) @ ( s @ A_27b @ V5r_2E0 ) ) ) ) ) @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V1f_2E0 ) @ ( s @ A_27a @ V6y_2E0 ) ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epmap_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ V2g_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V3p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Efinite__plink,axiom,
! [A_27a: d,A_27b: d,V0p1_2E0: u,V1p2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Eplink_2E2 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p1_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p2_2E0 ) ) ) ) ) )
<=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p1_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p2_2E0 ) ) ) ) ) ) ).
thf(thm_2Epath_2Efirst__plink,axiom,
! [A_27a: d,A_27b: d,V0p1_2E0: u,V1p2_2E0: u] :
( ( ( s @ A_27a @ ( c_2Epath_2Elast_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p1_2E0 ) ) )
= ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p2_2E0 ) ) ) )
=> ( ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Eplink_2E2 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p1_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p2_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p1_2E0 ) ) ) ) ) ).
thf(thm_2Epath_2Elast__plink,axiom,
! [A_27a: d,A_27b: d,V0p1_2E0: u,V1p2_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p1_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p2_2E0 ) ) ) )
& ( ( s @ A_27a @ ( c_2Epath_2Elast_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p1_2E0 ) ) )
= ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p2_2E0 ) ) ) ) )
=> ( ( s @ A_27a @ ( c_2Epath_2Elast_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Eplink_2E2 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p1_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p2_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Epath_2Elast_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p2_2E0 ) ) ) ) ) ).
thf(thm_2Epath_2Eokpath__plink,axiom,
! [A_27a: d,A_27b: d,V0R_2E0: u,V1p1_2E0: u,V2p2_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p1_2E0 ) ) ) )
& ( ( s @ A_27a @ ( c_2Epath_2Elast_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p1_2E0 ) ) )
= ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p2_2E0 ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Eplink_2E2 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p1_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p2_2E0 ) ) ) ) ) )
<=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p1_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p2_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Eokpath__take,axiom,
! [A_27a: d,A_27b: d,V0R_2E0: u,V1p_2E0: u,V2i: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V2i @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etake_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Eokpath__drop,axiom,
! [A_27a: d,A_27b: d,V0R_2E0: u,V1p_2E0: u,V2i: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V2i @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Edrop_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Eokpath__seg,axiom,
! [A_27a: d,A_27b: d,V0R_2E0: u,V1p_2E0: u,V2i: mono_2Etyop_2Enum_2Enum,V3j: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V2i @ V3j )
& ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V3j @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Eseg_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2i ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3j ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2ESN__finite__paths,axiom,
! [A_27a: d,A_27b: d,V0R_2E0: u,V1p_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2ESN_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) ) ).
thf(thm_2Epath_2Efinite__paths__SN,axiom,
! [A_27a: d,A_27b: d,V0R_2E0: u] :
( ! [V1p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2ESN_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) ) ) ) ) ).
thf(thm_2Epath_2ESN__finite__paths__EQ,axiom,
! [A_27a: d,A_27b: d,V0R_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2ESN_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) ) ) )
<=> ! [V1p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) ) ) ).
thf(thm_2Epath_2Elabels__LMAP,axiom,
! [A_27a: d,A_27b: d,V0p_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Epath_2Elabels_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27b ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Ellist_2Ellist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ ( c_2Epath_2EfromPath_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Elabels__plink,axiom,
! [A_27a: d,A_27b: d,V0p1_2E0: u,V1p2_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Epath_2Elabels_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Eplink_2E2 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p1_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p2_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Ellist_2ELAPPEND_2E2 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Epath_2Elabels_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p1_2E0 ) ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Epath_2Elabels_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p2_2E0 ) ) ) ) ) ) ).
thf(thm_2Epath_2Efinite__labels,axiom,
! [A_27a: d,A_27b: d,V0p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ellist_2ELFINITE_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Epath_2Elabels_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) ) ) ).
