TPTP Problem File: SLH0666^1.p

%------------------------------------------------------------------------------
% File     : SLH0000^1 : TPTP v8.2.0. Released v8.2.0.
% Domain   : Archive of Formal Proofs
% Problem  :
% Version  : Especial.
% English  :

% Refs     : [Des23] Desharnais (2023), Email to Geoff Sutcliffe
% Source   : [Des23]
% Names    : FO_Theory_Rewriting/0051_Multihole_Context/prob_00537_021563__18370906_1 [Des23]

% Status   : Theorem
% Rating   : ? v8.2.0
% Syntax   : Number of formulae    : 1898 ( 689 unt; 624 typ;   0 def)
%            Number of atoms       : 3489 (1364 equ;   0 cnn)
%            Maximal formula atoms :   20 (   2 avg)
%            Number of connectives : 10655 ( 185   ~;  10   |; 139   &;9051   @)
%                                         (   0 <=>;1270  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   6 avg)
%            Number of types       :   64 (  63 usr)
%            Number of type conns  : 4505 (4505   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  564 ( 561 usr;  20 con; 0-5 aty)
%            Number of variables   : 3904 ( 472   ^;3364   !;  68   ?;3904   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2023-01-19 12:00:56.481
%------------------------------------------------------------------------------
% Could-be-implicit typings (63)
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_M_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_J,type,
    set_Pr9036761696576656435xt_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_M_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_J,type,
    set_Pr8131422468521715813xt_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_M_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_J_J,type,
    set_Pr8796965451986337883list_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_M_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J,type,
    produc5683466111014092243xt_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_M_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J,type,
    produc5956155440505932549xt_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_M_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_J,type,
    produc3044767985951407611list_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_M_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_J_J,type,
    set_Pr770470488129649324list_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_M_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_J_J,type,
    set_Pr5636780074650139358list_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_M_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_J_J,type,
    set_Pr1013263123567674224xt_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_M_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_J,type,
    produc6423750584600236748list_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_M_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_J,type,
    produc4127645531870415870list_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_M_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_J,type,
    produc8823150311724842384xt_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J,type,
    set_Pr5839317327662470821xt_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    produc420090126769944851xt_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    produc7347357110894899781xt_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J,type,
    produc767570952302678203list_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J,type,
    produc2745072675574436617xt_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_J,type,
    set_Pr7630595734861755952xt_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_M_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_J_J,type,
    set_Pr5544284923275595840list_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_M_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_J,type,
    set_Pr3280023335470083854xt_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J,type,
    produc1635315984519752016xt_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_M_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_J,type,
    produc5125836498238150368list_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_M_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J,type,
    produc8094751872729218222xt_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J,type,
    set_Pr2918931875556005383xt_a_b: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_J,type,
    set_na6008912749387833063list_b: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_J,type,
    set_na664922679713831477xt_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    produc1652119919080531751xt_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J,type,
    set_Pr1895186847599665920list_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J,type,
    set_Pr3872688570871424334xt_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    set_Pr7682762132356531903at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    produc746580111399690912list_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    produc5647625992154082286xt_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    produc1932156733058919263at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J,type,
    produc8373899037510109440at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    produc7248412053542808358at_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__List__Olist_Itf__b_J_J_J,type,
    set_Pr7665282455119567943list_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_M_Eo_J,type,
    produc6481442714050758067_a_b_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    produc4044283025580285595xt_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J,type,
    set_se6625423409757081292xt_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    produc3963297410138542439list_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    set_Pr1261947904930325089at_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J,type,
    produc7811952446676219690list_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Nat__Onat_J,type,
    produc6020613750378442500_b_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    set_Mu3903433398966807788xt_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__List__Olist_Itf__b_J_M_Eo_J,type,
    produc2420475512092800890st_b_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__List__Olist_Itf__b_J_J,type,
    produc5666708989857747476list_b: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_It__List__Olist_Itf__b_J_J_J,type,
    set_set_list_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    product_prod_nat_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    set_Product_prod_o_o: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    set_nat_nat: $tType ).

thf(ty_n_t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    multihole_mctxt_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
    product_prod_nat_o: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
    product_prod_o_nat: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
    set_set_nat: $tType ).

thf(ty_n_t__Set__Oset_It__List__Olist_Itf__b_J_J,type,
    set_list_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
    product_prod_o_o: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_I_Eo_J_J,type,
    set_set_o: $tType ).

thf(ty_n_t__Set__Oset_I_062_I_Eo_M_Eo_J_J,type,
    set_o_o: $tType ).

thf(ty_n_t__Term__Oterm_Itf__a_Mtf__b_J,type,
    term_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
    set_nat: $tType ).

thf(ty_n_t__List__Olist_Itf__b_J,type,
    list_b: $tType ).

thf(ty_n_t__Set__Oset_I_Eo_J,type,
    set_o: $tType ).

thf(ty_n_t__Nat__Onat,type,
    nat: $tType ).

% Explicit typings (561)
thf(sy_c_Abstract__Rewriting_Orestrict_001_Eo,type,
    abstract_restrict_o: set_Product_prod_o_o > set_o > set_Product_prod_o_o ).

thf(sy_c_BNF__Def_OGrp_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
    bNF_Gr3847987472475283150at_nat: set_nat_nat > ( ( nat > nat ) > nat > nat ) > ( nat > nat ) > ( nat > nat ) > $o ).

thf(sy_c_BNF__Def_OGrp_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_001_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J,type,
    bNF_Gr3902530357237781285list_b: set_na664922679713831477xt_a_b > ( ( nat > produc5647625992154082286xt_a_b ) > nat > list_b ) > ( nat > produc5647625992154082286xt_a_b ) > ( nat > list_b ) > $o ).

thf(sy_c_BNF__Def_OGrp_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_001_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    bNF_Gr5747004589486111148xt_a_b: set_na664922679713831477xt_a_b > ( ( nat > produc5647625992154082286xt_a_b ) > nat > multihole_mctxt_a_b ) > ( nat > produc5647625992154082286xt_a_b ) > ( nat > multihole_mctxt_a_b ) > $o ).

thf(sy_c_BNF__Def_OGrp_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_001_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J,type,
    bNF_Gr6198635409967602163list_b: set_na6008912749387833063list_b > ( ( nat > produc746580111399690912list_b ) > nat > list_b ) > ( nat > produc746580111399690912list_b ) > ( nat > list_b ) > $o ).

thf(sy_c_BNF__Def_OGrp_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_001_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    bNF_Gr5474315259994270842xt_a_b: set_na6008912749387833063list_b > ( ( nat > produc746580111399690912list_b ) > nat > multihole_mctxt_a_b ) > ( nat > produc746580111399690912list_b ) > ( nat > multihole_mctxt_a_b ) > $o ).

thf(sy_c_BNF__Def_OGrp_001_Eo_001_Eo,type,
    bNF_Grp_o_o: set_o > ( $o > $o ) > $o > $o > $o ).

thf(sy_c_BNF__Def_OGrp_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    bNF_Gr4349803078253886990list_b: set_list_b > ( list_b > list_b ) > list_b > list_b > $o ).

thf(sy_c_BNF__Def_OGrp_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    bNF_Gr4324690944090783765xt_a_b: set_list_b > ( list_b > multihole_mctxt_a_b ) > list_b > multihole_mctxt_a_b > $o ).

thf(sy_c_BNF__Def_OGrp_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    bNF_Gr3706198758728502087list_b: set_Mu3903433398966807788xt_a_b > ( multihole_mctxt_a_b > list_b ) > multihole_mctxt_a_b > list_b > $o ).

thf(sy_c_BNF__Def_OGrp_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    bNF_Gr2548120569987561294xt_a_b: set_Mu3903433398966807788xt_a_b > ( multihole_mctxt_a_b > multihole_mctxt_a_b ) > multihole_mctxt_a_b > multihole_mctxt_a_b > $o ).

thf(sy_c_BNF__Def_OGrp_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_Grp_nat_nat: set_nat > ( nat > nat ) > nat > nat > $o ).

thf(sy_c_BNF__Def_OGrp_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__List__Olist_Itf__b_J,type,
    bNF_Gr3936827293007548773list_b: set_Pr3872688570871424334xt_a_b > ( produc5647625992154082286xt_a_b > list_b ) > produc5647625992154082286xt_a_b > list_b > $o ).

thf(sy_c_BNF__Def_OGrp_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    bNF_Gr6945608680004897132xt_a_b: set_Pr3872688570871424334xt_a_b > ( produc5647625992154082286xt_a_b > multihole_mctxt_a_b ) > produc5647625992154082286xt_a_b > multihole_mctxt_a_b > $o ).

thf(sy_c_BNF__Def_OGrp_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__List__Olist_Itf__b_J,type,
    bNF_Gr7082935421558533171list_b: set_Pr1895186847599665920list_b > ( produc746580111399690912list_b > list_b ) > produc746580111399690912list_b > list_b > $o ).

thf(sy_c_BNF__Def_OGrp_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    bNF_Gr18341695879942202xt_a_b: set_Pr1895186847599665920list_b > ( produc746580111399690912list_b > multihole_mctxt_a_b ) > produc746580111399690912list_b > multihole_mctxt_a_b > $o ).

thf(sy_c_BNF__Def_Oconvol_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_co805650143699787099at_nat: ( nat > nat ) > ( nat > nat ) > nat > product_prod_nat_nat ).

thf(sy_c_BNF__Def_Ocsquare_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001_Eo_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
    bNF_cs6420615464401995480od_o_o: set_Product_prod_o_o > ( product_prod_o_o > $o ) > ( product_prod_o_o > $o ) > ( product_prod_o_o > product_prod_o_o ) > ( product_prod_o_o > product_prod_o_o ) > $o ).

thf(sy_c_BNF__Def_Ocsquare_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__List__Olist_Itf__b_J_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__List__Olist_Itf__b_J_J_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    bNF_cs4731316694088296171list_b: set_Pr7665282455119567943list_b > ( produc3963297410138542439list_b > list_b ) > ( produc3963297410138542439list_b > list_b ) > ( produc3963297410138542439list_b > produc3963297410138542439list_b ) > ( produc3963297410138542439list_b > produc3963297410138542439list_b ) > $o ).

thf(sy_c_BNF__Def_Ocsquare_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__List__Olist_Itf__b_J_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    bNF_cs1829493375424135524list_b: set_Pr7665282455119567943list_b > ( produc5647625992154082286xt_a_b > multihole_mctxt_a_b ) > ( produc746580111399690912list_b > multihole_mctxt_a_b ) > ( produc3963297410138542439list_b > produc5647625992154082286xt_a_b ) > ( produc3963297410138542439list_b > produc746580111399690912list_b ) > $o ).

thf(sy_c_BNF__Def_Ocsquare_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__List__Olist_Itf__b_J_J_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    bNF_cs1883607401310078891xt_a_b: set_Pr3872688570871424334xt_a_b > ( produc3963297410138542439list_b > list_b ) > ( produc5647625992154082286xt_a_b > list_b ) > ( produc5647625992154082286xt_a_b > produc3963297410138542439list_b ) > ( produc5647625992154082286xt_a_b > produc5647625992154082286xt_a_b ) > $o ).

thf(sy_c_BNF__Def_Ocsquare_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    bNF_cs6184644846197688868xt_a_b: set_Pr3872688570871424334xt_a_b > ( produc5647625992154082286xt_a_b > multihole_mctxt_a_b ) > ( produc1652119919080531751xt_a_b > multihole_mctxt_a_b ) > ( produc5647625992154082286xt_a_b > produc5647625992154082286xt_a_b ) > ( produc5647625992154082286xt_a_b > produc1652119919080531751xt_a_b ) > $o ).

thf(sy_c_BNF__Def_Ocsquare_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    bNF_cs4566955500544489259list_b: set_Pr1895186847599665920list_b > ( produc746580111399690912list_b > list_b ) > ( produc3963297410138542439list_b > list_b ) > ( produc746580111399690912list_b > produc746580111399690912list_b ) > ( produc746580111399690912list_b > produc3963297410138542439list_b ) > $o ).

thf(sy_c_BNF__Def_Ocsquare_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    bNF_cs8973424432489419172list_b: set_Pr1895186847599665920list_b > ( produc1652119919080531751xt_a_b > multihole_mctxt_a_b ) > ( produc746580111399690912list_b > multihole_mctxt_a_b ) > ( produc746580111399690912list_b > produc1652119919080531751xt_a_b ) > ( produc746580111399690912list_b > produc746580111399690912list_b ) > $o ).

thf(sy_c_BNF__Def_Ocsquare_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    bNF_cs1790445340265650155xt_a_b: set_Pr2918931875556005383xt_a_b > ( produc746580111399690912list_b > list_b ) > ( produc5647625992154082286xt_a_b > list_b ) > ( produc1652119919080531751xt_a_b > produc746580111399690912list_b ) > ( produc1652119919080531751xt_a_b > produc5647625992154082286xt_a_b ) > $o ).

thf(sy_c_BNF__Def_Ocsquare_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    bNF_cs4644519502363695716xt_a_b: set_Pr2918931875556005383xt_a_b > ( produc1652119919080531751xt_a_b > multihole_mctxt_a_b ) > ( produc1652119919080531751xt_a_b > multihole_mctxt_a_b ) > ( produc1652119919080531751xt_a_b > produc1652119919080531751xt_a_b ) > ( produc1652119919080531751xt_a_b > produc1652119919080531751xt_a_b ) > $o ).

thf(sy_c_BNF__Def_Ocsquare_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    bNF_cs7448163979520790438at_nat: set_Pr1261947904930325089at_nat > ( product_prod_nat_nat > nat ) > ( product_prod_nat_nat > nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ).

thf(sy_c_BNF__Def_OfstOp_001_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_001_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    bNF_fs7622806390863915544xt_a_b: ( ( nat > list_b ) > ( nat > produc5647625992154082286xt_a_b ) > $o ) > ( ( nat > produc5647625992154082286xt_a_b ) > ( nat > multihole_mctxt_a_b ) > $o ) > produc8094751872729218222xt_a_b > produc8823150311724842384xt_a_b ).

thf(sy_c_BNF__Def_OfstOp_001_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_001_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J,type,
    bNF_fs5822184879409743590list_b: ( ( nat > multihole_mctxt_a_b ) > ( nat > produc746580111399690912list_b ) > $o ) > ( ( nat > produc746580111399690912list_b ) > ( nat > list_b ) > $o ) > produc5125836498238150368list_b > produc3044767985951407611list_b ).

thf(sy_c_BNF__Def_OfstOp_001_Eo_001_Eo_001_Eo,type,
    bNF_fstOp_o_o_o: ( $o > $o > $o ) > ( $o > $o > $o ) > product_prod_o_o > product_prod_o_o ).

thf(sy_c_BNF__Def_OfstOp_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    bNF_fs4460400041868295571list_b: ( list_b > list_b > $o ) > ( list_b > list_b > $o ) > produc3963297410138542439list_b > produc3963297410138542439list_b ).

thf(sy_c_BNF__Def_OfstOp_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    bNF_fs4750163954569552282xt_a_b: ( list_b > list_b > $o ) > ( list_b > multihole_mctxt_a_b > $o ) > produc5647625992154082286xt_a_b > produc3963297410138542439list_b ).

thf(sy_c_BNF__Def_OfstOp_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    bNF_fs4131671769207270604list_b: ( list_b > multihole_mctxt_a_b > $o ) > ( multihole_mctxt_a_b > list_b > $o ) > produc3963297410138542439list_b > produc5647625992154082286xt_a_b ).

thf(sy_c_BNF__Def_OfstOp_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    bNF_fs6894104479137331923xt_a_b: ( list_b > multihole_mctxt_a_b > $o ) > ( multihole_mctxt_a_b > multihole_mctxt_a_b > $o ) > produc5647625992154082286xt_a_b > produc5647625992154082286xt_a_b ).

thf(sy_c_BNF__Def_OfstOp_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    bNF_fs5383721789538498929xt_a_b: ( list_b > produc5647625992154082286xt_a_b > $o ) > ( produc5647625992154082286xt_a_b > multihole_mctxt_a_b > $o ) > produc5647625992154082286xt_a_b > produc1635315984519752016xt_a_b ).

thf(sy_c_BNF__Def_OfstOp_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    bNF_fs8763394141750842138list_b: ( multihole_mctxt_a_b > list_b > $o ) > ( list_b > list_b > $o ) > produc746580111399690912list_b > produc746580111399690912list_b ).

thf(sy_c_BNF__Def_OfstOp_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    bNF_fs7855130708986367265xt_a_b: ( multihole_mctxt_a_b > list_b > $o ) > ( list_b > multihole_mctxt_a_b > $o ) > produc1652119919080531751xt_a_b > produc746580111399690912list_b ).

thf(sy_c_BNF__Def_OfstOp_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    bNF_fs7236638523624085587list_b: ( multihole_mctxt_a_b > multihole_mctxt_a_b > $o ) > ( multihole_mctxt_a_b > list_b > $o ) > produc746580111399690912list_b > produc1652119919080531751xt_a_b ).

thf(sy_c_BNF__Def_OfstOp_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    bNF_fs8789942433486863450xt_a_b: ( multihole_mctxt_a_b > multihole_mctxt_a_b > $o ) > ( multihole_mctxt_a_b > multihole_mctxt_a_b > $o ) > produc1652119919080531751xt_a_b > produc1652119919080531751xt_a_b ).

thf(sy_c_BNF__Def_OfstOp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_fs6799373675401686564at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > product_prod_nat_nat > product_prod_nat_nat ).

thf(sy_c_BNF__Def_Opick__middlep_001_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_001_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    bNF_pi6984799623963337318xt_a_b: ( ( nat > list_b ) > ( nat > produc5647625992154082286xt_a_b ) > $o ) > ( ( nat > produc5647625992154082286xt_a_b ) > ( nat > multihole_mctxt_a_b ) > $o ) > ( nat > list_b ) > ( nat > multihole_mctxt_a_b ) > nat > produc5647625992154082286xt_a_b ).

thf(sy_c_BNF__Def_Opick__middlep_001_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_001_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J,type,
    bNF_pi5184178112509165364list_b: ( ( nat > multihole_mctxt_a_b ) > ( nat > produc746580111399690912list_b ) > $o ) > ( ( nat > produc746580111399690912list_b ) > ( nat > list_b ) > $o ) > ( nat > multihole_mctxt_a_b ) > ( nat > list_b ) > nat > produc746580111399690912list_b ).

thf(sy_c_BNF__Def_Opick__middlep_001_Eo_001_Eo_001_Eo,type,
    bNF_pi6189367155476860724_o_o_o: ( $o > $o > $o ) > ( $o > $o > $o ) > $o > $o > $o ).

thf(sy_c_BNF__Def_Opick__middlep_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    bNF_pi399958225447633377list_b: ( list_b > list_b > $o ) > ( list_b > list_b > $o ) > list_b > list_b > list_b ).

thf(sy_c_BNF__Def_Opick__middlep_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    bNF_pi5120686890154856936xt_a_b: ( list_b > list_b > $o ) > ( list_b > multihole_mctxt_a_b > $o ) > list_b > multihole_mctxt_a_b > list_b ).

thf(sy_c_BNF__Def_Opick__middlep_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    bNF_pi4502194704792575258list_b: ( list_b > multihole_mctxt_a_b > $o ) > ( multihole_mctxt_a_b > list_b > $o ) > list_b > list_b > multihole_mctxt_a_b ).

thf(sy_c_BNF__Def_Opick__middlep_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    bNF_pi215304164717827873xt_a_b: ( list_b > multihole_mctxt_a_b > $o ) > ( multihole_mctxt_a_b > multihole_mctxt_a_b > $o ) > list_b > multihole_mctxt_a_b > multihole_mctxt_a_b ).

thf(sy_c_BNF__Def_Opick__middlep_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    bNF_pi1062526254230083775xt_a_b: ( list_b > produc5647625992154082286xt_a_b > $o ) > ( produc5647625992154082286xt_a_b > multihole_mctxt_a_b > $o ) > list_b > multihole_mctxt_a_b > produc5647625992154082286xt_a_b ).

thf(sy_c_BNF__Def_Opick__middlep_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    bNF_pi9133917077336146792list_b: ( multihole_mctxt_a_b > list_b > $o ) > ( list_b > list_b > $o ) > multihole_mctxt_a_b > list_b > list_b ).

thf(sy_c_BNF__Def_Opick__middlep_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    bNF_pi1176330394566863215xt_a_b: ( multihole_mctxt_a_b > list_b > $o ) > ( list_b > multihole_mctxt_a_b > $o ) > multihole_mctxt_a_b > multihole_mctxt_a_b > list_b ).

thf(sy_c_BNF__Def_Opick__middlep_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    bNF_pi557838209204581537list_b: ( multihole_mctxt_a_b > multihole_mctxt_a_b > $o ) > ( multihole_mctxt_a_b > list_b > $o ) > multihole_mctxt_a_b > list_b > multihole_mctxt_a_b ).

thf(sy_c_BNF__Def_Opick__middlep_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    bNF_pi2247075006714987688xt_a_b: ( multihole_mctxt_a_b > multihole_mctxt_a_b > $o ) > ( multihole_mctxt_a_b > multihole_mctxt_a_b > $o ) > multihole_mctxt_a_b > multihole_mctxt_a_b > multihole_mctxt_a_b ).

thf(sy_c_BNF__Def_Opick__middlep_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_pi7484965678128203350at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > nat > nat > nat ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_M_062_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J_001_062_I_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_M_062_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J,type,
    bNF_re3108638643152158461_nat_o: ( ( nat > nat > $o ) > ( nat > nat > $o ) > $o ) > ( ( ( nat > nat > $o ) > ( nat > nat ) > $o ) > ( ( nat > nat > $o ) > ( nat > nat ) > $o ) > $o ) > ( ( nat > nat > $o ) > ( nat > nat > $o ) > ( nat > nat ) > $o ) > ( ( nat > nat > $o ) > ( nat > nat > $o ) > ( nat > nat ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
    bNF_re2012056497951032797_nat_o: ( ( nat > nat > $o ) > ( nat > nat > $o ) > $o ) > ( ( ( nat > nat ) > $o ) > ( ( nat > nat ) > $o ) > $o ) > ( ( nat > nat > $o ) > ( nat > nat ) > $o ) > ( ( nat > nat > $o ) > ( nat > nat ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    bNF_re3262823321055862553at_nat: ( ( nat > nat ) > ( nat > nat ) > $o ) > ( ( ( nat > nat ) > nat > nat ) > ( ( nat > nat ) > nat > nat ) > $o ) > ( ( nat > nat ) > ( nat > nat ) > nat > nat ) > ( ( nat > nat ) > ( nat > nat ) > nat > nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
    bNF_re239970166668089693at_nat: ( ( nat > nat ) > ( nat > nat ) > $o ) > ( ( nat > nat ) > ( nat > nat ) > $o ) > ( ( nat > nat ) > nat > nat ) > ( ( nat > nat ) > nat > nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
    bNF_re1334470082001271389at_o_o: ( ( nat > nat ) > ( nat > nat ) > $o ) > ( $o > $o > $o ) > ( ( nat > nat ) > $o ) > ( ( nat > nat ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001_062_It__List__Olist_Itf__b_J_M_Eo_J_001_062_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_M_Eo_J,type,
    bNF_re5537899745017807951_a_b_o: ( list_b > multihole_mctxt_a_b > $o ) > ( ( list_b > $o ) > ( multihole_mctxt_a_b > $o ) > $o ) > ( list_b > list_b > $o ) > ( multihole_mctxt_a_b > multihole_mctxt_a_b > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001_062_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_M_Eo_J_001_062_It__List__Olist_Itf__b_J_M_Eo_J,type,
    bNF_re7400526925355327567st_b_o: ( list_b > multihole_mctxt_a_b > $o ) > ( ( multihole_mctxt_a_b > $o ) > ( list_b > $o ) > $o ) > ( list_b > multihole_mctxt_a_b > $o ) > ( multihole_mctxt_a_b > list_b > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001_Eo_001_Eo,type,
    bNF_re8490395077849316260_b_o_o: ( list_b > multihole_mctxt_a_b > $o ) > ( $o > $o > $o ) > ( list_b > $o ) > ( multihole_mctxt_a_b > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001_062_It__List__Olist_Itf__b_J_M_Eo_J_001_062_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_M_Eo_J,type,
    bNF_re5517021838360836993_a_b_o: ( multihole_mctxt_a_b > list_b > $o ) > ( ( list_b > $o ) > ( multihole_mctxt_a_b > $o ) > $o ) > ( multihole_mctxt_a_b > list_b > $o ) > ( list_b > multihole_mctxt_a_b > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001_062_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_M_Eo_J_001_062_It__List__Olist_Itf__b_J_M_Eo_J,type,
    bNF_re7379649018698356609st_b_o: ( multihole_mctxt_a_b > list_b > $o ) > ( ( multihole_mctxt_a_b > $o ) > ( list_b > $o ) > $o ) > ( multihole_mctxt_a_b > multihole_mctxt_a_b > $o ) > ( list_b > list_b > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001_Eo_001_Eo,type,
    bNF_re5925240994597992406_b_o_o: ( multihole_mctxt_a_b > list_b > $o ) > ( $o > $o > $o ) > ( multihole_mctxt_a_b > $o ) > ( list_b > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
    bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001_Eo,type,
    bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    bNF_re7910447939628189510xt_a_b: ( nat > nat > $o ) > ( list_b > multihole_mctxt_a_b > $o ) > ( nat > list_b ) > ( nat > multihole_mctxt_a_b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    bNF_re7291955754265907832list_b: ( nat > nat > $o ) > ( multihole_mctxt_a_b > list_b > $o ) > ( nat > multihole_mctxt_a_b ) > ( nat > list_b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_re5653821019739307937at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( nat > nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    bNF_re7338882136821462045list_b: ( produc5647625992154082286xt_a_b > produc5647625992154082286xt_a_b > $o ) > ( list_b > list_b > $o ) > ( produc5647625992154082286xt_a_b > list_b ) > ( produc5647625992154082286xt_a_b > list_b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    bNF_re5350685653480569181xt_a_b: ( produc5647625992154082286xt_a_b > produc5647625992154082286xt_a_b > $o ) > ( multihole_mctxt_a_b > multihole_mctxt_a_b > $o ) > ( produc5647625992154082286xt_a_b > multihole_mctxt_a_b ) > ( produc5647625992154082286xt_a_b > multihole_mctxt_a_b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    bNF_re7495894085839512534xt_a_b: ( produc5647625992154082286xt_a_b > produc746580111399690912list_b > $o ) > ( list_b > multihole_mctxt_a_b > $o ) > ( produc5647625992154082286xt_a_b > list_b ) > ( produc746580111399690912list_b > multihole_mctxt_a_b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    bNF_re6877401900477230856list_b: ( produc5647625992154082286xt_a_b > produc746580111399690912list_b > $o ) > ( multihole_mctxt_a_b > list_b > $o ) > ( produc5647625992154082286xt_a_b > multihole_mctxt_a_b ) > ( produc746580111399690912list_b > list_b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    bNF_re7612423800577053938xt_a_b: ( produc746580111399690912list_b > produc5647625992154082286xt_a_b > $o ) > ( list_b > multihole_mctxt_a_b > $o ) > ( produc746580111399690912list_b > list_b ) > ( produc5647625992154082286xt_a_b > multihole_mctxt_a_b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    bNF_re6993931615214772260list_b: ( produc746580111399690912list_b > produc5647625992154082286xt_a_b > $o ) > ( multihole_mctxt_a_b > list_b > $o ) > ( produc746580111399690912list_b > multihole_mctxt_a_b ) > ( produc5647625992154082286xt_a_b > list_b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    bNF_re2106300878112453789list_b: ( produc746580111399690912list_b > produc746580111399690912list_b > $o ) > ( list_b > list_b > $o ) > ( produc746580111399690912list_b > list_b ) > ( produc746580111399690912list_b > list_b ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    bNF_re3446365231100426717xt_a_b: ( produc746580111399690912list_b > produc746580111399690912list_b > $o ) > ( multihole_mctxt_a_b > multihole_mctxt_a_b > $o ) > ( produc746580111399690912list_b > multihole_mctxt_a_b ) > ( produc746580111399690912list_b > multihole_mctxt_a_b ) > $o ).

thf(sy_c_BNF__Def_OsndOp_001_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_001_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    bNF_sn6226833157980286806xt_a_b: ( ( nat > list_b ) > ( nat > produc5647625992154082286xt_a_b ) > $o ) > ( ( nat > produc5647625992154082286xt_a_b ) > ( nat > multihole_mctxt_a_b ) > $o ) > produc8094751872729218222xt_a_b > produc5956155440505932549xt_a_b ).

thf(sy_c_BNF__Def_OsndOp_001_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_001_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J,type,
    bNF_sn4426211646526114852list_b: ( ( nat > multihole_mctxt_a_b ) > ( nat > produc746580111399690912list_b ) > $o ) > ( ( nat > produc746580111399690912list_b ) > ( nat > list_b ) > $o ) > produc5125836498238150368list_b > produc6423750584600236748list_b ).

thf(sy_c_BNF__Def_OsndOp_001_Eo_001_Eo_001_Eo,type,
    bNF_sndOp_o_o_o: ( $o > $o > $o ) > ( $o > $o > $o ) > product_prod_o_o > product_prod_o_o ).

thf(sy_c_BNF__Def_OsndOp_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    bNF_sn7302738427532062417list_b: ( list_b > list_b > $o ) > ( list_b > list_b > $o ) > produc3963297410138542439list_b > produc3963297410138542439list_b ).

thf(sy_c_BNF__Def_OsndOp_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    bNF_sn4673656379119230680xt_a_b: ( list_b > list_b > $o ) > ( list_b > multihole_mctxt_a_b > $o ) > produc5647625992154082286xt_a_b > produc5647625992154082286xt_a_b ).

thf(sy_c_BNF__Def_OsndOp_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    bNF_sn4055164193756949002list_b: ( list_b > multihole_mctxt_a_b > $o ) > ( multihole_mctxt_a_b > list_b > $o ) > produc3963297410138542439list_b > produc746580111399690912list_b ).

thf(sy_c_BNF__Def_OsndOp_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    bNF_sn7894307914016310289xt_a_b: ( list_b > multihole_mctxt_a_b > $o ) > ( multihole_mctxt_a_b > multihole_mctxt_a_b > $o ) > produc5647625992154082286xt_a_b > produc1652119919080531751xt_a_b ).

thf(sy_c_BNF__Def_OsndOp_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    bNF_sn1677556937511116207xt_a_b: ( list_b > produc5647625992154082286xt_a_b > $o ) > ( produc5647625992154082286xt_a_b > multihole_mctxt_a_b > $o ) > produc5647625992154082286xt_a_b > produc7347357110894899781xt_a_b ).

thf(sy_c_BNF__Def_OsndOp_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    bNF_sn8686886566300520536list_b: ( multihole_mctxt_a_b > list_b > $o ) > ( list_b > list_b > $o ) > produc746580111399690912list_b > produc3963297410138542439list_b ).

thf(sy_c_BNF__Def_OsndOp_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    bNF_sn8855334143865345631xt_a_b: ( multihole_mctxt_a_b > list_b > $o ) > ( list_b > multihole_mctxt_a_b > $o ) > produc1652119919080531751xt_a_b > produc5647625992154082286xt_a_b ).

thf(sy_c_BNF__Def_OsndOp_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    bNF_sn8236841958503063953list_b: ( multihole_mctxt_a_b > multihole_mctxt_a_b > $o ) > ( multihole_mctxt_a_b > list_b > $o ) > produc746580111399690912list_b > produc746580111399690912list_b ).

thf(sy_c_BNF__Def_OsndOp_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    bNF_sn8437382630723965336xt_a_b: ( multihole_mctxt_a_b > multihole_mctxt_a_b > $o ) > ( multihole_mctxt_a_b > multihole_mctxt_a_b > $o ) > produc1652119919080531751xt_a_b > produc1652119919080531751xt_a_b ).

thf(sy_c_BNF__Def_OsndOp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_sn8916957246138178918at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > product_prod_nat_nat > product_prod_nat_nat ).

thf(sy_c_BNF__Def_Ovimage2p_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
    bNF_vi6667456707345531737_nat_o: ( nat > nat ) > ( nat > nat ) > ( nat > nat > $o ) > nat > nat > $o ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001_Eo_001_Eo_001_Eo,type,
    bNF_Gr6698568825248092222_o_o_o: set_o > ( $o > $o ) > ( $o > $o ) > set_Product_prod_o_o ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001_Eo_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    bNF_Gr9063183054812448510list_b: set_o > ( $o > list_b ) > ( $o > list_b ) > set_Pr7665282455119567943list_b ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001_Eo_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    bNF_Gr1724143576852326661xt_a_b: set_o > ( $o > list_b ) > ( $o > multihole_mctxt_a_b ) > set_Pr3872688570871424334xt_a_b ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001_Eo_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    bNF_Gr1105651391490044983list_b: set_o > ( $o > multihole_mctxt_a_b ) > ( $o > list_b ) > set_Pr1895186847599665920list_b ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__List__Olist_Itf__b_J_001_Eo_001_Eo,type,
    bNF_Gr104565956902713387_b_o_o: set_list_b > ( list_b > $o ) > ( list_b > $o ) > set_Product_prod_o_o ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Nat__Onat_001_Eo_001_Eo,type,
    bNF_Gr7385549216828995882at_o_o: set_nat > ( nat > $o ) > ( nat > $o ) > set_Product_prod_o_o ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Nat__Onat_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    bNF_Gr8841899351857821674list_b: set_nat > ( nat > list_b ) > ( nat > list_b ) > set_Pr7665282455119567943list_b ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Nat__Onat_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    bNF_Gr241138994731930097xt_a_b: set_nat > ( nat > list_b ) > ( nat > multihole_mctxt_a_b ) > set_Pr3872688570871424334xt_a_b ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Nat__Onat_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    bNF_Gr8846018846224424227list_b: set_nat > ( nat > multihole_mctxt_a_b ) > ( nat > list_b ) > set_Pr1895186847599665920list_b ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Set__Oset_I_Eo_J_001_Eo_001_Eo,type,
    bNF_Gr8091873193056382750_o_o_o: set_set_o > ( set_o > $o ) > ( set_o > $o ) > set_Product_prod_o_o ).

thf(sy_c_Basic__BNF__LFPs_Oprod_Osize__prod_001t__Nat__Onat_001t__Nat__Onat,type,
    basic_876126793109182934at_nat: ( nat > nat ) > ( nat > nat ) > product_prod_nat_nat > nat ).

thf(sy_c_Basic__BNFs_Ofstsp_001_Eo_001_Eo,type,
    basic_fstsp_o_o: product_prod_o_o > $o > $o ).

thf(sy_c_Basic__BNFs_Ofstsp_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    basic_5911698558650257769list_b: produc3963297410138542439list_b > list_b > $o ).

thf(sy_c_Basic__BNFs_Ofstsp_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    basic_1625185206584947056xt_a_b: produc5647625992154082286xt_a_b > list_b > $o ).

thf(sy_c_Basic__BNFs_Ofstsp_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    basic_1006693021222665378list_b: produc746580111399690912list_b > multihole_mctxt_a_b > $o ).

thf(sy_c_Basic__BNFs_Ofstsp_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    basic_3885822791963969193xt_a_b: produc1652119919080531751xt_a_b > multihole_mctxt_a_b > $o ).

thf(sy_c_Basic__BNFs_Ofstsp_001t__Nat__Onat_001t__Nat__Onat,type,
    basic_fstsp_nat_nat: product_prod_nat_nat > nat > $o ).

thf(sy_c_Basic__BNFs_Opred__fun_001t__Nat__Onat_001_Eo,type,
    basic_pred_fun_nat_o: ( nat > $o ) > ( $o > $o ) > ( nat > $o ) > $o ).

thf(sy_c_Basic__BNFs_Opred__fun_001t__Nat__Onat_001t__Nat__Onat,type,
    basic_843401206580270149at_nat: ( nat > $o ) > ( nat > $o ) > ( nat > nat ) > $o ).

thf(sy_c_Basic__BNFs_Opred__prod_001_Eo_001_Eo,type,
    basic_pred_prod_o_o: ( $o > $o ) > ( $o > $o ) > product_prod_o_o > $o ).

thf(sy_c_Basic__BNFs_Opred__prod_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    basic_1932318408880543091list_b: ( list_b > $o ) > ( list_b > $o ) > produc3963297410138542439list_b > $o ).

thf(sy_c_Basic__BNFs_Opred__prod_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    basic_5777512433536448890xt_a_b: ( list_b > $o ) > ( multihole_mctxt_a_b > $o ) > produc5647625992154082286xt_a_b > $o ).

thf(sy_c_Basic__BNFs_Opred__prod_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    basic_5159020248174167212list_b: ( multihole_mctxt_a_b > $o ) > ( list_b > $o ) > produc746580111399690912list_b > $o ).

thf(sy_c_Basic__BNFs_Opred__prod_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    basic_3223324150106804915xt_a_b: ( multihole_mctxt_a_b > $o ) > ( multihole_mctxt_a_b > $o ) > produc1652119919080531751xt_a_b > $o ).

thf(sy_c_Basic__BNFs_Opred__prod_001t__Nat__Onat_001t__Nat__Onat,type,
    basic_570253317919918037at_nat: ( nat > $o ) > ( nat > $o ) > product_prod_nat_nat > $o ).

thf(sy_c_Basic__BNFs_Orel__prod_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    basic_1215337403475127669xt_a_b: ( list_b > list_b > $o ) > ( multihole_mctxt_a_b > multihole_mctxt_a_b > $o ) > produc5647625992154082286xt_a_b > produc5647625992154082286xt_a_b > $o ).

thf(sy_c_Basic__BNFs_Orel__prod_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    basic_1557871447961881333list_b: ( list_b > multihole_mctxt_a_b > $o ) > ( multihole_mctxt_a_b > list_b > $o ) > produc5647625992154082286xt_a_b > produc746580111399690912list_b > $o ).

thf(sy_c_Basic__BNFs_Orel__prod_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    basic_6965198497647680501xt_a_b: ( multihole_mctxt_a_b > list_b > $o ) > ( list_b > multihole_mctxt_a_b > $o ) > produc746580111399690912list_b > produc5647625992154082286xt_a_b > $o ).

thf(sy_c_Basic__BNFs_Orel__prod_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    basic_1755056647974194549list_b: ( multihole_mctxt_a_b > multihole_mctxt_a_b > $o ) > ( list_b > list_b > $o ) > produc746580111399690912list_b > produc746580111399690912list_b > $o ).

thf(sy_c_Basic__BNFs_Osndsp_001_Eo_001_Eo,type,
    basic_sndsp_o_o: product_prod_o_o > $o > $o ).

thf(sy_c_Basic__BNFs_Osndsp_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    basic_832676007215906219list_b: produc3963297410138542439list_b > list_b > $o ).

thf(sy_c_Basic__BNFs_Osndsp_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    basic_4089264441466474930xt_a_b: produc5647625992154082286xt_a_b > multihole_mctxt_a_b > $o ).

thf(sy_c_Basic__BNFs_Osndsp_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    basic_3470772256104193252list_b: produc746580111399690912list_b > list_b > $o ).

thf(sy_c_Basic__BNFs_Osndsp_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    basic_4467741268980112107xt_a_b: produc1652119919080531751xt_a_b > multihole_mctxt_a_b > $o ).

thf(sy_c_Basic__BNFs_Osndsp_001t__Nat__Onat_001t__Nat__Onat,type,
    basic_sndsp_nat_nat: product_prod_nat_nat > nat > $o ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001_062_I_Eo_M_Eo_J,type,
    complete_Sup_Sup_o_o: set_o_o > $o > $o ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001_Eo,type,
    complete_Sup_Sup_o: set_o > $o ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Nat__Onat,type,
    complete_Sup_Sup_nat: set_nat > nat ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_I_Eo_J,type,
    comple90263536869209701_set_o: set_set_o > set_o ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_It__List__Olist_Itf__b_J_J,type,
    comple6999952072667322706list_b: set_set_list_b > set_list_b ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    comple2548993463255921113xt_a_b: set_se6625423409757081292xt_a_b > set_Mu3903433398966807788xt_a_b ).

thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_It__Nat__Onat_J,type,
    comple7399068483239264473et_nat: set_set_nat > set_nat ).

thf(sy_c_Complete__Partial__Order_Occpo_Oadmissible_001_Eo,type,
    comple8949206149834442853ible_o: ( set_o > $o ) > ( $o > $o > $o ) > ( $o > $o ) > $o ).

thf(sy_c_Complete__Partial__Order_Occpo__class_Ofixp_001_Eo,type,
    comple2713996627985145509fixp_o: ( $o > $o ) > $o ).

thf(sy_c_Complete__Partial__Order_Occpo__class_Oiterates_001_Eo,type,
    comple449408542198671847ates_o: ( $o > $o ) > set_o ).

thf(sy_c_Complete__Partial__Order_Ochain_001_Eo,type,
    comple520228465662580424hain_o: ( $o > $o > $o ) > set_o > $o ).

thf(sy_c_Conditionally__Complete__Lattices_Opreorder__class_Obdd__above_001_Eo,type,
    condit5488710616941104124bove_o: set_o > $o ).

thf(sy_c_Conditionally__Complete__Lattices_Opreorder__class_Obdd__above_001t__Nat__Onat,type,
    condit2214826472909112428ve_nat: set_nat > $o ).

thf(sy_c_Finite__Set_OFpow_001t__Nat__Onat,type,
    finite_Fpow_nat: set_nat > set_set_nat ).

thf(sy_c_Finite__Set_Ocomp__fun__commute__on_001_Eo_001t__Nat__Onat,type,
    finite4703585013658510744_o_nat: set_o > ( $o > nat > nat ) > $o ).

thf(sy_c_Finite__Set_Ocomp__fun__idem__on_001_Eo_001t__Nat__Onat,type,
    finite2426395113773319005_o_nat: set_o > ( $o > nat > nat ) > $o ).

thf(sy_c_Fun_Ocomp_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    comp_n2788925183216866620at_nat: ( ( nat > nat ) > nat > nat ) > ( produc1932156733058919263at_nat > nat > nat ) > produc1932156733058919263at_nat > nat > nat ).

thf(sy_c_Fun_Ocomp_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_001_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_M_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_J,type,
    comp_n1237416365847547844list_b: ( ( nat > produc5647625992154082286xt_a_b ) > nat > list_b ) > ( produc4127645531870415870list_b > nat > produc5647625992154082286xt_a_b ) > produc4127645531870415870list_b > nat > list_b ).

thf(sy_c_Fun_Ocomp_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_001_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_M_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_J,type,
    comp_n3886679972654106180list_b: ( ( nat > produc746580111399690912list_b ) > nat > list_b ) > ( produc6423750584600236748list_b > nat > produc746580111399690912list_b ) > produc6423750584600236748list_b > nat > list_b ).

thf(sy_c_Fun_Ocomp_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_001_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_M_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J,type,
    comp_n2651844997665186820xt_a_b: ( ( nat > produc746580111399690912list_b ) > nat > multihole_mctxt_a_b ) > ( produc5683466111014092243xt_a_b > nat > produc746580111399690912list_b ) > produc5683466111014092243xt_a_b > nat > multihole_mctxt_a_b ).

thf(sy_c_Fun_Ocomp_001_Eo_001_Eo_001_Eo,type,
    comp_o_o_o: ( $o > $o ) > ( $o > $o ) > $o > $o ).

thf(sy_c_Fun_Ocomp_001_Eo_001_Eo_001t__Nat__Onat,type,
    comp_o_o_nat: ( $o > $o ) > ( nat > $o ) > nat > $o ).

thf(sy_c_Fun_Ocomp_001_Eo_001_Eo_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
    comp_o2958928929274947076od_o_o: ( $o > $o ) > ( product_prod_o_o > $o ) > product_prod_o_o > $o ).

thf(sy_c_Fun_Ocomp_001_Eo_001t__Nat__Onat_001t__Nat__Onat,type,
    comp_o_nat_nat: ( $o > nat ) > ( nat > $o ) > nat > nat ).

thf(sy_c_Fun_Ocomp_001_Eo_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
    comp_o3333229022555693340at_nat: ( $o > product_prod_nat_nat ) > ( nat > $o ) > nat > product_prod_nat_nat ).

thf(sy_c_Fun_Ocomp_001_Eo_001t__Set__Oset_I_Eo_J_001_062_I_Eo_M_Eo_J,type,
    comp_o_set_o_o_o: ( $o > set_o ) > ( ( $o > $o ) > $o ) > ( $o > $o ) > set_o ).

thf(sy_c_Fun_Ocomp_001_Eo_001t__Set__Oset_I_Eo_J_001t__Nat__Onat,type,
    comp_o_set_o_nat: ( $o > set_o ) > ( nat > $o ) > nat > set_o ).

thf(sy_c_Fun_Ocomp_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    comp_l174544490166145698list_b: ( list_b > list_b ) > ( list_b > list_b ) > list_b > list_b ).

thf(sy_c_Fun_Ocomp_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    comp_l4803390035063111044list_b: ( list_b > list_b ) > ( produc3963297410138542439list_b > list_b ) > produc3963297410138542439list_b > list_b ).

thf(sy_c_Fun_Ocomp_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    comp_l2129113565787646475xt_a_b: ( list_b > list_b ) > ( produc5647625992154082286xt_a_b > list_b ) > produc5647625992154082286xt_a_b > list_b ).

thf(sy_c_Fun_Ocomp_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    comp_l6451439721888030909list_b: ( list_b > list_b ) > ( produc746580111399690912list_b > list_b ) > produc746580111399690912list_b > list_b ).

thf(sy_c_Fun_Ocomp_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    comp_l244608897766244669list_b: ( list_b > multihole_mctxt_a_b ) > ( produc3963297410138542439list_b > list_b ) > produc3963297410138542439list_b > multihole_mctxt_a_b ).

thf(sy_c_Fun_Ocomp_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    comp_l6057078126495733700xt_a_b: ( list_b > multihole_mctxt_a_b ) > ( produc5647625992154082286xt_a_b > list_b ) > produc5647625992154082286xt_a_b > multihole_mctxt_a_b ).

thf(sy_c_Fun_Ocomp_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    comp_l1156032245741342326list_b: ( list_b > multihole_mctxt_a_b ) > ( produc746580111399690912list_b > list_b ) > produc746580111399690912list_b > multihole_mctxt_a_b ).

thf(sy_c_Fun_Ocomp_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__List__Olist_Itf__b_J_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    comp_l8139176909817314217xt_a_b: ( list_b > produc3963297410138542439list_b ) > ( produc5647625992154082286xt_a_b > list_b ) > produc5647625992154082286xt_a_b > produc3963297410138542439list_b ).

thf(sy_c_Fun_Ocomp_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__List__Olist_Itf__b_J_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    comp_l3238131029062922843list_b: ( list_b > produc3963297410138542439list_b ) > ( produc746580111399690912list_b > list_b ) > produc746580111399690912list_b > produc3963297410138542439list_b ).

thf(sy_c_Fun_Ocomp_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    comp_M1546340790364679442xt_a_b: ( multihole_mctxt_a_b > list_b ) > ( produc5647625992154082286xt_a_b > multihole_mctxt_a_b ) > produc5647625992154082286xt_a_b > list_b ).

thf(sy_c_Fun_Ocomp_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    comp_M5868666946465063876list_b: ( multihole_mctxt_a_b > list_b ) > ( produc746580111399690912list_b > multihole_mctxt_a_b ) > produc746580111399690912list_b > list_b ).

thf(sy_c_Fun_Ocomp_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    comp_M1627911043960361035xt_a_b: ( multihole_mctxt_a_b > list_b ) > ( produc1652119919080531751xt_a_b > multihole_mctxt_a_b ) > produc1652119919080531751xt_a_b > list_b ).

thf(sy_c_Fun_Ocomp_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    comp_M3425699811810050921xt_a_b: ( multihole_mctxt_a_b > multihole_mctxt_a_b ) > ( multihole_mctxt_a_b > multihole_mctxt_a_b ) > multihole_mctxt_a_b > multihole_mctxt_a_b ).

thf(sy_c_Fun_Ocomp_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    comp_M7841358257205866699xt_a_b: ( multihole_mctxt_a_b > multihole_mctxt_a_b ) > ( produc5647625992154082286xt_a_b > multihole_mctxt_a_b ) > produc5647625992154082286xt_a_b > multihole_mctxt_a_b ).

thf(sy_c_Fun_Ocomp_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    comp_M2940312376451475325list_b: ( multihole_mctxt_a_b > multihole_mctxt_a_b ) > ( produc746580111399690912list_b > multihole_mctxt_a_b ) > produc746580111399690912list_b > multihole_mctxt_a_b ).

thf(sy_c_Fun_Ocomp_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    comp_M8832391070236868100xt_a_b: ( multihole_mctxt_a_b > multihole_mctxt_a_b ) > ( produc1652119919080531751xt_a_b > multihole_mctxt_a_b ) > produc1652119919080531751xt_a_b > multihole_mctxt_a_b ).

thf(sy_c_Fun_Ocomp_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    comp_M6505873051800441456xt_a_b: ( multihole_mctxt_a_b > produc1652119919080531751xt_a_b ) > ( produc5647625992154082286xt_a_b > multihole_mctxt_a_b ) > produc5647625992154082286xt_a_b > produc1652119919080531751xt_a_b ).

thf(sy_c_Fun_Ocomp_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    comp_M1604827171046050082list_b: ( multihole_mctxt_a_b > produc1652119919080531751xt_a_b ) > ( produc746580111399690912list_b > multihole_mctxt_a_b ) > produc746580111399690912list_b > produc1652119919080531751xt_a_b ).

thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001_Eo_001_Eo,type,
    comp_nat_o_o: ( nat > $o ) > ( $o > nat ) > $o > $o ).

thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001_Eo_001t__Nat__Onat,type,
    comp_nat_o_nat: ( nat > $o ) > ( nat > nat ) > nat > $o ).

thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
    comp_nat_nat_nat: ( nat > nat ) > ( nat > nat ) > nat > nat ).

thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    comp_n2711240574518091068at_nat: ( nat > nat ) > ( product_prod_nat_nat > nat ) > product_prod_nat_nat > nat ).

thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
    comp_n8574565218330151774at_nat: ( nat > product_prod_nat_nat ) > ( nat > nat ) > nat > product_prod_nat_nat ).

thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Set__Oset_I_Eo_J_001_062_I_Eo_M_Eo_J,type,
    comp_nat_set_o_o_o: ( nat > set_o ) > ( ( $o > $o ) > nat ) > ( $o > $o ) > set_o ).

thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Set__Oset_I_Eo_J_001t__Nat__Onat,type,
    comp_nat_set_o_nat: ( nat > set_o ) > ( nat > nat ) > nat > set_o ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001_Eo_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
    comp_P5935651135916255507od_o_o: ( product_prod_o_o > $o ) > ( product_prod_o_o > product_prod_o_o ) > product_prod_o_o > $o ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__List__Olist_Itf__b_J_J_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    comp_P928982252139745894list_b: ( produc3963297410138542439list_b > list_b ) > ( produc3963297410138542439list_b > produc3963297410138542439list_b ) > produc3963297410138542439list_b > list_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__List__Olist_Itf__b_J_J_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    comp_P5990363157231710957xt_a_b: ( produc3963297410138542439list_b > list_b ) > ( produc5647625992154082286xt_a_b > produc3963297410138542439list_b ) > produc5647625992154082286xt_a_b > list_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__List__Olist_Itf__b_J_J_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    comp_P1089317276477319583list_b: ( produc3963297410138542439list_b > list_b ) > ( produc746580111399690912list_b > produc3963297410138542439list_b ) > produc746580111399690912list_b > list_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001_Eo_001t__Nat__Onat,type,
    comp_P6416659774363354717_o_nat: ( produc5647625992154082286xt_a_b > $o ) > ( nat > produc5647625992154082286xt_a_b ) > nat > $o ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__List__Olist_Itf__b_J_001t__Nat__Onat,type,
    comp_P2387776964271251914_b_nat: ( produc5647625992154082286xt_a_b > list_b ) > ( nat > produc5647625992154082286xt_a_b ) > nat > list_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    comp_P526186434445353453list_b: ( produc5647625992154082286xt_a_b > list_b ) > ( produc3963297410138542439list_b > produc5647625992154082286xt_a_b ) > produc3963297410138542439list_b > list_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    comp_P8325075377515255924xt_a_b: ( produc5647625992154082286xt_a_b > list_b ) > ( produc5647625992154082286xt_a_b > produc5647625992154082286xt_a_b ) > produc5647625992154082286xt_a_b > list_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    comp_P3424029496760864550list_b: ( produc5647625992154082286xt_a_b > list_b ) > ( produc746580111399690912list_b > produc5647625992154082286xt_a_b ) > produc746580111399690912list_b > list_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    comp_P1032284375231442861xt_a_b: ( produc5647625992154082286xt_a_b > list_b ) > ( produc1652119919080531751xt_a_b > produc5647625992154082286xt_a_b ) > produc1652119919080531751xt_a_b > list_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Nat__Onat,type,
    comp_P2996417359073641937_b_nat: ( produc5647625992154082286xt_a_b > multihole_mctxt_a_b ) > ( nat > produc5647625992154082286xt_a_b ) > nat > multihole_mctxt_a_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    comp_P6440570709493854118list_b: ( produc5647625992154082286xt_a_b > multihole_mctxt_a_b ) > ( produc3963297410138542439list_b > produc5647625992154082286xt_a_b ) > produc3963297410138542439list_b > multihole_mctxt_a_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    comp_P7245731588476948525xt_a_b: ( produc5647625992154082286xt_a_b > multihole_mctxt_a_b ) > ( produc5647625992154082286xt_a_b > produc5647625992154082286xt_a_b ) > produc5647625992154082286xt_a_b > multihole_mctxt_a_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    comp_P2344685707722557151list_b: ( produc5647625992154082286xt_a_b > multihole_mctxt_a_b ) > ( produc746580111399690912list_b > produc5647625992154082286xt_a_b ) > produc746580111399690912list_b > multihole_mctxt_a_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    comp_P6941710577075294566xt_a_b: ( produc5647625992154082286xt_a_b > multihole_mctxt_a_b ) > ( produc1652119919080531751xt_a_b > produc5647625992154082286xt_a_b ) > produc1652119919080531751xt_a_b > multihole_mctxt_a_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Nat__Onat_001t__Nat__Onat,type,
    comp_P5398456803681584877at_nat: ( produc5647625992154082286xt_a_b > nat ) > ( nat > produc5647625992154082286xt_a_b ) > nat > nat ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    comp_P8660005625159894603list_b: ( produc5647625992154082286xt_a_b > produc746580111399690912list_b ) > ( produc746580111399690912list_b > produc5647625992154082286xt_a_b ) > produc746580111399690912list_b > produc746580111399690912list_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001_Eo_001t__Nat__Onat,type,
    comp_P4804859795044233003_o_nat: ( produc746580111399690912list_b > $o ) > ( nat > produc746580111399690912list_b ) > nat > $o ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__List__Olist_Itf__b_J_001t__Nat__Onat,type,
    comp_P2296052985374803096_b_nat: ( produc746580111399690912list_b > list_b ) > ( nat > produc746580111399690912list_b ) > nat > list_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    comp_P2427654987725689503list_b: ( produc746580111399690912list_b > list_b ) > ( produc3963297410138542439list_b > produc746580111399690912list_b ) > produc3963297410138542439list_b > list_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    comp_P8501011119256231206xt_a_b: ( produc746580111399690912list_b > list_b ) > ( produc5647625992154082286xt_a_b > produc746580111399690912list_b ) > produc5647625992154082286xt_a_b > list_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    comp_P3599965238501839832list_b: ( produc746580111399690912list_b > list_b ) > ( produc746580111399690912list_b > produc746580111399690912list_b ) > produc746580111399690912list_b > list_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    comp_P7753359808300943455xt_a_b: ( produc746580111399690912list_b > list_b ) > ( produc1652119919080531751xt_a_b > produc746580111399690912list_b ) > produc1652119919080531751xt_a_b > list_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Nat__Onat,type,
    comp_P5220818572353508511_b_nat: ( produc746580111399690912list_b > multihole_mctxt_a_b ) > ( nat > produc746580111399690912list_b ) > nat > multihole_mctxt_a_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    comp_P6616506451234829400list_b: ( produc746580111399690912list_b > multihole_mctxt_a_b ) > ( produc3963297410138542439list_b > produc746580111399690912list_b ) > produc3963297410138542439list_b > multihole_mctxt_a_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    comp_P4743434984691673311xt_a_b: ( produc746580111399690912list_b > multihole_mctxt_a_b ) > ( produc5647625992154082286xt_a_b > produc746580111399690912list_b ) > produc5647625992154082286xt_a_b > multihole_mctxt_a_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    comp_P9065761140792057745list_b: ( produc746580111399690912list_b > multihole_mctxt_a_b ) > ( produc746580111399690912list_b > produc746580111399690912list_b ) > produc746580111399690912list_b > multihole_mctxt_a_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    comp_P7940805974138666520xt_a_b: ( produc746580111399690912list_b > multihole_mctxt_a_b ) > ( produc1652119919080531751xt_a_b > produc746580111399690912list_b ) > produc1652119919080531751xt_a_b > multihole_mctxt_a_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__Nat__Onat_001t__Nat__Onat,type,
    comp_P115382347248037279at_nat: ( produc746580111399690912list_b > nat ) > ( nat > produc746580111399690912list_b ) > nat > nat ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    comp_P8043882148310014845xt_a_b: ( produc746580111399690912list_b > produc5647625992154082286xt_a_b ) > ( produc5647625992154082286xt_a_b > produc746580111399690912list_b ) > produc5647625992154082286xt_a_b > produc5647625992154082286xt_a_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    comp_P1113565280179474022xt_a_b: ( produc1652119919080531751xt_a_b > multihole_mctxt_a_b ) > ( produc5647625992154082286xt_a_b > produc1652119919080531751xt_a_b ) > produc5647625992154082286xt_a_b > multihole_mctxt_a_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    comp_P5435891436279858456list_b: ( produc1652119919080531751xt_a_b > multihole_mctxt_a_b ) > ( produc746580111399690912list_b > produc1652119919080531751xt_a_b ) > produc746580111399690912list_b > multihole_mctxt_a_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    comp_P1228403674089159071xt_a_b: ( produc1652119919080531751xt_a_b > multihole_mctxt_a_b ) > ( produc1652119919080531751xt_a_b > produc1652119919080531751xt_a_b ) > produc1652119919080531751xt_a_b > multihole_mctxt_a_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001t__Nat__Onat,type,
    comp_P1291532814139040010_o_nat: ( product_prod_nat_nat > $o ) > ( nat > product_prod_nat_nat ) > nat > $o ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
    comp_P1955610211387027840at_nat: ( product_prod_nat_nat > nat ) > ( nat > product_prod_nat_nat ) > nat > nat ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    comp_P1567445206330693457at_nat: ( product_prod_nat_nat > nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > nat ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
    comp_P7430769850142754163at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > ( nat > product_prod_nat_nat ) > nat > product_prod_nat_nat ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    comp_P2240441846945064862at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).

thf(sy_c_Fun_Ocomp_001t__Set__Oset_I_Eo_J_001_Eo_001_062_I_Eo_M_Eo_J,type,
    comp_set_o_o_o_o: ( set_o > $o ) > ( ( $o > $o ) > set_o ) > ( $o > $o ) > $o ).

thf(sy_c_Fun_Ocomp_001t__Set__Oset_I_Eo_J_001_Eo_001t__Nat__Onat,type,
    comp_set_o_o_nat: ( set_o > $o ) > ( nat > set_o ) > nat > $o ).

thf(sy_c_Fun_Ocomp_001t__Set__Oset_I_Eo_J_001t__Nat__Onat_001_062_I_Eo_M_Eo_J,type,
    comp_set_o_nat_o_o: ( set_o > nat ) > ( ( $o > $o ) > set_o ) > ( $o > $o ) > nat ).

thf(sy_c_Fun_Ocomp_001t__Set__Oset_I_Eo_J_001t__Nat__Onat_001t__Nat__Onat,type,
    comp_set_o_nat_nat: ( set_o > nat ) > ( nat > set_o ) > nat > nat ).

thf(sy_c_Fun_Ocomp_001t__Set__Oset_I_Eo_J_001t__Set__Oset_I_Eo_J_001_062_I_Eo_M_Eo_J,type,
    comp_set_o_set_o_o_o: ( set_o > set_o ) > ( ( $o > $o ) > set_o ) > ( $o > $o ) > set_o ).

thf(sy_c_Fun_Oid_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
    id_nat_nat: ( nat > nat ) > nat > nat ).

thf(sy_c_Fun_Oid_001_Eo,type,
    id_o: $o > $o ).

thf(sy_c_Fun_Oid_001t__Nat__Onat,type,
    id_nat: nat > nat ).

thf(sy_c_Fun_Oid_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    id_Pro7664240512220884831xt_a_b: produc5647625992154082286xt_a_b > produc5647625992154082286xt_a_b ).

thf(sy_c_Fun_Oid_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    id_Pro2763194631466493457list_b: produc746580111399690912list_b > produc746580111399690912list_b ).

thf(sy_c_Fun_Oinj__on_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
    inj_on2461717442902640625at_nat: ( ( nat > nat ) > nat > nat ) > set_nat_nat > $o ).

thf(sy_c_Fun_Oinj__on_001_Eo_001_Eo,type,
    inj_on_o_o: ( $o > $o ) > set_o > $o ).

thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001_Eo,type,
    inj_on_nat_o: ( nat > $o ) > set_nat > $o ).

thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat,type,
    inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).

thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    inj_on3558359446568221091list_b: ( produc5647625992154082286xt_a_b > produc746580111399690912list_b ) > set_Pr3872688570871424334xt_a_b > $o ).

thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    inj_on5222288482278673599xt_a_b: ( produc746580111399690912list_b > produc5647625992154082286xt_a_b ) > set_Pr1895186847599665920list_b > $o ).

thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    inj_on8969904277767023793at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat > $o ).

thf(sy_c_Fun_Oinj__on_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
    inj_on4604407203859583615et_nat: ( set_nat > set_nat ) > set_set_nat > $o ).

thf(sy_c_Fun_Omonotone__on_001_Eo_001_Eo,type,
    monotone_on_o_o: set_o > ( $o > $o > $o ) > ( $o > $o > $o ) > ( $o > $o ) > $o ).

thf(sy_c_Fun_Omonotone__on_001_Eo_001t__Nat__Onat,type,
    monotone_on_o_nat: set_o > ( $o > $o > $o ) > ( nat > nat > $o ) > ( $o > nat ) > $o ).

thf(sy_c_Fun_Omonotone__on_001t__Nat__Onat_001_Eo,type,
    monotone_on_nat_o: set_nat > ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > $o ).

thf(sy_c_Fun_Omonotone__on_001t__Nat__Onat_001t__Nat__Onat,type,
    monotone_on_nat_nat: set_nat > ( nat > nat > $o ) > ( nat > nat > $o ) > ( nat > nat ) > $o ).

thf(sy_c_Fun_Omonotone__on_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
    monoto6489329683466618047et_nat: set_nat > ( nat > nat > $o ) > ( set_nat > set_nat > $o ) > ( nat > set_nat ) > $o ).

thf(sy_c_Fun_Omonotone__on_001t__Set__Oset_I_Eo_J_001t__Set__Oset_I_Eo_J,type,
    monoto3902964759935319015_set_o: set_set_o > ( set_o > set_o > $o ) > ( set_o > set_o > $o ) > ( set_o > set_o ) > $o ).

thf(sy_c_Fun_Omonotone__on_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
    monoto1748750089227133045et_nat: set_set_nat > ( set_nat > set_nat > $o ) > ( set_nat > set_nat > $o ) > ( set_nat > set_nat ) > $o ).

thf(sy_c_Inductive_Ocomplete__lattice__class_Ogfp_001_Eo,type,
    comple1228283932920895894_gfp_o: ( $o > $o ) > $o ).

thf(sy_c_Inductive_Ocomplete__lattice__class_Ogfp_001t__Set__Oset_I_Eo_J,type,
    comple5578320350976157814_set_o: ( set_o > set_o ) > set_o ).

thf(sy_c_Inductive_Ocomplete__lattice__class_Ogfp_001t__Set__Oset_It__Nat__Onat_J,type,
    comple1596078789208929544et_nat: ( set_nat > set_nat ) > set_nat ).

thf(sy_c_Inductive_Ocomplete__lattice__class_Olfp_001_Eo,type,
    comple5737750096767067345_lfp_o: ( $o > $o ) > $o ).

thf(sy_c_Inductive_Ocomplete__lattice__class_Olfp_001t__Set__Oset_I_Eo_J,type,
    comple3077273498168821681_set_o: ( set_o > set_o ) > set_o ).

thf(sy_c_Lattices_Osup__class_Osup_001_062_I_Eo_M_Eo_J,type,
    sup_sup_o_o: ( $o > $o ) > ( $o > $o ) > $o > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001_Eo,type,
    sup_sup_o: $o > $o > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
    sup_sup_nat: nat > nat > nat ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_I_Eo_J,type,
    sup_sup_set_o: set_o > set_o > set_o ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
    sup_sup_set_nat: set_nat > set_nat > set_nat ).

thf(sy_c_Lifting_OQuotient_001t__Nat__Onat_001t__Nat__Onat,type,
    quotient_nat_nat: ( nat > nat > $o ) > ( nat > nat ) > ( nat > nat ) > ( nat > nat > $o ) > $o ).

thf(sy_c_List_OBleast_001_Eo,type,
    bleast_o: set_o > ( $o > $o ) > $o ).

thf(sy_c_List_Oabort__Bleast_001_Eo,type,
    abort_Bleast_o: set_o > ( $o > $o ) > $o ).

thf(sy_c_Multihole__Context_Onum__holes_001tf__a_001tf__b,type,
    multih3217256941434035760es_a_b: multihole_mctxt_a_b > nat ).

thf(sy_c_Multihole__Context_Osplit__vars_001tf__a_001tf__b,type,
    multih5110136180555822405rs_a_b: term_a_b > produc746580111399690912list_b ).

thf(sy_c_Nat_OSuc,type,
    suc: nat > nat ).

thf(sy_c_Nat_Ocompow_001_062_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    compow4371056112333882794at_nat: nat > ( ( nat > nat ) > nat > nat ) > ( nat > nat ) > nat > nat ).

thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
    compow_nat_nat: nat > ( nat > nat ) > nat > nat ).

thf(sy_c_Nat_Ocompow_001_062_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    compow8708494347934031032et_nat: nat > ( set_nat > set_nat ) > set_nat > set_nat ).

thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_Itf__b_J,type,
    size_size_list_b: list_b > nat ).

thf(sy_c_Orderings_Obot__class_Obot_001_Eo,type,
    bot_bot_o: $o ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Nat__Onat,type,
    bot_bot_nat: nat ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_I_Eo_J,type,
    bot_bot_set_o: set_o ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__List__Olist_Itf__b_J_J,type,
    bot_bot_set_list_b: set_list_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    bot_bo3530618752887112024xt_a_b: set_Mu3903433398966807788xt_a_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
    bot_bot_set_nat: set_nat ).

thf(sy_c_Orderings_Oord__class_OLeast_001_Eo,type,
    ord_Least_o: ( $o > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_OLeast_001t__Nat__Onat,type,
    ord_Least_nat: ( nat > $o ) > nat ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_M_Eo_J,type,
    ord_less_eq_o_o: ( $o > $o ) > ( $o > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Nat__Onat_J,type,
    ord_less_eq_o_nat: ( $o > nat ) > ( $o > nat ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J,type,
    ord_le2646555220125990790_nat_o: ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_Eo,type,
    ord_less_eq_o: $o > $o > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
    ord_less_eq_nat: nat > nat > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_062_I_Eo_M_Eo_J_J,type,
    ord_less_eq_set_o_o: set_o_o > set_o_o > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    ord_le9059583361652607317at_nat: set_nat_nat > set_nat_nat > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_J,type,
    ord_le5399802526449369557xt_a_b: set_na664922679713831477xt_a_b > set_na664922679713831477xt_a_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_J,type,
    ord_le1520420559268595335list_b: set_na6008912749387833063list_b > set_na6008912749387833063list_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_Eo_J,type,
    ord_less_eq_set_o: set_o > set_o > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__List__Olist_Itf__b_J_J,type,
    ord_le8932221534207217157list_b: set_list_b > set_list_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
    ord_less_eq_set_nat: set_nat > set_nat > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    ord_le192195778054999463od_o_o: set_Product_prod_o_o > set_Product_prod_o_o > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__List__Olist_Itf__b_J_J_J,type,
    ord_le2250082383302046695list_b: set_Pr7665282455119567943list_b > set_Pr7665282455119567943list_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J,type,
    ord_le3146644855780900078xt_a_b: set_Pr3872688570871424334xt_a_b > set_Pr3872688570871424334xt_a_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J,type,
    ord_le1169143132509141664list_b: set_Pr1895186847599665920list_b > set_Pr1895186847599665920list_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J,type,
    ord_le8781602985985617319xt_a_b: set_Pr2918931875556005383xt_a_b > set_Pr2918931875556005383xt_a_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    ord_le3146513528884898305at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_I_Eo_J_J,type,
    ord_le4374716579403074808_set_o: set_set_o > set_set_o > $o ).

thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Nat__Onat,type,
    order_Greatest_nat: ( nat > $o ) > nat ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Nat__Onat_M_Eo_J,type,
    top_top_nat_o: nat > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_Eo,type,
    top_top_o: $o ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    top_top_set_nat_nat: set_nat_nat ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_Eo_J,type,
    top_top_set_o: set_o ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__List__Olist_Itf__b_J_J,type,
    top_top_set_list_b: set_list_b ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    top_to3428735846572888636xt_a_b: set_Mu3903433398966807788xt_a_b ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
    top_top_set_nat: set_nat ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J,type,
    top_to8354912097173050014xt_a_b: set_Pr3872688570871424334xt_a_b ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J,type,
    top_to6377410373901291600list_b: set_Pr1895186847599665920list_b ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    top_to4669805908274784177at_nat: set_Pr1261947904930325089at_nat ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_I_Eo_J_J,type,
    top_top_set_set_o: set_set_o ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
    top_top_set_set_nat: set_set_nat ).

thf(sy_c_Product__Type_OPair_001_Eo_001_Eo,type,
    product_Pair_o_o: $o > $o > product_prod_o_o ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    produc1564554178308465111list_b: list_b > list_b > produc3963297410138542439list_b ).

thf(sy_c_Product__Type_OPair_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc8821373537598205406xt_a_b: list_b > multihole_mctxt_a_b > produc5647625992154082286xt_a_b ).

thf(sy_c_Product__Type_OPair_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    produc8202881352235923728list_b: multihole_mctxt_a_b > list_b > produc746580111399690912list_b ).

thf(sy_c_Product__Type_OPair_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc67882520014434071xt_a_b: multihole_mctxt_a_b > multihole_mctxt_a_b > produc1652119919080531751xt_a_b ).

thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
    product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).

thf(sy_c_Product__Type_OSigma_001_Eo_001_Eo,type,
    product_Sigma_o_o: set_o > ( $o > set_o ) > set_Product_prod_o_o ).

thf(sy_c_Product__Type_OSigma_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc2081261787124289679xt_a_b: set_list_b > ( list_b > set_Mu3903433398966807788xt_a_b ) > set_Pr3872688570871424334xt_a_b ).

thf(sy_c_Product__Type_OSigma_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    produc1462769601762008001list_b: set_Mu3903433398966807788xt_a_b > ( multihole_mctxt_a_b > set_list_b ) > set_Pr1895186847599665920list_b ).

thf(sy_c_Product__Type_OSigma_001t__Nat__Onat_001t__Nat__Onat,type,
    produc457027306803732586at_nat: set_nat > ( nat > set_nat ) > set_Pr1261947904930325089at_nat ).

thf(sy_c_Product__Type_Oapfst_001_Eo_001_Eo_001_Eo,type,
    product_apfst_o_o_o: ( $o > $o ) > product_prod_o_o > product_prod_o_o ).

thf(sy_c_Product__Type_Oapfst_001_Eo_001t__List__Olist_Itf__b_J_001_Eo,type,
    produc4251543932716285871st_b_o: ( $o > list_b ) > product_prod_o_o > produc2420475512092800890st_b_o ).

thf(sy_c_Product__Type_Oapfst_001_Eo_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    produc5858490838226100252list_b: ( $o > list_b ) > produc5666708989857747476list_b > produc3963297410138542439list_b ).

thf(sy_c_Product__Type_Oapfst_001_Eo_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc7722734716265565731xt_a_b: ( $o > list_b ) > produc4044283025580285595xt_a_b > produc5647625992154082286xt_a_b ).

thf(sy_c_Product__Type_Oapfst_001_Eo_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001_Eo,type,
    produc7765306332744332776_a_b_o: ( $o > multihole_mctxt_a_b ) > product_prod_o_o > produc6481442714050758067_a_b_o ).

thf(sy_c_Product__Type_Oapfst_001_Eo_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    produc7104242530903284053list_b: ( $o > multihole_mctxt_a_b ) > produc5666708989857747476list_b > produc746580111399690912list_b ).

thf(sy_c_Product__Type_Oapfst_001t__List__Olist_Itf__b_J_001_Eo_001_Eo,type,
    produc896052780560656201_b_o_o: ( list_b > $o ) > produc2420475512092800890st_b_o > product_prod_o_o ).

thf(sy_c_Product__Type_Oapfst_001t__List__Olist_Itf__b_J_001_Eo_001t__List__Olist_Itf__b_J,type,
    produc2306196218926843318list_b: ( list_b > $o ) > produc3963297410138542439list_b > produc5666708989857747476list_b ).

thf(sy_c_Product__Type_Oapfst_001t__List__Olist_Itf__b_J_001_Eo_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc321465489333671869xt_a_b: ( list_b > $o ) > produc5647625992154082286xt_a_b > produc4044283025580285595xt_a_b ).

thf(sy_c_Product__Type_Oapfst_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    produc3068595108723027977list_b: ( list_b > list_b ) > produc3963297410138542439list_b > produc3963297410138542439list_b ).

thf(sy_c_Product__Type_Oapfst_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc8543842510834618384xt_a_b: ( list_b > list_b ) > produc5647625992154082286xt_a_b > produc5647625992154082286xt_a_b ).

thf(sy_c_Product__Type_Oapfst_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    produc7925350325472336706list_b: ( list_b > multihole_mctxt_a_b ) > produc3963297410138542439list_b > produc746580111399690912list_b ).

thf(sy_c_Product__Type_Oapfst_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc7877392743006725449xt_a_b: ( list_b > multihole_mctxt_a_b ) > produc5647625992154082286xt_a_b > produc1652119919080531751xt_a_b ).

thf(sy_c_Product__Type_Oapfst_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001_Eo_001_Eo,type,
    produc5202512041193914064_b_o_o: ( multihole_mctxt_a_b > $o ) > produc6481442714050758067_a_b_o > product_prod_o_o ).

thf(sy_c_Product__Type_Oapfst_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001_Eo_001t__List__Olist_Itf__b_J,type,
    produc7032382957099276861list_b: ( multihole_mctxt_a_b > $o ) > produc746580111399690912list_b > produc5666708989857747476list_b ).

thf(sy_c_Product__Type_Oapfst_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    produc3333700661161132432list_b: ( multihole_mctxt_a_b > list_b ) > produc746580111399690912list_b > produc3963297410138542439list_b ).

thf(sy_c_Product__Type_Oapfst_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc8838418972855760791xt_a_b: ( multihole_mctxt_a_b > list_b ) > produc1652119919080531751xt_a_b > produc5647625992154082286xt_a_b ).

thf(sy_c_Product__Type_Oapfst_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    produc8219926787493479113list_b: ( multihole_mctxt_a_b > multihole_mctxt_a_b ) > produc746580111399690912list_b > produc746580111399690912list_b ).

thf(sy_c_Product__Type_Oapfst_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc4042296519137796816xt_a_b: ( multihole_mctxt_a_b > multihole_mctxt_a_b ) > produc1652119919080531751xt_a_b > produc1652119919080531751xt_a_b ).

thf(sy_c_Product__Type_Oapfst_001t__Nat__Onat_001_Eo_001_Eo,type,
    produc3652104818163562380at_o_o: ( nat > $o ) > product_prod_nat_o > product_prod_o_o ).

thf(sy_c_Product__Type_Oapfst_001t__Nat__Onat_001_Eo_001t__Nat__Onat,type,
    produc8275519816112921820_o_nat: ( nat > $o ) > product_prod_nat_nat > product_prod_o_nat ).

thf(sy_c_Product__Type_Oapfst_001t__Nat__Onat_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    produc4279361589058445900list_b: ( nat > list_b ) > produc7811952446676219690list_b > produc3963297410138542439list_b ).

thf(sy_c_Product__Type_Oapfst_001t__Nat__Onat_001t__List__Olist_Itf__b_J_001t__Nat__Onat,type,
    produc1375249994641956169_b_nat: ( nat > list_b ) > product_prod_nat_nat > produc6020613750378442500_b_nat ).

thf(sy_c_Product__Type_Oapfst_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
    produc986720760941809198at_nat: ( nat > nat ) > product_prod_nat_nat > product_prod_nat_nat ).

thf(sy_c_Product__Type_Oapfst_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
    produc3001624868188084037at_nat: ( nat > product_prod_nat_nat ) > product_prod_nat_nat > produc8373899037510109440at_nat ).

thf(sy_c_Product__Type_Oapfst_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc1579030810084249465xt_a_b: ( produc5647625992154082286xt_a_b > list_b ) > produc7347357110894899781xt_a_b > produc5647625992154082286xt_a_b ).

thf(sy_c_Product__Type_Oapfst_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc1634506678232684331xt_a_b: ( produc746580111399690912list_b > list_b ) > produc420090126769944851xt_a_b > produc5647625992154082286xt_a_b ).

thf(sy_c_Product__Type_Oapsnd_001_Eo_001_Eo_001_Eo,type,
    product_apsnd_o_o_o: ( $o > $o ) > product_prod_o_o > product_prod_o_o ).

thf(sy_c_Product__Type_Oapsnd_001_Eo_001t__List__Olist_Itf__b_J_001_Eo,type,
    produc3436890133996231661st_b_o: ( $o > list_b ) > product_prod_o_o > produc5666708989857747476list_b ).

thf(sy_c_Product__Type_Oapsnd_001_Eo_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    produc6411472997232821850list_b: ( $o > list_b ) > produc2420475512092800890st_b_o > produc3963297410138542439list_b ).

thf(sy_c_Product__Type_Oapsnd_001_Eo_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc2110809005894369377xt_a_b: ( $o > list_b ) > produc6481442714050758067_a_b_o > produc746580111399690912list_b ).

thf(sy_c_Product__Type_Oapsnd_001_Eo_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001_Eo,type,
    produc6446368593757314598_a_b_o: ( $o > multihole_mctxt_a_b ) > product_prod_o_o > produc4044283025580285595xt_a_b ).

thf(sy_c_Product__Type_Oapsnd_001_Eo_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    produc1492316820532087699list_b: ( $o > multihole_mctxt_a_b ) > produc2420475512092800890st_b_o > produc5647625992154082286xt_a_b ).

thf(sy_c_Product__Type_Oapsnd_001t__List__Olist_Itf__b_J_001_Eo_001_Eo,type,
    produc81398981840601991_b_o_o: ( list_b > $o ) > produc5666708989857747476list_b > product_prod_o_o ).

thf(sy_c_Product__Type_Oapsnd_001t__List__Olist_Itf__b_J_001_Eo_001t__List__Olist_Itf__b_J,type,
    produc2859178377933564916list_b: ( list_b > $o ) > produc3963297410138542439list_b > produc2420475512092800890st_b_o ).

thf(sy_c_Product__Type_Oapsnd_001t__List__Olist_Itf__b_J_001_Eo_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc3932911815817251323xt_a_b: ( list_b > $o ) > produc746580111399690912list_b > produc6481442714050758067_a_b_o ).

thf(sy_c_Product__Type_Oapsnd_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    produc4607378222123999303list_b: ( list_b > list_b ) > produc3963297410138542439list_b > produc3963297410138542439list_b ).

thf(sy_c_Product__Type_Oapsnd_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc6277155750876564558xt_a_b: ( list_b > list_b ) > produc746580111399690912list_b > produc746580111399690912list_b ).

thf(sy_c_Product__Type_Oapsnd_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    produc5658663565514282880list_b: ( list_b > multihole_mctxt_a_b ) > produc3963297410138542439list_b > produc5647625992154082286xt_a_b ).

thf(sy_c_Product__Type_Oapsnd_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc7278294437744766343xt_a_b: ( list_b > multihole_mctxt_a_b ) > produc746580111399690912list_b > produc1652119919080531751xt_a_b ).

thf(sy_c_Product__Type_Oapsnd_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001_Eo_001_Eo,type,
    produc3883574302206895886_b_o_o: ( multihole_mctxt_a_b > $o ) > produc4044283025580285595xt_a_b > product_prod_o_o ).

thf(sy_c_Product__Type_Oapsnd_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001_Eo_001t__List__Olist_Itf__b_J,type,
    produc1420457246728080507list_b: ( multihole_mctxt_a_b > $o ) > produc5647625992154082286xt_a_b > produc2420475512092800890st_b_o ).

thf(sy_c_Product__Type_Oapsnd_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    produc1067013901203078606list_b: ( multihole_mctxt_a_b > list_b ) > produc5647625992154082286xt_a_b > produc3963297410138542439list_b ).

thf(sy_c_Product__Type_Oapsnd_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc8239320667593801685xt_a_b: ( multihole_mctxt_a_b > list_b ) > produc1652119919080531751xt_a_b > produc746580111399690912list_b ).

thf(sy_c_Product__Type_Oapsnd_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    produc7620828482231520007list_b: ( multihole_mctxt_a_b > multihole_mctxt_a_b ) > produc5647625992154082286xt_a_b > produc5647625992154082286xt_a_b ).

thf(sy_c_Product__Type_Oapsnd_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc3600230912178009870xt_a_b: ( multihole_mctxt_a_b > multihole_mctxt_a_b ) > produc1652119919080531751xt_a_b > produc1652119919080531751xt_a_b ).

thf(sy_c_Product__Type_Oapsnd_001t__Nat__Onat_001_Eo_001_Eo,type,
    produc8182697654502551758at_o_o: ( nat > $o ) > product_prod_o_nat > product_prod_o_o ).

thf(sy_c_Product__Type_Oapsnd_001t__Nat__Onat_001_Eo_001t__Nat__Onat,type,
    produc5802879076734728218_o_nat: ( nat > $o ) > product_prod_nat_nat > product_prod_nat_o ).

thf(sy_c_Product__Type_Oapsnd_001t__Nat__Onat_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    produc2646826920715929486list_b: ( nat > list_b ) > produc6020613750378442500_b_nat > produc3963297410138542439list_b ).