thf(thm_2Epath_2Eunfold__thm,axiom,
! [A_27a: d,A_27b: d,A_27c: d,F1_2E0: u,F0_2E0: u] :
( ! [V0proj_2E0: u,V2s_2E0: u,V1f_2E0: u,V4s_27_2E0: u,V5l_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0proj_2E0 ) ) ) @ ( s @ A_27a @ V2s_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ V1f_2E0 ) ) ) @ ( s @ A_27a @ V4s_27_2E0 ) ) ) @ ( s @ A_27c @ V5l_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0proj_2E0 ) @ ( s @ A_27a @ V2s_2E0 ) ) ) @ ( s @ A_27c @ V5l_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epath_2Eunfold_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0proj_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ V1f_2E0 ) @ ( s @ A_27a @ V4s_27_2E0 ) ) ) ) ) )
=> ( ! [V0proj_2E0: u,V2s_2E0: u,V1f_2E0: u,V3v_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0proj_2E0 ) ) ) @ ( s @ A_27a @ V2s_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ V1f_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ V3v_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ V3v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0proj_2E0 ) ) ) @ ( s @ A_27a @ V2s_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ V1f_2E0 ) ) ) ) ) )
=> ! [V0proj_2E0: u,V1f_2E0: u,V2s_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epath_2Eunfold_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0proj_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ V1f_2E0 ) @ ( s @ A_27a @ V2s_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ V1f_2E0 ) @ ( s @ A_27a @ V2s_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0proj_2E0 ) @ ( s @ A_27a @ V2s_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0proj_2E0 ) ) ) @ ( s @ A_27a @ V2s_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ V1f_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Eunfold__thm2,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0proj_2E0: u,V1f_2E0: u,V2x_2E0: u,V3v1_2E0: u,V4v2_2E0: u] :
( ( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ V1f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ c_2Eoption_2ENONE_2E0 ) )
=> ( ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epath_2Eunfold_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0proj_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ V1f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0proj_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) )
& ( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ V1f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3v1_2E0 ) @ ( s @ A_27c @ V4v2_2E0 ) ) ) ) ) )
=> ( ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epath_2Eunfold_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0proj_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ V1f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0proj_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27c @ V4v2_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epath_2Eunfold_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0proj_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ V1f_2E0 ) @ ( s @ A_27a @ V3v1_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Elabels__unfold,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0proj_2E0: u,V1f_2E0: u,V2s_2E0: u] :
( ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( c_2Epath_2Elabels_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epath_2Eunfold_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0proj_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ V1f_2E0 ) @ ( s @ A_27a @ V2s_2E0 ) ) ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( c_2Ellist_2ELUNFOLD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ V1f_2E0 ) @ ( s @ A_27a @ V2s_2E0 ) ) ) ) ).
thf(thm_2Epath_2Eokpath__unfold,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0P_2E0: u,V1m_2E0: u,V2proj_2E0: u,V3f_2E0: u,V4s_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 @ V4s_2E0 ) ) ) )
& ! [V5s_2E0: u,V6s_27_2E0: u,V7l_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 @ V5s_2E0 ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ V3f_2E0 ) @ ( s @ A_27a @ V5s_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V6s_27_2E0 ) @ ( s @ A_27c @ V7l_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 @ V6s_27_2E0 ) ) ) ) )
& ! [V8s_2E0: u,V9s_27_2E0: u,V10l_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 @ V8s_2E0 ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ V3f_2E0 ) @ ( s @ A_27a @ V8s_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V9s_27_2E0 ) @ ( s @ A_27c @ V10l_2E0 ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ V1m_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2proj_2E0 ) @ ( s @ A_27a @ V8s_2E0 ) ) ) ) ) @ ( s @ A_27c @ V10l_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2proj_2E0 ) @ ( s @ A_27a @ V9s_27_2E0 ) ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ V1m_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epath_2Eunfold_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2proj_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ V3f_2E0 ) @ ( s @ A_27a @ V4s_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Etrace__machine__thm,axiom,
! [A_27a: d,V0P_2E0: u,V1tr_2E0: u] :
( ! [V2n: 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 @ V2n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1tr_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3l_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V3l_2E0 ) ) ) ) )
=> ? [V4p_2E0: u] :
( ( ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ V1tr_2E0 )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27a ) @ ( c_2Epath_2Elabels_2E1 @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27a ) @ V4p_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epath_2Etrace__machine_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27a ) @ V4p_2E0 ) ) ) )
& ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27a ) @ V4p_2E0 ) ) )
= ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ).