thf(sy_c_Product__Type_Oapsnd_001t__Nat__Onat_001t__List__Olist_Itf__b_J_001t__Nat__Onat,type,
    produc2041552131524264583_b_nat: ( nat > list_b ) > product_prod_nat_nat > produc7811952446676219690list_b ).

thf(sy_c_Product__Type_Oapsnd_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
    produc3094765310956027504at_nat: ( nat > nat ) > product_prod_nat_nat > product_prod_nat_nat ).

thf(sy_c_Product__Type_Oapsnd_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
    produc1784090006485240963at_nat: ( nat > product_prod_nat_nat ) > product_prod_nat_nat > produc7248412053542808358at_nat ).

thf(sy_c_Product__Type_Oapsnd_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc8451700898548183735xt_a_b: ( produc5647625992154082286xt_a_b > list_b ) > produc2745072675574436617xt_a_b > produc746580111399690912list_b ).

thf(sy_c_Product__Type_Oapsnd_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc8507176766696618601xt_a_b: ( produc746580111399690912list_b > list_b ) > produc767570952302678203list_b > produc746580111399690912list_b ).

thf(sy_c_Product__Type_Ocurry_001_Eo_001_Eo_001_Eo,type,
    product_curry_o_o_o: ( product_prod_o_o > $o ) > $o > $o > $o ).

thf(sy_c_Product__Type_Ocurry_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J_001_Eo,type,
    produc6829973082055895501st_b_o: ( produc3963297410138542439list_b > $o ) > list_b > list_b > $o ).

thf(sy_c_Product__Type_Ocurry_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001_Eo,type,
    produc8471990777825750022_a_b_o: ( produc5647625992154082286xt_a_b > $o ) > list_b > multihole_mctxt_a_b > $o ).

thf(sy_c_Product__Type_Ocurry_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    produc5982366047203965299list_b: ( produc5647625992154082286xt_a_b > list_b ) > list_b > multihole_mctxt_a_b > list_b ).

thf(sy_c_Product__Type_Ocurry_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc8200905328278969722xt_a_b: ( produc5647625992154082286xt_a_b > multihole_mctxt_a_b ) > list_b > multihole_mctxt_a_b > multihole_mctxt_a_b ).

thf(sy_c_Product__Type_Ocurry_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    produc2492098109056437262list_b: ( produc5647625992154082286xt_a_b > produc746580111399690912list_b ) > list_b > multihole_mctxt_a_b > produc746580111399690912list_b ).

thf(sy_c_Product__Type_Ocurry_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001_Eo,type,
    produc5216961383963826260st_b_o: ( produc746580111399690912list_b > $o ) > multihole_mctxt_a_b > list_b > $o ).

thf(sy_c_Product__Type_Ocurry_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001_Eo,type,
    produc353760711170994317_a_b_o: ( produc1652119919080531751xt_a_b > $o ) > multihole_mctxt_a_b > multihole_mctxt_a_b > $o ).

thf(sy_c_Product__Type_Ointernal__case__prod_001_Eo_001_Eo_001_Eo,type,
    produc331225583472661270_o_o_o: ( $o > $o > $o ) > product_prod_o_o > $o ).

thf(sy_c_Product__Type_Ointernal__case__prod_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001_Eo,type,
    produc8837310327220950671_a_b_o: ( list_b > multihole_mctxt_a_b > $o ) > produc5647625992154082286xt_a_b > $o ).

thf(sy_c_Product__Type_Ointernal__case__prod_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    produc927258620547716860list_b: ( list_b > multihole_mctxt_a_b > list_b ) > produc5647625992154082286xt_a_b > list_b ).

thf(sy_c_Product__Type_Ointernal__case__prod_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc5361274526421632259xt_a_b: ( list_b > multihole_mctxt_a_b > multihole_mctxt_a_b ) > produc5647625992154082286xt_a_b > multihole_mctxt_a_b ).

thf(sy_c_Product__Type_Ointernal__case__prod_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    produc1496949917810534935list_b: ( list_b > multihole_mctxt_a_b > produc746580111399690912list_b ) > produc5647625992154082286xt_a_b > produc746580111399690912list_b ).

thf(sy_c_Product__Type_Omap__prod_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc1327442379091988662xt_a_b: ( list_b > list_b ) > ( multihole_mctxt_a_b > multihole_mctxt_a_b ) > produc5647625992154082286xt_a_b > produc5647625992154082286xt_a_b ).

thf(sy_c_Product__Type_Omap__prod_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    produc1669976423578742326list_b: ( list_b > multihole_mctxt_a_b ) > ( multihole_mctxt_a_b > list_b ) > produc5647625992154082286xt_a_b > produc746580111399690912list_b ).

thf(sy_c_Product__Type_Omap__prod_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc7077303473264541494xt_a_b: ( multihole_mctxt_a_b > list_b ) > ( list_b > multihole_mctxt_a_b ) > produc746580111399690912list_b > produc5647625992154082286xt_a_b ).

thf(sy_c_Product__Type_Omap__prod_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    produc1867161623591055542list_b: ( multihole_mctxt_a_b > multihole_mctxt_a_b ) > ( list_b > list_b ) > produc746580111399690912list_b > produc746580111399690912list_b ).

thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
    produc6977886695330630970at_nat: ( nat > nat ) > ( nat > nat ) > product_prod_nat_nat > product_prod_nat_nat ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_001_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001_Eo,type,
    produc8975932433296855461_a_b_o: ( ( nat > list_b ) > ( nat > multihole_mctxt_a_b ) > $o ) > produc8094751872729218222xt_a_b > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_001_Eo,type,
    produc6855914207928862147_a_b_o: ( ( nat > list_b ) > ( nat > produc5647625992154082286xt_a_b ) > $o ) > produc8823150311724842384xt_a_b > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_001_Eo,type,
    produc477927949550467699st_b_o: ( ( nat > multihole_mctxt_a_b ) > ( nat > list_b ) > $o ) > produc5125836498238150368list_b > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_001_Eo,type,
    produc6118959495424706968st_b_o: ( ( nat > multihole_mctxt_a_b ) > ( nat > produc746580111399690912list_b ) > $o ) > produc3044767985951407611list_b > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo,type,
    produc5295663322308424044_nat_o: ( ( nat > nat ) > ( nat > nat ) > $o ) > produc1932156733058919263at_nat > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_001_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_001_Eo,type,
    produc719654758968605269st_b_o: ( ( nat > produc5647625992154082286xt_a_b ) > ( nat > list_b ) > $o ) > produc4127645531870415870list_b > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_001_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001_Eo,type,
    produc1885532244741406222_a_b_o: ( ( nat > produc5647625992154082286xt_a_b ) > ( nat > multihole_mctxt_a_b ) > $o ) > produc5956155440505932549xt_a_b > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_001_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_001_Eo,type,
    produc3817622485218950151st_b_o: ( ( nat > produc746580111399690912list_b ) > ( nat > list_b ) > $o ) > produc6423750584600236748list_b > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_001_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001_Eo,type,
    produc2939875012228043712_a_b_o: ( ( nat > produc746580111399690912list_b ) > ( nat > multihole_mctxt_a_b ) > $o ) > produc5683466111014092243xt_a_b > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_Eo_001_Eo_001_Eo,type,
    produc6197397395684419436_o_o_o: ( $o > $o > $o ) > product_prod_o_o > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_Eo_001_Eo_001t__Set__Oset_I_Eo_J,type,
    produc1238384690215476812_set_o: ( $o > $o > set_o ) > product_prod_o_o > set_o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_Eo_001_Eo_001t__Set__Oset_It__List__Olist_Itf__b_J_J,type,
    produc1707798961248329273list_b: ( $o > $o > set_list_b ) > product_prod_o_o > set_list_b ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_Eo_001_Eo_001t__Set__Oset_It__Nat__Onat_J,type,
    produc6723186405834743986et_nat: ( $o > $o > set_nat ) > product_prod_o_o > set_nat ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001_Eo_001_Eo_001t__Set__Oset_It__Set__Oset_I_Eo_J_J,type,
    produc1752788702180839724_set_o: ( $o > $o > set_set_o ) > product_prod_o_o > set_set_o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J_001_Eo,type,
    produc6051822690389492396st_b_o: ( list_b > list_b > $o ) > produc3963297410138542439list_b > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J_001t__Set__Oset_I_Eo_J,type,
    produc6324044751052175756_set_o: ( list_b > list_b > set_o ) > produc3963297410138542439list_b > set_o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J_001t__Set__Oset_It__Nat__Onat_J,type,
    produc4846079126225884530et_nat: ( list_b > list_b > set_nat ) > produc3963297410138542439list_b > set_nat ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001_Eo,type,
    produc1221931734719695589_a_b_o: ( list_b > multihole_mctxt_a_b > $o ) > produc5647625992154082286xt_a_b > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    produc5071610215621926226list_b: ( list_b > multihole_mctxt_a_b > list_b ) > produc5647625992154082286xt_a_b > list_b ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc6892829578239444825xt_a_b: ( list_b > multihole_mctxt_a_b > multihole_mctxt_a_b ) > produc5647625992154082286xt_a_b > multihole_mctxt_a_b ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    produc3271728269314753389list_b: ( list_b > multihole_mctxt_a_b > produc746580111399690912list_b ) > produc5647625992154082286xt_a_b > produc746580111399690912list_b ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Set__Oset_I_Eo_J,type,
    produc8799683814798138821_set_o: ( list_b > multihole_mctxt_a_b > set_o ) > produc5647625992154082286xt_a_b > set_o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Set__Oset_It__Nat__Onat_J,type,
    produc7038115184564154745et_nat: ( list_b > multihole_mctxt_a_b > set_nat ) > produc5647625992154082286xt_a_b > set_nat ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001_Eo,type,
    produc4710150075370709635_a_b_o: ( list_b > produc5647625992154082286xt_a_b > $o ) > produc1635315984519752016xt_a_b > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001_Eo,type,
    produc7190274377712547635st_b_o: ( multihole_mctxt_a_b > list_b > $o ) > produc746580111399690912list_b > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    produc479960551310721952list_b: ( multihole_mctxt_a_b > list_b > list_b ) > produc746580111399690912list_b > list_b ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc7853855808088480167xt_a_b: ( multihole_mctxt_a_b > list_b > multihole_mctxt_a_b ) > produc746580111399690912list_b > multihole_mctxt_a_b ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    produc3662036813938090505xt_a_b: ( multihole_mctxt_a_b > list_b > produc5647625992154082286xt_a_b ) > produc746580111399690912list_b > produc5647625992154082286xt_a_b ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001t__Set__Oset_I_Eo_J,type,
    produc6050732325701653011_set_o: ( multihole_mctxt_a_b > list_b > set_o ) > produc746580111399690912list_b > set_o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001t__Set__Oset_It__Nat__Onat_J,type,
    produc1070828641548463275et_nat: ( multihole_mctxt_a_b > list_b > set_nat ) > produc746580111399690912list_b > set_nat ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001_Eo,type,
    produc3751450646053246316_a_b_o: ( multihole_mctxt_a_b > multihole_mctxt_a_b > $o ) > produc1652119919080531751xt_a_b > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
    produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001_Eo,type,
    produc2838803774393728846_a_b_o: ( produc5647625992154082286xt_a_b > multihole_mctxt_a_b > $o ) > produc7347357110894899781xt_a_b > $o ).

thf(sy_c_Product__Type_Oprod_Ofst_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
    produc9004644904754006275at_nat: produc1932156733058919263at_nat > nat > nat ).

thf(sy_c_Product__Type_Oprod_Ofst_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_001_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J,type,
    produc4406183396323733594list_b: produc4127645531870415870list_b > nat > produc5647625992154082286xt_a_b ).

thf(sy_c_Product__Type_Oprod_Ofst_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_001_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J,type,
    produc6702288449053554472list_b: produc6423750584600236748list_b > nat > produc746580111399690912list_b ).

thf(sy_c_Product__Type_Oprod_Ofst_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_001_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    produc4622812557051431855xt_a_b: produc5683466111014092243xt_a_b > nat > produc746580111399690912list_b ).

thf(sy_c_Product__Type_Oprod_Ofst_001_Eo_001_Eo,type,
    product_fst_o_o: product_prod_o_o > $o ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    produc7649009375908944835list_b: produc3963297410138542439list_b > list_b ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc6500241281145331658xt_a_b: produc5647625992154082286xt_a_b > list_b ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    produc5881749095783049980list_b: produc746580111399690912list_b > multihole_mctxt_a_b ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc2029583840371251459xt_a_b: produc1652119919080531751xt_a_b > multihole_mctxt_a_b ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Nat__Onat,type,
    product_fst_nat_nat: product_prod_nat_nat > nat ).

thf(sy_c_Product__Type_Oprod_Osnd_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
    produc159067601377291077at_nat: produc1932156733058919263at_nat > nat > nat ).

thf(sy_c_Product__Type_Oprod_Osnd_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_001_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J,type,
    produc6969454212247003292list_b: produc4127645531870415870list_b > nat > list_b ).

thf(sy_c_Product__Type_Oprod_Osnd_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_001_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J,type,
    produc42187228122048362list_b: produc6423750584600236748list_b > nat > list_b ).

thf(sy_c_Product__Type_Oprod_Osnd_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_001_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    produc3597091874480877553xt_a_b: produc5683466111014092243xt_a_b > nat > multihole_mctxt_a_b ).

thf(sy_c_Product__Type_Oprod_Osnd_001_Eo_001_Eo,type,
    product_snd_o_o: product_prod_o_o > $o ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    produc3345134588468168965list_b: produc3963297410138542439list_b > list_b ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc6725609433235685644xt_a_b: produc5647625992154082286xt_a_b > multihole_mctxt_a_b ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    produc6107117247873403966list_b: produc746580111399690912list_b > list_b ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc4775144687201070661xt_a_b: produc1652119919080531751xt_a_b > multihole_mctxt_a_b ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Nat__Onat,type,
    product_snd_nat_nat: product_prod_nat_nat > nat ).

thf(sy_c_Product__Type_Oprod_Oswap_001_Eo_001_Eo,type,
    product_swap_o_o: product_prod_o_o > product_prod_o_o ).

thf(sy_c_Product__Type_Oprod_Oswap_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    produc6495775440487448439list_b: produc3963297410138542439list_b > produc3963297410138542439list_b ).

thf(sy_c_Product__Type_Oprod_Oswap_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc4642366622444604286xt_a_b: produc5647625992154082286xt_a_b > produc746580111399690912list_b ).

thf(sy_c_Product__Type_Oprod_Oswap_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    produc4023874437082322608list_b: produc746580111399690912list_b > produc5647625992154082286xt_a_b ).

thf(sy_c_Product__Type_Oprod_Oswap_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    produc1108858440263912631xt_a_b: produc1652119919080531751xt_a_b > produc1652119919080531751xt_a_b ).

thf(sy_c_Product__Type_Oprod_Oswap_001t__Nat__Onat_001t__Nat__Onat,type,
    product_swap_nat_nat: product_prod_nat_nat > product_prod_nat_nat ).

thf(sy_c_Relation_Oconversep_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_001_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J,type,
    conver8732461567001031628list_b: ( ( nat > produc5647625992154082286xt_a_b ) > ( nat > list_b ) > $o ) > ( nat > list_b ) > ( nat > produc5647625992154082286xt_a_b ) > $o ).

thf(sy_c_Relation_Oconversep_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_001_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    conver1419177986811044641xt_a_b: ( ( nat > produc746580111399690912list_b ) > ( nat > multihole_mctxt_a_b ) > $o ) > ( nat > multihole_mctxt_a_b ) > ( nat > produc746580111399690912list_b ) > $o ).

thf(sy_c_Relation_Oconversep_001t__Nat__Onat_001t__Nat__Onat,type,
    conversep_nat_nat: ( nat > nat > $o ) > nat > nat > $o ).

thf(sy_c_Relation_Oconversep_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__List__Olist_Itf__b_J,type,
    conver2075301813112946444list_b: ( produc5647625992154082286xt_a_b > list_b > $o ) > list_b > produc5647625992154082286xt_a_b > $o ).

thf(sy_c_Relation_Oconversep_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    conver810234233312416737xt_a_b: ( produc746580111399690912list_b > multihole_mctxt_a_b > $o ) > multihole_mctxt_a_b > produc746580111399690912list_b > $o ).

thf(sy_c_Relation_Orelcompp_001_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_001_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    relcom5838476793205533529xt_a_b: ( ( nat > list_b ) > ( nat > produc5647625992154082286xt_a_b ) > $o ) > ( ( nat > produc5647625992154082286xt_a_b ) > ( nat > multihole_mctxt_a_b ) > $o ) > ( nat > list_b ) > ( nat > multihole_mctxt_a_b ) > $o ).

thf(sy_c_Relation_Orelcompp_001_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_001_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J,type,
    relcom4037855281751361575list_b: ( ( nat > multihole_mctxt_a_b ) > ( nat > produc746580111399690912list_b ) > $o ) > ( ( nat > produc746580111399690912list_b ) > ( nat > list_b ) > $o ) > ( nat > multihole_mctxt_a_b ) > ( nat > list_b ) > $o ).

thf(sy_c_Relation_Orelcompp_001_Eo_001_Eo_001_Eo,type,
    relcompp_o_o_o: ( $o > $o > $o ) > ( $o > $o > $o ) > $o > $o > $o ).

thf(sy_c_Relation_Orelcompp_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    relcom3042044877837805780list_b: ( list_b > list_b > $o ) > ( list_b > list_b > $o ) > list_b > list_b > $o ).

thf(sy_c_Relation_Orelcompp_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    relcom6602897104211838683xt_a_b: ( list_b > list_b > $o ) > ( list_b > multihole_mctxt_a_b > $o ) > list_b > multihole_mctxt_a_b > $o ).

thf(sy_c_Relation_Orelcompp_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    relcom5984404918849557005list_b: ( list_b > multihole_mctxt_a_b > $o ) > ( multihole_mctxt_a_b > list_b > $o ) > list_b > list_b > $o ).

thf(sy_c_Relation_Orelcompp_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    relcom1134127583608674836xt_a_b: ( list_b > multihole_mctxt_a_b > $o ) > ( multihole_mctxt_a_b > multihole_mctxt_a_b > $o ) > list_b > multihole_mctxt_a_b > $o ).

thf(sy_c_Relation_Orelcompp_001t__List__Olist_Itf__b_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    relcom2105089833257999154xt_a_b: ( list_b > produc5647625992154082286xt_a_b > $o ) > ( produc5647625992154082286xt_a_b > multihole_mctxt_a_b > $o ) > list_b > multihole_mctxt_a_b > $o ).

thf(sy_c_Relation_Orelcompp_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001t__List__Olist_Itf__b_J,type,
    relcom1392755254538352731list_b: ( multihole_mctxt_a_b > list_b > $o ) > ( list_b > list_b > $o ) > multihole_mctxt_a_b > list_b > $o ).

thf(sy_c_Relation_Orelcompp_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    relcom2095153813457710178xt_a_b: ( multihole_mctxt_a_b > list_b > $o ) > ( list_b > multihole_mctxt_a_b > $o ) > multihole_mctxt_a_b > multihole_mctxt_a_b > $o ).

thf(sy_c_Relation_Orelcompp_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__List__Olist_Itf__b_J,type,
    relcom1476661628095428500list_b: ( multihole_mctxt_a_b > multihole_mctxt_a_b > $o ) > ( multihole_mctxt_a_b > list_b > $o ) > multihole_mctxt_a_b > list_b > $o ).

thf(sy_c_Relation_Orelcompp_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    relcom5598437220703425947xt_a_b: ( multihole_mctxt_a_b > multihole_mctxt_a_b > $o ) > ( multihole_mctxt_a_b > multihole_mctxt_a_b > $o ) > multihole_mctxt_a_b > multihole_mctxt_a_b > $o ).

thf(sy_c_Relation_Orelcompp_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__List__Olist_Itf__b_J,type,
    relcom4353153964112099584list_b: ( multihole_mctxt_a_b > produc746580111399690912list_b > $o ) > ( produc746580111399690912list_b > list_b > $o ) > multihole_mctxt_a_b > list_b > $o ).

thf(sy_c_Relation_Orelcompp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
    relcompp_nat_nat_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > nat > nat > $o ).

thf(sy_c_Set_OCollect_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
    collect_nat_nat: ( ( nat > nat ) > $o ) > set_nat_nat ).

thf(sy_c_Set_OCollect_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J,type,
    collec8943654641036559040xt_a_b: ( ( nat > produc5647625992154082286xt_a_b ) > $o ) > set_na664922679713831477xt_a_b ).

thf(sy_c_Set_OCollect_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J,type,
    collec6966152917764800626list_b: ( ( nat > produc746580111399690912list_b ) > $o ) > set_na6008912749387833063list_b ).

thf(sy_c_Set_OCollect_001_Eo,type,
    collect_o: ( $o > $o ) > set_o ).

thf(sy_c_Set_OCollect_001t__List__Olist_Itf__b_J,type,
    collect_list_b: ( list_b > $o ) > set_list_b ).

thf(sy_c_Set_OCollect_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    collec7587487095821320951xt_a_b: ( multihole_mctxt_a_b > $o ) > set_Mu3903433398966807788xt_a_b ).

thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
    collect_nat: ( nat > $o ) > set_nat ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_M_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J,type,
    collec3970827031609289497xt_a_b: ( produc8094751872729218222xt_a_b > $o ) > set_Pr3280023335470083854xt_a_b ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_M_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_J,type,
    collec856815870434662267xt_a_b: ( produc8823150311724842384xt_a_b > $o ) > set_Pr1013263123567674224xt_a_b ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_M_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_J,type,
    collec1001911657118221643list_b: ( produc5125836498238150368list_b > $o ) > set_Pr5544284923275595840list_b ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_M_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_J,type,
    collec7047008785119843814list_b: ( produc3044767985951407611list_b > $o ) > set_Pr8796965451986337883list_b ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    collec2757435396427831370at_nat: ( produc1932156733058919263at_nat > $o ) > set_Pr7682762132356531903at_nat ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_M_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_J,type,
    collec5384683127435011561list_b: ( produc4127645531870415870list_b > $o ) > set_Pr5636780074650139358list_b ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_M_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J,type,
    collec735024202819592944xt_a_b: ( produc5956155440505932549xt_a_b > $o ) > set_Pr8131422468521715813xt_a_b ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_M_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_J,type,
    collec7680788180164832439list_b: ( produc6423750584600236748list_b > $o ) > set_Pr770470488129649324list_b ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_M_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J,type,
    collec462334873327752638xt_a_b: ( produc5683466111014092243xt_a_b > $o ) > set_Pr9036761696576656435xt_a_b ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
    collec3167064739498627218od_o_o: ( product_prod_o_o > $o ) > set_Product_prod_o_o ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    collec4964980819554056914list_b: ( produc3963297410138542439list_b > $o ) > set_Pr7665282455119567943list_b ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    collec1611458371973403481xt_a_b: ( produc5647625992154082286xt_a_b > $o ) > set_Pr3872688570871424334xt_a_b ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J,type,
    collec2632839920380509243xt_a_b: ( produc1635315984519752016xt_a_b > $o ) > set_Pr7630595734861755952xt_a_b ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    collec5933784528073787915list_b: ( produc746580111399690912list_b > $o ) > set_Pr1895186847599665920list_b ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    collec3715850105416846482xt_a_b: ( produc1652119919080531751xt_a_b > $o ) > set_Pr2918931875556005383xt_a_b ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    collec3392354462482085612at_nat: ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat ).

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    collec4227569900337431344xt_a_b: ( produc7347357110894899781xt_a_b > $o ) > set_Pr5839317327662470821xt_a_b ).

thf(sy_c_Set_OCollect_001t__Set__Oset_I_Eo_J,type,
    collect_set_o: ( set_o > $o ) > set_set_o ).

thf(sy_c_Set_OPow_001t__Nat__Onat,type,
    pow_nat: set_nat > set_set_nat ).

thf(sy_c_Set_Oimage_001_062_I_Eo_M_Eo_J_001_Eo,type,
    image_o_o_o: ( ( $o > $o ) > $o ) > set_o_o > set_o ).

thf(sy_c_Set_Oimage_001_062_I_Eo_M_Eo_J_001t__Nat__Onat,type,
    image_o_o_nat: ( ( $o > $o ) > nat ) > set_o_o > set_nat ).

thf(sy_c_Set_Oimage_001_062_I_Eo_M_Eo_J_001t__Set__Oset_I_Eo_J,type,
    image_o_o_set_o: ( ( $o > $o ) > set_o ) > set_o_o > set_set_o ).

thf(sy_c_Set_Oimage_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J,type,
    image_7255227558896101957xt_a_b: ( ( nat > produc5647625992154082286xt_a_b ) > nat > produc5647625992154082286xt_a_b ) > set_na664922679713831477xt_a_b > set_na664922679713831477xt_a_b ).

thf(sy_c_Set_Oimage_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J,type,
    image_5277725835624343543list_b: ( ( nat > produc5647625992154082286xt_a_b ) > nat > produc746580111399690912list_b ) > set_na664922679713831477xt_a_b > set_na6008912749387833063list_b ).

thf(sy_c_Set_Oimage_001_Eo_001_Eo,type,
    image_o_o: ( $o > $o ) > set_o > set_o ).

thf(sy_c_Set_Oimage_001_Eo_001t__List__Olist_Itf__b_J,type,
    image_o_list_b: ( $o > list_b ) > set_o > set_list_b ).

thf(sy_c_Set_Oimage_001_Eo_001t__Nat__Onat,type,
    image_o_nat: ( $o > nat ) > set_o > set_nat ).

thf(sy_c_Set_Oimage_001_Eo_001t__Set__Oset_I_Eo_J,type,
    image_o_set_o: ( $o > set_o ) > set_o > set_set_o ).

thf(sy_c_Set_Oimage_001_Eo_001t__Set__Oset_It__Nat__Onat_J,type,
    image_o_set_nat: ( $o > set_nat ) > set_o > set_set_nat ).

thf(sy_c_Set_Oimage_001t__List__Olist_Itf__b_J_001_Eo,type,
    image_list_b_o: ( list_b > $o ) > set_list_b > set_o ).

thf(sy_c_Set_Oimage_001t__List__Olist_Itf__b_J_001t__Nat__Onat,type,
    image_list_b_nat: ( list_b > nat ) > set_list_b > set_nat ).

thf(sy_c_Set_Oimage_001t__List__Olist_Itf__b_J_001t__Set__Oset_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    image_5892124603837329964xt_a_b: ( list_b > set_Mu3903433398966807788xt_a_b ) > set_list_b > set_se6625423409757081292xt_a_b ).

thf(sy_c_Set_Oimage_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_001t__Set__Oset_It__List__Olist_Itf__b_J_J,type,
    image_6332848988479007454list_b: ( multihole_mctxt_a_b > set_list_b ) > set_Mu3903433398966807788xt_a_b > set_set_list_b ).

thf(sy_c_Set_Oimage_001t__Nat__Onat_001_Eo,type,
    image_nat_o: ( nat > $o ) > set_nat > set_o ).

thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__List__Olist_Itf__b_J,type,
    image_nat_list_b: ( nat > list_b ) > set_nat > set_list_b ).

thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
    image_nat_nat: ( nat > nat ) > set_nat > set_nat ).

thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    image_812790401321666007xt_a_b: ( nat > produc5647625992154082286xt_a_b ) > set_nat > set_Pr3872688570871424334xt_a_b ).

thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    image_5135116557422050441list_b: ( nat > produc746580111399690912list_b ) > set_nat > set_Pr1895186847599665920list_b ).

thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    image_5846123807819985514at_nat: ( nat > product_prod_nat_nat ) > set_nat > set_Pr1261947904930325089at_nat ).

thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_I_Eo_J,type,
    image_nat_set_o: ( nat > set_o ) > set_nat > set_set_o ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001_Eo,type,
    image_7896445794123959606_o_o_o: ( product_prod_o_o > $o ) > set_Product_prod_o_o > set_o ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
    image_9131363867636255685od_o_o: ( product_prod_o_o > product_prod_o_o ) > set_Product_prod_o_o > set_Product_prod_o_o ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__List__Olist_Itf__b_J_J_001t__List__Olist_Itf__b_J,type,
    image_7865409632269190755list_b: ( produc3963297410138542439list_b > list_b ) > set_Pr7665282455119567943list_b > set_list_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__List__Olist_Itf__b_J_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    image_3063139515468067781list_b: ( produc3963297410138542439list_b > produc3963297410138542439list_b ) > set_Pr7665282455119567943list_b > set_Pr7665282455119567943list_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001_Eo,type,
    image_8261397660998149807_a_b_o: ( produc5647625992154082286xt_a_b > $o ) > set_Pr3872688570871424334xt_a_b > set_o ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__List__Olist_Itf__b_J,type,
    image_5978867512307746588list_b: ( produc5647625992154082286xt_a_b > list_b ) > set_Pr3872688570871424334xt_a_b > set_list_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    image_4915618970390574371xt_a_b: ( produc5647625992154082286xt_a_b > multihole_mctxt_a_b ) > set_Pr3872688570871424334xt_a_b > set_Mu3903433398966807788xt_a_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Nat__Onat,type,
    image_7093515819370167417_b_nat: ( produc5647625992154082286xt_a_b > nat ) > set_Pr3872688570871424334xt_a_b > set_nat ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    image_1828724688096913975list_b: ( produc5647625992154082286xt_a_b > produc746580111399690912list_b ) > set_Pr3872688570871424334xt_a_b > set_Pr1895186847599665920list_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001_Eo,type,
    image_2580685047486449533st_b_o: ( produc746580111399690912list_b > $o ) > set_Pr1895186847599665920list_b > set_o ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__List__Olist_Itf__b_J,type,
    image_9124975640858730986list_b: ( produc746580111399690912list_b > list_b ) > set_Pr1895186847599665920list_b > set_list_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    image_7211724023120395249xt_a_b: ( produc746580111399690912list_b > multihole_mctxt_a_b ) > set_Pr1895186847599665920list_b > set_Mu3903433398966807788xt_a_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__Nat__Onat,type,
    image_6047115928211467051_b_nat: ( produc746580111399690912list_b > nat ) > set_Pr1895186847599665920list_b > set_nat ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    image_3492653723807366483xt_a_b: ( produc746580111399690912list_b > produc5647625992154082286xt_a_b ) > set_Pr1895186847599665920list_b > set_Pr3872688570871424334xt_a_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    image_2825928036690640042xt_a_b: ( produc1652119919080531751xt_a_b > multihole_mctxt_a_b ) > set_Pr2918931875556005383xt_a_b > set_Mu3903433398966807788xt_a_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    image_3034241489052758981xt_a_b: ( produc1652119919080531751xt_a_b > produc1652119919080531751xt_a_b ) > set_Pr2918931875556005383xt_a_b > set_Pr2918931875556005383xt_a_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
    image_2486076414777270412at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > set_nat ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    image_5168914502847457605at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(sy_c_Set_Oimage_001t__Set__Oset_I_Eo_J_001_062_I_Eo_M_Eo_J,type,
    image_set_o_o_o: ( set_o > $o > $o ) > set_set_o > set_o_o ).

thf(sy_c_Set_Oimage_001t__Set__Oset_I_Eo_J_001_Eo,type,
    image_set_o_o: ( set_o > $o ) > set_set_o > set_o ).

thf(sy_c_Set_Oimage_001t__Set__Oset_I_Eo_J_001t__Nat__Onat,type,
    image_set_o_nat: ( set_o > nat ) > set_set_o > set_nat ).

thf(sy_c_Set_Oimage_001t__Set__Oset_I_Eo_J_001t__Set__Oset_I_Eo_J,type,
    image_set_o_set_o: ( set_o > set_o ) > set_set_o > set_set_o ).

thf(sy_c_Transfer_Obi__total_001t__Nat__Onat_001t__Nat__Onat,type,
    bi_total_nat_nat: ( nat > nat > $o ) > $o ).

thf(sy_c_Transitive__Closure_Otrancl_001t__Nat__Onat,type,
    transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(sy_c_Typedef_Otype__definition_001t__Nat__Onat_001t__Nat__Onat,type,
    type_d6250493948777748686at_nat: ( nat > nat ) > ( nat > nat ) > set_nat > $o ).

thf(sy_c_Utils_Ovars__term__list_001tf__a_001tf__b,type,
    vars_term_list_a_b: term_a_b > list_b ).

thf(sy_c_member_001_062_I_Eo_M_Eo_J,type,
    member_o_o: ( $o > $o ) > set_o_o > $o ).

thf(sy_c_member_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
    member_nat_nat: ( nat > nat ) > set_nat_nat > $o ).

thf(sy_c_member_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J,type,
    member3828642050509981054xt_a_b: ( nat > produc5647625992154082286xt_a_b ) > set_na664922679713831477xt_a_b > $o ).

thf(sy_c_member_001_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J,type,
    member1851140327238222640list_b: ( nat > produc746580111399690912list_b ) > set_na6008912749387833063list_b > $o ).

thf(sy_c_member_001_Eo,type,
    member_o: $o > set_o > $o ).

thf(sy_c_member_001t__List__Olist_Itf__b_J,type,
    member_list_b: list_b > set_list_b > $o ).

thf(sy_c_member_001t__Multihole____Context__Omctxt_Itf__a_Mtf__b_J,type,
    member4915921492409311157xt_a_b: multihole_mctxt_a_b > set_Mu3903433398966807788xt_a_b > $o ).

thf(sy_c_member_001t__Nat__Onat,type,
    member_nat: nat > set_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_M_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J,type,
    member5015363498307123415xt_a_b: produc8094751872729218222xt_a_b > set_Pr3280023335470083854xt_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_M_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_J,type,
    member7754590689969029177xt_a_b: produc8823150311724842384xt_a_b > set_Pr1013263123567674224xt_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_M_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_J,type,
    member2046448123816055561list_b: produc5125836498238150368list_b > set_Pr5544284923275595840list_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_M_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_J,type,
    member4439946314538814116list_b: produc3044767985951407611list_b > set_Pr8796965451986337883list_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    member1096249278104964872at_nat: produc1932156733058919263at_nat > set_Pr7682762132356531903at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_M_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_J,type,
    member3059085910114602663list_b: produc4127645531870415870list_b > set_Pr5636780074650139358list_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J_M_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J,type,
    member7351333769093339054xt_a_b: produc5956155440505932549xt_a_b > set_Pr8131422468521715813xt_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_M_062_It__Nat__Onat_Mt__List__Olist_Itf__b_J_J_J,type,
    member5355190962844423541list_b: produc6423750584600236748list_b > set_Pr770470488129649324list_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J_J_M_062_It__Nat__Onat_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J,type,
    member7078644439601498748xt_a_b: produc5683466111014092243xt_a_b > set_Pr9036761696576656435xt_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
    member7466972457876170832od_o_o: product_prod_o_o > set_Product_prod_o_o > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    member2990321877988238992list_b: produc3963297410138542439list_b > set_Pr7665282455119567943list_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    member8473537726404135703xt_a_b: produc5647625992154082286xt_a_b > set_Pr3872688570871424334xt_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_J,type,
    member4998021903520026361xt_a_b: produc1635315984519752016xt_a_b > set_Pr7630595734861755952xt_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__List__Olist_Itf__b_J_J,type,
    member3572491845649744329list_b: produc746580111399690912list_b > set_Pr1895186847599665920list_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    member6103717091360755792xt_a_b: produc1652119919080531751xt_a_b > set_Pr2918931875556005383xt_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_Itf__b_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J_Mt__Multihole____Context__Omctxt_Itf__a_Mtf__b_J_J,type,
    member1744449530997989870xt_a_b: produc7347357110894899781xt_a_b > set_Pr5839317327662470821xt_a_b > $o ).

thf(sy_c_member_001t__Set__Oset_I_Eo_J,type,
    member_set_o: set_o > set_set_o > $o ).

thf(sy_v_t,type,
    t: term_a_b ).

% Relevant facts (1273)
thf(fact_0_prod_Oexpand,axiom,
    ! [Prod: produc1652119919080531751xt_a_b,Prod2: produc1652119919080531751xt_a_b] :
      ( ( ( ( produc2029583840371251459xt_a_b @ Prod )
          = ( produc2029583840371251459xt_a_b @ Prod2 ) )
        & ( ( produc4775144687201070661xt_a_b @ Prod )
          = ( produc4775144687201070661xt_a_b @ Prod2 ) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
thf(fact_1_prod_Oexpand,axiom,
    ! [Prod: produc3963297410138542439list_b,Prod2: produc3963297410138542439list_b] :
      ( ( ( ( produc7649009375908944835list_b @ Prod )
          = ( produc7649009375908944835list_b @ Prod2 ) )
        & ( ( produc3345134588468168965list_b @ Prod )
          = ( produc3345134588468168965list_b @ Prod2 ) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
thf(fact_2_prod_Oexpand,axiom,
    ! [Prod: product_prod_o_o,Prod2: product_prod_o_o] :
      ( ( ( ( product_fst_o_o @ Prod )
          = ( product_fst_o_o @ Prod2 ) )
        & ( ( product_snd_o_o @ Prod )
          = ( product_snd_o_o @ Prod2 ) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
thf(fact_3_prod_Oexpand,axiom,
    ! [Prod: product_prod_nat_nat,Prod2: product_prod_nat_nat] :
      ( ( ( ( product_fst_nat_nat @ Prod )
          = ( product_fst_nat_nat @ Prod2 ) )
        & ( ( product_snd_nat_nat @ Prod )
          = ( product_snd_nat_nat @ Prod2 ) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
thf(fact_4_prod_Oexpand,axiom,
    ! [Prod: produc5647625992154082286xt_a_b,Prod2: produc5647625992154082286xt_a_b] :
      ( ( ( ( produc6500241281145331658xt_a_b @ Prod )
          = ( produc6500241281145331658xt_a_b @ Prod2 ) )
        & ( ( produc6725609433235685644xt_a_b @ Prod )
          = ( produc6725609433235685644xt_a_b @ Prod2 ) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
thf(fact_5_prod_Oexpand,axiom,
    ! [Prod: produc746580111399690912list_b,Prod2: produc746580111399690912list_b] :
      ( ( ( ( produc5881749095783049980list_b @ Prod )
          = ( produc5881749095783049980list_b @ Prod2 ) )
        & ( ( produc6107117247873403966list_b @ Prod )
          = ( produc6107117247873403966list_b @ Prod2 ) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
thf(fact_6_prod__eqI,axiom,
    ! [P: produc1652119919080531751xt_a_b,Q: produc1652119919080531751xt_a_b] :
      ( ( ( produc2029583840371251459xt_a_b @ P )
        = ( produc2029583840371251459xt_a_b @ Q ) )
     => ( ( ( produc4775144687201070661xt_a_b @ P )
          = ( produc4775144687201070661xt_a_b @ Q ) )
       => ( P = Q ) ) ) ).

% prod_eqI
thf(fact_7_prod__eqI,axiom,
    ! [P: produc3963297410138542439list_b,Q: produc3963297410138542439list_b] :
      ( ( ( produc7649009375908944835list_b @ P )
        = ( produc7649009375908944835list_b @ Q ) )
     => ( ( ( produc3345134588468168965list_b @ P )
          = ( produc3345134588468168965list_b @ Q ) )
       => ( P = Q ) ) ) ).

% prod_eqI
thf(fact_8_prod__eqI,axiom,
    ! [P: product_prod_o_o,Q: product_prod_o_o] :
      ( ( ( product_fst_o_o @ P )
        = ( product_fst_o_o @ Q ) )
     => ( ( ( product_snd_o_o @ P )
          = ( product_snd_o_o @ Q ) )
       => ( P = Q ) ) ) ).

% prod_eqI
thf(fact_9_prod__eqI,axiom,
    ! [P: product_prod_nat_nat,Q: product_prod_nat_nat] :
      ( ( ( product_fst_nat_nat @ P )
        = ( product_fst_nat_nat @ Q ) )
     => ( ( ( product_snd_nat_nat @ P )
          = ( product_snd_nat_nat @ Q ) )
       => ( P = Q ) ) ) ).

% prod_eqI
thf(fact_10_prod__eqI,axiom,
    ! [P: produc5647625992154082286xt_a_b,Q: produc5647625992154082286xt_a_b] :
      ( ( ( produc6500241281145331658xt_a_b @ P )
        = ( produc6500241281145331658xt_a_b @ Q ) )
     => ( ( ( produc6725609433235685644xt_a_b @ P )
          = ( produc6725609433235685644xt_a_b @ Q ) )
       => ( P = Q ) ) ) ).

% prod_eqI
thf(fact_11_prod__eqI,axiom,
    ! [P: produc746580111399690912list_b,Q: produc746580111399690912list_b] :
      ( ( ( produc5881749095783049980list_b @ P )
        = ( produc5881749095783049980list_b @ Q ) )
     => ( ( ( produc6107117247873403966list_b @ P )
          = ( produc6107117247873403966list_b @ Q ) )
       => ( P = Q ) ) ) ).

% prod_eqI
thf(fact_12_exE__realizer_H,axiom,
    ! [P2: multihole_mctxt_a_b > multihole_mctxt_a_b > $o,P: produc1652119919080531751xt_a_b] :
      ( ( P2 @ ( produc4775144687201070661xt_a_b @ P ) @ ( produc2029583840371251459xt_a_b @ P ) )
     => ~ ! [X: multihole_mctxt_a_b,Y: multihole_mctxt_a_b] :
            ~ ( P2 @ Y @ X ) ) ).

% exE_realizer'
thf(fact_13_exE__realizer_H,axiom,
    ! [P2: list_b > list_b > $o,P: produc3963297410138542439list_b] :
      ( ( P2 @ ( produc3345134588468168965list_b @ P ) @ ( produc7649009375908944835list_b @ P ) )
     => ~ ! [X: list_b,Y: list_b] :
            ~ ( P2 @ Y @ X ) ) ).

% exE_realizer'
thf(fact_14_exE__realizer_H,axiom,
    ! [P2: $o > $o > $o,P: product_prod_o_o] :
      ( ( P2 @ ( product_snd_o_o @ P ) @ ( product_fst_o_o @ P ) )
     => ~ ! [X: $o,Y: $o] :
            ~ ( P2 @ Y @ X ) ) ).

% exE_realizer'
thf(fact_15_exE__realizer_H,axiom,
    ! [P2: nat > nat > $o,P: product_prod_nat_nat] :
      ( ( P2 @ ( product_snd_nat_nat @ P ) @ ( product_fst_nat_nat @ P ) )
     => ~ ! [X: nat,Y: nat] :
            ~ ( P2 @ Y @ X ) ) ).

% exE_realizer'
thf(fact_16_exE__realizer_H,axiom,
    ! [P2: multihole_mctxt_a_b > list_b > $o,P: produc5647625992154082286xt_a_b] :
      ( ( P2 @ ( produc6725609433235685644xt_a_b @ P ) @ ( produc6500241281145331658xt_a_b @ P ) )
     => ~ ! [X: list_b,Y: multihole_mctxt_a_b] :
            ~ ( P2 @ Y @ X ) ) ).

% exE_realizer'
thf(fact_17_exE__realizer_H,axiom,
    ! [P2: list_b > multihole_mctxt_a_b > $o,P: produc746580111399690912list_b] :
      ( ( P2 @ ( produc6107117247873403966list_b @ P ) @ ( produc5881749095783049980list_b @ P ) )
     => ~ ! [X: multihole_mctxt_a_b,Y: list_b] :
            ~ ( P2 @ Y @ X ) ) ).

% exE_realizer'
thf(fact_18_prod__eq__iff,axiom,
    ( ( ^ [Y2: produc1652119919080531751xt_a_b,Z: produc1652119919080531751xt_a_b] : ( Y2 = Z ) )
    = ( ^ [S: produc1652119919080531751xt_a_b,T: produc1652119919080531751xt_a_b] :
          ( ( ( produc2029583840371251459xt_a_b @ S )
            = ( produc2029583840371251459xt_a_b @ T ) )
          & ( ( produc4775144687201070661xt_a_b @ S )
            = ( produc4775144687201070661xt_a_b @ T ) ) ) ) ) ).

% prod_eq_iff
thf(fact_19_prod__eq__iff,axiom,
    ( ( ^ [Y2: produc3963297410138542439list_b,Z: produc3963297410138542439list_b] : ( Y2 = Z ) )
    = ( ^ [S: produc3963297410138542439list_b,T: produc3963297410138542439list_b] :
          ( ( ( produc7649009375908944835list_b @ S )
            = ( produc7649009375908944835list_b @ T ) )
          & ( ( produc3345134588468168965list_b @ S )
            = ( produc3345134588468168965list_b @ T ) ) ) ) ) ).

% prod_eq_iff
thf(fact_20_prod__eq__iff,axiom,
    ( ( ^ [Y2: product_prod_o_o,Z: product_prod_o_o] : ( Y2 = Z ) )
    = ( ^ [S: product_prod_o_o,T: product_prod_o_o] :
          ( ( ( product_fst_o_o @ S )
            = ( product_fst_o_o @ T ) )
          & ( ( product_snd_o_o @ S )
            = ( product_snd_o_o @ T ) ) ) ) ) ).

% prod_eq_iff
thf(fact_21_prod__eq__iff,axiom,
    ( ( ^ [Y2: product_prod_nat_nat,Z: product_prod_nat_nat] : ( Y2 = Z ) )
    = ( ^ [S: product_prod_nat_nat,T: product_prod_nat_nat] :
          ( ( ( product_fst_nat_nat @ S )
            = ( product_fst_nat_nat @ T ) )
          & ( ( product_snd_nat_nat @ S )
            = ( product_snd_nat_nat @ T ) ) ) ) ) ).

% prod_eq_iff
thf(fact_22_prod__eq__iff,axiom,
    ( ( ^ [Y2: produc5647625992154082286xt_a_b,Z: produc5647625992154082286xt_a_b] : ( Y2 = Z ) )
    = ( ^ [S: produc5647625992154082286xt_a_b,T: produc5647625992154082286xt_a_b] :
          ( ( ( produc6500241281145331658xt_a_b @ S )
            = ( produc6500241281145331658xt_a_b @ T ) )
          & ( ( produc6725609433235685644xt_a_b @ S )
            = ( produc6725609433235685644xt_a_b @ T ) ) ) ) ) ).

% prod_eq_iff
thf(fact_23_prod__eq__iff,axiom,
    ( ( ^ [Y2: produc746580111399690912list_b,Z: produc746580111399690912list_b] : ( Y2 = Z ) )
    = ( ^ [S: produc746580111399690912list_b,T: produc746580111399690912list_b] :
          ( ( ( produc5881749095783049980list_b @ S )
            = ( produc5881749095783049980list_b @ T ) )
          & ( ( produc6107117247873403966list_b @ S )
            = ( produc6107117247873403966list_b @ T ) ) ) ) ) ).

% prod_eq_iff
thf(fact_24_split__vars__vars__term__list,axiom,
    ! [T2: term_a_b] :
      ( ( produc6107117247873403966list_b @ ( multih5110136180555822405rs_a_b @ T2 ) )
      = ( vars_term_list_a_b @ T2 ) ) ).

% split_vars_vars_term_list
thf(fact_25_Ex__list__of__length,axiom,
    ! [N: nat] :
    ? [Xs: list_b] :
      ( ( size_size_list_b @ Xs )
      = N ) ).

% Ex_list_of_length
thf(fact_26_neq__if__length__neq,axiom,
    ! [Xs2: list_b,Ys: list_b] :
      ( ( ( size_size_list_b @ Xs2 )
       != ( size_size_list_b @ Ys ) )
     => ( Xs2 != Ys ) ) ).

% neq_if_length_neq
thf(fact_27_size__neq__size__imp__neq,axiom,
    ! [X2: list_b,Y3: list_b] :
      ( ( ( size_size_list_b @ X2 )
       != ( size_size_list_b @ Y3 ) )
     => ( X2 != Y3 ) ) ).

% size_neq_size_imp_neq
thf(fact_28_fst__swap,axiom,
    ! [X2: produc1652119919080531751xt_a_b] :
      ( ( produc2029583840371251459xt_a_b @ ( produc1108858440263912631xt_a_b @ X2 ) )
      = ( produc4775144687201070661xt_a_b @ X2 ) ) ).

% fst_swap
thf(fact_29_fst__swap,axiom,
    ! [X2: produc3963297410138542439list_b] :
      ( ( produc7649009375908944835list_b @ ( produc6495775440487448439list_b @ X2 ) )
      = ( produc3345134588468168965list_b @ X2 ) ) ).

% fst_swap
thf(fact_30_fst__swap,axiom,
    ! [X2: product_prod_o_o] :
      ( ( product_fst_o_o @ ( product_swap_o_o @ X2 ) )
      = ( product_snd_o_o @ X2 ) ) ).

% fst_swap
thf(fact_31_fst__swap,axiom,
    ! [X2: product_prod_nat_nat] :
      ( ( product_fst_nat_nat @ ( product_swap_nat_nat @ X2 ) )
      = ( product_snd_nat_nat @ X2 ) ) ).

% fst_swap
thf(fact_32_fst__swap,axiom,
    ! [X2: produc5647625992154082286xt_a_b] :
      ( ( produc5881749095783049980list_b @ ( produc4642366622444604286xt_a_b @ X2 ) )
      = ( produc6725609433235685644xt_a_b @ X2 ) ) ).

% fst_swap
thf(fact_33_fst__swap,axiom,
    ! [X2: produc746580111399690912list_b] :
      ( ( produc6500241281145331658xt_a_b @ ( produc4023874437082322608list_b @ X2 ) )
      = ( produc6107117247873403966list_b @ X2 ) ) ).

% fst_swap
thf(fact_34_snd__swap,axiom,
    ! [X2: produc1652119919080531751xt_a_b] :
      ( ( produc4775144687201070661xt_a_b @ ( produc1108858440263912631xt_a_b @ X2 ) )
      = ( produc2029583840371251459xt_a_b @ X2 ) ) ).

% snd_swap
thf(fact_35_snd__swap,axiom,
    ! [X2: produc3963297410138542439list_b] :
      ( ( produc3345134588468168965list_b @ ( produc6495775440487448439list_b @ X2 ) )
      = ( produc7649009375908944835list_b @ X2 ) ) ).

% snd_swap
thf(fact_36_snd__swap,axiom,
    ! [X2: product_prod_o_o] :
      ( ( product_snd_o_o @ ( product_swap_o_o @ X2 ) )
      = ( product_fst_o_o @ X2 ) ) ).

% snd_swap
thf(fact_37_snd__swap,axiom,
    ! [X2: product_prod_nat_nat] :
      ( ( product_snd_nat_nat @ ( product_swap_nat_nat @ X2 ) )
      = ( product_fst_nat_nat @ X2 ) ) ).

% snd_swap
thf(fact_38_snd__swap,axiom,
    ! [X2: produc746580111399690912list_b] :
      ( ( produc6725609433235685644xt_a_b @ ( produc4023874437082322608list_b @ X2 ) )
      = ( produc5881749095783049980list_b @ X2 ) ) ).

% snd_swap
thf(fact_39_snd__swap,axiom,
    ! [X2: produc5647625992154082286xt_a_b] :
      ( ( produc6107117247873403966list_b @ ( produc4642366622444604286xt_a_b @ X2 ) )
      = ( produc6500241281145331658xt_a_b @ X2 ) ) ).

% snd_swap
thf(fact_40_prod_Ocollapse,axiom,
    ! [Prod: produc1652119919080531751xt_a_b] :
      ( ( produc67882520014434071xt_a_b @ ( produc2029583840371251459xt_a_b @ Prod ) @ ( produc4775144687201070661xt_a_b @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_41_prod_Ocollapse,axiom,
    ! [Prod: produc3963297410138542439list_b] :
      ( ( produc1564554178308465111list_b @ ( produc7649009375908944835list_b @ Prod ) @ ( produc3345134588468168965list_b @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_42_prod_Ocollapse,axiom,
    ! [Prod: product_prod_o_o] :
      ( ( product_Pair_o_o @ ( product_fst_o_o @ Prod ) @ ( product_snd_o_o @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_43_prod_Ocollapse,axiom,
    ! [Prod: product_prod_nat_nat] :
      ( ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_44_prod_Ocollapse,axiom,
    ! [Prod: produc746580111399690912list_b] :
      ( ( produc8202881352235923728list_b @ ( produc5881749095783049980list_b @ Prod ) @ ( produc6107117247873403966list_b @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_45_prod_Ocollapse,axiom,
    ! [Prod: produc5647625992154082286xt_a_b] :
      ( ( produc8821373537598205406xt_a_b @ ( produc6500241281145331658xt_a_b @ Prod ) @ ( produc6725609433235685644xt_a_b @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_46_pred__prod__beta,axiom,
    ( basic_3223324150106804915xt_a_b
    = ( ^ [P3: multihole_mctxt_a_b > $o,Q2: multihole_mctxt_a_b > $o,Xy: produc1652119919080531751xt_a_b] :
          ( ( P3 @ ( produc2029583840371251459xt_a_b @ Xy ) )
          & ( Q2 @ ( produc4775144687201070661xt_a_b @ Xy ) ) ) ) ) ).

% pred_prod_beta
thf(fact_47_pred__prod__beta,axiom,
    ( basic_1932318408880543091list_b
    = ( ^ [P3: list_b > $o,Q2: list_b > $o,Xy: produc3963297410138542439list_b] :
          ( ( P3 @ ( produc7649009375908944835list_b @ Xy ) )
          & ( Q2 @ ( produc3345134588468168965list_b @ Xy ) ) ) ) ) ).

% pred_prod_beta
thf(fact_48_pred__prod__beta,axiom,
    ( basic_pred_prod_o_o
    = ( ^ [P3: $o > $o,Q2: $o > $o,Xy: product_prod_o_o] :
          ( ( P3 @ ( product_fst_o_o @ Xy ) )
          & ( Q2 @ ( product_snd_o_o @ Xy ) ) ) ) ) ).

% pred_prod_beta
thf(fact_49_pred__prod__beta,axiom,
    ( basic_570253317919918037at_nat
    = ( ^ [P3: nat > $o,Q2: nat > $o,Xy: product_prod_nat_nat] :
          ( ( P3 @ ( product_fst_nat_nat @ Xy ) )
          & ( Q2 @ ( product_snd_nat_nat @ Xy ) ) ) ) ) ).

% pred_prod_beta
thf(fact_50_pred__prod__beta,axiom,
    ( basic_5159020248174167212list_b
    = ( ^ [P3: multihole_mctxt_a_b > $o,Q2: list_b > $o,Xy: produc746580111399690912list_b] :
          ( ( P3 @ ( produc5881749095783049980list_b @ Xy ) )
          & ( Q2 @ ( produc6107117247873403966list_b @ Xy ) ) ) ) ) ).

% pred_prod_beta
thf(fact_51_pred__prod__beta,axiom,
    ( basic_5777512433536448890xt_a_b
    = ( ^ [P3: list_b > $o,Q2: multihole_mctxt_a_b > $o,Xy: produc5647625992154082286xt_a_b] :
          ( ( P3 @ ( produc6500241281145331658xt_a_b @ Xy ) )
          & ( Q2 @ ( produc6725609433235685644xt_a_b @ Xy ) ) ) ) ) ).

% pred_prod_beta
thf(fact_52_prod_Oinject,axiom,
    ! [X1: list_b,X22: multihole_mctxt_a_b,Y1: list_b,Y22: multihole_mctxt_a_b] :
      ( ( ( produc8821373537598205406xt_a_b @ X1 @ X22 )
        = ( produc8821373537598205406xt_a_b @ Y1 @ Y22 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y22 ) ) ) ).

% prod.inject
thf(fact_53_prod_Oinject,axiom,
    ! [X1: multihole_mctxt_a_b,X22: list_b,Y1: multihole_mctxt_a_b,Y22: list_b] :
      ( ( ( produc8202881352235923728list_b @ X1 @ X22 )
        = ( produc8202881352235923728list_b @ Y1 @ Y22 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y22 ) ) ) ).

% prod.inject
thf(fact_54_prod_Oinject,axiom,
    ! [X1: list_b,X22: list_b,Y1: list_b,Y22: list_b] :
      ( ( ( produc1564554178308465111list_b @ X1 @ X22 )
        = ( produc1564554178308465111list_b @ Y1 @ Y22 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y22 ) ) ) ).

% prod.inject
thf(fact_55_prod_Oinject,axiom,
    ! [X1: multihole_mctxt_a_b,X22: multihole_mctxt_a_b,Y1: multihole_mctxt_a_b,Y22: multihole_mctxt_a_b] :
      ( ( ( produc67882520014434071xt_a_b @ X1 @ X22 )
        = ( produc67882520014434071xt_a_b @ Y1 @ Y22 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y22 ) ) ) ).

% prod.inject
thf(fact_56_prod_Oinject,axiom,
    ! [X1: $o,X22: $o,Y1: $o,Y22: $o] :
      ( ( ( product_Pair_o_o @ X1 @ X22 )
        = ( product_Pair_o_o @ Y1 @ Y22 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y22 ) ) ) ).

% prod.inject
thf(fact_57_old_Oprod_Oinject,axiom,
    ! [A: list_b,B: multihole_mctxt_a_b,A2: list_b,B2: multihole_mctxt_a_b] :
      ( ( ( produc8821373537598205406xt_a_b @ A @ B )
        = ( produc8821373537598205406xt_a_b @ A2 @ B2 ) )
      = ( ( A = A2 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_58_old_Oprod_Oinject,axiom,
    ! [A: multihole_mctxt_a_b,B: list_b,A2: multihole_mctxt_a_b,B2: list_b] :
      ( ( ( produc8202881352235923728list_b @ A @ B )
        = ( produc8202881352235923728list_b @ A2 @ B2 ) )
      = ( ( A = A2 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_59_old_Oprod_Oinject,axiom,
    ! [A: list_b,B: list_b,A2: list_b,B2: list_b] :
      ( ( ( produc1564554178308465111list_b @ A @ B )
        = ( produc1564554178308465111list_b @ A2 @ B2 ) )
      = ( ( A = A2 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_60_old_Oprod_Oinject,axiom,
    ! [A: multihole_mctxt_a_b,B: multihole_mctxt_a_b,A2: multihole_mctxt_a_b,B2: multihole_mctxt_a_b] :
      ( ( ( produc67882520014434071xt_a_b @ A @ B )
        = ( produc67882520014434071xt_a_b @ A2 @ B2 ) )
      = ( ( A = A2 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_61_old_Oprod_Oinject,axiom,
    ! [A: $o,B: $o,A2: $o,B2: $o] :
      ( ( ( product_Pair_o_o @ A @ B )
        = ( product_Pair_o_o @ A2 @ B2 ) )
      = ( ( A = A2 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_62_swap__swap,axiom,
    ! [P: produc5647625992154082286xt_a_b] :
      ( ( produc4023874437082322608list_b @ ( produc4642366622444604286xt_a_b @ P ) )
      = P ) ).

% swap_swap
thf(fact_63_swap__swap,axiom,
    ! [P: produc746580111399690912list_b] :
      ( ( produc4642366622444604286xt_a_b @ ( produc4023874437082322608list_b @ P ) )
      = P ) ).

% swap_swap
thf(fact_64_swap__simp,axiom,
    ! [X2: list_b,Y3: list_b] :
      ( ( produc6495775440487448439list_b @ ( produc1564554178308465111list_b @ X2 @ Y3 ) )
      = ( produc1564554178308465111list_b @ Y3 @ X2 ) ) ).

% swap_simp
thf(fact_65_swap__simp,axiom,
    ! [X2: multihole_mctxt_a_b,Y3: multihole_mctxt_a_b] :
      ( ( produc1108858440263912631xt_a_b @ ( produc67882520014434071xt_a_b @ X2 @ Y3 ) )
      = ( produc67882520014434071xt_a_b @ Y3 @ X2 ) ) ).

% swap_simp
thf(fact_66_swap__simp,axiom,
    ! [X2: $o,Y3: $o] :
      ( ( product_swap_o_o @ ( product_Pair_o_o @ X2 @ Y3 ) )
      = ( product_Pair_o_o @ Y3 @ X2 ) ) ).

% swap_simp
thf(fact_67_swap__simp,axiom,
    ! [X2: multihole_mctxt_a_b,Y3: list_b] :
      ( ( produc4023874437082322608list_b @ ( produc8202881352235923728list_b @ X2 @ Y3 ) )
      = ( produc8821373537598205406xt_a_b @ Y3 @ X2 ) ) ).

% swap_simp
thf(fact_68_swap__simp,axiom,
    ! [X2: list_b,Y3: multihole_mctxt_a_b] :
      ( ( produc4642366622444604286xt_a_b @ ( produc8821373537598205406xt_a_b @ X2 @ Y3 ) )
      = ( produc8202881352235923728list_b @ Y3 @ X2 ) ) ).

% swap_simp
thf(fact_69_old_Oprod_Oexhaust,axiom,
    ! [Y3: produc5647625992154082286xt_a_b] :
      ~ ! [A3: list_b,B3: multihole_mctxt_a_b] :
          ( Y3
         != ( produc8821373537598205406xt_a_b @ A3 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_70_old_Oprod_Oexhaust,axiom,
    ! [Y3: produc746580111399690912list_b] :
      ~ ! [A3: multihole_mctxt_a_b,B3: list_b] :
          ( Y3
         != ( produc8202881352235923728list_b @ A3 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_71_old_Oprod_Oexhaust,axiom,
    ! [Y3: produc3963297410138542439list_b] :
      ~ ! [A3: list_b,B3: list_b] :
          ( Y3
         != ( produc1564554178308465111list_b @ A3 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_72_old_Oprod_Oexhaust,axiom,
    ! [Y3: produc1652119919080531751xt_a_b] :
      ~ ! [A3: multihole_mctxt_a_b,B3: multihole_mctxt_a_b] :
          ( Y3
         != ( produc67882520014434071xt_a_b @ A3 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_73_old_Oprod_Oexhaust,axiom,
    ! [Y3: product_prod_o_o] :
      ~ ! [A3: $o,B3: $o] :
          ( Y3
         != ( product_Pair_o_o @ A3 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_74_surj__pair,axiom,
    ! [P: produc5647625992154082286xt_a_b] :
    ? [X: list_b,Y: multihole_mctxt_a_b] :
      ( P
      = ( produc8821373537598205406xt_a_b @ X @ Y ) ) ).

% surj_pair
thf(fact_75_surj__pair,axiom,
    ! [P: produc746580111399690912list_b] :
    ? [X: multihole_mctxt_a_b,Y: list_b] :
      ( P
      = ( produc8202881352235923728list_b @ X @ Y ) ) ).

% surj_pair
thf(fact_76_surj__pair,axiom,
    ! [P: produc3963297410138542439list_b] :
    ? [X: list_b,Y: list_b] :
      ( P
      = ( produc1564554178308465111list_b @ X @ Y ) ) ).

% surj_pair
thf(fact_77_surj__pair,axiom,
    ! [P: produc1652119919080531751xt_a_b] :
    ? [X: multihole_mctxt_a_b,Y: multihole_mctxt_a_b] :
      ( P
      = ( produc67882520014434071xt_a_b @ X @ Y ) ) ).

% surj_pair
thf(fact_78_surj__pair,axiom,
    ! [P: product_prod_o_o] :
    ? [X: $o,Y: $o] :
      ( P
      = ( product_Pair_o_o @ X @ Y ) ) ).

% surj_pair
thf(fact_79_pred__prod__split,axiom,
    ! [P2: $o > $o,Q3: list_b > $o,R: list_b > $o,Xy2: produc3963297410138542439list_b] :
      ( ( P2 @ ( basic_1932318408880543091list_b @ Q3 @ R @ Xy2 ) )
      = ( ! [X3: list_b,Y4: list_b] :
            ( ( Xy2
              = ( produc1564554178308465111list_b @ X3 @ Y4 ) )
           => ( P2
              @ ( ( Q3 @ X3 )
                & ( R @ Y4 ) ) ) ) ) ) ).

% pred_prod_split
thf(fact_80_pred__prod__split,axiom,
    ! [P2: $o > $o,Q3: multihole_mctxt_a_b > $o,R: multihole_mctxt_a_b > $o,Xy2: produc1652119919080531751xt_a_b] :
      ( ( P2 @ ( basic_3223324150106804915xt_a_b @ Q3 @ R @ Xy2 ) )
      = ( ! [X3: multihole_mctxt_a_b,Y4: multihole_mctxt_a_b] :
            ( ( Xy2
              = ( produc67882520014434071xt_a_b @ X3 @ Y4 ) )
           => ( P2
              @ ( ( Q3 @ X3 )
                & ( R @ Y4 ) ) ) ) ) ) ).

% pred_prod_split
thf(fact_81_pred__prod__split,axiom,
    ! [P2: $o > $o,Q3: $o > $o,R: $o > $o,Xy2: product_prod_o_o] :
      ( ( P2 @ ( basic_pred_prod_o_o @ Q3 @ R @ Xy2 ) )
      = ( ! [X3: $o,Y4: $o] :
            ( ( Xy2
              = ( product_Pair_o_o @ X3 @ Y4 ) )
           => ( P2
              @ ( ( Q3 @ X3 )
                & ( R @ Y4 ) ) ) ) ) ) ).

% pred_prod_split
thf(fact_82_pred__prod__split,axiom,
    ! [P2: $o > $o,Q3: list_b > $o,R: multihole_mctxt_a_b > $o,Xy2: produc5647625992154082286xt_a_b] :
      ( ( P2 @ ( basic_5777512433536448890xt_a_b @ Q3 @ R @ Xy2 ) )
      = ( ! [X3: list_b,Y4: multihole_mctxt_a_b] :
            ( ( Xy2
              = ( produc8821373537598205406xt_a_b @ X3 @ Y4 ) )
           => ( P2
              @ ( ( Q3 @ X3 )
                & ( R @ Y4 ) ) ) ) ) ) ).

% pred_prod_split
thf(fact_83_pred__prod__split,axiom,
    ! [P2: $o > $o,Q3: multihole_mctxt_a_b > $o,R: list_b > $o,Xy2: produc746580111399690912list_b] :
      ( ( P2 @ ( basic_5159020248174167212list_b @ Q3 @ R @ Xy2 ) )
      = ( ! [X3: multihole_mctxt_a_b,Y4: list_b] :
            ( ( Xy2
              = ( produc8202881352235923728list_b @ X3 @ Y4 ) )
           => ( P2
              @ ( ( Q3 @ X3 )
                & ( R @ Y4 ) ) ) ) ) ) ).

% pred_prod_split
thf(fact_84_prod__cases,axiom,
    ! [P2: produc5647625992154082286xt_a_b > $o,P: produc5647625992154082286xt_a_b] :
      ( ! [A3: list_b,B3: multihole_mctxt_a_b] : ( P2 @ ( produc8821373537598205406xt_a_b @ A3 @ B3 ) )
     => ( P2 @ P ) ) ).

% prod_cases
thf(fact_85_prod__cases,axiom,
    ! [P2: produc746580111399690912list_b > $o,P: produc746580111399690912list_b] :
      ( ! [A3: multihole_mctxt_a_b,B3: list_b] : ( P2 @ ( produc8202881352235923728list_b @ A3 @ B3 ) )
     => ( P2 @ P ) ) ).

% prod_cases
thf(fact_86_prod__cases,axiom,
    ! [P2: produc3963297410138542439list_b > $o,P: produc3963297410138542439list_b] :
      ( ! [A3: list_b,B3: list_b] : ( P2 @ ( produc1564554178308465111list_b @ A3 @ B3 ) )
     => ( P2 @ P ) ) ).

% prod_cases
thf(fact_87_prod__cases,axiom,
    ! [P2: produc1652119919080531751xt_a_b > $o,P: produc1652119919080531751xt_a_b] :
      ( ! [A3: multihole_mctxt_a_b,B3: multihole_mctxt_a_b] : ( P2 @ ( produc67882520014434071xt_a_b @ A3 @ B3 ) )
     => ( P2 @ P ) ) ).

% prod_cases
thf(fact_88_prod__cases,axiom,
    ! [P2: product_prod_o_o > $o,P: product_prod_o_o] :
      ( ! [A3: $o,B3: $o] : ( P2 @ ( product_Pair_o_o @ A3 @ B3 ) )
     => ( P2 @ P ) ) ).

% prod_cases
thf(fact_89_Pair__inject,axiom,
    ! [A: list_b,B: multihole_mctxt_a_b,A2: list_b,B2: multihole_mctxt_a_b] :
      ( ( ( produc8821373537598205406xt_a_b @ A @ B )
        = ( produc8821373537598205406xt_a_b @ A2 @ B2 ) )
     => ~ ( ( A = A2 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_90_Pair__inject,axiom,
    ! [A: multihole_mctxt_a_b,B: list_b,A2: multihole_mctxt_a_b,B2: list_b] :
      ( ( ( produc8202881352235923728list_b @ A @ B )
        = ( produc8202881352235923728list_b @ A2 @ B2 ) )
     => ~ ( ( A = A2 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_91_Pair__inject,axiom,
    ! [A: list_b,B: list_b,A2: list_b,B2: list_b] :
      ( ( ( produc1564554178308465111list_b @ A @ B )
        = ( produc1564554178308465111list_b @ A2 @ B2 ) )
     => ~ ( ( A = A2 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_92_Pair__inject,axiom,
    ! [A: multihole_mctxt_a_b,B: multihole_mctxt_a_b,A2: multihole_mctxt_a_b,B2: multihole_mctxt_a_b] :
      ( ( ( produc67882520014434071xt_a_b @ A @ B )
        = ( produc67882520014434071xt_a_b @ A2 @ B2 ) )
     => ~ ( ( A = A2 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_93_Pair__inject,axiom,
    ! [A: $o,B: $o,A2: $o,B2: $o] :
      ( ( ( product_Pair_o_o @ A @ B )
        = ( product_Pair_o_o @ A2 @ B2 ) )
     => ~ ( ( A = A2 )
         => ( B = ~ B2 ) ) ) ).

% Pair_inject
thf(fact_94_fst__conv,axiom,
    ! [X1: list_b,X22: list_b] :
      ( ( produc7649009375908944835list_b @ ( produc1564554178308465111list_b @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_95_fst__conv,axiom,
    ! [X1: multihole_mctxt_a_b,X22: multihole_mctxt_a_b] :
      ( ( produc2029583840371251459xt_a_b @ ( produc67882520014434071xt_a_b @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_96_fst__conv,axiom,
    ! [X1: $o,X22: $o] :
      ( ( product_fst_o_o @ ( product_Pair_o_o @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_97_fst__conv,axiom,
    ! [X1: nat,X22: nat] :
      ( ( product_fst_nat_nat @ ( product_Pair_nat_nat @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_98_fst__conv,axiom,
    ! [X1: multihole_mctxt_a_b,X22: list_b] :
      ( ( produc5881749095783049980list_b @ ( produc8202881352235923728list_b @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_99_fst__conv,axiom,
    ! [X1: list_b,X22: multihole_mctxt_a_b] :
      ( ( produc6500241281145331658xt_a_b @ ( produc8821373537598205406xt_a_b @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_100_fst__eqD,axiom,
    ! [X2: list_b,Y3: list_b,A: list_b] :
      ( ( ( produc7649009375908944835list_b @ ( produc1564554178308465111list_b @ X2 @ Y3 ) )
        = A )
     => ( X2 = A ) ) ).

% fst_eqD
thf(fact_101_fst__eqD,axiom,
    ! [X2: multihole_mctxt_a_b,Y3: multihole_mctxt_a_b,A: multihole_mctxt_a_b] :
      ( ( ( produc2029583840371251459xt_a_b @ ( produc67882520014434071xt_a_b @ X2 @ Y3 ) )
        = A )
     => ( X2 = A ) ) ).

% fst_eqD
thf(fact_102_fst__eqD,axiom,
    ! [X2: $o,Y3: $o,A: $o] :
      ( ( ( product_fst_o_o @ ( product_Pair_o_o @ X2 @ Y3 ) )
        = A )
     => ( X2 = A ) ) ).

% fst_eqD
thf(fact_103_fst__eqD,axiom,
    ! [X2: nat,Y3: nat,A: nat] :
      ( ( ( product_fst_nat_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) )
        = A )
     => ( X2 = A ) ) ).

% fst_eqD
thf(fact_104_fst__eqD,axiom,
    ! [X2: multihole_mctxt_a_b,Y3: list_b,A: multihole_mctxt_a_b] :
      ( ( ( produc5881749095783049980list_b @ ( produc8202881352235923728list_b @ X2 @ Y3 ) )
        = A )
     => ( X2 = A ) ) ).

% fst_eqD
thf(fact_105_fst__eqD,axiom,
    ! [X2: list_b,Y3: multihole_mctxt_a_b,A: list_b] :
      ( ( ( produc6500241281145331658xt_a_b @ ( produc8821373537598205406xt_a_b @ X2 @ Y3 ) )
        = A )
     => ( X2 = A ) ) ).

% fst_eqD
thf(fact_106_snd__conv,axiom,
    ! [X1: multihole_mctxt_a_b,X22: multihole_mctxt_a_b] :
      ( ( produc4775144687201070661xt_a_b @ ( produc67882520014434071xt_a_b @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_107_snd__conv,axiom,
    ! [X1: list_b,X22: list_b] :
      ( ( produc3345134588468168965list_b @ ( produc1564554178308465111list_b @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_108_snd__conv,axiom,
    ! [X1: $o,X22: $o] :
      ( ( product_snd_o_o @ ( product_Pair_o_o @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_109_snd__conv,axiom,
    ! [X1: nat,X22: nat] :
      ( ( product_snd_nat_nat @ ( product_Pair_nat_nat @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_110_snd__conv,axiom,
    ! [X1: multihole_mctxt_a_b,X22: list_b] :
      ( ( produc6107117247873403966list_b @ ( produc8202881352235923728list_b @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_111_snd__conv,axiom,
    ! [X1: list_b,X22: multihole_mctxt_a_b] :
      ( ( produc6725609433235685644xt_a_b @ ( produc8821373537598205406xt_a_b @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_112_snd__eqD,axiom,
    ! [X2: multihole_mctxt_a_b,Y3: multihole_mctxt_a_b,A: multihole_mctxt_a_b] :
      ( ( ( produc4775144687201070661xt_a_b @ ( produc67882520014434071xt_a_b @ X2 @ Y3 ) )
        = A )
     => ( Y3 = A ) ) ).

% snd_eqD
thf(fact_113_snd__eqD,axiom,
    ! [X2: list_b,Y3: list_b,A: list_b] :
      ( ( ( produc3345134588468168965list_b @ ( produc1564554178308465111list_b @ X2 @ Y3 ) )
        = A )
     => ( Y3 = A ) ) ).

% snd_eqD
thf(fact_114_snd__eqD,axiom,
    ! [X2: $o,Y3: $o,A: $o] :
      ( ( ( product_snd_o_o @ ( product_Pair_o_o @ X2 @ Y3 ) )
        = A )
     => ( Y3 = A ) ) ).

% snd_eqD
thf(fact_115_snd__eqD,axiom,
    ! [X2: nat,Y3: nat,A: nat] :
      ( ( ( product_snd_nat_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) )
        = A )
     => ( Y3 = A ) ) ).

% snd_eqD
thf(fact_116_snd__eqD,axiom,
    ! [X2: multihole_mctxt_a_b,Y3: list_b,A: list_b] :
      ( ( ( produc6107117247873403966list_b @ ( produc8202881352235923728list_b @ X2 @ Y3 ) )
        = A )
     => ( Y3 = A ) ) ).

% snd_eqD
thf(fact_117_snd__eqD,axiom,
    ! [X2: list_b,Y3: multihole_mctxt_a_b,A: multihole_mctxt_a_b] :
      ( ( ( produc6725609433235685644xt_a_b @ ( produc8821373537598205406xt_a_b @ X2 @ Y3 ) )
        = A )
     => ( Y3 = A ) ) ).

% snd_eqD
thf(fact_118_prod_Oswap__def,axiom,
    ( produc1108858440263912631xt_a_b
    = ( ^ [P4: produc1652119919080531751xt_a_b] : ( produc67882520014434071xt_a_b @ ( produc4775144687201070661xt_a_b @ P4 ) @ ( produc2029583840371251459xt_a_b @ P4 ) ) ) ) ).

% prod.swap_def
thf(fact_119_prod_Oswap__def,axiom,
    ( produc6495775440487448439list_b
    = ( ^ [P4: produc3963297410138542439list_b] : ( produc1564554178308465111list_b @ ( produc3345134588468168965list_b @ P4 ) @ ( produc7649009375908944835list_b @ P4 ) ) ) ) ).

% prod.swap_def
thf(fact_120_prod_Oswap__def,axiom,
    ( product_swap_o_o
    = ( ^ [P4: product_prod_o_o] : ( product_Pair_o_o @ ( product_snd_o_o @ P4 ) @ ( product_fst_o_o @ P4 ) ) ) ) ).

% prod.swap_def
thf(fact_121_prod_Oswap__def,axiom,
    ( product_swap_nat_nat
    = ( ^ [P4: product_prod_nat_nat] : ( product_Pair_nat_nat @ ( product_snd_nat_nat @ P4 ) @ ( product_fst_nat_nat @ P4 ) ) ) ) ).

% prod.swap_def
thf(fact_122_prod_Oswap__def,axiom,
    ( produc4023874437082322608list_b
    = ( ^ [P4: produc746580111399690912list_b] : ( produc8821373537598205406xt_a_b @ ( produc6107117247873403966list_b @ P4 ) @ ( produc5881749095783049980list_b @ P4 ) ) ) ) ).

% prod.swap_def
thf(fact_123_prod_Oswap__def,axiom,
    ( produc4642366622444604286xt_a_b
    = ( ^ [P4: produc5647625992154082286xt_a_b] : ( produc8202881352235923728list_b @ ( produc6725609433235685644xt_a_b @ P4 ) @ ( produc6500241281145331658xt_a_b @ P4 ) ) ) ) ).

% prod.swap_def
thf(fact_124_surjective__pairing,axiom,
    ! [T2: produc1652119919080531751xt_a_b] :
      ( T2
      = ( produc67882520014434071xt_a_b @ ( produc2029583840371251459xt_a_b @ T2 ) @ ( produc4775144687201070661xt_a_b @ T2 ) ) ) ).

% surjective_pairing
thf(fact_125_surjective__pairing,axiom,
    ! [T2: produc3963297410138542439list_b] :
      ( T2
      = ( produc1564554178308465111list_b @ ( produc7649009375908944835list_b @ T2 ) @ ( produc3345134588468168965list_b @ T2 ) ) ) ).

% surjective_pairing
thf(fact_126_surjective__pairing,axiom,
    ! [T2: product_prod_o_o] :
      ( T2
      = ( product_Pair_o_o @ ( product_fst_o_o @ T2 ) @ ( product_snd_o_o @ T2 ) ) ) ).

% surjective_pairing
thf(fact_127_surjective__pairing,axiom,
    ! [T2: product_prod_nat_nat] :
      ( T2
      = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ T2 ) @ ( product_snd_nat_nat @ T2 ) ) ) ).

% surjective_pairing
thf(fact_128_surjective__pairing,axiom,
    ! [T2: produc746580111399690912list_b] :
      ( T2
      = ( produc8202881352235923728list_b @ ( produc5881749095783049980list_b @ T2 ) @ ( produc6107117247873403966list_b @ T2 ) ) ) ).

% surjective_pairing
thf(fact_129_surjective__pairing,axiom,
    ! [T2: produc5647625992154082286xt_a_b] :
      ( T2
      = ( produc8821373537598205406xt_a_b @ ( produc6500241281145331658xt_a_b @ T2 ) @ ( produc6725609433235685644xt_a_b @ T2 ) ) ) ).

% surjective_pairing
thf(fact_130_conjI__realizer,axiom,
    ! [P2: multihole_mctxt_a_b > $o,P: multihole_mctxt_a_b,Q3: multihole_mctxt_a_b > $o,Q: multihole_mctxt_a_b] :
      ( ( P2 @ P )
     => ( ( Q3 @ Q )
       => ( ( P2 @ ( produc2029583840371251459xt_a_b @ ( produc67882520014434071xt_a_b @ P @ Q ) ) )
          & ( Q3 @ ( produc4775144687201070661xt_a_b @ ( produc67882520014434071xt_a_b @ P @ Q ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_131_conjI__realizer,axiom,
    ! [P2: list_b > $o,P: list_b,Q3: list_b > $o,Q: list_b] :
      ( ( P2 @ P )
     => ( ( Q3 @ Q )
       => ( ( P2 @ ( produc7649009375908944835list_b @ ( produc1564554178308465111list_b @ P @ Q ) ) )
          & ( Q3 @ ( produc3345134588468168965list_b @ ( produc1564554178308465111list_b @ P @ Q ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_132_conjI__realizer,axiom,
    ! [P2: $o > $o,P: $o,Q3: $o > $o,Q: $o] :
      ( ( P2 @ P )
     => ( ( Q3 @ Q )
       => ( ( P2 @ ( product_fst_o_o @ ( product_Pair_o_o @ P @ Q ) ) )
          & ( Q3 @ ( product_snd_o_o @ ( product_Pair_o_o @ P @ Q ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_133_conjI__realizer,axiom,
    ! [P2: nat > $o,P: nat,Q3: nat > $o,Q: nat] :
      ( ( P2 @ P )
     => ( ( Q3 @ Q )
       => ( ( P2 @ ( product_fst_nat_nat @ ( product_Pair_nat_nat @ P @ Q ) ) )
          & ( Q3 @ ( product_snd_nat_nat @ ( product_Pair_nat_nat @ P @ Q ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_134_conjI__realizer,axiom,
    ! [P2: multihole_mctxt_a_b > $o,P: multihole_mctxt_a_b,Q3: list_b > $o,Q: list_b] :
      ( ( P2 @ P )
     => ( ( Q3 @ Q )
       => ( ( P2 @ ( produc5881749095783049980list_b @ ( produc8202881352235923728list_b @ P @ Q ) ) )
          & ( Q3 @ ( produc6107117247873403966list_b @ ( produc8202881352235923728list_b @ P @ Q ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_135_conjI__realizer,axiom,
    ! [P2: list_b > $o,P: list_b,Q3: multihole_mctxt_a_b > $o,Q: multihole_mctxt_a_b] :
      ( ( P2 @ P )
     => ( ( Q3 @ Q )
       => ( ( P2 @ ( produc6500241281145331658xt_a_b @ ( produc8821373537598205406xt_a_b @ P @ Q ) ) )
          & ( Q3 @ ( produc6725609433235685644xt_a_b @ ( produc8821373537598205406xt_a_b @ P @ Q ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_136_exI__realizer,axiom,
    ! [P2: multihole_mctxt_a_b > multihole_mctxt_a_b > $o,Y3: multihole_mctxt_a_b,X2: multihole_mctxt_a_b] :
      ( ( P2 @ Y3 @ X2 )
     => ( P2 @ ( produc4775144687201070661xt_a_b @ ( produc67882520014434071xt_a_b @ X2 @ Y3 ) ) @ ( produc2029583840371251459xt_a_b @ ( produc67882520014434071xt_a_b @ X2 @ Y3 ) ) ) ) ).