thf(thm_2Epath_2Etrace__machine__thm2,axiom,
! [A_27a: d,A_27b: d,V0n: mono_2Etyop_2Enum_2Enum,V1l_2E0: u,V2P_2E0: u,V3p_2E0: u,V4init_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epath_2Etrace__machine_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27a ) @ V3p_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27a ) @ V3p_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_2Epath_2Elabels_2E1 @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27a ) @ V3p_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Elist_2Elist @ A_27a ) @ A_27a ) @ V3p_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2ELTAKE__labels,axiom,
! [A_27a: d,A_27b: d,V0n: mono_2Etyop_2Enum_2Enum,V1p_2E0: u,V2l_2E0: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Epath_2Elabels_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V2l_2E0 ) ) ) )
<=> ( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V0n @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( c_2Ellist_2EtoList_2E1 @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Epath_2Elabels_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Etake_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V2l_2E0 ) ) ) ) ) ) ).
thf(thm_2Epath_2Edrop__eq__pcons,axiom,
! [A_27a: d,A_27b: d,V0n: mono_2Etyop_2Enum_2Enum,V1p_2E0: u,V2h_2E0: u,V3l_2E0: u,V4t_2E0: u] :
( ( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ V0n @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) )
& ( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Edrop_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ V2h_2E0 ) @ ( s @ A_27b @ V3l_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V4t_2E0 ) ) ) ) )
=> ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V0n @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) ) ) ).
thf(thm_2Epath_2Eokpath__parallel__comp,axiom,
! [A_27a: d,A_27b: d,A_27c: d,F1_2E0: u,F0_2E0: u] :
( ! [V4x_2E0: u] :
( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27c ) @ F1_2E0 ) @ ( s @ A_27c @ V4x_2E0 ) ) )
= ( s @ A_27c @ V4x_2E0 ) )
=> ( ! [V3x_2E0: u] :
( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27c ) @ F0_2E0 ) @ ( s @ A_27c @ V3x_2E0 ) ) )
= ( s @ A_27c @ V3x_2E0 ) )
=> ! [V0p_2E0: u,V1m1_2E0: u,V2m2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epath_2Eparallel__comp_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V1m1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ V2m2_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c ) @ V0p_2E0 ) ) ) )
<=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V1m1_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ ( c_2Epath_2Epmap_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27c ) @ F0_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c ) @ V0p_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ V2m2_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ ( c_2Epath_2Epmap_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27b ) @ c_2Epair_2ESND_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27c ) @ F1_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27c ) @ V0p_2E0 ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Ebuild__pcomp__trace,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0m1_2E0: u,V1p1_2E0: u,V2m2_2E0: u,V3p2_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0m1_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p1_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) ) @ V2m2_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27b ) @ V3p2_2E0 ) ) ) )
& ( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Epath_2Elabels_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p1_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Epath_2Elabels_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27b ) @ V3p2_2E0 ) ) ) ) )
=> ? [V4p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epath_2Eparallel__comp_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V0m1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) ) @ V2m2_2E0 ) ) ) @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ V4p_2E0 ) ) ) )
& ( ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Epath_2Elabels_2E1 @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ V4p_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Epath_2Elabels_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p1_2E0 ) ) ) )
& ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ V4p_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p1_2E0 ) ) ) @ ( s @ A_27c @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27c @ A_27b ) @ V3p2_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Enth__label__LNTH,axiom,
! [A_27a: d,A_27b: d,V0n: mono_2Etyop_2Enum_2Enum,V1p_2E0: u,V2x_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_2Epath_2Elabels_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V2x_2E0 ) ) ) )
<=> ( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V0n @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( c_2Epath_2EPL_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) )
& ( ( s @ A_27b @ ( c_2Epath_2Enth__label_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) )
= ( s @ A_27b @ V2x_2E0 ) ) ) ) ).