% exI_realizer
thf(fact_137_exI__realizer,axiom,
    ! [P2: list_b > list_b > $o,Y3: list_b,X2: list_b] :
      ( ( P2 @ Y3 @ X2 )
     => ( P2 @ ( produc3345134588468168965list_b @ ( produc1564554178308465111list_b @ X2 @ Y3 ) ) @ ( produc7649009375908944835list_b @ ( produc1564554178308465111list_b @ X2 @ Y3 ) ) ) ) ).

% exI_realizer
thf(fact_138_exI__realizer,axiom,
    ! [P2: $o > $o > $o,Y3: $o,X2: $o] :
      ( ( P2 @ Y3 @ X2 )
     => ( P2 @ ( product_snd_o_o @ ( product_Pair_o_o @ X2 @ Y3 ) ) @ ( product_fst_o_o @ ( product_Pair_o_o @ X2 @ Y3 ) ) ) ) ).

% exI_realizer
thf(fact_139_exI__realizer,axiom,
    ! [P2: nat > nat > $o,Y3: nat,X2: nat] :
      ( ( P2 @ Y3 @ X2 )
     => ( P2 @ ( product_snd_nat_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) ) @ ( product_fst_nat_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) ) ) ) ).

% exI_realizer
thf(fact_140_exI__realizer,axiom,
    ! [P2: list_b > multihole_mctxt_a_b > $o,Y3: list_b,X2: multihole_mctxt_a_b] :
      ( ( P2 @ Y3 @ X2 )
     => ( P2 @ ( produc6107117247873403966list_b @ ( produc8202881352235923728list_b @ X2 @ Y3 ) ) @ ( produc5881749095783049980list_b @ ( produc8202881352235923728list_b @ X2 @ Y3 ) ) ) ) ).

% exI_realizer
thf(fact_141_exI__realizer,axiom,
    ! [P2: multihole_mctxt_a_b > list_b > $o,Y3: multihole_mctxt_a_b,X2: list_b] :
      ( ( P2 @ Y3 @ X2 )
     => ( P2 @ ( produc6725609433235685644xt_a_b @ ( produc8821373537598205406xt_a_b @ X2 @ Y3 ) ) @ ( produc6500241281145331658xt_a_b @ ( produc8821373537598205406xt_a_b @ X2 @ Y3 ) ) ) ) ).

% exI_realizer
thf(fact_142_prod_Oexhaust__sel,axiom,
    ! [Prod: produc1652119919080531751xt_a_b] :
      ( Prod
      = ( produc67882520014434071xt_a_b @ ( produc2029583840371251459xt_a_b @ Prod ) @ ( produc4775144687201070661xt_a_b @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_143_prod_Oexhaust__sel,axiom,
    ! [Prod: produc3963297410138542439list_b] :
      ( Prod
      = ( produc1564554178308465111list_b @ ( produc7649009375908944835list_b @ Prod ) @ ( produc3345134588468168965list_b @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_144_prod_Oexhaust__sel,axiom,
    ! [Prod: product_prod_o_o] :
      ( Prod
      = ( product_Pair_o_o @ ( product_fst_o_o @ Prod ) @ ( product_snd_o_o @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_145_prod_Oexhaust__sel,axiom,
    ! [Prod: product_prod_nat_nat] :
      ( Prod
      = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_146_prod_Oexhaust__sel,axiom,
    ! [Prod: produc746580111399690912list_b] :
      ( Prod
      = ( produc8202881352235923728list_b @ ( produc5881749095783049980list_b @ Prod ) @ ( produc6107117247873403966list_b @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_147_prod_Oexhaust__sel,axiom,
    ! [Prod: produc5647625992154082286xt_a_b] :
      ( Prod
      = ( produc8821373537598205406xt_a_b @ ( produc6500241281145331658xt_a_b @ Prod ) @ ( produc6725609433235685644xt_a_b @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_148_pred__prod__inject,axiom,
    ! [P1: list_b > $o,P22: list_b > $o,A: list_b,B: list_b] :
      ( ( basic_1932318408880543091list_b @ P1 @ P22 @ ( produc1564554178308465111list_b @ A @ B ) )
      = ( ( P1 @ A )
        & ( P22 @ B ) ) ) ).

% pred_prod_inject
thf(fact_149_pred__prod__inject,axiom,
    ! [P1: multihole_mctxt_a_b > $o,P22: multihole_mctxt_a_b > $o,A: multihole_mctxt_a_b,B: multihole_mctxt_a_b] :
      ( ( basic_3223324150106804915xt_a_b @ P1 @ P22 @ ( produc67882520014434071xt_a_b @ A @ B ) )
      = ( ( P1 @ A )
        & ( P22 @ B ) ) ) ).

% pred_prod_inject
thf(fact_150_pred__prod__inject,axiom,
    ! [P1: $o > $o,P22: $o > $o,A: $o,B: $o] :
      ( ( basic_pred_prod_o_o @ P1 @ P22 @ ( product_Pair_o_o @ A @ B ) )
      = ( ( P1 @ A )
        & ( P22 @ B ) ) ) ).

% pred_prod_inject
thf(fact_151_pred__prod__inject,axiom,
    ! [P1: list_b > $o,P22: multihole_mctxt_a_b > $o,A: list_b,B: multihole_mctxt_a_b] :
      ( ( basic_5777512433536448890xt_a_b @ P1 @ P22 @ ( produc8821373537598205406xt_a_b @ A @ B ) )
      = ( ( P1 @ A )
        & ( P22 @ B ) ) ) ).

% pred_prod_inject
thf(fact_152_pred__prod__inject,axiom,
    ! [P1: multihole_mctxt_a_b > $o,P22: list_b > $o,A: multihole_mctxt_a_b,B: list_b] :
      ( ( basic_5159020248174167212list_b @ P1 @ P22 @ ( produc8202881352235923728list_b @ A @ B ) )
      = ( ( P1 @ A )
        & ( P22 @ B ) ) ) ).

% pred_prod_inject
thf(fact_153_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P2: multihole_mctxt_a_b > multihole_mctxt_a_b > $o,X2: multihole_mctxt_a_b,Y3: multihole_mctxt_a_b,A: produc1652119919080531751xt_a_b] :
      ( ( P2 @ X2 @ Y3 )
     => ( ( A
          = ( produc67882520014434071xt_a_b @ X2 @ Y3 ) )
       => ( P2 @ ( produc2029583840371251459xt_a_b @ A ) @ ( produc4775144687201070661xt_a_b @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_154_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P2: list_b > list_b > $o,X2: list_b,Y3: list_b,A: produc3963297410138542439list_b] :
      ( ( P2 @ X2 @ Y3 )
     => ( ( A
          = ( produc1564554178308465111list_b @ X2 @ Y3 ) )
       => ( P2 @ ( produc7649009375908944835list_b @ A ) @ ( produc3345134588468168965list_b @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_155_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P2: $o > $o > $o,X2: $o,Y3: $o,A: product_prod_o_o] :
      ( ( P2 @ X2 @ Y3 )
     => ( ( A
          = ( product_Pair_o_o @ X2 @ Y3 ) )
       => ( P2 @ ( product_fst_o_o @ A ) @ ( product_snd_o_o @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_156_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P2: nat > nat > $o,X2: nat,Y3: nat,A: product_prod_nat_nat] :
      ( ( P2 @ X2 @ Y3 )
     => ( ( A
          = ( product_Pair_nat_nat @ X2 @ Y3 ) )
       => ( P2 @ ( product_fst_nat_nat @ A ) @ ( product_snd_nat_nat @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_157_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P2: multihole_mctxt_a_b > list_b > $o,X2: multihole_mctxt_a_b,Y3: list_b,A: produc746580111399690912list_b] :
      ( ( P2 @ X2 @ Y3 )
     => ( ( A
          = ( produc8202881352235923728list_b @ X2 @ Y3 ) )
       => ( P2 @ ( produc5881749095783049980list_b @ A ) @ ( produc6107117247873403966list_b @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_158_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P2: list_b > multihole_mctxt_a_b > $o,X2: list_b,Y3: multihole_mctxt_a_b,A: produc5647625992154082286xt_a_b] :
      ( ( P2 @ X2 @ Y3 )
     => ( ( A
          = ( produc8821373537598205406xt_a_b @ X2 @ Y3 ) )
       => ( P2 @ ( produc6500241281145331658xt_a_b @ A ) @ ( produc6725609433235685644xt_a_b @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_159_pred__prod_Ocases,axiom,
    ! [P1: list_b > $o,P22: list_b > $o,A: produc3963297410138542439list_b] :
      ( ( basic_1932318408880543091list_b @ P1 @ P22 @ A )
     => ~ ! [A3: list_b,B3: list_b] :
            ( ( A
              = ( produc1564554178308465111list_b @ A3 @ B3 ) )
           => ( ( P1 @ A3 )
             => ~ ( P22 @ B3 ) ) ) ) ).

% pred_prod.cases
thf(fact_160_pred__prod_Ocases,axiom,
    ! [P1: multihole_mctxt_a_b > $o,P22: multihole_mctxt_a_b > $o,A: produc1652119919080531751xt_a_b] :
      ( ( basic_3223324150106804915xt_a_b @ P1 @ P22 @ A )
     => ~ ! [A3: multihole_mctxt_a_b,B3: multihole_mctxt_a_b] :
            ( ( A
              = ( produc67882520014434071xt_a_b @ A3 @ B3 ) )
           => ( ( P1 @ A3 )
             => ~ ( P22 @ B3 ) ) ) ) ).

% pred_prod.cases
thf(fact_161_pred__prod_Ocases,axiom,
    ! [P1: $o > $o,P22: $o > $o,A: product_prod_o_o] :
      ( ( basic_pred_prod_o_o @ P1 @ P22 @ A )
     => ~ ! [A3: $o,B3: $o] :
            ( ( A
              = ( product_Pair_o_o @ A3 @ B3 ) )
           => ( ( P1 @ A3 )
             => ~ ( P22 @ B3 ) ) ) ) ).

% pred_prod.cases
thf(fact_162_pred__prod_Ocases,axiom,
    ! [P1: list_b > $o,P22: multihole_mctxt_a_b > $o,A: produc5647625992154082286xt_a_b] :
      ( ( basic_5777512433536448890xt_a_b @ P1 @ P22 @ A )
     => ~ ! [A3: list_b,B3: multihole_mctxt_a_b] :
            ( ( A
              = ( produc8821373537598205406xt_a_b @ A3 @ B3 ) )
           => ( ( P1 @ A3 )
             => ~ ( P22 @ B3 ) ) ) ) ).

% pred_prod.cases
thf(fact_163_pred__prod_Ocases,axiom,
    ! [P1: multihole_mctxt_a_b > $o,P22: list_b > $o,A: produc746580111399690912list_b] :
      ( ( basic_5159020248174167212list_b @ P1 @ P22 @ A )
     => ~ ! [A3: multihole_mctxt_a_b,B3: list_b] :
            ( ( A
              = ( produc8202881352235923728list_b @ A3 @ B3 ) )
           => ( ( P1 @ A3 )
             => ~ ( P22 @ B3 ) ) ) ) ).

% pred_prod.cases
thf(fact_164_mem__Collect__eq,axiom,
    ! [A: list_b,P2: list_b > $o] :
      ( ( member_list_b @ A @ ( collect_list_b @ P2 ) )
      = ( P2 @ A ) ) ).

% mem_Collect_eq
thf(fact_165_mem__Collect__eq,axiom,
    ! [A: set_o,P2: set_o > $o] :
      ( ( member_set_o @ A @ ( collect_set_o @ P2 ) )
      = ( P2 @ A ) ) ).

% mem_Collect_eq
thf(fact_166_mem__Collect__eq,axiom,
    ! [A: nat,P2: nat > $o] :
      ( ( member_nat @ A @ ( collect_nat @ P2 ) )
      = ( P2 @ A ) ) ).

% mem_Collect_eq
thf(fact_167_mem__Collect__eq,axiom,
    ! [A: nat > produc746580111399690912list_b,P2: ( nat > produc746580111399690912list_b ) > $o] :
      ( ( member1851140327238222640list_b @ A @ ( collec6966152917764800626list_b @ P2 ) )
      = ( P2 @ A ) ) ).

% mem_Collect_eq
thf(fact_168_mem__Collect__eq,axiom,
    ! [A: nat > produc5647625992154082286xt_a_b,P2: ( nat > produc5647625992154082286xt_a_b ) > $o] :
      ( ( member3828642050509981054xt_a_b @ A @ ( collec8943654641036559040xt_a_b @ P2 ) )
      = ( P2 @ A ) ) ).

% mem_Collect_eq
thf(fact_169_mem__Collect__eq,axiom,
    ! [A: nat > nat,P2: ( nat > nat ) > $o] :
      ( ( member_nat_nat @ A @ ( collect_nat_nat @ P2 ) )
      = ( P2 @ A ) ) ).

% mem_Collect_eq
thf(fact_170_mem__Collect__eq,axiom,
    ! [A: $o,P2: $o > $o] :
      ( ( member_o @ A @ ( collect_o @ P2 ) )
      = ( P2 @ A ) ) ).

% mem_Collect_eq
thf(fact_171_Collect__mem__eq,axiom,
    ! [A4: set_list_b] :
      ( ( collect_list_b
        @ ^ [X3: list_b] : ( member_list_b @ X3 @ A4 ) )
      = A4 ) ).

% Collect_mem_eq
thf(fact_172_Collect__mem__eq,axiom,
    ! [A4: set_set_o] :
      ( ( collect_set_o
        @ ^ [X3: set_o] : ( member_set_o @ X3 @ A4 ) )
      = A4 ) ).

% Collect_mem_eq
thf(fact_173_Collect__mem__eq,axiom,
    ! [A4: set_nat] :
      ( ( collect_nat
        @ ^ [X3: nat] : ( member_nat @ X3 @ A4 ) )
      = A4 ) ).

% Collect_mem_eq
thf(fact_174_Collect__mem__eq,axiom,
    ! [A4: set_na6008912749387833063list_b] :
      ( ( collec6966152917764800626list_b
        @ ^ [X3: nat > produc746580111399690912list_b] : ( member1851140327238222640list_b @ X3 @ A4 ) )
      = A4 ) ).

% Collect_mem_eq
thf(fact_175_Collect__mem__eq,axiom,
    ! [A4: set_na664922679713831477xt_a_b] :
      ( ( collec8943654641036559040xt_a_b
        @ ^ [X3: nat > produc5647625992154082286xt_a_b] : ( member3828642050509981054xt_a_b @ X3 @ A4 ) )
      = A4 ) ).

% Collect_mem_eq
thf(fact_176_Collect__mem__eq,axiom,
    ! [A4: set_nat_nat] :
      ( ( collect_nat_nat
        @ ^ [X3: nat > nat] : ( member_nat_nat @ X3 @ A4 ) )
      = A4 ) ).

% Collect_mem_eq
thf(fact_177_Collect__mem__eq,axiom,
    ! [A4: set_o] :
      ( ( collect_o
        @ ^ [X3: $o] : ( member_o @ X3 @ A4 ) )
      = A4 ) ).

% Collect_mem_eq
thf(fact_178_Collect__cong,axiom,
    ! [P2: $o > $o,Q3: $o > $o] :
      ( ! [X: $o] :
          ( ( P2 @ X )
          = ( Q3 @ X ) )
     => ( ( collect_o @ P2 )
        = ( collect_o @ Q3 ) ) ) ).

% Collect_cong
thf(fact_179_Collect__cong,axiom,
    ! [P2: nat > $o,Q3: nat > $o] :
      ( ! [X: nat] :
          ( ( P2 @ X )
          = ( Q3 @ X ) )
     => ( ( collect_nat @ P2 )
        = ( collect_nat @ Q3 ) ) ) ).

% Collect_cong
thf(fact_180_Collect__cong,axiom,
    ! [P2: ( nat > produc746580111399690912list_b ) > $o,Q3: ( nat > produc746580111399690912list_b ) > $o] :
      ( ! [X: nat > produc746580111399690912list_b] :
          ( ( P2 @ X )
          = ( Q3 @ X ) )
     => ( ( collec6966152917764800626list_b @ P2 )
        = ( collec6966152917764800626list_b @ Q3 ) ) ) ).

% Collect_cong
thf(fact_181_Collect__cong,axiom,
    ! [P2: ( nat > produc5647625992154082286xt_a_b ) > $o,Q3: ( nat > produc5647625992154082286xt_a_b ) > $o] :
      ( ! [X: nat > produc5647625992154082286xt_a_b] :
          ( ( P2 @ X )
          = ( Q3 @ X ) )
     => ( ( collec8943654641036559040xt_a_b @ P2 )
        = ( collec8943654641036559040xt_a_b @ Q3 ) ) ) ).

% Collect_cong
thf(fact_182_Collect__cong,axiom,
    ! [P2: ( nat > nat ) > $o,Q3: ( nat > nat ) > $o] :
      ( ! [X: nat > nat] :
          ( ( P2 @ X )
          = ( Q3 @ X ) )
     => ( ( collect_nat_nat @ P2 )
        = ( collect_nat_nat @ Q3 ) ) ) ).

% Collect_cong
thf(fact_183_pred__prod_Osimps,axiom,
    ( basic_1932318408880543091list_b
    = ( ^ [P12: list_b > $o,P23: list_b > $o,A5: produc3963297410138542439list_b] :
        ? [B4: list_b,C: list_b] :
          ( ( A5
            = ( produc1564554178308465111list_b @ B4 @ C ) )
          & ( P12 @ B4 )
          & ( P23 @ C ) ) ) ) ).

% pred_prod.simps
thf(fact_184_pred__prod_Osimps,axiom,
    ( basic_3223324150106804915xt_a_b
    = ( ^ [P12: multihole_mctxt_a_b > $o,P23: multihole_mctxt_a_b > $o,A5: produc1652119919080531751xt_a_b] :
        ? [B4: multihole_mctxt_a_b,C: multihole_mctxt_a_b] :
          ( ( A5
            = ( produc67882520014434071xt_a_b @ B4 @ C ) )
          & ( P12 @ B4 )
          & ( P23 @ C ) ) ) ) ).

% pred_prod.simps
thf(fact_185_pred__prod_Osimps,axiom,
    ( basic_pred_prod_o_o
    = ( ^ [P12: $o > $o,P23: $o > $o,A5: product_prod_o_o] :
        ? [B4: $o,C: $o] :
          ( ( A5
            = ( product_Pair_o_o @ B4 @ C ) )
          & ( P12 @ B4 )
          & ( P23 @ C ) ) ) ) ).

% pred_prod.simps
thf(fact_186_pred__prod_Osimps,axiom,
    ( basic_5777512433536448890xt_a_b
    = ( ^ [P12: list_b > $o,P23: multihole_mctxt_a_b > $o,A5: produc5647625992154082286xt_a_b] :
        ? [B4: list_b,C: multihole_mctxt_a_b] :
          ( ( A5
            = ( produc8821373537598205406xt_a_b @ B4 @ C ) )
          & ( P12 @ B4 )
          & ( P23 @ C ) ) ) ) ).

% pred_prod.simps
thf(fact_187_pred__prod_Osimps,axiom,
    ( basic_5159020248174167212list_b
    = ( ^ [P12: multihole_mctxt_a_b > $o,P23: list_b > $o,A5: produc746580111399690912list_b] :
        ? [B4: multihole_mctxt_a_b,C: list_b] :
          ( ( A5
            = ( produc8202881352235923728list_b @ B4 @ C ) )
          & ( P12 @ B4 )
          & ( P23 @ C ) ) ) ) ).

% pred_prod.simps
thf(fact_188_pred__prod_Ointros,axiom,
    ! [P1: list_b > $o,A: list_b,P22: list_b > $o,B: list_b] :
      ( ( P1 @ A )
     => ( ( P22 @ B )
       => ( basic_1932318408880543091list_b @ P1 @ P22 @ ( produc1564554178308465111list_b @ A @ B ) ) ) ) ).

% pred_prod.intros
thf(fact_189_pred__prod_Ointros,axiom,
    ! [P1: multihole_mctxt_a_b > $o,A: multihole_mctxt_a_b,P22: multihole_mctxt_a_b > $o,B: multihole_mctxt_a_b] :
      ( ( P1 @ A )
     => ( ( P22 @ B )
       => ( basic_3223324150106804915xt_a_b @ P1 @ P22 @ ( produc67882520014434071xt_a_b @ A @ B ) ) ) ) ).

% pred_prod.intros
thf(fact_190_pred__prod_Ointros,axiom,
    ! [P1: $o > $o,A: $o,P22: $o > $o,B: $o] :
      ( ( P1 @ A )
     => ( ( P22 @ B )
       => ( basic_pred_prod_o_o @ P1 @ P22 @ ( product_Pair_o_o @ A @ B ) ) ) ) ).

% pred_prod.intros
thf(fact_191_pred__prod_Ointros,axiom,
    ! [P1: list_b > $o,A: list_b,P22: multihole_mctxt_a_b > $o,B: multihole_mctxt_a_b] :
      ( ( P1 @ A )
     => ( ( P22 @ B )
       => ( basic_5777512433536448890xt_a_b @ P1 @ P22 @ ( produc8821373537598205406xt_a_b @ A @ B ) ) ) ) ).

% pred_prod.intros
thf(fact_192_pred__prod_Ointros,axiom,
    ! [P1: multihole_mctxt_a_b > $o,A: multihole_mctxt_a_b,P22: list_b > $o,B: list_b] :
      ( ( P1 @ A )
     => ( ( P22 @ B )
       => ( basic_5159020248174167212list_b @ P1 @ P22 @ ( produc8202881352235923728list_b @ A @ B ) ) ) ) ).

% pred_prod.intros
thf(fact_193_eq__snd__iff,axiom,
    ! [B: multihole_mctxt_a_b,P: produc1652119919080531751xt_a_b] :
      ( ( B
        = ( produc4775144687201070661xt_a_b @ P ) )
      = ( ? [A5: multihole_mctxt_a_b] :
            ( P
            = ( produc67882520014434071xt_a_b @ A5 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_194_eq__snd__iff,axiom,
    ! [B: list_b,P: produc3963297410138542439list_b] :
      ( ( B
        = ( produc3345134588468168965list_b @ P ) )
      = ( ? [A5: list_b] :
            ( P
            = ( produc1564554178308465111list_b @ A5 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_195_eq__snd__iff,axiom,
    ! [B: $o,P: product_prod_o_o] :
      ( ( B
        = ( product_snd_o_o @ P ) )
      = ( ? [A5: $o] :
            ( P
            = ( product_Pair_o_o @ A5 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_196_eq__snd__iff,axiom,
    ! [B: nat,P: product_prod_nat_nat] :
      ( ( B
        = ( product_snd_nat_nat @ P ) )
      = ( ? [A5: nat] :
            ( P
            = ( product_Pair_nat_nat @ A5 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_197_eq__snd__iff,axiom,
    ! [B: list_b,P: produc746580111399690912list_b] :
      ( ( B
        = ( produc6107117247873403966list_b @ P ) )
      = ( ? [A5: multihole_mctxt_a_b] :
            ( P
            = ( produc8202881352235923728list_b @ A5 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_198_eq__snd__iff,axiom,
    ! [B: multihole_mctxt_a_b,P: produc5647625992154082286xt_a_b] :
      ( ( B
        = ( produc6725609433235685644xt_a_b @ P ) )
      = ( ? [A5: list_b] :
            ( P
            = ( produc8821373537598205406xt_a_b @ A5 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_199_sndI,axiom,
    ! [X2: produc1652119919080531751xt_a_b,Y3: multihole_mctxt_a_b,Z2: multihole_mctxt_a_b] :
      ( ( X2
        = ( produc67882520014434071xt_a_b @ Y3 @ Z2 ) )
     => ( ( produc4775144687201070661xt_a_b @ X2 )
        = Z2 ) ) ).

% sndI
thf(fact_200_sndI,axiom,
    ! [X2: produc3963297410138542439list_b,Y3: list_b,Z2: list_b] :
      ( ( X2
        = ( produc1564554178308465111list_b @ Y3 @ Z2 ) )
     => ( ( produc3345134588468168965list_b @ X2 )
        = Z2 ) ) ).

% sndI
thf(fact_201_sndI,axiom,
    ! [X2: product_prod_o_o,Y3: $o,Z2: $o] :
      ( ( X2
        = ( product_Pair_o_o @ Y3 @ Z2 ) )
     => ( ( product_snd_o_o @ X2 )
        = Z2 ) ) ).

% sndI
thf(fact_202_sndI,axiom,
    ! [X2: product_prod_nat_nat,Y3: nat,Z2: nat] :
      ( ( X2
        = ( product_Pair_nat_nat @ Y3 @ Z2 ) )
     => ( ( product_snd_nat_nat @ X2 )
        = Z2 ) ) ).

% sndI
thf(fact_203_sndI,axiom,
    ! [X2: produc746580111399690912list_b,Y3: multihole_mctxt_a_b,Z2: list_b] :
      ( ( X2
        = ( produc8202881352235923728list_b @ Y3 @ Z2 ) )
     => ( ( produc6107117247873403966list_b @ X2 )
        = Z2 ) ) ).

% sndI
thf(fact_204_sndI,axiom,
    ! [X2: produc5647625992154082286xt_a_b,Y3: list_b,Z2: multihole_mctxt_a_b] :
      ( ( X2
        = ( produc8821373537598205406xt_a_b @ Y3 @ Z2 ) )
     => ( ( produc6725609433235685644xt_a_b @ X2 )
        = Z2 ) ) ).

% sndI
thf(fact_205_eq__fst__iff,axiom,
    ! [A: list_b,P: produc3963297410138542439list_b] :
      ( ( A
        = ( produc7649009375908944835list_b @ P ) )
      = ( ? [B4: list_b] :
            ( P
            = ( produc1564554178308465111list_b @ A @ B4 ) ) ) ) ).

% eq_fst_iff
thf(fact_206_eq__fst__iff,axiom,
    ! [A: multihole_mctxt_a_b,P: produc1652119919080531751xt_a_b] :
      ( ( A
        = ( produc2029583840371251459xt_a_b @ P ) )
      = ( ? [B4: multihole_mctxt_a_b] :
            ( P
            = ( produc67882520014434071xt_a_b @ A @ B4 ) ) ) ) ).

% eq_fst_iff
thf(fact_207_eq__fst__iff,axiom,
    ! [A: $o,P: product_prod_o_o] :
      ( ( A
        = ( product_fst_o_o @ P ) )
      = ( ? [B4: $o] :
            ( P
            = ( product_Pair_o_o @ A @ B4 ) ) ) ) ).

% eq_fst_iff
thf(fact_208_eq__fst__iff,axiom,
    ! [A: nat,P: product_prod_nat_nat] :
      ( ( A
        = ( product_fst_nat_nat @ P ) )
      = ( ? [B4: nat] :
            ( P
            = ( product_Pair_nat_nat @ A @ B4 ) ) ) ) ).

% eq_fst_iff
thf(fact_209_eq__fst__iff,axiom,
    ! [A: multihole_mctxt_a_b,P: produc746580111399690912list_b] :
      ( ( A
        = ( produc5881749095783049980list_b @ P ) )
      = ( ? [B4: list_b] :
            ( P
            = ( produc8202881352235923728list_b @ A @ B4 ) ) ) ) ).

% eq_fst_iff
thf(fact_210_eq__fst__iff,axiom,
    ! [A: list_b,P: produc5647625992154082286xt_a_b] :
      ( ( A
        = ( produc6500241281145331658xt_a_b @ P ) )
      = ( ? [B4: multihole_mctxt_a_b] :
            ( P
            = ( produc8821373537598205406xt_a_b @ A @ B4 ) ) ) ) ).

% eq_fst_iff
thf(fact_211_fstI,axiom,
    ! [X2: produc3963297410138542439list_b,Y3: list_b,Z2: list_b] :
      ( ( X2
        = ( produc1564554178308465111list_b @ Y3 @ Z2 ) )
     => ( ( produc7649009375908944835list_b @ X2 )
        = Y3 ) ) ).

% fstI
thf(fact_212_fstI,axiom,
    ! [X2: produc1652119919080531751xt_a_b,Y3: multihole_mctxt_a_b,Z2: multihole_mctxt_a_b] :
      ( ( X2
        = ( produc67882520014434071xt_a_b @ Y3 @ Z2 ) )
     => ( ( produc2029583840371251459xt_a_b @ X2 )
        = Y3 ) ) ).

% fstI
thf(fact_213_fstI,axiom,
    ! [X2: product_prod_o_o,Y3: $o,Z2: $o] :
      ( ( X2
        = ( product_Pair_o_o @ Y3 @ Z2 ) )
     => ( ( product_fst_o_o @ X2 )
        = Y3 ) ) ).

% fstI
thf(fact_214_fstI,axiom,
    ! [X2: product_prod_nat_nat,Y3: nat,Z2: nat] :
      ( ( X2
        = ( product_Pair_nat_nat @ Y3 @ Z2 ) )
     => ( ( product_fst_nat_nat @ X2 )
        = Y3 ) ) ).

% fstI
thf(fact_215_fstI,axiom,
    ! [X2: produc746580111399690912list_b,Y3: multihole_mctxt_a_b,Z2: list_b] :
      ( ( X2
        = ( produc8202881352235923728list_b @ Y3 @ Z2 ) )
     => ( ( produc5881749095783049980list_b @ X2 )
        = Y3 ) ) ).

% fstI
thf(fact_216_fstI,axiom,
    ! [X2: produc5647625992154082286xt_a_b,Y3: list_b,Z2: multihole_mctxt_a_b] :
      ( ( X2
        = ( produc8821373537598205406xt_a_b @ Y3 @ Z2 ) )
     => ( ( produc6500241281145331658xt_a_b @ X2 )
        = Y3 ) ) ).

% fstI
thf(fact_217_fstOp__def,axiom,
    ( bNF_fs8763394141750842138list_b
    = ( ^ [P3: multihole_mctxt_a_b > list_b > $o,Q2: list_b > list_b > $o,Ac: produc746580111399690912list_b] : ( produc8202881352235923728list_b @ ( produc5881749095783049980list_b @ Ac ) @ ( bNF_pi9133917077336146792list_b @ P3 @ Q2 @ ( produc5881749095783049980list_b @ Ac ) @ ( produc6107117247873403966list_b @ Ac ) ) ) ) ) ).

% fstOp_def
thf(fact_218_fstOp__def,axiom,
    ( bNF_fs7236638523624085587list_b
    = ( ^ [P3: multihole_mctxt_a_b > multihole_mctxt_a_b > $o,Q2: multihole_mctxt_a_b > list_b > $o,Ac: produc746580111399690912list_b] : ( produc67882520014434071xt_a_b @ ( produc5881749095783049980list_b @ Ac ) @ ( bNF_pi557838209204581537list_b @ P3 @ Q2 @ ( produc5881749095783049980list_b @ Ac ) @ ( produc6107117247873403966list_b @ Ac ) ) ) ) ) ).

% fstOp_def
thf(fact_219_fstOp__def,axiom,
    ( bNF_fs6894104479137331923xt_a_b
    = ( ^ [P3: list_b > multihole_mctxt_a_b > $o,Q2: multihole_mctxt_a_b > multihole_mctxt_a_b > $o,Ac: produc5647625992154082286xt_a_b] : ( produc8821373537598205406xt_a_b @ ( produc6500241281145331658xt_a_b @ Ac ) @ ( bNF_pi215304164717827873xt_a_b @ P3 @ Q2 @ ( produc6500241281145331658xt_a_b @ Ac ) @ ( produc6725609433235685644xt_a_b @ Ac ) ) ) ) ) ).

% fstOp_def
thf(fact_220_fstOp__def,axiom,
    ( bNF_fs4750163954569552282xt_a_b
    = ( ^ [P3: list_b > list_b > $o,Q2: list_b > multihole_mctxt_a_b > $o,Ac: produc5647625992154082286xt_a_b] : ( produc1564554178308465111list_b @ ( produc6500241281145331658xt_a_b @ Ac ) @ ( bNF_pi5120686890154856936xt_a_b @ P3 @ Q2 @ ( produc6500241281145331658xt_a_b @ Ac ) @ ( produc6725609433235685644xt_a_b @ Ac ) ) ) ) ) ).

% fstOp_def
thf(fact_221_fstOp__def,axiom,
    ( bNF_fs7855130708986367265xt_a_b
    = ( ^ [P3: multihole_mctxt_a_b > list_b > $o,Q2: list_b > multihole_mctxt_a_b > $o,Ac: produc1652119919080531751xt_a_b] : ( produc8202881352235923728list_b @ ( produc2029583840371251459xt_a_b @ Ac ) @ ( bNF_pi1176330394566863215xt_a_b @ P3 @ Q2 @ ( produc2029583840371251459xt_a_b @ Ac ) @ ( produc4775144687201070661xt_a_b @ Ac ) ) ) ) ) ).

% fstOp_def
thf(fact_222_fstOp__def,axiom,
    ( bNF_fs8789942433486863450xt_a_b
    = ( ^ [P3: multihole_mctxt_a_b > multihole_mctxt_a_b > $o,Q2: multihole_mctxt_a_b > multihole_mctxt_a_b > $o,Ac: produc1652119919080531751xt_a_b] : ( produc67882520014434071xt_a_b @ ( produc2029583840371251459xt_a_b @ Ac ) @ ( bNF_pi2247075006714987688xt_a_b @ P3 @ Q2 @ ( produc2029583840371251459xt_a_b @ Ac ) @ ( produc4775144687201070661xt_a_b @ Ac ) ) ) ) ) ).

% fstOp_def
thf(fact_223_fstOp__def,axiom,
    ( bNF_fs4131671769207270604list_b
    = ( ^ [P3: list_b > multihole_mctxt_a_b > $o,Q2: multihole_mctxt_a_b > list_b > $o,Ac: produc3963297410138542439list_b] : ( produc8821373537598205406xt_a_b @ ( produc7649009375908944835list_b @ Ac ) @ ( bNF_pi4502194704792575258list_b @ P3 @ Q2 @ ( produc7649009375908944835list_b @ Ac ) @ ( produc3345134588468168965list_b @ Ac ) ) ) ) ) ).

% fstOp_def
thf(fact_224_fstOp__def,axiom,
    ( bNF_fs4460400041868295571list_b
    = ( ^ [P3: list_b > list_b > $o,Q2: list_b > list_b > $o,Ac: produc3963297410138542439list_b] : ( produc1564554178308465111list_b @ ( produc7649009375908944835list_b @ Ac ) @ ( bNF_pi399958225447633377list_b @ P3 @ Q2 @ ( produc7649009375908944835list_b @ Ac ) @ ( produc3345134588468168965list_b @ Ac ) ) ) ) ) ).

% fstOp_def
thf(fact_225_fstOp__def,axiom,
    ( bNF_fstOp_o_o_o
    = ( ^ [P3: $o > $o > $o,Q2: $o > $o > $o,Ac: product_prod_o_o] : ( product_Pair_o_o @ ( product_fst_o_o @ Ac ) @ ( bNF_pi6189367155476860724_o_o_o @ P3 @ Q2 @ ( product_fst_o_o @ Ac ) @ ( product_snd_o_o @ Ac ) ) ) ) ) ).

% fstOp_def
thf(fact_226_sndOp__def,axiom,
    ( bNF_sn8236841958503063953list_b
    = ( ^ [P3: multihole_mctxt_a_b > multihole_mctxt_a_b > $o,Q2: multihole_mctxt_a_b > list_b > $o,Ac: produc746580111399690912list_b] : ( produc8202881352235923728list_b @ ( bNF_pi557838209204581537list_b @ P3 @ Q2 @ ( produc5881749095783049980list_b @ Ac ) @ ( produc6107117247873403966list_b @ Ac ) ) @ ( produc6107117247873403966list_b @ Ac ) ) ) ) ).

% sndOp_def
thf(fact_227_sndOp__def,axiom,
    ( bNF_sn8686886566300520536list_b
    = ( ^ [P3: multihole_mctxt_a_b > list_b > $o,Q2: list_b > list_b > $o,Ac: produc746580111399690912list_b] : ( produc1564554178308465111list_b @ ( bNF_pi9133917077336146792list_b @ P3 @ Q2 @ ( produc5881749095783049980list_b @ Ac ) @ ( produc6107117247873403966list_b @ Ac ) ) @ ( produc6107117247873403966list_b @ Ac ) ) ) ) ).

% sndOp_def
thf(fact_228_sndOp__def,axiom,
    ( bNF_sn4673656379119230680xt_a_b
    = ( ^ [P3: list_b > list_b > $o,Q2: list_b > multihole_mctxt_a_b > $o,Ac: produc5647625992154082286xt_a_b] : ( produc8821373537598205406xt_a_b @ ( bNF_pi5120686890154856936xt_a_b @ P3 @ Q2 @ ( produc6500241281145331658xt_a_b @ Ac ) @ ( produc6725609433235685644xt_a_b @ Ac ) ) @ ( produc6725609433235685644xt_a_b @ Ac ) ) ) ) ).

% sndOp_def
thf(fact_229_sndOp__def,axiom,
    ( bNF_sn7894307914016310289xt_a_b
    = ( ^ [P3: list_b > multihole_mctxt_a_b > $o,Q2: multihole_mctxt_a_b > multihole_mctxt_a_b > $o,Ac: produc5647625992154082286xt_a_b] : ( produc67882520014434071xt_a_b @ ( bNF_pi215304164717827873xt_a_b @ P3 @ Q2 @ ( produc6500241281145331658xt_a_b @ Ac ) @ ( produc6725609433235685644xt_a_b @ Ac ) ) @ ( produc6725609433235685644xt_a_b @ Ac ) ) ) ) ).

% sndOp_def
thf(fact_230_sndOp__def,axiom,
    ( bNF_sn8855334143865345631xt_a_b
    = ( ^ [P3: multihole_mctxt_a_b > list_b > $o,Q2: list_b > multihole_mctxt_a_b > $o,Ac: produc1652119919080531751xt_a_b] : ( produc8821373537598205406xt_a_b @ ( bNF_pi1176330394566863215xt_a_b @ P3 @ Q2 @ ( produc2029583840371251459xt_a_b @ Ac ) @ ( produc4775144687201070661xt_a_b @ Ac ) ) @ ( produc4775144687201070661xt_a_b @ Ac ) ) ) ) ).

% sndOp_def
thf(fact_231_sndOp__def,axiom,
    ( bNF_sn8437382630723965336xt_a_b
    = ( ^ [P3: multihole_mctxt_a_b > multihole_mctxt_a_b > $o,Q2: multihole_mctxt_a_b > multihole_mctxt_a_b > $o,Ac: produc1652119919080531751xt_a_b] : ( produc67882520014434071xt_a_b @ ( bNF_pi2247075006714987688xt_a_b @ P3 @ Q2 @ ( produc2029583840371251459xt_a_b @ Ac ) @ ( produc4775144687201070661xt_a_b @ Ac ) ) @ ( produc4775144687201070661xt_a_b @ Ac ) ) ) ) ).

% sndOp_def
thf(fact_232_sndOp__def,axiom,
    ( bNF_sn4055164193756949002list_b
    = ( ^ [P3: list_b > multihole_mctxt_a_b > $o,Q2: multihole_mctxt_a_b > list_b > $o,Ac: produc3963297410138542439list_b] : ( produc8202881352235923728list_b @ ( bNF_pi4502194704792575258list_b @ P3 @ Q2 @ ( produc7649009375908944835list_b @ Ac ) @ ( produc3345134588468168965list_b @ Ac ) ) @ ( produc3345134588468168965list_b @ Ac ) ) ) ) ).

% sndOp_def
thf(fact_233_sndOp__def,axiom,
    ( bNF_sn7302738427532062417list_b
    = ( ^ [P3: list_b > list_b > $o,Q2: list_b > list_b > $o,Ac: produc3963297410138542439list_b] : ( produc1564554178308465111list_b @ ( bNF_pi399958225447633377list_b @ P3 @ Q2 @ ( produc7649009375908944835list_b @ Ac ) @ ( produc3345134588468168965list_b @ Ac ) ) @ ( produc3345134588468168965list_b @ Ac ) ) ) ) ).

% sndOp_def
thf(fact_234_sndOp__def,axiom,
    ( bNF_sndOp_o_o_o
    = ( ^ [P3: $o > $o > $o,Q2: $o > $o > $o,Ac: product_prod_o_o] : ( product_Pair_o_o @ ( bNF_pi6189367155476860724_o_o_o @ P3 @ Q2 @ ( product_fst_o_o @ Ac ) @ ( product_snd_o_o @ Ac ) ) @ ( product_snd_o_o @ Ac ) ) ) ) ).

% sndOp_def
thf(fact_235_image2__eqI,axiom,
    ! [B: $o,F: $o > $o,X2: $o,C2: $o,G: $o > $o,A4: set_o] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( C2
          = ( G @ X2 ) )
       => ( ( member_o @ X2 @ A4 )
         => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ B @ C2 ) @ ( bNF_Gr6698568825248092222_o_o_o @ A4 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_236_image2__eqI,axiom,
    ! [B: $o,F: nat > $o,X2: nat,C2: $o,G: nat > $o,A4: set_nat] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( C2
          = ( G @ X2 ) )
       => ( ( member_nat @ X2 @ A4 )
         => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ B @ C2 ) @ ( bNF_Gr7385549216828995882at_o_o @ A4 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_237_image2__eqI,axiom,
    ! [B: $o,F: list_b > $o,X2: list_b,C2: $o,G: list_b > $o,A4: set_list_b] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( C2
          = ( G @ X2 ) )
       => ( ( member_list_b @ X2 @ A4 )
         => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ B @ C2 ) @ ( bNF_Gr104565956902713387_b_o_o @ A4 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_238_image2__eqI,axiom,
    ! [B: $o,F: set_o > $o,X2: set_o,C2: $o,G: set_o > $o,A4: set_set_o] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( C2
          = ( G @ X2 ) )
       => ( ( member_set_o @ X2 @ A4 )
         => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ B @ C2 ) @ ( bNF_Gr8091873193056382750_o_o_o @ A4 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_239_image2__eqI,axiom,
    ! [B: list_b,F: $o > list_b,X2: $o,C2: list_b,G: $o > list_b,A4: set_o] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( C2
          = ( G @ X2 ) )
       => ( ( member_o @ X2 @ A4 )
         => ( member2990321877988238992list_b @ ( produc1564554178308465111list_b @ B @ C2 ) @ ( bNF_Gr9063183054812448510list_b @ A4 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_240_image2__eqI,axiom,
    ! [B: list_b,F: nat > list_b,X2: nat,C2: list_b,G: nat > list_b,A4: set_nat] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( C2
          = ( G @ X2 ) )
       => ( ( member_nat @ X2 @ A4 )
         => ( member2990321877988238992list_b @ ( produc1564554178308465111list_b @ B @ C2 ) @ ( bNF_Gr8841899351857821674list_b @ A4 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_241_image2__eqI,axiom,
    ! [B: list_b,F: $o > list_b,X2: $o,C2: multihole_mctxt_a_b,G: $o > multihole_mctxt_a_b,A4: set_o] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( C2
          = ( G @ X2 ) )
       => ( ( member_o @ X2 @ A4 )
         => ( member8473537726404135703xt_a_b @ ( produc8821373537598205406xt_a_b @ B @ C2 ) @ ( bNF_Gr1724143576852326661xt_a_b @ A4 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_242_image2__eqI,axiom,
    ! [B: list_b,F: nat > list_b,X2: nat,C2: multihole_mctxt_a_b,G: nat > multihole_mctxt_a_b,A4: set_nat] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( C2
          = ( G @ X2 ) )
       => ( ( member_nat @ X2 @ A4 )
         => ( member8473537726404135703xt_a_b @ ( produc8821373537598205406xt_a_b @ B @ C2 ) @ ( bNF_Gr241138994731930097xt_a_b @ A4 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_243_image2__eqI,axiom,
    ! [B: multihole_mctxt_a_b,F: $o > multihole_mctxt_a_b,X2: $o,C2: list_b,G: $o > list_b,A4: set_o] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( C2
          = ( G @ X2 ) )
       => ( ( member_o @ X2 @ A4 )
         => ( member3572491845649744329list_b @ ( produc8202881352235923728list_b @ B @ C2 ) @ ( bNF_Gr1105651391490044983list_b @ A4 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_244_image2__eqI,axiom,
    ! [B: multihole_mctxt_a_b,F: nat > multihole_mctxt_a_b,X2: nat,C2: list_b,G: nat > list_b,A4: set_nat] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( C2
          = ( G @ X2 ) )
       => ( ( member_nat @ X2 @ A4 )
         => ( member3572491845649744329list_b @ ( produc8202881352235923728list_b @ B @ C2 ) @ ( bNF_Gr8846018846224424227list_b @ A4 @ F @ G ) ) ) ) ) ).

% image2_eqI
thf(fact_245_prod_Osplit__sel,axiom,
    ! [P2: multihole_mctxt_a_b > $o,F: list_b > multihole_mctxt_a_b > multihole_mctxt_a_b,Prod: produc5647625992154082286xt_a_b] :
      ( ( P2 @ ( produc6892829578239444825xt_a_b @ F @ Prod ) )
      = ( ( Prod
          = ( produc8821373537598205406xt_a_b @ ( produc6500241281145331658xt_a_b @ Prod ) @ ( produc6725609433235685644xt_a_b @ Prod ) ) )
       => ( P2 @ ( F @ ( produc6500241281145331658xt_a_b @ Prod ) @ ( produc6725609433235685644xt_a_b @ Prod ) ) ) ) ) ).

% prod.split_sel
thf(fact_246_prod_Osplit__sel,axiom,
    ! [P2: produc746580111399690912list_b > $o,F: list_b > multihole_mctxt_a_b > produc746580111399690912list_b,Prod: produc5647625992154082286xt_a_b] :
      ( ( P2 @ ( produc3271728269314753389list_b @ F @ Prod ) )
      = ( ( Prod
          = ( produc8821373537598205406xt_a_b @ ( produc6500241281145331658xt_a_b @ Prod ) @ ( produc6725609433235685644xt_a_b @ Prod ) ) )
       => ( P2 @ ( F @ ( produc6500241281145331658xt_a_b @ Prod ) @ ( produc6725609433235685644xt_a_b @ Prod ) ) ) ) ) ).

% prod.split_sel
thf(fact_247_prod_Osplit__sel,axiom,
    ! [P2: list_b > $o,F: list_b > multihole_mctxt_a_b > list_b,Prod: produc5647625992154082286xt_a_b] :
      ( ( P2 @ ( produc5071610215621926226list_b @ F @ Prod ) )
      = ( ( Prod
          = ( produc8821373537598205406xt_a_b @ ( produc6500241281145331658xt_a_b @ Prod ) @ ( produc6725609433235685644xt_a_b @ Prod ) ) )
       => ( P2 @ ( F @ ( produc6500241281145331658xt_a_b @ Prod ) @ ( produc6725609433235685644xt_a_b @ Prod ) ) ) ) ) ).

% prod.split_sel
thf(fact_248_prod_Osplit__sel,axiom,
    ! [P2: $o > $o,F: list_b > multihole_mctxt_a_b > $o,Prod: produc5647625992154082286xt_a_b] :
      ( ( P2 @ ( produc1221931734719695589_a_b_o @ F @ Prod ) )
      = ( ( Prod
          = ( produc8821373537598205406xt_a_b @ ( produc6500241281145331658xt_a_b @ Prod ) @ ( produc6725609433235685644xt_a_b @ Prod ) ) )
       => ( P2 @ ( F @ ( produc6500241281145331658xt_a_b @ Prod ) @ ( produc6725609433235685644xt_a_b @ Prod ) ) ) ) ) ).

% prod.split_sel
thf(fact_249_prod_Osplit__sel,axiom,
    ! [P2: $o > $o,F: $o > $o > $o,Prod: product_prod_o_o] :
      ( ( P2 @ ( produc6197397395684419436_o_o_o @ F @ Prod ) )
      = ( ( Prod
          = ( product_Pair_o_o @ ( product_fst_o_o @ Prod ) @ ( product_snd_o_o @ Prod ) ) )
       => ( P2 @ ( F @ ( product_fst_o_o @ Prod ) @ ( product_snd_o_o @ Prod ) ) ) ) ) ).

% prod.split_sel
thf(fact_250_prod_Osplit__sel__asm,axiom,
    ! [P2: multihole_mctxt_a_b > $o,F: list_b > multihole_mctxt_a_b > multihole_mctxt_a_b,Prod: produc5647625992154082286xt_a_b] :
      ( ( P2 @ ( produc6892829578239444825xt_a_b @ F @ Prod ) )
      = ( ~ ( ( Prod
              = ( produc8821373537598205406xt_a_b @ ( produc6500241281145331658xt_a_b @ Prod ) @ ( produc6725609433235685644xt_a_b @ Prod ) ) )
            & ~ ( P2 @ ( F @ ( produc6500241281145331658xt_a_b @ Prod ) @ ( produc6725609433235685644xt_a_b @ Prod ) ) ) ) ) ) ).

% prod.split_sel_asm
thf(fact_251_prod_Osplit__sel__asm,axiom,
    ! [P2: produc746580111399690912list_b > $o,F: list_b > multihole_mctxt_a_b > produc746580111399690912list_b,Prod: produc5647625992154082286xt_a_b] :
      ( ( P2 @ ( produc3271728269314753389list_b @ F @ Prod ) )
      = ( ~ ( ( Prod
              = ( produc8821373537598205406xt_a_b @ ( produc6500241281145331658xt_a_b @ Prod ) @ ( produc6725609433235685644xt_a_b @ Prod ) ) )
            & ~ ( P2 @ ( F @ ( produc6500241281145331658xt_a_b @ Prod ) @ ( produc6725609433235685644xt_a_b @ Prod ) ) ) ) ) ) ).

% prod.split_sel_asm
thf(fact_252_prod_Osplit__sel__asm,axiom,
    ! [P2: list_b > $o,F: list_b > multihole_mctxt_a_b > list_b,Prod: produc5647625992154082286xt_a_b] :
      ( ( P2 @ ( produc5071610215621926226list_b @ F @ Prod ) )
      = ( ~ ( ( Prod
              = ( produc8821373537598205406xt_a_b @ ( produc6500241281145331658xt_a_b @ Prod ) @ ( produc6725609433235685644xt_a_b @ Prod ) ) )
            & ~ ( P2 @ ( F @ ( produc6500241281145331658xt_a_b @ Prod ) @ ( produc6725609433235685644xt_a_b @ Prod ) ) ) ) ) ) ).

% prod.split_sel_asm
thf(fact_253_prod_Osplit__sel__asm,axiom,
    ! [P2: $o > $o,F: list_b > multihole_mctxt_a_b > $o,Prod: produc5647625992154082286xt_a_b] :
      ( ( P2 @ ( produc1221931734719695589_a_b_o @ F @ Prod ) )
      = ( ~ ( ( Prod
              = ( produc8821373537598205406xt_a_b @ ( produc6500241281145331658xt_a_b @ Prod ) @ ( produc6725609433235685644xt_a_b @ Prod ) ) )
            & ~ ( P2 @ ( F @ ( produc6500241281145331658xt_a_b @ Prod ) @ ( produc6725609433235685644xt_a_b @ Prod ) ) ) ) ) ) ).

% prod.split_sel_asm
thf(fact_254_prod_Osplit__sel__asm,axiom,
    ! [P2: $o > $o,F: $o > $o > $o,Prod: product_prod_o_o] :
      ( ( P2 @ ( produc6197397395684419436_o_o_o @ F @ Prod ) )
      = ( ~ ( ( Prod
              = ( product_Pair_o_o @ ( product_fst_o_o @ Prod ) @ ( product_snd_o_o @ Prod ) ) )
            & ~ ( P2 @ ( F @ ( product_fst_o_o @ Prod ) @ ( product_snd_o_o @ Prod ) ) ) ) ) ) ).

% prod.split_sel_asm
thf(fact_255_ssubst__Pair__rhs,axiom,
    ! [R2: list_b,S2: multihole_mctxt_a_b,R: set_Pr3872688570871424334xt_a_b,S3: multihole_mctxt_a_b] :
      ( ( member8473537726404135703xt_a_b @ ( produc8821373537598205406xt_a_b @ R2 @ S2 ) @ R )
     => ( ( S3 = S2 )
       => ( member8473537726404135703xt_a_b @ ( produc8821373537598205406xt_a_b @ R2 @ S3 ) @ R ) ) ) ).

% ssubst_Pair_rhs
thf(fact_256_ssubst__Pair__rhs,axiom,
    ! [R2: multihole_mctxt_a_b,S2: list_b,R: set_Pr1895186847599665920list_b,S3: list_b] :
      ( ( member3572491845649744329list_b @ ( produc8202881352235923728list_b @ R2 @ S2 ) @ R )
     => ( ( S3 = S2 )
       => ( member3572491845649744329list_b @ ( produc8202881352235923728list_b @ R2 @ S3 ) @ R ) ) ) ).

% ssubst_Pair_rhs
thf(fact_257_ssubst__Pair__rhs,axiom,
    ! [R2: list_b,S2: list_b,R: set_Pr7665282455119567943list_b,S3: list_b] :
      ( ( member2990321877988238992list_b @ ( produc1564554178308465111list_b @ R2 @ S2 ) @ R )
     => ( ( S3 = S2 )
       => ( member2990321877988238992list_b @ ( produc1564554178308465111list_b @ R2 @ S3 ) @ R ) ) ) ).

% ssubst_Pair_rhs
thf(fact_258_ssubst__Pair__rhs,axiom,
    ! [R2: multihole_mctxt_a_b,S2: multihole_mctxt_a_b,R: set_Pr2918931875556005383xt_a_b,S3: multihole_mctxt_a_b] :
      ( ( member6103717091360755792xt_a_b @ ( produc67882520014434071xt_a_b @ R2 @ S2 ) @ R )
     => ( ( S3 = S2 )
       => ( member6103717091360755792xt_a_b @ ( produc67882520014434071xt_a_b @ R2 @ S3 ) @ R ) ) ) ).

% ssubst_Pair_rhs
thf(fact_259_ssubst__Pair__rhs,axiom,
    ! [R2: $o,S2: $o,R: set_Product_prod_o_o,S3: $o] :
      ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ R2 @ S2 ) @ R )
     => ( ( S3 = S2 )
       => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ R2 @ S3 ) @ R ) ) ) ).

% ssubst_Pair_rhs
thf(fact_260_sndsp_Ocases,axiom,
    ! [P: produc1652119919080531751xt_a_b,A: multihole_mctxt_a_b] :
      ( ( basic_4467741268980112107xt_a_b @ P @ A )
     => ( A
        = ( produc4775144687201070661xt_a_b @ P ) ) ) ).

% sndsp.cases
thf(fact_261_sndsp_Ocases,axiom,
    ! [P: produc3963297410138542439list_b,A: list_b] :
      ( ( basic_832676007215906219list_b @ P @ A )
     => ( A
        = ( produc3345134588468168965list_b @ P ) ) ) ).

% sndsp.cases
thf(fact_262_sndsp_Ocases,axiom,
    ! [P: product_prod_o_o,A: $o] :
      ( ( basic_sndsp_o_o @ P @ A )
     => ( A
        = ( product_snd_o_o @ P ) ) ) ).

% sndsp.cases
thf(fact_263_sndsp_Ocases,axiom,
    ! [P: product_prod_nat_nat,A: nat] :
      ( ( basic_sndsp_nat_nat @ P @ A )
     => ( A
        = ( product_snd_nat_nat @ P ) ) ) ).

% sndsp.cases
thf(fact_264_sndsp_Ocases,axiom,
    ! [P: produc746580111399690912list_b,A: list_b] :
      ( ( basic_3470772256104193252list_b @ P @ A )
     => ( A
        = ( produc6107117247873403966list_b @ P ) ) ) ).

% sndsp.cases
thf(fact_265_sndsp_Ocases,axiom,
    ! [P: produc5647625992154082286xt_a_b,A: multihole_mctxt_a_b] :
      ( ( basic_4089264441466474930xt_a_b @ P @ A )
     => ( A
        = ( produc6725609433235685644xt_a_b @ P ) ) ) ).

% sndsp.cases
thf(fact_266_sndsp_Osimps,axiom,
    ( basic_4467741268980112107xt_a_b
    = ( ^ [P4: produc1652119919080531751xt_a_b,A5: multihole_mctxt_a_b] :
          ( A5
          = ( produc4775144687201070661xt_a_b @ P4 ) ) ) ) ).

% sndsp.simps
thf(fact_267_sndsp_Osimps,axiom,
    ( basic_832676007215906219list_b
    = ( ^ [P4: produc3963297410138542439list_b,A5: list_b] :
          ( A5
          = ( produc3345134588468168965list_b @ P4 ) ) ) ) ).

% sndsp.simps
thf(fact_268_sndsp_Osimps,axiom,
    ( basic_sndsp_o_o
    = ( ^ [P4: product_prod_o_o,A5: $o] :
          ( A5
          = ( product_snd_o_o @ P4 ) ) ) ) ).

% sndsp.simps
thf(fact_269_sndsp_Osimps,axiom,
    ( basic_sndsp_nat_nat
    = ( ^ [P4: product_prod_nat_nat,A5: nat] :
          ( A5
          = ( product_snd_nat_nat @ P4 ) ) ) ) ).

% sndsp.simps
thf(fact_270_sndsp_Osimps,axiom,
    ( basic_3470772256104193252list_b
    = ( ^ [P4: produc746580111399690912list_b,A5: list_b] :
          ( A5
          = ( produc6107117247873403966list_b @ P4 ) ) ) ) ).

% sndsp.simps
thf(fact_271_sndsp_Osimps,axiom,
    ( basic_4089264441466474930xt_a_b
    = ( ^ [P4: produc5647625992154082286xt_a_b,A5: multihole_mctxt_a_b] :
          ( A5
          = ( produc6725609433235685644xt_a_b @ P4 ) ) ) ) ).

% sndsp.simps
thf(fact_272_sndsp_Ointros,axiom,
    ! [P: produc1652119919080531751xt_a_b] : ( basic_4467741268980112107xt_a_b @ P @ ( produc4775144687201070661xt_a_b @ P ) ) ).

% sndsp.intros
thf(fact_273_sndsp_Ointros,axiom,
    ! [P: produc3963297410138542439list_b] : ( basic_832676007215906219list_b @ P @ ( produc3345134588468168965list_b @ P ) ) ).

% sndsp.intros
thf(fact_274_sndsp_Ointros,axiom,
    ! [P: product_prod_o_o] : ( basic_sndsp_o_o @ P @ ( product_snd_o_o @ P ) ) ).

% sndsp.intros
thf(fact_275_sndsp_Ointros,axiom,
    ! [P: product_prod_nat_nat] : ( basic_sndsp_nat_nat @ P @ ( product_snd_nat_nat @ P ) ) ).

% sndsp.intros
thf(fact_276_sndsp_Ointros,axiom,
    ! [P: produc746580111399690912list_b] : ( basic_3470772256104193252list_b @ P @ ( produc6107117247873403966list_b @ P ) ) ).

% sndsp.intros
thf(fact_277_sndsp_Ointros,axiom,
    ! [P: produc5647625992154082286xt_a_b] : ( basic_4089264441466474930xt_a_b @ P @ ( produc6725609433235685644xt_a_b @ P ) ) ).

% sndsp.intros
thf(fact_278_curryI,axiom,
    ! [F: produc5647625992154082286xt_a_b > $o,A: list_b,B: multihole_mctxt_a_b] :
      ( ( F @ ( produc8821373537598205406xt_a_b @ A @ B ) )
     => ( produc8471990777825750022_a_b_o @ F @ A @ B ) ) ).

% curryI
thf(fact_279_curryI,axiom,
    ! [F: produc746580111399690912list_b > $o,A: multihole_mctxt_a_b,B: list_b] :
      ( ( F @ ( produc8202881352235923728list_b @ A @ B ) )
     => ( produc5216961383963826260st_b_o @ F @ A @ B ) ) ).

% curryI
thf(fact_280_curryI,axiom,
    ! [F: produc3963297410138542439list_b > $o,A: list_b,B: list_b] :
      ( ( F @ ( produc1564554178308465111list_b @ A @ B ) )
     => ( produc6829973082055895501st_b_o @ F @ A @ B ) ) ).

% curryI
thf(fact_281_curryI,axiom,
    ! [F: produc1652119919080531751xt_a_b > $o,A: multihole_mctxt_a_b,B: multihole_mctxt_a_b] :
      ( ( F @ ( produc67882520014434071xt_a_b @ A @ B ) )
     => ( produc353760711170994317_a_b_o @ F @ A @ B ) ) ).

% curryI
thf(fact_282_curryI,axiom,
    ! [F: product_prod_o_o > $o,A: $o,B: $o] :
      ( ( F @ ( product_Pair_o_o @ A @ B ) )
     => ( product_curry_o_o_o @ F @ A @ B ) ) ).

% curryI
thf(fact_283_curry__case__prod,axiom,
    ! [F: list_b > multihole_mctxt_a_b > multihole_mctxt_a_b] :
      ( ( produc8200905328278969722xt_a_b @ ( produc6892829578239444825xt_a_b @ F ) )
      = F ) ).

% curry_case_prod
thf(fact_284_curry__case__prod,axiom,
    ! [F: list_b > multihole_mctxt_a_b > produc746580111399690912list_b] :
      ( ( produc2492098109056437262list_b @ ( produc3271728269314753389list_b @ F ) )
      = F ) ).

% curry_case_prod
thf(fact_285_curry__case__prod,axiom,
    ! [F: list_b > multihole_mctxt_a_b > list_b] :
      ( ( produc5982366047203965299list_b @ ( produc5071610215621926226list_b @ F ) )
      = F ) ).

% curry_case_prod
thf(fact_286_curry__case__prod,axiom,
    ! [F: list_b > multihole_mctxt_a_b > $o] :
      ( ( produc8471990777825750022_a_b_o @ ( produc1221931734719695589_a_b_o @ F ) )
      = F ) ).

% curry_case_prod
thf(fact_287_curry__case__prod,axiom,
    ! [F: $o > $o > $o] :
      ( ( product_curry_o_o_o @ ( produc6197397395684419436_o_o_o @ F ) )
      = F ) ).

% curry_case_prod
thf(fact_288_case__prod__curry,axiom,
    ! [F: produc5647625992154082286xt_a_b > multihole_mctxt_a_b] :
      ( ( produc6892829578239444825xt_a_b @ ( produc8200905328278969722xt_a_b @ F ) )
      = F ) ).

% case_prod_curry
thf(fact_289_case__prod__curry,axiom,
    ! [F: produc5647625992154082286xt_a_b > produc746580111399690912list_b] :
      ( ( produc3271728269314753389list_b @ ( produc2492098109056437262list_b @ F ) )
      = F ) ).

% case_prod_curry
thf(fact_290_case__prod__curry,axiom,
    ! [F: produc5647625992154082286xt_a_b > list_b] :
      ( ( produc5071610215621926226list_b @ ( produc5982366047203965299list_b @ F ) )
      = F ) ).

% case_prod_curry
thf(fact_291_case__prod__curry,axiom,
    ! [F: produc5647625992154082286xt_a_b > $o] :
      ( ( produc1221931734719695589_a_b_o @ ( produc8471990777825750022_a_b_o @ F ) )
      = F ) ).

% case_prod_curry
thf(fact_292_case__prod__curry,axiom,
    ! [F: product_prod_o_o > $o] :
      ( ( produc6197397395684419436_o_o_o @ ( product_curry_o_o_o @ F ) )
      = F ) ).

% case_prod_curry
thf(fact_293_mem__case__prodE,axiom,
    ! [Z2: $o,C2: $o > $o > set_o,P: product_prod_o_o] :
      ( ( member_o @ Z2 @ ( produc1238384690215476812_set_o @ C2 @ P ) )
     => ~ ! [X: $o,Y: $o] :
            ( ( P
              = ( product_Pair_o_o @ X @ Y ) )
           => ~ ( member_o @ Z2 @ ( C2 @ X @ Y ) ) ) ) ).

% mem_case_prodE
thf(fact_294_mem__case__prodE,axiom,
    ! [Z2: nat,C2: $o > $o > set_nat,P: product_prod_o_o] :
      ( ( member_nat @ Z2 @ ( produc6723186405834743986et_nat @ C2 @ P ) )
     => ~ ! [X: $o,Y: $o] :
            ( ( P
              = ( product_Pair_o_o @ X @ Y ) )
           => ~ ( member_nat @ Z2 @ ( C2 @ X @ Y ) ) ) ) ).

% mem_case_prodE
thf(fact_295_mem__case__prodE,axiom,
    ! [Z2: list_b,C2: $o > $o > set_list_b,P: product_prod_o_o] :
      ( ( member_list_b @ Z2 @ ( produc1707798961248329273list_b @ C2 @ P ) )
     => ~ ! [X: $o,Y: $o] :
            ( ( P
              = ( product_Pair_o_o @ X @ Y ) )
           => ~ ( member_list_b @ Z2 @ ( C2 @ X @ Y ) ) ) ) ).

% mem_case_prodE
thf(fact_296_mem__case__prodE,axiom,
    ! [Z2: set_o,C2: $o > $o > set_set_o,P: product_prod_o_o] :
      ( ( member_set_o @ Z2 @ ( produc1752788702180839724_set_o @ C2 @ P ) )
     => ~ ! [X: $o,Y: $o] :
            ( ( P
              = ( product_Pair_o_o @ X @ Y ) )
           => ~ ( member_set_o @ Z2 @ ( C2 @ X @ Y ) ) ) ) ).

% mem_case_prodE
thf(fact_297_mem__case__prodE,axiom,
    ! [Z2: $o,C2: list_b > list_b > set_o,P: produc3963297410138542439list_b] :
      ( ( member_o @ Z2 @ ( produc6324044751052175756_set_o @ C2 @ P ) )
     => ~ ! [X: list_b,Y: list_b] :
            ( ( P
              = ( produc1564554178308465111list_b @ X @ Y ) )
           => ~ ( member_o @ Z2 @ ( C2 @ X @ Y ) ) ) ) ).

% mem_case_prodE
thf(fact_298_mem__case__prodE,axiom,
    ! [Z2: nat,C2: list_b > list_b > set_nat,P: produc3963297410138542439list_b] :
      ( ( member_nat @ Z2 @ ( produc4846079126225884530et_nat @ C2 @ P ) )
     => ~ ! [X: list_b,Y: list_b] :
            ( ( P
              = ( produc1564554178308465111list_b @ X @ Y ) )
           => ~ ( member_nat @ Z2 @ ( C2 @ X @ Y ) ) ) ) ).

% mem_case_prodE
thf(fact_299_mem__case__prodE,axiom,
    ! [Z2: $o,C2: list_b > multihole_mctxt_a_b > set_o,P: produc5647625992154082286xt_a_b] :
      ( ( member_o @ Z2 @ ( produc8799683814798138821_set_o @ C2 @ P ) )
     => ~ ! [X: list_b,Y: multihole_mctxt_a_b] :
            ( ( P
              = ( produc8821373537598205406xt_a_b @ X @ Y ) )
           => ~ ( member_o @ Z2 @ ( C2 @ X @ Y ) ) ) ) ).

% mem_case_prodE
thf(fact_300_mem__case__prodE,axiom,
    ! [Z2: nat,C2: list_b > multihole_mctxt_a_b > set_nat,P: produc5647625992154082286xt_a_b] :
      ( ( member_nat @ Z2 @ ( produc7038115184564154745et_nat @ C2 @ P ) )
     => ~ ! [X: list_b,Y: multihole_mctxt_a_b] :
            ( ( P
              = ( produc8821373537598205406xt_a_b @ X @ Y ) )
           => ~ ( member_nat @ Z2 @ ( C2 @ X @ Y ) ) ) ) ).

% mem_case_prodE
thf(fact_301_mem__case__prodE,axiom,
    ! [Z2: $o,C2: multihole_mctxt_a_b > list_b > set_o,P: produc746580111399690912list_b] :
      ( ( member_o @ Z2 @ ( produc6050732325701653011_set_o @ C2 @ P ) )
     => ~ ! [X: multihole_mctxt_a_b,Y: list_b] :
            ( ( P
              = ( produc8202881352235923728list_b @ X @ Y ) )
           => ~ ( member_o @ Z2 @ ( C2 @ X @ Y ) ) ) ) ).

% mem_case_prodE
thf(fact_302_mem__case__prodE,axiom,
    ! [Z2: nat,C2: multihole_mctxt_a_b > list_b > set_nat,P: produc746580111399690912list_b] :
      ( ( member_nat @ Z2 @ ( produc1070828641548463275et_nat @ C2 @ P ) )
     => ~ ! [X: multihole_mctxt_a_b,Y: list_b] :
            ( ( P
              = ( produc8202881352235923728list_b @ X @ Y ) )
           => ~ ( member_nat @ Z2 @ ( C2 @ X @ Y ) ) ) ) ).

% mem_case_prodE
thf(fact_303_old_Oprod_Ocase,axiom,
    ! [F: list_b > multihole_mctxt_a_b > multihole_mctxt_a_b,X1: list_b,X22: multihole_mctxt_a_b] :
      ( ( produc6892829578239444825xt_a_b @ F @ ( produc8821373537598205406xt_a_b @ X1 @ X22 ) )
      = ( F @ X1 @ X22 ) ) ).

% old.prod.case
thf(fact_304_old_Oprod_Ocase,axiom,
    ! [F: list_b > multihole_mctxt_a_b > produc746580111399690912list_b,X1: list_b,X22: multihole_mctxt_a_b] :
      ( ( produc3271728269314753389list_b @ F @ ( produc8821373537598205406xt_a_b @ X1 @ X22 ) )
      = ( F @ X1 @ X22 ) ) ).

% old.prod.case
thf(fact_305_old_Oprod_Ocase,axiom,
    ! [F: list_b > multihole_mctxt_a_b > list_b,X1: list_b,X22: multihole_mctxt_a_b] :
      ( ( produc5071610215621926226list_b @ F @ ( produc8821373537598205406xt_a_b @ X1 @ X22 ) )
      = ( F @ X1 @ X22 ) ) ).

% old.prod.case
thf(fact_306_old_Oprod_Ocase,axiom,
    ! [F: list_b > multihole_mctxt_a_b > $o,X1: list_b,X22: multihole_mctxt_a_b] :
      ( ( produc1221931734719695589_a_b_o @ F @ ( produc8821373537598205406xt_a_b @ X1 @ X22 ) )
      = ( F @ X1 @ X22 ) ) ).

% old.prod.case
thf(fact_307_old_Oprod_Ocase,axiom,
    ! [F: $o > $o > $o,X1: $o,X22: $o] :
      ( ( produc6197397395684419436_o_o_o @ F @ ( product_Pair_o_o @ X1 @ X22 ) )
      = ( F @ X1 @ X22 ) ) ).

% old.prod.case
thf(fact_308_curryD,axiom,
    ! [F: produc5647625992154082286xt_a_b > $o,A: list_b,B: multihole_mctxt_a_b] :
      ( ( produc8471990777825750022_a_b_o @ F @ A @ B )
     => ( F @ ( produc8821373537598205406xt_a_b @ A @ B ) ) ) ).

% curryD
thf(fact_309_curryD,axiom,
    ! [F: produc746580111399690912list_b > $o,A: multihole_mctxt_a_b,B: list_b] :
      ( ( produc5216961383963826260st_b_o @ F @ A @ B )
     => ( F @ ( produc8202881352235923728list_b @ A @ B ) ) ) ).

% curryD
thf(fact_310_curryD,axiom,
    ! [F: produc3963297410138542439list_b > $o,A: list_b,B: list_b] :
      ( ( produc6829973082055895501st_b_o @ F @ A @ B )
     => ( F @ ( produc1564554178308465111list_b @ A @ B ) ) ) ).

% curryD
thf(fact_311_curryD,axiom,
    ! [F: produc1652119919080531751xt_a_b > $o,A: multihole_mctxt_a_b,B: multihole_mctxt_a_b] :
      ( ( produc353760711170994317_a_b_o @ F @ A @ B )
     => ( F @ ( produc67882520014434071xt_a_b @ A @ B ) ) ) ).

% curryD
thf(fact_312_curryD,axiom,
    ! [F: product_prod_o_o > $o,A: $o,B: $o] :
      ( ( product_curry_o_o_o @ F @ A @ B )
     => ( F @ ( product_Pair_o_o @ A @ B ) ) ) ).

% curryD
thf(fact_313_curryE,axiom,
    ! [F: produc5647625992154082286xt_a_b > $o,A: list_b,B: multihole_mctxt_a_b] :
      ( ( produc8471990777825750022_a_b_o @ F @ A @ B )
     => ( F @ ( produc8821373537598205406xt_a_b @ A @ B ) ) ) ).

% curryE
thf(fact_314_curryE,axiom,
    ! [F: produc746580111399690912list_b > $o,A: multihole_mctxt_a_b,B: list_b] :
      ( ( produc5216961383963826260st_b_o @ F @ A @ B )
     => ( F @ ( produc8202881352235923728list_b @ A @ B ) ) ) ).

% curryE
thf(fact_315_curryE,axiom,
    ! [F: produc3963297410138542439list_b > $o,A: list_b,B: list_b] :
      ( ( produc6829973082055895501st_b_o @ F @ A @ B )
     => ( F @ ( produc1564554178308465111list_b @ A @ B ) ) ) ).

% curryE
thf(fact_316_curryE,axiom,
    ! [F: produc1652119919080531751xt_a_b > $o,A: multihole_mctxt_a_b,B: multihole_mctxt_a_b] :
      ( ( produc353760711170994317_a_b_o @ F @ A @ B )
     => ( F @ ( produc67882520014434071xt_a_b @ A @ B ) ) ) ).

% curryE
thf(fact_317_curryE,axiom,
    ! [F: product_prod_o_o > $o,A: $o,B: $o] :
      ( ( product_curry_o_o_o @ F @ A @ B )
     => ( F @ ( product_Pair_o_o @ A @ B ) ) ) ).

% curryE
thf(fact_318_Product__Type_OCollect__case__prodD,axiom,
    ! [X2: produc1652119919080531751xt_a_b,A4: multihole_mctxt_a_b > multihole_mctxt_a_b > $o] :
      ( ( member6103717091360755792xt_a_b @ X2 @ ( collec3715850105416846482xt_a_b @ ( produc3751450646053246316_a_b_o @ A4 ) ) )
     => ( A4 @ ( produc2029583840371251459xt_a_b @ X2 ) @ ( produc4775144687201070661xt_a_b @ X2 ) ) ) ).

% Product_Type.Collect_case_prodD
thf(fact_319_Product__Type_OCollect__case__prodD,axiom,
    ! [X2: produc3963297410138542439list_b,A4: list_b > list_b > $o] :
      ( ( member2990321877988238992list_b @ X2 @ ( collec4964980819554056914list_b @ ( produc6051822690389492396st_b_o @ A4 ) ) )
     => ( A4 @ ( produc7649009375908944835list_b @ X2 ) @ ( produc3345134588468168965list_b @ X2 ) ) ) ).

% Product_Type.Collect_case_prodD
thf(fact_320_Product__Type_OCollect__case__prodD,axiom,
    ! [X2: product_prod_nat_nat,A4: nat > nat > $o] :
      ( ( member8440522571783428010at_nat @ X2 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ A4 ) ) )
     => ( A4 @ ( product_fst_nat_nat @ X2 ) @ ( product_snd_nat_nat @ X2 ) ) ) ).

% Product_Type.Collect_case_prodD
thf(fact_321_Product__Type_OCollect__case__prodD,axiom,
    ! [X2: product_prod_o_o,A4: $o > $o > $o] :
      ( ( member7466972457876170832od_o_o @ X2 @ ( collec3167064739498627218od_o_o @ ( produc6197397395684419436_o_o_o @ A4 ) ) )
     => ( A4 @ ( product_fst_o_o @ X2 ) @ ( product_snd_o_o @ X2 ) ) ) ).

% Product_Type.Collect_case_prodD
thf(fact_322_Product__Type_OCollect__case__prodD,axiom,
    ! [X2: produc746580111399690912list_b,A4: multihole_mctxt_a_b > list_b > $o] :
      ( ( member3572491845649744329list_b @ X2 @ ( collec5933784528073787915list_b @ ( produc7190274377712547635st_b_o @ A4 ) ) )
     => ( A4 @ ( produc5881749095783049980list_b @ X2 ) @ ( produc6107117247873403966list_b @ X2 ) ) ) ).

% Product_Type.Collect_case_prodD
thf(fact_323_Product__Type_OCollect__case__prodD,axiom,
    ! [X2: produc5647625992154082286xt_a_b,A4: list_b > multihole_mctxt_a_b > $o] :
      ( ( member8473537726404135703xt_a_b @ X2 @ ( collec1611458371973403481xt_a_b @ ( produc1221931734719695589_a_b_o @ A4 ) ) )
     => ( A4 @ ( produc6500241281145331658xt_a_b @ X2 ) @ ( produc6725609433235685644xt_a_b @ X2 ) ) ) ).

% Product_Type.Collect_case_prodD
thf(fact_324_case__prod__beta,axiom,
    ( produc6892829578239444825xt_a_b
    = ( ^ [F2: list_b > multihole_mctxt_a_b > multihole_mctxt_a_b,P4: produc5647625992154082286xt_a_b] : ( F2 @ ( produc6500241281145331658xt_a_b @ P4 ) @ ( produc6725609433235685644xt_a_b @ P4 ) ) ) ) ).

% case_prod_beta
thf(fact_325_case__prod__beta,axiom,
    ( produc3271728269314753389list_b
    = ( ^ [F2: list_b > multihole_mctxt_a_b > produc746580111399690912list_b,P4: produc5647625992154082286xt_a_b] : ( F2 @ ( produc6500241281145331658xt_a_b @ P4 ) @ ( produc6725609433235685644xt_a_b @ P4 ) ) ) ) ).

% case_prod_beta
thf(fact_326_case__prod__beta,axiom,
    ( produc5071610215621926226list_b
    = ( ^ [F2: list_b > multihole_mctxt_a_b > list_b,P4: produc5647625992154082286xt_a_b] : ( F2 @ ( produc6500241281145331658xt_a_b @ P4 ) @ ( produc6725609433235685644xt_a_b @ P4 ) ) ) ) ).

% case_prod_beta
thf(fact_327_case__prod__beta,axiom,
    ( produc1221931734719695589_a_b_o
    = ( ^ [F2: list_b > multihole_mctxt_a_b > $o,P4: produc5647625992154082286xt_a_b] : ( F2 @ ( produc6500241281145331658xt_a_b @ P4 ) @ ( produc6725609433235685644xt_a_b @ P4 ) ) ) ) ).

% case_prod_beta
thf(fact_328_case__prod__beta,axiom,
    ( produc6197397395684419436_o_o_o
    = ( ^ [F2: $o > $o > $o,P4: product_prod_o_o] : ( F2 @ ( product_fst_o_o @ P4 ) @ ( product_snd_o_o @ P4 ) ) ) ) ).

% case_prod_beta
thf(fact_329_split__beta,axiom,
    ( produc6892829578239444825xt_a_b
    = ( ^ [F2: list_b > multihole_mctxt_a_b > multihole_mctxt_a_b,Prod3: produc5647625992154082286xt_a_b] : ( F2 @ ( produc6500241281145331658xt_a_b @ Prod3 ) @ ( produc6725609433235685644xt_a_b @ Prod3 ) ) ) ) ).

% split_beta
thf(fact_330_split__beta,axiom,
    ( produc3271728269314753389list_b
    = ( ^ [F2: list_b > multihole_mctxt_a_b > produc746580111399690912list_b,Prod3: produc5647625992154082286xt_a_b] : ( F2 @ ( produc6500241281145331658xt_a_b @ Prod3 ) @ ( produc6725609433235685644xt_a_b @ Prod3 ) ) ) ) ).

% split_beta
thf(fact_331_split__beta,axiom,
    ( produc5071610215621926226list_b
    = ( ^ [F2: list_b > multihole_mctxt_a_b > list_b,Prod3: produc5647625992154082286xt_a_b] : ( F2 @ ( produc6500241281145331658xt_a_b @ Prod3 ) @ ( produc6725609433235685644xt_a_b @ Prod3 ) ) ) ) ).

% split_beta
thf(fact_332_split__beta,axiom,
    ( produc1221931734719695589_a_b_o
    = ( ^ [F2: list_b > multihole_mctxt_a_b > $o,Prod3: produc5647625992154082286xt_a_b] : ( F2 @ ( produc6500241281145331658xt_a_b @ Prod3 ) @ ( produc6725609433235685644xt_a_b @ Prod3 ) ) ) ) ).

% split_beta
thf(fact_333_split__beta,axiom,
    ( produc6197397395684419436_o_o_o
    = ( ^ [F2: $o > $o > $o,Prod3: product_prod_o_o] : ( F2 @ ( product_fst_o_o @ Prod3 ) @ ( product_snd_o_o @ Prod3 ) ) ) ) ).

% split_beta
thf(fact_334_internal__case__prod__def,axiom,
    produc5361274526421632259xt_a_b = produc6892829578239444825xt_a_b ).

% internal_case_prod_def
thf(fact_335_internal__case__prod__def,axiom,
    produc1496949917810534935list_b = produc3271728269314753389list_b ).

% internal_case_prod_def
thf(fact_336_internal__case__prod__def,axiom,
    produc927258620547716860list_b = produc5071610215621926226list_b ).

% internal_case_prod_def
thf(fact_337_internal__case__prod__def,axiom,
    produc8837310327220950671_a_b_o = produc1221931734719695589_a_b_o ).

% internal_case_prod_def
thf(fact_338_internal__case__prod__def,axiom,
    produc331225583472661270_o_o_o = produc6197397395684419436_o_o_o ).

% internal_case_prod_def
thf(fact_339_split__cong,axiom,
    ! [Q: produc5647625992154082286xt_a_b,F: list_b > multihole_mctxt_a_b > multihole_mctxt_a_b,G: list_b > multihole_mctxt_a_b > multihole_mctxt_a_b,P: produc5647625992154082286xt_a_b] :
      ( ! [X: list_b,Y: multihole_mctxt_a_b] :
          ( ( ( produc8821373537598205406xt_a_b @ X @ Y )
            = Q )
         => ( ( F @ X @ Y )
            = ( G @ X @ Y ) ) )
     => ( ( P = Q )
       => ( ( produc6892829578239444825xt_a_b @ F @ P )
          = ( produc6892829578239444825xt_a_b @ G @ Q ) ) ) ) ).

% split_cong
thf(fact_340_split__cong,axiom,
    ! [Q: produc5647625992154082286xt_a_b,F: list_b > multihole_mctxt_a_b > produc746580111399690912list_b,G: list_b > multihole_mctxt_a_b > produc746580111399690912list_b,P: produc5647625992154082286xt_a_b] :
      ( ! [X: list_b,Y: multihole_mctxt_a_b] :
          ( ( ( produc8821373537598205406xt_a_b @ X @ Y )
            = Q )
         => ( ( F @ X @ Y )
            = ( G @ X @ Y ) ) )
     => ( ( P = Q )
       => ( ( produc3271728269314753389list_b @ F @ P )
          = ( produc3271728269314753389list_b @ G @ Q ) ) ) ) ).

% split_cong
thf(fact_341_split__cong,axiom,
    ! [Q: produc5647625992154082286xt_a_b,F: list_b > multihole_mctxt_a_b > list_b,G: list_b > multihole_mctxt_a_b > list_b,P: produc5647625992154082286xt_a_b] :
      ( ! [X: list_b,Y: multihole_mctxt_a_b] :
          ( ( ( produc8821373537598205406xt_a_b @ X @ Y )
            = Q )
         => ( ( F @ X @ Y )
            = ( G @ X @ Y ) ) )
     => ( ( P = Q )
       => ( ( produc5071610215621926226list_b @ F @ P )
          = ( produc5071610215621926226list_b @ G @ Q ) ) ) ) ).

% split_cong
thf(fact_342_split__cong,axiom,
    ! [Q: produc5647625992154082286xt_a_b,F: list_b > multihole_mctxt_a_b > $o,G: list_b > multihole_mctxt_a_b > $o,P: produc5647625992154082286xt_a_b] :
      ( ! [X: list_b,Y: multihole_mctxt_a_b] :
          ( ( ( produc8821373537598205406xt_a_b @ X @ Y )
            = Q )
         => ( ( F @ X @ Y )
            = ( G @ X @ Y ) ) )
     => ( ( P = Q )
       => ( ( produc1221931734719695589_a_b_o @ F @ P )
          = ( produc1221931734719695589_a_b_o @ G @ Q ) ) ) ) ).

% split_cong
thf(fact_343_split__cong,axiom,
    ! [Q: product_prod_o_o,F: $o > $o > $o,G: $o > $o > $o,P: product_prod_o_o] :
      ( ! [X: $o,Y: $o] :
          ( ( ( product_Pair_o_o @ X @ Y )
            = Q )
         => ( ( F @ X @ Y )
            = ( G @ X @ Y ) ) )
     => ( ( P = Q )
       => ( ( produc6197397395684419436_o_o_o @ F @ P )
          = ( produc6197397395684419436_o_o_o @ G @ Q ) ) ) ) ).

% split_cong
thf(fact_344_csquare__fstOp__sndOp,axiom,
    ! [F: ( list_b > list_b > $o ) > produc3963297410138542439list_b > $o,P2: list_b > multihole_mctxt_a_b > $o,Q3: multihole_mctxt_a_b > list_b > $o] : ( bNF_cs1829493375424135524list_b @ ( collec4964980819554056914list_b @ ( F @ ( relcom5984404918849557005list_b @ P2 @ Q3 ) ) ) @ produc6725609433235685644xt_a_b @ produc5881749095783049980list_b @ ( bNF_fs4131671769207270604list_b @ P2 @ Q3 ) @ ( bNF_sn4055164193756949002list_b @ P2 @ Q3 ) ) ).

% csquare_fstOp_sndOp
thf(fact_345_csquare__fstOp__sndOp,axiom,
    ! [F: ( multihole_mctxt_a_b > multihole_mctxt_a_b > $o ) > produc1652119919080531751xt_a_b > $o,P2: multihole_mctxt_a_b > list_b > $o,Q3: list_b > multihole_mctxt_a_b > $o] : ( bNF_cs1790445340265650155xt_a_b @ ( collec3715850105416846482xt_a_b @ ( F @ ( relcom2095153813457710178xt_a_b @ P2 @ Q3 ) ) ) @ produc6107117247873403966list_b @ produc6500241281145331658xt_a_b @ ( bNF_fs7855130708986367265xt_a_b @ P2 @ Q3 ) @ ( bNF_sn8855334143865345631xt_a_b @ P2 @ Q3 ) ) ).

% csquare_fstOp_sndOp
thf(fact_346_csquare__fstOp__sndOp,axiom,
    ! [F: ( $o > $o > $o ) > product_prod_o_o > $o,P2: $o > $o > $o,Q3: $o > $o > $o] : ( bNF_cs6420615464401995480od_o_o @ ( collec3167064739498627218od_o_o @ ( F @ ( relcompp_o_o_o @ P2 @ Q3 ) ) ) @ product_snd_o_o @ product_fst_o_o @ ( bNF_fstOp_o_o_o @ P2 @ Q3 ) @ ( bNF_sndOp_o_o_o @ P2 @ Q3 ) ) ).

% csquare_fstOp_sndOp
thf(fact_347_csquare__fstOp__sndOp,axiom,
    ! [F: ( nat > nat > $o ) > product_prod_nat_nat > $o,P2: nat > nat > $o,Q3: nat > nat > $o] : ( bNF_cs7448163979520790438at_nat @ ( collec3392354462482085612at_nat @ ( F @ ( relcompp_nat_nat_nat @ P2 @ Q3 ) ) ) @ product_snd_nat_nat @ product_fst_nat_nat @ ( bNF_fs6799373675401686564at_nat @ P2 @ Q3 ) @ ( bNF_sn8916957246138178918at_nat @ P2 @ Q3 ) ) ).

% csquare_fstOp_sndOp
thf(fact_348_csquare__fstOp__sndOp,axiom,
    ! [F: ( list_b > list_b > $o ) > produc3963297410138542439list_b > $o,P2: list_b > list_b > $o,Q3: list_b > list_b > $o] : ( bNF_cs4731316694088296171list_b @ ( collec4964980819554056914list_b @ ( F @ ( relcom3042044877837805780list_b @ P2 @ Q3 ) ) ) @ produc3345134588468168965list_b @ produc7649009375908944835list_b @ ( bNF_fs4460400041868295571list_b @ P2 @ Q3 ) @ ( bNF_sn7302738427532062417list_b @ P2 @ Q3 ) ) ).

% csquare_fstOp_sndOp
thf(fact_349_csquare__fstOp__sndOp,axiom,
    ! [F: ( multihole_mctxt_a_b > list_b > $o ) > produc746580111399690912list_b > $o,P2: multihole_mctxt_a_b > list_b > $o,Q3: list_b > list_b > $o] : ( bNF_cs4566955500544489259list_b @ ( collec5933784528073787915list_b @ ( F @ ( relcom1392755254538352731list_b @ P2 @ Q3 ) ) ) @ produc6107117247873403966list_b @ produc7649009375908944835list_b @ ( bNF_fs8763394141750842138list_b @ P2 @ Q3 ) @ ( bNF_sn8686886566300520536list_b @ P2 @ Q3 ) ) ).

% csquare_fstOp_sndOp
thf(fact_350_csquare__fstOp__sndOp,axiom,
    ! [F: ( list_b > multihole_mctxt_a_b > $o ) > produc5647625992154082286xt_a_b > $o,P2: list_b > list_b > $o,Q3: list_b > multihole_mctxt_a_b > $o] : ( bNF_cs1883607401310078891xt_a_b @ ( collec1611458371973403481xt_a_b @ ( F @ ( relcom6602897104211838683xt_a_b @ P2 @ Q3 ) ) ) @ produc3345134588468168965list_b @ produc6500241281145331658xt_a_b @ ( bNF_fs4750163954569552282xt_a_b @ P2 @ Q3 ) @ ( bNF_sn4673656379119230680xt_a_b @ P2 @ Q3 ) ) ).

% csquare_fstOp_sndOp
thf(fact_351_csquare__fstOp__sndOp,axiom,
    ! [F: ( list_b > multihole_mctxt_a_b > $o ) > produc5647625992154082286xt_a_b > $o,P2: list_b > multihole_mctxt_a_b > $o,Q3: multihole_mctxt_a_b > multihole_mctxt_a_b > $o] : ( bNF_cs6184644846197688868xt_a_b @ ( collec1611458371973403481xt_a_b @ ( F @ ( relcom1134127583608674836xt_a_b @ P2 @ Q3 ) ) ) @ produc6725609433235685644xt_a_b @ produc2029583840371251459xt_a_b @ ( bNF_fs6894104479137331923xt_a_b @ P2 @ Q3 ) @ ( bNF_sn7894307914016310289xt_a_b @ P2 @ Q3 ) ) ).

% csquare_fstOp_sndOp
thf(fact_352_csquare__fstOp__sndOp,axiom,
    ! [F: ( multihole_mctxt_a_b > list_b > $o ) > produc746580111399690912list_b > $o,P2: multihole_mctxt_a_b > multihole_mctxt_a_b > $o,Q3: multihole_mctxt_a_b > list_b > $o] : ( bNF_cs8973424432489419172list_b @ ( collec5933784528073787915list_b @ ( F @ ( relcom1476661628095428500list_b @ P2 @ Q3 ) ) ) @ produc4775144687201070661xt_a_b @ produc5881749095783049980list_b @ ( bNF_fs7236638523624085587list_b @ P2 @ Q3 ) @ ( bNF_sn8236841958503063953list_b @ P2 @ Q3 ) ) ).

% csquare_fstOp_sndOp
thf(fact_353_csquare__fstOp__sndOp,axiom,
    ! [F: ( multihole_mctxt_a_b > multihole_mctxt_a_b > $o ) > produc1652119919080531751xt_a_b > $o,P2: multihole_mctxt_a_b > multihole_mctxt_a_b > $o,Q3: multihole_mctxt_a_b > multihole_mctxt_a_b > $o] : ( bNF_cs4644519502363695716xt_a_b @ ( collec3715850105416846482xt_a_b @ ( F @ ( relcom5598437220703425947xt_a_b @ P2 @ Q3 ) ) ) @ produc4775144687201070661xt_a_b @ produc2029583840371251459xt_a_b @ ( bNF_fs8789942433486863450xt_a_b @ P2 @ Q3 ) @ ( bNF_sn8437382630723965336xt_a_b @ P2 @ Q3 ) ) ).

% csquare_fstOp_sndOp
thf(fact_354_fstsp_Ointros,axiom,
    ! [P: produc3963297410138542439list_b] : ( basic_5911698558650257769list_b @ P @ ( produc7649009375908944835list_b @ P ) ) ).

% fstsp.intros
thf(fact_355_fstsp_Ointros,axiom,
    ! [P: produc1652119919080531751xt_a_b] : ( basic_3885822791963969193xt_a_b @ P @ ( produc2029583840371251459xt_a_b @ P ) ) ).

% fstsp.intros
thf(fact_356_fstsp_Ointros,axiom,
    ! [P: product_prod_o_o] : ( basic_fstsp_o_o @ P @ ( product_fst_o_o @ P ) ) ).

% fstsp.intros
thf(fact_357_fstsp_Ointros,axiom,
    ! [P: product_prod_nat_nat] : ( basic_fstsp_nat_nat @ P @ ( product_fst_nat_nat @ P ) ) ).

% fstsp.intros
thf(fact_358_fstsp_Ointros,axiom,
    ! [P: produc746580111399690912list_b] : ( basic_1006693021222665378list_b @ P @ ( produc5881749095783049980list_b @ P ) ) ).

% fstsp.intros
thf(fact_359_fstsp_Ointros,axiom,
    ! [P: produc5647625992154082286xt_a_b] : ( basic_1625185206584947056xt_a_b @ P @ ( produc6500241281145331658xt_a_b @ P ) ) ).

% fstsp.intros
thf(fact_360_fstsp_Osimps,axiom,
    ( basic_5911698558650257769list_b
    = ( ^ [P4: produc3963297410138542439list_b,A5: list_b] :
          ( A5
          = ( produc7649009375908944835list_b @ P4 ) ) ) ) ).

% fstsp.simps
thf(fact_361_fstsp_Osimps,axiom,
    ( basic_3885822791963969193xt_a_b
    = ( ^ [P4: produc1652119919080531751xt_a_b,A5: multihole_mctxt_a_b] :
          ( A5
          = ( produc2029583840371251459xt_a_b @ P4 ) ) ) ) ).

% fstsp.simps
thf(fact_362_fstsp_Osimps,axiom,
    ( basic_fstsp_o_o
    = ( ^ [P4: product_prod_o_o,A5: $o] :
          ( A5
          = ( product_fst_o_o @ P4 ) ) ) ) ).

% fstsp.simps
thf(fact_363_fstsp_Osimps,axiom,
    ( basic_fstsp_nat_nat
    = ( ^ [P4: product_prod_nat_nat,A5: nat] :
          ( A5
          = ( product_fst_nat_nat @ P4 ) ) ) ) ).

% fstsp.simps
thf(fact_364_fstsp_Osimps,axiom,
    ( basic_1006693021222665378list_b
    = ( ^ [P4: produc746580111399690912list_b,A5: multihole_mctxt_a_b] :
          ( A5
          = ( produc5881749095783049980list_b @ P4 ) ) ) ) ).

% fstsp.simps
thf(fact_365_fstsp_Osimps,axiom,
    ( basic_1625185206584947056xt_a_b
    = ( ^ [P4: produc5647625992154082286xt_a_b,A5: list_b] :
          ( A5
          = ( produc6500241281145331658xt_a_b @ P4 ) ) ) ) ).

% fstsp.simps
thf(fact_366_fstsp_Ocases,axiom,
    ! [P: produc3963297410138542439list_b,A: list_b] :
      ( ( basic_5911698558650257769list_b @ P @ A )
     => ( A
        = ( produc7649009375908944835list_b @ P ) ) ) ).

% fstsp.cases
thf(fact_367_fstsp_Ocases,axiom,
    ! [P: produc1652119919080531751xt_a_b,A: multihole_mctxt_a_b] :
      ( ( basic_3885822791963969193xt_a_b @ P @ A )
     => ( A
        = ( produc2029583840371251459xt_a_b @ P ) ) ) ).

% fstsp.cases
thf(fact_368_fstsp_Ocases,axiom,
    ! [P: product_prod_o_o,A: $o] :
      ( ( basic_fstsp_o_o @ P @ A )
     => ( A
        = ( product_fst_o_o @ P ) ) ) ).

% fstsp.cases
thf(fact_369_fstsp_Ocases,axiom,
    ! [P: product_prod_nat_nat,A: nat] :
      ( ( basic_fstsp_nat_nat @ P @ A )
     => ( A
        = ( product_fst_nat_nat @ P ) ) ) ).

% fstsp.cases
thf(fact_370_fstsp_Ocases,axiom,
    ! [P: produc746580111399690912list_b,A: multihole_mctxt_a_b] :
      ( ( basic_1006693021222665378list_b @ P @ A )
     => ( A
        = ( produc5881749095783049980list_b @ P ) ) ) ).

% fstsp.cases
thf(fact_371_fstsp_Ocases,axiom,
    ! [P: produc5647625992154082286xt_a_b,A: list_b] :
      ( ( basic_1625185206584947056xt_a_b @ P @ A )
     => ( A
        = ( produc6500241281145331658xt_a_b @ P ) ) ) ).

% fstsp.cases
thf(fact_372_pair__in__swap__image,axiom,
    ! [Y3: list_b,X2: list_b,A4: set_Pr7665282455119567943list_b] :
      ( ( member2990321877988238992list_b @ ( produc1564554178308465111list_b @ Y3 @ X2 ) @ ( image_3063139515468067781list_b @ produc6495775440487448439list_b @ A4 ) )
      = ( member2990321877988238992list_b @ ( produc1564554178308465111list_b @ X2 @ Y3 ) @ A4 ) ) ).

% pair_in_swap_image
thf(fact_373_pair__in__swap__image,axiom,
    ! [Y3: multihole_mctxt_a_b,X2: multihole_mctxt_a_b,A4: set_Pr2918931875556005383xt_a_b] :
      ( ( member6103717091360755792xt_a_b @ ( produc67882520014434071xt_a_b @ Y3 @ X2 ) @ ( image_3034241489052758981xt_a_b @ produc1108858440263912631xt_a_b @ A4 ) )
      = ( member6103717091360755792xt_a_b @ ( produc67882520014434071xt_a_b @ X2 @ Y3 ) @ A4 ) ) ).

% pair_in_swap_image
thf(fact_374_pair__in__swap__image,axiom,
    ! [Y3: $o,X2: $o,A4: set_Product_prod_o_o] :
      ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ Y3 @ X2 ) @ ( image_9131363867636255685od_o_o @ product_swap_o_o @ A4 ) )
      = ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X2 @ Y3 ) @ A4 ) ) ).

% pair_in_swap_image
thf(fact_375_pair__in__swap__image,axiom,
    ! [Y3: list_b,X2: multihole_mctxt_a_b,A4: set_Pr1895186847599665920list_b] :
      ( ( member8473537726404135703xt_a_b @ ( produc8821373537598205406xt_a_b @ Y3 @ X2 ) @ ( image_3492653723807366483xt_a_b @ produc4023874437082322608list_b @ A4 ) )
      = ( member3572491845649744329list_b @ ( produc8202881352235923728list_b @ X2 @ Y3 ) @ A4 ) ) ).

% pair_in_swap_image
thf(fact_376_pair__in__swap__image,axiom,
    ! [Y3: multihole_mctxt_a_b,X2: list_b,A4: set_Pr3872688570871424334xt_a_b] :
      ( ( member3572491845649744329list_b @ ( produc8202881352235923728list_b @ Y3 @ X2 ) @ ( image_1828724688096913975list_b @ produc4642366622444604286xt_a_b @ A4 ) )
      = ( member8473537726404135703xt_a_b @ ( produc8821373537598205406xt_a_b @ X2 @ Y3 ) @ A4 ) ) ).

% pair_in_swap_image
thf(fact_377_snd__sndOp,axiom,
    ! [P2: multihole_mctxt_a_b > list_b > $o,Q3: list_b > list_b > $o] :
      ( produc6107117247873403966list_b
      = ( comp_P1089317276477319583list_b @ produc3345134588468168965list_b @ ( bNF_sn8686886566300520536list_b @ P2 @ Q3 ) ) ) ).

% snd_sndOp
thf(fact_378_snd__sndOp,axiom,
    ! [P2: list_b > multihole_mctxt_a_b > $o,Q3: multihole_mctxt_a_b > multihole_mctxt_a_b > $o] :
      ( produc6725609433235685644xt_a_b
      = ( comp_P1113565280179474022xt_a_b @ produc4775144687201070661xt_a_b @ ( bNF_sn7894307914016310289xt_a_b @ P2 @ Q3 ) ) ) ).

% snd_sndOp
thf(fact_379_snd__sndOp,axiom,
    ! [P2: multihole_mctxt_a_b > list_b > $o,Q3: list_b > multihole_mctxt_a_b > $o] :
      ( produc4775144687201070661xt_a_b
      = ( comp_P6941710577075294566xt_a_b @ produc6725609433235685644xt_a_b @ ( bNF_sn8855334143865345631xt_a_b @ P2 @ Q3 ) ) ) ).

% snd_sndOp
thf(fact_380_snd__sndOp,axiom,
    ! [P2: multihole_mctxt_a_b > multihole_mctxt_a_b > $o,Q3: multihole_mctxt_a_b > multihole_mctxt_a_b > $o] :
      ( produc4775144687201070661xt_a_b
      = ( comp_P1228403674089159071xt_a_b @ produc4775144687201070661xt_a_b @ ( bNF_sn8437382630723965336xt_a_b @ P2 @ Q3 ) ) ) ).

% snd_sndOp
thf(fact_381_snd__sndOp,axiom,
    ! [P2: list_b > multihole_mctxt_a_b > $o,Q3: multihole_mctxt_a_b > list_b > $o] :
      ( produc3345134588468168965list_b
      = ( comp_P2427654987725689503list_b @ produc6107117247873403966list_b @ ( bNF_sn4055164193756949002list_b @ P2 @ Q3 ) ) ) ).

% snd_sndOp
thf(fact_382_snd__sndOp,axiom,
    ! [P2: list_b > list_b > $o,Q3: list_b > list_b > $o] :
      ( produc3345134588468168965list_b
      = ( comp_P928982252139745894list_b @ produc3345134588468168965list_b @ ( bNF_sn7302738427532062417list_b @ P2 @ Q3 ) ) ) ).

% snd_sndOp
thf(fact_383_snd__sndOp,axiom,
    ! [P2: $o > $o > $o,Q3: $o > $o > $o] :
      ( product_snd_o_o
      = ( comp_P5935651135916255507od_o_o @ product_snd_o_o @ ( bNF_sndOp_o_o_o @ P2 @ Q3 ) ) ) ).

% snd_sndOp
thf(fact_384_snd__sndOp,axiom,
    ! [P2: nat > nat > $o,Q3: nat > nat > $o] :
      ( product_snd_nat_nat
      = ( comp_P1567445206330693457at_nat @ product_snd_nat_nat @ ( bNF_sn8916957246138178918at_nat @ P2 @ Q3 ) ) ) ).

% snd_sndOp
thf(fact_385_snd__sndOp,axiom,
    ! [P2: multihole_mctxt_a_b > multihole_mctxt_a_b > $o,Q3: multihole_mctxt_a_b > list_b > $o] :
      ( produc6107117247873403966list_b
      = ( comp_P3599965238501839832list_b @ produc6107117247873403966list_b @ ( bNF_sn8236841958503063953list_b @ P2 @ Q3 ) ) ) ).

% snd_sndOp
thf(fact_386_snd__sndOp,axiom,
    ! [P2: list_b > list_b > $o,Q3: list_b > multihole_mctxt_a_b > $o] :
      ( produc6725609433235685644xt_a_b
      = ( comp_P7245731588476948525xt_a_b @ produc6725609433235685644xt_a_b @ ( bNF_sn4673656379119230680xt_a_b @ P2 @ Q3 ) ) ) ).

% snd_sndOp
thf(fact_387_fst__fstOp,axiom,
    ! [P2: multihole_mctxt_a_b > multihole_mctxt_a_b > $o,Q3: multihole_mctxt_a_b > list_b > $o] :
      ( produc5881749095783049980list_b
      = ( comp_P5435891436279858456list_b @ produc2029583840371251459xt_a_b @ ( bNF_fs7236638523624085587list_b @ P2 @ Q3 ) ) ) ).

% fst_fstOp
thf(fact_388_fst__fstOp,axiom,
    ! [P2: list_b > list_b > $o,Q3: list_b > multihole_mctxt_a_b > $o] :
      ( produc6500241281145331658xt_a_b
      = ( comp_P5990363157231710957xt_a_b @ produc7649009375908944835list_b @ ( bNF_fs4750163954569552282xt_a_b @ P2 @ Q3 ) ) ) ).

% fst_fstOp
thf(fact_389_fst__fstOp,axiom,
    ! [P2: list_b > multihole_mctxt_a_b > $o,Q3: multihole_mctxt_a_b > list_b > $o] :
      ( produc7649009375908944835list_b
      = ( comp_P526186434445353453list_b @ produc6500241281145331658xt_a_b @ ( bNF_fs4131671769207270604list_b @ P2 @ Q3 ) ) ) ).

% fst_fstOp
thf(fact_390_fst__fstOp,axiom,
    ! [P2: list_b > list_b > $o,Q3: list_b > list_b > $o] :
      ( produc7649009375908944835list_b
      = ( comp_P928982252139745894list_b @ produc7649009375908944835list_b @ ( bNF_fs4460400041868295571list_b @ P2 @ Q3 ) ) ) ).

% fst_fstOp
thf(fact_391_fst__fstOp,axiom,
    ! [P2: multihole_mctxt_a_b > list_b > $o,Q3: list_b > multihole_mctxt_a_b > $o] :
      ( produc2029583840371251459xt_a_b
      = ( comp_P7940805974138666520xt_a_b @ produc5881749095783049980list_b @ ( bNF_fs7855130708986367265xt_a_b @ P2 @ Q3 ) ) ) ).

% fst_fstOp
thf(fact_392_fst__fstOp,axiom,
    ! [P2: multihole_mctxt_a_b > multihole_mctxt_a_b > $o,Q3: multihole_mctxt_a_b > multihole_mctxt_a_b > $o] :
      ( produc2029583840371251459xt_a_b
      = ( comp_P1228403674089159071xt_a_b @ produc2029583840371251459xt_a_b @ ( bNF_fs8789942433486863450xt_a_b @ P2 @ Q3 ) ) ) ).

% fst_fstOp
thf(fact_393_fst__fstOp,axiom,
    ! [P2: $o > $o > $o,Q3: $o > $o > $o] :
      ( product_fst_o_o
      = ( comp_P5935651135916255507od_o_o @ product_fst_o_o @ ( bNF_fstOp_o_o_o @ P2 @ Q3 ) ) ) ).

% fst_fstOp
thf(fact_394_fst__fstOp,axiom,
    ! [P2: nat > nat > $o,Q3: nat > nat > $o] :
      ( product_fst_nat_nat
      = ( comp_P1567445206330693457at_nat @ product_fst_nat_nat @ ( bNF_fs6799373675401686564at_nat @ P2 @ Q3 ) ) ) ).

% fst_fstOp
thf(fact_395_fst__fstOp,axiom,
    ! [P2: multihole_mctxt_a_b > list_b > $o,Q3: list_b > list_b > $o] :
      ( produc5881749095783049980list_b
      = ( comp_P9065761140792057745list_b @ produc5881749095783049980list_b @ ( bNF_fs8763394141750842138list_b @ P2 @ Q3 ) ) ) ).

% fst_fstOp
thf(fact_396_fst__fstOp,axiom,
    ! [P2: list_b > multihole_mctxt_a_b > $o,Q3: multihole_mctxt_a_b > multihole_mctxt_a_b > $o] :
      ( produc6500241281145331658xt_a_b
      = ( comp_P8325075377515255924xt_a_b @ produc6500241281145331658xt_a_b @ ( bNF_fs6894104479137331923xt_a_b @ P2 @ Q3 ) ) ) ).

% fst_fstOp
thf(fact_397_comp__cong,axiom,
    ! [F: list_b > list_b,G: produc746580111399690912list_b > list_b,X2: produc746580111399690912list_b,F3: list_b > list_b,G2: produc746580111399690912list_b > list_b,X4: produc746580111399690912list_b] :
      ( ( ( F @ ( G @ X2 ) )
        = ( F3 @ ( G2 @ X4 ) ) )
     => ( ( comp_l6451439721888030909list_b @ F @ G @ X2 )
        = ( comp_l6451439721888030909list_b @ F3 @ G2 @ X4 ) ) ) ).

% comp_cong
thf(fact_398_comp__cong,axiom,
    ! [F: list_b > list_b,G: produc746580111399690912list_b > list_b,X2: produc746580111399690912list_b,F3: list_b > list_b,G2: produc5647625992154082286xt_a_b > list_b,X4: produc5647625992154082286xt_a_b] :
      ( ( ( F @ ( G @ X2 ) )
        = ( F3 @ ( G2 @ X4 ) ) )
     => ( ( comp_l6451439721888030909list_b @ F @ G @ X2 )
        = ( comp_l2129113565787646475xt_a_b @ F3 @ G2 @ X4 ) ) ) ).

% comp_cong
thf(fact_399_comp__cong,axiom,
    ! [F: list_b > list_b,G: produc5647625992154082286xt_a_b > list_b,X2: produc5647625992154082286xt_a_b,F3: list_b > list_b,G2: produc746580111399690912list_b > list_b,X4: produc746580111399690912list_b] :
      ( ( ( F @ ( G @ X2 ) )
        = ( F3 @ ( G2 @ X4 ) ) )
     => ( ( comp_l2129113565787646475xt_a_b @ F @ G @ X2 )
        = ( comp_l6451439721888030909list_b @ F3 @ G2 @ X4 ) ) ) ).

% comp_cong
thf(fact_400_comp__cong,axiom,
    ! [F: list_b > list_b,G: produc5647625992154082286xt_a_b > list_b,X2: produc5647625992154082286xt_a_b,F3: list_b > list_b,G2: produc5647625992154082286xt_a_b > list_b,X4: produc5647625992154082286xt_a_b] :
      ( ( ( F @ ( G @ X2 ) )
        = ( F3 @ ( G2 @ X4 ) ) )
     => ( ( comp_l2129113565787646475xt_a_b @ F @ G @ X2 )
        = ( comp_l2129113565787646475xt_a_b @ F3 @ G2 @ X4 ) ) ) ).

% comp_cong
thf(fact_401_comp__cong,axiom,
    ! [F: $o > $o,G: nat > $o,X2: nat,F3: $o > $o,G2: nat > $o,X4: nat] :
      ( ( ( F @ ( G @ X2 ) )
        = ( F3 @ ( G2 @ X4 ) ) )
     => ( ( comp_o_o_nat @ F @ G @ X2 )
        = ( comp_o_o_nat @ F3 @ G2 @ X4 ) ) ) ).

% comp_cong
thf(fact_402_comp__cong,axiom,
    ! [F: $o > $o,G: nat > $o,X2: nat,F3: nat > $o,G2: nat > nat,X4: nat] :
      ( ( ( F @ ( G @ X2 ) )
        = ( F3 @ ( G2 @ X4 ) ) )
     => ( ( comp_o_o_nat @ F @ G @ X2 )
        = ( comp_nat_o_nat @ F3 @ G2 @ X4 ) ) ) ).

% comp_cong
thf(fact_403_comp__cong,axiom,
    ! [F: nat > product_prod_nat_nat,G: nat > nat,X2: nat,F3: nat > product_prod_nat_nat,G2: nat > nat,X4: nat] :
      ( ( ( F @ ( G @ X2 ) )
        = ( F3 @ ( G2 @ X4 ) ) )
     => ( ( comp_n8574565218330151774at_nat @ F @ G @ X2 )
        = ( comp_n8574565218330151774at_nat @ F3 @ G2 @ X4 ) ) ) ).

% comp_cong
thf(fact_404_comp__cong,axiom,
    ! [F: nat > $o,G: nat > nat,X2: nat,F3: $o > $o,G2: nat > $o,X4: nat] :
      ( ( ( F @ ( G @ X2 ) )
        = ( F3 @ ( G2 @ X4 ) ) )
     => ( ( comp_nat_o_nat @ F @ G @ X2 )
        = ( comp_o_o_nat @ F3 @ G2 @ X4 ) ) ) ).

% comp_cong
thf(fact_405_comp__cong,axiom,
    ! [F: nat > $o,G: nat > nat,X2: nat,F3: nat > $o,G2: nat > nat,X4: nat] :
      ( ( ( F @ ( G @ X2 ) )
        = ( F3 @ ( G2 @ X4 ) ) )
     => ( ( comp_nat_o_nat @ F @ G @ X2 )
        = ( comp_nat_o_nat @ F3 @ G2 @ X4 ) ) ) ).

% comp_cong
thf(fact_406_comp__cong,axiom,
    ! [F: nat > nat,G: nat > nat,X2: nat,F3: nat > nat,G2: nat > nat,X4: nat] :
      ( ( ( F @ ( G @ X2 ) )
        = ( F3 @ ( G2 @ X4 ) ) )
     => ( ( comp_nat_nat_nat @ F @ G @ X2 )
        = ( comp_nat_nat_nat @ F3 @ G2 @ X4 ) ) ) ).

% comp_cong
thf(fact_407_fun_Omap__comp,axiom,
    ! [G: nat > nat,F: nat > nat,V: nat > nat] :
      ( ( comp_nat_nat_nat @ G @ ( comp_nat_nat_nat @ F @ V ) )
      = ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_408_fun_Omap__comp,axiom,
    ! [G: $o > nat,F: nat > $o,V: nat > nat] :
      ( ( comp_o_nat_nat @ G @ ( comp_nat_o_nat @ F @ V ) )
      = ( comp_nat_nat_nat @ ( comp_o_nat_nat @ G @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_409_fun_Omap__comp,axiom,
    ! [G: $o > $o,F: $o > $o,V: nat > $o] :
      ( ( comp_o_o_nat @ G @ ( comp_o_o_nat @ F @ V ) )
      = ( comp_o_o_nat @ ( comp_o_o_o @ G @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_410_fun_Omap__comp,axiom,
    ! [G: $o > $o,F: nat > $o,V: nat > nat] :
      ( ( comp_o_o_nat @ G @ ( comp_nat_o_nat @ F @ V ) )
      = ( comp_nat_o_nat @ ( comp_o_o_nat @ G @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_411_fun_Omap__comp,axiom,
    ! [G: nat > $o,F: $o > nat,V: nat > $o] :
      ( ( comp_nat_o_nat @ G @ ( comp_o_nat_nat @ F @ V ) )
      = ( comp_o_o_nat @ ( comp_nat_o_o @ G @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_412_fun_Omap__comp,axiom,
    ! [G: nat > $o,F: nat > nat,V: nat > nat] :
      ( ( comp_nat_o_nat @ G @ ( comp_nat_nat_nat @ F @ V ) )
      = ( comp_nat_o_nat @ ( comp_nat_o_nat @ G @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_413_fun_Omap__comp,axiom,
    ! [G: product_prod_nat_nat > nat,F: nat > product_prod_nat_nat,V: nat > nat] :
      ( ( comp_P1955610211387027840at_nat @ G @ ( comp_n8574565218330151774at_nat @ F @ V ) )
      = ( comp_nat_nat_nat @ ( comp_P1955610211387027840at_nat @ G @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_414_fun_Omap__comp,axiom,
    ! [G: product_prod_nat_nat > $o,F: nat > product_prod_nat_nat,V: nat > nat] :
      ( ( comp_P1291532814139040010_o_nat @ G @ ( comp_n8574565218330151774at_nat @ F @ V ) )
      = ( comp_nat_o_nat @ ( comp_P1291532814139040010_o_nat @ G @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_415_fun_Omap__comp,axiom,
    ! [G: $o > product_prod_nat_nat,F: nat > $o,V: nat > nat] :
      ( ( comp_o3333229022555693340at_nat @ G @ ( comp_nat_o_nat @ F @ V ) )
      = ( comp_n8574565218330151774at_nat @ ( comp_o3333229022555693340at_nat @ G @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_416_fun_Omap__comp,axiom,
    ! [G: nat > product_prod_nat_nat,F: nat > nat,V: nat > nat] :
      ( ( comp_n8574565218330151774at_nat @ G @ ( comp_nat_nat_nat @ F @ V ) )
      = ( comp_n8574565218330151774at_nat @ ( comp_n8574565218330151774at_nat @ G @ F ) @ V ) ) ).

% fun.map_comp
thf(fact_417_comp__apply__eq,axiom,
    ! [F: list_b > list_b,G: produc746580111399690912list_b > list_b,X2: produc746580111399690912list_b,H: list_b > list_b,K: produc746580111399690912list_b > list_b] :
      ( ( ( F @ ( G @ X2 ) )
        = ( H @ ( K @ X2 ) ) )
     => ( ( comp_l6451439721888030909list_b @ F @ G @ X2 )
        = ( comp_l6451439721888030909list_b @ H @ K @ X2 ) ) ) ).

% comp_apply_eq
thf(fact_418_comp__apply__eq,axiom,
    ! [F: list_b > list_b,G: produc5647625992154082286xt_a_b > list_b,X2: produc5647625992154082286xt_a_b,H: list_b > list_b,K: produc5647625992154082286xt_a_b > list_b] :
      ( ( ( F @ ( G @ X2 ) )
        = ( H @ ( K @ X2 ) ) )
     => ( ( comp_l2129113565787646475xt_a_b @ F @ G @ X2 )
        = ( comp_l2129113565787646475xt_a_b @ H @ K @ X2 ) ) ) ).

% comp_apply_eq
thf(fact_419_comp__apply__eq,axiom,
    ! [F: $o > $o,G: nat > $o,X2: nat,H: $o > $o,K: nat > $o] :
      ( ( ( F @ ( G @ X2 ) )
        = ( H @ ( K @ X2 ) ) )
     => ( ( comp_o_o_nat @ F @ G @ X2 )
        = ( comp_o_o_nat @ H @ K @ X2 ) ) ) ).

% comp_apply_eq
thf(fact_420_comp__apply__eq,axiom,
    ! [F: $o > $o,G: nat > $o,X2: nat,H: nat > $o,K: nat > nat] :
      ( ( ( F @ ( G @ X2 ) )
        = ( H @ ( K @ X2 ) ) )
     => ( ( comp_o_o_nat @ F @ G @ X2 )
        = ( comp_nat_o_nat @ H @ K @ X2 ) ) ) ).

% comp_apply_eq
thf(fact_421_comp__apply__eq,axiom,
    ! [F: nat > product_prod_nat_nat,G: nat > nat,X2: nat,H: nat > product_prod_nat_nat,K: nat > nat] :
      ( ( ( F @ ( G @ X2 ) )
        = ( H @ ( K @ X2 ) ) )
     => ( ( comp_n8574565218330151774at_nat @ F @ G @ X2 )
        = ( comp_n8574565218330151774at_nat @ H @ K @ X2 ) ) ) ).

% comp_apply_eq
thf(fact_422_comp__apply__eq,axiom,
    ! [F: nat > $o,G: nat > nat,X2: nat,H: $o > $o,K: nat > $o] :
      ( ( ( F @ ( G @ X2 ) )
        = ( H @ ( K @ X2 ) ) )
     => ( ( comp_nat_o_nat @ F @ G @ X2 )
        = ( comp_o_o_nat @ H @ K @ X2 ) ) ) ).

% comp_apply_eq
thf(fact_423_comp__apply__eq,axiom,
    ! [F: nat > $o,G: nat > nat,X2: nat,H: nat > $o,K: nat > nat] :
      ( ( ( F @ ( G @ X2 ) )
        = ( H @ ( K @ X2 ) ) )
     => ( ( comp_nat_o_nat @ F @ G @ X2 )
        = ( comp_nat_o_nat @ H @ K @ X2 ) ) ) ).

% comp_apply_eq
thf(fact_424_comp__apply__eq,axiom,
    ! [F: nat > nat,G: nat > nat,X2: nat,H: nat > nat,K: nat > nat] :
      ( ( ( F @ ( G @ X2 ) )
        = ( H @ ( K @ X2 ) ) )
     => ( ( comp_nat_nat_nat @ F @ G @ X2 )
        = ( comp_nat_nat_nat @ H @ K @ X2 ) ) ) ).

% comp_apply_eq
thf(fact_425_pick__middlep,axiom,
    ! [P2: list_b > multihole_mctxt_a_b > $o,Q3: multihole_mctxt_a_b > list_b > $o,A: list_b,C2: list_b] :
      ( ( relcom5984404918849557005list_b @ P2 @ Q3 @ A @ C2 )
     => ( ( P2 @ A @ ( bNF_pi4502194704792575258list_b @ P2 @ Q3 @ A @ C2 ) )
        & ( Q3 @ ( bNF_pi4502194704792575258list_b @ P2 @ Q3 @ A @ C2 ) @ C2 ) ) ) ).

% pick_middlep
thf(fact_426_pick__middlep,axiom,
    ! [P2: list_b > produc5647625992154082286xt_a_b > $o,Q3: produc5647625992154082286xt_a_b > multihole_mctxt_a_b > $o,A: list_b,C2: multihole_mctxt_a_b] :
      ( ( relcom2105089833257999154xt_a_b @ P2 @ Q3 @ A @ C2 )
     => ( ( P2 @ A @ ( bNF_pi1062526254230083775xt_a_b @ P2 @ Q3 @ A @ C2 ) )
        & ( Q3 @ ( bNF_pi1062526254230083775xt_a_b @ P2 @ Q3 @ A @ C2 ) @ C2 ) ) ) ).

% pick_middlep
thf(fact_427_pick__middlep,axiom,
    ! [P2: nat > nat > $o,Q3: nat > nat > $o,A: nat,C2: nat] :
      ( ( relcompp_nat_nat_nat @ P2 @ Q3 @ A @ C2 )
     => ( ( P2 @ A @ ( bNF_pi7484965678128203350at_nat @ P2 @ Q3 @ A @ C2 ) )
        & ( Q3 @ ( bNF_pi7484965678128203350at_nat @ P2 @ Q3 @ A @ C2 ) @ C2 ) ) ) ).

% pick_middlep
thf(fact_428_pick__middlep,axiom,
    ! [P2: ( nat > multihole_mctxt_a_b ) > ( nat > produc746580111399690912list_b ) > $o,Q3: ( nat > produc746580111399690912list_b ) > ( nat > list_b ) > $o,A: nat > multihole_mctxt_a_b,C2: nat > list_b] :
      ( ( relcom4037855281751361575list_b @ P2 @ Q3 @ A @ C2 )
     => ( ( P2 @ A @ ( bNF_pi5184178112509165364list_b @ P2 @ Q3 @ A @ C2 ) )
        & ( Q3 @ ( bNF_pi5184178112509165364list_b @ P2 @ Q3 @ A @ C2 ) @ C2 ) ) ) ).

% pick_middlep
thf(fact_429_pick__middlep,axiom,
    ! [P2: ( nat > list_b ) > ( nat > produc5647625992154082286xt_a_b ) > $o,Q3: ( nat > produc5647625992154082286xt_a_b ) > ( nat > multihole_mctxt_a_b ) > $o,A: nat > list_b,C2: nat > multihole_mctxt_a_b] :
      ( ( relcom5838476793205533529xt_a_b @ P2 @ Q3 @ A @ C2 )
     => ( ( P2 @ A @ ( bNF_pi6984799623963337318xt_a_b @ P2 @ Q3 @ A @ C2 ) )
        & ( Q3 @ ( bNF_pi6984799623963337318xt_a_b @ P2 @ Q3 @ A @ C2 ) @ C2 ) ) ) ).

% pick_middlep
thf(fact_430_fstOp__in,axiom,
    ! [Ac2: produc1652119919080531751xt_a_b,P2: multihole_mctxt_a_b > list_b > $o,Q3: list_b > multihole_mctxt_a_b > $o] :
      ( ( member6103717091360755792xt_a_b @ Ac2 @ ( collec3715850105416846482xt_a_b @ ( produc3751450646053246316_a_b_o @ ( relcom2095153813457710178xt_a_b @ P2 @ Q3 ) ) ) )
     => ( member3572491845649744329list_b @ ( bNF_fs7855130708986367265xt_a_b @ P2 @ Q3 @ Ac2 ) @ ( collec5933784528073787915list_b @ ( produc7190274377712547635st_b_o @ P2 ) ) ) ) ).

% fstOp_in
thf(fact_431_fstOp__in,axiom,
    ! [Ac2: produc746580111399690912list_b,P2: multihole_mctxt_a_b > list_b > $o,Q3: list_b > list_b > $o] :
      ( ( member3572491845649744329list_b @ Ac2 @ ( collec5933784528073787915list_b @ ( produc7190274377712547635st_b_o @ ( relcom1392755254538352731list_b @ P2 @ Q3 ) ) ) )
     => ( member3572491845649744329list_b @ ( bNF_fs8763394141750842138list_b @ P2 @ Q3 @ Ac2 ) @ ( collec5933784528073787915list_b @ ( produc7190274377712547635st_b_o @ P2 ) ) ) ) ).

% fstOp_in
thf(fact_432_fstOp__in,axiom,
    ! [Ac2: product_prod_nat_nat,P2: nat > nat > $o,Q3: nat > nat > $o] :
      ( ( member8440522571783428010at_nat @ Ac2 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ( relcompp_nat_nat_nat @ P2 @ Q3 ) ) ) )
     => ( member8440522571783428010at_nat @ ( bNF_fs6799373675401686564at_nat @ P2 @ Q3 @ Ac2 ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ P2 ) ) ) ) ).

% fstOp_in
thf(fact_433_fstOp__in,axiom,
    ! [Ac2: produc5125836498238150368list_b,P2: ( nat > multihole_mctxt_a_b ) > ( nat > produc746580111399690912list_b ) > $o,Q3: ( nat > produc746580111399690912list_b ) > ( nat > list_b ) > $o] :
      ( ( member2046448123816055561list_b @ Ac2 @ ( collec1001911657118221643list_b @ ( produc477927949550467699st_b_o @ ( relcom4037855281751361575list_b @ P2 @ Q3 ) ) ) )
     => ( member4439946314538814116list_b @ ( bNF_fs5822184879409743590list_b @ P2 @ Q3 @ Ac2 ) @ ( collec7047008785119843814list_b @ ( produc6118959495424706968st_b_o @ P2 ) ) ) ) ).

% fstOp_in
thf(fact_434_fstOp__in,axiom,
    ! [Ac2: produc8094751872729218222xt_a_b,P2: ( nat > list_b ) > ( nat > produc5647625992154082286xt_a_b ) > $o,Q3: ( nat > produc5647625992154082286xt_a_b ) > ( nat > multihole_mctxt_a_b ) > $o] :
      ( ( member5015363498307123415xt_a_b @ Ac2 @ ( collec3970827031609289497xt_a_b @ ( produc8975932433296855461_a_b_o @ ( relcom5838476793205533529xt_a_b @ P2 @ Q3 ) ) ) )
     => ( member7754590689969029177xt_a_b @ ( bNF_fs7622806390863915544xt_a_b @ P2 @ Q3 @ Ac2 ) @ ( collec856815870434662267xt_a_b @ ( produc6855914207928862147_a_b_o @ P2 ) ) ) ) ).

% fstOp_in
thf(fact_435_fstOp__in,axiom,
    ! [Ac2: produc3963297410138542439list_b,P2: list_b > multihole_mctxt_a_b > $o,Q3: multihole_mctxt_a_b > list_b > $o] :
      ( ( member2990321877988238992list_b @ Ac2 @ ( collec4964980819554056914list_b @ ( produc6051822690389492396st_b_o @ ( relcom5984404918849557005list_b @ P2 @ Q3 ) ) ) )
     => ( member8473537726404135703xt_a_b @ ( bNF_fs4131671769207270604list_b @ P2 @ Q3 @ Ac2 ) @ ( collec1611458371973403481xt_a_b @ ( produc1221931734719695589_a_b_o @ P2 ) ) ) ) ).

% fstOp_in
thf(fact_436_fstOp__in,axiom,
    ! [Ac2: produc5647625992154082286xt_a_b,P2: list_b > produc5647625992154082286xt_a_b > $o,Q3: produc5647625992154082286xt_a_b > multihole_mctxt_a_b > $o] :
      ( ( member8473537726404135703xt_a_b @ Ac2 @ ( collec1611458371973403481xt_a_b @ ( produc1221931734719695589_a_b_o @ ( relcom2105089833257999154xt_a_b @ P2 @ Q3 ) ) ) )
     => ( member4998021903520026361xt_a_b @ ( bNF_fs5383721789538498929xt_a_b @ P2 @ Q3 @ Ac2 ) @ ( collec2632839920380509243xt_a_b @ ( produc4710150075370709635_a_b_o @ P2 ) ) ) ) ).

% fstOp_in
thf(fact_437_fstOp__in,axiom,
    ! [Ac2: produc5647625992154082286xt_a_b,P2: list_b > multihole_mctxt_a_b > $o,Q3: multihole_mctxt_a_b > multihole_mctxt_a_b > $o] :
      ( ( member8473537726404135703xt_a_b @ Ac2 @ ( collec1611458371973403481xt_a_b @ ( produc1221931734719695589_a_b_o @ ( relcom1134127583608674836xt_a_b @ P2 @ Q3 ) ) ) )
     => ( member8473537726404135703xt_a_b @ ( bNF_fs6894104479137331923xt_a_b @ P2 @ Q3 @ Ac2 ) @ ( collec1611458371973403481xt_a_b @ ( produc1221931734719695589_a_b_o @ P2 ) ) ) ) ).

% fstOp_in
thf(fact_438_fstOp__in,axiom,
    ! [Ac2: product_prod_o_o,P2: $o > $o > $o,Q3: $o > $o > $o] :
      ( ( member7466972457876170832od_o_o @ Ac2 @ ( collec3167064739498627218od_o_o @ ( produc6197397395684419436_o_o_o @ ( relcompp_o_o_o @ P2 @ Q3 ) ) ) )
     => ( member7466972457876170832od_o_o @ ( bNF_fstOp_o_o_o @ P2 @ Q3 @ Ac2 ) @ ( collec3167064739498627218od_o_o @ ( produc6197397395684419436_o_o_o @ P2 ) ) ) ) ).

% fstOp_in
thf(fact_439_sndOp__in,axiom,
    ! [Ac2: produc746580111399690912list_b,P2: multihole_mctxt_a_b > multihole_mctxt_a_b > $o,Q3: multihole_mctxt_a_b > list_b > $o] :
      ( ( member3572491845649744329list_b @ Ac2 @ ( collec5933784528073787915list_b @ ( produc7190274377712547635st_b_o @ ( relcom1476661628095428500list_b @ P2 @ Q3 ) ) ) )
     => ( member3572491845649744329list_b @ ( bNF_sn8236841958503063953list_b @ P2 @ Q3 @ Ac2 ) @ ( collec5933784528073787915list_b @ ( produc7190274377712547635st_b_o @ Q3 ) ) ) ) ).

% sndOp_in
thf(fact_440_sndOp__in,axiom,
    ! [Ac2: produc3963297410138542439list_b,P2: list_b > multihole_mctxt_a_b > $o,Q3: multihole_mctxt_a_b > list_b > $o] :
      ( ( member2990321877988238992list_b @ Ac2 @ ( collec4964980819554056914list_b @ ( produc6051822690389492396st_b_o @ ( relcom5984404918849557005list_b @ P2 @ Q3 ) ) ) )
     => ( member3572491845649744329list_b @ ( bNF_sn4055164193756949002list_b @ P2 @ Q3 @ Ac2 ) @ ( collec5933784528073787915list_b @ ( produc7190274377712547635st_b_o @ Q3 ) ) ) ) ).

% sndOp_in
thf(fact_441_sndOp__in,axiom,
    ! [Ac2: product_prod_nat_nat,P2: nat > nat > $o,Q3: nat > nat > $o] :
      ( ( member8440522571783428010at_nat @ Ac2 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ( relcompp_nat_nat_nat @ P2 @ Q3 ) ) ) )
     => ( member8440522571783428010at_nat @ ( bNF_sn8916957246138178918at_nat @ P2 @ Q3 @ Ac2 ) @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ Q3 ) ) ) ) ).

% sndOp_in
thf(fact_442_sndOp__in,axiom,
    ! [Ac2: produc5125836498238150368list_b,P2: ( nat > multihole_mctxt_a_b ) > ( nat > produc746580111399690912list_b ) > $o,Q3: ( nat > produc746580111399690912list_b ) > ( nat > list_b ) > $o] :
      ( ( member2046448123816055561list_b @ Ac2 @ ( collec1001911657118221643list_b @ ( produc477927949550467699st_b_o @ ( relcom4037855281751361575list_b @ P2 @ Q3 ) ) ) )
     => ( member5355190962844423541list_b @ ( bNF_sn4426211646526114852list_b @ P2 @ Q3 @ Ac2 ) @ ( collec7680788180164832439list_b @ ( produc3817622485218950151st_b_o @ Q3 ) ) ) ) ).

% sndOp_in
thf(fact_443_sndOp__in,axiom,
    ! [Ac2: produc8094751872729218222xt_a_b,P2: ( nat > list_b ) > ( nat > produc5647625992154082286xt_a_b ) > $o,Q3: ( nat > produc5647625992154082286xt_a_b ) > ( nat > multihole_mctxt_a_b ) > $o] :
      ( ( member5015363498307123415xt_a_b @ Ac2 @ ( collec3970827031609289497xt_a_b @ ( produc8975932433296855461_a_b_o @ ( relcom5838476793205533529xt_a_b @ P2 @ Q3 ) ) ) )
     => ( member7351333769093339054xt_a_b @ ( bNF_sn6226833157980286806xt_a_b @ P2 @ Q3 @ Ac2 ) @ ( collec735024202819592944xt_a_b @ ( produc1885532244741406222_a_b_o @ Q3 ) ) ) ) ).

% sndOp_in
thf(fact_444_sndOp__in,axiom,
    ! [Ac2: produc1652119919080531751xt_a_b,P2: multihole_mctxt_a_b > list_b > $o,Q3: list_b > multihole_mctxt_a_b > $o] :
      ( ( member6103717091360755792xt_a_b @ Ac2 @ ( collec3715850105416846482xt_a_b @ ( produc3751450646053246316_a_b_o @ ( relcom2095153813457710178xt_a_b @ P2 @ Q3 ) ) ) )
     => ( member8473537726404135703xt_a_b @ ( bNF_sn8855334143865345631xt_a_b @ P2 @ Q3 @ Ac2 ) @ ( collec1611458371973403481xt_a_b @ ( produc1221931734719695589_a_b_o @ Q3 ) ) ) ) ).

% sndOp_in
thf(fact_445_sndOp__in,axiom,
    ! [Ac2: produc5647625992154082286xt_a_b,P2: list_b > produc5647625992154082286xt_a_b > $o,Q3: produc5647625992154082286xt_a_b > multihole_mctxt_a_b > $o] :
      ( ( member8473537726404135703xt_a_b @ Ac2 @ ( collec1611458371973403481xt_a_b @ ( produc1221931734719695589_a_b_o @ ( relcom2105089833257999154xt_a_b @ P2 @ Q3 ) ) ) )
     => ( member1744449530997989870xt_a_b @ ( bNF_sn1677556937511116207xt_a_b @ P2 @ Q3 @ Ac2 ) @ ( collec4227569900337431344xt_a_b @ ( produc2838803774393728846_a_b_o @ Q3 ) ) ) ) ).

% sndOp_in
thf(fact_446_sndOp__in,axiom,
    ! [Ac2: produc5647625992154082286xt_a_b,P2: list_b > list_b > $o,Q3: list_b > multihole_mctxt_a_b > $o] :
      ( ( member8473537726404135703xt_a_b @ Ac2 @ ( collec1611458371973403481xt_a_b @ ( produc1221931734719695589_a_b_o @ ( relcom6602897104211838683xt_a_b @ P2 @ Q3 ) ) ) )
     => ( member8473537726404135703xt_a_b @ ( bNF_sn4673656379119230680xt_a_b @ P2 @ Q3 @ Ac2 ) @ ( collec1611458371973403481xt_a_b @ ( produc1221931734719695589_a_b_o @ Q3 ) ) ) ) ).

% sndOp_in
thf(fact_447_sndOp__in,axiom,
    ! [Ac2: product_prod_o_o,P2: $o > $o > $o,Q3: $o > $o > $o] :
      ( ( member7466972457876170832od_o_o @ Ac2 @ ( collec3167064739498627218od_o_o @ ( produc6197397395684419436_o_o_o @ ( relcompp_o_o_o @ P2 @ Q3 ) ) ) )
     => ( member7466972457876170832od_o_o @ ( bNF_sndOp_o_o_o @ P2 @ Q3 @ Ac2 ) @ ( collec3167064739498627218od_o_o @ ( produc6197397395684419436_o_o_o @ Q3 ) ) ) ) ).

% sndOp_in
thf(fact_448_csquare__def,axiom,
    ( bNF_cs1829493375424135524list_b
    = ( ^ [A6: set_Pr7665282455119567943list_b,F1: produc5647625992154082286xt_a_b > multihole_mctxt_a_b,F22: produc746580111399690912list_b > multihole_mctxt_a_b,P13: produc3963297410138542439list_b > produc5647625992154082286xt_a_b,P24: produc3963297410138542439list_b > produc746580111399690912list_b] :
        ! [X3: produc3963297410138542439list_b] :
          ( ( member2990321877988238992list_b @ X3 @ A6 )
         => ( ( F1 @ ( P13 @ X3 ) )
            = ( F22 @ ( P24 @ X3 ) ) ) ) ) ) ).

% csquare_def
thf(fact_449_csquare__def,axiom,
    ( bNF_cs1790445340265650155xt_a_b
    = ( ^ [A6: set_Pr2918931875556005383xt_a_b,F1: produc746580111399690912list_b > list_b,F22: produc5647625992154082286xt_a_b > list_b,P13: produc1652119919080531751xt_a_b > produc746580111399690912list_b,P24: produc1652119919080531751xt_a_b > produc5647625992154082286xt_a_b] :
        ! [X3: produc1652119919080531751xt_a_b] :
          ( ( member6103717091360755792xt_a_b @ X3 @ A6 )
         => ( ( F1 @ ( P13 @ X3 ) )
            = ( F22 @ ( P24 @ X3 ) ) ) ) ) ) ).

% csquare_def
thf(fact_450_comp__apply,axiom,
    ( comp_l6451439721888030909list_b
    = ( ^ [F2: list_b > list_b,G3: produc746580111399690912list_b > list_b,X3: produc746580111399690912list_b] : ( F2 @ ( G3 @ X3 ) ) ) ) ).

% comp_apply
thf(fact_451_comp__apply,axiom,
    ( comp_l2129113565787646475xt_a_b
    = ( ^ [F2: list_b > list_b,G3: produc5647625992154082286xt_a_b > list_b,X3: produc5647625992154082286xt_a_b] : ( F2 @ ( G3 @ X3 ) ) ) ) ).

% comp_apply
thf(fact_452_comp__apply,axiom,
    ( comp_o_o_nat
    = ( ^ [F2: $o > $o,G3: nat > $o,X3: nat] : ( F2 @ ( G3 @ X3 ) ) ) ) ).

% comp_apply
thf(fact_453_comp__apply,axiom,
    ( comp_n8574565218330151774at_nat
    = ( ^ [F2: nat > product_prod_nat_nat,G3: nat > nat,X3: nat] : ( F2 @ ( G3 @ X3 ) ) ) ) ).

% comp_apply
thf(fact_454_comp__apply,axiom,
    ( comp_nat_o_nat
    = ( ^ [F2: nat > $o,G3: nat > nat,X3: nat] : ( F2 @ ( G3 @ X3 ) ) ) ) ).

% comp_apply
thf(fact_455_comp__apply,axiom,
    ( comp_nat_nat_nat
    = ( ^ [F2: nat > nat,G3: nat > nat,X3: nat] : ( F2 @ ( G3 @ X3 ) ) ) ) ).

% comp_apply
thf(fact_456_image__eqI,axiom,
    ! [B: $o,F: $o > $o,X2: $o,A4: set_o] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( member_o @ X2 @ A4 )
       => ( member_o @ B @ ( image_o_o @ F @ A4 ) ) ) ) ).

% image_eqI
thf(fact_457_image__eqI,axiom,
    ! [B: nat,F: $o > nat,X2: $o,A4: set_o] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( member_o @ X2 @ A4 )
       => ( member_nat @ B @ ( image_o_nat @ F @ A4 ) ) ) ) ).

% image_eqI
thf(fact_458_image__eqI,axiom,
    ! [B: $o,F: nat > $o,X2: nat,A4: set_nat] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( member_nat @ X2 @ A4 )
       => ( member_o @ B @ ( image_nat_o @ F @ A4 ) ) ) ) ).

% image_eqI
thf(fact_459_image__eqI,axiom,
    ! [B: nat,F: nat > nat,X2: nat,A4: set_nat] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( member_nat @ X2 @ A4 )
       => ( member_nat @ B @ ( image_nat_nat @ F @ A4 ) ) ) ) ).

% image_eqI
thf(fact_460_image__eqI,axiom,
    ! [B: list_b,F: $o > list_b,X2: $o,A4: set_o] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( member_o @ X2 @ A4 )
       => ( member_list_b @ B @ ( image_o_list_b @ F @ A4 ) ) ) ) ).

% image_eqI
thf(fact_461_image__eqI,axiom,
    ! [B: set_o,F: $o > set_o,X2: $o,A4: set_o] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( member_o @ X2 @ A4 )
       => ( member_set_o @ B @ ( image_o_set_o @ F @ A4 ) ) ) ) ).

% image_eqI
thf(fact_462_image__eqI,axiom,
    ! [B: $o,F: list_b > $o,X2: list_b,A4: set_list_b] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( member_list_b @ X2 @ A4 )
       => ( member_o @ B @ ( image_list_b_o @ F @ A4 ) ) ) ) ).

% image_eqI
thf(fact_463_image__eqI,axiom,
    ! [B: nat,F: list_b > nat,X2: list_b,A4: set_list_b] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( member_list_b @ X2 @ A4 )
       => ( member_nat @ B @ ( image_list_b_nat @ F @ A4 ) ) ) ) ).

% image_eqI
thf(fact_464_image__eqI,axiom,
    ! [B: $o,F: set_o > $o,X2: set_o,A4: set_set_o] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( member_set_o @ X2 @ A4 )
       => ( member_o @ B @ ( image_set_o_o @ F @ A4 ) ) ) ) ).

% image_eqI
thf(fact_465_image__eqI,axiom,
    ! [B: nat,F: set_o > nat,X2: set_o,A4: set_set_o] :
      ( ( B
        = ( F @ X2 ) )
     => ( ( member_set_o @ X2 @ A4 )
       => ( member_nat @ B @ ( image_set_o_nat @ F @ A4 ) ) ) ) ).

% image_eqI
thf(fact_466_image__eq__imp__comp,axiom,
    ! [F: nat > nat,A4: set_nat,G: nat > nat,B5: set_nat,H: nat > nat] :
      ( ( ( image_nat_nat @ F @ A4 )
        = ( image_nat_nat @ G @ B5 ) )
     => ( ( image_nat_nat @ ( comp_nat_nat_nat @ H @ F ) @ A4 )
        = ( image_nat_nat @ ( comp_nat_nat_nat @ H @ G ) @ B5 ) ) ) ).

% image_eq_imp_comp
thf(fact_467_image__eq__imp__comp,axiom,
    ! [F: nat > $o,A4: set_nat,G: nat > $o,B5: set_nat,H: $o > $o] :
      ( ( ( image_nat_o @ F @ A4 )
        = ( image_nat_o @ G @ B5 ) )
     => ( ( image_nat_o @ ( comp_o_o_nat @ H @ F ) @ A4 )
        = ( image_nat_o @ ( comp_o_o_nat @ H @ G ) @ B5 ) ) ) ).

% image_eq_imp_comp
thf(fact_468_image__eq__imp__comp,axiom,
    ! [F: nat > $o,A4: set_nat,G: nat > $o,B5: set_nat,H: $o > nat] :
      ( ( ( image_nat_o @ F @ A4 )
        = ( image_nat_o @ G @ B5 ) )
     => ( ( image_nat_nat @ ( comp_o_nat_nat @ H @ F ) @ A4 )
        = ( image_nat_nat @ ( comp_o_nat_nat @ H @ G ) @ B5 ) ) ) ).

% image_eq_imp_comp
thf(fact_469_image__eq__imp__comp,axiom,
    ! [F: nat > nat,A4: set_nat,G: nat > nat,B5: set_nat,H: nat > $o] :
      ( ( ( image_nat_nat @ F @ A4 )
        = ( image_nat_nat @ G @ B5 ) )
     => ( ( image_nat_o @ ( comp_nat_o_nat @ H @ F ) @ A4 )
        = ( image_nat_o @ ( comp_nat_o_nat @ H @ G ) @ B5 ) ) ) ).

% image_eq_imp_comp
thf(fact_470_image__eq__imp__comp,axiom,
    ! [F: nat > nat,A4: set_nat,G: nat > nat,B5: set_nat,H: nat > product_prod_nat_nat] :
      ( ( ( image_nat_nat @ F @ A4 )
        = ( image_nat_nat @ G @ B5 ) )
     => ( ( image_5846123807819985514at_nat @ ( comp_n8574565218330151774at_nat @ H @ F ) @ A4 )
        = ( image_5846123807819985514at_nat @ ( comp_n8574565218330151774at_nat @ H @ G ) @ B5 ) ) ) ).

% image_eq_imp_comp
thf(fact_471_image__eq__imp__comp,axiom,
    ! [F: ( $o > $o ) > $o,A4: set_o_o,G: nat > $o,B5: set_nat,H: $o > set_o] :
      ( ( ( image_o_o_o @ F @ A4 )
        = ( image_nat_o @ G @ B5 ) )
     => ( ( image_o_o_set_o @ ( comp_o_set_o_o_o @ H @ F ) @ A4 )
        = ( image_nat_set_o @ ( comp_o_set_o_nat @ H @ G ) @ B5 ) ) ) ).

% image_eq_imp_comp
thf(fact_472_image__eq__imp__comp,axiom,
    ! [F: ( $o > $o ) > nat,A4: set_o_o,G: nat > nat,B5: set_nat,H: nat > set_o] :
      ( ( ( image_o_o_nat @ F @ A4 )
        = ( image_nat_nat @ G @ B5 ) )
     => ( ( image_o_o_set_o @ ( comp_nat_set_o_o_o @ H @ F ) @ A4 )
        = ( image_nat_set_o @ ( comp_nat_set_o_nat @ H @ G ) @ B5 ) ) ) ).

% image_eq_imp_comp
thf(fact_473_image__eq__imp__comp,axiom,
    ! [F: nat > set_o,A4: set_nat,G: ( $o > $o ) > set_o,B5: set_o_o,H: set_o > $o] :
      ( ( ( image_nat_set_o @ F @ A4 )
        = ( image_o_o_set_o @ G @ B5 ) )
     => ( ( image_nat_o @ ( comp_set_o_o_nat @ H @ F ) @ A4 )
        = ( image_o_o_o @ ( comp_set_o_o_o_o @ H @ G ) @ B5 ) ) ) ).

% image_eq_imp_comp
thf(fact_474_image__eq__imp__comp,axiom,
    ! [F: nat > set_o,A4: set_nat,G: ( $o > $o ) > set_o,B5: set_o_o,H: set_o > nat] :
      ( ( ( image_nat_set_o @ F @ A4 )
        = ( image_o_o_set_o @ G @ B5 ) )
     => ( ( image_nat_nat @ ( comp_set_o_nat_nat @ H @ F ) @ A4 )
        = ( image_o_o_nat @ ( comp_set_o_nat_o_o @ H @ G ) @ B5 ) ) ) ).

% image_eq_imp_comp
thf(fact_475_image__eq__imp__comp,axiom,
    ! [F: nat > $o,A4: set_nat,G: ( $o > $o ) > $o,B5: set_o_o,H: $o > set_o] :
      ( ( ( image_nat_o @ F @ A4 )
        = ( image_o_o_o @ G @ B5 ) )
     => ( ( image_nat_set_o @ ( comp_o_set_o_nat @ H @ F ) @ A4 )
        = ( image_o_o_set_o @ ( comp_o_set_o_o_o @ H @ G ) @ B5 ) ) ) ).

% image_eq_imp_comp
thf(fact_476_image__comp,axiom,
    ! [F: nat > nat,G: nat > nat,R2: set_nat] :
      ( ( image_nat_nat @ F @ ( image_nat_nat @ G @ R2 ) )
      = ( image_nat_nat @ ( comp_nat_nat_nat @ F @ G ) @ R2 ) ) ).

% image_comp
thf(fact_477_image__comp,axiom,
    ! [F: $o > $o,G: nat > $o,R2: set_nat] :
      ( ( image_o_o @ F @ ( image_nat_o @ G @ R2 ) )
      = ( image_nat_o @ ( comp_o_o_nat @ F @ G ) @ R2 ) ) ).

% image_comp
thf(fact_478_image__comp,axiom,
    ! [F: $o > nat,G: nat > $o,R2: set_nat] :
      ( ( image_o_nat @ F @ ( image_nat_o @ G @ R2 ) )
      = ( image_nat_nat @ ( comp_o_nat_nat @ F @ G ) @ R2 ) ) ).

% image_comp
thf(fact_479_image__comp,axiom,
    ! [F: nat > $o,G: nat > nat,R2: set_nat] :
      ( ( image_nat_o @ F @ ( image_nat_nat @ G @ R2 ) )
      = ( image_nat_o @ ( comp_nat_o_nat @ F @ G ) @ R2 ) ) ).

% image_comp
thf(fact_480_image__comp,axiom,
    ! [F: nat > product_prod_nat_nat,G: nat > nat,R2: set_nat] :
      ( ( image_5846123807819985514at_nat @ F @ ( image_nat_nat @ G @ R2 ) )
      = ( image_5846123807819985514at_nat @ ( comp_n8574565218330151774at_nat @ F @ G ) @ R2 ) ) ).

% image_comp
thf(fact_481_image__comp,axiom,
    ! [F: set_o > set_o,G: ( $o > $o ) > set_o,R2: set_o_o] :
      ( ( image_set_o_set_o @ F @ ( image_o_o_set_o @ G @ R2 ) )
      = ( image_o_o_set_o @ ( comp_set_o_set_o_o_o @ F @ G ) @ R2 ) ) ).

% image_comp
thf(fact_482_image__comp,axiom,
    ! [F: produc746580111399690912list_b > $o,G: nat > produc746580111399690912list_b,R2: set_nat] :
      ( ( image_2580685047486449533st_b_o @ F @ ( image_5135116557422050441list_b @ G @ R2 ) )
      = ( image_nat_o @ ( comp_P4804859795044233003_o_nat @ F @ G ) @ R2 ) ) ).

% image_comp
thf(fact_483_image__comp,axiom,
    ! [F: produc746580111399690912list_b > nat,G: nat > produc746580111399690912list_b,R2: set_nat] :
      ( ( image_6047115928211467051_b_nat @ F @ ( image_5135116557422050441list_b @ G @ R2 ) )
      = ( image_nat_nat @ ( comp_P115382347248037279at_nat @ F @ G ) @ R2 ) ) ).

% image_comp
thf(fact_484_image__comp,axiom,
    ! [F: produc5647625992154082286xt_a_b > $o,G: nat > produc5647625992154082286xt_a_b,R2: set_nat] :
      ( ( image_8261397660998149807_a_b_o @ F @ ( image_812790401321666007xt_a_b @ G @ R2 ) )
      = ( image_nat_o @ ( comp_P6416659774363354717_o_nat @ F @ G ) @ R2 ) ) ).

% image_comp
thf(fact_485_image__comp,axiom,
    ! [F: produc5647625992154082286xt_a_b > nat,G: nat > produc5647625992154082286xt_a_b,R2: set_nat] :
      ( ( image_7093515819370167417_b_nat @ F @ ( image_812790401321666007xt_a_b @ G @ R2 ) )
      = ( image_nat_nat @ ( comp_P5398456803681584877at_nat @ F @ G ) @ R2 ) ) ).

% image_comp
thf(fact_486_Sup_OSUP__image,axiom,
    ! [Sup: set_nat > nat,G: nat > nat,F: nat > nat,A4: set_nat] :
      ( ( Sup @ ( image_nat_nat @ G @ ( image_nat_nat @ F @ A4 ) ) )
      = ( Sup @ ( image_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ A4 ) ) ) ).

% Sup.SUP_image
thf(fact_487_Sup_OSUP__image,axiom,
    ! [Sup: set_o > $o,G: $o > $o,F: nat > $o,A4: set_nat] :
      ( ( Sup @ ( image_o_o @ G @ ( image_nat_o @ F @ A4 ) ) )
      = ( Sup @ ( image_nat_o @ ( comp_o_o_nat @ G @ F ) @ A4 ) ) ) ).

% Sup.SUP_image
thf(fact_488_Sup_OSUP__image,axiom,
    ! [Sup: set_nat > nat,G: $o > nat,F: nat > $o,A4: set_nat] :
      ( ( Sup @ ( image_o_nat @ G @ ( image_nat_o @ F @ A4 ) ) )
      = ( Sup @ ( image_nat_nat @ ( comp_o_nat_nat @ G @ F ) @ A4 ) ) ) ).

% Sup.SUP_image
thf(fact_489_Sup_OSUP__image,axiom,
    ! [Sup: set_o > $o,G: nat > $o,F: nat > nat,A4: set_nat] :
      ( ( Sup @ ( image_nat_o @ G @ ( image_nat_nat @ F @ A4 ) ) )
      = ( Sup @ ( image_nat_o @ ( comp_nat_o_nat @ G @ F ) @ A4 ) ) ) ).

% Sup.SUP_image
thf(fact_490_Sup_OSUP__image,axiom,
    ! [Sup: set_Pr1261947904930325089at_nat > product_prod_nat_nat,G: nat > product_prod_nat_nat,F: nat > nat,A4: set_nat] :
      ( ( Sup @ ( image_5846123807819985514at_nat @ G @ ( image_nat_nat @ F @ A4 ) ) )
      = ( Sup @ ( image_5846123807819985514at_nat @ ( comp_n8574565218330151774at_nat @ G @ F ) @ A4 ) ) ) ).

% Sup.SUP_image
thf(fact_491_Sup_OSUP__image,axiom,
    ! [Sup: set_set_o > set_o,G: set_o > set_o,F: ( $o > $o ) > set_o,A4: set_o_o] :
      ( ( Sup @ ( image_set_o_set_o @ G @ ( image_o_o_set_o @ F @ A4 ) ) )
      = ( Sup @ ( image_o_o_set_o @ ( comp_set_o_set_o_o_o @ G @ F ) @ A4 ) ) ) ).

% Sup.SUP_image
thf(fact_492_Sup_OSUP__image,axiom,
    ! [Sup: set_o > $o,G: produc746580111399690912list_b > $o,F: nat > produc746580111399690912list_b,A4: set_nat] :
      ( ( Sup @ ( image_2580685047486449533st_b_o @ G @ ( image_5135116557422050441list_b @ F @ A4 ) ) )
      = ( Sup @ ( image_nat_o @ ( comp_P4804859795044233003_o_nat @ G @ F ) @ A4 ) ) ) ).

% Sup.SUP_image
thf(fact_493_Sup_OSUP__image,axiom,
    ! [Sup: set_nat > nat,G: produc746580111399690912list_b > nat,F: nat > produc746580111399690912list_b,A4: set_nat] :
      ( ( Sup @ ( image_6047115928211467051_b_nat @ G @ ( image_5135116557422050441list_b @ F @ A4 ) ) )
      = ( Sup @ ( image_nat_nat @ ( comp_P115382347248037279at_nat @ G @ F ) @ A4 ) ) ) ).

% Sup.SUP_image
thf(fact_494_Sup_OSUP__image,axiom,
    ! [Sup: set_o > $o,G: produc5647625992154082286xt_a_b > $o,F: nat > produc5647625992154082286xt_a_b,A4: set_nat] :
      ( ( Sup @ ( image_8261397660998149807_a_b_o @ G @ ( image_812790401321666007xt_a_b @ F @ A4 ) ) )
      = ( Sup @ ( image_nat_o @ ( comp_P6416659774363354717_o_nat @ G @ F ) @ A4 ) ) ) ).

% Sup.SUP_image
thf(fact_495_Sup_OSUP__image,axiom,
    ! [Sup: set_nat > nat,G: produc5647625992154082286xt_a_b > nat,F: nat > produc5647625992154082286xt_a_b,A4: set_nat] :
      ( ( Sup @ ( image_7093515819370167417_b_nat @ G @ ( image_812790401321666007xt_a_b @ F @ A4 ) ) )
      = ( Sup @ ( image_nat_nat @ ( comp_P5398456803681584877at_nat @ G @ F ) @ A4 ) ) ) ).

% Sup.SUP_image
thf(fact_496_Inf_OINF__image,axiom,
    ! [Inf: set_nat > nat,G: nat > nat,F: nat > nat,A4: set_nat] :
      ( ( Inf @ ( image_nat_nat @ G @ ( image_nat_nat @ F @ A4 ) ) )
      = ( Inf @ ( image_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ A4 ) ) ) ).

% Inf.INF_image
thf(fact_497_Inf_OINF__image,axiom,
    ! [Inf: set_o > $o,G: $o > $o,F: nat > $o,A4: set_nat] :
      ( ( Inf @ ( image_o_o @ G @ ( image_nat_o @ F @ A4 ) ) )
      = ( Inf @ ( image_nat_o @ ( comp_o_o_nat @ G @ F ) @ A4 ) ) ) ).

% Inf.INF_image
thf(fact_498_Inf_OINF__image,axiom,
    ! [Inf: set_nat > nat,G: $o > nat,F: nat > $o,A4: set_nat] :
      ( ( Inf @ ( image_o_nat @ G @ ( image_nat_o @ F @ A4 ) ) )
      = ( Inf @ ( image_nat_nat @ ( comp_o_nat_nat @ G @ F ) @ A4 ) ) ) ).

% Inf.INF_image
thf(fact_499_Inf_OINF__image,axiom,
    ! [Inf: set_o > $o,G: nat > $o,F: nat > nat,A4: set_nat] :
      ( ( Inf @ ( image_nat_o @ G @ ( image_nat_nat @ F @ A4 ) ) )
      = ( Inf @ ( image_nat_o @ ( comp_nat_o_nat @ G @ F ) @ A4 ) ) ) ).

% Inf.INF_image
thf(fact_500_Inf_OINF__image,axiom,
    ! [Inf: set_Pr1261947904930325089at_nat > product_prod_nat_nat,G: nat > product_prod_nat_nat,F: nat > nat,A4: set_nat] :
      ( ( Inf @ ( image_5846123807819985514at_nat @ G @ ( image_nat_nat @ F @ A4 ) ) )
      = ( Inf @ ( image_5846123807819985514at_nat @ ( comp_n8574565218330151774at_nat @ G @ F ) @ A4 ) ) ) ).

% Inf.INF_image
thf(fact_501_Inf_OINF__image,axiom,
    ! [Inf: set_set_o > set_o,G: set_o > set_o,F: ( $o > $o ) > set_o,A4: set_o_o] :
      ( ( Inf @ ( image_set_o_set_o @ G @ ( image_o_o_set_o @ F @ A4 ) ) )
      = ( Inf @ ( image_o_o_set_o @ ( comp_set_o_set_o_o_o @ G @ F ) @ A4 ) ) ) ).

% Inf.INF_image
thf(fact_502_Inf_OINF__image,axiom,
    ! [Inf: set_o > $o,G: produc746580111399690912list_b > $o,F: nat > produc746580111399690912list_b,A4: set_nat] :
      ( ( Inf @ ( image_2580685047486449533st_b_o @ G @ ( image_5135116557422050441list_b @ F @ A4 ) ) )
      = ( Inf @ ( image_nat_o @ ( comp_P4804859795044233003_o_nat @ G @ F ) @ A4 ) ) ) ).

% Inf.INF_image
thf(fact_503_Inf_OINF__image,axiom,
    ! [Inf: set_nat > nat,G: produc746580111399690912list_b > nat,F: nat > produc746580111399690912list_b,A4: set_nat] :
      ( ( Inf @ ( image_6047115928211467051_b_nat @ G @ ( image_5135116557422050441list_b @ F @ A4 ) ) )
      = ( Inf @ ( image_nat_nat @ ( comp_P115382347248037279at_nat @ G @ F ) @ A4 ) ) ) ).

% Inf.INF_image
thf(fact_504_Inf_OINF__image,axiom,
    ! [Inf: set_o > $o,G: produc5647625992154082286xt_a_b > $o,F: nat > produc5647625992154082286xt_a_b,A4: set_nat] :
      ( ( Inf @ ( image_8261397660998149807_a_b_o @ G @ ( image_812790401321666007xt_a_b @ F @ A4 ) ) )
      = ( Inf @ ( image_nat_o @ ( comp_P6416659774363354717_o_nat @ G @ F ) @ A4 ) ) ) ).

% Inf.INF_image
thf(fact_505_Inf_OINF__image,axiom,
    ! [Inf: set_nat > nat,G: produc5647625992154082286xt_a_b > nat,F: nat > produc5647625992154082286xt_a_b,A4: set_nat] :
      ( ( Inf @ ( image_7093515819370167417_b_nat @ G @ ( image_812790401321666007xt_a_b @ F @ A4 ) ) )
      = ( Inf @ ( image_nat_nat @ ( comp_P5398456803681584877at_nat @ G @ F ) @ A4 ) ) ) ).

% Inf.INF_image
thf(fact_506_snd__comp__apsnd,axiom,
    ! [F: multihole_mctxt_a_b > list_b] :
      ( ( comp_P7753359808300943455xt_a_b @ produc6107117247873403966list_b @ ( produc8239320667593801685xt_a_b @ F ) )
      = ( comp_M1627911043960361035xt_a_b @ F @ produc4775144687201070661xt_a_b ) ) ).

% snd_comp_apsnd
thf(fact_507_snd__comp__apsnd,axiom,
    ! [F: list_b > multihole_mctxt_a_b] :
      ( ( comp_P6440570709493854118list_b @ produc6725609433235685644xt_a_b @ ( produc5658663565514282880list_b @ F ) )
      = ( comp_l244608897766244669list_b @ F @ produc3345134588468168965list_b ) ) ).

% snd_comp_apsnd
thf(fact_508_snd__comp__apsnd,axiom,
    ! [F: list_b > multihole_mctxt_a_b] :
      ( ( comp_P5435891436279858456list_b @ produc4775144687201070661xt_a_b @ ( produc7278294437744766343xt_a_b @ F ) )
      = ( comp_l1156032245741342326list_b @ F @ produc6107117247873403966list_b ) ) ).

% snd_comp_apsnd
thf(fact_509_snd__comp__apsnd,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b] :
      ( ( comp_P1228403674089159071xt_a_b @ produc4775144687201070661xt_a_b @ ( produc3600230912178009870xt_a_b @ F ) )
      = ( comp_M8832391070236868100xt_a_b @ F @ produc4775144687201070661xt_a_b ) ) ).

% snd_comp_apsnd
thf(fact_510_snd__comp__apsnd,axiom,
    ! [F: multihole_mctxt_a_b > list_b] :
      ( ( comp_P5990363157231710957xt_a_b @ produc3345134588468168965list_b @ ( produc1067013901203078606list_b @ F ) )
      = ( comp_M1546340790364679442xt_a_b @ F @ produc6725609433235685644xt_a_b ) ) ).

% snd_comp_apsnd
thf(fact_511_snd__comp__apsnd,axiom,
    ! [F: list_b > list_b] :
      ( ( comp_P928982252139745894list_b @ produc3345134588468168965list_b @ ( produc4607378222123999303list_b @ F ) )
      = ( comp_l4803390035063111044list_b @ F @ produc3345134588468168965list_b ) ) ).

% snd_comp_apsnd
thf(fact_512_snd__comp__apsnd,axiom,
    ! [F: $o > $o] :
      ( ( comp_P5935651135916255507od_o_o @ product_snd_o_o @ ( product_apsnd_o_o_o @ F ) )
      = ( comp_o2958928929274947076od_o_o @ F @ product_snd_o_o ) ) ).

% snd_comp_apsnd
thf(fact_513_snd__comp__apsnd,axiom,
    ! [F: nat > nat] :
      ( ( comp_P1567445206330693457at_nat @ product_snd_nat_nat @ ( produc3094765310956027504at_nat @ F ) )
      = ( comp_n2711240574518091068at_nat @ F @ product_snd_nat_nat ) ) ).

% snd_comp_apsnd
thf(fact_514_snd__comp__apsnd,axiom,
    ! [F: list_b > list_b] :
      ( ( comp_P3599965238501839832list_b @ produc6107117247873403966list_b @ ( produc6277155750876564558xt_a_b @ F ) )
      = ( comp_l6451439721888030909list_b @ F @ produc6107117247873403966list_b ) ) ).

% snd_comp_apsnd
thf(fact_515_snd__comp__apsnd,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b] :
      ( ( comp_P7245731588476948525xt_a_b @ produc6725609433235685644xt_a_b @ ( produc7620828482231520007list_b @ F ) )
      = ( comp_M7841358257205866699xt_a_b @ F @ produc6725609433235685644xt_a_b ) ) ).