thf(thm_2Epath_2Enth__label__LTAKE,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0n: mono_2Etyop_2Enum_2Enum,V1p_2E0: u,V2l_2E0: u,V3i: mono_2Etyop_2Enum_2Enum,V4v_2E0: u] :
( ( ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( c_2Ellist_2ELTAKE_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0n ) ) @ ( s @ ( tyop_2Ellist_2Ellist @ A_27b ) @ ( c_2Epath_2Elabels_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V2l_2E0 ) ) ) )
& ( mono_2Ec_2Eprim__rec_2E_3C @ V3i @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V2l_2E0 ) ) ) ) ) )
=> ( ( s @ A_27b @ ( c_2Epath_2Enth__label_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3i ) ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V1p_2E0 ) ) )
= ( s @ A_27b @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V3i ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V2l_2E0 ) ) ) ) ) ).
thf(thm_2Epath_2Efinite__path__end__cases,axiom,
! [A_27a: d,A_27b: d,V0p_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Efinite_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 ) ) ) )
=> ( ? [V1x_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) )
| ? [V2p_27_2E0: u,V3l_2E0: u,V4s_2E0: u] :
( ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V0p_2E0 )
= ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Eplink_2E2 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_27_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Epcons_2E3 @ ( s @ A_27a @ ( c_2Epath_2Elast_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ V2p_27_2E0 ) ) ) @ ( s @ A_27b @ V3l_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27b ) @ ( c_2Epath_2Estopped__at_2E1 @ ( s @ A_27a @ V4s_2E0 ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Epath_2Esimulation__trace__inclusion,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0R_2E0: u,V1M1_2E0: u,V2M2_2E0: u,V3p_2E0: u,V4t__init_2E0: u] :
( ( ! [V5s1_2E0: u,V6l_2E0: u,V7s2_2E0: u,V8t1_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ A_27a @ V5s1_2E0 ) ) ) @ ( s @ A_27b @ V8t1_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_27c @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V1M1_2E0 ) @ ( s @ A_27a @ V5s1_2E0 ) ) ) @ ( s @ A_27c @ V6l_2E0 ) ) ) @ ( s @ A_27a @ V7s2_2E0 ) ) ) ) )
=> ? [V9t2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ A_27a @ V7s2_2E0 ) ) ) @ ( s @ A_27b @ V9t2_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ V2M2_2E0 ) @ ( s @ A_27b @ V8t1_2E0 ) ) ) @ ( s @ A_27c @ V6l_2E0 ) ) ) @ ( s @ A_27b @ V9t2_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ V1M1_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ V3p_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ A_27a @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ V3p_2E0 ) ) ) ) ) @ ( s @ A_27b @ V4t__init_2E0 ) ) ) ) )
=> ? [V10q_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eokpath_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ V2M2_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ V10q_2E0 ) ) ) )
& ( ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( c_2Epath_2Elabels_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27a @ A_27c ) @ V3p_2E0 ) ) )
= ( s @ ( tyop_2Ellist_2Ellist @ A_27c ) @ ( c_2Epath_2Elabels_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ V10q_2E0 ) ) ) )
& ( ( s @ A_27b @ ( c_2Epath_2Efirst_2E1 @ ( s @ ( tyop_2Epath_2Epath @ A_27b @ A_27c ) @ V10q_2E0 ) ) )
= ( s @ A_27b @ V4t__init_2E0 ) ) ) ) ).
%------------------------------------------------------------------------------