% snd_comp_apsnd
thf(fact_516_fst__comp__apfst,axiom,
    ! [F: list_b > multihole_mctxt_a_b] :
      ( ( comp_P6616506451234829400list_b @ produc5881749095783049980list_b @ ( produc7925350325472336706list_b @ F ) )
      = ( comp_l244608897766244669list_b @ F @ produc7649009375908944835list_b ) ) ).

% fst_comp_apfst
thf(fact_517_fst__comp__apfst,axiom,
    ! [F: multihole_mctxt_a_b > list_b] :
      ( ( comp_P1032284375231442861xt_a_b @ produc6500241281145331658xt_a_b @ ( produc8838418972855760791xt_a_b @ F ) )
      = ( comp_M1627911043960361035xt_a_b @ F @ produc2029583840371251459xt_a_b ) ) ).

% fst_comp_apfst
thf(fact_518_fst__comp__apfst,axiom,
    ! [F: multihole_mctxt_a_b > list_b] :
      ( ( comp_P1089317276477319583list_b @ produc7649009375908944835list_b @ ( produc3333700661161132432list_b @ F ) )
      = ( comp_M5868666946465063876list_b @ F @ produc5881749095783049980list_b ) ) ).

% fst_comp_apfst
thf(fact_519_fst__comp__apfst,axiom,
    ! [F: list_b > list_b] :
      ( ( comp_P928982252139745894list_b @ produc7649009375908944835list_b @ ( produc3068595108723027977list_b @ F ) )
      = ( comp_l4803390035063111044list_b @ F @ produc7649009375908944835list_b ) ) ).

% fst_comp_apfst
thf(fact_520_fst__comp__apfst,axiom,
    ! [F: list_b > multihole_mctxt_a_b] :
      ( ( comp_P1113565280179474022xt_a_b @ produc2029583840371251459xt_a_b @ ( produc7877392743006725449xt_a_b @ F ) )
      = ( comp_l6057078126495733700xt_a_b @ F @ produc6500241281145331658xt_a_b ) ) ).

% fst_comp_apfst
thf(fact_521_fst__comp__apfst,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b] :
      ( ( comp_P1228403674089159071xt_a_b @ produc2029583840371251459xt_a_b @ ( produc4042296519137796816xt_a_b @ F ) )
      = ( comp_M8832391070236868100xt_a_b @ F @ produc2029583840371251459xt_a_b ) ) ).

% fst_comp_apfst
thf(fact_522_fst__comp__apfst,axiom,
    ! [F: $o > $o] :
      ( ( comp_P5935651135916255507od_o_o @ product_fst_o_o @ ( product_apfst_o_o_o @ F ) )
      = ( comp_o2958928929274947076od_o_o @ F @ product_fst_o_o ) ) ).

% fst_comp_apfst
thf(fact_523_fst__comp__apfst,axiom,
    ! [F: nat > nat] :
      ( ( comp_P1567445206330693457at_nat @ product_fst_nat_nat @ ( produc986720760941809198at_nat @ F ) )
      = ( comp_n2711240574518091068at_nat @ F @ product_fst_nat_nat ) ) ).

% fst_comp_apfst
thf(fact_524_fst__comp__apfst,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b] :
      ( ( comp_P9065761140792057745list_b @ produc5881749095783049980list_b @ ( produc8219926787493479113list_b @ F ) )
      = ( comp_M2940312376451475325list_b @ F @ produc5881749095783049980list_b ) ) ).

% fst_comp_apfst
thf(fact_525_fst__comp__apfst,axiom,
    ! [F: list_b > list_b] :
      ( ( comp_P8325075377515255924xt_a_b @ produc6500241281145331658xt_a_b @ ( produc8543842510834618384xt_a_b @ F ) )
      = ( comp_l2129113565787646475xt_a_b @ F @ produc6500241281145331658xt_a_b ) ) ).

% fst_comp_apfst
thf(fact_526_Collect__split__mono__strong,axiom,
    ! [X5: set_Mu3903433398966807788xt_a_b,A4: set_Pr2918931875556005383xt_a_b,Y5: set_Mu3903433398966807788xt_a_b,P2: multihole_mctxt_a_b > multihole_mctxt_a_b > $o,Q3: multihole_mctxt_a_b > multihole_mctxt_a_b > $o] :
      ( ( X5
        = ( image_2825928036690640042xt_a_b @ produc2029583840371251459xt_a_b @ A4 ) )
     => ( ( Y5
          = ( image_2825928036690640042xt_a_b @ produc4775144687201070661xt_a_b @ A4 ) )
       => ( ! [X: multihole_mctxt_a_b] :
              ( ( member4915921492409311157xt_a_b @ X @ X5 )
             => ! [Xa: multihole_mctxt_a_b] :
                  ( ( member4915921492409311157xt_a_b @ Xa @ Y5 )
                 => ( ( P2 @ X @ Xa )
                   => ( Q3 @ X @ Xa ) ) ) )
         => ( ( ord_le8781602985985617319xt_a_b @ A4 @ ( collec3715850105416846482xt_a_b @ ( produc3751450646053246316_a_b_o @ P2 ) ) )
           => ( ord_le8781602985985617319xt_a_b @ A4 @ ( collec3715850105416846482xt_a_b @ ( produc3751450646053246316_a_b_o @ Q3 ) ) ) ) ) ) ) ).

% Collect_split_mono_strong
thf(fact_527_Collect__split__mono__strong,axiom,
    ! [X5: set_list_b,A4: set_Pr7665282455119567943list_b,Y5: set_list_b,P2: list_b > list_b > $o,Q3: list_b > list_b > $o] :
      ( ( X5
        = ( image_7865409632269190755list_b @ produc7649009375908944835list_b @ A4 ) )
     => ( ( Y5
          = ( image_7865409632269190755list_b @ produc3345134588468168965list_b @ A4 ) )
       => ( ! [X: list_b] :
              ( ( member_list_b @ X @ X5 )
             => ! [Xa: list_b] :
                  ( ( member_list_b @ Xa @ Y5 )
                 => ( ( P2 @ X @ Xa )
                   => ( Q3 @ X @ Xa ) ) ) )
         => ( ( ord_le2250082383302046695list_b @ A4 @ ( collec4964980819554056914list_b @ ( produc6051822690389492396st_b_o @ P2 ) ) )
           => ( ord_le2250082383302046695list_b @ A4 @ ( collec4964980819554056914list_b @ ( produc6051822690389492396st_b_o @ Q3 ) ) ) ) ) ) ) ).

% Collect_split_mono_strong
thf(fact_528_Collect__split__mono__strong,axiom,
    ! [X5: set_nat,A4: set_Pr1261947904930325089at_nat,Y5: set_nat,P2: nat > nat > $o,Q3: nat > nat > $o] :
      ( ( X5
        = ( image_2486076414777270412at_nat @ product_fst_nat_nat @ A4 ) )
     => ( ( Y5
          = ( image_2486076414777270412at_nat @ product_snd_nat_nat @ A4 ) )
       => ( ! [X: nat] :
              ( ( member_nat @ X @ X5 )
             => ! [Xa: nat] :
                  ( ( member_nat @ Xa @ Y5 )
                 => ( ( P2 @ X @ Xa )
                   => ( Q3 @ X @ Xa ) ) ) )
         => ( ( ord_le3146513528884898305at_nat @ A4 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ P2 ) ) )
           => ( ord_le3146513528884898305at_nat @ A4 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ Q3 ) ) ) ) ) ) ) ).

% Collect_split_mono_strong
thf(fact_529_Collect__split__mono__strong,axiom,
    ! [X5: set_o,A4: set_Product_prod_o_o,Y5: set_o,P2: $o > $o > $o,Q3: $o > $o > $o] :
      ( ( X5
        = ( image_7896445794123959606_o_o_o @ product_fst_o_o @ A4 ) )
     => ( ( Y5
          = ( image_7896445794123959606_o_o_o @ product_snd_o_o @ A4 ) )
       => ( ! [X: $o] :
              ( ( member_o @ X @ X5 )
             => ! [Xa: $o] :
                  ( ( member_o @ Xa @ Y5 )
                 => ( ( P2 @ X @ Xa )
                   => ( Q3 @ X @ Xa ) ) ) )
         => ( ( ord_le192195778054999463od_o_o @ A4 @ ( collec3167064739498627218od_o_o @ ( produc6197397395684419436_o_o_o @ P2 ) ) )
           => ( ord_le192195778054999463od_o_o @ A4 @ ( collec3167064739498627218od_o_o @ ( produc6197397395684419436_o_o_o @ Q3 ) ) ) ) ) ) ) ).

% Collect_split_mono_strong
thf(fact_530_Collect__split__mono__strong,axiom,
    ! [X5: set_Mu3903433398966807788xt_a_b,A4: set_Pr1895186847599665920list_b,Y5: set_list_b,P2: multihole_mctxt_a_b > list_b > $o,Q3: multihole_mctxt_a_b > list_b > $o] :
      ( ( X5
        = ( image_7211724023120395249xt_a_b @ produc5881749095783049980list_b @ A4 ) )
     => ( ( Y5
          = ( image_9124975640858730986list_b @ produc6107117247873403966list_b @ A4 ) )
       => ( ! [X: multihole_mctxt_a_b] :
              ( ( member4915921492409311157xt_a_b @ X @ X5 )
             => ! [Xa: list_b] :
                  ( ( member_list_b @ Xa @ Y5 )
                 => ( ( P2 @ X @ Xa )
                   => ( Q3 @ X @ Xa ) ) ) )
         => ( ( ord_le1169143132509141664list_b @ A4 @ ( collec5933784528073787915list_b @ ( produc7190274377712547635st_b_o @ P2 ) ) )
           => ( ord_le1169143132509141664list_b @ A4 @ ( collec5933784528073787915list_b @ ( produc7190274377712547635st_b_o @ Q3 ) ) ) ) ) ) ) ).

% Collect_split_mono_strong
thf(fact_531_Collect__split__mono__strong,axiom,
    ! [X5: set_list_b,A4: set_Pr3872688570871424334xt_a_b,Y5: set_Mu3903433398966807788xt_a_b,P2: list_b > multihole_mctxt_a_b > $o,Q3: list_b > multihole_mctxt_a_b > $o] :
      ( ( X5
        = ( image_5978867512307746588list_b @ produc6500241281145331658xt_a_b @ A4 ) )
     => ( ( Y5
          = ( image_4915618970390574371xt_a_b @ produc6725609433235685644xt_a_b @ A4 ) )
       => ( ! [X: list_b] :
              ( ( member_list_b @ X @ X5 )
             => ! [Xa: multihole_mctxt_a_b] :
                  ( ( member4915921492409311157xt_a_b @ Xa @ Y5 )
                 => ( ( P2 @ X @ Xa )
                   => ( Q3 @ X @ Xa ) ) ) )
         => ( ( ord_le3146644855780900078xt_a_b @ A4 @ ( collec1611458371973403481xt_a_b @ ( produc1221931734719695589_a_b_o @ P2 ) ) )
           => ( ord_le3146644855780900078xt_a_b @ A4 @ ( collec1611458371973403481xt_a_b @ ( produc1221931734719695589_a_b_o @ Q3 ) ) ) ) ) ) ) ).

% Collect_split_mono_strong
thf(fact_532_Collect__case__prod__Grp__eqD,axiom,
    ! [Z2: produc746580111399690912list_b,A4: set_Mu3903433398966807788xt_a_b,F: multihole_mctxt_a_b > list_b] :
      ( ( member3572491845649744329list_b @ Z2 @ ( collec5933784528073787915list_b @ ( produc7190274377712547635st_b_o @ ( bNF_Gr3706198758728502087list_b @ A4 @ F ) ) ) )
     => ( ( comp_M5868666946465063876list_b @ F @ produc5881749095783049980list_b @ Z2 )
        = ( produc6107117247873403966list_b @ Z2 ) ) ) ).

% Collect_case_prod_Grp_eqD
thf(fact_533_Collect__case__prod__Grp__eqD,axiom,
    ! [Z2: produc5647625992154082286xt_a_b,A4: set_list_b,F: list_b > multihole_mctxt_a_b] :
      ( ( member8473537726404135703xt_a_b @ Z2 @ ( collec1611458371973403481xt_a_b @ ( produc1221931734719695589_a_b_o @ ( bNF_Gr4324690944090783765xt_a_b @ A4 @ F ) ) ) )
     => ( ( comp_l6057078126495733700xt_a_b @ F @ produc6500241281145331658xt_a_b @ Z2 )
        = ( produc6725609433235685644xt_a_b @ Z2 ) ) ) ).

% Collect_case_prod_Grp_eqD
thf(fact_534_Collect__case__prod__Grp__eqD,axiom,
    ! [Z2: product_prod_nat_nat,A4: set_nat,F: nat > nat] :
      ( ( member8440522571783428010at_nat @ Z2 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ( bNF_Grp_nat_nat @ A4 @ F ) ) ) )
     => ( ( comp_n2711240574518091068at_nat @ F @ product_fst_nat_nat @ Z2 )
        = ( product_snd_nat_nat @ Z2 ) ) ) ).

% Collect_case_prod_Grp_eqD
thf(fact_535_Collect__case__prod__Grp__eqD,axiom,
    ! [Z2: product_prod_o_o,A4: set_o,F: $o > $o] :
      ( ( member7466972457876170832od_o_o @ Z2 @ ( collec3167064739498627218od_o_o @ ( produc6197397395684419436_o_o_o @ ( bNF_Grp_o_o @ A4 @ F ) ) ) )
     => ( ( comp_o2958928929274947076od_o_o @ F @ product_fst_o_o @ Z2 )
        = ( product_snd_o_o @ Z2 ) ) ) ).

% Collect_case_prod_Grp_eqD
thf(fact_536_Collect__case__prod__Grp__eqD,axiom,
    ! [Z2: produc3963297410138542439list_b,A4: set_list_b,F: list_b > list_b] :
      ( ( member2990321877988238992list_b @ Z2 @ ( collec4964980819554056914list_b @ ( produc6051822690389492396st_b_o @ ( bNF_Gr4349803078253886990list_b @ A4 @ F ) ) ) )
     => ( ( comp_l4803390035063111044list_b @ F @ produc7649009375908944835list_b @ Z2 )
        = ( produc3345134588468168965list_b @ Z2 ) ) ) ).

% Collect_case_prod_Grp_eqD
thf(fact_537_Collect__case__prod__Grp__eqD,axiom,
    ! [Z2: produc1932156733058919263at_nat,A4: set_nat_nat,F: ( nat > nat ) > nat > nat] :
      ( ( member1096249278104964872at_nat @ Z2 @ ( collec2757435396427831370at_nat @ ( produc5295663322308424044_nat_o @ ( bNF_Gr3847987472475283150at_nat @ A4 @ F ) ) ) )
     => ( ( comp_n2788925183216866620at_nat @ F @ produc9004644904754006275at_nat @ Z2 )
        = ( produc159067601377291077at_nat @ Z2 ) ) ) ).

% Collect_case_prod_Grp_eqD
thf(fact_538_Collect__case__prod__Grp__eqD,axiom,
    ! [Z2: produc1652119919080531751xt_a_b,A4: set_Mu3903433398966807788xt_a_b,F: multihole_mctxt_a_b > multihole_mctxt_a_b] :
      ( ( member6103717091360755792xt_a_b @ Z2 @ ( collec3715850105416846482xt_a_b @ ( produc3751450646053246316_a_b_o @ ( bNF_Gr2548120569987561294xt_a_b @ A4 @ F ) ) ) )
     => ( ( comp_M8832391070236868100xt_a_b @ F @ produc2029583840371251459xt_a_b @ Z2 )
        = ( produc4775144687201070661xt_a_b @ Z2 ) ) ) ).

% Collect_case_prod_Grp_eqD
thf(fact_539_Collect__case__prod__Grp__eqD,axiom,
    ! [Z2: produc6423750584600236748list_b,A4: set_na6008912749387833063list_b,F: ( nat > produc746580111399690912list_b ) > nat > list_b] :
      ( ( member5355190962844423541list_b @ Z2 @ ( collec7680788180164832439list_b @ ( produc3817622485218950151st_b_o @ ( bNF_Gr6198635409967602163list_b @ A4 @ F ) ) ) )
     => ( ( comp_n3886679972654106180list_b @ F @ produc6702288449053554472list_b @ Z2 )
        = ( produc42187228122048362list_b @ Z2 ) ) ) ).

% Collect_case_prod_Grp_eqD
thf(fact_540_Collect__case__prod__Grp__eqD,axiom,
    ! [Z2: produc4127645531870415870list_b,A4: set_na664922679713831477xt_a_b,F: ( nat > produc5647625992154082286xt_a_b ) > nat > list_b] :
      ( ( member3059085910114602663list_b @ Z2 @ ( collec5384683127435011561list_b @ ( produc719654758968605269st_b_o @ ( bNF_Gr3902530357237781285list_b @ A4 @ F ) ) ) )
     => ( ( comp_n1237416365847547844list_b @ F @ produc4406183396323733594list_b @ Z2 )
        = ( produc6969454212247003292list_b @ Z2 ) ) ) ).

% Collect_case_prod_Grp_eqD
thf(fact_541_Collect__case__prod__Grp__eqD,axiom,
    ! [Z2: produc5683466111014092243xt_a_b,A4: set_na6008912749387833063list_b,F: ( nat > produc746580111399690912list_b ) > nat > multihole_mctxt_a_b] :
      ( ( member7078644439601498748xt_a_b @ Z2 @ ( collec462334873327752638xt_a_b @ ( produc2939875012228043712_a_b_o @ ( bNF_Gr5474315259994270842xt_a_b @ A4 @ F ) ) ) )
     => ( ( comp_n2651844997665186820xt_a_b @ F @ produc4622812557051431855xt_a_b @ Z2 )
        = ( produc3597091874480877553xt_a_b @ Z2 ) ) ) ).

% Collect_case_prod_Grp_eqD
thf(fact_542_subsetI,axiom,
    ! [A4: set_list_b,B5: set_list_b] :
      ( ! [X: list_b] :
          ( ( member_list_b @ X @ A4 )
         => ( member_list_b @ X @ B5 ) )
     => ( ord_le8932221534207217157list_b @ A4 @ B5 ) ) ).

% subsetI
thf(fact_543_subsetI,axiom,
    ! [A4: set_set_o,B5: set_set_o] :
      ( ! [X: set_o] :
          ( ( member_set_o @ X @ A4 )
         => ( member_set_o @ X @ B5 ) )
     => ( ord_le4374716579403074808_set_o @ A4 @ B5 ) ) ).

% subsetI
thf(fact_544_subsetI,axiom,
    ! [A4: set_na6008912749387833063list_b,B5: set_na6008912749387833063list_b] :
      ( ! [X: nat > produc746580111399690912list_b] :
          ( ( member1851140327238222640list_b @ X @ A4 )
         => ( member1851140327238222640list_b @ X @ B5 ) )
     => ( ord_le1520420559268595335list_b @ A4 @ B5 ) ) ).

% subsetI
thf(fact_545_subsetI,axiom,
    ! [A4: set_na664922679713831477xt_a_b,B5: set_na664922679713831477xt_a_b] :
      ( ! [X: nat > produc5647625992154082286xt_a_b] :
          ( ( member3828642050509981054xt_a_b @ X @ A4 )
         => ( member3828642050509981054xt_a_b @ X @ B5 ) )
     => ( ord_le5399802526449369557xt_a_b @ A4 @ B5 ) ) ).

% subsetI
thf(fact_546_subsetI,axiom,
    ! [A4: set_nat,B5: set_nat] :
      ( ! [X: nat] :
          ( ( member_nat @ X @ A4 )
         => ( member_nat @ X @ B5 ) )
     => ( ord_less_eq_set_nat @ A4 @ B5 ) ) ).

% subsetI
thf(fact_547_subsetI,axiom,
    ! [A4: set_o,B5: set_o] :
      ( ! [X: $o] :
          ( ( member_o @ X @ A4 )
         => ( member_o @ X @ B5 ) )
     => ( ord_less_eq_set_o @ A4 @ B5 ) ) ).

% subsetI
thf(fact_548_subset__antisym,axiom,
    ! [A4: set_o,B5: set_o] :
      ( ( ord_less_eq_set_o @ A4 @ B5 )
     => ( ( ord_less_eq_set_o @ B5 @ A4 )
       => ( A4 = B5 ) ) ) ).

% subset_antisym
thf(fact_549_subset__antisym,axiom,
    ! [A4: set_nat,B5: set_nat] :
      ( ( ord_less_eq_set_nat @ A4 @ B5 )
     => ( ( ord_less_eq_set_nat @ B5 @ A4 )
       => ( A4 = B5 ) ) ) ).

% subset_antisym
thf(fact_550_apfst__conv,axiom,
    ! [F: list_b > multihole_mctxt_a_b,X2: list_b,Y3: multihole_mctxt_a_b] :
      ( ( produc7877392743006725449xt_a_b @ F @ ( produc8821373537598205406xt_a_b @ X2 @ Y3 ) )
      = ( produc67882520014434071xt_a_b @ ( F @ X2 ) @ Y3 ) ) ).

% apfst_conv
thf(fact_551_apfst__conv,axiom,
    ! [F: multihole_mctxt_a_b > list_b,X2: multihole_mctxt_a_b,Y3: list_b] :
      ( ( produc3333700661161132432list_b @ F @ ( produc8202881352235923728list_b @ X2 @ Y3 ) )
      = ( produc1564554178308465111list_b @ ( F @ X2 ) @ Y3 ) ) ).

% apfst_conv
thf(fact_552_apfst__conv,axiom,
    ! [F: list_b > multihole_mctxt_a_b,X2: list_b,Y3: list_b] :
      ( ( produc7925350325472336706list_b @ F @ ( produc1564554178308465111list_b @ X2 @ Y3 ) )
      = ( produc8202881352235923728list_b @ ( F @ X2 ) @ Y3 ) ) ).

% apfst_conv
thf(fact_553_apfst__conv,axiom,
    ! [F: list_b > list_b,X2: list_b,Y3: list_b] :
      ( ( produc3068595108723027977list_b @ F @ ( produc1564554178308465111list_b @ X2 @ Y3 ) )
      = ( produc1564554178308465111list_b @ ( F @ X2 ) @ Y3 ) ) ).

% apfst_conv
thf(fact_554_apfst__conv,axiom,
    ! [F: multihole_mctxt_a_b > list_b,X2: multihole_mctxt_a_b,Y3: multihole_mctxt_a_b] :
      ( ( produc8838418972855760791xt_a_b @ F @ ( produc67882520014434071xt_a_b @ X2 @ Y3 ) )
      = ( produc8821373537598205406xt_a_b @ ( F @ X2 ) @ Y3 ) ) ).

% apfst_conv
thf(fact_555_apfst__conv,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b,X2: multihole_mctxt_a_b,Y3: multihole_mctxt_a_b] :
      ( ( produc4042296519137796816xt_a_b @ F @ ( produc67882520014434071xt_a_b @ X2 @ Y3 ) )
      = ( produc67882520014434071xt_a_b @ ( F @ X2 ) @ Y3 ) ) ).

% apfst_conv
thf(fact_556_apfst__conv,axiom,
    ! [F: $o > $o,X2: $o,Y3: $o] :
      ( ( product_apfst_o_o_o @ F @ ( product_Pair_o_o @ X2 @ Y3 ) )
      = ( product_Pair_o_o @ ( F @ X2 ) @ Y3 ) ) ).

% apfst_conv
thf(fact_557_apfst__conv,axiom,
    ! [F: list_b > list_b,X2: list_b,Y3: multihole_mctxt_a_b] :
      ( ( produc8543842510834618384xt_a_b @ F @ ( produc8821373537598205406xt_a_b @ X2 @ Y3 ) )
      = ( produc8821373537598205406xt_a_b @ ( F @ X2 ) @ Y3 ) ) ).

% apfst_conv
thf(fact_558_apfst__conv,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b,X2: multihole_mctxt_a_b,Y3: list_b] :
      ( ( produc8219926787493479113list_b @ F @ ( produc8202881352235923728list_b @ X2 @ Y3 ) )
      = ( produc8202881352235923728list_b @ ( F @ X2 ) @ Y3 ) ) ).

% apfst_conv
thf(fact_559_apfst__conv,axiom,
    ! [F: nat > nat,X2: nat,Y3: nat] :
      ( ( produc986720760941809198at_nat @ F @ ( product_Pair_nat_nat @ X2 @ Y3 ) )
      = ( product_Pair_nat_nat @ ( F @ X2 ) @ Y3 ) ) ).

% apfst_conv
thf(fact_560_apsnd__conv,axiom,
    ! [F: multihole_mctxt_a_b > list_b,X2: list_b,Y3: multihole_mctxt_a_b] :
      ( ( produc1067013901203078606list_b @ F @ ( produc8821373537598205406xt_a_b @ X2 @ Y3 ) )
      = ( produc1564554178308465111list_b @ X2 @ ( F @ Y3 ) ) ) ).

% apsnd_conv
thf(fact_561_apsnd__conv,axiom,
    ! [F: list_b > multihole_mctxt_a_b,X2: multihole_mctxt_a_b,Y3: list_b] :
      ( ( produc7278294437744766343xt_a_b @ F @ ( produc8202881352235923728list_b @ X2 @ Y3 ) )
      = ( produc67882520014434071xt_a_b @ X2 @ ( F @ Y3 ) ) ) ).

% apsnd_conv
thf(fact_562_apsnd__conv,axiom,
    ! [F: list_b > multihole_mctxt_a_b,X2: list_b,Y3: list_b] :
      ( ( produc5658663565514282880list_b @ F @ ( produc1564554178308465111list_b @ X2 @ Y3 ) )
      = ( produc8821373537598205406xt_a_b @ X2 @ ( F @ Y3 ) ) ) ).

% apsnd_conv
thf(fact_563_apsnd__conv,axiom,
    ! [F: list_b > list_b,X2: list_b,Y3: list_b] :
      ( ( produc4607378222123999303list_b @ F @ ( produc1564554178308465111list_b @ X2 @ Y3 ) )
      = ( produc1564554178308465111list_b @ X2 @ ( F @ Y3 ) ) ) ).

% apsnd_conv
thf(fact_564_apsnd__conv,axiom,
    ! [F: multihole_mctxt_a_b > list_b,X2: multihole_mctxt_a_b,Y3: multihole_mctxt_a_b] :
      ( ( produc8239320667593801685xt_a_b @ F @ ( produc67882520014434071xt_a_b @ X2 @ Y3 ) )
      = ( produc8202881352235923728list_b @ X2 @ ( F @ Y3 ) ) ) ).

% apsnd_conv
thf(fact_565_apsnd__conv,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b,X2: multihole_mctxt_a_b,Y3: multihole_mctxt_a_b] :
      ( ( produc3600230912178009870xt_a_b @ F @ ( produc67882520014434071xt_a_b @ X2 @ Y3 ) )
      = ( produc67882520014434071xt_a_b @ X2 @ ( F @ Y3 ) ) ) ).

% apsnd_conv
thf(fact_566_apsnd__conv,axiom,
    ! [F: $o > $o,X2: $o,Y3: $o] :
      ( ( product_apsnd_o_o_o @ F @ ( product_Pair_o_o @ X2 @ Y3 ) )
      = ( product_Pair_o_o @ X2 @ ( F @ Y3 ) ) ) ).

% apsnd_conv
thf(fact_567_apsnd__conv,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b,X2: list_b,Y3: multihole_mctxt_a_b] :
      ( ( produc7620828482231520007list_b @ F @ ( produc8821373537598205406xt_a_b @ X2 @ Y3 ) )
      = ( produc8821373537598205406xt_a_b @ X2 @ ( F @ Y3 ) ) ) ).

% apsnd_conv
thf(fact_568_apsnd__conv,axiom,
    ! [F: list_b > list_b,X2: multihole_mctxt_a_b,Y3: list_b] :
      ( ( produc6277155750876564558xt_a_b @ F @ ( produc8202881352235923728list_b @ X2 @ Y3 ) )
      = ( produc8202881352235923728list_b @ X2 @ ( F @ Y3 ) ) ) ).

% apsnd_conv
thf(fact_569_apsnd__conv,axiom,
    ! [F: nat > nat,X2: nat,Y3: nat] :
      ( ( produc3094765310956027504at_nat @ F @ ( product_Pair_nat_nat @ X2 @ Y3 ) )
      = ( product_Pair_nat_nat @ X2 @ ( F @ Y3 ) ) ) ).

% apsnd_conv
thf(fact_570_apfst__eq__conv,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b,X2: produc746580111399690912list_b,G: multihole_mctxt_a_b > multihole_mctxt_a_b] :
      ( ( ( produc8219926787493479113list_b @ F @ X2 )
        = ( produc8219926787493479113list_b @ G @ X2 ) )
      = ( ( F @ ( produc5881749095783049980list_b @ X2 ) )
        = ( G @ ( produc5881749095783049980list_b @ X2 ) ) ) ) ).

% apfst_eq_conv
thf(fact_571_apfst__eq__conv,axiom,
    ! [F: list_b > list_b,X2: produc5647625992154082286xt_a_b,G: list_b > list_b] :
      ( ( ( produc8543842510834618384xt_a_b @ F @ X2 )
        = ( produc8543842510834618384xt_a_b @ G @ X2 ) )
      = ( ( F @ ( produc6500241281145331658xt_a_b @ X2 ) )
        = ( G @ ( produc6500241281145331658xt_a_b @ X2 ) ) ) ) ).

% apfst_eq_conv
thf(fact_572_apfst__eq__conv,axiom,
    ! [F: nat > nat,X2: product_prod_nat_nat,G: nat > nat] :
      ( ( ( produc986720760941809198at_nat @ F @ X2 )
        = ( produc986720760941809198at_nat @ G @ X2 ) )
      = ( ( F @ ( product_fst_nat_nat @ X2 ) )
        = ( G @ ( product_fst_nat_nat @ X2 ) ) ) ) ).

% apfst_eq_conv
thf(fact_573_fst__apfst,axiom,
    ! [F: list_b > multihole_mctxt_a_b,X2: produc3963297410138542439list_b] :
      ( ( produc5881749095783049980list_b @ ( produc7925350325472336706list_b @ F @ X2 ) )
      = ( F @ ( produc7649009375908944835list_b @ X2 ) ) ) ).

% fst_apfst
thf(fact_574_fst__apfst,axiom,
    ! [F: multihole_mctxt_a_b > list_b,X2: produc1652119919080531751xt_a_b] :
      ( ( produc6500241281145331658xt_a_b @ ( produc8838418972855760791xt_a_b @ F @ X2 ) )
      = ( F @ ( produc2029583840371251459xt_a_b @ X2 ) ) ) ).

% fst_apfst
thf(fact_575_fst__apfst,axiom,
    ! [F: multihole_mctxt_a_b > list_b,X2: produc746580111399690912list_b] :
      ( ( produc7649009375908944835list_b @ ( produc3333700661161132432list_b @ F @ X2 ) )
      = ( F @ ( produc5881749095783049980list_b @ X2 ) ) ) ).

% fst_apfst
thf(fact_576_fst__apfst,axiom,
    ! [F: list_b > list_b,X2: produc3963297410138542439list_b] :
      ( ( produc7649009375908944835list_b @ ( produc3068595108723027977list_b @ F @ X2 ) )
      = ( F @ ( produc7649009375908944835list_b @ X2 ) ) ) ).

% fst_apfst
thf(fact_577_fst__apfst,axiom,
    ! [F: list_b > multihole_mctxt_a_b,X2: produc5647625992154082286xt_a_b] :
      ( ( produc2029583840371251459xt_a_b @ ( produc7877392743006725449xt_a_b @ F @ X2 ) )
      = ( F @ ( produc6500241281145331658xt_a_b @ X2 ) ) ) ).

% fst_apfst
thf(fact_578_fst__apfst,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b,X2: produc1652119919080531751xt_a_b] :
      ( ( produc2029583840371251459xt_a_b @ ( produc4042296519137796816xt_a_b @ F @ X2 ) )
      = ( F @ ( produc2029583840371251459xt_a_b @ X2 ) ) ) ).

% fst_apfst
thf(fact_579_fst__apfst,axiom,
    ! [F: $o > $o,X2: product_prod_o_o] :
      ( ( product_fst_o_o @ ( product_apfst_o_o_o @ F @ X2 ) )
      = ( F @ ( product_fst_o_o @ X2 ) ) ) ).

% fst_apfst
thf(fact_580_fst__apfst,axiom,
    ! [F: nat > nat,X2: product_prod_nat_nat] :
      ( ( product_fst_nat_nat @ ( produc986720760941809198at_nat @ F @ X2 ) )
      = ( F @ ( product_fst_nat_nat @ X2 ) ) ) ).

% fst_apfst
thf(fact_581_fst__apfst,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b,X2: produc746580111399690912list_b] :
      ( ( produc5881749095783049980list_b @ ( produc8219926787493479113list_b @ F @ X2 ) )
      = ( F @ ( produc5881749095783049980list_b @ X2 ) ) ) ).

% fst_apfst
thf(fact_582_fst__apfst,axiom,
    ! [F: list_b > list_b,X2: produc5647625992154082286xt_a_b] :
      ( ( produc6500241281145331658xt_a_b @ ( produc8543842510834618384xt_a_b @ F @ X2 ) )
      = ( F @ ( produc6500241281145331658xt_a_b @ X2 ) ) ) ).

% fst_apfst
thf(fact_583_snd__apfst,axiom,
    ! [F: list_b > multihole_mctxt_a_b,X2: produc3963297410138542439list_b] :
      ( ( produc6107117247873403966list_b @ ( produc7925350325472336706list_b @ F @ X2 ) )
      = ( produc3345134588468168965list_b @ X2 ) ) ).

% snd_apfst
thf(fact_584_snd__apfst,axiom,
    ! [F: multihole_mctxt_a_b > list_b,X2: produc1652119919080531751xt_a_b] :
      ( ( produc6725609433235685644xt_a_b @ ( produc8838418972855760791xt_a_b @ F @ X2 ) )
      = ( produc4775144687201070661xt_a_b @ X2 ) ) ).

% snd_apfst
thf(fact_585_snd__apfst,axiom,
    ! [F: list_b > multihole_mctxt_a_b,X2: produc5647625992154082286xt_a_b] :
      ( ( produc4775144687201070661xt_a_b @ ( produc7877392743006725449xt_a_b @ F @ X2 ) )
      = ( produc6725609433235685644xt_a_b @ X2 ) ) ).

% snd_apfst
thf(fact_586_snd__apfst,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b,X2: produc1652119919080531751xt_a_b] :
      ( ( produc4775144687201070661xt_a_b @ ( produc4042296519137796816xt_a_b @ F @ X2 ) )
      = ( produc4775144687201070661xt_a_b @ X2 ) ) ).

% snd_apfst
thf(fact_587_snd__apfst,axiom,
    ! [F: multihole_mctxt_a_b > list_b,X2: produc746580111399690912list_b] :
      ( ( produc3345134588468168965list_b @ ( produc3333700661161132432list_b @ F @ X2 ) )
      = ( produc6107117247873403966list_b @ X2 ) ) ).

% snd_apfst
thf(fact_588_snd__apfst,axiom,
    ! [F: list_b > list_b,X2: produc3963297410138542439list_b] :
      ( ( produc3345134588468168965list_b @ ( produc3068595108723027977list_b @ F @ X2 ) )
      = ( produc3345134588468168965list_b @ X2 ) ) ).

% snd_apfst
thf(fact_589_snd__apfst,axiom,
    ! [F: $o > $o,X2: product_prod_o_o] :
      ( ( product_snd_o_o @ ( product_apfst_o_o_o @ F @ X2 ) )
      = ( product_snd_o_o @ X2 ) ) ).

% snd_apfst
thf(fact_590_snd__apfst,axiom,
    ! [F: nat > nat,X2: product_prod_nat_nat] :
      ( ( product_snd_nat_nat @ ( produc986720760941809198at_nat @ F @ X2 ) )
      = ( product_snd_nat_nat @ X2 ) ) ).

% snd_apfst
thf(fact_591_snd__apfst,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b,X2: produc746580111399690912list_b] :
      ( ( produc6107117247873403966list_b @ ( produc8219926787493479113list_b @ F @ X2 ) )
      = ( produc6107117247873403966list_b @ X2 ) ) ).

% snd_apfst
thf(fact_592_snd__apfst,axiom,
    ! [F: list_b > list_b,X2: produc5647625992154082286xt_a_b] :
      ( ( produc6725609433235685644xt_a_b @ ( produc8543842510834618384xt_a_b @ F @ X2 ) )
      = ( produc6725609433235685644xt_a_b @ X2 ) ) ).

% snd_apfst
thf(fact_593_fst__apsnd,axiom,
    ! [F: multihole_mctxt_a_b > list_b,X2: produc1652119919080531751xt_a_b] :
      ( ( produc5881749095783049980list_b @ ( produc8239320667593801685xt_a_b @ F @ X2 ) )
      = ( produc2029583840371251459xt_a_b @ X2 ) ) ).

% fst_apsnd
thf(fact_594_fst__apsnd,axiom,
    ! [F: list_b > multihole_mctxt_a_b,X2: produc3963297410138542439list_b] :
      ( ( produc6500241281145331658xt_a_b @ ( produc5658663565514282880list_b @ F @ X2 ) )
      = ( produc7649009375908944835list_b @ X2 ) ) ).

% fst_apsnd
thf(fact_595_fst__apsnd,axiom,
    ! [F: multihole_mctxt_a_b > list_b,X2: produc5647625992154082286xt_a_b] :
      ( ( produc7649009375908944835list_b @ ( produc1067013901203078606list_b @ F @ X2 ) )
      = ( produc6500241281145331658xt_a_b @ X2 ) ) ).

% fst_apsnd
thf(fact_596_fst__apsnd,axiom,
    ! [F: list_b > list_b,X2: produc3963297410138542439list_b] :
      ( ( produc7649009375908944835list_b @ ( produc4607378222123999303list_b @ F @ X2 ) )
      = ( produc7649009375908944835list_b @ X2 ) ) ).

% fst_apsnd
thf(fact_597_fst__apsnd,axiom,
    ! [F: list_b > multihole_mctxt_a_b,X2: produc746580111399690912list_b] :
      ( ( produc2029583840371251459xt_a_b @ ( produc7278294437744766343xt_a_b @ F @ X2 ) )
      = ( produc5881749095783049980list_b @ X2 ) ) ).

% fst_apsnd
thf(fact_598_fst__apsnd,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b,X2: produc1652119919080531751xt_a_b] :
      ( ( produc2029583840371251459xt_a_b @ ( produc3600230912178009870xt_a_b @ F @ X2 ) )
      = ( produc2029583840371251459xt_a_b @ X2 ) ) ).

% fst_apsnd
thf(fact_599_fst__apsnd,axiom,
    ! [F: $o > $o,X2: product_prod_o_o] :
      ( ( product_fst_o_o @ ( product_apsnd_o_o_o @ F @ X2 ) )
      = ( product_fst_o_o @ X2 ) ) ).

% fst_apsnd
thf(fact_600_fst__apsnd,axiom,
    ! [F: nat > nat,X2: product_prod_nat_nat] :
      ( ( product_fst_nat_nat @ ( produc3094765310956027504at_nat @ F @ X2 ) )
      = ( product_fst_nat_nat @ X2 ) ) ).

% fst_apsnd
thf(fact_601_fst__apsnd,axiom,
    ! [F: list_b > list_b,X2: produc746580111399690912list_b] :
      ( ( produc5881749095783049980list_b @ ( produc6277155750876564558xt_a_b @ F @ X2 ) )
      = ( produc5881749095783049980list_b @ X2 ) ) ).

% fst_apsnd
thf(fact_602_fst__apsnd,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b,X2: produc5647625992154082286xt_a_b] :
      ( ( produc6500241281145331658xt_a_b @ ( produc7620828482231520007list_b @ F @ X2 ) )
      = ( produc6500241281145331658xt_a_b @ X2 ) ) ).

% fst_apsnd
thf(fact_603_apsnd__eq__conv,axiom,
    ! [F: list_b > list_b,X2: produc746580111399690912list_b,G: list_b > list_b] :
      ( ( ( produc6277155750876564558xt_a_b @ F @ X2 )
        = ( produc6277155750876564558xt_a_b @ G @ X2 ) )
      = ( ( F @ ( produc6107117247873403966list_b @ X2 ) )
        = ( G @ ( produc6107117247873403966list_b @ X2 ) ) ) ) ).

% apsnd_eq_conv
thf(fact_604_apsnd__eq__conv,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b,X2: produc5647625992154082286xt_a_b,G: multihole_mctxt_a_b > multihole_mctxt_a_b] :
      ( ( ( produc7620828482231520007list_b @ F @ X2 )
        = ( produc7620828482231520007list_b @ G @ X2 ) )
      = ( ( F @ ( produc6725609433235685644xt_a_b @ X2 ) )
        = ( G @ ( produc6725609433235685644xt_a_b @ X2 ) ) ) ) ).

% apsnd_eq_conv
thf(fact_605_apsnd__eq__conv,axiom,
    ! [F: nat > nat,X2: product_prod_nat_nat,G: nat > nat] :
      ( ( ( produc3094765310956027504at_nat @ F @ X2 )
        = ( produc3094765310956027504at_nat @ G @ X2 ) )
      = ( ( F @ ( product_snd_nat_nat @ X2 ) )
        = ( G @ ( product_snd_nat_nat @ X2 ) ) ) ) ).

% apsnd_eq_conv
thf(fact_606_snd__apsnd,axiom,
    ! [F: multihole_mctxt_a_b > list_b,X2: produc1652119919080531751xt_a_b] :
      ( ( produc6107117247873403966list_b @ ( produc8239320667593801685xt_a_b @ F @ X2 ) )
      = ( F @ ( produc4775144687201070661xt_a_b @ X2 ) ) ) ).

% snd_apsnd
thf(fact_607_snd__apsnd,axiom,
    ! [F: list_b > multihole_mctxt_a_b,X2: produc3963297410138542439list_b] :
      ( ( produc6725609433235685644xt_a_b @ ( produc5658663565514282880list_b @ F @ X2 ) )
      = ( F @ ( produc3345134588468168965list_b @ X2 ) ) ) ).

% snd_apsnd
thf(fact_608_snd__apsnd,axiom,
    ! [F: list_b > multihole_mctxt_a_b,X2: produc746580111399690912list_b] :
      ( ( produc4775144687201070661xt_a_b @ ( produc7278294437744766343xt_a_b @ F @ X2 ) )
      = ( F @ ( produc6107117247873403966list_b @ X2 ) ) ) ).

% snd_apsnd
thf(fact_609_snd__apsnd,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b,X2: produc1652119919080531751xt_a_b] :
      ( ( produc4775144687201070661xt_a_b @ ( produc3600230912178009870xt_a_b @ F @ X2 ) )
      = ( F @ ( produc4775144687201070661xt_a_b @ X2 ) ) ) ).

% snd_apsnd
thf(fact_610_snd__apsnd,axiom,
    ! [F: multihole_mctxt_a_b > list_b,X2: produc5647625992154082286xt_a_b] :
      ( ( produc3345134588468168965list_b @ ( produc1067013901203078606list_b @ F @ X2 ) )
      = ( F @ ( produc6725609433235685644xt_a_b @ X2 ) ) ) ).

% snd_apsnd
thf(fact_611_snd__apsnd,axiom,
    ! [F: list_b > list_b,X2: produc3963297410138542439list_b] :
      ( ( produc3345134588468168965list_b @ ( produc4607378222123999303list_b @ F @ X2 ) )
      = ( F @ ( produc3345134588468168965list_b @ X2 ) ) ) ).

% snd_apsnd
thf(fact_612_snd__apsnd,axiom,
    ! [F: $o > $o,X2: product_prod_o_o] :
      ( ( product_snd_o_o @ ( product_apsnd_o_o_o @ F @ X2 ) )
      = ( F @ ( product_snd_o_o @ X2 ) ) ) ).

% snd_apsnd
thf(fact_613_snd__apsnd,axiom,
    ! [F: nat > nat,X2: product_prod_nat_nat] :
      ( ( product_snd_nat_nat @ ( produc3094765310956027504at_nat @ F @ X2 ) )
      = ( F @ ( product_snd_nat_nat @ X2 ) ) ) ).

% snd_apsnd
thf(fact_614_snd__apsnd,axiom,
    ! [F: list_b > list_b,X2: produc746580111399690912list_b] :
      ( ( produc6107117247873403966list_b @ ( produc6277155750876564558xt_a_b @ F @ X2 ) )
      = ( F @ ( produc6107117247873403966list_b @ X2 ) ) ) ).

% snd_apsnd
thf(fact_615_snd__apsnd,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b,X2: produc5647625992154082286xt_a_b] :
      ( ( produc6725609433235685644xt_a_b @ ( produc7620828482231520007list_b @ F @ X2 ) )
      = ( F @ ( produc6725609433235685644xt_a_b @ X2 ) ) ) ).

% snd_apsnd
thf(fact_616_snd__comp__apfst,axiom,
    ! [F: list_b > multihole_mctxt_a_b] :
      ( ( comp_P2427654987725689503list_b @ produc6107117247873403966list_b @ ( produc7925350325472336706list_b @ F ) )
      = produc3345134588468168965list_b ) ).

% snd_comp_apfst
thf(fact_617_snd__comp__apfst,axiom,
    ! [F: multihole_mctxt_a_b > list_b] :
      ( ( comp_P6941710577075294566xt_a_b @ produc6725609433235685644xt_a_b @ ( produc8838418972855760791xt_a_b @ F ) )
      = produc4775144687201070661xt_a_b ) ).

% snd_comp_apfst
thf(fact_618_snd__comp__apfst,axiom,
    ! [F: list_b > multihole_mctxt_a_b] :
      ( ( comp_P1113565280179474022xt_a_b @ produc4775144687201070661xt_a_b @ ( produc7877392743006725449xt_a_b @ F ) )
      = produc6725609433235685644xt_a_b ) ).

% snd_comp_apfst
thf(fact_619_snd__comp__apfst,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b] :
      ( ( comp_P1228403674089159071xt_a_b @ produc4775144687201070661xt_a_b @ ( produc4042296519137796816xt_a_b @ F ) )
      = produc4775144687201070661xt_a_b ) ).

% snd_comp_apfst
thf(fact_620_snd__comp__apfst,axiom,
    ! [F: multihole_mctxt_a_b > list_b] :
      ( ( comp_P1089317276477319583list_b @ produc3345134588468168965list_b @ ( produc3333700661161132432list_b @ F ) )
      = produc6107117247873403966list_b ) ).

% snd_comp_apfst
thf(fact_621_snd__comp__apfst,axiom,
    ! [F: list_b > list_b] :
      ( ( comp_P928982252139745894list_b @ produc3345134588468168965list_b @ ( produc3068595108723027977list_b @ F ) )
      = produc3345134588468168965list_b ) ).

% snd_comp_apfst
thf(fact_622_snd__comp__apfst,axiom,
    ! [F: $o > $o] :
      ( ( comp_P5935651135916255507od_o_o @ product_snd_o_o @ ( product_apfst_o_o_o @ F ) )
      = product_snd_o_o ) ).

% snd_comp_apfst
thf(fact_623_snd__comp__apfst,axiom,
    ! [F: nat > nat] :
      ( ( comp_P1567445206330693457at_nat @ product_snd_nat_nat @ ( produc986720760941809198at_nat @ F ) )
      = product_snd_nat_nat ) ).

% snd_comp_apfst
thf(fact_624_snd__comp__apfst,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b] :
      ( ( comp_P3599965238501839832list_b @ produc6107117247873403966list_b @ ( produc8219926787493479113list_b @ F ) )
      = produc6107117247873403966list_b ) ).

% snd_comp_apfst
thf(fact_625_snd__comp__apfst,axiom,
    ! [F: list_b > list_b] :
      ( ( comp_P7245731588476948525xt_a_b @ produc6725609433235685644xt_a_b @ ( produc8543842510834618384xt_a_b @ F ) )
      = produc6725609433235685644xt_a_b ) ).

% snd_comp_apfst
thf(fact_626_fst__comp__apsnd,axiom,
    ! [F: multihole_mctxt_a_b > list_b] :
      ( ( comp_P7940805974138666520xt_a_b @ produc5881749095783049980list_b @ ( produc8239320667593801685xt_a_b @ F ) )
      = produc2029583840371251459xt_a_b ) ).

% fst_comp_apsnd
thf(fact_627_fst__comp__apsnd,axiom,
    ! [F: list_b > multihole_mctxt_a_b] :
      ( ( comp_P526186434445353453list_b @ produc6500241281145331658xt_a_b @ ( produc5658663565514282880list_b @ F ) )
      = produc7649009375908944835list_b ) ).

% fst_comp_apsnd
thf(fact_628_fst__comp__apsnd,axiom,
    ! [F: multihole_mctxt_a_b > list_b] :
      ( ( comp_P5990363157231710957xt_a_b @ produc7649009375908944835list_b @ ( produc1067013901203078606list_b @ F ) )
      = produc6500241281145331658xt_a_b ) ).

% fst_comp_apsnd
thf(fact_629_fst__comp__apsnd,axiom,
    ! [F: list_b > list_b] :
      ( ( comp_P928982252139745894list_b @ produc7649009375908944835list_b @ ( produc4607378222123999303list_b @ F ) )
      = produc7649009375908944835list_b ) ).

% fst_comp_apsnd
thf(fact_630_fst__comp__apsnd,axiom,
    ! [F: list_b > multihole_mctxt_a_b] :
      ( ( comp_P5435891436279858456list_b @ produc2029583840371251459xt_a_b @ ( produc7278294437744766343xt_a_b @ F ) )
      = produc5881749095783049980list_b ) ).

% fst_comp_apsnd
thf(fact_631_fst__comp__apsnd,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b] :
      ( ( comp_P1228403674089159071xt_a_b @ produc2029583840371251459xt_a_b @ ( produc3600230912178009870xt_a_b @ F ) )
      = produc2029583840371251459xt_a_b ) ).

% fst_comp_apsnd
thf(fact_632_fst__comp__apsnd,axiom,
    ! [F: $o > $o] :
      ( ( comp_P5935651135916255507od_o_o @ product_fst_o_o @ ( product_apsnd_o_o_o @ F ) )
      = product_fst_o_o ) ).

% fst_comp_apsnd
thf(fact_633_fst__comp__apsnd,axiom,
    ! [F: nat > nat] :
      ( ( comp_P1567445206330693457at_nat @ product_fst_nat_nat @ ( produc3094765310956027504at_nat @ F ) )
      = product_fst_nat_nat ) ).

% fst_comp_apsnd
thf(fact_634_fst__comp__apsnd,axiom,
    ! [F: list_b > list_b] :
      ( ( comp_P9065761140792057745list_b @ produc5881749095783049980list_b @ ( produc6277155750876564558xt_a_b @ F ) )
      = produc5881749095783049980list_b ) ).

% fst_comp_apsnd
thf(fact_635_fst__comp__apsnd,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b] :
      ( ( comp_P8325075377515255924xt_a_b @ produc6500241281145331658xt_a_b @ ( produc7620828482231520007list_b @ F ) )
      = produc6500241281145331658xt_a_b ) ).

% fst_comp_apsnd
thf(fact_636_apsnd__apfst,axiom,
    ! [F: $o > $o,G: $o > $o,X2: product_prod_o_o] :
      ( ( product_apsnd_o_o_o @ F @ ( product_apfst_o_o_o @ G @ X2 ) )
      = ( product_Pair_o_o @ ( G @ ( product_fst_o_o @ X2 ) ) @ ( F @ ( product_snd_o_o @ X2 ) ) ) ) ).

% apsnd_apfst
thf(fact_637_apsnd__apfst,axiom,
    ! [F: nat > $o,G: nat > $o,X2: product_prod_nat_nat] :
      ( ( produc8182697654502551758at_o_o @ F @ ( produc8275519816112921820_o_nat @ G @ X2 ) )
      = ( product_Pair_o_o @ ( G @ ( product_fst_nat_nat @ X2 ) ) @ ( F @ ( product_snd_nat_nat @ X2 ) ) ) ) ).

% apsnd_apfst
thf(fact_638_apsnd__apfst,axiom,
    ! [F: nat > nat,G: nat > nat,X2: product_prod_nat_nat] :
      ( ( produc3094765310956027504at_nat @ F @ ( produc986720760941809198at_nat @ G @ X2 ) )
      = ( product_Pair_nat_nat @ ( G @ ( product_fst_nat_nat @ X2 ) ) @ ( F @ ( product_snd_nat_nat @ X2 ) ) ) ) ).

% apsnd_apfst
thf(fact_639_apsnd__apfst,axiom,
    ! [F: list_b > $o,G: list_b > $o,X2: produc3963297410138542439list_b] :
      ( ( produc81398981840601991_b_o_o @ F @ ( produc2306196218926843318list_b @ G @ X2 ) )
      = ( product_Pair_o_o @ ( G @ ( produc7649009375908944835list_b @ X2 ) ) @ ( F @ ( produc3345134588468168965list_b @ X2 ) ) ) ) ).

% apsnd_apfst
thf(fact_640_apsnd__apfst,axiom,
    ! [F: $o > list_b,G: $o > list_b,X2: product_prod_o_o] :
      ( ( produc6411472997232821850list_b @ F @ ( produc4251543932716285871st_b_o @ G @ X2 ) )
      = ( produc1564554178308465111list_b @ ( G @ ( product_fst_o_o @ X2 ) ) @ ( F @ ( product_snd_o_o @ X2 ) ) ) ) ).

% apsnd_apfst
thf(fact_641_apsnd__apfst,axiom,
    ! [F: nat > list_b,G: nat > list_b,X2: product_prod_nat_nat] :
      ( ( produc2646826920715929486list_b @ F @ ( produc1375249994641956169_b_nat @ G @ X2 ) )
      = ( produc1564554178308465111list_b @ ( G @ ( product_fst_nat_nat @ X2 ) ) @ ( F @ ( product_snd_nat_nat @ X2 ) ) ) ) ).

% apsnd_apfst
thf(fact_642_apsnd__apfst,axiom,
    ! [F: list_b > $o,G: multihole_mctxt_a_b > $o,X2: produc746580111399690912list_b] :
      ( ( produc81398981840601991_b_o_o @ F @ ( produc7032382957099276861list_b @ G @ X2 ) )
      = ( product_Pair_o_o @ ( G @ ( produc5881749095783049980list_b @ X2 ) ) @ ( F @ ( produc6107117247873403966list_b @ X2 ) ) ) ) ).

% apsnd_apfst
thf(fact_643_apsnd__apfst,axiom,
    ! [F: multihole_mctxt_a_b > $o,G: list_b > $o,X2: produc5647625992154082286xt_a_b] :
      ( ( produc3883574302206895886_b_o_o @ F @ ( produc321465489333671869xt_a_b @ G @ X2 ) )
      = ( product_Pair_o_o @ ( G @ ( produc6500241281145331658xt_a_b @ X2 ) ) @ ( F @ ( produc6725609433235685644xt_a_b @ X2 ) ) ) ) ).

% apsnd_apfst
thf(fact_644_apsnd__apfst,axiom,
    ! [F: $o > multihole_mctxt_a_b,G: $o > list_b,X2: product_prod_o_o] :
      ( ( produc1492316820532087699list_b @ F @ ( produc4251543932716285871st_b_o @ G @ X2 ) )
      = ( produc8821373537598205406xt_a_b @ ( G @ ( product_fst_o_o @ X2 ) ) @ ( F @ ( product_snd_o_o @ X2 ) ) ) ) ).

% apsnd_apfst
thf(fact_645_apsnd__apfst,axiom,
    ! [F: $o > list_b,G: $o > multihole_mctxt_a_b,X2: product_prod_o_o] :
      ( ( produc2110809005894369377xt_a_b @ F @ ( produc7765306332744332776_a_b_o @ G @ X2 ) )
      = ( produc8202881352235923728list_b @ ( G @ ( product_fst_o_o @ X2 ) ) @ ( F @ ( product_snd_o_o @ X2 ) ) ) ) ).

% apsnd_apfst
thf(fact_646_apfst__apsnd,axiom,
    ! [F: $o > $o,G: $o > $o,X2: product_prod_o_o] :
      ( ( product_apfst_o_o_o @ F @ ( product_apsnd_o_o_o @ G @ X2 ) )
      = ( product_Pair_o_o @ ( F @ ( product_fst_o_o @ X2 ) ) @ ( G @ ( product_snd_o_o @ X2 ) ) ) ) ).

% apfst_apsnd
thf(fact_647_apfst__apsnd,axiom,
    ! [F: nat > $o,G: nat > $o,X2: product_prod_nat_nat] :
      ( ( produc3652104818163562380at_o_o @ F @ ( produc5802879076734728218_o_nat @ G @ X2 ) )
      = ( product_Pair_o_o @ ( F @ ( product_fst_nat_nat @ X2 ) ) @ ( G @ ( product_snd_nat_nat @ X2 ) ) ) ) ).

% apfst_apsnd
thf(fact_648_apfst__apsnd,axiom,
    ! [F: nat > nat,G: nat > nat,X2: product_prod_nat_nat] :
      ( ( produc986720760941809198at_nat @ F @ ( produc3094765310956027504at_nat @ G @ X2 ) )
      = ( product_Pair_nat_nat @ ( F @ ( product_fst_nat_nat @ X2 ) ) @ ( G @ ( product_snd_nat_nat @ X2 ) ) ) ) ).

% apfst_apsnd
thf(fact_649_apfst__apsnd,axiom,
    ! [F: list_b > $o,G: list_b > $o,X2: produc3963297410138542439list_b] :
      ( ( produc896052780560656201_b_o_o @ F @ ( produc2859178377933564916list_b @ G @ X2 ) )
      = ( product_Pair_o_o @ ( F @ ( produc7649009375908944835list_b @ X2 ) ) @ ( G @ ( produc3345134588468168965list_b @ X2 ) ) ) ) ).

% apfst_apsnd
thf(fact_650_apfst__apsnd,axiom,
    ! [F: $o > list_b,G: $o > list_b,X2: product_prod_o_o] :
      ( ( produc5858490838226100252list_b @ F @ ( produc3436890133996231661st_b_o @ G @ X2 ) )
      = ( produc1564554178308465111list_b @ ( F @ ( product_fst_o_o @ X2 ) ) @ ( G @ ( product_snd_o_o @ X2 ) ) ) ) ).

% apfst_apsnd
thf(fact_651_apfst__apsnd,axiom,
    ! [F: nat > list_b,G: nat > list_b,X2: product_prod_nat_nat] :
      ( ( produc4279361589058445900list_b @ F @ ( produc2041552131524264583_b_nat @ G @ X2 ) )
      = ( produc1564554178308465111list_b @ ( F @ ( product_fst_nat_nat @ X2 ) ) @ ( G @ ( product_snd_nat_nat @ X2 ) ) ) ) ).

% apfst_apsnd
thf(fact_652_apfst__apsnd,axiom,
    ! [F: multihole_mctxt_a_b > $o,G: list_b > $o,X2: produc746580111399690912list_b] :
      ( ( produc5202512041193914064_b_o_o @ F @ ( produc3932911815817251323xt_a_b @ G @ X2 ) )
      = ( product_Pair_o_o @ ( F @ ( produc5881749095783049980list_b @ X2 ) ) @ ( G @ ( produc6107117247873403966list_b @ X2 ) ) ) ) ).

% apfst_apsnd
thf(fact_653_apfst__apsnd,axiom,
    ! [F: list_b > $o,G: multihole_mctxt_a_b > $o,X2: produc5647625992154082286xt_a_b] :
      ( ( produc896052780560656201_b_o_o @ F @ ( produc1420457246728080507list_b @ G @ X2 ) )
      = ( product_Pair_o_o @ ( F @ ( produc6500241281145331658xt_a_b @ X2 ) ) @ ( G @ ( produc6725609433235685644xt_a_b @ X2 ) ) ) ) ).

% apfst_apsnd
thf(fact_654_apfst__apsnd,axiom,
    ! [F: $o > list_b,G: $o > multihole_mctxt_a_b,X2: product_prod_o_o] :
      ( ( produc7722734716265565731xt_a_b @ F @ ( produc6446368593757314598_a_b_o @ G @ X2 ) )
      = ( produc8821373537598205406xt_a_b @ ( F @ ( product_fst_o_o @ X2 ) ) @ ( G @ ( product_snd_o_o @ X2 ) ) ) ) ).

% apfst_apsnd
thf(fact_655_apfst__apsnd,axiom,
    ! [F: $o > multihole_mctxt_a_b,G: $o > list_b,X2: product_prod_o_o] :
      ( ( produc7104242530903284053list_b @ F @ ( produc3436890133996231661st_b_o @ G @ X2 ) )
      = ( produc8202881352235923728list_b @ ( F @ ( product_fst_o_o @ X2 ) ) @ ( G @ ( product_snd_o_o @ X2 ) ) ) ) ).

% apfst_apsnd
thf(fact_656_GrpI,axiom,
    ! [F: ( nat > produc746580111399690912list_b ) > nat > multihole_mctxt_a_b,X2: nat > produc746580111399690912list_b,Y3: nat > multihole_mctxt_a_b,A4: set_na6008912749387833063list_b] :
      ( ( ( F @ X2 )
        = Y3 )
     => ( ( member1851140327238222640list_b @ X2 @ A4 )
       => ( bNF_Gr5474315259994270842xt_a_b @ A4 @ F @ X2 @ Y3 ) ) ) ).

% GrpI
thf(fact_657_GrpI,axiom,
    ! [F: ( nat > produc746580111399690912list_b ) > nat > list_b,X2: nat > produc746580111399690912list_b,Y3: nat > list_b,A4: set_na6008912749387833063list_b] :
      ( ( ( F @ X2 )
        = Y3 )
     => ( ( member1851140327238222640list_b @ X2 @ A4 )
       => ( bNF_Gr6198635409967602163list_b @ A4 @ F @ X2 @ Y3 ) ) ) ).

% GrpI
thf(fact_658_GrpI,axiom,
    ! [F: ( nat > produc5647625992154082286xt_a_b ) > nat > multihole_mctxt_a_b,X2: nat > produc5647625992154082286xt_a_b,Y3: nat > multihole_mctxt_a_b,A4: set_na664922679713831477xt_a_b] :
      ( ( ( F @ X2 )
        = Y3 )
     => ( ( member3828642050509981054xt_a_b @ X2 @ A4 )
       => ( bNF_Gr5747004589486111148xt_a_b @ A4 @ F @ X2 @ Y3 ) ) ) ).

% GrpI
thf(fact_659_GrpI,axiom,
    ! [F: ( nat > produc5647625992154082286xt_a_b ) > nat > list_b,X2: nat > produc5647625992154082286xt_a_b,Y3: nat > list_b,A4: set_na664922679713831477xt_a_b] :
      ( ( ( F @ X2 )
        = Y3 )
     => ( ( member3828642050509981054xt_a_b @ X2 @ A4 )
       => ( bNF_Gr3902530357237781285list_b @ A4 @ F @ X2 @ Y3 ) ) ) ).

% GrpI
thf(fact_660_GrpI,axiom,
    ! [F: ( nat > nat ) > nat > nat,X2: nat > nat,Y3: nat > nat,A4: set_nat_nat] :
      ( ( ( F @ X2 )
        = Y3 )
     => ( ( member_nat_nat @ X2 @ A4 )
       => ( bNF_Gr3847987472475283150at_nat @ A4 @ F @ X2 @ Y3 ) ) ) ).

% GrpI
thf(fact_661_GrpE,axiom,
    ! [A4: set_na6008912749387833063list_b,F: ( nat > produc746580111399690912list_b ) > nat > multihole_mctxt_a_b,X2: nat > produc746580111399690912list_b,Y3: nat > multihole_mctxt_a_b] :
      ( ( bNF_Gr5474315259994270842xt_a_b @ A4 @ F @ X2 @ Y3 )
     => ~ ( ( ( F @ X2 )
            = Y3 )
         => ~ ( member1851140327238222640list_b @ X2 @ A4 ) ) ) ).

% GrpE
thf(fact_662_GrpE,axiom,
    ! [A4: set_na6008912749387833063list_b,F: ( nat > produc746580111399690912list_b ) > nat > list_b,X2: nat > produc746580111399690912list_b,Y3: nat > list_b] :
      ( ( bNF_Gr6198635409967602163list_b @ A4 @ F @ X2 @ Y3 )
     => ~ ( ( ( F @ X2 )
            = Y3 )
         => ~ ( member1851140327238222640list_b @ X2 @ A4 ) ) ) ).

% GrpE
thf(fact_663_GrpE,axiom,
    ! [A4: set_na664922679713831477xt_a_b,F: ( nat > produc5647625992154082286xt_a_b ) > nat > multihole_mctxt_a_b,X2: nat > produc5647625992154082286xt_a_b,Y3: nat > multihole_mctxt_a_b] :
      ( ( bNF_Gr5747004589486111148xt_a_b @ A4 @ F @ X2 @ Y3 )
     => ~ ( ( ( F @ X2 )
            = Y3 )
         => ~ ( member3828642050509981054xt_a_b @ X2 @ A4 ) ) ) ).

% GrpE
thf(fact_664_GrpE,axiom,
    ! [A4: set_na664922679713831477xt_a_b,F: ( nat > produc5647625992154082286xt_a_b ) > nat > list_b,X2: nat > produc5647625992154082286xt_a_b,Y3: nat > list_b] :
      ( ( bNF_Gr3902530357237781285list_b @ A4 @ F @ X2 @ Y3 )
     => ~ ( ( ( F @ X2 )
            = Y3 )
         => ~ ( member3828642050509981054xt_a_b @ X2 @ A4 ) ) ) ).

% GrpE
thf(fact_665_GrpE,axiom,
    ! [A4: set_nat_nat,F: ( nat > nat ) > nat > nat,X2: nat > nat,Y3: nat > nat] :
      ( ( bNF_Gr3847987472475283150at_nat @ A4 @ F @ X2 @ Y3 )
     => ~ ( ( ( F @ X2 )
            = Y3 )
         => ~ ( member_nat_nat @ X2 @ A4 ) ) ) ).

% GrpE
thf(fact_666_in__mono,axiom,
    ! [A4: set_list_b,B5: set_list_b,X2: list_b] :
      ( ( ord_le8932221534207217157list_b @ A4 @ B5 )
     => ( ( member_list_b @ X2 @ A4 )
       => ( member_list_b @ X2 @ B5 ) ) ) ).

% in_mono
thf(fact_667_in__mono,axiom,
    ! [A4: set_set_o,B5: set_set_o,X2: set_o] :
      ( ( ord_le4374716579403074808_set_o @ A4 @ B5 )
     => ( ( member_set_o @ X2 @ A4 )
       => ( member_set_o @ X2 @ B5 ) ) ) ).

% in_mono
thf(fact_668_in__mono,axiom,
    ! [A4: set_na6008912749387833063list_b,B5: set_na6008912749387833063list_b,X2: nat > produc746580111399690912list_b] :
      ( ( ord_le1520420559268595335list_b @ A4 @ B5 )
     => ( ( member1851140327238222640list_b @ X2 @ A4 )
       => ( member1851140327238222640list_b @ X2 @ B5 ) ) ) ).

% in_mono
thf(fact_669_in__mono,axiom,
    ! [A4: set_na664922679713831477xt_a_b,B5: set_na664922679713831477xt_a_b,X2: nat > produc5647625992154082286xt_a_b] :
      ( ( ord_le5399802526449369557xt_a_b @ A4 @ B5 )
     => ( ( member3828642050509981054xt_a_b @ X2 @ A4 )
       => ( member3828642050509981054xt_a_b @ X2 @ B5 ) ) ) ).

% in_mono
thf(fact_670_in__mono,axiom,
    ! [A4: set_nat,B5: set_nat,X2: nat] :
      ( ( ord_less_eq_set_nat @ A4 @ B5 )
     => ( ( member_nat @ X2 @ A4 )
       => ( member_nat @ X2 @ B5 ) ) ) ).

% in_mono
thf(fact_671_in__mono,axiom,
    ! [A4: set_o,B5: set_o,X2: $o] :
      ( ( ord_less_eq_set_o @ A4 @ B5 )
     => ( ( member_o @ X2 @ A4 )
       => ( member_o @ X2 @ B5 ) ) ) ).

% in_mono
thf(fact_672_subsetD,axiom,
    ! [A4: set_list_b,B5: set_list_b,C2: list_b] :
      ( ( ord_le8932221534207217157list_b @ A4 @ B5 )
     => ( ( member_list_b @ C2 @ A4 )
       => ( member_list_b @ C2 @ B5 ) ) ) ).

% subsetD
thf(fact_673_subsetD,axiom,
    ! [A4: set_set_o,B5: set_set_o,C2: set_o] :
      ( ( ord_le4374716579403074808_set_o @ A4 @ B5 )
     => ( ( member_set_o @ C2 @ A4 )
       => ( member_set_o @ C2 @ B5 ) ) ) ).

% subsetD
thf(fact_674_subsetD,axiom,
    ! [A4: set_na6008912749387833063list_b,B5: set_na6008912749387833063list_b,C2: nat > produc746580111399690912list_b] :
      ( ( ord_le1520420559268595335list_b @ A4 @ B5 )
     => ( ( member1851140327238222640list_b @ C2 @ A4 )
       => ( member1851140327238222640list_b @ C2 @ B5 ) ) ) ).

% subsetD
thf(fact_675_subsetD,axiom,
    ! [A4: set_na664922679713831477xt_a_b,B5: set_na664922679713831477xt_a_b,C2: nat > produc5647625992154082286xt_a_b] :
      ( ( ord_le5399802526449369557xt_a_b @ A4 @ B5 )
     => ( ( member3828642050509981054xt_a_b @ C2 @ A4 )
       => ( member3828642050509981054xt_a_b @ C2 @ B5 ) ) ) ).

% subsetD
thf(fact_676_subsetD,axiom,
    ! [A4: set_nat,B5: set_nat,C2: nat] :
      ( ( ord_less_eq_set_nat @ A4 @ B5 )
     => ( ( member_nat @ C2 @ A4 )
       => ( member_nat @ C2 @ B5 ) ) ) ).

% subsetD
thf(fact_677_subsetD,axiom,
    ! [A4: set_o,B5: set_o,C2: $o] :
      ( ( ord_less_eq_set_o @ A4 @ B5 )
     => ( ( member_o @ C2 @ A4 )
       => ( member_o @ C2 @ B5 ) ) ) ).

% subsetD
thf(fact_678_equalityE,axiom,
    ! [A4: set_o,B5: set_o] :
      ( ( A4 = B5 )
     => ~ ( ( ord_less_eq_set_o @ A4 @ B5 )
         => ~ ( ord_less_eq_set_o @ B5 @ A4 ) ) ) ).

% equalityE
thf(fact_679_equalityE,axiom,
    ! [A4: set_nat,B5: set_nat] :
      ( ( A4 = B5 )
     => ~ ( ( ord_less_eq_set_nat @ A4 @ B5 )
         => ~ ( ord_less_eq_set_nat @ B5 @ A4 ) ) ) ).

% equalityE
thf(fact_680_subset__eq,axiom,
    ( ord_le8932221534207217157list_b
    = ( ^ [A6: set_list_b,B6: set_list_b] :
        ! [X3: list_b] :
          ( ( member_list_b @ X3 @ A6 )
         => ( member_list_b @ X3 @ B6 ) ) ) ) ).

% subset_eq
thf(fact_681_subset__eq,axiom,
    ( ord_le4374716579403074808_set_o
    = ( ^ [A6: set_set_o,B6: set_set_o] :
        ! [X3: set_o] :
          ( ( member_set_o @ X3 @ A6 )
         => ( member_set_o @ X3 @ B6 ) ) ) ) ).

% subset_eq
thf(fact_682_subset__eq,axiom,
    ( ord_le1520420559268595335list_b
    = ( ^ [A6: set_na6008912749387833063list_b,B6: set_na6008912749387833063list_b] :
        ! [X3: nat > produc746580111399690912list_b] :
          ( ( member1851140327238222640list_b @ X3 @ A6 )
         => ( member1851140327238222640list_b @ X3 @ B6 ) ) ) ) ).

% subset_eq
thf(fact_683_subset__eq,axiom,
    ( ord_le5399802526449369557xt_a_b
    = ( ^ [A6: set_na664922679713831477xt_a_b,B6: set_na664922679713831477xt_a_b] :
        ! [X3: nat > produc5647625992154082286xt_a_b] :
          ( ( member3828642050509981054xt_a_b @ X3 @ A6 )
         => ( member3828642050509981054xt_a_b @ X3 @ B6 ) ) ) ) ).

% subset_eq
thf(fact_684_subset__eq,axiom,
    ( ord_less_eq_set_nat
    = ( ^ [A6: set_nat,B6: set_nat] :
        ! [X3: nat] :
          ( ( member_nat @ X3 @ A6 )
         => ( member_nat @ X3 @ B6 ) ) ) ) ).

% subset_eq
thf(fact_685_subset__eq,axiom,
    ( ord_less_eq_set_o
    = ( ^ [A6: set_o,B6: set_o] :
        ! [X3: $o] :
          ( ( member_o @ X3 @ A6 )
         => ( member_o @ X3 @ B6 ) ) ) ) ).

% subset_eq
thf(fact_686_equalityD1,axiom,
    ! [A4: set_o,B5: set_o] :
      ( ( A4 = B5 )
     => ( ord_less_eq_set_o @ A4 @ B5 ) ) ).

% equalityD1
thf(fact_687_equalityD1,axiom,
    ! [A4: set_nat,B5: set_nat] :
      ( ( A4 = B5 )
     => ( ord_less_eq_set_nat @ A4 @ B5 ) ) ).

% equalityD1
thf(fact_688_equalityD2,axiom,
    ! [A4: set_o,B5: set_o] :
      ( ( A4 = B5 )
     => ( ord_less_eq_set_o @ B5 @ A4 ) ) ).

% equalityD2
thf(fact_689_equalityD2,axiom,
    ! [A4: set_nat,B5: set_nat] :
      ( ( A4 = B5 )
     => ( ord_less_eq_set_nat @ B5 @ A4 ) ) ).

% equalityD2
thf(fact_690_subset__iff,axiom,
    ( ord_le8932221534207217157list_b
    = ( ^ [A6: set_list_b,B6: set_list_b] :
        ! [T: list_b] :
          ( ( member_list_b @ T @ A6 )
         => ( member_list_b @ T @ B6 ) ) ) ) ).

% subset_iff
thf(fact_691_subset__iff,axiom,
    ( ord_le4374716579403074808_set_o
    = ( ^ [A6: set_set_o,B6: set_set_o] :
        ! [T: set_o] :
          ( ( member_set_o @ T @ A6 )
         => ( member_set_o @ T @ B6 ) ) ) ) ).

% subset_iff
thf(fact_692_subset__iff,axiom,
    ( ord_le1520420559268595335list_b
    = ( ^ [A6: set_na6008912749387833063list_b,B6: set_na6008912749387833063list_b] :
        ! [T: nat > produc746580111399690912list_b] :
          ( ( member1851140327238222640list_b @ T @ A6 )
         => ( member1851140327238222640list_b @ T @ B6 ) ) ) ) ).

% subset_iff
thf(fact_693_subset__iff,axiom,
    ( ord_le5399802526449369557xt_a_b
    = ( ^ [A6: set_na664922679713831477xt_a_b,B6: set_na664922679713831477xt_a_b] :
        ! [T: nat > produc5647625992154082286xt_a_b] :
          ( ( member3828642050509981054xt_a_b @ T @ A6 )
         => ( member3828642050509981054xt_a_b @ T @ B6 ) ) ) ) ).

% subset_iff
thf(fact_694_subset__iff,axiom,
    ( ord_less_eq_set_nat
    = ( ^ [A6: set_nat,B6: set_nat] :
        ! [T: nat] :
          ( ( member_nat @ T @ A6 )
         => ( member_nat @ T @ B6 ) ) ) ) ).

% subset_iff
thf(fact_695_subset__iff,axiom,
    ( ord_less_eq_set_o
    = ( ^ [A6: set_o,B6: set_o] :
        ! [T: $o] :
          ( ( member_o @ T @ A6 )
         => ( member_o @ T @ B6 ) ) ) ) ).

% subset_iff
thf(fact_696_subset__refl,axiom,
    ! [A4: set_o] : ( ord_less_eq_set_o @ A4 @ A4 ) ).

% subset_refl
thf(fact_697_subset__refl,axiom,
    ! [A4: set_nat] : ( ord_less_eq_set_nat @ A4 @ A4 ) ).

% subset_refl
thf(fact_698_Collect__mono,axiom,
    ! [P2: ( nat > produc746580111399690912list_b ) > $o,Q3: ( nat > produc746580111399690912list_b ) > $o] :
      ( ! [X: nat > produc746580111399690912list_b] :
          ( ( P2 @ X )
         => ( Q3 @ X ) )
     => ( ord_le1520420559268595335list_b @ ( collec6966152917764800626list_b @ P2 ) @ ( collec6966152917764800626list_b @ Q3 ) ) ) ).

% Collect_mono
thf(fact_699_Collect__mono,axiom,
    ! [P2: ( nat > produc5647625992154082286xt_a_b ) > $o,Q3: ( nat > produc5647625992154082286xt_a_b ) > $o] :
      ( ! [X: nat > produc5647625992154082286xt_a_b] :
          ( ( P2 @ X )
         => ( Q3 @ X ) )
     => ( ord_le5399802526449369557xt_a_b @ ( collec8943654641036559040xt_a_b @ P2 ) @ ( collec8943654641036559040xt_a_b @ Q3 ) ) ) ).

% Collect_mono
thf(fact_700_Collect__mono,axiom,
    ! [P2: ( nat > nat ) > $o,Q3: ( nat > nat ) > $o] :
      ( ! [X: nat > nat] :
          ( ( P2 @ X )
         => ( Q3 @ X ) )
     => ( ord_le9059583361652607317at_nat @ ( collect_nat_nat @ P2 ) @ ( collect_nat_nat @ Q3 ) ) ) ).

% Collect_mono
thf(fact_701_Collect__mono,axiom,
    ! [P2: $o > $o,Q3: $o > $o] :
      ( ! [X: $o] :
          ( ( P2 @ X )
         => ( Q3 @ X ) )
     => ( ord_less_eq_set_o @ ( collect_o @ P2 ) @ ( collect_o @ Q3 ) ) ) ).

% Collect_mono
thf(fact_702_Collect__mono,axiom,
    ! [P2: nat > $o,Q3: nat > $o] :
      ( ! [X: nat] :
          ( ( P2 @ X )
         => ( Q3 @ X ) )
     => ( ord_less_eq_set_nat @ ( collect_nat @ P2 ) @ ( collect_nat @ Q3 ) ) ) ).

% Collect_mono
thf(fact_703_subset__trans,axiom,
    ! [A4: set_o,B5: set_o,C3: set_o] :
      ( ( ord_less_eq_set_o @ A4 @ B5 )
     => ( ( ord_less_eq_set_o @ B5 @ C3 )
       => ( ord_less_eq_set_o @ A4 @ C3 ) ) ) ).

% subset_trans
thf(fact_704_subset__trans,axiom,
    ! [A4: set_nat,B5: set_nat,C3: set_nat] :
      ( ( ord_less_eq_set_nat @ A4 @ B5 )
     => ( ( ord_less_eq_set_nat @ B5 @ C3 )
       => ( ord_less_eq_set_nat @ A4 @ C3 ) ) ) ).

% subset_trans
thf(fact_705_set__eq__subset,axiom,
    ( ( ^ [Y2: set_o,Z: set_o] : ( Y2 = Z ) )
    = ( ^ [A6: set_o,B6: set_o] :
          ( ( ord_less_eq_set_o @ A6 @ B6 )
          & ( ord_less_eq_set_o @ B6 @ A6 ) ) ) ) ).

% set_eq_subset
thf(fact_706_set__eq__subset,axiom,
    ( ( ^ [Y2: set_nat,Z: set_nat] : ( Y2 = Z ) )
    = ( ^ [A6: set_nat,B6: set_nat] :
          ( ( ord_less_eq_set_nat @ A6 @ B6 )
          & ( ord_less_eq_set_nat @ B6 @ A6 ) ) ) ) ).

% set_eq_subset
thf(fact_707_Collect__mono__iff,axiom,
    ! [P2: ( nat > produc746580111399690912list_b ) > $o,Q3: ( nat > produc746580111399690912list_b ) > $o] :
      ( ( ord_le1520420559268595335list_b @ ( collec6966152917764800626list_b @ P2 ) @ ( collec6966152917764800626list_b @ Q3 ) )
      = ( ! [X3: nat > produc746580111399690912list_b] :
            ( ( P2 @ X3 )
           => ( Q3 @ X3 ) ) ) ) ).

% Collect_mono_iff
thf(fact_708_Collect__mono__iff,axiom,
    ! [P2: ( nat > produc5647625992154082286xt_a_b ) > $o,Q3: ( nat > produc5647625992154082286xt_a_b ) > $o] :
      ( ( ord_le5399802526449369557xt_a_b @ ( collec8943654641036559040xt_a_b @ P2 ) @ ( collec8943654641036559040xt_a_b @ Q3 ) )
      = ( ! [X3: nat > produc5647625992154082286xt_a_b] :
            ( ( P2 @ X3 )
           => ( Q3 @ X3 ) ) ) ) ).

% Collect_mono_iff
thf(fact_709_Collect__mono__iff,axiom,
    ! [P2: ( nat > nat ) > $o,Q3: ( nat > nat ) > $o] :
      ( ( ord_le9059583361652607317at_nat @ ( collect_nat_nat @ P2 ) @ ( collect_nat_nat @ Q3 ) )
      = ( ! [X3: nat > nat] :
            ( ( P2 @ X3 )
           => ( Q3 @ X3 ) ) ) ) ).

% Collect_mono_iff
thf(fact_710_Collect__mono__iff,axiom,
    ! [P2: $o > $o,Q3: $o > $o] :
      ( ( ord_less_eq_set_o @ ( collect_o @ P2 ) @ ( collect_o @ Q3 ) )
      = ( ! [X3: $o] :
            ( ( P2 @ X3 )
           => ( Q3 @ X3 ) ) ) ) ).

% Collect_mono_iff
thf(fact_711_Collect__mono__iff,axiom,
    ! [P2: nat > $o,Q3: nat > $o] :
      ( ( ord_less_eq_set_nat @ ( collect_nat @ P2 ) @ ( collect_nat @ Q3 ) )
      = ( ! [X3: nat] :
            ( ( P2 @ X3 )
           => ( Q3 @ X3 ) ) ) ) ).

% Collect_mono_iff
thf(fact_712_apsnd__apfst__commute,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b,G: list_b > list_b,P: produc5647625992154082286xt_a_b] :
      ( ( produc7620828482231520007list_b @ F @ ( produc8543842510834618384xt_a_b @ G @ P ) )
      = ( produc8543842510834618384xt_a_b @ G @ ( produc7620828482231520007list_b @ F @ P ) ) ) ).

% apsnd_apfst_commute
thf(fact_713_apsnd__apfst__commute,axiom,
    ! [F: list_b > list_b,G: multihole_mctxt_a_b > multihole_mctxt_a_b,P: produc746580111399690912list_b] :
      ( ( produc6277155750876564558xt_a_b @ F @ ( produc8219926787493479113list_b @ G @ P ) )
      = ( produc8219926787493479113list_b @ G @ ( produc6277155750876564558xt_a_b @ F @ P ) ) ) ).

% apsnd_apfst_commute
thf(fact_714_apsnd__apfst__commute,axiom,
    ! [F: nat > nat,G: nat > nat,P: product_prod_nat_nat] :
      ( ( produc3094765310956027504at_nat @ F @ ( produc986720760941809198at_nat @ G @ P ) )
      = ( produc986720760941809198at_nat @ G @ ( produc3094765310956027504at_nat @ F @ P ) ) ) ).

% apsnd_apfst_commute
thf(fact_715_image__mono,axiom,
    ! [A4: set_o_o,B5: set_o_o,F: ( $o > $o ) > set_o] :
      ( ( ord_less_eq_set_o_o @ A4 @ B5 )
     => ( ord_le4374716579403074808_set_o @ ( image_o_o_set_o @ F @ A4 ) @ ( image_o_o_set_o @ F @ B5 ) ) ) ).

% image_mono
thf(fact_716_image__mono,axiom,
    ! [A4: set_o,B5: set_o,F: $o > $o] :
      ( ( ord_less_eq_set_o @ A4 @ B5 )
     => ( ord_less_eq_set_o @ ( image_o_o @ F @ A4 ) @ ( image_o_o @ F @ B5 ) ) ) ).

% image_mono
thf(fact_717_image__mono,axiom,
    ! [A4: set_o,B5: set_o,F: $o > nat] :
      ( ( ord_less_eq_set_o @ A4 @ B5 )
     => ( ord_less_eq_set_nat @ ( image_o_nat @ F @ A4 ) @ ( image_o_nat @ F @ B5 ) ) ) ).

% image_mono
thf(fact_718_image__mono,axiom,
    ! [A4: set_nat,B5: set_nat,F: nat > produc746580111399690912list_b] :
      ( ( ord_less_eq_set_nat @ A4 @ B5 )
     => ( ord_le1169143132509141664list_b @ ( image_5135116557422050441list_b @ F @ A4 ) @ ( image_5135116557422050441list_b @ F @ B5 ) ) ) ).

% image_mono
thf(fact_719_image__mono,axiom,
    ! [A4: set_nat,B5: set_nat,F: nat > produc5647625992154082286xt_a_b] :
      ( ( ord_less_eq_set_nat @ A4 @ B5 )
     => ( ord_le3146644855780900078xt_a_b @ ( image_812790401321666007xt_a_b @ F @ A4 ) @ ( image_812790401321666007xt_a_b @ F @ B5 ) ) ) ).

% image_mono
thf(fact_720_image__mono,axiom,
    ! [A4: set_nat,B5: set_nat,F: nat > $o] :
      ( ( ord_less_eq_set_nat @ A4 @ B5 )
     => ( ord_less_eq_set_o @ ( image_nat_o @ F @ A4 ) @ ( image_nat_o @ F @ B5 ) ) ) ).

% image_mono
thf(fact_721_image__mono,axiom,
    ! [A4: set_nat,B5: set_nat,F: nat > nat] :
      ( ( ord_less_eq_set_nat @ A4 @ B5 )
     => ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ ( image_nat_nat @ F @ B5 ) ) ) ).

% image_mono
thf(fact_722_image__subsetI,axiom,
    ! [A4: set_o,F: $o > $o,B5: set_o] :
      ( ! [X: $o] :
          ( ( member_o @ X @ A4 )
         => ( member_o @ ( F @ X ) @ B5 ) )
     => ( ord_less_eq_set_o @ ( image_o_o @ F @ A4 ) @ B5 ) ) ).

% image_subsetI
thf(fact_723_image__subsetI,axiom,
    ! [A4: set_nat,F: nat > $o,B5: set_o] :
      ( ! [X: nat] :
          ( ( member_nat @ X @ A4 )
         => ( member_o @ ( F @ X ) @ B5 ) )
     => ( ord_less_eq_set_o @ ( image_nat_o @ F @ A4 ) @ B5 ) ) ).

% image_subsetI
thf(fact_724_image__subsetI,axiom,
    ! [A4: set_o,F: $o > nat,B5: set_nat] :
      ( ! [X: $o] :
          ( ( member_o @ X @ A4 )
         => ( member_nat @ ( F @ X ) @ B5 ) )
     => ( ord_less_eq_set_nat @ ( image_o_nat @ F @ A4 ) @ B5 ) ) ).

% image_subsetI
thf(fact_725_image__subsetI,axiom,
    ! [A4: set_nat,F: nat > nat,B5: set_nat] :
      ( ! [X: nat] :
          ( ( member_nat @ X @ A4 )
         => ( member_nat @ ( F @ X ) @ B5 ) )
     => ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ B5 ) ) ).

% image_subsetI
thf(fact_726_image__subsetI,axiom,
    ! [A4: set_o,F: $o > list_b,B5: set_list_b] :
      ( ! [X: $o] :
          ( ( member_o @ X @ A4 )
         => ( member_list_b @ ( F @ X ) @ B5 ) )
     => ( ord_le8932221534207217157list_b @ ( image_o_list_b @ F @ A4 ) @ B5 ) ) ).

% image_subsetI
thf(fact_727_image__subsetI,axiom,
    ! [A4: set_o,F: $o > set_o,B5: set_set_o] :
      ( ! [X: $o] :
          ( ( member_o @ X @ A4 )
         => ( member_set_o @ ( F @ X ) @ B5 ) )
     => ( ord_le4374716579403074808_set_o @ ( image_o_set_o @ F @ A4 ) @ B5 ) ) ).

% image_subsetI
thf(fact_728_image__subsetI,axiom,
    ! [A4: set_nat,F: nat > list_b,B5: set_list_b] :
      ( ! [X: nat] :
          ( ( member_nat @ X @ A4 )
         => ( member_list_b @ ( F @ X ) @ B5 ) )
     => ( ord_le8932221534207217157list_b @ ( image_nat_list_b @ F @ A4 ) @ B5 ) ) ).

% image_subsetI
thf(fact_729_image__subsetI,axiom,
    ! [A4: set_nat,F: nat > set_o,B5: set_set_o] :
      ( ! [X: nat] :
          ( ( member_nat @ X @ A4 )
         => ( member_set_o @ ( F @ X ) @ B5 ) )
     => ( ord_le4374716579403074808_set_o @ ( image_nat_set_o @ F @ A4 ) @ B5 ) ) ).

% image_subsetI
thf(fact_730_image__subsetI,axiom,
    ! [A4: set_list_b,F: list_b > $o,B5: set_o] :
      ( ! [X: list_b] :
          ( ( member_list_b @ X @ A4 )
         => ( member_o @ ( F @ X ) @ B5 ) )
     => ( ord_less_eq_set_o @ ( image_list_b_o @ F @ A4 ) @ B5 ) ) ).

% image_subsetI
thf(fact_731_image__subsetI,axiom,
    ! [A4: set_set_o,F: set_o > $o,B5: set_o] :
      ( ! [X: set_o] :
          ( ( member_set_o @ X @ A4 )
         => ( member_o @ ( F @ X ) @ B5 ) )
     => ( ord_less_eq_set_o @ ( image_set_o_o @ F @ A4 ) @ B5 ) ) ).

% image_subsetI
thf(fact_732_subset__imageE,axiom,
    ! [B5: set_set_o,F: ( $o > $o ) > set_o,A4: set_o_o] :
      ( ( ord_le4374716579403074808_set_o @ B5 @ ( image_o_o_set_o @ F @ A4 ) )
     => ~ ! [C4: set_o_o] :
            ( ( ord_less_eq_set_o_o @ C4 @ A4 )
           => ( B5
             != ( image_o_o_set_o @ F @ C4 ) ) ) ) ).

% subset_imageE
thf(fact_733_subset__imageE,axiom,
    ! [B5: set_Pr1895186847599665920list_b,F: nat > produc746580111399690912list_b,A4: set_nat] :
      ( ( ord_le1169143132509141664list_b @ B5 @ ( image_5135116557422050441list_b @ F @ A4 ) )
     => ~ ! [C4: set_nat] :
            ( ( ord_less_eq_set_nat @ C4 @ A4 )
           => ( B5
             != ( image_5135116557422050441list_b @ F @ C4 ) ) ) ) ).

% subset_imageE
thf(fact_734_subset__imageE,axiom,
    ! [B5: set_Pr3872688570871424334xt_a_b,F: nat > produc5647625992154082286xt_a_b,A4: set_nat] :
      ( ( ord_le3146644855780900078xt_a_b @ B5 @ ( image_812790401321666007xt_a_b @ F @ A4 ) )
     => ~ ! [C4: set_nat] :
            ( ( ord_less_eq_set_nat @ C4 @ A4 )
           => ( B5
             != ( image_812790401321666007xt_a_b @ F @ C4 ) ) ) ) ).

% subset_imageE
thf(fact_735_subset__imageE,axiom,
    ! [B5: set_o,F: $o > $o,A4: set_o] :
      ( ( ord_less_eq_set_o @ B5 @ ( image_o_o @ F @ A4 ) )
     => ~ ! [C4: set_o] :
            ( ( ord_less_eq_set_o @ C4 @ A4 )
           => ( B5
             != ( image_o_o @ F @ C4 ) ) ) ) ).

% subset_imageE
thf(fact_736_subset__imageE,axiom,
    ! [B5: set_o,F: nat > $o,A4: set_nat] :
      ( ( ord_less_eq_set_o @ B5 @ ( image_nat_o @ F @ A4 ) )
     => ~ ! [C4: set_nat] :
            ( ( ord_less_eq_set_nat @ C4 @ A4 )
           => ( B5
             != ( image_nat_o @ F @ C4 ) ) ) ) ).

% subset_imageE
thf(fact_737_subset__imageE,axiom,
    ! [B5: set_nat,F: $o > nat,A4: set_o] :
      ( ( ord_less_eq_set_nat @ B5 @ ( image_o_nat @ F @ A4 ) )
     => ~ ! [C4: set_o] :
            ( ( ord_less_eq_set_o @ C4 @ A4 )
           => ( B5
             != ( image_o_nat @ F @ C4 ) ) ) ) ).

% subset_imageE
thf(fact_738_subset__imageE,axiom,
    ! [B5: set_nat,F: nat > nat,A4: set_nat] :
      ( ( ord_less_eq_set_nat @ B5 @ ( image_nat_nat @ F @ A4 ) )
     => ~ ! [C4: set_nat] :
            ( ( ord_less_eq_set_nat @ C4 @ A4 )
           => ( B5
             != ( image_nat_nat @ F @ C4 ) ) ) ) ).

% subset_imageE
thf(fact_739_image__subset__iff,axiom,
    ! [F: nat > produc746580111399690912list_b,A4: set_nat,B5: set_Pr1895186847599665920list_b] :
      ( ( ord_le1169143132509141664list_b @ ( image_5135116557422050441list_b @ F @ A4 ) @ B5 )
      = ( ! [X3: nat] :
            ( ( member_nat @ X3 @ A4 )
           => ( member3572491845649744329list_b @ ( F @ X3 ) @ B5 ) ) ) ) ).

% image_subset_iff
thf(fact_740_image__subset__iff,axiom,
    ! [F: nat > produc5647625992154082286xt_a_b,A4: set_nat,B5: set_Pr3872688570871424334xt_a_b] :
      ( ( ord_le3146644855780900078xt_a_b @ ( image_812790401321666007xt_a_b @ F @ A4 ) @ B5 )
      = ( ! [X3: nat] :
            ( ( member_nat @ X3 @ A4 )
           => ( member8473537726404135703xt_a_b @ ( F @ X3 ) @ B5 ) ) ) ) ).

% image_subset_iff
thf(fact_741_image__subset__iff,axiom,
    ! [F: ( $o > $o ) > set_o,A4: set_o_o,B5: set_set_o] :
      ( ( ord_le4374716579403074808_set_o @ ( image_o_o_set_o @ F @ A4 ) @ B5 )
      = ( ! [X3: $o > $o] :
            ( ( member_o_o @ X3 @ A4 )
           => ( member_set_o @ ( F @ X3 ) @ B5 ) ) ) ) ).

% image_subset_iff
thf(fact_742_image__subset__iff,axiom,
    ! [F: nat > $o,A4: set_nat,B5: set_o] :
      ( ( ord_less_eq_set_o @ ( image_nat_o @ F @ A4 ) @ B5 )
      = ( ! [X3: nat] :
            ( ( member_nat @ X3 @ A4 )
           => ( member_o @ ( F @ X3 ) @ B5 ) ) ) ) ).

% image_subset_iff
thf(fact_743_image__subset__iff,axiom,
    ! [F: nat > nat,A4: set_nat,B5: set_nat] :
      ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ B5 )
      = ( ! [X3: nat] :
            ( ( member_nat @ X3 @ A4 )
           => ( member_nat @ ( F @ X3 ) @ B5 ) ) ) ) ).

% image_subset_iff
thf(fact_744_subset__image__iff,axiom,
    ! [B5: set_set_o,F: ( $o > $o ) > set_o,A4: set_o_o] :
      ( ( ord_le4374716579403074808_set_o @ B5 @ ( image_o_o_set_o @ F @ A4 ) )
      = ( ? [AA: set_o_o] :
            ( ( ord_less_eq_set_o_o @ AA @ A4 )
            & ( B5
              = ( image_o_o_set_o @ F @ AA ) ) ) ) ) ).

% subset_image_iff
thf(fact_745_subset__image__iff,axiom,
    ! [B5: set_Pr1895186847599665920list_b,F: nat > produc746580111399690912list_b,A4: set_nat] :
      ( ( ord_le1169143132509141664list_b @ B5 @ ( image_5135116557422050441list_b @ F @ A4 ) )
      = ( ? [AA: set_nat] :
            ( ( ord_less_eq_set_nat @ AA @ A4 )
            & ( B5
              = ( image_5135116557422050441list_b @ F @ AA ) ) ) ) ) ).

% subset_image_iff
thf(fact_746_subset__image__iff,axiom,
    ! [B5: set_Pr3872688570871424334xt_a_b,F: nat > produc5647625992154082286xt_a_b,A4: set_nat] :
      ( ( ord_le3146644855780900078xt_a_b @ B5 @ ( image_812790401321666007xt_a_b @ F @ A4 ) )
      = ( ? [AA: set_nat] :
            ( ( ord_less_eq_set_nat @ AA @ A4 )
            & ( B5
              = ( image_812790401321666007xt_a_b @ F @ AA ) ) ) ) ) ).

% subset_image_iff
thf(fact_747_subset__image__iff,axiom,
    ! [B5: set_o,F: $o > $o,A4: set_o] :
      ( ( ord_less_eq_set_o @ B5 @ ( image_o_o @ F @ A4 ) )
      = ( ? [AA: set_o] :
            ( ( ord_less_eq_set_o @ AA @ A4 )
            & ( B5
              = ( image_o_o @ F @ AA ) ) ) ) ) ).

% subset_image_iff
thf(fact_748_subset__image__iff,axiom,
    ! [B5: set_o,F: nat > $o,A4: set_nat] :
      ( ( ord_less_eq_set_o @ B5 @ ( image_nat_o @ F @ A4 ) )
      = ( ? [AA: set_nat] :
            ( ( ord_less_eq_set_nat @ AA @ A4 )
            & ( B5
              = ( image_nat_o @ F @ AA ) ) ) ) ) ).

% subset_image_iff
thf(fact_749_subset__image__iff,axiom,
    ! [B5: set_nat,F: $o > nat,A4: set_o] :
      ( ( ord_less_eq_set_nat @ B5 @ ( image_o_nat @ F @ A4 ) )
      = ( ? [AA: set_o] :
            ( ( ord_less_eq_set_o @ AA @ A4 )
            & ( B5
              = ( image_o_nat @ F @ AA ) ) ) ) ) ).

% subset_image_iff
thf(fact_750_subset__image__iff,axiom,
    ! [B5: set_nat,F: nat > nat,A4: set_nat] :
      ( ( ord_less_eq_set_nat @ B5 @ ( image_nat_nat @ F @ A4 ) )
      = ( ? [AA: set_nat] :
            ( ( ord_less_eq_set_nat @ AA @ A4 )
            & ( B5
              = ( image_nat_nat @ F @ AA ) ) ) ) ) ).

% subset_image_iff
thf(fact_751_apfst__compose,axiom,
    ! [F: nat > product_prod_nat_nat,G: nat > nat,X2: product_prod_nat_nat] :
      ( ( produc3001624868188084037at_nat @ F @ ( produc986720760941809198at_nat @ G @ X2 ) )
      = ( produc3001624868188084037at_nat @ ( comp_n8574565218330151774at_nat @ F @ G ) @ X2 ) ) ).

% apfst_compose
thf(fact_752_apfst__compose,axiom,
    ! [F: nat > $o,G: nat > nat,X2: product_prod_nat_nat] :
      ( ( produc8275519816112921820_o_nat @ F @ ( produc986720760941809198at_nat @ G @ X2 ) )
      = ( produc8275519816112921820_o_nat @ ( comp_nat_o_nat @ F @ G ) @ X2 ) ) ).

% apfst_compose
thf(fact_753_apfst__compose,axiom,
    ! [F: list_b > list_b,G: produc746580111399690912list_b > list_b,X2: produc420090126769944851xt_a_b] :
      ( ( produc8543842510834618384xt_a_b @ F @ ( produc1634506678232684331xt_a_b @ G @ X2 ) )
      = ( produc1634506678232684331xt_a_b @ ( comp_l6451439721888030909list_b @ F @ G ) @ X2 ) ) ).

% apfst_compose
thf(fact_754_apfst__compose,axiom,
    ! [F: list_b > list_b,G: produc5647625992154082286xt_a_b > list_b,X2: produc7347357110894899781xt_a_b] :
      ( ( produc8543842510834618384xt_a_b @ F @ ( produc1579030810084249465xt_a_b @ G @ X2 ) )
      = ( produc1579030810084249465xt_a_b @ ( comp_l2129113565787646475xt_a_b @ F @ G ) @ X2 ) ) ).

% apfst_compose
thf(fact_755_apfst__compose,axiom,
    ! [F: list_b > list_b,G: list_b > list_b,X2: produc5647625992154082286xt_a_b] :
      ( ( produc8543842510834618384xt_a_b @ F @ ( produc8543842510834618384xt_a_b @ G @ X2 ) )
      = ( produc8543842510834618384xt_a_b @ ( comp_l174544490166145698list_b @ F @ G ) @ X2 ) ) ).

% apfst_compose
thf(fact_756_apfst__compose,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b,G: multihole_mctxt_a_b > multihole_mctxt_a_b,X2: produc746580111399690912list_b] :
      ( ( produc8219926787493479113list_b @ F @ ( produc8219926787493479113list_b @ G @ X2 ) )
      = ( produc8219926787493479113list_b @ ( comp_M3425699811810050921xt_a_b @ F @ G ) @ X2 ) ) ).

% apfst_compose
thf(fact_757_apfst__compose,axiom,
    ! [F: nat > nat,G: nat > nat,X2: product_prod_nat_nat] :
      ( ( produc986720760941809198at_nat @ F @ ( produc986720760941809198at_nat @ G @ X2 ) )
      = ( produc986720760941809198at_nat @ ( comp_nat_nat_nat @ F @ G ) @ X2 ) ) ).

% apfst_compose
thf(fact_758_apsnd__compose,axiom,
    ! [F: nat > product_prod_nat_nat,G: nat > nat,X2: product_prod_nat_nat] :
      ( ( produc1784090006485240963at_nat @ F @ ( produc3094765310956027504at_nat @ G @ X2 ) )
      = ( produc1784090006485240963at_nat @ ( comp_n8574565218330151774at_nat @ F @ G ) @ X2 ) ) ).

% apsnd_compose
thf(fact_759_apsnd__compose,axiom,
    ! [F: nat > $o,G: nat > nat,X2: product_prod_nat_nat] :
      ( ( produc5802879076734728218_o_nat @ F @ ( produc3094765310956027504at_nat @ G @ X2 ) )
      = ( produc5802879076734728218_o_nat @ ( comp_nat_o_nat @ F @ G ) @ X2 ) ) ).

% apsnd_compose
thf(fact_760_apsnd__compose,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b,G: multihole_mctxt_a_b > multihole_mctxt_a_b,X2: produc5647625992154082286xt_a_b] :
      ( ( produc7620828482231520007list_b @ F @ ( produc7620828482231520007list_b @ G @ X2 ) )
      = ( produc7620828482231520007list_b @ ( comp_M3425699811810050921xt_a_b @ F @ G ) @ X2 ) ) ).

% apsnd_compose
thf(fact_761_apsnd__compose,axiom,
    ! [F: list_b > list_b,G: produc746580111399690912list_b > list_b,X2: produc767570952302678203list_b] :
      ( ( produc6277155750876564558xt_a_b @ F @ ( produc8507176766696618601xt_a_b @ G @ X2 ) )
      = ( produc8507176766696618601xt_a_b @ ( comp_l6451439721888030909list_b @ F @ G ) @ X2 ) ) ).

% apsnd_compose
thf(fact_762_apsnd__compose,axiom,
    ! [F: list_b > list_b,G: produc5647625992154082286xt_a_b > list_b,X2: produc2745072675574436617xt_a_b] :
      ( ( produc6277155750876564558xt_a_b @ F @ ( produc8451700898548183735xt_a_b @ G @ X2 ) )
      = ( produc8451700898548183735xt_a_b @ ( comp_l2129113565787646475xt_a_b @ F @ G ) @ X2 ) ) ).

% apsnd_compose
thf(fact_763_apsnd__compose,axiom,
    ! [F: list_b > list_b,G: list_b > list_b,X2: produc746580111399690912list_b] :
      ( ( produc6277155750876564558xt_a_b @ F @ ( produc6277155750876564558xt_a_b @ G @ X2 ) )
      = ( produc6277155750876564558xt_a_b @ ( comp_l174544490166145698list_b @ F @ G ) @ X2 ) ) ).

% apsnd_compose
thf(fact_764_apsnd__compose,axiom,
    ! [F: nat > nat,G: nat > nat,X2: product_prod_nat_nat] :
      ( ( produc3094765310956027504at_nat @ F @ ( produc3094765310956027504at_nat @ G @ X2 ) )
      = ( produc3094765310956027504at_nat @ ( comp_nat_nat_nat @ F @ G ) @ X2 ) ) ).

% apsnd_compose
thf(fact_765_Collect__case__prod__Grp__in,axiom,
    ! [Z2: produc746580111399690912list_b,A4: set_Mu3903433398966807788xt_a_b,F: multihole_mctxt_a_b > list_b] :
      ( ( member3572491845649744329list_b @ Z2 @ ( collec5933784528073787915list_b @ ( produc7190274377712547635st_b_o @ ( bNF_Gr3706198758728502087list_b @ A4 @ F ) ) ) )
     => ( member4915921492409311157xt_a_b @ ( produc5881749095783049980list_b @ Z2 ) @ A4 ) ) ).

% Collect_case_prod_Grp_in
thf(fact_766_Collect__case__prod__Grp__in,axiom,
    ! [Z2: produc5647625992154082286xt_a_b,A4: set_list_b,F: list_b > multihole_mctxt_a_b] :
      ( ( member8473537726404135703xt_a_b @ Z2 @ ( collec1611458371973403481xt_a_b @ ( produc1221931734719695589_a_b_o @ ( bNF_Gr4324690944090783765xt_a_b @ A4 @ F ) ) ) )
     => ( member_list_b @ ( produc6500241281145331658xt_a_b @ Z2 ) @ A4 ) ) ).

% Collect_case_prod_Grp_in
thf(fact_767_Collect__case__prod__Grp__in,axiom,
    ! [Z2: product_prod_nat_nat,A4: set_nat,F: nat > nat] :
      ( ( member8440522571783428010at_nat @ Z2 @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ( bNF_Grp_nat_nat @ A4 @ F ) ) ) )
     => ( member_nat @ ( product_fst_nat_nat @ Z2 ) @ A4 ) ) ).

% Collect_case_prod_Grp_in
thf(fact_768_Collect__case__prod__Grp__in,axiom,
    ! [Z2: product_prod_o_o,A4: set_o,F: $o > $o] :
      ( ( member7466972457876170832od_o_o @ Z2 @ ( collec3167064739498627218od_o_o @ ( produc6197397395684419436_o_o_o @ ( bNF_Grp_o_o @ A4 @ F ) ) ) )
     => ( member_o @ ( product_fst_o_o @ Z2 ) @ A4 ) ) ).

% Collect_case_prod_Grp_in
thf(fact_769_Collect__case__prod__Grp__in,axiom,
    ! [Z2: produc3963297410138542439list_b,A4: set_list_b,F: list_b > list_b] :
      ( ( member2990321877988238992list_b @ Z2 @ ( collec4964980819554056914list_b @ ( produc6051822690389492396st_b_o @ ( bNF_Gr4349803078253886990list_b @ A4 @ F ) ) ) )
     => ( member_list_b @ ( produc7649009375908944835list_b @ Z2 ) @ A4 ) ) ).

% Collect_case_prod_Grp_in
thf(fact_770_Collect__case__prod__Grp__in,axiom,
    ! [Z2: produc1932156733058919263at_nat,A4: set_nat_nat,F: ( nat > nat ) > nat > nat] :
      ( ( member1096249278104964872at_nat @ Z2 @ ( collec2757435396427831370at_nat @ ( produc5295663322308424044_nat_o @ ( bNF_Gr3847987472475283150at_nat @ A4 @ F ) ) ) )
     => ( member_nat_nat @ ( produc9004644904754006275at_nat @ Z2 ) @ A4 ) ) ).

% Collect_case_prod_Grp_in
thf(fact_771_Collect__case__prod__Grp__in,axiom,
    ! [Z2: produc1652119919080531751xt_a_b,A4: set_Mu3903433398966807788xt_a_b,F: multihole_mctxt_a_b > multihole_mctxt_a_b] :
      ( ( member6103717091360755792xt_a_b @ Z2 @ ( collec3715850105416846482xt_a_b @ ( produc3751450646053246316_a_b_o @ ( bNF_Gr2548120569987561294xt_a_b @ A4 @ F ) ) ) )
     => ( member4915921492409311157xt_a_b @ ( produc2029583840371251459xt_a_b @ Z2 ) @ A4 ) ) ).

% Collect_case_prod_Grp_in
thf(fact_772_Collect__case__prod__Grp__in,axiom,
    ! [Z2: produc6423750584600236748list_b,A4: set_na6008912749387833063list_b,F: ( nat > produc746580111399690912list_b ) > nat > list_b] :
      ( ( member5355190962844423541list_b @ Z2 @ ( collec7680788180164832439list_b @ ( produc3817622485218950151st_b_o @ ( bNF_Gr6198635409967602163list_b @ A4 @ F ) ) ) )
     => ( member1851140327238222640list_b @ ( produc6702288449053554472list_b @ Z2 ) @ A4 ) ) ).

% Collect_case_prod_Grp_in
thf(fact_773_Collect__case__prod__Grp__in,axiom,
    ! [Z2: produc4127645531870415870list_b,A4: set_na664922679713831477xt_a_b,F: ( nat > produc5647625992154082286xt_a_b ) > nat > list_b] :
      ( ( member3059085910114602663list_b @ Z2 @ ( collec5384683127435011561list_b @ ( produc719654758968605269st_b_o @ ( bNF_Gr3902530357237781285list_b @ A4 @ F ) ) ) )
     => ( member3828642050509981054xt_a_b @ ( produc4406183396323733594list_b @ Z2 ) @ A4 ) ) ).

% Collect_case_prod_Grp_in
thf(fact_774_Collect__case__prod__Grp__in,axiom,
    ! [Z2: produc5683466111014092243xt_a_b,A4: set_na6008912749387833063list_b,F: ( nat > produc746580111399690912list_b ) > nat > multihole_mctxt_a_b] :
      ( ( member7078644439601498748xt_a_b @ Z2 @ ( collec462334873327752638xt_a_b @ ( produc2939875012228043712_a_b_o @ ( bNF_Gr5474315259994270842xt_a_b @ A4 @ F ) ) ) )
     => ( member1851140327238222640list_b @ ( produc4622812557051431855xt_a_b @ Z2 ) @ A4 ) ) ).

% Collect_case_prod_Grp_in
thf(fact_775_Inf_OINF__cong,axiom,
    ! [A4: set_o_o,B5: set_o_o,C3: ( $o > $o ) > set_o,D: ( $o > $o ) > set_o,Inf: set_set_o > set_o] :
      ( ( A4 = B5 )
     => ( ! [X: $o > $o] :
            ( ( member_o_o @ X @ B5 )
           => ( ( C3 @ X )
              = ( D @ X ) ) )
       => ( ( Inf @ ( image_o_o_set_o @ C3 @ A4 ) )
          = ( Inf @ ( image_o_o_set_o @ D @ B5 ) ) ) ) ) ).

% Inf.INF_cong
thf(fact_776_Inf_OINF__cong,axiom,
    ! [A4: set_nat,B5: set_nat,C3: nat > produc746580111399690912list_b,D: nat > produc746580111399690912list_b,Inf: set_Pr1895186847599665920list_b > produc746580111399690912list_b] :
      ( ( A4 = B5 )
     => ( ! [X: nat] :
            ( ( member_nat @ X @ B5 )
           => ( ( C3 @ X )
              = ( D @ X ) ) )
       => ( ( Inf @ ( image_5135116557422050441list_b @ C3 @ A4 ) )
          = ( Inf @ ( image_5135116557422050441list_b @ D @ B5 ) ) ) ) ) ).

% Inf.INF_cong
thf(fact_777_Inf_OINF__cong,axiom,
    ! [A4: set_nat,B5: set_nat,C3: nat > produc5647625992154082286xt_a_b,D: nat > produc5647625992154082286xt_a_b,Inf: set_Pr3872688570871424334xt_a_b > produc5647625992154082286xt_a_b] :
      ( ( A4 = B5 )
     => ( ! [X: nat] :
            ( ( member_nat @ X @ B5 )
           => ( ( C3 @ X )
              = ( D @ X ) ) )
       => ( ( Inf @ ( image_812790401321666007xt_a_b @ C3 @ A4 ) )
          = ( Inf @ ( image_812790401321666007xt_a_b @ D @ B5 ) ) ) ) ) ).

% Inf.INF_cong
thf(fact_778_Inf_OINF__cong,axiom,
    ! [A4: set_nat,B5: set_nat,C3: nat > $o,D: nat > $o,Inf: set_o > $o] :
      ( ( A4 = B5 )
     => ( ! [X: nat] :
            ( ( member_nat @ X @ B5 )
           => ( ( C3 @ X )
              = ( D @ X ) ) )
       => ( ( Inf @ ( image_nat_o @ C3 @ A4 ) )
          = ( Inf @ ( image_nat_o @ D @ B5 ) ) ) ) ) ).

% Inf.INF_cong
thf(fact_779_Inf_OINF__cong,axiom,
    ! [A4: set_nat,B5: set_nat,C3: nat > nat,D: nat > nat,Inf: set_nat > nat] :
      ( ( A4 = B5 )
     => ( ! [X: nat] :
            ( ( member_nat @ X @ B5 )
           => ( ( C3 @ X )
              = ( D @ X ) ) )
       => ( ( Inf @ ( image_nat_nat @ C3 @ A4 ) )
          = ( Inf @ ( image_nat_nat @ D @ B5 ) ) ) ) ) ).

% Inf.INF_cong
thf(fact_780_Sup_OSUP__cong,axiom,
    ! [A4: set_o_o,B5: set_o_o,C3: ( $o > $o ) > set_o,D: ( $o > $o ) > set_o,Sup: set_set_o > set_o] :
      ( ( A4 = B5 )
     => ( ! [X: $o > $o] :
            ( ( member_o_o @ X @ B5 )
           => ( ( C3 @ X )
              = ( D @ X ) ) )
       => ( ( Sup @ ( image_o_o_set_o @ C3 @ A4 ) )
          = ( Sup @ ( image_o_o_set_o @ D @ B5 ) ) ) ) ) ).

% Sup.SUP_cong
thf(fact_781_Sup_OSUP__cong,axiom,
    ! [A4: set_nat,B5: set_nat,C3: nat > produc746580111399690912list_b,D: nat > produc746580111399690912list_b,Sup: set_Pr1895186847599665920list_b > produc746580111399690912list_b] :
      ( ( A4 = B5 )
     => ( ! [X: nat] :
            ( ( member_nat @ X @ B5 )
           => ( ( C3 @ X )
              = ( D @ X ) ) )
       => ( ( Sup @ ( image_5135116557422050441list_b @ C3 @ A4 ) )
          = ( Sup @ ( image_5135116557422050441list_b @ D @ B5 ) ) ) ) ) ).

% Sup.SUP_cong
thf(fact_782_Sup_OSUP__cong,axiom,
    ! [A4: set_nat,B5: set_nat,C3: nat > produc5647625992154082286xt_a_b,D: nat > produc5647625992154082286xt_a_b,Sup: set_Pr3872688570871424334xt_a_b > produc5647625992154082286xt_a_b] :
      ( ( A4 = B5 )
     => ( ! [X: nat] :
            ( ( member_nat @ X @ B5 )
           => ( ( C3 @ X )
              = ( D @ X ) ) )
       => ( ( Sup @ ( image_812790401321666007xt_a_b @ C3 @ A4 ) )
          = ( Sup @ ( image_812790401321666007xt_a_b @ D @ B5 ) ) ) ) ) ).

% Sup.SUP_cong
thf(fact_783_Sup_OSUP__cong,axiom,
    ! [A4: set_nat,B5: set_nat,C3: nat > $o,D: nat > $o,Sup: set_o > $o] :
      ( ( A4 = B5 )
     => ( ! [X: nat] :
            ( ( member_nat @ X @ B5 )
           => ( ( C3 @ X )
              = ( D @ X ) ) )
       => ( ( Sup @ ( image_nat_o @ C3 @ A4 ) )
          = ( Sup @ ( image_nat_o @ D @ B5 ) ) ) ) ) ).

% Sup.SUP_cong
thf(fact_784_Sup_OSUP__cong,axiom,
    ! [A4: set_nat,B5: set_nat,C3: nat > nat,D: nat > nat,Sup: set_nat > nat] :
      ( ( A4 = B5 )
     => ( ! [X: nat] :
            ( ( member_nat @ X @ B5 )
           => ( ( C3 @ X )
              = ( D @ X ) ) )
       => ( ( Sup @ ( image_nat_nat @ C3 @ A4 ) )
          = ( Sup @ ( image_nat_nat @ D @ B5 ) ) ) ) ) ).

% Sup.SUP_cong
thf(fact_785_imageI,axiom,
    ! [X2: nat > produc5647625992154082286xt_a_b,A4: set_na664922679713831477xt_a_b,F: ( nat > produc5647625992154082286xt_a_b ) > nat > produc746580111399690912list_b] :
      ( ( member3828642050509981054xt_a_b @ X2 @ A4 )
     => ( member1851140327238222640list_b @ ( F @ X2 ) @ ( image_5277725835624343543list_b @ F @ A4 ) ) ) ).

% imageI
thf(fact_786_imageI,axiom,
    ! [X2: nat > produc5647625992154082286xt_a_b,A4: set_na664922679713831477xt_a_b,F: ( nat > produc5647625992154082286xt_a_b ) > nat > produc5647625992154082286xt_a_b] :
      ( ( member3828642050509981054xt_a_b @ X2 @ A4 )
     => ( member3828642050509981054xt_a_b @ ( F @ X2 ) @ ( image_7255227558896101957xt_a_b @ F @ A4 ) ) ) ).

% imageI
thf(fact_787_imageI,axiom,
    ! [X2: $o,A4: set_o,F: $o > $o] :
      ( ( member_o @ X2 @ A4 )
     => ( member_o @ ( F @ X2 ) @ ( image_o_o @ F @ A4 ) ) ) ).

% imageI
thf(fact_788_rev__image__eqI,axiom,
    ! [X2: $o,A4: set_o,B: $o,F: $o > $o] :
      ( ( member_o @ X2 @ A4 )
     => ( ( B
          = ( F @ X2 ) )
       => ( member_o @ B @ ( image_o_o @ F @ A4 ) ) ) ) ).

% rev_image_eqI
thf(fact_789_comp__def,axiom,
    ( comp_nat_nat_nat
    = ( ^ [F2: nat > nat,G3: nat > nat,X3: nat] : ( F2 @ ( G3 @ X3 ) ) ) ) ).

% comp_def
thf(fact_790_comp__assoc,axiom,
    ! [F: nat > nat,G: nat > nat,H: nat > nat] :
      ( ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ F @ G ) @ H )
      = ( comp_nat_nat_nat @ F @ ( comp_nat_nat_nat @ G @ H ) ) ) ).

% comp_assoc
thf(fact_791_comp__eq__dest,axiom,
    ! [A: nat > nat,B: nat > nat,C2: nat > nat,D2: nat > nat,V: nat] :
      ( ( ( comp_nat_nat_nat @ A @ B )
        = ( comp_nat_nat_nat @ C2 @ D2 ) )
     => ( ( A @ ( B @ V ) )
        = ( C2 @ ( D2 @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_792_comp__eq__elim,axiom,
    ! [A: nat > nat,B: nat > nat,C2: nat > nat,D2: nat > nat] :
      ( ( ( comp_nat_nat_nat @ A @ B )
        = ( comp_nat_nat_nat @ C2 @ D2 ) )
     => ! [V2: nat] :
          ( ( A @ ( B @ V2 ) )
          = ( C2 @ ( D2 @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_793_comp__eq__dest__lhs,axiom,
    ! [A: nat > nat,B: nat > nat,C2: nat > nat,V: nat] :
      ( ( ( comp_nat_nat_nat @ A @ B )
        = C2 )
     => ( ( A @ ( B @ V ) )
        = ( C2 @ V ) ) ) ).

% comp_eq_dest_lhs
thf(fact_794_order__refl,axiom,
    ! [X2: nat] : ( ord_less_eq_nat @ X2 @ X2 ) ).

% order_refl
thf(fact_795_dual__order_Orefl,axiom,
    ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).

% dual_order.refl
thf(fact_796_snd__comp__map__prod,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b,G: list_b > list_b] :
      ( ( comp_P3599965238501839832list_b @ produc6107117247873403966list_b @ ( produc1867161623591055542list_b @ F @ G ) )
      = ( comp_l6451439721888030909list_b @ G @ produc6107117247873403966list_b ) ) ).

% snd_comp_map_prod
thf(fact_797_snd__comp__map__prod,axiom,
    ! [F: list_b > multihole_mctxt_a_b,G: multihole_mctxt_a_b > list_b] :
      ( ( comp_P8501011119256231206xt_a_b @ produc6107117247873403966list_b @ ( produc1669976423578742326list_b @ F @ G ) )
      = ( comp_M1546340790364679442xt_a_b @ G @ produc6725609433235685644xt_a_b ) ) ).

% snd_comp_map_prod
thf(fact_798_snd__comp__map__prod,axiom,
    ! [F: multihole_mctxt_a_b > list_b,G: list_b > multihole_mctxt_a_b] :
      ( ( comp_P2344685707722557151list_b @ produc6725609433235685644xt_a_b @ ( produc7077303473264541494xt_a_b @ F @ G ) )
      = ( comp_l1156032245741342326list_b @ G @ produc6107117247873403966list_b ) ) ).

% snd_comp_map_prod
thf(fact_799_snd__comp__map__prod,axiom,
    ! [F: list_b > list_b,G: multihole_mctxt_a_b > multihole_mctxt_a_b] :
      ( ( comp_P7245731588476948525xt_a_b @ produc6725609433235685644xt_a_b @ ( produc1327442379091988662xt_a_b @ F @ G ) )
      = ( comp_M7841358257205866699xt_a_b @ G @ produc6725609433235685644xt_a_b ) ) ).

% snd_comp_map_prod
thf(fact_800_fst__map__prod,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b,G: list_b > list_b,X2: produc746580111399690912list_b] :
      ( ( produc5881749095783049980list_b @ ( produc1867161623591055542list_b @ F @ G @ X2 ) )
      = ( F @ ( produc5881749095783049980list_b @ X2 ) ) ) ).

% fst_map_prod
thf(fact_801_fst__map__prod,axiom,
    ! [F: list_b > multihole_mctxt_a_b,G: multihole_mctxt_a_b > list_b,X2: produc5647625992154082286xt_a_b] :
      ( ( produc5881749095783049980list_b @ ( produc1669976423578742326list_b @ F @ G @ X2 ) )
      = ( F @ ( produc6500241281145331658xt_a_b @ X2 ) ) ) ).

% fst_map_prod
thf(fact_802_fst__map__prod,axiom,
    ! [F: multihole_mctxt_a_b > list_b,G: list_b > multihole_mctxt_a_b,X2: produc746580111399690912list_b] :
      ( ( produc6500241281145331658xt_a_b @ ( produc7077303473264541494xt_a_b @ F @ G @ X2 ) )
      = ( F @ ( produc5881749095783049980list_b @ X2 ) ) ) ).

% fst_map_prod
thf(fact_803_fst__map__prod,axiom,
    ! [F: list_b > list_b,G: multihole_mctxt_a_b > multihole_mctxt_a_b,X2: produc5647625992154082286xt_a_b] :
      ( ( produc6500241281145331658xt_a_b @ ( produc1327442379091988662xt_a_b @ F @ G @ X2 ) )
      = ( F @ ( produc6500241281145331658xt_a_b @ X2 ) ) ) ).

% fst_map_prod
thf(fact_804_snd__map__prod,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b,G: list_b > list_b,X2: produc746580111399690912list_b] :
      ( ( produc6107117247873403966list_b @ ( produc1867161623591055542list_b @ F @ G @ X2 ) )
      = ( G @ ( produc6107117247873403966list_b @ X2 ) ) ) ).

% snd_map_prod
thf(fact_805_snd__map__prod,axiom,
    ! [F: list_b > multihole_mctxt_a_b,G: multihole_mctxt_a_b > list_b,X2: produc5647625992154082286xt_a_b] :
      ( ( produc6107117247873403966list_b @ ( produc1669976423578742326list_b @ F @ G @ X2 ) )
      = ( G @ ( produc6725609433235685644xt_a_b @ X2 ) ) ) ).

% snd_map_prod
thf(fact_806_snd__map__prod,axiom,
    ! [F: multihole_mctxt_a_b > list_b,G: list_b > multihole_mctxt_a_b,X2: produc746580111399690912list_b] :
      ( ( produc6725609433235685644xt_a_b @ ( produc7077303473264541494xt_a_b @ F @ G @ X2 ) )
      = ( G @ ( produc6107117247873403966list_b @ X2 ) ) ) ).

% snd_map_prod
thf(fact_807_snd__map__prod,axiom,
    ! [F: list_b > list_b,G: multihole_mctxt_a_b > multihole_mctxt_a_b,X2: produc5647625992154082286xt_a_b] :
      ( ( produc6725609433235685644xt_a_b @ ( produc1327442379091988662xt_a_b @ F @ G @ X2 ) )
      = ( G @ ( produc6725609433235685644xt_a_b @ X2 ) ) ) ).

% snd_map_prod
thf(fact_808_fst__comp__map__prod,axiom,
    ! [F: multihole_mctxt_a_b > multihole_mctxt_a_b,G: list_b > list_b] :
      ( ( comp_P9065761140792057745list_b @ produc5881749095783049980list_b @ ( produc1867161623591055542list_b @ F @ G ) )
      = ( comp_M2940312376451475325list_b @ F @ produc5881749095783049980list_b ) ) ).

% fst_comp_map_prod
thf(fact_809_fst__comp__map__prod,axiom,
    ! [F: list_b > multihole_mctxt_a_b,G: multihole_mctxt_a_b > list_b] :
      ( ( comp_P4743434984691673311xt_a_b @ produc5881749095783049980list_b @ ( produc1669976423578742326list_b @ F @ G ) )
      = ( comp_l6057078126495733700xt_a_b @ F @ produc6500241281145331658xt_a_b ) ) ).

% fst_comp_map_prod
thf(fact_810_fst__comp__map__prod,axiom,
    ! [F: multihole_mctxt_a_b > list_b,G: list_b > multihole_mctxt_a_b] :
      ( ( comp_P3424029496760864550list_b @ produc6500241281145331658xt_a_b @ ( produc7077303473264541494xt_a_b @ F @ G ) )
      = ( comp_M5868666946465063876list_b @ F @ produc5881749095783049980list_b ) ) ).

% fst_comp_map_prod
thf(fact_811_fst__comp__map__prod,axiom,
    ! [F: list_b > list_b,G: multihole_mctxt_a_b > multihole_mctxt_a_b] :
      ( ( comp_P8325075377515255924xt_a_b @ produc6500241281145331658xt_a_b @ ( produc1327442379091988662xt_a_b @ F @ G ) )
      = ( comp_l2129113565787646475xt_a_b @ F @ produc6500241281145331658xt_a_b ) ) ).

% fst_comp_map_prod
thf(fact_812_fun_Omap__transfer,axiom,
    ! [Rb: nat > nat > $o,Sd: nat > nat > $o] :
      ( bNF_re3262823321055862553at_nat @ ( bNF_re5653821019739307937at_nat @ Rb @ Sd )
      @ ( bNF_re239970166668089693at_nat
        @ ( bNF_re5653821019739307937at_nat
          @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
          @ Rb )
        @ ( bNF_re5653821019739307937at_nat
          @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
          @ Sd ) )
      @ comp_nat_nat_nat
      @ comp_nat_nat_nat ) ).

% fun.map_transfer
thf(fact_813_map__prod_Ocomp,axiom,
    ! [F: nat > nat,G: nat > nat,H: nat > nat,I: nat > nat] :
      ( ( comp_P2240441846945064862at_nat @ ( produc6977886695330630970at_nat @ F @ G ) @ ( produc6977886695330630970at_nat @ H @ I ) )
      = ( produc6977886695330630970at_nat @ ( comp_nat_nat_nat @ F @ H ) @ ( comp_nat_nat_nat @ G @ I ) ) ) ).

% map_prod.comp
thf(fact_814_map__prod_Ocompositionality,axiom,
    ! [F: nat > nat,G: nat > nat,H: nat > nat,I: nat > nat,Prod: product_prod_nat_nat] :
      ( ( produc6977886695330630970at_nat @ F @ G @ ( produc6977886695330630970at_nat @ H @ I @ Prod ) )
      = ( produc6977886695330630970at_nat @ ( comp_nat_nat_nat @ F @ H ) @ ( comp_nat_nat_nat @ G @ I ) @ Prod ) ) ).

% map_prod.compositionality
thf(fact_815_map__prod__compose,axiom,
    ! [F12: nat > nat,F23: nat > nat,G1: nat > nat,G22: nat > nat] :
      ( ( produc6977886695330630970at_nat @ ( comp_nat_nat_nat @ F12 @ F23 ) @ ( comp_nat_nat_nat @ G1 @ G22 ) )
      = ( comp_P2240441846945064862at_nat @ ( produc6977886695330630970at_nat @ F12 @ G1 ) @ ( produc6977886695330630970at_nat @ F23 @ G22 ) ) ) ).

% map_prod_compose
thf(fact_816_prod_Omap__comp,axiom,
    ! [G1: nat > nat,G22: nat > nat,F12: nat > nat,F23: nat > nat,V: product_prod_nat_nat] :
      ( ( produc6977886695330630970at_nat @ G1 @ G22 @ ( produc6977886695330630970at_nat @ F12 @ F23 @ V ) )
      = ( produc6977886695330630970at_nat @ ( comp_nat_nat_nat @ G1 @ F12 ) @ ( comp_nat_nat_nat @ G22 @ F23 ) @ V ) ) ).

% prod.map_comp
thf(fact_817_order__antisym__conv,axiom,
    ! [Y3: nat,X2: nat] :
      ( ( ord_less_eq_nat @ Y3 @ X2 )
     => ( ( ord_less_eq_nat @ X2 @ Y3 )
        = ( X2 = Y3 ) ) ) ).

% order_antisym_conv
thf(fact_818_linorder__le__cases,axiom,
    ! [X2: nat,Y3: nat] :
      ( ~ ( ord_less_eq_nat @ X2 @ Y3 )
     => ( ord_less_eq_nat @ Y3 @ X2 ) ) ).

% linorder_le_cases
thf(fact_819_ord__le__eq__subst,axiom,
    ! [A: nat,B: nat,F: nat > nat,C2: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ( F @ B )
          = C2 )
       => ( ! [X: nat,Y: nat] :
              ( ( ord_less_eq_nat @ X @ Y )
             => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y ) ) )
         => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).

% ord_le_eq_subst
thf(fact_820_ord__eq__le__subst,axiom,
    ! [A: nat,F: nat > nat,B: nat,C2: nat] :
      ( ( A
        = ( F @ B ) )
     => ( ( ord_less_eq_nat @ B @ C2 )
       => ( ! [X: nat,Y: nat] :
              ( ( ord_less_eq_nat @ X @ Y )
             => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y ) ) )
         => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_821_linorder__linear,axiom,
    ! [X2: nat,Y3: nat] :
      ( ( ord_less_eq_nat @ X2 @ Y3 )
      | ( ord_less_eq_nat @ Y3 @ X2 ) ) ).

% linorder_linear
thf(fact_822_order__eq__refl,axiom,
    ! [X2: nat,Y3: nat] :
      ( ( X2 = Y3 )
     => ( ord_less_eq_nat @ X2 @ Y3 ) ) ).

% order_eq_refl
thf(fact_823_order__subst2,axiom,
    ! [A: nat,B: nat,F: nat > nat,C2: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ ( F @ B ) @ C2 )
       => ( ! [X: nat,Y: nat] :
              ( ( ord_less_eq_nat @ X @ Y )
             => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y ) ) )
         => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).

% order_subst2
thf(fact_824_order__subst1,axiom,
    ! [A: nat,F: nat > nat,B: nat,C2: nat] :
      ( ( ord_less_eq_nat @ A @ ( F @ B ) )
     => ( ( ord_less_eq_nat @ B @ C2 )
       => ( ! [X: nat,Y: nat] :
              ( ( ord_less_eq_nat @ X @ Y )
             => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y ) ) )
         => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).

% order_subst1
thf(fact_825_Orderings_Oorder__eq__iff,axiom,
    ( ( ^ [Y2: nat,Z: nat] : ( Y2 = Z ) )
    = ( ^ [A5: nat,B4: nat] :
          ( ( ord_less_eq_nat @ A5 @ B4 )
          & ( ord_less_eq_nat @ B4 @ A5 ) ) ) ) ).

% Orderings.order_eq_iff
thf(fact_826_antisym,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ A )
       => ( A = B ) ) ) ).

% antisym
thf(fact_827_dual__order_Otrans,axiom,
    ! [B: nat,A: nat,C2: nat] :
      ( ( ord_less_eq_nat @ B @ A )
     => ( ( ord_less_eq_nat @ C2 @ B )
       => ( ord_less_eq_nat @ C2 @ A ) ) ) ).

% dual_order.trans
thf(fact_828_dual__order_Oantisym,axiom,
    ! [B: nat,A: nat] :
      ( ( ord_less_eq_nat @ B @ A )
     => ( ( ord_less_eq_nat @ A @ B )
       => ( A = B ) ) ) ).

% dual_order.antisym
thf(fact_829_dual__order_Oeq__iff,axiom,
    ( ( ^ [Y2: nat,Z: nat] : ( Y2 = Z ) )
    = ( ^ [A5: nat,B4: nat] :
          ( ( ord_less_eq_nat @ B4 @ A5 )
          & ( ord_less_eq_nat @ A5 @ B4 ) ) ) ) ).

% dual_order.eq_iff
thf(fact_830_linorder__wlog,axiom,
    ! [P2: nat > nat > $o,A: nat,B: nat] :
      ( ! [A3: nat,B3: nat] :
          ( ( ord_less_eq_nat @ A3 @ B3 )
         => ( P2 @ A3 @ B3 ) )
     => ( ! [A3: nat,B3: nat] :
            ( ( P2 @ B3 @ A3 )
           => ( P2 @ A3 @ B3 ) )
       => ( P2 @ A @ B ) ) ) ).

% linorder_wlog
thf(fact_831_order__trans,axiom,
    ! [X2: nat,Y3: nat,Z2: nat] :
      ( ( ord_less_eq_nat @ X2 @ Y3 )
     => ( ( ord_less_eq_nat @ Y3 @ Z2 )
       => ( ord_less_eq_nat @ X2 @ Z2 ) ) ) ).

% order_trans
thf(fact_832_order_Otrans,axiom,
    ! [A: nat,B: nat,C2: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ C2 )
       => ( ord_less_eq_nat @ A @ C2 ) ) ) ).

% order.trans
thf(fact_833_order__antisym,axiom,
    ! [X2: nat,Y3: nat] :
      ( ( ord_less_eq_nat @ X2 @ Y3 )
     => ( ( ord_less_eq_nat @ Y3 @ X2 )
       => ( X2 = Y3 ) ) ) ).

% order_antisym
thf(fact_834_ord__le__eq__trans,axiom,
    ! [A: nat,B: nat,C2: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( B = C2 )
       => ( ord_less_eq_nat @ A @ C2 ) ) ) ).

% ord_le_eq_trans
thf(fact_835_ord__eq__le__trans,axiom,
    ! [A: nat,B: nat,C2: nat] :
      ( ( A = B )
     => ( ( ord_less_eq_nat @ B @ C2 )
       => ( ord_less_eq_nat @ A @ C2 ) ) ) ).

% ord_eq_le_trans
thf(fact_836_order__class_Oorder__eq__iff,axiom,
    ( ( ^ [Y2: nat,Z: nat] : ( Y2 = Z ) )
    = ( ^ [X3: nat,Y4: nat] :
          ( ( ord_less_eq_nat @ X3 @ Y4 )
          & ( ord_less_eq_nat @ Y4 @ X3 ) ) ) ) ).

% order_class.order_eq_iff
thf(fact_837_le__cases3,axiom,
    ! [X2: nat,Y3: nat,Z2: nat] :
      ( ( ( ord_less_eq_nat @ X2 @ Y3 )
       => ~ ( ord_less_eq_nat @ Y3 @ Z2 ) )
     => ( ( ( ord_less_eq_nat @ Y3 @ X2 )
         => ~ ( ord_less_eq_nat @ X2 @ Z2 ) )
       => ( ( ( ord_less_eq_nat @ X2 @ Z2 )
           => ~ ( ord_less_eq_nat @ Z2 @ Y3 ) )
         => ( ( ( ord_less_eq_nat @ Z2 @ Y3 )
             => ~ ( ord_less_eq_nat @ Y3 @ X2 ) )
           => ( ( ( ord_less_eq_nat @ Y3 @ Z2 )
               => ~ ( ord_less_eq_nat @ Z2 @ X2 ) )
             => ~ ( ( ord_less_eq_nat @ Z2 @ X2 )
                 => ~ ( ord_less_eq_nat @ X2 @ Y3 ) ) ) ) ) ) ) ).

% le_cases3
thf(fact_838_nle__le,axiom,
    ! [A: nat,B: nat] :
      ( ( ~ ( ord_less_eq_nat @ A @ B ) )
      = ( ( ord_less_eq_nat @ B @ A )
        & ( B != A ) ) ) ).

% nle_le
thf(fact_839_map__prod__o__convol,axiom,
    ! [H1: nat > nat,H2: nat > nat,F: nat > nat,G: nat > nat] :
      ( ( comp_P7430769850142754163at_nat @ ( produc6977886695330630970at_nat @ H1 @ H2 ) @ ( bNF_co805650143699787099at_nat @ F @ G ) )
      = ( bNF_co805650143699787099at_nat @ ( comp_nat_nat_nat @ H1 @ F ) @ ( comp_nat_nat_nat @ H2 @ G ) ) ) ).

% map_prod_o_convol
thf(fact_840_convol__o,axiom,
    ! [F: nat > nat,G: nat > nat,H: nat > nat] :
      ( ( comp_n8574565218330151774at_nat @ ( bNF_co805650143699787099at_nat @ F @ G ) @ H )
      = ( bNF_co805650143699787099at_nat @ ( comp_nat_nat_nat @ F @ H ) @ ( comp_nat_nat_nat @ G @ H ) ) ) ).

% convol_o
thf(fact_841_type__copy__map__cong0,axiom,
    ! [M: nat > nat,G: nat > nat,X2: nat,N2: nat > nat,H: nat > nat,F: nat > nat] :
      ( ( ( M @ ( G @ X2 ) )
        = ( N2 @ ( H @ X2 ) ) )
     => ( ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ F @ M ) @ G @ X2 )
        = ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ F @ N2 ) @ H @ X2 ) ) ) ).

% type_copy_map_cong0
thf(fact_842_rewriteL__comp__comp,axiom,
    ! [F: nat > nat,G: nat > nat,L: nat > nat,H: nat > nat] :
      ( ( ( comp_nat_nat_nat @ F @ G )
        = L )
     => ( ( comp_nat_nat_nat @ F @ ( comp_nat_nat_nat @ G @ H ) )
        = ( comp_nat_nat_nat @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_843_rewriteR__comp__comp,axiom,
    ! [G: nat > nat,H: nat > nat,R2: nat > nat,F: nat > nat] :
      ( ( ( comp_nat_nat_nat @ G @ H )
        = R2 )
     => ( ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ F @ G ) @ H )
        = ( comp_nat_nat_nat @ F @ R2 ) ) ) ).

% rewriteR_comp_comp
thf(fact_844_rewriteL__comp__comp2,axiom,
    ! [F: nat > nat,G: nat > nat,L1: nat > nat,L2: nat > nat,H: nat > nat,R2: nat > nat] :
      ( ( ( comp_nat_nat_nat @ F @ G )
        = ( comp_nat_nat_nat @ L1 @ L2 ) )
     => ( ( ( comp_nat_nat_nat @ L2 @ H )
          = R2 )
       => ( ( comp_nat_nat_nat @ F @ ( comp_nat_nat_nat @ G @ H ) )
          = ( comp_nat_nat_nat @ L1 @ R2 ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_845_rewriteR__comp__comp2,axiom,
    ! [G: nat > nat,H: nat > nat,R1: nat > nat,R22: nat > nat,F: nat > nat,L: nat > nat] :
      ( ( ( comp_nat_nat_nat @ G @ H )
        = ( comp_nat_nat_nat @ R1 @ R22 ) )
     => ( ( ( comp_nat_nat_nat @ F @ R1 )
          = L )
       => ( ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ F @ G ) @ H )
          = ( comp_nat_nat_nat @ L @ R22 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_846_comp__transfer,axiom,
    ! [B5: nat > nat > $o,C3: nat > nat > $o,A4: nat > nat > $o] : ( bNF_re3262823321055862553at_nat @ ( bNF_re5653821019739307937at_nat @ B5 @ C3 ) @ ( bNF_re239970166668089693at_nat @ ( bNF_re5653821019739307937at_nat @ A4 @ B5 ) @ ( bNF_re5653821019739307937at_nat @ A4 @ C3 ) ) @ comp_nat_nat_nat @ comp_nat_nat_nat ) ).

% comp_transfer
thf(fact_847_o__rsp_I2_J,axiom,
    ! [R12: nat > nat > $o] :
      ( bNF_re3262823321055862553at_nat
      @ ^ [Y2: nat > nat,Z: nat > nat] : ( Y2 = Z )
      @ ( bNF_re239970166668089693at_nat
        @ ( bNF_re5653821019739307937at_nat @ R12
          @ ^ [Y2: nat,Z: nat] : ( Y2 = Z ) )
        @ ( bNF_re5653821019739307937at_nat @ R12
          @ ^ [Y2: nat,Z: nat] : ( Y2 = Z ) ) )
      @ comp_nat_nat_nat
      @ comp_nat_nat_nat ) ).

% o_rsp(2)
thf(fact_848_o__rsp_I1_J,axiom,
    ! [R23: nat > nat > $o,R3: nat > nat > $o,R12: nat > nat > $o] : ( bNF_re3262823321055862553at_nat @ ( bNF_re5653821019739307937at_nat @ R23 @ R3 ) @ ( bNF_re239970166668089693at_nat @ ( bNF_re5653821019739307937at_nat @ R12 @ R23 ) @ ( bNF_re5653821019739307937at_nat @ R12 @ R3 ) ) @ comp_nat_nat_nat @ comp_nat_nat_nat ) ).

% o_rsp(1)
thf(fact_849_prod_Osize__gen__o__map,axiom,
    ! [F: nat > nat,Fa: nat > nat,G: nat > nat,Ga: nat > nat] :
      ( ( comp_P1567445206330693457at_nat @ ( basic_876126793109182934at_nat @ F @ Fa ) @ ( produc6977886695330630970at_nat @ G @ Ga ) )
      = ( basic_876126793109182934at_nat @ ( comp_nat_nat_nat @ F @ G ) @ ( comp_nat_nat_nat @ Fa @ Ga ) ) ) ).

% prod.size_gen_o_map
thf(fact_850_fun_Omap__id,axiom,
    ! [T2: nat > nat] :
      ( ( comp_nat_nat_nat @ id_nat @ T2 )
      = T2 ) ).

% fun.map_id
thf(fact_851_id__comp,axiom,
    ! [G: nat > nat] :
      ( ( comp_nat_nat_nat @ id_nat @ G )
      = G ) ).

% id_comp
thf(fact_852_comp__id,axiom,
    ! [F: nat > nat] :
      ( ( comp_nat_nat_nat @ F @ id_nat )
      = F ) ).

% comp_id
thf(fact_853_swap__comp__swap,axiom,
    ( ( comp_P8043882148310014845xt_a_b @ produc4023874437082322608list_b @ produc4642366622444604286xt_a_b )
    = id_Pro7664240512220884831xt_a_b ) ).

% swap_comp_swap
thf(fact_854_swap__comp__swap,axiom,
    ( ( comp_P8660005625159894603list_b @ produc4642366622444604286xt_a_b @ produc4023874437082322608list_b )
    = id_Pro2763194631466493457list_b ) ).

% swap_comp_swap
thf(fact_855_fun_Omap__id0,axiom,
    ( ( comp_nat_nat_nat @ id_nat )
    = id_nat_nat ) ).

% fun.map_id0
thf(fact_856_comp__eq__id__dest,axiom,
    ! [A: nat > nat,B: nat > nat,C2: nat > nat,V: nat] :
      ( ( ( comp_nat_nat_nat @ A @ B )
        = ( comp_nat_nat_nat @ id_nat @ C2 ) )
     => ( ( A @ ( B @ V ) )
        = ( C2 @ V ) ) ) ).

% comp_eq_id_dest
thf(fact_857_pointfree__idE,axiom,
    ! [F: nat > nat,G: nat > nat,X2: nat] :
      ( ( ( comp_nat_nat_nat @ F @ G )
        = id_nat )
     => ( ( F @ ( G @ X2 ) )
        = X2 ) ) ).

% pointfree_idE
thf(fact_858_Greatest__equality,axiom,
    ! [P2: nat > $o,X2: nat] :
      ( ( P2 @ X2 )
     => ( ! [Y: nat] :
            ( ( P2 @ Y )
           => ( ord_less_eq_nat @ Y @ X2 ) )
       => ( ( order_Greatest_nat @ P2 )
          = X2 ) ) ) ).

% Greatest_equality
thf(fact_859_GreatestI2__order,axiom,
    ! [P2: nat > $o,X2: nat,Q3: nat > $o] :
      ( ( P2 @ X2 )
     => ( ! [Y: nat] :
            ( ( P2 @ Y )
           => ( ord_less_eq_nat @ Y @ X2 ) )
       => ( ! [X: nat] :
              ( ( P2 @ X )
             => ( ! [Y6: nat] :
                    ( ( P2 @ Y6 )
                   => ( ord_less_eq_nat @ Y6 @ X ) )
               => ( Q3 @ X ) ) )
         => ( Q3 @ ( order_Greatest_nat @ P2 ) ) ) ) ) ).

% GreatestI2_order
thf(fact_860_surj__swap,axiom,
    ( ( image_3492653723807366483xt_a_b @ produc4023874437082322608list_b @ top_to6377410373901291600list_b )
    = top_to8354912097173050014xt_a_b ) ).

% surj_swap
thf(fact_861_surj__swap,axiom,
    ( ( image_1828724688096913975list_b @ produc4642366622444604286xt_a_b @ top_to8354912097173050014xt_a_b )
    = top_to6377410373901291600list_b ) ).

% surj_swap
thf(fact_862_verit__comp__simplify1_I2_J,axiom,
    ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).

% verit_comp_simplify1(2)
thf(fact_863_verit__la__disequality,axiom,
    ! [A: nat,B: nat] :
      ( ( A = B )
      | ~ ( ord_less_eq_nat @ A @ B )
      | ~ ( ord_less_eq_nat @ B @ A ) ) ).

% verit_la_disequality
thf(fact_864_UNIV__I,axiom,
    ! [X2: $o] : ( member_o @ X2 @ top_top_set_o ) ).

% UNIV_I
thf(fact_865_UNIV__I,axiom,
    ! [X2: nat] : ( member_nat @ X2 @ top_top_set_nat ) ).

% UNIV_I
thf(fact_866_Pow__UNIV,axiom,
    ( ( pow_nat @ top_top_set_nat )
    = top_top_set_set_nat ) ).

% Pow_UNIV
thf(fact_867_range__fst,axiom,
    ( ( image_7211724023120395249xt_a_b @ produc5881749095783049980list_b @ top_to6377410373901291600list_b )
    = top_to3428735846572888636xt_a_b ) ).

% range_fst
thf(fact_868_range__fst,axiom,
    ( ( image_5978867512307746588list_b @ produc6500241281145331658xt_a_b @ top_to8354912097173050014xt_a_b )
    = top_top_set_list_b ) ).

% range_fst
thf(fact_869_range__snd,axiom,
    ( ( image_9124975640858730986list_b @ produc6107117247873403966list_b @ top_to6377410373901291600list_b )
    = top_top_set_list_b ) ).

% range_snd
thf(fact_870_range__snd,axiom,
    ( ( image_4915618970390574371xt_a_b @ produc6725609433235685644xt_a_b @ top_to8354912097173050014xt_a_b )
    = top_to3428735846572888636xt_a_b ) ).

% range_snd
thf(fact_871_UNIV__eq__I,axiom,
    ! [A4: set_o] :
      ( ! [X: $o] : ( member_o @ X @ A4 )
     => ( top_top_set_o = A4 ) ) ).

% UNIV_eq_I
thf(fact_872_UNIV__eq__I,axiom,
    ! [A4: set_nat] :
      ( ! [X: nat] : ( member_nat @ X @ A4 )
     => ( top_top_set_nat = A4 ) ) ).

% UNIV_eq_I
thf(fact_873_UNIV__witness,axiom,
    ? [X: $o] : ( member_o @ X @ top_top_set_o ) ).

% UNIV_witness
thf(fact_874_UNIV__witness,axiom,
    ? [X: nat] : ( member_nat @ X @ top_top_set_nat ) ).

% UNIV_witness
thf(fact_875_top__greatest,axiom,
    ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ top_top_set_nat ) ).

% top_greatest
thf(fact_876_top_Oextremum__unique,axiom,
    ! [A: set_nat] :
      ( ( ord_less_eq_set_nat @ top_top_set_nat @ A )
      = ( A = top_top_set_nat ) ) ).

% top.extremum_unique
thf(fact_877_top_Oextremum__uniqueI,axiom,
    ! [A: set_nat] :
      ( ( ord_less_eq_set_nat @ top_top_set_nat @ A )
     => ( A = top_top_set_nat ) ) ).

% top.extremum_uniqueI
thf(fact_878_fst__transfer,axiom,
    ! [A4: multihole_mctxt_a_b > multihole_mctxt_a_b > $o,B5: list_b > list_b > $o] : ( bNF_re3446365231100426717xt_a_b @ ( basic_1755056647974194549list_b @ A4 @ B5 ) @ A4 @ produc5881749095783049980list_b @ produc5881749095783049980list_b ) ).

% fst_transfer
thf(fact_879_fst__transfer,axiom,
    ! [A4: multihole_mctxt_a_b > list_b > $o,B5: list_b > multihole_mctxt_a_b > $o] : ( bNF_re6993931615214772260list_b @ ( basic_6965198497647680501xt_a_b @ A4 @ B5 ) @ A4 @ produc5881749095783049980list_b @ produc6500241281145331658xt_a_b ) ).

% fst_transfer
thf(fact_880_fst__transfer,axiom,
    ! [A4: list_b > multihole_mctxt_a_b > $o,B5: multihole_mctxt_a_b > list_b > $o] : ( bNF_re7495894085839512534xt_a_b @ ( basic_1557871447961881333list_b @ A4 @ B5 ) @ A4 @ produc6500241281145331658xt_a_b @ produc5881749095783049980list_b ) ).

% fst_transfer
thf(fact_881_fst__transfer,axiom,
    ! [A4: list_b > list_b > $o,B5: multihole_mctxt_a_b > multihole_mctxt_a_b > $o] : ( bNF_re7338882136821462045list_b @ ( basic_1215337403475127669xt_a_b @ A4 @ B5 ) @ A4 @ produc6500241281145331658xt_a_b @ produc6500241281145331658xt_a_b ) ).

% fst_transfer
thf(fact_882_snd__transfer,axiom,
    ! [A4: multihole_mctxt_a_b > multihole_mctxt_a_b > $o,B5: list_b > list_b > $o] : ( bNF_re2106300878112453789list_b @ ( basic_1755056647974194549list_b @ A4 @ B5 ) @ B5 @ produc6107117247873403966list_b @ produc6107117247873403966list_b ) ).

% snd_transfer
thf(fact_883_snd__transfer,axiom,
    ! [A4: multihole_mctxt_a_b > list_b > $o,B5: list_b > multihole_mctxt_a_b > $o] : ( bNF_re7612423800577053938xt_a_b @ ( basic_6965198497647680501xt_a_b @ A4 @ B5 ) @ B5 @ produc6107117247873403966list_b @ produc6725609433235685644xt_a_b ) ).

% snd_transfer
thf(fact_884_snd__transfer,axiom,
    ! [A4: list_b > multihole_mctxt_a_b > $o,B5: multihole_mctxt_a_b > list_b > $o] : ( bNF_re6877401900477230856list_b @ ( basic_1557871447961881333list_b @ A4 @ B5 ) @ B5 @ produc6725609433235685644xt_a_b @ produc6107117247873403966list_b ) ).

% snd_transfer
thf(fact_885_snd__transfer,axiom,
    ! [A4: list_b > list_b > $o,B5: multihole_mctxt_a_b > multihole_mctxt_a_b > $o] : ( bNF_re5350685653480569181xt_a_b @ ( basic_1215337403475127669xt_a_b @ A4 @ B5 ) @ B5 @ produc6725609433235685644xt_a_b @ produc6725609433235685644xt_a_b ) ).

% snd_transfer
thf(fact_886_range__eqI,axiom,
    ! [B: $o,F: nat > $o,X2: nat] :
      ( ( B
        = ( F @ X2 ) )
     => ( member_o @ B @ ( image_nat_o @ F @ top_top_set_nat ) ) ) ).

% range_eqI
thf(fact_887_surj__def,axiom,
    ! [F: nat > nat] :
      ( ( ( image_nat_nat @ F @ top_top_set_nat )
        = top_top_set_nat )
      = ( ! [Y4: nat] :
          ? [X3: nat] :
            ( Y4
            = ( F @ X3 ) ) ) ) ).

% surj_def
thf(fact_888_rangeI,axiom,
    ! [F: nat > $o,X2: nat] : ( member_o @ ( F @ X2 ) @ ( image_nat_o @ F @ top_top_set_nat ) ) ).

% rangeI
thf(fact_889_surjI,axiom,
    ! [G: nat > nat,F: nat > nat] :
      ( ! [X: nat] :
          ( ( G @ ( F @ X ) )
          = X )
     => ( ( image_nat_nat @ G @ top_top_set_nat )
        = top_top_set_nat ) ) ).

% surjI
thf(fact_890_surjE,axiom,
    ! [F: nat > nat,Y3: nat] :
      ( ( ( image_nat_nat @ F @ top_top_set_nat )
        = top_top_set_nat )
     => ~ ! [X: nat] :
            ( Y3
           != ( F @ X ) ) ) ).

% surjE
thf(fact_891_surjD,axiom,
    ! [F: nat > nat,Y3: nat] :
      ( ( ( image_nat_nat @ F @ top_top_set_nat )
        = top_top_set_nat )
     => ? [X: nat] :
          ( Y3
          = ( F @ X ) ) ) ).

% surjD
thf(fact_892_subset__UNIV,axiom,
    ! [A4: set_nat] : ( ord_less_eq_set_nat @ A4 @ top_top_set_nat ) ).

% subset_UNIV
thf(fact_893_map__prod__surj,axiom,
    ! [F: nat > nat,G: nat > nat] :
      ( ( ( image_nat_nat @ F @ top_top_set_nat )
        = top_top_set_nat )
     => ( ( ( image_nat_nat @ G @ top_top_set_nat )
          = top_top_set_nat )
       => ( ( image_5168914502847457605at_nat @ ( produc6977886695330630970at_nat @ F @ G ) @ top_to4669805908274784177at_nat )
          = top_to4669805908274784177at_nat ) ) ) ).

% map_prod_surj
thf(fact_894_rel__prod__sel,axiom,
    ( basic_1755056647974194549list_b
    = ( ^ [R13: multihole_mctxt_a_b > multihole_mctxt_a_b > $o,R24: list_b > list_b > $o,P4: produc746580111399690912list_b,Q4: produc746580111399690912list_b] :
          ( ( R13 @ ( produc5881749095783049980list_b @ P4 ) @ ( produc5881749095783049980list_b @ Q4 ) )
          & ( R24 @ ( produc6107117247873403966list_b @ P4 ) @ ( produc6107117247873403966list_b @ Q4 ) ) ) ) ) ).

% rel_prod_sel
thf(fact_895_rel__prod__sel,axiom,
    ( basic_6965198497647680501xt_a_b
    = ( ^ [R13: multihole_mctxt_a_b > list_b > $o,R24: list_b > multihole_mctxt_a_b > $o,P4: produc746580111399690912list_b,Q4: produc5647625992154082286xt_a_b] :
          ( ( R13 @ ( produc5881749095783049980list_b @ P4 ) @ ( produc6500241281145331658xt_a_b @ Q4 ) )
          & ( R24 @ ( produc6107117247873403966list_b @ P4 ) @ ( produc6725609433235685644xt_a_b @ Q4 ) ) ) ) ) ).

% rel_prod_sel
thf(fact_896_rel__prod__sel,axiom,
    ( basic_1557871447961881333list_b
    = ( ^ [R13: list_b > multihole_mctxt_a_b > $o,R24: multihole_mctxt_a_b > list_b > $o,P4: produc5647625992154082286xt_a_b,Q4: produc746580111399690912list_b] :
          ( ( R13 @ ( produc6500241281145331658xt_a_b @ P4 ) @ ( produc5881749095783049980list_b @ Q4 ) )
          & ( R24 @ ( produc6725609433235685644xt_a_b @ P4 ) @ ( produc6107117247873403966list_b @ Q4 ) ) ) ) ) ).

% rel_prod_sel
thf(fact_897_rel__prod__sel,axiom,
    ( basic_1215337403475127669xt_a_b
    = ( ^ [R13: list_b > list_b > $o,R24: multihole_mctxt_a_b > multihole_mctxt_a_b > $o,P4: produc5647625992154082286xt_a_b,Q4: produc5647625992154082286xt_a_b] :
          ( ( R13 @ ( produc6500241281145331658xt_a_b @ P4 ) @ ( produc6500241281145331658xt_a_b @ Q4 ) )
          & ( R24 @ ( produc6725609433235685644xt_a_b @ P4 ) @ ( produc6725609433235685644xt_a_b @ Q4 ) ) ) ) ) ).

% rel_prod_sel
thf(fact_898_fun_Orel__cong,axiom,
    ! [X2: nat > $o,Ya: nat > $o,Y3: nat > $o,Xa2: nat > $o,R: $o > $o > $o,Ra: $o > $o > $o] :
      ( ( X2 = Ya )
     => ( ( Y3 = Xa2 )
       => ( ! [Z3: $o,Yb: $o] :
              ( ( member_o @ Z3 @ ( image_nat_o @ Ya @ top_top_set_nat ) )
             => ( ( member_o @ Yb @ ( image_nat_o @ Xa2 @ top_top_set_nat ) )
               => ( ( R @ Z3 @ Yb )
                  = ( Ra @ Z3 @ Yb ) ) ) )
         => ( ( bNF_re4705727531993890431at_o_o
              @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
              @ R
              @ X2
              @ Y3 )
            = ( bNF_re4705727531993890431at_o_o
              @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
              @ Ra
              @ Ya
              @ Xa2 ) ) ) ) ) ).

% fun.rel_cong
thf(fact_899_fun_Orel__mono__strong,axiom,
    ! [R: $o > $o > $o,X2: nat > $o,Y3: nat > $o,Ra: $o > $o > $o] :
      ( ( bNF_re4705727531993890431at_o_o
        @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
        @ R
        @ X2
        @ Y3 )
     => ( ! [Z3: $o,Yb: $o] :
            ( ( member_o @ Z3 @ ( image_nat_o @ X2 @ top_top_set_nat ) )
           => ( ( member_o @ Yb @ ( image_nat_o @ Y3 @ top_top_set_nat ) )
             => ( ( R @ Z3 @ Yb )
               => ( Ra @ Z3 @ Yb ) ) ) )
       => ( bNF_re4705727531993890431at_o_o
          @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
          @ Ra
          @ X2
          @ Y3 ) ) ) ).

% fun.rel_mono_strong
thf(fact_900_fun_Orel__refl__strong,axiom,
    ! [X2: nat > $o,Ra: $o > $o > $o] :
      ( ! [Z3: $o] :
          ( ( member_o @ Z3 @ ( image_nat_o @ X2 @ top_top_set_nat ) )
         => ( Ra @ Z3 @ Z3 ) )
     => ( bNF_re4705727531993890431at_o_o
        @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
        @ Ra
        @ X2
        @ X2 ) ) ).

% fun.rel_refl_strong
thf(fact_901_range__subsetD,axiom,
    ! [F: nat > $o,B5: set_o,I: nat] :
      ( ( ord_less_eq_set_o @ ( image_nat_o @ F @ top_top_set_nat ) @ B5 )
     => ( member_o @ ( F @ I ) @ B5 ) ) ).

% range_subsetD
thf(fact_902_surj__fun__eq,axiom,
    ! [F: nat > nat,X5: set_nat,G1: nat > nat,G22: nat > nat] :
      ( ( ( image_nat_nat @ F @ X5 )
        = top_top_set_nat )
     => ( ! [X: nat] :
            ( ( member_nat @ X @ X5 )
           => ( ( comp_nat_nat_nat @ G1 @ F @ X )
              = ( comp_nat_nat_nat @ G22 @ F @ X ) ) )
       => ( G1 = G22 ) ) ) ).

% surj_fun_eq
thf(fact_903_fun_Oset__map,axiom,
    ! [F: nat > nat,V: nat > nat] :
      ( ( image_nat_nat @ ( comp_nat_nat_nat @ F @ V ) @ top_top_set_nat )
      = ( image_nat_nat @ F @ ( image_nat_nat @ V @ top_top_set_nat ) ) ) ).

% fun.set_map
thf(fact_904_fun_Omap__cong,axiom,
    ! [X2: nat > nat,Ya: nat > nat,F: nat > nat,G: nat > nat] :
      ( ( X2 = Ya )
     => ( ! [Z3: nat] :
            ( ( member_nat @ Z3 @ ( image_nat_nat @ Ya @ top_top_set_nat ) )
           => ( ( F @ Z3 )
              = ( G @ Z3 ) ) )
       => ( ( comp_nat_nat_nat @ F @ X2 )
          = ( comp_nat_nat_nat @ G @ Ya ) ) ) ) ).

% fun.map_cong
thf(fact_905_fun_Omap__cong0,axiom,
    ! [X2: nat > nat,F: nat > nat,G: nat > nat] :
      ( ! [Z3: nat] :
          ( ( member_nat @ Z3 @ ( image_nat_nat @ X2 @ top_top_set_nat ) )
         => ( ( F @ Z3 )
            = ( G @ Z3 ) ) )
     => ( ( comp_nat_nat_nat @ F @ X2 )
        = ( comp_nat_nat_nat @ G @ X2 ) ) ) ).

% fun.map_cong0
thf(fact_906_fun_Oinj__map__strong,axiom,
    ! [X2: nat > nat,Xa2: nat > nat,F: nat > nat,Fa: nat > nat] :
      ( ! [Z3: nat,Za: nat] :
          ( ( member_nat @ Z3 @ ( image_nat_nat @ X2 @ top_top_set_nat ) )
         => ( ( member_nat @ Za @ ( image_nat_nat @ Xa2 @ top_top_set_nat ) )
           => ( ( ( F @ Z3 )
                = ( Fa @ Za ) )
             => ( Z3 = Za ) ) ) )
     => ( ( ( comp_nat_nat_nat @ F @ X2 )
          = ( comp_nat_nat_nat @ Fa @ Xa2 ) )
       => ( X2 = Xa2 ) ) ) ).

% fun.inj_map_strong
thf(fact_907_fun_Omap__ident__strong,axiom,
    ! [T2: nat > nat,F: nat > nat] :
      ( ! [Z3: nat] :
          ( ( member_nat @ Z3 @ ( image_nat_nat @ T2 @ top_top_set_nat ) )
         => ( ( F @ Z3 )
            = Z3 ) )
     => ( ( comp_nat_nat_nat @ F @ T2 )
        = T2 ) ) ).

% fun.map_ident_strong
thf(fact_908_fun_Omap__ident__strong,axiom,
    ! [T2: nat > $o,F: $o > $o] :
      ( ! [Z3: $o] :
          ( ( member_o @ Z3 @ ( image_nat_o @ T2 @ top_top_set_nat ) )
         => ( ( F @ Z3 )
            = Z3 ) )
     => ( ( comp_o_o_nat @ F @ T2 )
        = T2 ) ) ).

% fun.map_ident_strong
thf(fact_909_comp__surj,axiom,
    ! [F: nat > nat,G: nat > nat] :
      ( ( ( image_nat_nat @ F @ top_top_set_nat )
        = top_top_set_nat )
     => ( ( ( image_nat_nat @ G @ top_top_set_nat )
          = top_top_set_nat )
       => ( ( image_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ top_top_set_nat )
          = top_top_set_nat ) ) ) ).

% comp_surj
thf(fact_910_surj__id,axiom,
    ( ( image_nat_nat @ id_nat @ top_top_set_nat )
    = top_top_set_nat ) ).

% surj_id
thf(fact_911_Grp__UNIV__idI,axiom,
    ! [X2: nat,Y3: nat] :
      ( ( X2 = Y3 )
     => ( bNF_Grp_nat_nat @ top_top_set_nat @ id_nat @ X2 @ Y3 ) ) ).

% Grp_UNIV_idI
thf(fact_912_eq__alt,axiom,
    ( ( ^ [Y2: nat,Z: nat] : ( Y2 = Z ) )
    = ( bNF_Grp_nat_nat @ top_top_set_nat @ id_nat ) ) ).

% eq_alt
thf(fact_913_top__set__def,axiom,
    ( top_top_set_nat
    = ( collect_nat @ top_top_nat_o ) ) ).

% top_set_def
thf(fact_914_mono__transfer,axiom,
    ! [A4: nat > nat > $o,B5: nat > nat > $o] :
      ( ( bi_total_nat_nat @ A4 )
     => ( ( bNF_re578469030762574527_nat_o @ A4
          @ ( bNF_re4705727531993890431at_o_o @ A4
            @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
          @ ord_less_eq_nat
          @ ord_less_eq_nat )
       => ( ( bNF_re578469030762574527_nat_o @ B5
            @ ( bNF_re4705727531993890431at_o_o @ B5
              @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
            @ ord_less_eq_nat
            @ ord_less_eq_nat )
         => ( bNF_re1334470082001271389at_o_o @ ( bNF_re5653821019739307937at_nat @ A4 @ B5 )
            @ ^ [Y2: $o,Z: $o] : ( Y2 = Z )
            @ ( monotone_on_nat_nat @ top_top_set_nat @ ord_less_eq_nat @ ord_less_eq_nat )
            @ ( monotone_on_nat_nat @ top_top_set_nat @ ord_less_eq_nat @ ord_less_eq_nat ) ) ) ) ) ).

% mono_transfer
thf(fact_915_monotone__parametric,axiom,
    ! [A4: nat > nat > $o,B5: nat > nat > $o] :
      ( ( bi_total_nat_nat @ A4 )
     => ( bNF_re3108638643152158461_nat_o
        @ ( bNF_re578469030762574527_nat_o @ A4
          @ ( bNF_re4705727531993890431at_o_o @ A4
            @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) ) )
        @ ( bNF_re2012056497951032797_nat_o
          @ ( bNF_re578469030762574527_nat_o @ B5
            @ ( bNF_re4705727531993890431at_o_o @ B5
              @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) ) )
          @ ( bNF_re1334470082001271389at_o_o @ ( bNF_re5653821019739307937at_nat @ A4 @ B5 )
            @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) ) )
        @ ( monotone_on_nat_nat @ top_top_set_nat )
        @ ( monotone_on_nat_nat @ top_top_set_nat ) ) ) ).

% monotone_parametric
thf(fact_916_Grp__fst__snd,axiom,
    ! [R: multihole_mctxt_a_b > list_b > $o] :
      ( ( relcom4353153964112099584list_b @ ( conver810234233312416737xt_a_b @ ( bNF_Gr18341695879942202xt_a_b @ ( collec5933784528073787915list_b @ ( produc7190274377712547635st_b_o @ R ) ) @ produc5881749095783049980list_b ) ) @ ( bNF_Gr7082935421558533171list_b @ ( collec5933784528073787915list_b @ ( produc7190274377712547635st_b_o @ R ) ) @ produc6107117247873403966list_b ) )
      = R ) ).

% Grp_fst_snd
thf(fact_917_Grp__fst__snd,axiom,
    ! [R: list_b > multihole_mctxt_a_b > $o] :
      ( ( relcom2105089833257999154xt_a_b @ ( conver2075301813112946444list_b @ ( bNF_Gr3936827293007548773list_b @ ( collec1611458371973403481xt_a_b @ ( produc1221931734719695589_a_b_o @ R ) ) @ produc6500241281145331658xt_a_b ) ) @ ( bNF_Gr6945608680004897132xt_a_b @ ( collec1611458371973403481xt_a_b @ ( produc1221931734719695589_a_b_o @ R ) ) @ produc6725609433235685644xt_a_b ) )
      = R ) ).

% Grp_fst_snd
thf(fact_918_ord_Omono__onD,axiom,
    ! [A4: set_o,Less_eq: $o > $o > $o,F: $o > nat,R2: $o,S2: $o] :
      ( ( monotone_on_o_nat @ A4 @ Less_eq @ ord_less_eq_nat @ F )
     => ( ( member_o @ R2 @ A4 )
       => ( ( member_o @ S2 @ A4 )
         => ( ( Less_eq @ R2 @ S2 )
           => ( ord_less_eq_nat @ ( F @ R2 ) @ ( F @ S2 ) ) ) ) ) ) ).

% ord.mono_onD
thf(fact_919_ord_Omono__onD,axiom,
    ! [A4: set_nat,Less_eq: nat > nat > $o,F: nat > nat,R2: nat,S2: nat] :
      ( ( monotone_on_nat_nat @ A4 @ Less_eq @ ord_less_eq_nat @ F )
     => ( ( member_nat @ R2 @ A4 )
       => ( ( member_nat @ S2 @ A4 )
         => ( ( Less_eq @ R2 @ S2 )
           => ( ord_less_eq_nat @ ( F @ R2 ) @ ( F @ S2 ) ) ) ) ) ) ).

% ord.mono_onD
thf(fact_920_ord_Omono__onI,axiom,
    ! [A4: set_o,Less_eq: $o > $o > $o,F: $o > nat] :
      ( ! [R4: $o,S4: $o] :
          ( ( member_o @ R4 @ A4 )
         => ( ( member_o @ S4 @ A4 )
           => ( ( Less_eq @ R4 @ S4 )
             => ( ord_less_eq_nat @ ( F @ R4 ) @ ( F @ S4 ) ) ) ) )
     => ( monotone_on_o_nat @ A4 @ Less_eq @ ord_less_eq_nat @ F ) ) ).

% ord.mono_onI
thf(fact_921_ord_Omono__onI,axiom,
    ! [A4: set_nat,Less_eq: nat > nat > $o,F: nat > nat] :
      ( ! [R4: nat,S4: nat] :
          ( ( member_nat @ R4 @ A4 )
         => ( ( member_nat @ S4 @ A4 )
           => ( ( Less_eq @ R4 @ S4 )
             => ( ord_less_eq_nat @ ( F @ R4 ) @ ( F @ S4 ) ) ) ) )
     => ( monotone_on_nat_nat @ A4 @ Less_eq @ ord_less_eq_nat @ F ) ) ).

% ord.mono_onI
thf(fact_922_ord_Omono__on__def,axiom,
    ! [A4: set_o,Less_eq: $o > $o > $o,F: $o > nat] :
      ( ( monotone_on_o_nat @ A4 @ Less_eq @ ord_less_eq_nat @ F )
      = ( ! [R5: $o,S: $o] :
            ( ( ( member_o @ R5 @ A4 )
              & ( member_o @ S @ A4 )
              & ( Less_eq @ R5 @ S ) )
           => ( ord_less_eq_nat @ ( F @ R5 ) @ ( F @ S ) ) ) ) ) ).

% ord.mono_on_def
thf(fact_923_ord_Omono__on__def,axiom,
    ! [A4: set_nat,Less_eq: nat > nat > $o,F: nat > nat] :
      ( ( monotone_on_nat_nat @ A4 @ Less_eq @ ord_less_eq_nat @ F )
      = ( ! [R5: nat,S: nat] :
            ( ( ( member_nat @ R5 @ A4 )
              & ( member_nat @ S @ A4 )
              & ( Less_eq @ R5 @ S ) )
           => ( ord_less_eq_nat @ ( F @ R5 ) @ ( F @ S ) ) ) ) ) ).

% ord.mono_on_def
thf(fact_924_mono__onD,axiom,
    ! [A4: set_o,F: $o > nat,R2: $o,S2: $o] :
      ( ( monotone_on_o_nat @ A4 @ ord_less_eq_o @ ord_less_eq_nat @ F )
     => ( ( member_o @ R2 @ A4 )
       => ( ( member_o @ S2 @ A4 )
         => ( ( ord_less_eq_o @ R2 @ S2 )
           => ( ord_less_eq_nat @ ( F @ R2 ) @ ( F @ S2 ) ) ) ) ) ) ).

% mono_onD
thf(fact_925_mono__onD,axiom,
    ! [A4: set_nat,F: nat > nat,R2: nat,S2: nat] :
      ( ( monotone_on_nat_nat @ A4 @ ord_less_eq_nat @ ord_less_eq_nat @ F )
     => ( ( member_nat @ R2 @ A4 )
       => ( ( member_nat @ S2 @ A4 )
         => ( ( ord_less_eq_nat @ R2 @ S2 )
           => ( ord_less_eq_nat @ ( F @ R2 ) @ ( F @ S2 ) ) ) ) ) ) ).

% mono_onD
thf(fact_926_mono__onI,axiom,
    ! [A4: set_o,F: $o > nat] :
      ( ! [R4: $o,S4: $o] :
          ( ( member_o @ R4 @ A4 )
         => ( ( member_o @ S4 @ A4 )
           => ( ( ord_less_eq_o @ R4 @ S4 )
             => ( ord_less_eq_nat @ ( F @ R4 ) @ ( F @ S4 ) ) ) ) )
     => ( monotone_on_o_nat @ A4 @ ord_less_eq_o @ ord_less_eq_nat @ F ) ) ).

% mono_onI
thf(fact_927_mono__onI,axiom,
    ! [A4: set_nat,F: nat > nat] :
      ( ! [R4: nat,S4: nat] :
          ( ( member_nat @ R4 @ A4 )
         => ( ( member_nat @ S4 @ A4 )
           => ( ( ord_less_eq_nat @ R4 @ S4 )
             => ( ord_less_eq_nat @ ( F @ R4 ) @ ( F @ S4 ) ) ) ) )
     => ( monotone_on_nat_nat @ A4 @ ord_less_eq_nat @ ord_less_eq_nat @ F ) ) ).

% mono_onI
thf(fact_928_monotoneI,axiom,
    ! [Orda: nat > nat > $o,Ordb: nat > nat > $o,F: nat > nat] :
      ( ! [X: nat,Y: nat] :
          ( ( Orda @ X @ Y )
         => ( Ordb @ ( F @ X ) @ ( F @ Y ) ) )
     => ( monotone_on_nat_nat @ top_top_set_nat @ Orda @ Ordb @ F ) ) ).

% monotoneI
thf(fact_929_monotoneD,axiom,
    ! [Orda: nat > nat > $o,Ordb: nat > nat > $o,F: nat > nat,X2: nat,Y3: nat] :
      ( ( monotone_on_nat_nat @ top_top_set_nat @ Orda @ Ordb @ F )
     => ( ( Orda @ X2 @ Y3 )
       => ( Ordb @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ) ).

% monotoneD
thf(fact_930_monotone__on__subset,axiom,
    ! [A4: set_nat,Orda: nat > nat > $o,Ordb: nat > nat > $o,F: nat > nat,B5: set_nat] :
      ( ( monotone_on_nat_nat @ A4 @ Orda @ Ordb @ F )
     => ( ( ord_less_eq_set_nat @ B5 @ A4 )
       => ( monotone_on_nat_nat @ B5 @ Orda @ Ordb @ F ) ) ) ).

% monotone_on_subset
thf(fact_931_monotone__onD,axiom,
    ! [A4: set_nat,Orda: nat > nat > $o,Ordb: nat > nat > $o,F: nat > nat,X2: nat,Y3: nat] :
      ( ( monotone_on_nat_nat @ A4 @ Orda @ Ordb @ F )
     => ( ( member_nat @ X2 @ A4 )
       => ( ( member_nat @ Y3 @ A4 )
         => ( ( Orda @ X2 @ Y3 )
           => ( Ordb @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ) ) ) ).

% monotone_onD
thf(fact_932_monotone__onI,axiom,
    ! [A4: set_nat,Orda: nat > nat > $o,Ordb: nat > nat > $o,F: nat > nat] :
      ( ! [X: nat,Y: nat] :
          ( ( member_nat @ X @ A4 )
         => ( ( member_nat @ Y @ A4 )
           => ( ( Orda @ X @ Y )
             => ( Ordb @ ( F @ X ) @ ( F @ Y ) ) ) ) )
     => ( monotone_on_nat_nat @ A4 @ Orda @ Ordb @ F ) ) ).

% monotone_onI
thf(fact_933_monotone__on__def,axiom,
    ( monotone_on_nat_nat
    = ( ^ [A6: set_nat,Orda2: nat > nat > $o,Ordb2: nat > nat > $o,F2: nat > nat] :
        ! [X3: nat] :
          ( ( member_nat @ X3 @ A6 )
         => ! [Y4: nat] :
              ( ( member_nat @ Y4 @ A6 )
             => ( ( Orda2 @ X3 @ Y4 )
               => ( Ordb2 @ ( F2 @ X3 ) @ ( F2 @ Y4 ) ) ) ) ) ) ) ).

% monotone_on_def
thf(fact_934_comp__fun__commute__on__def,axiom,
    ( finite4703585013658510744_o_nat
    = ( ^ [S5: set_o,F2: $o > nat > nat] :
        ! [X3: $o,Y4: $o] :
          ( ( member_o @ X3 @ S5 )
         => ( ( member_o @ Y4 @ S5 )
           => ( ( comp_nat_nat_nat @ ( F2 @ Y4 ) @ ( F2 @ X3 ) )
              = ( comp_nat_nat_nat @ ( F2 @ X3 ) @ ( F2 @ Y4 ) ) ) ) ) ) ) ).

% comp_fun_commute_on_def
thf(fact_935_comp__fun__commute__on_Ocomp__fun__commute__on,axiom,
    ! [S6: set_o,F: $o > nat > nat,X2: $o,Y3: $o] :
      ( ( finite4703585013658510744_o_nat @ S6 @ F )
     => ( ( member_o @ X2 @ S6 )
       => ( ( member_o @ Y3 @ S6 )
         => ( ( comp_nat_nat_nat @ ( F @ Y3 ) @ ( F @ X2 ) )
            = ( comp_nat_nat_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ) ) ) ).

% comp_fun_commute_on.comp_fun_commute_on
thf(fact_936_comp__fun__commute__on_Ocommute__left__comp,axiom,
    ! [S6: set_o,F: $o > nat > nat,X2: $o,Y3: $o,G: nat > nat] :
      ( ( finite4703585013658510744_o_nat @ S6 @ F )
     => ( ( member_o @ X2 @ S6 )
       => ( ( member_o @ Y3 @ S6 )
         => ( ( comp_nat_nat_nat @ ( F @ Y3 ) @ ( comp_nat_nat_nat @ ( F @ X2 ) @ G ) )
            = ( comp_nat_nat_nat @ ( F @ X2 ) @ ( comp_nat_nat_nat @ ( F @ Y3 ) @ G ) ) ) ) ) ) ).

% comp_fun_commute_on.commute_left_comp
thf(fact_937_comp__fun__commute__on_Ointro,axiom,
    ! [S6: set_o,F: $o > nat > nat] :
      ( ! [X: $o,Y: $o] :
          ( ( member_o @ X @ S6 )
         => ( ( member_o @ Y @ S6 )
           => ( ( comp_nat_nat_nat @ ( F @ Y ) @ ( F @ X ) )
              = ( comp_nat_nat_nat @ ( F @ X ) @ ( F @ Y ) ) ) ) )
     => ( finite4703585013658510744_o_nat @ S6 @ F ) ) ).

% comp_fun_commute_on.intro
thf(fact_938_mono__imp__mono__on,axiom,
    ! [F: nat > nat,A4: set_nat] :
      ( ( monotone_on_nat_nat @ top_top_set_nat @ ord_less_eq_nat @ ord_less_eq_nat @ F )
     => ( monotone_on_nat_nat @ A4 @ ord_less_eq_nat @ ord_less_eq_nat @ F ) ) ).

% mono_imp_mono_on
thf(fact_939_monoI,axiom,
    ! [F: nat > nat] :
      ( ! [X: nat,Y: nat] :
          ( ( ord_less_eq_nat @ X @ Y )
         => ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y ) ) )
     => ( monotone_on_nat_nat @ top_top_set_nat @ ord_less_eq_nat @ ord_less_eq_nat @ F ) ) ).

% monoI
thf(fact_940_monoE,axiom,
    ! [F: nat > nat,X2: nat,Y3: nat] :
      ( ( monotone_on_nat_nat @ top_top_set_nat @ ord_less_eq_nat @ ord_less_eq_nat @ F )
     => ( ( ord_less_eq_nat @ X2 @ Y3 )
       => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ) ).

% monoE
thf(fact_941_monoD,axiom,
    ! [F: nat > nat,X2: nat,Y3: nat] :
      ( ( monotone_on_nat_nat @ top_top_set_nat @ ord_less_eq_nat @ ord_less_eq_nat @ F )
     => ( ( ord_less_eq_nat @ X2 @ Y3 )
       => ( ord_less_eq_nat @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ) ).

% monoD
thf(fact_942_mono__on__subset,axiom,
    ! [A4: set_nat,F: nat > nat,B5: set_nat] :
      ( ( monotone_on_nat_nat @ A4 @ ord_less_eq_nat @ ord_less_eq_nat @ F )
     => ( ( ord_less_eq_set_nat @ B5 @ A4 )
       => ( monotone_on_nat_nat @ B5 @ ord_less_eq_nat @ ord_less_eq_nat @ F ) ) ) ).

% mono_on_subset
thf(fact_943_ord_Omono__on__subset,axiom,
    ! [A4: set_nat,Less_eq: nat > nat > $o,F: nat > nat,B5: set_nat] :
      ( ( monotone_on_nat_nat @ A4 @ Less_eq @ ord_less_eq_nat @ F )
     => ( ( ord_less_eq_set_nat @ B5 @ A4 )
       => ( monotone_on_nat_nat @ B5 @ Less_eq @ ord_less_eq_nat @ F ) ) ) ).

% ord.mono_on_subset
thf(fact_944_comp__fun__idem__on_Ocomp__fun__idem__on,axiom,
    ! [S6: set_o,F: $o > nat > nat,X2: $o] :
      ( ( finite2426395113773319005_o_nat @ S6 @ F )
     => ( ( member_o @ X2 @ S6 )
       => ( ( comp_nat_nat_nat @ ( F @ X2 ) @ ( F @ X2 ) )
          = ( F @ X2 ) ) ) ) ).

% comp_fun_idem_on.comp_fun_idem_on
thf(fact_945_monotone__on__o,axiom,
    ! [A4: set_nat,Orda: nat > nat > $o,Ordb: nat > nat > $o,F: nat > nat,B5: set_nat,Ordc: nat > nat > $o,G: nat > nat] :
      ( ( monotone_on_nat_nat @ A4 @ Orda @ Ordb @ F )
     => ( ( monotone_on_nat_nat @ B5 @ Ordc @ Orda @ G )
       => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ G @ B5 ) @ A4 )
         => ( monotone_on_nat_nat @ B5 @ Ordc @ Ordb @ ( comp_nat_nat_nat @ F @ G ) ) ) ) ) ).

% monotone_on_o
thf(fact_946_Grp__UNIV__id,axiom,
    ! [F: nat > nat] :
      ( ( F = id_nat )
     => ( ( relcompp_nat_nat_nat @ ( conversep_nat_nat @ ( bNF_Grp_nat_nat @ top_top_set_nat @ F ) ) @ ( bNF_Grp_nat_nat @ top_top_set_nat @ F ) )
        = ( bNF_Grp_nat_nat @ top_top_set_nat @ F ) ) ) ).

% Grp_UNIV_id
thf(fact_947_Quotient__alt__def5,axiom,
    ( quotient_nat_nat
    = ( ^ [R6: nat > nat > $o,Abs: nat > nat,Rep: nat > nat,T3: nat > nat > $o] :
          ( ( ord_le2646555220125990790_nat_o @ T3 @ ( bNF_Grp_nat_nat @ top_top_set_nat @ Abs ) )
          & ( ord_le2646555220125990790_nat_o @ ( bNF_Grp_nat_nat @ top_top_set_nat @ Rep ) @ ( conversep_nat_nat @ T3 ) )
          & ( R6
            = ( relcompp_nat_nat_nat @ T3 @ ( conversep_nat_nat @ T3 ) ) ) ) ) ) ).

% Quotient_alt_def5
thf(fact_948_fun_Oin__rel,axiom,
    ! [R: multihole_mctxt_a_b > list_b > $o,A: nat > multihole_mctxt_a_b,B: nat > list_b] :
      ( ( bNF_re7291955754265907832list_b
        @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
        @ R
        @ A
        @ B )
      = ( ? [Z4: nat > produc746580111399690912list_b] :
            ( ( member1851140327238222640list_b @ Z4
              @ ( collec6966152917764800626list_b
                @ ^ [X3: nat > produc746580111399690912list_b] : ( ord_le1169143132509141664list_b @ ( image_5135116557422050441list_b @ X3 @ top_top_set_nat ) @ ( collec5933784528073787915list_b @ ( produc7190274377712547635st_b_o @ R ) ) ) ) )
            & ( ( comp_P5220818572353508511_b_nat @ produc5881749095783049980list_b @ Z4 )
              = A )
            & ( ( comp_P2296052985374803096_b_nat @ produc6107117247873403966list_b @ Z4 )
              = B ) ) ) ) ).

% fun.in_rel
thf(fact_949_fun_Oin__rel,axiom,
    ! [R: list_b > multihole_mctxt_a_b > $o,A: nat > list_b,B: nat > multihole_mctxt_a_b] :
      ( ( bNF_re7910447939628189510xt_a_b
        @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
        @ R
        @ A
        @ B )
      = ( ? [Z4: nat > produc5647625992154082286xt_a_b] :
            ( ( member3828642050509981054xt_a_b @ Z4
              @ ( collec8943654641036559040xt_a_b
                @ ^ [X3: nat > produc5647625992154082286xt_a_b] : ( ord_le3146644855780900078xt_a_b @ ( image_812790401321666007xt_a_b @ X3 @ top_top_set_nat ) @ ( collec1611458371973403481xt_a_b @ ( produc1221931734719695589_a_b_o @ R ) ) ) ) )
            & ( ( comp_P2387776964271251914_b_nat @ produc6500241281145331658xt_a_b @ Z4 )
              = A )
            & ( ( comp_P2996417359073641937_b_nat @ produc6725609433235685644xt_a_b @ Z4 )
              = B ) ) ) ) ).

% fun.in_rel
thf(fact_950_Kleene__iter__gpfp,axiom,
    ! [F: set_nat > set_nat,P: set_nat,K: nat] :
      ( ( monoto1748750089227133045et_nat @ top_top_set_set_nat @ ord_less_eq_set_nat @ ord_less_eq_set_nat @ F )
     => ( ( ord_less_eq_set_nat @ P @ ( F @ P ) )
       => ( ord_less_eq_set_nat @ P @ ( compow8708494347934031032et_nat @ K @ F @ top_top_set_nat ) ) ) ) ).

% Kleene_iter_gpfp
thf(fact_951_surj__fn,axiom,
    ! [F: nat > nat,N: nat] :
      ( ( ( image_nat_nat @ F @ top_top_set_nat )
        = top_top_set_nat )
     => ( ( image_nat_nat @ ( compow_nat_nat @ N @ F ) @ top_top_set_nat )
        = top_top_set_nat ) ) ).

% surj_fn
thf(fact_952_rangeE,axiom,
    ! [B: $o,F: nat > $o] :
      ( ( member_o @ B @ ( image_nat_o @ F @ top_top_set_nat ) )
     => ~ ! [X: nat] :
            ( B
            = ( ~ ( F @ X ) ) ) ) ).

% rangeE
thf(fact_953_antimono__funpow,axiom,
    ! [Q3: set_nat > set_nat] :
      ( ( monoto1748750089227133045et_nat @ top_top_set_set_nat @ ord_less_eq_set_nat @ ord_less_eq_set_nat @ Q3 )
     => ( monoto6489329683466618047et_nat @ top_top_set_nat @ ord_less_eq_nat
        @ ^ [X3: set_nat,Y4: set_nat] : ( ord_less_eq_set_nat @ Y4 @ X3 )
        @ ^ [I2: nat] : ( compow8708494347934031032et_nat @ I2 @ Q3 @ top_top_set_nat ) ) ) ).

% antimono_funpow
thf(fact_954_UNIV__def,axiom,
    ( top_top_set_nat
    = ( collect_nat
      @ ^ [X3: nat] : $true ) ) ).

% UNIV_def
thf(fact_955_comp__funpow,axiom,
    ! [N: nat,F: nat > nat] :
      ( ( compow4371056112333882794at_nat @ N @ ( comp_nat_nat_nat @ F ) )
      = ( comp_nat_nat_nat @ ( compow_nat_nat @ N @ F ) ) ) ).

% comp_funpow
thf(fact_956_fun_Omap__ident,axiom,
    ! [T2: nat > nat] :
      ( ( comp_nat_nat_nat
        @ ^ [X3: nat] : X3
        @ T2 )
      = T2 ) ).

% fun.map_ident
thf(fact_957_snd__def,axiom,
    ( produc6107117247873403966list_b
    = ( produc479960551310721952list_b
      @ ^ [X12: multihole_mctxt_a_b,X23: list_b] : X23 ) ) ).

% snd_def
thf(fact_958_snd__def,axiom,
    ( produc6725609433235685644xt_a_b
    = ( produc6892829578239444825xt_a_b
      @ ^ [X12: list_b,X23: multihole_mctxt_a_b] : X23 ) ) ).

% snd_def
thf(fact_959_fst__def,axiom,
    ( produc5881749095783049980list_b
    = ( produc7853855808088480167xt_a_b
      @ ^ [X12: multihole_mctxt_a_b,X23: list_b] : X12 ) ) ).

% fst_def
thf(fact_960_fst__def,axiom,
    ( produc6500241281145331658xt_a_b
    = ( produc5071610215621926226list_b
      @ ^ [X12: list_b,X23: multihole_mctxt_a_b] : X12 ) ) ).

% fst_def
thf(fact_961_imageE,axiom,
    ! [B: $o,F: $o > $o,A4: set_o] :
      ( ( member_o @ B @ ( image_o_o @ F @ A4 ) )
     => ~ ! [X: $o] :
            ( ( B
              = ( F @ X ) )
           => ~ ( member_o @ X @ A4 ) ) ) ).

% imageE
thf(fact_962_Compr__image__eq,axiom,
    ! [F: $o > $o,A4: set_o,P2: $o > $o] :
      ( ( collect_o
        @ ^ [X3: $o] :
            ( ( member_o @ X3 @ ( image_o_o @ F @ A4 ) )
            & ( P2 @ X3 ) ) )
      = ( image_o_o @ F
        @ ( collect_o
          @ ^ [X3: $o] :
              ( ( member_o @ X3 @ A4 )
              & ( P2 @ ( F @ X3 ) ) ) ) ) ) ).

% Compr_image_eq
thf(fact_963_prop__restrict,axiom,
    ! [X2: $o,Z5: set_o,X5: set_o,P2: $o > $o] :
      ( ( member_o @ X2 @ Z5 )
     => ( ( ord_less_eq_set_o @ Z5
          @ ( collect_o
            @ ^ [X3: $o] :
                ( ( member_o @ X3 @ X5 )
                & ( P2 @ X3 ) ) ) )
       => ( P2 @ X2 ) ) ) ).

% prop_restrict
thf(fact_964_Collect__restrict,axiom,
    ! [X5: set_o,P2: $o > $o] :
      ( ord_less_eq_set_o
      @ ( collect_o
        @ ^ [X3: $o] :
            ( ( member_o @ X3 @ X5 )
            & ( P2 @ X3 ) ) )
      @ X5 ) ).

% Collect_restrict
thf(fact_965_Collect__subset,axiom,
    ! [A4: set_o,P2: $o > $o] :
      ( ord_less_eq_set_o
      @ ( collect_o
        @ ^ [X3: $o] :
            ( ( member_o @ X3 @ A4 )
            & ( P2 @ X3 ) ) )
      @ A4 ) ).

% Collect_subset
thf(fact_966_subset__CollectI,axiom,
    ! [B5: set_o,A4: set_o,Q3: $o > $o,P2: $o > $o] :
      ( ( ord_less_eq_set_o @ B5 @ A4 )
     => ( ! [X: $o] :
            ( ( member_o @ X @ B5 )
           => ( ( Q3 @ X )
             => ( P2 @ X ) ) )
       => ( ord_less_eq_set_o
          @ ( collect_o
            @ ^ [X3: $o] :
                ( ( member_o @ X3 @ B5 )
                & ( Q3 @ X3 ) ) )
          @ ( collect_o
            @ ^ [X3: $o] :
                ( ( member_o @ X3 @ A4 )
                & ( P2 @ X3 ) ) ) ) ) ) ).

% subset_CollectI
thf(fact_967_subset__Collect__iff,axiom,
    ! [B5: set_o,A4: set_o,P2: $o > $o] :
      ( ( ord_less_eq_set_o @ B5 @ A4 )
     => ( ( ord_less_eq_set_o @ B5
          @ ( collect_o
            @ ^ [X3: $o] :
                ( ( member_o @ X3 @ A4 )
                & ( P2 @ X3 ) ) ) )
        = ( ! [X3: $o] :
              ( ( member_o @ X3 @ B5 )
             => ( P2 @ X3 ) ) ) ) ) ).

% subset_Collect_iff
thf(fact_968_less__eq__set__def,axiom,
    ( ord_less_eq_set_o
    = ( ^ [A6: set_o,B6: set_o] :
          ( ord_less_eq_o_o
          @ ^ [X3: $o] : ( member_o @ X3 @ A6 )
          @ ^ [X3: $o] : ( member_o @ X3 @ B6 ) ) ) ) ).

% less_eq_set_def
thf(fact_969_pred__subset__eq,axiom,
    ! [R: set_o,S6: set_o] :
      ( ( ord_less_eq_o_o
        @ ^ [X3: $o] : ( member_o @ X3 @ R )
        @ ^ [X3: $o] : ( member_o @ X3 @ S6 ) )
      = ( ord_less_eq_set_o @ R @ S6 ) ) ).

% pred_subset_eq
thf(fact_970_type__copy__vimage2p__Grp__Rep,axiom,
    ! [Rep2: nat > nat,Abs2: nat > nat,F: nat > nat,P2: nat > $o,H: nat > nat] :
      ( ( type_d6250493948777748686at_nat @ Rep2 @ Abs2 @ top_top_set_nat )
     => ( ( bNF_vi6667456707345531737_nat_o @ F @ Rep2 @ ( bNF_Grp_nat_nat @ ( collect_nat @ P2 ) @ H ) )
        = ( bNF_Grp_nat_nat
          @ ( collect_nat
            @ ^ [X3: nat] : ( P2 @ ( F @ X3 ) ) )
          @ ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ Abs2 @ H ) @ F ) ) ) ) ).

% type_copy_vimage2p_Grp_Rep
thf(fact_971_type__copy__vimage2p__Grp__Abs,axiom,
    ! [Rep2: nat > nat,Abs2: nat > nat,G: nat > nat,P2: nat > $o,H: nat > nat] :
      ( ( type_d6250493948777748686at_nat @ Rep2 @ Abs2 @ top_top_set_nat )
     => ( ( bNF_vi6667456707345531737_nat_o @ G @ Abs2 @ ( bNF_Grp_nat_nat @ ( collect_nat @ P2 ) @ H ) )
        = ( bNF_Grp_nat_nat
          @ ( collect_nat
            @ ^ [X3: nat] : ( P2 @ ( G @ X3 ) ) )
          @ ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ Rep2 @ H ) @ G ) ) ) ) ).

% type_copy_vimage2p_Grp_Abs
thf(fact_972_antimonoD,axiom,
    ! [F: nat > nat,X2: nat,Y3: nat] :
      ( ( monotone_on_nat_nat @ top_top_set_nat @ ord_less_eq_nat
        @ ^ [X3: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X3 )
        @ F )
     => ( ( ord_less_eq_nat @ X2 @ Y3 )
       => ( ord_less_eq_nat @ ( F @ Y3 ) @ ( F @ X2 ) ) ) ) ).

% antimonoD
thf(fact_973_antimonoE,axiom,
    ! [F: nat > nat,X2: nat,Y3: nat] :
      ( ( monotone_on_nat_nat @ top_top_set_nat @ ord_less_eq_nat
        @ ^ [X3: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X3 )
        @ F )
     => ( ( ord_less_eq_nat @ X2 @ Y3 )
       => ( ord_less_eq_nat @ ( F @ Y3 ) @ ( F @ X2 ) ) ) ) ).

% antimonoE
thf(fact_974_antimonoI,axiom,
    ! [F: nat > nat] :
      ( ! [X: nat,Y: nat] :
          ( ( ord_less_eq_nat @ X @ Y )
         => ( ord_less_eq_nat @ ( F @ Y ) @ ( F @ X ) ) )
     => ( monotone_on_nat_nat @ top_top_set_nat @ ord_less_eq_nat
        @ ^ [X3: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X3 )
        @ F ) ) ).

% antimonoI
thf(fact_975_fst__diag__fst,axiom,
    ( ( comp_P5435891436279858456list_b @ produc2029583840371251459xt_a_b
      @ ( comp_M1604827171046050082list_b
        @ ^ [X3: multihole_mctxt_a_b] : ( produc67882520014434071xt_a_b @ X3 @ X3 )
        @ produc5881749095783049980list_b ) )
    = produc5881749095783049980list_b ) ).

% fst_diag_fst
thf(fact_976_fst__diag__fst,axiom,
    ( ( comp_P5990363157231710957xt_a_b @ produc7649009375908944835list_b
      @ ( comp_l8139176909817314217xt_a_b
        @ ^ [X3: list_b] : ( produc1564554178308465111list_b @ X3 @ X3 )
        @ produc6500241281145331658xt_a_b ) )
    = produc6500241281145331658xt_a_b ) ).

% fst_diag_fst
thf(fact_977_snd__diag__snd,axiom,
    ( ( comp_P1089317276477319583list_b @ produc3345134588468168965list_b
      @ ( comp_l3238131029062922843list_b
        @ ^ [X3: list_b] : ( produc1564554178308465111list_b @ X3 @ X3 )
        @ produc6107117247873403966list_b ) )
    = produc6107117247873403966list_b ) ).

% snd_diag_snd
thf(fact_978_snd__diag__snd,axiom,
    ( ( comp_P1113565280179474022xt_a_b @ produc4775144687201070661xt_a_b
      @ ( comp_M6505873051800441456xt_a_b
        @ ^ [X3: multihole_mctxt_a_b] : ( produc67882520014434071xt_a_b @ X3 @ X3 )
        @ produc6725609433235685644xt_a_b ) )
    = produc6725609433235685644xt_a_b ) ).

% snd_diag_snd
thf(fact_979_type__copy__map__comp0,axiom,
    ! [Rep2: nat > nat,Abs2: nat > nat,M: nat > nat,M1: nat > nat,M2: nat > nat,F: nat > nat,G: nat > nat] :
      ( ( type_d6250493948777748686at_nat @ Rep2 @ Abs2 @ top_top_set_nat )
     => ( ( M
          = ( comp_nat_nat_nat @ M1 @ M2 ) )
       => ( ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ F @ M ) @ G )
          = ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ F @ M1 ) @ Rep2 ) @ ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ Abs2 @ M2 ) @ G ) ) ) ) ) ).

% type_copy_map_comp0
thf(fact_980_type__copy__map__comp0__undo,axiom,
    ! [Rep2: nat > nat,Abs2: nat > nat,Rep3: nat > nat,Abs3: nat > nat,Rep4: nat > nat,Abs4: nat > nat,M: nat > nat,M1: nat > nat,M2: nat > nat] :
      ( ( type_d6250493948777748686at_nat @ Rep2 @ Abs2 @ top_top_set_nat )
     => ( ( type_d6250493948777748686at_nat @ Rep3 @ Abs3 @ top_top_set_nat )
       => ( ( type_d6250493948777748686at_nat @ Rep4 @ Abs4 @ top_top_set_nat )
         => ( ( ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ Abs3 @ M ) @ Rep4 )
              = ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ Abs3 @ M1 ) @ Rep2 ) @ ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ Abs2 @ M2 ) @ Rep4 ) ) )
           => ( ( comp_nat_nat_nat @ M1 @ M2 )
              = M ) ) ) ) ) ).

% type_copy_map_comp0_undo
thf(fact_981_fun_Orel__compp__Grp,axiom,
    ! [R: multihole_mctxt_a_b > list_b > $o] :
      ( ( bNF_re7291955754265907832list_b
        @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
        @ R )
      = ( relcom4037855281751361575list_b
        @ ( conver1419177986811044641xt_a_b
          @ ( bNF_Gr5474315259994270842xt_a_b
            @ ( collec6966152917764800626list_b
              @ ^ [X3: nat > produc746580111399690912list_b] : ( ord_le1169143132509141664list_b @ ( image_5135116557422050441list_b @ X3 @ top_top_set_nat ) @ ( collec5933784528073787915list_b @ ( produc7190274377712547635st_b_o @ R ) ) ) )
            @ ( comp_P5220818572353508511_b_nat @ produc5881749095783049980list_b ) ) )
        @ ( bNF_Gr6198635409967602163list_b
          @ ( collec6966152917764800626list_b
            @ ^ [X3: nat > produc746580111399690912list_b] : ( ord_le1169143132509141664list_b @ ( image_5135116557422050441list_b @ X3 @ top_top_set_nat ) @ ( collec5933784528073787915list_b @ ( produc7190274377712547635st_b_o @ R ) ) ) )
          @ ( comp_P2296052985374803096_b_nat @ produc6107117247873403966list_b ) ) ) ) ).

% fun.rel_compp_Grp
thf(fact_982_fun_Orel__compp__Grp,axiom,
    ! [R: list_b > multihole_mctxt_a_b > $o] :
      ( ( bNF_re7910447939628189510xt_a_b
        @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
        @ R )
      = ( relcom5838476793205533529xt_a_b
        @ ( conver8732461567001031628list_b
          @ ( bNF_Gr3902530357237781285list_b
            @ ( collec8943654641036559040xt_a_b
              @ ^ [X3: nat > produc5647625992154082286xt_a_b] : ( ord_le3146644855780900078xt_a_b @ ( image_812790401321666007xt_a_b @ X3 @ top_top_set_nat ) @ ( collec1611458371973403481xt_a_b @ ( produc1221931734719695589_a_b_o @ R ) ) ) )
            @ ( comp_P2387776964271251914_b_nat @ produc6500241281145331658xt_a_b ) ) )
        @ ( bNF_Gr5747004589486111148xt_a_b
          @ ( collec8943654641036559040xt_a_b
            @ ^ [X3: nat > produc5647625992154082286xt_a_b] : ( ord_le3146644855780900078xt_a_b @ ( image_812790401321666007xt_a_b @ X3 @ top_top_set_nat ) @ ( collec1611458371973403481xt_a_b @ ( produc1221931734719695589_a_b_o @ R ) ) ) )
          @ ( comp_P2996417359073641937_b_nat @ produc6725609433235685644xt_a_b ) ) ) ) ).

% fun.rel_compp_Grp
thf(fact_983_fst__snd__flip,axiom,
    ( produc6500241281145331658xt_a_b
    = ( comp_P8501011119256231206xt_a_b @ produc6107117247873403966list_b
      @ ( produc3271728269314753389list_b
        @ ^ [X3: list_b,Y4: multihole_mctxt_a_b] : ( produc8202881352235923728list_b @ Y4 @ X3 ) ) ) ) ).

% fst_snd_flip
thf(fact_984_fst__snd__flip,axiom,
    ( produc5881749095783049980list_b
    = ( comp_P2344685707722557151list_b @ produc6725609433235685644xt_a_b
      @ ( produc3662036813938090505xt_a_b
        @ ^ [X3: multihole_mctxt_a_b,Y4: list_b] : ( produc8821373537598205406xt_a_b @ Y4 @ X3 ) ) ) ) ).

% fst_snd_flip
thf(fact_985_snd__fst__flip,axiom,
    ( produc6107117247873403966list_b
    = ( comp_P3424029496760864550list_b @ produc6500241281145331658xt_a_b
      @ ( produc3662036813938090505xt_a_b
        @ ^ [X3: multihole_mctxt_a_b,Y4: list_b] : ( produc8821373537598205406xt_a_b @ Y4 @ X3 ) ) ) ) ).

% snd_fst_flip
thf(fact_986_snd__fst__flip,axiom,
    ( produc6725609433235685644xt_a_b
    = ( comp_P4743434984691673311xt_a_b @ produc5881749095783049980list_b
      @ ( produc3271728269314753389list_b
        @ ^ [X3: list_b,Y4: multihole_mctxt_a_b] : ( produc8202881352235923728list_b @ Y4 @ X3 ) ) ) ) ).

% snd_fst_flip
thf(fact_987_fst__diag__snd,axiom,
    ( ( comp_P1089317276477319583list_b @ produc7649009375908944835list_b
      @ ( comp_l3238131029062922843list_b
        @ ^ [X3: list_b] : ( produc1564554178308465111list_b @ X3 @ X3 )
        @ produc6107117247873403966list_b ) )
    = produc6107117247873403966list_b ) ).

% fst_diag_snd
thf(fact_988_fst__diag__snd,axiom,
    ( ( comp_P1113565280179474022xt_a_b @ produc2029583840371251459xt_a_b
      @ ( comp_M6505873051800441456xt_a_b
        @ ^ [X3: multihole_mctxt_a_b] : ( produc67882520014434071xt_a_b @ X3 @ X3 )
        @ produc6725609433235685644xt_a_b ) )
    = produc6725609433235685644xt_a_b ) ).

% fst_diag_snd
thf(fact_989_snd__diag__fst,axiom,
    ( ( comp_P5435891436279858456list_b @ produc4775144687201070661xt_a_b
      @ ( comp_M1604827171046050082list_b
        @ ^ [X3: multihole_mctxt_a_b] : ( produc67882520014434071xt_a_b @ X3 @ X3 )
        @ produc5881749095783049980list_b ) )
    = produc5881749095783049980list_b ) ).

% snd_diag_fst
thf(fact_990_snd__diag__fst,axiom,
    ( ( comp_P5990363157231710957xt_a_b @ produc3345134588468168965list_b
      @ ( comp_l8139176909817314217xt_a_b
        @ ^ [X3: list_b] : ( produc1564554178308465111list_b @ X3 @ X3 )
        @ produc6500241281145331658xt_a_b ) )
    = produc6500241281145331658xt_a_b ) ).

% snd_diag_fst
thf(fact_991_fun_Orel__Grp,axiom,
    ! [A4: set_nat,F: nat > nat] :
      ( ( bNF_re5653821019739307937at_nat
        @ ^ [Y2: nat,Z: nat] : ( Y2 = Z )
        @ ( bNF_Grp_nat_nat @ A4 @ F ) )
      = ( bNF_Gr3847987472475283150at_nat
        @ ( collect_nat_nat
          @ ^ [X3: nat > nat] : ( ord_less_eq_set_nat @ ( image_nat_nat @ X3 @ top_top_set_nat ) @ A4 ) )
        @ ( comp_nat_nat_nat @ F ) ) ) ).

% fun.rel_Grp
thf(fact_992_predicate2__transferD,axiom,
    ! [R12: multihole_mctxt_a_b > list_b > $o,R23: multihole_mctxt_a_b > list_b > $o,P2: multihole_mctxt_a_b > multihole_mctxt_a_b > $o,Q3: list_b > list_b > $o,A: produc746580111399690912list_b,A4: set_Pr1895186847599665920list_b,B: produc746580111399690912list_b,B5: set_Pr1895186847599665920list_b] :
      ( ( bNF_re7379649018698356609st_b_o @ R12
        @ ( bNF_re5925240994597992406_b_o_o @ R23
          @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
        @ P2
        @ Q3 )
     => ( ( member3572491845649744329list_b @ A @ A4 )
       => ( ( member3572491845649744329list_b @ B @ B5 )
         => ( ( ord_le1169143132509141664list_b @ A4 @ ( collec5933784528073787915list_b @ ( produc7190274377712547635st_b_o @ R12 ) ) )
           => ( ( ord_le1169143132509141664list_b @ B5 @ ( collec5933784528073787915list_b @ ( produc7190274377712547635st_b_o @ R23 ) ) )
             => ( ( P2 @ ( produc5881749095783049980list_b @ A ) @ ( produc5881749095783049980list_b @ B ) )
                = ( Q3 @ ( produc6107117247873403966list_b @ A ) @ ( produc6107117247873403966list_b @ B ) ) ) ) ) ) ) ) ).

% predicate2_transferD
thf(fact_993_predicate2__transferD,axiom,
    ! [R12: multihole_mctxt_a_b > list_b > $o,R23: list_b > multihole_mctxt_a_b > $o,P2: multihole_mctxt_a_b > list_b > $o,Q3: list_b > multihole_mctxt_a_b > $o,A: produc746580111399690912list_b,A4: set_Pr1895186847599665920list_b,B: produc5647625992154082286xt_a_b,B5: set_Pr3872688570871424334xt_a_b] :
      ( ( bNF_re5517021838360836993_a_b_o @ R12
        @ ( bNF_re8490395077849316260_b_o_o @ R23
          @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
        @ P2
        @ Q3 )
     => ( ( member3572491845649744329list_b @ A @ A4 )
       => ( ( member8473537726404135703xt_a_b @ B @ B5 )
         => ( ( ord_le1169143132509141664list_b @ A4 @ ( collec5933784528073787915list_b @ ( produc7190274377712547635st_b_o @ R12 ) ) )
           => ( ( ord_le3146644855780900078xt_a_b @ B5 @ ( collec1611458371973403481xt_a_b @ ( produc1221931734719695589_a_b_o @ R23 ) ) )
             => ( ( P2 @ ( produc5881749095783049980list_b @ A ) @ ( produc6500241281145331658xt_a_b @ B ) )
                = ( Q3 @ ( produc6107117247873403966list_b @ A ) @ ( produc6725609433235685644xt_a_b @ B ) ) ) ) ) ) ) ) ).

% predicate2_transferD
thf(fact_994_predicate2__transferD,axiom,
    ! [R12: list_b > multihole_mctxt_a_b > $o,R23: multihole_mctxt_a_b > list_b > $o,P2: list_b > multihole_mctxt_a_b > $o,Q3: multihole_mctxt_a_b > list_b > $o,A: produc5647625992154082286xt_a_b,A4: set_Pr3872688570871424334xt_a_b,B: produc746580111399690912list_b,B5: set_Pr1895186847599665920list_b] :
      ( ( bNF_re7400526925355327567st_b_o @ R12
        @ ( bNF_re5925240994597992406_b_o_o @ R23
          @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
        @ P2
        @ Q3 )
     => ( ( member8473537726404135703xt_a_b @ A @ A4 )
       => ( ( member3572491845649744329list_b @ B @ B5 )
         => ( ( ord_le3146644855780900078xt_a_b @ A4 @ ( collec1611458371973403481xt_a_b @ ( produc1221931734719695589_a_b_o @ R12 ) ) )
           => ( ( ord_le1169143132509141664list_b @ B5 @ ( collec5933784528073787915list_b @ ( produc7190274377712547635st_b_o @ R23 ) ) )
             => ( ( P2 @ ( produc6500241281145331658xt_a_b @ A ) @ ( produc5881749095783049980list_b @ B ) )
                = ( Q3 @ ( produc6725609433235685644xt_a_b @ A ) @ ( produc6107117247873403966list_b @ B ) ) ) ) ) ) ) ) ).

% predicate2_transferD
thf(fact_995_predicate2__transferD,axiom,
    ! [R12: list_b > multihole_mctxt_a_b > $o,R23: list_b > multihole_mctxt_a_b > $o,P2: list_b > list_b > $o,Q3: multihole_mctxt_a_b > multihole_mctxt_a_b > $o,A: produc5647625992154082286xt_a_b,A4: set_Pr3872688570871424334xt_a_b,B: produc5647625992154082286xt_a_b,B5: set_Pr3872688570871424334xt_a_b] :
      ( ( bNF_re5537899745017807951_a_b_o @ R12
        @ ( bNF_re8490395077849316260_b_o_o @ R23
          @ ^ [Y2: $o,Z: $o] : ( Y2 = Z ) )
        @ P2
        @ Q3 )
     => ( ( member8473537726404135703xt_a_b @ A @ A4 )
       => ( ( member8473537726404135703xt_a_b @ B @ B5 )
         => ( ( ord_le3146644855780900078xt_a_b @ A4 @ ( collec1611458371973403481xt_a_b @ ( produc1221931734719695589_a_b_o @ R12 ) ) )
           => ( ( ord_le3146644855780900078xt_a_b @ B5 @ ( collec1611458371973403481xt_a_b @ ( produc1221931734719695589_a_b_o @ R23 ) ) )
             => ( ( P2 @ ( produc6500241281145331658xt_a_b @ A ) @ ( produc6500241281145331658xt_a_b @ B ) )
                = ( Q3 @ ( produc6725609433235685644xt_a_b @ A ) @ ( produc6725609433235685644xt_a_b @ B ) ) ) ) ) ) ) ) ).

% predicate2_transferD
thf(fact_996_funpow__mono2,axiom,
    ! [F: nat > nat,I: nat,J: nat,X2: nat,Y3: nat] :
      ( ( monotone_on_nat_nat @ top_top_set_nat @ ord_less_eq_nat @ ord_less_eq_nat @ F )
     => ( ( ord_less_eq_nat @ I @ J )
       => ( ( ord_less_eq_nat @ X2 @ Y3 )
         => ( ( ord_less_eq_nat @ X2 @ ( F @ X2 ) )
           => ( ord_less_eq_nat @ ( compow_nat_nat @ I @ F @ X2 ) @ ( compow_nat_nat @ J @ F @ Y3 ) ) ) ) ) ) ).

% funpow_mono2
thf(fact_997_funpow__mono,axiom,
    ! [F: nat > nat,A4: nat,B5: nat,N: nat] :
      ( ( monotone_on_nat_nat @ top_top_set_nat @ ord_less_eq_nat @ ord_less_eq_nat @ F )
     => ( ( ord_less_eq_nat @ A4 @ B5 )
       => ( ord_less_eq_nat @ ( compow_nat_nat @ N @ F @ A4 ) @ ( compow_nat_nat @ N @ F @ B5 ) ) ) ) ).

% funpow_mono
thf(fact_998_Quotient__compose,axiom,
    ! [R12: nat > nat > $o,Abs1: nat > nat,Rep1: nat > nat,T1: nat > nat > $o,R23: nat > nat > $o,Abs22: nat > nat,Rep22: nat > nat,T22: nat > nat > $o] :
      ( ( quotient_nat_nat @ R12 @ Abs1 @ Rep1 @ T1 )
     => ( ( quotient_nat_nat @ R23 @ Abs22 @ Rep22 @ T22 )
       => ( quotient_nat_nat @ ( relcompp_nat_nat_nat @ T1 @ ( relcompp_nat_nat_nat @ R23 @ ( conversep_nat_nat @ T1 ) ) ) @ ( comp_nat_nat_nat @ Abs22 @ Abs1 ) @ ( comp_nat_nat_nat @ Rep1 @ Rep22 ) @ ( relcompp_nat_nat_nat @ T1 @ T22 ) ) ) ) ).

% Quotient_compose
thf(fact_999_type__copy__Rep__o__Abs,axiom,
    ! [Rep2: nat > nat,Abs2: nat > nat] :
      ( ( type_d6250493948777748686at_nat @ Rep2 @ Abs2 @ top_top_set_nat )
     => ( ( comp_nat_nat_nat @ Rep2 @ Abs2 )
        = id_nat ) ) ).

% type_copy_Rep_o_Abs
thf(fact_1000_type__copy__Abs__o__Rep,axiom,
    ! [Rep2: nat > nat,Abs2: nat > nat] :
      ( ( type_d6250493948777748686at_nat @ Rep2 @ Abs2 @ top_top_set_nat )
     => ( ( comp_nat_nat_nat @ Abs2 @ Rep2 )
        = id_nat ) ) ).

% type_copy_Abs_o_Rep
thf(fact_1001_type__copy__map__id0,axiom,
    ! [Rep2: nat > nat,Abs2: nat > nat,M: nat > nat] :
      ( ( type_d6250493948777748686at_nat @ Rep2 @ Abs2 @ top_top_set_nat )
     => ( ( M = id_nat )
       => ( ( comp_nat_nat_nat @ ( comp_nat_nat_nat @ Abs2 @ M ) @ Rep2 )
          = id_nat ) ) ) ).

% type_copy_map_id0
thf(fact_1002_funpow__increasing,axiom,
    ! [M3: nat,N: nat,F: set_nat > set_nat] :
      ( ( ord_less_eq_nat @ M3 @ N )
     => ( ( monoto1748750089227133045et_nat @ top_top_set_set_nat @ ord_less_eq_set_nat @ ord_less_eq_set_nat @ F )
       => ( ord_less_eq_set_nat @ ( compow8708494347934031032et_nat @ N @ F @ top_top_set_nat ) @ ( compow8708494347934031032et_nat @ M3 @ F @ top_top_set_nat ) ) ) ) ).

% funpow_increasing
thf(fact_1003_restrict__def,axiom,
    ( abstract_restrict_o
    = ( ^ [R5: set_Product_prod_o_o,S5: set_o] :
          ( collec3167064739498627218od_o_o
          @ ( produc6197397395684419436_o_o_o
            @ ^ [X3: $o,Y4: $o] :
                ( ( member_o @ X3 @ S5 )
                & ( member_o @ Y4 @ S5 )
                & ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X3 @ Y4 ) @ R5 ) ) ) ) ) ) ).

% restrict_def
thf(fact_1004_Least__mono,axiom,
    ! [F: $o > $o,S6: set_o] :
      ( ( monotone_on_o_o @ top_top_set_o @ ord_less_eq_o @ ord_less_eq_o @ F )
     => ( ? [X6: $o] :
            ( ( member_o @ X6 @ S6 )
            & ! [Xa: $o] :
                ( ( member_o @ Xa @ S6 )
               => ( ord_less_eq_o @ X6 @ Xa ) ) )
       => ( ( ord_Least_o
            @ ^ [Y4: $o] : ( member_o @ Y4 @ ( image_o_o @ F @ S6 ) ) )
          = ( F
            @ ( ord_Least_o
              @ ^ [X3: $o] : ( member_o @ X3 @ S6 ) ) ) ) ) ) ).

% Least_mono
thf(fact_1005_Least__mono,axiom,
    ! [F: $o > nat,S6: set_o] :
      ( ( monotone_on_o_nat @ top_top_set_o @ ord_less_eq_o @ ord_less_eq_nat @ F )
     => ( ? [X6: $o] :
            ( ( member_o @ X6 @ S6 )
            & ! [Xa: $o] :
                ( ( member_o @ Xa @ S6 )
               => ( ord_less_eq_o @ X6 @ Xa ) ) )
       => ( ( ord_Least_nat
            @ ^ [Y4: nat] : ( member_nat @ Y4 @ ( image_o_nat @ F @ S6 ) ) )
          = ( F
            @ ( ord_Least_o
              @ ^ [X3: $o] : ( member_o @ X3 @ S6 ) ) ) ) ) ) ).

% Least_mono
thf(fact_1006_Least__mono,axiom,
    ! [F: nat > $o,S6: set_nat] :
      ( ( monotone_on_nat_o @ top_top_set_nat @ ord_less_eq_nat @ ord_less_eq_o @ F )
     => ( ? [X6: nat] :
            ( ( member_nat @ X6 @ S6 )
            & ! [Xa: nat] :
                ( ( member_nat @ Xa @ S6 )
               => ( ord_less_eq_nat @ X6 @ Xa ) ) )
       => ( ( ord_Least_o
            @ ^ [Y4: $o] : ( member_o @ Y4 @ ( image_nat_o @ F @ S6 ) ) )
          = ( F
            @ ( ord_Least_nat
              @ ^ [X3: nat] : ( member_nat @ X3 @ S6 ) ) ) ) ) ) ).

% Least_mono
thf(fact_1007_Least__mono,axiom,
    ! [F: nat > nat,S6: set_nat] :
      ( ( monotone_on_nat_nat @ top_top_set_nat @ ord_less_eq_nat @ ord_less_eq_nat @ F )
     => ( ? [X6: nat] :
            ( ( member_nat @ X6 @ S6 )
            & ! [Xa: nat] :
                ( ( member_nat @ Xa @ S6 )
               => ( ord_less_eq_nat @ X6 @ Xa ) ) )
       => ( ( ord_Least_nat
            @ ^ [Y4: nat] : ( member_nat @ Y4 @ ( image_nat_nat @ F @ S6 ) ) )
          = ( F
            @ ( ord_Least_nat
              @ ^ [X3: nat] : ( member_nat @ X3 @ S6 ) ) ) ) ) ) ).

% Least_mono
thf(fact_1008_Nat_Oex__has__greatest__nat,axiom,
    ! [P2: nat > $o,K: nat,B: nat] :
      ( ( P2 @ K )
     => ( ! [Y: nat] :
            ( ( P2 @ Y )
           => ( ord_less_eq_nat @ Y @ B ) )
       => ? [X: nat] :
            ( ( P2 @ X )
            & ! [Y6: nat] :
                ( ( P2 @ Y6 )
               => ( ord_less_eq_nat @ Y6 @ X ) ) ) ) ) ).

% Nat.ex_has_greatest_nat
thf(fact_1009_GreatestI__ex__nat,axiom,
    ! [P2: nat > $o,B: nat] :
      ( ? [X_1: nat] : ( P2 @ X_1 )
     => ( ! [Y: nat] :
            ( ( P2 @ Y )
           => ( ord_less_eq_nat @ Y @ B ) )
       => ( P2 @ ( order_Greatest_nat @ P2 ) ) ) ) ).

% GreatestI_ex_nat
thf(fact_1010_Greatest__le__nat,axiom,
    ! [P2: nat > $o,K: nat,B: nat] :
      ( ( P2 @ K )
     => ( ! [Y: nat] :
            ( ( P2 @ Y )
           => ( ord_less_eq_nat @ Y @ B ) )
       => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P2 ) ) ) ) ).

% Greatest_le_nat
thf(fact_1011_nat__le__linear,axiom,
    ! [M3: nat,N: nat] :
      ( ( ord_less_eq_nat @ M3 @ N )
      | ( ord_less_eq_nat @ N @ M3 ) ) ).

% nat_le_linear
thf(fact_1012_GreatestI__nat,axiom,
    ! [P2: nat > $o,K: nat,B: nat] :
      ( ( P2 @ K )
     => ( ! [Y: nat] :
            ( ( P2 @ Y )
           => ( ord_less_eq_nat @ Y @ B ) )
       => ( P2 @ ( order_Greatest_nat @ P2 ) ) ) ) ).

% GreatestI_nat
thf(fact_1013_le__antisym,axiom,
    ! [M3: nat,N: nat] :
      ( ( ord_less_eq_nat @ M3 @ N )
     => ( ( ord_less_eq_nat @ N @ M3 )
       => ( M3 = N ) ) ) ).

% le_antisym
thf(fact_1014_eq__imp__le,axiom,
    ! [M3: nat,N: nat] :
      ( ( M3 = N )
     => ( ord_less_eq_nat @ M3 @ N ) ) ).

% eq_imp_le
thf(fact_1015_le__trans,axiom,
    ! [I: nat,J: nat,K: nat] :
      ( ( ord_less_eq_nat @ I @ J )
     => ( ( ord_less_eq_nat @ J @ K )
       => ( ord_less_eq_nat @ I @ K ) ) ) ).

% le_trans
thf(fact_1016_le__refl,axiom,
    ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).

% le_refl
thf(fact_1017_LeastI2__wellorder__ex,axiom,
    ! [P2: nat > $o,Q3: nat > $o] :
      ( ? [X_1: nat] : ( P2 @ X_1 )
     => ( ! [A3: nat] :
            ( ( P2 @ A3 )
           => ( ! [B7: nat] :
                  ( ( P2 @ B7 )
                 => ( ord_less_eq_nat @ A3 @ B7 ) )
             => ( Q3 @ A3 ) ) )
       => ( Q3 @ ( ord_Least_nat @ P2 ) ) ) ) ).

% LeastI2_wellorder_ex
thf(fact_1018_LeastI2__wellorder,axiom,
    ! [P2: nat > $o,A: nat,Q3: nat > $o] :
      ( ( P2 @ A )
     => ( ! [A3: nat] :
            ( ( P2 @ A3 )
           => ( ! [B7: nat] :
                  ( ( P2 @ B7 )
                 => ( ord_less_eq_nat @ A3 @ B7 ) )
             => ( Q3 @ A3 ) ) )
       => ( Q3 @ ( ord_Least_nat @ P2 ) ) ) ) ).

% LeastI2_wellorder
thf(fact_1019_Least__equality,axiom,
    ! [P2: nat > $o,X2: nat] :
      ( ( P2 @ X2 )
     => ( ! [Y: nat] :
            ( ( P2 @ Y )
           => ( ord_less_eq_nat @ X2 @ Y ) )
       => ( ( ord_Least_nat @ P2 )
          = X2 ) ) ) ).

% Least_equality
thf(fact_1020_LeastI2__order,axiom,
    ! [P2: nat > $o,X2: nat,Q3: nat > $o] :
      ( ( P2 @ X2 )
     => ( ! [Y: nat] :
            ( ( P2 @ Y )
           => ( ord_less_eq_nat @ X2 @ Y ) )
       => ( ! [X: nat] :
              ( ( P2 @ X )
             => ( ! [Y6: nat] :
                    ( ( P2 @ Y6 )
                   => ( ord_less_eq_nat @ X @ Y6 ) )
               => ( Q3 @ X ) ) )
         => ( Q3 @ ( ord_Least_nat @ P2 ) ) ) ) ) ).

% LeastI2_order
thf(fact_1021_Least1__le,axiom,
    ! [P2: nat > $o,Z2: nat] :
      ( ? [X6: nat] :
          ( ( P2 @ X6 )
          & ! [Y: nat] :
              ( ( P2 @ Y )
             => ( ord_less_eq_nat @ X6 @ Y ) )
          & ! [Y: nat] :
              ( ( ( P2 @ Y )
                & ! [Ya2: nat] :
                    ( ( P2 @ Ya2 )
                   => ( ord_less_eq_nat @ Y @ Ya2 ) ) )
             => ( Y = X6 ) ) )
     => ( ( P2 @ Z2 )
       => ( ord_less_eq_nat @ ( ord_Least_nat @ P2 ) @ Z2 ) ) ) ).

% Least1_le
thf(fact_1022_Least1I,axiom,
    ! [P2: nat > $o] :
      ( ? [X6: nat] :
          ( ( P2 @ X6 )
          & ! [Y: nat] :
              ( ( P2 @ Y )
             => ( ord_less_eq_nat @ X6 @ Y ) )
          & ! [Y: nat] :
              ( ( ( P2 @ Y )
                & ! [Ya2: nat] :
                    ( ( P2 @ Ya2 )
                   => ( ord_less_eq_nat @ Y @ Ya2 ) ) )
             => ( Y = X6 ) ) )
     => ( P2 @ ( ord_Least_nat @ P2 ) ) ) ).

% Least1I
thf(fact_1023_Least__le,axiom,
    ! [P2: nat > $o,K: nat] :
      ( ( P2 @ K )
     => ( ord_less_eq_nat @ ( ord_Least_nat @ P2 ) @ K ) ) ).

% Least_le
thf(fact_1024_mono__funpow,axiom,
    ! [Q3: nat > nat] :
      ( ( monotone_on_nat_nat @ top_top_set_nat @ ord_less_eq_nat @ ord_less_eq_nat @ Q3 )
     => ( monotone_on_nat_nat @ top_top_set_nat @ ord_less_eq_nat @ ord_less_eq_nat
        @ ^ [I2: nat] : ( compow_nat_nat @ I2 @ Q3 @ bot_bot_nat ) ) ) ).

% mono_funpow
thf(fact_1025_abort__Bleast__def,axiom,
    ( abort_Bleast_o
    = ( ^ [S5: set_o,P3: $o > $o] :
          ( ord_Least_o
          @ ^ [X3: $o] :
              ( ( member_o @ X3 @ S5 )
              & ( P3 @ X3 ) ) ) ) ) ).

% abort_Bleast_def
thf(fact_1026_Bleast__def,axiom,
    ( bleast_o
    = ( ^ [S5: set_o,P3: $o > $o] :
          ( ord_Least_o
          @ ^ [X3: $o] :
              ( ( member_o @ X3 @ S5 )
              & ( P3 @ X3 ) ) ) ) ) ).

% Bleast_def
thf(fact_1027_Collect__const,axiom,
    ! [P2: $o] :
      ( ( P2
       => ( ( collect_nat
            @ ^ [S: nat] : P2 )
          = top_top_set_nat ) )
      & ( ~ P2
       => ( ( collect_nat
            @ ^ [S: nat] : P2 )
          = bot_bot_set_nat ) ) ) ).

% Collect_const
thf(fact_1028_empty__not__UNIV,axiom,
    bot_bot_set_nat != top_top_set_nat ).

% empty_not_UNIV
thf(fact_1029_subset__emptyI,axiom,
    ! [A4: set_o] :
      ( ! [X: $o] :
          ~ ( member_o @ X @ A4 )
     => ( ord_less_eq_set_o @ A4 @ bot_bot_set_o ) ) ).

% subset_emptyI
thf(fact_1030_bot_Oextremum__uniqueI,axiom,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ A @ bot_bot_nat )
     => ( A = bot_bot_nat ) ) ).

% bot.extremum_uniqueI
thf(fact_1031_bot_Oextremum__unique,axiom,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ A @ bot_bot_nat )
      = ( A = bot_bot_nat ) ) ).

% bot.extremum_unique
thf(fact_1032_bot_Oextremum,axiom,
    ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).

% bot.extremum
thf(fact_1033_monotone__on__empty,axiom,
    ! [Orda: nat > nat > $o,Ordb: nat > nat > $o,F: nat > nat] : ( monotone_on_nat_nat @ bot_bot_set_nat @ Orda @ Ordb @ F ) ).

% monotone_on_empty
thf(fact_1034_Kleene__iter__lpfp,axiom,
    ! [F: nat > nat,P: nat,K: nat] :
      ( ( monotone_on_nat_nat @ top_top_set_nat @ ord_less_eq_nat @ ord_less_eq_nat @ F )
     => ( ( ord_less_eq_nat @ ( F @ P ) @ P )
       => ( ord_less_eq_nat @ ( compow_nat_nat @ K @ F @ bot_bot_nat ) @ P ) ) ) ).

% Kleene_iter_lpfp
thf(fact_1035_funpow__decreasing,axiom,
    ! [M3: nat,N: nat,F: nat > nat] :
      ( ( ord_less_eq_nat @ M3 @ N )
     => ( ( monotone_on_nat_nat @ top_top_set_nat @ ord_less_eq_nat @ ord_less_eq_nat @ F )
       => ( ord_less_eq_nat @ ( compow_nat_nat @ M3 @ F @ bot_bot_nat ) @ ( compow_nat_nat @ N @ F @ bot_bot_nat ) ) ) ) ).

% funpow_decreasing
thf(fact_1036_antimono__iff__le__Suc,axiom,
    ! [F: nat > nat] :
      ( ( monotone_on_nat_nat @ top_top_set_nat @ ord_less_eq_nat
        @ ^ [X3: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X3 )
        @ F )
      = ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) ) ) ) ).

% antimono_iff_le_Suc
thf(fact_1037_all__not__in__conv,axiom,
    ! [A4: set_o] :
      ( ( ! [X3: $o] :
            ~ ( member_o @ X3 @ A4 ) )
      = ( A4 = bot_bot_set_o ) ) ).

% all_not_in_conv
thf(fact_1038_empty__iff,axiom,
    ! [C2: $o] :
      ~ ( member_o @ C2 @ bot_bot_set_o ) ).

% empty_iff
thf(fact_1039_nat_Oinject,axiom,
    ! [X22: nat,Y22: nat] :
      ( ( ( suc @ X22 )
        = ( suc @ Y22 ) )
      = ( X22 = Y22 ) ) ).

% nat.inject
thf(fact_1040_old_Onat_Oinject,axiom,
    ! [Nat: nat,Nat2: nat] :
      ( ( ( suc @ Nat )
        = ( suc @ Nat2 ) )
      = ( Nat = Nat2 ) ) ).

% old.nat.inject
thf(fact_1041_Suc__le__mono,axiom,
    ! [N: nat,M3: nat] :
      ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M3 ) )
      = ( ord_less_eq_nat @ N @ M3 ) ) ).

% Suc_le_mono
thf(fact_1042_ex__in__conv,axiom,
    ! [A4: set_o] :
      ( ( ? [X3: $o] : ( member_o @ X3 @ A4 ) )
      = ( A4 != bot_bot_set_o ) ) ).

% ex_in_conv
thf(fact_1043_equals0I,axiom,
    ! [A4: set_o] :
      ( ! [Y: $o] :
          ~ ( member_o @ Y @ A4 )
     => ( A4 = bot_bot_set_o ) ) ).

% equals0I
thf(fact_1044_equals0D,axiom,
    ! [A4: set_o,A: $o] :
      ( ( A4 = bot_bot_set_o )
     => ~ ( member_o @ A @ A4 ) ) ).

% equals0D
thf(fact_1045_emptyE,axiom,
    ! [A: $o] :
      ~ ( member_o @ A @ bot_bot_set_o ) ).

% emptyE
thf(fact_1046_Suc__inject,axiom,
    ! [X2: nat,Y3: nat] :
      ( ( ( suc @ X2 )
        = ( suc @ Y3 ) )
     => ( X2 = Y3 ) ) ).

% Suc_inject
thf(fact_1047_n__not__Suc__n,axiom,
    ! [N: nat] :
      ( N
     != ( suc @ N ) ) ).

% n_not_Suc_n
thf(fact_1048_card_Ocomp__fun__commute__on,axiom,
    ( ( comp_nat_nat_nat @ suc @ suc )
    = ( comp_nat_nat_nat @ suc @ suc ) ) ).

% card.comp_fun_commute_on
thf(fact_1049_Suc__leD,axiom,
    ! [M3: nat,N: nat] :
      ( ( ord_less_eq_nat @ ( suc @ M3 ) @ N )
     => ( ord_less_eq_nat @ M3 @ N ) ) ).

% Suc_leD
thf(fact_1050_le__SucE,axiom,
    ! [M3: nat,N: nat] :
      ( ( ord_less_eq_nat @ M3 @ ( suc @ N ) )
     => ( ~ ( ord_less_eq_nat @ M3 @ N )
       => ( M3
          = ( suc @ N ) ) ) ) ).

% le_SucE
thf(fact_1051_le__SucI,axiom,
    ! [M3: nat,N: nat] :
      ( ( ord_less_eq_nat @ M3 @ N )
     => ( ord_less_eq_nat @ M3 @ ( suc @ N ) ) ) ).

% le_SucI
thf(fact_1052_Suc__le__D,axiom,
    ! [N: nat,M4: nat] :
      ( ( ord_less_eq_nat @ ( suc @ N ) @ M4 )
     => ? [M5: nat] :
          ( M4
          = ( suc @ M5 ) ) ) ).

% Suc_le_D
thf(fact_1053_le__Suc__eq,axiom,
    ! [M3: nat,N: nat] :
      ( ( ord_less_eq_nat @ M3 @ ( suc @ N ) )
      = ( ( ord_less_eq_nat @ M3 @ N )
        | ( M3
          = ( suc @ N ) ) ) ) ).

% le_Suc_eq
thf(fact_1054_Suc__n__not__le__n,axiom,
    ! [N: nat] :
      ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).

% Suc_n_not_le_n
thf(fact_1055_not__less__eq__eq,axiom,
    ! [M3: nat,N: nat] :
      ( ( ~ ( ord_less_eq_nat @ M3 @ N ) )
      = ( ord_less_eq_nat @ ( suc @ N ) @ M3 ) ) ).

% not_less_eq_eq
thf(fact_1056_full__nat__induct,axiom,
    ! [P2: nat > $o,N: nat] :
      ( ! [N4: nat] :
          ( ! [M6: nat] :
              ( ( ord_less_eq_nat @ ( suc @ M6 ) @ N4 )
             => ( P2 @ M6 ) )
         => ( P2 @ N4 ) )
     => ( P2 @ N ) ) ).

% full_nat_induct
thf(fact_1057_nat__induct__at__least,axiom,
    ! [M3: nat,N: nat,P2: nat > $o] :
      ( ( ord_less_eq_nat @ M3 @ N )
     => ( ( P2 @ M3 )
       => ( ! [N4: nat] :
              ( ( ord_less_eq_nat @ M3 @ N4 )
             => ( ( P2 @ N4 )
               => ( P2 @ ( suc @ N4 ) ) ) )
         => ( P2 @ N ) ) ) ) ).

% nat_induct_at_least
thf(fact_1058_transitive__stepwise__le,axiom,
    ! [M3: nat,N: nat,R: nat > nat > $o] :
      ( ( ord_less_eq_nat @ M3 @ N )
     => ( ! [X: nat] : ( R @ X @ X )
       => ( ! [X: nat,Y: nat,Z3: nat] :
              ( ( R @ X @ Y )
             => ( ( R @ Y @ Z3 )
               => ( R @ X @ Z3 ) ) )
         => ( ! [N4: nat] : ( R @ N4 @ ( suc @ N4 ) )
           => ( R @ M3 @ N ) ) ) ) ) ).

% transitive_stepwise_le
thf(fact_1059_fun_Omap__cong__pred,axiom,
    ! [X2: nat > nat,Ya: nat > nat,F: nat > nat,G: nat > nat] :
      ( ( X2 = Ya )
     => ( ( basic_843401206580270149at_nat
          @ ^ [Uu: nat] : $true
          @ ^ [Z4: nat] :
              ( ( F @ Z4 )
              = ( G @ Z4 ) )
          @ Ya )
       => ( ( comp_nat_nat_nat @ F @ X2 )
          = ( comp_nat_nat_nat @ G @ Ya ) ) ) ) ).

% fun.map_cong_pred
thf(fact_1060_lift__Suc__antimono__le,axiom,
    ! [F: nat > nat,N: nat,N5: nat] :
      ( ! [N4: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N4 ) ) @ ( F @ N4 ) )
     => ( ( ord_less_eq_nat @ N @ N5 )
       => ( ord_less_eq_nat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).

% lift_Suc_antimono_le
thf(fact_1061_lift__Suc__mono__le,axiom,
    ! [F: nat > nat,N: nat,N5: nat] :
      ( ! [N4: nat] : ( ord_less_eq_nat @ ( F @ N4 ) @ ( F @ ( suc @ N4 ) ) )
     => ( ( ord_less_eq_nat @ N @ N5 )
       => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).

% lift_Suc_mono_le
thf(fact_1062_funpow__Suc__right,axiom,
    ! [N: nat,F: nat > nat] :
      ( ( compow_nat_nat @ ( suc @ N ) @ F )
      = ( comp_nat_nat_nat @ ( compow_nat_nat @ N @ F ) @ F ) ) ).

% funpow_Suc_right
thf(fact_1063_funpow_Osimps_I2_J,axiom,
    ! [N: nat,F: nat > nat] :
      ( ( compow_nat_nat @ ( suc @ N ) @ F )
      = ( comp_nat_nat_nat @ F @ ( compow_nat_nat @ N @ F ) ) ) ).

% funpow.simps(2)
thf(fact_1064_mono__Suc,axiom,
    monotone_on_nat_nat @ top_top_set_nat @ ord_less_eq_nat @ ord_less_eq_nat @ suc ).

% mono_Suc
thf(fact_1065_fun_Opred__cong,axiom,
    ! [X2: nat > $o,Ya: nat > $o,P2: $o > $o,Pa: $o > $o] :
      ( ( X2 = Ya )
     => ( ! [Z3: $o] :
            ( ( member_o @ Z3 @ ( image_nat_o @ Ya @ top_top_set_nat ) )
           => ( ( P2 @ Z3 )
              = ( Pa @ Z3 ) ) )
       => ( ( basic_pred_fun_nat_o
            @ ^ [Uu: nat] : $true
            @ P2
            @ X2 )
          = ( basic_pred_fun_nat_o
            @ ^ [Uu: nat] : $true
            @ Pa
            @ Ya ) ) ) ) ).

% fun.pred_cong
thf(fact_1066_fun_Opred__mono__strong,axiom,
    ! [P2: $o > $o,X2: nat > $o,Pa: $o > $o] :
      ( ( basic_pred_fun_nat_o
        @ ^ [Uu: nat] : $true
        @ P2
        @ X2 )
     => ( ! [Z3: $o] :
            ( ( member_o @ Z3 @ ( image_nat_o @ X2 @ top_top_set_nat ) )
           => ( ( P2 @ Z3 )
             => ( Pa @ Z3 ) ) )
       => ( basic_pred_fun_nat_o
          @ ^ [Uu: nat] : $true
          @ Pa
          @ X2 ) ) ) ).

% fun.pred_mono_strong
thf(fact_1067_fun_Opred__map,axiom,
    ! [Q3: nat > $o,F: nat > nat,X2: nat > nat] :
      ( ( basic_843401206580270149at_nat
        @ ^ [Uu: nat] : $true
        @ Q3
        @ ( comp_nat_nat_nat @ F @ X2 ) )
      = ( basic_843401206580270149at_nat
        @ ^ [Uu: nat] : $true
        @ ( comp_nat_o_nat @ Q3 @ F )
        @ X2 ) ) ).

% fun.pred_map
thf(fact_1068_mono__iff__le__Suc,axiom,
    ! [F: nat > nat] :
      ( ( monotone_on_nat_nat @ top_top_set_nat @ ord_less_eq_nat @ ord_less_eq_nat @ F )
      = ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) ) ) ) ).

% mono_iff_le_Suc
thf(fact_1069_gfp__Kleene__iter,axiom,
    ! [F: set_nat > set_nat,K: nat] :
      ( ( monoto1748750089227133045et_nat @ top_top_set_set_nat @ ord_less_eq_set_nat @ ord_less_eq_set_nat @ F )
     => ( ( ( compow8708494347934031032et_nat @ ( suc @ K ) @ F @ top_top_set_nat )
          = ( compow8708494347934031032et_nat @ K @ F @ top_top_set_nat ) )
       => ( ( comple1596078789208929544et_nat @ F )
          = ( compow8708494347934031032et_nat @ K @ F @ top_top_set_nat ) ) ) ) ).

% gfp_Kleene_iter
thf(fact_1070_le__rel__bool__arg__iff,axiom,
    ( ord_less_eq_o_nat
    = ( ^ [X7: $o > nat,Y7: $o > nat] :
          ( ( ord_less_eq_nat @ ( X7 @ $false ) @ ( Y7 @ $false ) )
          & ( ord_less_eq_nat @ ( X7 @ $true ) @ ( Y7 @ $true ) ) ) ) ) ).

% le_rel_bool_arg_iff
thf(fact_1071_weak__coinduct,axiom,
    ! [A: $o,X5: set_o,F: set_o > set_o] :
      ( ( member_o @ A @ X5 )
     => ( ( ord_less_eq_set_o @ X5 @ ( F @ X5 ) )
       => ( member_o @ A @ ( comple5578320350976157814_set_o @ F ) ) ) ) ).

% weak_coinduct
thf(fact_1072_weak__coinduct__image,axiom,
    ! [A: $o,X5: set_o,G: $o > $o,F: set_o > set_o] :
      ( ( member_o @ A @ X5 )
     => ( ( ord_less_eq_set_o @ ( image_o_o @ G @ X5 ) @ ( F @ ( image_o_o @ G @ X5 ) ) )
       => ( member_o @ ( G @ A ) @ ( comple5578320350976157814_set_o @ F ) ) ) ) ).

% weak_coinduct_image
thf(fact_1073_K__record__comp,axiom,
    ! [C2: nat,F: nat > nat] :
      ( ( comp_nat_nat_nat
        @ ^ [X3: nat] : C2
        @ F )
      = ( ^ [X3: nat] : C2 ) ) ).

% K_record_comp
thf(fact_1074_iterates__fixp,axiom,
    ! [F: $o > $o] :
      ( ( monotone_on_o_o @ top_top_set_o @ ord_less_eq_o @ ord_less_eq_o @ F )
     => ( member_o @ ( comple2713996627985145509fixp_o @ F ) @ ( comple449408542198671847ates_o @ F ) ) ) ).

% iterates_fixp
thf(fact_1075_iterates__le__f,axiom,
    ! [X2: $o,F: $o > $o] :
      ( ( member_o @ X2 @ ( comple449408542198671847ates_o @ F ) )
     => ( ( monotone_on_o_o @ top_top_set_o @ ord_less_eq_o @ ord_less_eq_o @ F )
       => ( ord_less_eq_o @ X2 @ ( F @ X2 ) ) ) ) ).

% iterates_le_f
thf(fact_1076_mem__Sigma__iff,axiom,
    ! [A: $o,B: $o,A4: set_o,B5: $o > set_o] :
      ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ ( product_Sigma_o_o @ A4 @ B5 ) )
      = ( ( member_o @ A @ A4 )
        & ( member_o @ B @ ( B5 @ A ) ) ) ) ).

% mem_Sigma_iff
thf(fact_1077_SigmaI,axiom,
    ! [A: $o,A4: set_o,B: $o,B5: $o > set_o] :
      ( ( member_o @ A @ A4 )
     => ( ( member_o @ B @ ( B5 @ A ) )
       => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ ( product_Sigma_o_o @ A4 @ B5 ) ) ) ) ).

% SigmaI
thf(fact_1078_UNIV__Times__UNIV,axiom,
    ( ( produc457027306803732586at_nat @ top_top_set_nat
      @ ^ [Uu: nat] : top_top_set_nat )
    = top_to4669805908274784177at_nat ) ).

% UNIV_Times_UNIV
thf(fact_1079_fst__image__times,axiom,
    ! [B5: set_list_b,A4: set_Mu3903433398966807788xt_a_b] :
      ( ( ( B5 = bot_bot_set_list_b )
       => ( ( image_7211724023120395249xt_a_b @ produc5881749095783049980list_b
            @ ( produc1462769601762008001list_b @ A4
              @ ^ [Uu: multihole_mctxt_a_b] : B5 ) )
          = bot_bo3530618752887112024xt_a_b ) )
      & ( ( B5 != bot_bot_set_list_b )
       => ( ( image_7211724023120395249xt_a_b @ produc5881749095783049980list_b
            @ ( produc1462769601762008001list_b @ A4
              @ ^ [Uu: multihole_mctxt_a_b] : B5 ) )
          = A4 ) ) ) ).

% fst_image_times
thf(fact_1080_fst__image__times,axiom,
    ! [B5: set_Mu3903433398966807788xt_a_b,A4: set_list_b] :
      ( ( ( B5 = bot_bo3530618752887112024xt_a_b )
       => ( ( image_5978867512307746588list_b @ produc6500241281145331658xt_a_b
            @ ( produc2081261787124289679xt_a_b @ A4
              @ ^ [Uu: list_b] : B5 ) )
          = bot_bot_set_list_b ) )
      & ( ( B5 != bot_bo3530618752887112024xt_a_b )
       => ( ( image_5978867512307746588list_b @ produc6500241281145331658xt_a_b
            @ ( produc2081261787124289679xt_a_b @ A4
              @ ^ [Uu: list_b] : B5 ) )
          = A4 ) ) ) ).

% fst_image_times
thf(fact_1081_snd__image__times,axiom,
    ! [A4: set_Mu3903433398966807788xt_a_b,B5: set_list_b] :
      ( ( ( A4 = bot_bo3530618752887112024xt_a_b )
       => ( ( image_9124975640858730986list_b @ produc6107117247873403966list_b
            @ ( produc1462769601762008001list_b @ A4
              @ ^ [Uu: multihole_mctxt_a_b] : B5 ) )
          = bot_bot_set_list_b ) )
      & ( ( A4 != bot_bo3530618752887112024xt_a_b )
       => ( ( image_9124975640858730986list_b @ produc6107117247873403966list_b
            @ ( produc1462769601762008001list_b @ A4
              @ ^ [Uu: multihole_mctxt_a_b] : B5 ) )
          = B5 ) ) ) ).

% snd_image_times
thf(fact_1082_snd__image__times,axiom,
    ! [A4: set_list_b,B5: set_Mu3903433398966807788xt_a_b] :
      ( ( ( A4 = bot_bot_set_list_b )
       => ( ( image_4915618970390574371xt_a_b @ produc6725609433235685644xt_a_b
            @ ( produc2081261787124289679xt_a_b @ A4
              @ ^ [Uu: list_b] : B5 ) )
          = bot_bo3530618752887112024xt_a_b ) )
      & ( ( A4 != bot_bot_set_list_b )
       => ( ( image_4915618970390574371xt_a_b @ produc6725609433235685644xt_a_b
            @ ( produc2081261787124289679xt_a_b @ A4
              @ ^ [Uu: list_b] : B5 ) )
          = B5 ) ) ) ).

% snd_image_times
thf(fact_1083_SigmaE,axiom,
    ! [C2: product_prod_o_o,A4: set_o,B5: $o > set_o] :
      ( ( member7466972457876170832od_o_o @ C2 @ ( product_Sigma_o_o @ A4 @ B5 ) )
     => ~ ! [X: $o] :
            ( ( member_o @ X @ A4 )
           => ! [Y: $o] :
                ( ( member_o @ Y @ ( B5 @ X ) )
               => ( C2
                 != ( product_Pair_o_o @ X @ Y ) ) ) ) ) ).

% SigmaE
thf(fact_1084_SigmaE2,axiom,
    ! [A: $o,B: $o,A4: set_o,B5: $o > set_o] :
      ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ ( product_Sigma_o_o @ A4 @ B5 ) )
     => ~ ( ( member_o @ A @ A4 )
         => ~ ( member_o @ B @ ( B5 @ A ) ) ) ) ).

% SigmaE2
thf(fact_1085_mem__Times__iff,axiom,
    ! [X2: product_prod_o_o,A4: set_o,B5: set_o] :
      ( ( member7466972457876170832od_o_o @ X2
        @ ( product_Sigma_o_o @ A4
          @ ^ [Uu: $o] : B5 ) )
      = ( ( member_o @ ( product_fst_o_o @ X2 ) @ A4 )
        & ( member_o @ ( product_snd_o_o @ X2 ) @ B5 ) ) ) ).

% mem_Times_iff
thf(fact_1086_mem__Times__iff,axiom,
    ! [X2: produc746580111399690912list_b,A4: set_Mu3903433398966807788xt_a_b,B5: set_list_b] :
      ( ( member3572491845649744329list_b @ X2
        @ ( produc1462769601762008001list_b @ A4
          @ ^ [Uu: multihole_mctxt_a_b] : B5 ) )
      = ( ( member4915921492409311157xt_a_b @ ( produc5881749095783049980list_b @ X2 ) @ A4 )
        & ( member_list_b @ ( produc6107117247873403966list_b @ X2 ) @ B5 ) ) ) ).

% mem_Times_iff
thf(fact_1087_mem__Times__iff,axiom,
    ! [X2: produc5647625992154082286xt_a_b,A4: set_list_b,B5: set_Mu3903433398966807788xt_a_b] :
      ( ( member8473537726404135703xt_a_b @ X2
        @ ( produc2081261787124289679xt_a_b @ A4
          @ ^ [Uu: list_b] : B5 ) )
      = ( ( member_list_b @ ( produc6500241281145331658xt_a_b @ X2 ) @ A4 )
        & ( member4915921492409311157xt_a_b @ ( produc6725609433235685644xt_a_b @ X2 ) @ B5 ) ) ) ).

% mem_Times_iff
thf(fact_1088_product__swap,axiom,
    ! [A4: set_Mu3903433398966807788xt_a_b,B5: set_list_b] :
      ( ( image_3492653723807366483xt_a_b @ produc4023874437082322608list_b
        @ ( produc1462769601762008001list_b @ A4
          @ ^ [Uu: multihole_mctxt_a_b] : B5 ) )
      = ( produc2081261787124289679xt_a_b @ B5
        @ ^ [Uu: list_b] : A4 ) ) ).

% product_swap
thf(fact_1089_product__swap,axiom,
    ! [A4: set_list_b,B5: set_Mu3903433398966807788xt_a_b] :
      ( ( image_1828724688096913975list_b @ produc4642366622444604286xt_a_b
        @ ( produc2081261787124289679xt_a_b @ A4
          @ ^ [Uu: list_b] : B5 ) )
      = ( produc1462769601762008001list_b @ B5
        @ ^ [Uu: multihole_mctxt_a_b] : A4 ) ) ).

% product_swap
thf(fact_1090_fst__image__Sigma,axiom,
    ! [A4: set_Mu3903433398966807788xt_a_b,B5: multihole_mctxt_a_b > set_list_b] :
      ( ( image_7211724023120395249xt_a_b @ produc5881749095783049980list_b @ ( produc1462769601762008001list_b @ A4 @ B5 ) )
      = ( collec7587487095821320951xt_a_b
        @ ^ [X3: multihole_mctxt_a_b] :
            ( ( member4915921492409311157xt_a_b @ X3 @ A4 )
            & ( ( B5 @ X3 )
             != bot_bot_set_list_b ) ) ) ) ).

% fst_image_Sigma
thf(fact_1091_fst__image__Sigma,axiom,
    ! [A4: set_list_b,B5: list_b > set_Mu3903433398966807788xt_a_b] :
      ( ( image_5978867512307746588list_b @ produc6500241281145331658xt_a_b @ ( produc2081261787124289679xt_a_b @ A4 @ B5 ) )
      = ( collect_list_b
        @ ^ [X3: list_b] :
            ( ( member_list_b @ X3 @ A4 )
            & ( ( B5 @ X3 )
             != bot_bo3530618752887112024xt_a_b ) ) ) ) ).

% fst_image_Sigma
thf(fact_1092_subset__fst__snd,axiom,
    ! [A4: set_Pr1895186847599665920list_b] :
      ( ord_le1169143132509141664list_b @ A4
      @ ( produc1462769601762008001list_b @ ( image_7211724023120395249xt_a_b @ produc5881749095783049980list_b @ A4 )
        @ ^ [Uu: multihole_mctxt_a_b] : ( image_9124975640858730986list_b @ produc6107117247873403966list_b @ A4 ) ) ) ).

% subset_fst_snd
thf(fact_1093_subset__fst__snd,axiom,
    ! [A4: set_Pr3872688570871424334xt_a_b] :
      ( ord_le3146644855780900078xt_a_b @ A4
      @ ( produc2081261787124289679xt_a_b @ ( image_5978867512307746588list_b @ produc6500241281145331658xt_a_b @ A4 )
        @ ^ [Uu: list_b] : ( image_4915618970390574371xt_a_b @ produc6725609433235685644xt_a_b @ A4 ) ) ) ).

% subset_fst_snd
thf(fact_1094_snd__image__Sigma,axiom,
    ! [A4: set_Mu3903433398966807788xt_a_b,B5: multihole_mctxt_a_b > set_list_b] :
      ( ( image_9124975640858730986list_b @ produc6107117247873403966list_b @ ( produc1462769601762008001list_b @ A4 @ B5 ) )
      = ( comple6999952072667322706list_b @ ( image_6332848988479007454list_b @ B5 @ A4 ) ) ) ).

% snd_image_Sigma
thf(fact_1095_snd__image__Sigma,axiom,
    ! [A4: set_list_b,B5: list_b > set_Mu3903433398966807788xt_a_b] :
      ( ( image_4915618970390574371xt_a_b @ produc6725609433235685644xt_a_b @ ( produc2081261787124289679xt_a_b @ A4 @ B5 ) )
      = ( comple2548993463255921113xt_a_b @ ( image_5892124603837329964xt_a_b @ B5 @ A4 ) ) ) ).

% snd_image_Sigma
thf(fact_1096_UnionI,axiom,
    ! [X5: set_o,C3: set_set_o,A4: $o] :
      ( ( member_set_o @ X5 @ C3 )
     => ( ( member_o @ A4 @ X5 )
       => ( member_o @ A4 @ ( comple90263536869209701_set_o @ C3 ) ) ) ) ).

% UnionI
thf(fact_1097_Union__iff,axiom,
    ! [A4: $o,C3: set_set_o] :
      ( ( member_o @ A4 @ ( comple90263536869209701_set_o @ C3 ) )
      = ( ? [X3: set_o] :
            ( ( member_set_o @ X3 @ C3 )
            & ( member_o @ A4 @ X3 ) ) ) ) ).

% Union_iff
thf(fact_1098_Sup__bot__conv_I1_J,axiom,
    ! [A4: set_o] :
      ( ( ( complete_Sup_Sup_o @ A4 )
        = bot_bot_o )
      = ( ! [X3: $o] :
            ( ( member_o @ X3 @ A4 )
           => ( X3 = bot_bot_o ) ) ) ) ).

% Sup_bot_conv(1)
thf(fact_1099_Sup__bot__conv_I2_J,axiom,
    ! [A4: set_o] :
      ( ( bot_bot_o
        = ( complete_Sup_Sup_o @ A4 ) )
      = ( ! [X3: $o] :
            ( ( member_o @ X3 @ A4 )
           => ( X3 = bot_bot_o ) ) ) ) ).

% Sup_bot_conv(2)
thf(fact_1100_SUP__identity__eq,axiom,
    ! [A4: set_o] :
      ( ( complete_Sup_Sup_o
        @ ( image_o_o
          @ ^ [X3: $o] : X3
          @ A4 ) )
      = ( complete_Sup_Sup_o @ A4 ) ) ).

% SUP_identity_eq
thf(fact_1101_UN__I,axiom,
    ! [A: $o,A4: set_o,B: $o,B5: $o > set_o] :
      ( ( member_o @ A @ A4 )
     => ( ( member_o @ B @ ( B5 @ A ) )
       => ( member_o @ B @ ( comple90263536869209701_set_o @ ( image_o_set_o @ B5 @ A4 ) ) ) ) ) ).

% UN_I
thf(fact_1102_Sup__empty,axiom,
    ( ( complete_Sup_Sup_o @ bot_bot_set_o )
    = bot_bot_o ) ).

% Sup_empty
thf(fact_1103_Sup__UNIV,axiom,
    ( ( comple7399068483239264473et_nat @ top_top_set_set_nat )
    = top_top_set_nat ) ).

% Sup_UNIV
thf(fact_1104_Sup__UNIV,axiom,
    ( ( complete_Sup_Sup_o @ top_top_set_o )
    = top_top_o ) ).

% Sup_UNIV
thf(fact_1105_SUP__id__eq,axiom,
    ! [A4: set_o] :
      ( ( complete_Sup_Sup_o @ ( image_o_o @ id_o @ A4 ) )
      = ( complete_Sup_Sup_o @ A4 ) ) ).

% SUP_id_eq
thf(fact_1106_SUP__eq,axiom,
    ! [A4: set_o,B5: set_o,F: $o > $o,G: $o > $o] :
      ( ! [I3: $o] :
          ( ( member_o @ I3 @ A4 )
         => ? [X6: $o] :
              ( ( member_o @ X6 @ B5 )
              & ( ord_less_eq_o @ ( F @ I3 ) @ ( G @ X6 ) ) ) )
     => ( ! [J2: $o] :
            ( ( member_o @ J2 @ B5 )
           => ? [X6: $o] :
                ( ( member_o @ X6 @ A4 )
                & ( ord_less_eq_o @ ( G @ J2 ) @ ( F @ X6 ) ) ) )
       => ( ( complete_Sup_Sup_o @ ( image_o_o @ F @ A4 ) )
          = ( complete_Sup_Sup_o @ ( image_o_o @ G @ B5 ) ) ) ) ) ).

% SUP_eq
thf(fact_1107_less__eq__Sup,axiom,
    ! [A4: set_o,U: $o] :
      ( ! [V3: $o] :
          ( ( member_o @ V3 @ A4 )
         => ( ord_less_eq_o @ U @ V3 ) )
     => ( ( A4 != bot_bot_set_o )
       => ( ord_less_eq_o @ U @ ( complete_Sup_Sup_o @ A4 ) ) ) ) ).

% less_eq_Sup
thf(fact_1108_Sup__subset__mono,axiom,
    ! [A4: set_o,B5: set_o] :
      ( ( ord_less_eq_set_o @ A4 @ B5 )
     => ( ord_less_eq_o @ ( complete_Sup_Sup_o @ A4 ) @ ( complete_Sup_Sup_o @ B5 ) ) ) ).

% Sup_subset_mono
thf(fact_1109_Sup__upper2,axiom,
    ! [U: $o,A4: set_o,V: $o] :
      ( ( member_o @ U @ A4 )
     => ( ( ord_less_eq_o @ V @ U )
       => ( ord_less_eq_o @ V @ ( complete_Sup_Sup_o @ A4 ) ) ) ) ).

% Sup_upper2
thf(fact_1110_Sup__le__iff,axiom,
    ! [A4: set_o,B: $o] :
      ( ( ord_less_eq_o @ ( complete_Sup_Sup_o @ A4 ) @ B )
      = ( ! [X3: $o] :
            ( ( member_o @ X3 @ A4 )
           => ( ord_less_eq_o @ X3 @ B ) ) ) ) ).

% Sup_le_iff
thf(fact_1111_Sup__upper,axiom,
    ! [X2: $o,A4: set_o] :
      ( ( member_o @ X2 @ A4 )
     => ( ord_less_eq_o @ X2 @ ( complete_Sup_Sup_o @ A4 ) ) ) ).

% Sup_upper
thf(fact_1112_Sup__least,axiom,
    ! [A4: set_o,Z2: $o] :
      ( ! [X: $o] :
          ( ( member_o @ X @ A4 )
         => ( ord_less_eq_o @ X @ Z2 ) )
     => ( ord_less_eq_o @ ( complete_Sup_Sup_o @ A4 ) @ Z2 ) ) ).

% Sup_least
thf(fact_1113_Sup__mono,axiom,
    ! [A4: set_o,B5: set_o] :
      ( ! [A3: $o] :
          ( ( member_o @ A3 @ A4 )
         => ? [X6: $o] :
              ( ( member_o @ X6 @ B5 )
              & ( ord_less_eq_o @ A3 @ X6 ) ) )
     => ( ord_less_eq_o @ ( complete_Sup_Sup_o @ A4 ) @ ( complete_Sup_Sup_o @ B5 ) ) ) ).

% Sup_mono
thf(fact_1114_Sup__eqI,axiom,
    ! [A4: set_o,X2: $o] :
      ( ! [Y: $o] :
          ( ( member_o @ Y @ A4 )
         => ( ord_less_eq_o @ Y @ X2 ) )
     => ( ! [Y: $o] :
            ( ! [Z6: $o] :
                ( ( member_o @ Z6 @ A4 )
               => ( ord_less_eq_o @ Z6 @ Y ) )
           => ( ord_less_eq_o @ X2 @ Y ) )
       => ( ( complete_Sup_Sup_o @ A4 )
          = X2 ) ) ) ).

% Sup_eqI
thf(fact_1115_SUP__eq__const,axiom,
    ! [I4: set_o,F: $o > $o,X2: $o] :
      ( ( I4 != bot_bot_set_o )
     => ( ! [I3: $o] :
            ( ( member_o @ I3 @ I4 )
           => ( ( F @ I3 )
              = X2 ) )
       => ( ( complete_Sup_Sup_o @ ( image_o_o @ F @ I4 ) )
          = X2 ) ) ) ).

% SUP_eq_const
thf(fact_1116_SUP__image,axiom,
    ! [G: nat > nat,F: nat > nat,A4: set_nat] :
      ( ( complete_Sup_Sup_nat @ ( image_nat_nat @ G @ ( image_nat_nat @ F @ A4 ) ) )
      = ( complete_Sup_Sup_nat @ ( image_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ A4 ) ) ) ).

% SUP_image
thf(fact_1117_UN__E,axiom,
    ! [B: $o,B5: $o > set_o,A4: set_o] :
      ( ( member_o @ B @ ( comple90263536869209701_set_o @ ( image_o_set_o @ B5 @ A4 ) ) )
     => ~ ! [X: $o] :
            ( ( member_o @ X @ A4 )
           => ~ ( member_o @ B @ ( B5 @ X ) ) ) ) ).

% UN_E
thf(fact_1118_SUP__cong,axiom,
    ! [A4: set_o,B5: set_o,C3: $o > $o,D: $o > $o] :
      ( ( A4 = B5 )
     => ( ! [X: $o] :
            ( ( member_o @ X @ B5 )
           => ( ( C3 @ X )
              = ( D @ X ) ) )
       => ( ( complete_Sup_Sup_o @ ( image_o_o @ C3 @ A4 ) )
          = ( complete_Sup_Sup_o @ ( image_o_o @ D @ B5 ) ) ) ) ) ).

% SUP_cong
thf(fact_1119_UnionE,axiom,
    ! [A4: $o,C3: set_set_o] :
      ( ( member_o @ A4 @ ( comple90263536869209701_set_o @ C3 ) )
     => ~ ! [X8: set_o] :
            ( ( member_o @ A4 @ X8 )
           => ~ ( member_set_o @ X8 @ C3 ) ) ) ).

% UnionE
thf(fact_1120_ccpo__Sup__upper,axiom,
    ! [A4: set_o,X2: $o] :
      ( ( comple520228465662580424hain_o @ ord_less_eq_o @ A4 )
     => ( ( member_o @ X2 @ A4 )
       => ( ord_less_eq_o @ X2 @ ( complete_Sup_Sup_o @ A4 ) ) ) ) ).

% ccpo_Sup_upper
thf(fact_1121_ccpo__Sup__least,axiom,
    ! [A4: set_o,Z2: $o] :
      ( ( comple520228465662580424hain_o @ ord_less_eq_o @ A4 )
     => ( ! [X: $o] :
            ( ( member_o @ X @ A4 )
           => ( ord_less_eq_o @ X @ Z2 ) )
       => ( ord_less_eq_o @ ( complete_Sup_Sup_o @ A4 ) @ Z2 ) ) ) ).

% ccpo_Sup_least
thf(fact_1122_Union__UNIV,axiom,
    ( ( comple7399068483239264473et_nat @ top_top_set_set_nat )
    = top_top_set_nat ) ).

% Union_UNIV
thf(fact_1123_SUP__upper2,axiom,
    ! [I: $o,A4: set_o,U: $o,F: $o > $o] :
      ( ( member_o @ I @ A4 )
     => ( ( ord_less_eq_o @ U @ ( F @ I ) )
       => ( ord_less_eq_o @ U @ ( complete_Sup_Sup_o @ ( image_o_o @ F @ A4 ) ) ) ) ) ).

% SUP_upper2
thf(fact_1124_SUP__upper,axiom,
    ! [I: $o,A4: set_o,F: $o > $o] :
      ( ( member_o @ I @ A4 )
     => ( ord_less_eq_o @ ( F @ I ) @ ( complete_Sup_Sup_o @ ( image_o_o @ F @ A4 ) ) ) ) ).

% SUP_upper
thf(fact_1125_SUP__least,axiom,
    ! [A4: set_o,F: $o > $o,U: $o] :
      ( ! [I3: $o] :
          ( ( member_o @ I3 @ A4 )
         => ( ord_less_eq_o @ ( F @ I3 ) @ U ) )
     => ( ord_less_eq_o @ ( complete_Sup_Sup_o @ ( image_o_o @ F @ A4 ) ) @ U ) ) ).

% SUP_least
thf(fact_1126_SUP__eqI,axiom,
    ! [A4: set_o,F: $o > $o,X2: $o] :
      ( ! [I3: $o] :
          ( ( member_o @ I3 @ A4 )
         => ( ord_less_eq_o @ ( F @ I3 ) @ X2 ) )
     => ( ! [Y: $o] :
            ( ! [I5: $o] :
                ( ( member_o @ I5 @ A4 )
               => ( ord_less_eq_o @ ( F @ I5 ) @ Y ) )
           => ( ord_less_eq_o @ X2 @ Y ) )
       => ( ( complete_Sup_Sup_o @ ( image_o_o @ F @ A4 ) )
          = X2 ) ) ) ).

% SUP_eqI
thf(fact_1127_gfp__def,axiom,
    ( comple1228283932920895894_gfp_o
    = ( ^ [F2: $o > $o] :
          ( complete_Sup_Sup_o
          @ ( collect_o
            @ ^ [U2: $o] : ( ord_less_eq_o @ U2 @ ( F2 @ U2 ) ) ) ) ) ) ).

% gfp_def
thf(fact_1128_SUP__eq__iff,axiom,
    ! [I4: set_o,C2: $o,F: $o > $o] :
      ( ( I4 != bot_bot_set_o )
     => ( ! [I3: $o] :
            ( ( member_o @ I3 @ I4 )
           => ( ord_less_eq_o @ C2 @ ( F @ I3 ) ) )
       => ( ( ( complete_Sup_Sup_o @ ( image_o_o @ F @ I4 ) )
            = C2 )
          = ( ! [X3: $o] :
                ( ( member_o @ X3 @ I4 )
               => ( ( F @ X3 )
                  = C2 ) ) ) ) ) ) ).

% SUP_eq_iff
thf(fact_1129_SUP__subset__mono,axiom,
    ! [A4: set_o,B5: set_o,F: $o > $o,G: $o > $o] :
      ( ( ord_less_eq_set_o @ A4 @ B5 )
     => ( ! [X: $o] :
            ( ( member_o @ X @ A4 )
           => ( ord_less_eq_o @ ( F @ X ) @ ( G @ X ) ) )
       => ( ord_less_eq_o @ ( complete_Sup_Sup_o @ ( image_o_o @ F @ A4 ) ) @ ( complete_Sup_Sup_o @ ( image_o_o @ G @ B5 ) ) ) ) ) ).

% SUP_subset_mono
thf(fact_1130_iterates_OSup,axiom,
    ! [M: set_o,F: $o > $o] :
      ( ( comple520228465662580424hain_o @ ord_less_eq_o @ M )
     => ( ! [X: $o] :
            ( ( member_o @ X @ M )
           => ( member_o @ X @ ( comple449408542198671847ates_o @ F ) ) )
       => ( member_o @ ( complete_Sup_Sup_o @ M ) @ ( comple449408542198671847ates_o @ F ) ) ) ) ).

% iterates.Sup
thf(fact_1131_iterates_Ocases,axiom,
    ! [A: $o,F: $o > $o] :
      ( ( member_o @ A @ ( comple449408542198671847ates_o @ F ) )
     => ( ! [X: $o] :
            ( ( A
              = ( F @ X ) )
           => ~ ( member_o @ X @ ( comple449408542198671847ates_o @ F ) ) )
       => ~ ! [M7: set_o] :
              ( ( A
                = ( complete_Sup_Sup_o @ M7 ) )
             => ( ( comple520228465662580424hain_o @ ord_less_eq_o @ M7 )
               => ~ ! [X6: $o] :
                      ( ( member_o @ X6 @ M7 )
                     => ( member_o @ X6 @ ( comple449408542198671847ates_o @ F ) ) ) ) ) ) ) ).

% iterates.cases
thf(fact_1132_iterates_Osimps,axiom,
    ! [A: $o,F: $o > $o] :
      ( ( member_o @ A @ ( comple449408542198671847ates_o @ F ) )
      = ( ? [X3: $o] :
            ( ( A
              = ( F @ X3 ) )
            & ( member_o @ X3 @ ( comple449408542198671847ates_o @ F ) ) )
        | ? [M8: set_o] :
            ( ( A
              = ( complete_Sup_Sup_o @ M8 ) )
            & ( comple520228465662580424hain_o @ ord_less_eq_o @ M8 )
            & ! [X3: $o] :
                ( ( member_o @ X3 @ M8 )
               => ( member_o @ X3 @ ( comple449408542198671847ates_o @ F ) ) ) ) ) ) ).

% iterates.simps
thf(fact_1133_lfp__ordinal__induct,axiom,
    ! [F: $o > $o,P2: $o > $o] :
      ( ( monotone_on_o_o @ top_top_set_o @ ord_less_eq_o @ ord_less_eq_o @ F )
     => ( ! [S7: $o] :
            ( ( P2 @ S7 )
           => ( ( ord_less_eq_o @ S7 @ ( comple5737750096767067345_lfp_o @ F ) )
             => ( P2 @ ( F @ S7 ) ) ) )
       => ( ! [M7: set_o] :
              ( ! [X6: $o] :
                  ( ( member_o @ X6 @ M7 )
                 => ( P2 @ X6 ) )
             => ( P2 @ ( complete_Sup_Sup_o @ M7 ) ) )
         => ( P2 @ ( comple5737750096767067345_lfp_o @ F ) ) ) ) ) ).

% lfp_ordinal_induct
thf(fact_1134_mono__Sup,axiom,
    ! [F: $o > $o,A4: set_o] :
      ( ( monotone_on_o_o @ top_top_set_o @ ord_less_eq_o @ ord_less_eq_o @ F )
     => ( ord_less_eq_o @ ( complete_Sup_Sup_o @ ( image_o_o @ F @ A4 ) ) @ ( F @ ( complete_Sup_Sup_o @ A4 ) ) ) ) ).

% mono_Sup
thf(fact_1135_cSUP__least,axiom,
    ! [A4: set_o,F: $o > nat,M: nat] :
      ( ( A4 != bot_bot_set_o )
     => ( ! [X: $o] :
            ( ( member_o @ X @ A4 )
           => ( ord_less_eq_nat @ ( F @ X ) @ M ) )
       => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_o_nat @ F @ A4 ) ) @ M ) ) ) ).

% cSUP_least
thf(fact_1136_cSUP__least,axiom,
    ! [A4: set_o,F: $o > $o,M: $o] :
      ( ( A4 != bot_bot_set_o )
     => ( ! [X: $o] :
            ( ( member_o @ X @ A4 )
           => ( ord_less_eq_o @ ( F @ X ) @ M ) )
       => ( ord_less_eq_o @ ( complete_Sup_Sup_o @ ( image_o_o @ F @ A4 ) ) @ M ) ) ) ).

% cSUP_least
thf(fact_1137_cSup__eq__non__empty,axiom,
    ! [X5: set_nat,A: nat] :
      ( ( X5 != bot_bot_set_nat )
     => ( ! [X: nat] :
            ( ( member_nat @ X @ X5 )
           => ( ord_less_eq_nat @ X @ A ) )
       => ( ! [Y: nat] :
              ( ! [X6: nat] :
                  ( ( member_nat @ X6 @ X5 )
                 => ( ord_less_eq_nat @ X6 @ Y ) )
             => ( ord_less_eq_nat @ A @ Y ) )
         => ( ( complete_Sup_Sup_nat @ X5 )
            = A ) ) ) ) ).

% cSup_eq_non_empty
thf(fact_1138_cSup__eq__non__empty,axiom,
    ! [X5: set_o,A: $o] :
      ( ( X5 != bot_bot_set_o )
     => ( ! [X: $o] :
            ( ( member_o @ X @ X5 )
           => ( ord_less_eq_o @ X @ A ) )
       => ( ! [Y: $o] :
              ( ! [X6: $o] :
                  ( ( member_o @ X6 @ X5 )
                 => ( ord_less_eq_o @ X6 @ Y ) )
             => ( ord_less_eq_o @ A @ Y ) )
         => ( ( complete_Sup_Sup_o @ X5 )
            = A ) ) ) ) ).

% cSup_eq_non_empty
thf(fact_1139_SUP__Sup__eq,axiom,
    ! [S6: set_set_o] :
      ( ( complete_Sup_Sup_o_o
        @ ( image_set_o_o_o
          @ ^ [I2: set_o,X3: $o] : ( member_o @ X3 @ I2 )
          @ S6 ) )
      = ( ^ [X3: $o] : ( member_o @ X3 @ ( comple90263536869209701_set_o @ S6 ) ) ) ) ).

% SUP_Sup_eq
thf(fact_1140_Sup__set__def,axiom,
    ( comple90263536869209701_set_o
    = ( ^ [A6: set_set_o] :
          ( collect_o
          @ ^ [X3: $o] : ( complete_Sup_Sup_o @ ( image_set_o_o @ ( member_o @ X3 ) @ A6 ) ) ) ) ) ).

% Sup_set_def
thf(fact_1141_Sup__SUP__eq,axiom,
    ( complete_Sup_Sup_o_o
    = ( ^ [S5: set_o_o,X3: $o] : ( member_o @ X3 @ ( comple90263536869209701_set_o @ ( image_o_o_set_o @ collect_o @ S5 ) ) ) ) ) ).

% Sup_SUP_eq
thf(fact_1142_cSup__eq__maximum,axiom,
    ! [Z2: nat,X5: set_nat] :
      ( ( member_nat @ Z2 @ X5 )
     => ( ! [X: nat] :
            ( ( member_nat @ X @ X5 )
           => ( ord_less_eq_nat @ X @ Z2 ) )
       => ( ( complete_Sup_Sup_nat @ X5 )
          = Z2 ) ) ) ).

% cSup_eq_maximum
thf(fact_1143_cSup__eq__maximum,axiom,
    ! [Z2: $o,X5: set_o] :
      ( ( member_o @ Z2 @ X5 )
     => ( ! [X: $o] :
            ( ( member_o @ X @ X5 )
           => ( ord_less_eq_o @ X @ Z2 ) )
       => ( ( complete_Sup_Sup_o @ X5 )
          = Z2 ) ) ) ).

% cSup_eq_maximum
thf(fact_1144_cSup__least,axiom,
    ! [X5: set_nat,Z2: nat] :
      ( ( X5 != bot_bot_set_nat )
     => ( ! [X: nat] :
            ( ( member_nat @ X @ X5 )
           => ( ord_less_eq_nat @ X @ Z2 ) )
       => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ X5 ) @ Z2 ) ) ) ).

% cSup_least
thf(fact_1145_cSup__least,axiom,
    ! [X5: set_o,Z2: $o] :
      ( ( X5 != bot_bot_set_o )
     => ( ! [X: $o] :
            ( ( member_o @ X @ X5 )
           => ( ord_less_eq_o @ X @ Z2 ) )
       => ( ord_less_eq_o @ ( complete_Sup_Sup_o @ X5 ) @ Z2 ) ) ) ).

% cSup_least
thf(fact_1146_fixp__induct,axiom,
    ! [P2: $o > $o,F: $o > $o] :
      ( ( comple8949206149834442853ible_o @ complete_Sup_Sup_o @ ord_less_eq_o @ P2 )
     => ( ( monotone_on_o_o @ top_top_set_o @ ord_less_eq_o @ ord_less_eq_o @ F )
       => ( ( P2 @ ( complete_Sup_Sup_o @ bot_bot_set_o ) )
         => ( ! [X: $o] :
                ( ( P2 @ X )
               => ( P2 @ ( F @ X ) ) )
           => ( P2 @ ( comple2713996627985145509fixp_o @ F ) ) ) ) ) ) ).

% fixp_induct
thf(fact_1147_Sup__bool__def,axiom,
    ( complete_Sup_Sup_o
    = ( member_o @ $true ) ) ).

% Sup_bool_def
thf(fact_1148_admissible__disj,axiom,
    ! [P2: $o > $o,Q3: $o > $o] :
      ( ( comple8949206149834442853ible_o @ complete_Sup_Sup_o @ ord_less_eq_o @ P2 )
     => ( ( comple8949206149834442853ible_o @ complete_Sup_Sup_o @ ord_less_eq_o @ Q3 )
       => ( comple8949206149834442853ible_o @ complete_Sup_Sup_o @ ord_less_eq_o
          @ ^ [X3: $o] :
              ( ( P2 @ X3 )
              | ( Q3 @ X3 ) ) ) ) ) ).

% admissible_disj
thf(fact_1149_def__coinduct3,axiom,
    ! [A4: set_o,F: set_o > set_o,A: $o,X5: set_o] :
      ( ( A4
        = ( comple5578320350976157814_set_o @ F ) )
     => ( ( monoto3902964759935319015_set_o @ top_top_set_set_o @ ord_less_eq_set_o @ ord_less_eq_set_o @ F )
       => ( ( member_o @ A @ X5 )
         => ( ( ord_less_eq_set_o @ X5
              @ ( F
                @ ( comple3077273498168821681_set_o
                  @ ^ [X3: set_o] : ( sup_sup_set_o @ ( sup_sup_set_o @ ( F @ X3 ) @ X5 ) @ A4 ) ) ) )
           => ( member_o @ A @ A4 ) ) ) ) ) ).

% def_coinduct3
thf(fact_1150_Un__iff,axiom,
    ! [C2: $o,A4: set_o,B5: set_o] :
      ( ( member_o @ C2 @ ( sup_sup_set_o @ A4 @ B5 ) )
      = ( ( member_o @ C2 @ A4 )
        | ( member_o @ C2 @ B5 ) ) ) ).

% Un_iff
thf(fact_1151_UnCI,axiom,
    ! [C2: $o,B5: set_o,A4: set_o] :
      ( ( ~ ( member_o @ C2 @ B5 )
       => ( member_o @ C2 @ A4 ) )
     => ( member_o @ C2 @ ( sup_sup_set_o @ A4 @ B5 ) ) ) ).

% UnCI
thf(fact_1152_SUP__UNIV__bool__expand,axiom,
    ! [A4: $o > $o] :
      ( ( complete_Sup_Sup_o @ ( image_o_o @ A4 @ top_top_set_o ) )
      = ( sup_sup_o @ ( A4 @ $true ) @ ( A4 @ $false ) ) ) ).

% SUP_UNIV_bool_expand
thf(fact_1153_Sup__union__distrib,axiom,
    ! [A4: set_o,B5: set_o] :
      ( ( complete_Sup_Sup_o @ ( sup_sup_set_o @ A4 @ B5 ) )
      = ( sup_sup_o @ ( complete_Sup_Sup_o @ A4 ) @ ( complete_Sup_Sup_o @ B5 ) ) ) ).

% Sup_union_distrib
thf(fact_1154_SUP__absorb,axiom,
    ! [K: $o,I4: set_o,A4: $o > $o] :
      ( ( member_o @ K @ I4 )
     => ( ( sup_sup_o @ ( A4 @ K ) @ ( complete_Sup_Sup_o @ ( image_o_o @ A4 @ I4 ) ) )
        = ( complete_Sup_Sup_o @ ( image_o_o @ A4 @ I4 ) ) ) ) ).

% SUP_absorb
thf(fact_1155_Un__def,axiom,
    ( sup_sup_set_o
    = ( ^ [A6: set_o,B6: set_o] :
          ( collect_o
          @ ^ [X3: $o] :
              ( ( member_o @ X3 @ A6 )
              | ( member_o @ X3 @ B6 ) ) ) ) ) ).

% Un_def
thf(fact_1156_Un__UNIV__right,axiom,
    ! [A4: set_nat] :
      ( ( sup_sup_set_nat @ A4 @ top_top_set_nat )
      = top_top_set_nat ) ).

% Un_UNIV_right
thf(fact_1157_Un__UNIV__left,axiom,
    ! [B5: set_nat] :
      ( ( sup_sup_set_nat @ top_top_set_nat @ B5 )
      = top_top_set_nat ) ).

% Un_UNIV_left
thf(fact_1158_UnI2,axiom,
    ! [C2: $o,B5: set_o,A4: set_o] :
      ( ( member_o @ C2 @ B5 )
     => ( member_o @ C2 @ ( sup_sup_set_o @ A4 @ B5 ) ) ) ).

% UnI2
thf(fact_1159_UnI1,axiom,
    ! [C2: $o,A4: set_o,B5: set_o] :
      ( ( member_o @ C2 @ A4 )
     => ( member_o @ C2 @ ( sup_sup_set_o @ A4 @ B5 ) ) ) ).

% UnI1
thf(fact_1160_UnE,axiom,
    ! [C2: $o,A4: set_o,B5: set_o] :
      ( ( member_o @ C2 @ ( sup_sup_set_o @ A4 @ B5 ) )
     => ( ~ ( member_o @ C2 @ A4 )
       => ( member_o @ C2 @ B5 ) ) ) ).

% UnE
thf(fact_1161_mono__sup,axiom,
    ! [F: nat > nat,A4: nat,B5: nat] :
      ( ( monotone_on_nat_nat @ top_top_set_nat @ ord_less_eq_nat @ ord_less_eq_nat @ F )
     => ( ord_less_eq_nat @ ( sup_sup_nat @ ( F @ A4 ) @ ( F @ B5 ) ) @ ( F @ ( sup_sup_nat @ A4 @ B5 ) ) ) ) ).

% mono_sup
thf(fact_1162_def__coinduct__set,axiom,
    ! [A4: set_o,F: set_o > set_o,A: $o,X5: set_o] :
      ( ( A4
        = ( comple5578320350976157814_set_o @ F ) )
     => ( ( monoto3902964759935319015_set_o @ top_top_set_set_o @ ord_less_eq_set_o @ ord_less_eq_set_o @ F )
       => ( ( member_o @ A @ X5 )
         => ( ( ord_less_eq_set_o @ X5 @ ( F @ ( sup_sup_set_o @ X5 @ A4 ) ) )
           => ( member_o @ A @ A4 ) ) ) ) ) ).

% def_coinduct_set
thf(fact_1163_gfp__fun__UnI2,axiom,
    ! [F: set_o > set_o,A: $o,X5: set_o] :
      ( ( monoto3902964759935319015_set_o @ top_top_set_set_o @ ord_less_eq_set_o @ ord_less_eq_set_o @ F )
     => ( ( member_o @ A @ ( comple5578320350976157814_set_o @ F ) )
       => ( member_o @ A @ ( F @ ( sup_sup_set_o @ X5 @ ( comple5578320350976157814_set_o @ F ) ) ) ) ) ) ).

% gfp_fun_UnI2
thf(fact_1164_coinduct__set,axiom,
    ! [F: set_o > set_o,A: $o,X5: set_o] :
      ( ( monoto3902964759935319015_set_o @ top_top_set_set_o @ ord_less_eq_set_o @ ord_less_eq_set_o @ F )
     => ( ( member_o @ A @ X5 )
       => ( ( ord_less_eq_set_o @ X5 @ ( F @ ( sup_sup_set_o @ X5 @ ( comple5578320350976157814_set_o @ F ) ) ) )
         => ( member_o @ A @ ( comple5578320350976157814_set_o @ F ) ) ) ) ) ).

% coinduct_set
thf(fact_1165_def__Collect__coinduct,axiom,
    ! [A4: set_o,P2: set_o > $o > $o,A: $o,X5: set_o] :
      ( ( A4
        = ( comple5578320350976157814_set_o
          @ ^ [W: set_o] : ( collect_o @ ( P2 @ W ) ) ) )
     => ( ( monoto3902964759935319015_set_o @ top_top_set_set_o @ ord_less_eq_set_o @ ord_less_eq_set_o
          @ ^ [W: set_o] : ( collect_o @ ( P2 @ W ) ) )
       => ( ( member_o @ A @ X5 )
         => ( ! [Z3: $o] :
                ( ( member_o @ Z3 @ X5 )
               => ( P2 @ ( sup_sup_set_o @ X5 @ A4 ) @ Z3 ) )
           => ( member_o @ A @ A4 ) ) ) ) ) ).

% def_Collect_coinduct
thf(fact_1166_coinduct3,axiom,
    ! [F: set_o > set_o,A: $o,X5: set_o] :
      ( ( monoto3902964759935319015_set_o @ top_top_set_set_o @ ord_less_eq_set_o @ ord_less_eq_set_o @ F )
     => ( ( member_o @ A @ X5 )
       => ( ( ord_less_eq_set_o @ X5
            @ ( F
              @ ( comple3077273498168821681_set_o
                @ ^ [X3: set_o] : ( sup_sup_set_o @ ( sup_sup_set_o @ ( F @ X3 ) @ X5 ) @ ( comple5578320350976157814_set_o @ F ) ) ) ) )
         => ( member_o @ A @ ( comple5578320350976157814_set_o @ F ) ) ) ) ) ).

% coinduct3
thf(fact_1167_sup_Obounded__iff,axiom,
    ! [B: nat,C2: nat,A: nat] :
      ( ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C2 ) @ A )
      = ( ( ord_less_eq_nat @ B @ A )
        & ( ord_less_eq_nat @ C2 @ A ) ) ) ).

% sup.bounded_iff
thf(fact_1168_le__sup__iff,axiom,
    ! [X2: nat,Y3: nat,Z2: nat] :
      ( ( ord_less_eq_nat @ ( sup_sup_nat @ X2 @ Y3 ) @ Z2 )
      = ( ( ord_less_eq_nat @ X2 @ Z2 )
        & ( ord_less_eq_nat @ Y3 @ Z2 ) ) ) ).

% le_sup_iff
thf(fact_1169_sup__set__def,axiom,
    ( sup_sup_set_o
    = ( ^ [A6: set_o,B6: set_o] :
          ( collect_o
          @ ( sup_sup_o_o
            @ ^ [X3: $o] : ( member_o @ X3 @ A6 )
            @ ^ [X3: $o] : ( member_o @ X3 @ B6 ) ) ) ) ) ).

% sup_set_def
thf(fact_1170_sup_OcoboundedI2,axiom,
    ! [C2: nat,B: nat,A: nat] :
      ( ( ord_less_eq_nat @ C2 @ B )
     => ( ord_less_eq_nat @ C2 @ ( sup_sup_nat @ A @ B ) ) ) ).

% sup.coboundedI2
thf(fact_1171_sup_OcoboundedI1,axiom,
    ! [C2: nat,A: nat,B: nat] :
      ( ( ord_less_eq_nat @ C2 @ A )
     => ( ord_less_eq_nat @ C2 @ ( sup_sup_nat @ A @ B ) ) ) ).

% sup.coboundedI1
thf(fact_1172_sup_Oabsorb__iff2,axiom,
    ( ord_less_eq_nat
    = ( ^ [A5: nat,B4: nat] :
          ( ( sup_sup_nat @ A5 @ B4 )
          = B4 ) ) ) ).

% sup.absorb_iff2
thf(fact_1173_sup_Oabsorb__iff1,axiom,
    ( ord_less_eq_nat
    = ( ^ [B4: nat,A5: nat] :
          ( ( sup_sup_nat @ A5 @ B4 )
          = A5 ) ) ) ).

% sup.absorb_iff1
thf(fact_1174_sup_Ocobounded2,axiom,
    ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( sup_sup_nat @ A @ B ) ) ).

% sup.cobounded2
thf(fact_1175_sup_Ocobounded1,axiom,
    ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( sup_sup_nat @ A @ B ) ) ).

% sup.cobounded1
thf(fact_1176_sup_Oorder__iff,axiom,
    ( ord_less_eq_nat
    = ( ^ [B4: nat,A5: nat] :
          ( A5
          = ( sup_sup_nat @ A5 @ B4 ) ) ) ) ).

% sup.order_iff
thf(fact_1177_sup_OboundedI,axiom,
    ! [B: nat,A: nat,C2: nat] :
      ( ( ord_less_eq_nat @ B @ A )
     => ( ( ord_less_eq_nat @ C2 @ A )
       => ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C2 ) @ A ) ) ) ).

% sup.boundedI
thf(fact_1178_sup_OboundedE,axiom,
    ! [B: nat,C2: nat,A: nat] :
      ( ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C2 ) @ A )
     => ~ ( ( ord_less_eq_nat @ B @ A )
         => ~ ( ord_less_eq_nat @ C2 @ A ) ) ) ).

% sup.boundedE
thf(fact_1179_sup__absorb2,axiom,
    ! [X2: nat,Y3: nat] :
      ( ( ord_less_eq_nat @ X2 @ Y3 )
     => ( ( sup_sup_nat @ X2 @ Y3 )
        = Y3 ) ) ).

% sup_absorb2
thf(fact_1180_sup__absorb1,axiom,
    ! [Y3: nat,X2: nat] :
      ( ( ord_less_eq_nat @ Y3 @ X2 )
     => ( ( sup_sup_nat @ X2 @ Y3 )
        = X2 ) ) ).

% sup_absorb1
thf(fact_1181_sup_Oabsorb2,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( sup_sup_nat @ A @ B )
        = B ) ) ).

% sup.absorb2
thf(fact_1182_sup_Oabsorb1,axiom,
    ! [B: nat,A: nat] :
      ( ( ord_less_eq_nat @ B @ A )
     => ( ( sup_sup_nat @ A @ B )
        = A ) ) ).

% sup.absorb1
thf(fact_1183_sup__unique,axiom,
    ! [F: nat > nat > nat,X2: nat,Y3: nat] :
      ( ! [X: nat,Y: nat] : ( ord_less_eq_nat @ X @ ( F @ X @ Y ) )
     => ( ! [X: nat,Y: nat] : ( ord_less_eq_nat @ Y @ ( F @ X @ Y ) )
       => ( ! [X: nat,Y: nat,Z3: nat] :
              ( ( ord_less_eq_nat @ Y @ X )
             => ( ( ord_less_eq_nat @ Z3 @ X )
               => ( ord_less_eq_nat @ ( F @ Y @ Z3 ) @ X ) ) )
         => ( ( sup_sup_nat @ X2 @ Y3 )
            = ( F @ X2 @ Y3 ) ) ) ) ) ).

% sup_unique
thf(fact_1184_sup_OorderI,axiom,
    ! [A: nat,B: nat] :
      ( ( A
        = ( sup_sup_nat @ A @ B ) )
     => ( ord_less_eq_nat @ B @ A ) ) ).

% sup.orderI
thf(fact_1185_sup_OorderE,axiom,
    ! [B: nat,A: nat] :
      ( ( ord_less_eq_nat @ B @ A )
     => ( A
        = ( sup_sup_nat @ A @ B ) ) ) ).

% sup.orderE
thf(fact_1186_le__iff__sup,axiom,
    ( ord_less_eq_nat
    = ( ^ [X3: nat,Y4: nat] :
          ( ( sup_sup_nat @ X3 @ Y4 )
          = Y4 ) ) ) ).

% le_iff_sup
thf(fact_1187_sup__least,axiom,
    ! [Y3: nat,X2: nat,Z2: nat] :
      ( ( ord_less_eq_nat @ Y3 @ X2 )
     => ( ( ord_less_eq_nat @ Z2 @ X2 )
       => ( ord_less_eq_nat @ ( sup_sup_nat @ Y3 @ Z2 ) @ X2 ) ) ) ).

% sup_least
thf(fact_1188_sup__mono,axiom,
    ! [A: nat,C2: nat,B: nat,D2: nat] :
      ( ( ord_less_eq_nat @ A @ C2 )
     => ( ( ord_less_eq_nat @ B @ D2 )
       => ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ ( sup_sup_nat @ C2 @ D2 ) ) ) ) ).

% sup_mono
thf(fact_1189_sup_Omono,axiom,
    ! [C2: nat,A: nat,D2: nat,B: nat] :
      ( ( ord_less_eq_nat @ C2 @ A )
     => ( ( ord_less_eq_nat @ D2 @ B )
       => ( ord_less_eq_nat @ ( sup_sup_nat @ C2 @ D2 ) @ ( sup_sup_nat @ A @ B ) ) ) ) ).

% sup.mono
thf(fact_1190_le__supI2,axiom,
    ! [X2: nat,B: nat,A: nat] :
      ( ( ord_less_eq_nat @ X2 @ B )
     => ( ord_less_eq_nat @ X2 @ ( sup_sup_nat @ A @ B ) ) ) ).

% le_supI2
thf(fact_1191_le__supI1,axiom,
    ! [X2: nat,A: nat,B: nat] :
      ( ( ord_less_eq_nat @ X2 @ A )
     => ( ord_less_eq_nat @ X2 @ ( sup_sup_nat @ A @ B ) ) ) ).

% le_supI1
thf(fact_1192_sup__ge2,axiom,
    ! [Y3: nat,X2: nat] : ( ord_less_eq_nat @ Y3 @ ( sup_sup_nat @ X2 @ Y3 ) ) ).

% sup_ge2
thf(fact_1193_sup__ge1,axiom,
    ! [X2: nat,Y3: nat] : ( ord_less_eq_nat @ X2 @ ( sup_sup_nat @ X2 @ Y3 ) ) ).

% sup_ge1
thf(fact_1194_le__supI,axiom,
    ! [A: nat,X2: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ X2 )
     => ( ( ord_less_eq_nat @ B @ X2 )
       => ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ X2 ) ) ) ).

% le_supI
thf(fact_1195_le__supE,axiom,
    ! [A: nat,B: nat,X2: nat] :
      ( ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ X2 )
     => ~ ( ( ord_less_eq_nat @ A @ X2 )
         => ~ ( ord_less_eq_nat @ B @ X2 ) ) ) ).

% le_supE
thf(fact_1196_inf__sup__ord_I3_J,axiom,
    ! [X2: nat,Y3: nat] : ( ord_less_eq_nat @ X2 @ ( sup_sup_nat @ X2 @ Y3 ) ) ).

% inf_sup_ord(3)
thf(fact_1197_inf__sup__ord_I4_J,axiom,
    ! [Y3: nat,X2: nat] : ( ord_less_eq_nat @ Y3 @ ( sup_sup_nat @ X2 @ Y3 ) ) ).

% inf_sup_ord(4)
thf(fact_1198_inj__on__trancl__map__both,axiom,
    ! [F: nat > nat,R: set_Pr1261947904930325089at_nat] :
      ( ( inj_on_nat_nat @ F @ ( sup_sup_set_nat @ ( image_2486076414777270412at_nat @ product_fst_nat_nat @ R ) @ ( image_2486076414777270412at_nat @ product_snd_nat_nat @ R ) ) )
     => ( ( transi6264000038957366511cl_nat @ ( image_5168914502847457605at_nat @ ( produc6977886695330630970at_nat @ F @ F ) @ R ) )
        = ( image_5168914502847457605at_nat @ ( produc6977886695330630970at_nat @ F @ F ) @ ( transi6264000038957366511cl_nat @ R ) ) ) ) ).

% inj_on_trancl_map_both
thf(fact_1199_mono__cSup,axiom,
    ! [F: nat > nat,A4: set_nat] :
      ( ( monotone_on_nat_nat @ top_top_set_nat @ ord_less_eq_nat @ ord_less_eq_nat @ F )
     => ( ( condit2214826472909112428ve_nat @ A4 )
       => ( ( A4 != bot_bot_set_nat )
         => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( F @ ( complete_Sup_Sup_nat @ A4 ) ) ) ) ) ) ).

% mono_cSup
thf(fact_1200_mono__cSup,axiom,
    ! [F: $o > nat,A4: set_o] :
      ( ( monotone_on_o_nat @ top_top_set_o @ ord_less_eq_o @ ord_less_eq_nat @ F )
     => ( ( condit5488710616941104124bove_o @ A4 )
       => ( ( A4 != bot_bot_set_o )
         => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_o_nat @ F @ A4 ) ) @ ( F @ ( complete_Sup_Sup_o @ A4 ) ) ) ) ) ) ).

% mono_cSup
thf(fact_1201_mono__cSup,axiom,
    ! [F: nat > $o,A4: set_nat] :
      ( ( monotone_on_nat_o @ top_top_set_nat @ ord_less_eq_nat @ ord_less_eq_o @ F )
     => ( ( condit2214826472909112428ve_nat @ A4 )
       => ( ( A4 != bot_bot_set_nat )
         => ( ord_less_eq_o @ ( complete_Sup_Sup_o @ ( image_nat_o @ F @ A4 ) ) @ ( F @ ( complete_Sup_Sup_nat @ A4 ) ) ) ) ) ) ).

% mono_cSup
thf(fact_1202_mono__cSup,axiom,
    ! [F: $o > $o,A4: set_o] :
      ( ( monotone_on_o_o @ top_top_set_o @ ord_less_eq_o @ ord_less_eq_o @ F )
     => ( ( condit5488710616941104124bove_o @ A4 )
       => ( ( A4 != bot_bot_set_o )
         => ( ord_less_eq_o @ ( complete_Sup_Sup_o @ ( image_o_o @ F @ A4 ) ) @ ( F @ ( complete_Sup_Sup_o @ A4 ) ) ) ) ) ) ).

% mono_cSup
thf(fact_1203_inj__on__empty,axiom,
    ! [F: nat > nat] : ( inj_on_nat_nat @ F @ bot_bot_set_nat ) ).

% inj_on_empty
thf(fact_1204_bdd__above_OI,axiom,
    ! [A4: set_o,M: $o] :
      ( ! [X: $o] :
          ( ( member_o @ X @ A4 )
         => ( ord_less_eq_o @ X @ M ) )
     => ( condit5488710616941104124bove_o @ A4 ) ) ).

% bdd_above.I
thf(fact_1205_bdd__above_OI,axiom,
    ! [A4: set_nat,M: nat] :
      ( ! [X: nat] :
          ( ( member_nat @ X @ A4 )
         => ( ord_less_eq_nat @ X @ M ) )
     => ( condit2214826472909112428ve_nat @ A4 ) ) ).

% bdd_above.I
thf(fact_1206_inj__on__apfst,axiom,
    ! [F: nat > nat,A4: set_nat] :
      ( ( inj_on8969904277767023793at_nat @ ( produc986720760941809198at_nat @ F )
        @ ( produc457027306803732586at_nat @ A4
          @ ^ [Uu: nat] : top_top_set_nat ) )
      = ( inj_on_nat_nat @ F @ A4 ) ) ).

% inj_on_apfst
thf(fact_1207_inj__on__apsnd,axiom,
    ! [F: nat > nat,A4: set_nat] :
      ( ( inj_on8969904277767023793at_nat @ ( produc3094765310956027504at_nat @ F )
        @ ( produc457027306803732586at_nat @ top_top_set_nat
          @ ^ [Uu: nat] : A4 ) )
      = ( inj_on_nat_nat @ F @ A4 ) ) ).

% inj_on_apsnd
thf(fact_1208_inj__on__Un__image__eq__iff,axiom,
    ! [F: nat > nat,A4: set_nat,B5: set_nat] :
      ( ( inj_on_nat_nat @ F @ ( sup_sup_set_nat @ A4 @ B5 ) )
     => ( ( ( image_nat_nat @ F @ A4 )
          = ( image_nat_nat @ F @ B5 ) )
        = ( A4 = B5 ) ) ) ).

% inj_on_Un_image_eq_iff
thf(fact_1209_inj__compose,axiom,
    ! [F: nat > nat,G: nat > nat] :
      ( ( inj_on_nat_nat @ F @ top_top_set_nat )
     => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
       => ( inj_on_nat_nat @ ( comp_nat_nat_nat @ F @ G ) @ top_top_set_nat ) ) ) ).

% inj_compose
thf(fact_1210_fun_Oinj__map,axiom,
    ! [F: nat > nat] :
      ( ( inj_on_nat_nat @ F @ top_top_set_nat )
     => ( inj_on2461717442902640625at_nat @ ( comp_nat_nat_nat @ F ) @ top_top_set_nat_nat ) ) ).

% fun.inj_map
thf(fact_1211_inj__fn,axiom,
    ! [F: nat > nat,N: nat] :
      ( ( inj_on_nat_nat @ F @ top_top_set_nat )
     => ( inj_on_nat_nat @ ( compow_nat_nat @ N @ F ) @ top_top_set_nat ) ) ).

% inj_fn
thf(fact_1212_prod_Oinj__map,axiom,
    ! [F12: nat > nat,F23: nat > nat] :
      ( ( inj_on_nat_nat @ F12 @ top_top_set_nat )
     => ( ( inj_on_nat_nat @ F23 @ top_top_set_nat )
       => ( inj_on8969904277767023793at_nat @ ( produc6977886695330630970at_nat @ F12 @ F23 ) @ top_to4669805908274784177at_nat ) ) ) ).

% prod.inj_map
thf(fact_1213_sorted__list__of__set_Oinj__on,axiom,
    ( inj_on_nat_nat
    @ ^ [X3: nat] : X3
    @ top_top_set_nat ) ).

% sorted_list_of_set.inj_on
thf(fact_1214_inj__def,axiom,
    ! [F: nat > nat] :
      ( ( inj_on_nat_nat @ F @ top_top_set_nat )
      = ( ! [X3: nat,Y4: nat] :
            ( ( ( F @ X3 )
              = ( F @ Y4 ) )
           => ( X3 = Y4 ) ) ) ) ).

% inj_def
thf(fact_1215_inj__eq,axiom,
    ! [F: nat > nat,X2: nat,Y3: nat] :
      ( ( inj_on_nat_nat @ F @ top_top_set_nat )
     => ( ( ( F @ X2 )
          = ( F @ Y3 ) )
        = ( X2 = Y3 ) ) ) ).

% inj_eq
thf(fact_1216_injI,axiom,
    ! [F: nat > nat] :
      ( ! [X: nat,Y: nat] :
          ( ( ( F @ X )
            = ( F @ Y ) )
         => ( X = Y ) )
     => ( inj_on_nat_nat @ F @ top_top_set_nat ) ) ).

% injI
thf(fact_1217_injD,axiom,
    ! [F: nat > nat,X2: nat,Y3: nat] :
      ( ( inj_on_nat_nat @ F @ top_top_set_nat )
     => ( ( ( F @ X2 )
          = ( F @ Y3 ) )
       => ( X2 = Y3 ) ) ) ).

% injD
thf(fact_1218_inj__on__image__eq__iff,axiom,
    ! [F: nat > nat,C3: set_nat,A4: set_nat,B5: set_nat] :
      ( ( inj_on_nat_nat @ F @ C3 )
     => ( ( ord_less_eq_set_nat @ A4 @ C3 )
       => ( ( ord_less_eq_set_nat @ B5 @ C3 )
         => ( ( ( image_nat_nat @ F @ A4 )
              = ( image_nat_nat @ F @ B5 ) )
            = ( A4 = B5 ) ) ) ) ) ).

% inj_on_image_eq_iff
thf(fact_1219_inj__on__image__mem__iff,axiom,
    ! [F: nat > nat,B5: set_nat,A: nat,A4: set_nat] :
      ( ( inj_on_nat_nat @ F @ B5 )
     => ( ( member_nat @ A @ B5 )
       => ( ( ord_less_eq_set_nat @ A4 @ B5 )
         => ( ( member_nat @ ( F @ A ) @ ( image_nat_nat @ F @ A4 ) )
            = ( member_nat @ A @ A4 ) ) ) ) ) ).

% inj_on_image_mem_iff
thf(fact_1220_inj__on__image__mem__iff,axiom,
    ! [F: $o > $o,B5: set_o,A: $o,A4: set_o] :
      ( ( inj_on_o_o @ F @ B5 )
     => ( ( member_o @ A @ B5 )
       => ( ( ord_less_eq_set_o @ A4 @ B5 )
         => ( ( member_o @ ( F @ A ) @ ( image_o_o @ F @ A4 ) )
            = ( member_o @ A @ A4 ) ) ) ) ) ).

% inj_on_image_mem_iff
thf(fact_1221_bdd__above_OI2,axiom,
    ! [A4: set_o,F: $o > nat,M: nat] :
      ( ! [X: $o] :
          ( ( member_o @ X @ A4 )
         => ( ord_less_eq_nat @ ( F @ X ) @ M ) )
     => ( condit2214826472909112428ve_nat @ ( image_o_nat @ F @ A4 ) ) ) ).

% bdd_above.I2
thf(fact_1222_inj__image__mem__iff,axiom,
    ! [F: $o > $o,A: $o,A4: set_o] :
      ( ( inj_on_o_o @ F @ top_top_set_o )
     => ( ( member_o @ ( F @ A ) @ ( image_o_o @ F @ A4 ) )
        = ( member_o @ A @ A4 ) ) ) ).

% inj_image_mem_iff
thf(fact_1223_inj__image__mem__iff,axiom,
    ! [F: nat > nat,A: nat,A4: set_nat] :
      ( ( inj_on_nat_nat @ F @ top_top_set_nat )
     => ( ( member_nat @ ( F @ A ) @ ( image_nat_nat @ F @ A4 ) )
        = ( member_nat @ A @ A4 ) ) ) ).

% inj_image_mem_iff
thf(fact_1224_inj__image__mem__iff,axiom,
    ! [F: nat > $o,A: nat,A4: set_nat] :
      ( ( inj_on_nat_o @ F @ top_top_set_nat )
     => ( ( member_o @ ( F @ A ) @ ( image_nat_o @ F @ A4 ) )
        = ( member_nat @ A @ A4 ) ) ) ).

% inj_image_mem_iff
thf(fact_1225_inj__image__eq__iff,axiom,
    ! [F: nat > nat,A4: set_nat,B5: set_nat] :
      ( ( inj_on_nat_nat @ F @ top_top_set_nat )
     => ( ( ( image_nat_nat @ F @ A4 )
          = ( image_nat_nat @ F @ B5 ) )
        = ( A4 = B5 ) ) ) ).

% inj_image_eq_iff
thf(fact_1226_range__ex1__eq,axiom,
    ! [F: nat > nat,B: nat] :
      ( ( inj_on_nat_nat @ F @ top_top_set_nat )
     => ( ( member_nat @ B @ ( image_nat_nat @ F @ top_top_set_nat ) )
        = ( ? [X3: nat] :
              ( ( B
                = ( F @ X3 ) )
              & ! [Y4: nat] :
                  ( ( B
                    = ( F @ Y4 ) )
                 => ( Y4 = X3 ) ) ) ) ) ) ).

% range_ex1_eq
thf(fact_1227_range__ex1__eq,axiom,
    ! [F: nat > $o,B: $o] :
      ( ( inj_on_nat_o @ F @ top_top_set_nat )
     => ( ( member_o @ B @ ( image_nat_o @ F @ top_top_set_nat ) )
        = ( ? [X3: nat] :
              ( ( B
                = ( F @ X3 ) )
              & ! [Y4: nat] :
                  ( ( B
                    = ( F @ Y4 ) )
                 => ( Y4 = X3 ) ) ) ) ) ) ).

% range_ex1_eq
thf(fact_1228_comp__inj__on,axiom,
    ! [F: nat > nat,A4: set_nat,G: nat > nat] :
      ( ( inj_on_nat_nat @ F @ A4 )
     => ( ( inj_on_nat_nat @ G @ ( image_nat_nat @ F @ A4 ) )
       => ( inj_on_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ A4 ) ) ) ).

% comp_inj_on
thf(fact_1229_inj__on__imageI,axiom,
    ! [G: nat > nat,F: nat > nat,A4: set_nat] :
      ( ( inj_on_nat_nat @ ( comp_nat_nat_nat @ G @ F ) @ A4 )
     => ( inj_on_nat_nat @ G @ ( image_nat_nat @ F @ A4 ) ) ) ).

% inj_on_imageI
thf(fact_1230_comp__inj__on__iff,axiom,
    ! [F: nat > nat,A4: set_nat,F3: nat > nat] :
      ( ( inj_on_nat_nat @ F @ A4 )
     => ( ( inj_on_nat_nat @ F3 @ ( image_nat_nat @ F @ A4 ) )
        = ( inj_on_nat_nat @ ( comp_nat_nat_nat @ F3 @ F ) @ A4 ) ) ) ).

% comp_inj_on_iff
thf(fact_1231_inj__on__image__Pow,axiom,
    ! [F: nat > nat,A4: set_nat] :
      ( ( inj_on_nat_nat @ F @ A4 )
     => ( inj_on4604407203859583615et_nat @ ( image_nat_nat @ F ) @ ( pow_nat @ A4 ) ) ) ).

% inj_on_image_Pow
thf(fact_1232_inj__on__image__iff,axiom,
    ! [A4: set_nat,G: nat > nat,F: nat > nat] :
      ( ! [X: nat] :
          ( ( member_nat @ X @ A4 )
         => ! [Xa: nat] :
              ( ( member_nat @ Xa @ A4 )
             => ( ( ( G @ ( F @ X ) )
                  = ( G @ ( F @ Xa ) ) )
                = ( ( G @ X )
                  = ( G @ Xa ) ) ) ) )
     => ( ( inj_on_nat_nat @ F @ A4 )
       => ( ( inj_on_nat_nat @ G @ ( image_nat_nat @ F @ A4 ) )
          = ( inj_on_nat_nat @ G @ A4 ) ) ) ) ).

% inj_on_image_iff
thf(fact_1233_inj__on__image__Fpow,axiom,
    ! [F: nat > nat,A4: set_nat] :
      ( ( inj_on_nat_nat @ F @ A4 )
     => ( inj_on4604407203859583615et_nat @ ( image_nat_nat @ F ) @ ( finite_Fpow_nat @ A4 ) ) ) ).

% inj_on_image_Fpow
thf(fact_1234_inj__on__image,axiom,
    ! [F: nat > nat,A4: set_set_nat] :
      ( ( inj_on_nat_nat @ F @ ( comple7399068483239264473et_nat @ A4 ) )
     => ( inj_on4604407203859583615et_nat @ ( image_nat_nat @ F ) @ A4 ) ) ).

% inj_on_image
thf(fact_1235_inj__image__subset__iff,axiom,
    ! [F: nat > nat,A4: set_nat,B5: set_nat] :
      ( ( inj_on_nat_nat @ F @ top_top_set_nat )
     => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ ( image_nat_nat @ F @ B5 ) )
        = ( ord_less_eq_set_nat @ A4 @ B5 ) ) ) ).

% inj_image_subset_iff
thf(fact_1236_cSUP__upper,axiom,
    ! [X2: $o,A4: set_o,F: $o > nat] :
      ( ( member_o @ X2 @ A4 )
     => ( ( condit2214826472909112428ve_nat @ ( image_o_nat @ F @ A4 ) )
       => ( ord_less_eq_nat @ ( F @ X2 ) @ ( complete_Sup_Sup_nat @ ( image_o_nat @ F @ A4 ) ) ) ) ) ).

% cSUP_upper
thf(fact_1237_cSUP__upper,axiom,
    ! [X2: $o,A4: set_o,F: $o > $o] :
      ( ( member_o @ X2 @ A4 )
     => ( ( condit5488710616941104124bove_o @ ( image_o_o @ F @ A4 ) )
       => ( ord_less_eq_o @ ( F @ X2 ) @ ( complete_Sup_Sup_o @ ( image_o_o @ F @ A4 ) ) ) ) ) ).

% cSUP_upper
thf(fact_1238_cSUP__upper2,axiom,
    ! [F: $o > nat,A4: set_o,X2: $o,U: nat] :
      ( ( condit2214826472909112428ve_nat @ ( image_o_nat @ F @ A4 ) )
     => ( ( member_o @ X2 @ A4 )
       => ( ( ord_less_eq_nat @ U @ ( F @ X2 ) )
         => ( ord_less_eq_nat @ U @ ( complete_Sup_Sup_nat @ ( image_o_nat @ F @ A4 ) ) ) ) ) ) ).

% cSUP_upper2
thf(fact_1239_cSUP__upper2,axiom,
    ! [F: $o > $o,A4: set_o,X2: $o,U: $o] :
      ( ( condit5488710616941104124bove_o @ ( image_o_o @ F @ A4 ) )
     => ( ( member_o @ X2 @ A4 )
       => ( ( ord_less_eq_o @ U @ ( F @ X2 ) )
         => ( ord_less_eq_o @ U @ ( complete_Sup_Sup_o @ ( image_o_o @ F @ A4 ) ) ) ) ) ) ).

% cSUP_upper2
thf(fact_1240_cSup__mono,axiom,
    ! [B5: set_nat,A4: set_nat] :
      ( ( B5 != bot_bot_set_nat )
     => ( ( condit2214826472909112428ve_nat @ A4 )
       => ( ! [B3: nat] :
              ( ( member_nat @ B3 @ B5 )
             => ? [X6: nat] :
                  ( ( member_nat @ X6 @ A4 )
                  & ( ord_less_eq_nat @ B3 @ X6 ) ) )
         => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ B5 ) @ ( complete_Sup_Sup_nat @ A4 ) ) ) ) ) ).

% cSup_mono
thf(fact_1241_cSup__mono,axiom,
    ! [B5: set_o,A4: set_o] :
      ( ( B5 != bot_bot_set_o )
     => ( ( condit5488710616941104124bove_o @ A4 )
       => ( ! [B3: $o] :
              ( ( member_o @ B3 @ B5 )
             => ? [X6: $o] :
                  ( ( member_o @ X6 @ A4 )
                  & ( ord_less_eq_o @ B3 @ X6 ) ) )
         => ( ord_less_eq_o @ ( complete_Sup_Sup_o @ B5 ) @ ( complete_Sup_Sup_o @ A4 ) ) ) ) ) ).

% cSup_mono
thf(fact_1242_cSup__le__iff,axiom,
    ! [S6: set_nat,A: nat] :
      ( ( S6 != bot_bot_set_nat )
     => ( ( condit2214826472909112428ve_nat @ S6 )
       => ( ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ S6 ) @ A )
          = ( ! [X3: nat] :
                ( ( member_nat @ X3 @ S6 )
               => ( ord_less_eq_nat @ X3 @ A ) ) ) ) ) ) ).

% cSup_le_iff
thf(fact_1243_cSup__le__iff,axiom,
    ! [S6: set_o,A: $o] :
      ( ( S6 != bot_bot_set_o )
     => ( ( condit5488710616941104124bove_o @ S6 )
       => ( ( ord_less_eq_o @ ( complete_Sup_Sup_o @ S6 ) @ A )
          = ( ! [X3: $o] :
                ( ( member_o @ X3 @ S6 )
               => ( ord_less_eq_o @ X3 @ A ) ) ) ) ) ) ).

% cSup_le_iff
thf(fact_1244_cSup__upper2,axiom,
    ! [X2: nat,X5: set_nat,Y3: nat] :
      ( ( member_nat @ X2 @ X5 )
     => ( ( ord_less_eq_nat @ Y3 @ X2 )
       => ( ( condit2214826472909112428ve_nat @ X5 )
         => ( ord_less_eq_nat @ Y3 @ ( complete_Sup_Sup_nat @ X5 ) ) ) ) ) ).

% cSup_upper2
thf(fact_1245_cSup__upper2,axiom,
    ! [X2: $o,X5: set_o,Y3: $o] :
      ( ( member_o @ X2 @ X5 )
     => ( ( ord_less_eq_o @ Y3 @ X2 )
       => ( ( condit5488710616941104124bove_o @ X5 )
         => ( ord_less_eq_o @ Y3 @ ( complete_Sup_Sup_o @ X5 ) ) ) ) ) ).

% cSup_upper2
thf(fact_1246_cSup__upper,axiom,
    ! [X2: nat,X5: set_nat] :
      ( ( member_nat @ X2 @ X5 )
     => ( ( condit2214826472909112428ve_nat @ X5 )
       => ( ord_less_eq_nat @ X2 @ ( complete_Sup_Sup_nat @ X5 ) ) ) ) ).

% cSup_upper
thf(fact_1247_cSup__upper,axiom,
    ! [X2: $o,X5: set_o] :
      ( ( member_o @ X2 @ X5 )
     => ( ( condit5488710616941104124bove_o @ X5 )
       => ( ord_less_eq_o @ X2 @ ( complete_Sup_Sup_o @ X5 ) ) ) ) ).

% cSup_upper
thf(fact_1248_inj__Suc,axiom,
    ! [N2: set_nat] : ( inj_on_nat_nat @ suc @ N2 ) ).

% inj_Suc
thf(fact_1249_inj__on__id2,axiom,
    ! [A4: set_nat] :
      ( inj_on_nat_nat
      @ ^ [X3: nat] : X3
      @ A4 ) ).

% inj_on_id2
thf(fact_1250_inj__swap,axiom,
    ! [A4: set_Pr1895186847599665920list_b] : ( inj_on5222288482278673599xt_a_b @ produc4023874437082322608list_b @ A4 ) ).

% inj_swap
thf(fact_1251_inj__swap,axiom,
    ! [A4: set_Pr3872688570871424334xt_a_b] : ( inj_on3558359446568221091list_b @ produc4642366622444604286xt_a_b @ A4 ) ).

% inj_swap
thf(fact_1252_inj__on__inverseI,axiom,
    ! [A4: set_nat,G: nat > nat,F: nat > nat] :
      ( ! [X: nat] :
          ( ( member_nat @ X @ A4 )
         => ( ( G @ ( F @ X ) )
            = X ) )
     => ( inj_on_nat_nat @ F @ A4 ) ) ).

% inj_on_inverseI
thf(fact_1253_inj__on__contraD,axiom,
    ! [F: nat > nat,A4: set_nat,X2: nat,Y3: nat] :
      ( ( inj_on_nat_nat @ F @ A4 )
     => ( ( X2 != Y3 )
       => ( ( member_nat @ X2 @ A4 )
         => ( ( member_nat @ Y3 @ A4 )
           => ( ( F @ X2 )
             != ( F @ Y3 ) ) ) ) ) ) ).

% inj_on_contraD
thf(fact_1254_inj__on__eq__iff,axiom,
    ! [F: nat > nat,A4: set_nat,X2: nat,Y3: nat] :
      ( ( inj_on_nat_nat @ F @ A4 )
     => ( ( member_nat @ X2 @ A4 )
       => ( ( member_nat @ Y3 @ A4 )
         => ( ( ( F @ X2 )
              = ( F @ Y3 ) )
            = ( X2 = Y3 ) ) ) ) ) ).

% inj_on_eq_iff
thf(fact_1255_inj__on__cong,axiom,
    ! [A4: set_nat,F: nat > nat,G: nat > nat] :
      ( ! [A3: nat] :
          ( ( member_nat @ A3 @ A4 )
         => ( ( F @ A3 )
            = ( G @ A3 ) ) )
     => ( ( inj_on_nat_nat @ F @ A4 )
        = ( inj_on_nat_nat @ G @ A4 ) ) ) ).

% inj_on_cong
thf(fact_1256_inj__on__def,axiom,
    ( inj_on_nat_nat
    = ( ^ [F2: nat > nat,A6: set_nat] :
        ! [X3: nat] :
          ( ( member_nat @ X3 @ A6 )
         => ! [Y4: nat] :
              ( ( member_nat @ Y4 @ A6 )
             => ( ( ( F2 @ X3 )
                  = ( F2 @ Y4 ) )
               => ( X3 = Y4 ) ) ) ) ) ) ).

% inj_on_def
thf(fact_1257_inj__onI,axiom,
    ! [A4: set_nat,F: nat > nat] :
      ( ! [X: nat,Y: nat] :
          ( ( member_nat @ X @ A4 )
         => ( ( member_nat @ Y @ A4 )
           => ( ( ( F @ X )
                = ( F @ Y ) )
             => ( X = Y ) ) ) )
     => ( inj_on_nat_nat @ F @ A4 ) ) ).

% inj_onI
thf(fact_1258_inj__onD,axiom,
    ! [F: nat > nat,A4: set_nat,X2: nat,Y3: nat] :
      ( ( inj_on_nat_nat @ F @ A4 )
     => ( ( ( F @ X2 )
          = ( F @ Y3 ) )
       => ( ( member_nat @ X2 @ A4 )
         => ( ( member_nat @ Y3 @ A4 )
           => ( X2 = Y3 ) ) ) ) ) ).

% inj_onD
thf(fact_1259_inj__on__subset,axiom,
    ! [F: nat > nat,A4: set_nat,B5: set_nat] :
      ( ( inj_on_nat_nat @ F @ A4 )
     => ( ( ord_less_eq_set_nat @ B5 @ A4 )
       => ( inj_on_nat_nat @ F @ B5 ) ) ) ).

% inj_on_subset
thf(fact_1260_subset__inj__on,axiom,
    ! [F: nat > nat,B5: set_nat,A4: set_nat] :
      ( ( inj_on_nat_nat @ F @ B5 )
     => ( ( ord_less_eq_set_nat @ A4 @ B5 )
       => ( inj_on_nat_nat @ F @ A4 ) ) ) ).

% subset_inj_on
thf(fact_1261_inj__on__id,axiom,
    ! [A4: set_nat] : ( inj_on_nat_nat @ id_nat @ A4 ) ).

% inj_on_id
thf(fact_1262_map__prod__inj__on,axiom,
    ! [F: nat > nat,A4: set_nat,G: nat > nat,B5: set_nat] :
      ( ( inj_on_nat_nat @ F @ A4 )
     => ( ( inj_on_nat_nat @ G @ B5 )
       => ( inj_on8969904277767023793at_nat @ ( produc6977886695330630970at_nat @ F @ G )
          @ ( produc457027306803732586at_nat @ A4
            @ ^ [Uu: nat] : B5 ) ) ) ) ).

% map_prod_inj_on
thf(fact_1263_bdd__above_Ounfold,axiom,
    ( condit2214826472909112428ve_nat
    = ( ^ [A6: set_nat] :
        ? [M8: nat] :
        ! [X3: nat] :
          ( ( member_nat @ X3 @ A6 )
         => ( ord_less_eq_nat @ X3 @ M8 ) ) ) ) ).

% bdd_above.unfold
thf(fact_1264_bdd__above_OE,axiom,
    ! [A4: set_o] :
      ( ( condit5488710616941104124bove_o @ A4 )
     => ~ ! [M7: $o] :
            ~ ! [X6: $o] :
                ( ( member_o @ X6 @ A4 )
               => ( ord_less_eq_o @ X6 @ M7 ) ) ) ).

% bdd_above.E
thf(fact_1265_bdd__above_OE,axiom,
    ! [A4: set_nat] :
      ( ( condit2214826472909112428ve_nat @ A4 )
     => ~ ! [M7: nat] :
            ~ ! [X6: nat] :
                ( ( member_nat @ X6 @ A4 )
               => ( ord_less_eq_nat @ X6 @ M7 ) ) ) ).

% bdd_above.E
thf(fact_1266_inj__on__imageI2,axiom,
    ! [F3: nat > nat,F: nat > nat,A4: set_nat] :
      ( ( inj_on_nat_nat @ ( comp_nat_nat_nat @ F3 @ F ) @ A4 )
     => ( inj_on_nat_nat @ F @ A4 ) ) ).

% inj_on_imageI2
thf(fact_1267_inj__on__UNION__chain,axiom,
    ! [I4: set_o,A4: $o > set_nat,F: nat > nat] :
      ( ! [I3: $o,J2: $o] :
          ( ( member_o @ I3 @ I4 )
         => ( ( member_o @ J2 @ I4 )
           => ( ( ord_less_eq_set_nat @ ( A4 @ I3 ) @ ( A4 @ J2 ) )
              | ( ord_less_eq_set_nat @ ( A4 @ J2 ) @ ( A4 @ I3 ) ) ) ) )
     => ( ! [I3: $o] :
            ( ( member_o @ I3 @ I4 )
           => ( inj_on_nat_nat @ F @ ( A4 @ I3 ) ) )
       => ( inj_on_nat_nat @ F @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ A4 @ I4 ) ) ) ) ) ).

% inj_on_UNION_chain
thf(fact_1268_cSup__subset__mono,axiom,
    ! [A4: set_nat,B5: set_nat] :
      ( ( A4 != bot_bot_set_nat )
     => ( ( condit2214826472909112428ve_nat @ B5 )
       => ( ( ord_less_eq_set_nat @ A4 @ B5 )
         => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ A4 ) @ ( complete_Sup_Sup_nat @ B5 ) ) ) ) ) ).

% cSup_subset_mono
thf(fact_1269_cSup__subset__mono,axiom,
    ! [A4: set_o,B5: set_o] :
      ( ( A4 != bot_bot_set_o )
     => ( ( condit5488710616941104124bove_o @ B5 )
       => ( ( ord_less_eq_set_o @ A4 @ B5 )
         => ( ord_less_eq_o @ ( complete_Sup_Sup_o @ A4 ) @ ( complete_Sup_Sup_o @ B5 ) ) ) ) ) ).

% cSup_subset_mono
thf(fact_1270_bdd__above__image__mono,axiom,
    ! [F: nat > nat,A4: set_nat] :
      ( ( monotone_on_nat_nat @ top_top_set_nat @ ord_less_eq_nat @ ord_less_eq_nat @ F )
     => ( ( condit2214826472909112428ve_nat @ A4 )
       => ( condit2214826472909112428ve_nat @ ( image_nat_nat @ F @ A4 ) ) ) ) ).

% bdd_above_image_mono
thf(fact_1271_cSUP__subset__mono,axiom,
    ! [A4: set_o,G: $o > nat,B5: set_o,F: $o > nat] :
      ( ( A4 != bot_bot_set_o )
     => ( ( condit2214826472909112428ve_nat @ ( image_o_nat @ G @ B5 ) )
       => ( ( ord_less_eq_set_o @ A4 @ B5 )
         => ( ! [X: $o] :
                ( ( member_o @ X @ A4 )
               => ( ord_less_eq_nat @ ( F @ X ) @ ( G @ X ) ) )
           => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_o_nat @ F @ A4 ) ) @ ( complete_Sup_Sup_nat @ ( image_o_nat @ G @ B5 ) ) ) ) ) ) ) ).

% cSUP_subset_mono
thf(fact_1272_cSUP__subset__mono,axiom,
    ! [A4: set_o,G: $o > $o,B5: set_o,F: $o > $o] :
      ( ( A4 != bot_bot_set_o )
     => ( ( condit5488710616941104124bove_o @ ( image_o_o @ G @ B5 ) )
       => ( ( ord_less_eq_set_o @ A4 @ B5 )
         => ( ! [X: $o] :
                ( ( member_o @ X @ A4 )
               => ( ord_less_eq_o @ ( F @ X ) @ ( G @ X ) ) )
           => ( ord_less_eq_o @ ( complete_Sup_Sup_o @ ( image_o_o @ F @ A4 ) ) @ ( complete_Sup_Sup_o @ ( image_o_o @ G @ B5 ) ) ) ) ) ) ) ).

% cSUP_subset_mono

% Conjectures (1)
thf(conj_0,conjecture,
    ( ( multih3217256941434035760es_a_b @ ( produc5881749095783049980list_b @ ( multih5110136180555822405rs_a_b @ t ) ) )
    = ( size_size_list_b @ ( produc6107117247873403966list_b @ ( multih5110136180555822405rs_a_b @ t ) ) ) ) ).

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