%------------------------------------------------------------------------------
% 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    : Query_Optimization/0009_Dtree/prob_00887_037472__15082898_1 [Des23]

% Status   : Theorem
% Rating   : ? v8.2.0
% Syntax   : Number of formulae    : 1834 ( 657 unt; 556 typ;   0 def)
%            Number of atoms       : 3054 (1692 equ;   0 cnn)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives : 10291 ( 338   ~;  13   |; 102   &;8554   @)
%                                         (   0 <=>;1284  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   6 avg)
%            Number of types       :   64 (  63 usr)
%            Number of type conns  : 4701 (4701   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  494 ( 493 usr;  46 con; 0-6 aty)
%            Number of variables   : 4000 ( 198   ^;3700   !; 102   ?;4000   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2023-01-18 16:06:18.612
%------------------------------------------------------------------------------
% Could-be-implicit typings (63)
thf(ty_n_t__Product____Type__Oprod_It__Pair____Digraph__Opair____pre____digraph__Opair____pre____digraph____ext_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    produc7079444246281463442_a_b_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Pair____Digraph__Opair____pre____digraph__Opair____pre____digraph____ext_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_Mt__Product____Type__Ounit_J_J,type,
    produc2042437161806511672t_unit: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    produc6870677010558023550_a_b_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    set_Pr2755428042910921141_a_b_b: $tType ).

thf(ty_n_t__Pair____Digraph__Opair____pre____digraph__Opair____pre____digraph____ext_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Ounit_J,type,
    pair_p3556638718232885427t_unit: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    produc8908337785154950741_a_b_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_J_J,type,
    set_Pr3091785439476234199t_unit: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_Mt__Product____Type__Ounit_J,type,
    produc6596653366452172941t_unit: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_J,type,
    produc1562073732673760929t_unit: $tType ).

thf(ty_n_t__Pair____Digraph__Opair____pre____digraph__Opair____pre____digraph____ext_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
    pair_p7583798195187013628t_unit: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Ounit_J_Mt__Product____Type__Ounit_J_J,type,
    set_Pr1227941911400795239t_unit: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Set__Oset_It__Product____Type__Ounit_J_J_J,type,
    set_Pr217763282141584935t_unit: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mtf__b_J,type,
    produc6708371838016462714_b_b_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mtf__a_J,type,
    produc6708371833713233913_b_b_a: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    set_se3183138701204633190_a_b_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_J,type,
    set_Pr5094982260447487303t_unit: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Ounit_J_Mt__Product____Type__Ounit_J,type,
    produc9013008050180029063t_unit: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Set__Oset_It__Product____Type__Ounit_J_J,type,
    produc4787451486076709959t_unit: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    produc5177672665255943253ee_a_b: $tType ).

thf(ty_n_t__FSet__Ofset_It__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_J,type,
    fset_S6328958348615259029t_unit: $tType ).

thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_J,type,
    set_Su4110612849109743515t_unit: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_M_062_Itf__b_Mtf__a_J_J_J,type,
    set_Pr7494330017871143702it_b_a: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J_J,type,
    set_Pr5619283252532241417_a_b_a: $tType ).

thf(ty_n_t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    fset_P5281107635120001194_a_b_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_J,type,
    set_Pr6717515126349854430ee_a_b: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    set_Pr3012420139608375472_a_b_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_M_062_Itf__b_Mtf__a_J_J,type,
    produc1083523234014712191_b_b_a: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
    produc8459935480633519975t_unit: $tType ).

thf(ty_n_t__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
    sum_su8719719018421925477t_unit: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Ounit_M_062_Itf__b_Mtf__a_J_J,type,
    produc5776317634898194272it_b_a: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J,type,
    product_prod_b_a_b_a: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    produc3469756349985706280ee_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    produc4558475209616630778_a_b_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__a_J,type,
    produc4558475205313401977_a_b_a: $tType ).

thf(ty_n_t__Set__Oset_I_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J_J,type,
    set_b_a_b_a: $tType ).

thf(ty_n_t__FSet__Ofset_It__Set__Oset_It__Product____Type__Ounit_J_J,type,
    fset_s2847261894197522515t_unit: $tType ).

thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Ounit_J_J,type,
    set_set_Product_unit: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_Itf__b_Mtf__a_J_Mtf__b_J,type,
    product_prod_b_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_I_062_Itf__b_Mtf__a_J_Mtf__a_J,type,
    product_prod_b_a_a: $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__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    set_dtree_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b_Mt__Nat__Onat_J,type,
    product_prod_b_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a_Mt__Nat__Onat_J,type,
    product_prod_a_nat: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mtf__b_J,type,
    product_prod_nat_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mtf__a_J,type,
    product_prod_nat_a: $tType ).

thf(ty_n_t__FSet__Ofset_It__Product____Type__Ounit_J,type,
    fset_Product_unit: $tType ).

thf(ty_n_t__Set__Oset_It__Product____Type__Ounit_J,type,
    set_Product_unit: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b_Mtf__b_J,type,
    product_prod_b_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__b_Mtf__a_J,type,
    product_prod_b_a: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    product_prod_a_b: $tType ).

thf(ty_n_t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
    product_prod_a_a: $tType ).

thf(ty_n_t__Set__Oset_I_062_Itf__b_Mtf__a_J_J,type,
    set_b_a: $tType ).

thf(ty_n_t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    dtree_a_b: $tType ).

thf(ty_n_t__FSet__Ofset_It__Nat__Onat_J,type,
    fset_nat: $tType ).

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

thf(ty_n_t__Product____Type__Ounit,type,
    product_unit: $tType ).

thf(ty_n_t__FSet__Ofset_Itf__b_J,type,
    fset_b: $tType ).

thf(ty_n_t__FSet__Ofset_Itf__a_J,type,
    fset_a: $tType ).

thf(ty_n_t__Set__Oset_Itf__b_J,type,
    set_b: $tType ).

thf(ty_n_t__Set__Oset_Itf__a_J,type,
    set_a: $tType ).

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

thf(ty_n_tf__b,type,
    b: $tType ).

thf(ty_n_tf__a,type,
    a: $tType ).

% Explicit typings (493)
thf(sy_c_BNF__Def_OGr_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    bNF_Gr_dtree_a_b_b: set_dtree_a_b > ( dtree_a_b > b ) > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_BNF__Def_OGrp_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    bNF_Grp_dtree_a_b_b: set_dtree_a_b > ( dtree_a_b > b ) > dtree_a_b > b > $o ).

thf(sy_c_BNF__Def_OGrp_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
    bNF_Gr2512511087679822862t_unit: set_Product_unit > ( product_unit > product_unit ) > product_unit > product_unit > $o ).

thf(sy_c_BNF__Def_Oconvol_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J,type,
    bNF_co7059620845615007703_a_b_a: ( ( b > a ) > b > a ) > ( ( b > a ) > b > a ) > ( b > a ) > product_prod_b_a_b_a ).

thf(sy_c_BNF__Def_Oconvol_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    bNF_co684571163256649440_a_b_b: ( dtree_a_b > dtree_a_b ) > ( dtree_a_b > b ) > dtree_a_b > produc4558475209616630778_a_b_b ).

thf(sy_c_BNF__Def_OfstOp_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b_001tf__b,type,
    bNF_fs7198647118416170860_b_b_b: ( dtree_a_b > b > $o ) > ( b > b > $o ) > produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b ).

thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J_001_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J_001_062_I_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J_M_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J_J_001_062_I_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J_M_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J_J,type,
    bNF_re1473080822477210889_a_b_a: ( ( ( b > a ) > b > a ) > ( ( b > a ) > b > a ) > $o ) > ( ( ( ( b > a ) > b > a ) > ( b > a ) > b > a ) > ( ( ( b > a ) > b > a ) > ( b > a ) > b > a ) > $o ) > ( ( ( b > a ) > b > a ) > ( ( b > a ) > b > a ) > ( b > a ) > b > a ) > ( ( ( b > a ) > b > a ) > ( ( b > a ) > b > a ) > ( b > a ) > b > a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J_001_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J_001_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J_001_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J,type,
    bNF_re5527643775196010493_a_b_a: ( ( ( b > a ) > b > a ) > ( ( b > a ) > b > a ) > $o ) > ( ( ( b > a ) > b > a ) > ( ( b > a ) > b > a ) > $o ) > ( ( ( b > a ) > b > a ) > ( b > a ) > b > a ) > ( ( ( b > a ) > b > a ) > ( b > a ) > b > a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J,type,
    bNF_re7432613075280381681_a_b_a: ( ( b > a ) > ( b > a ) > $o ) > ( ( b > a ) > ( b > a ) > $o ) > ( ( b > a ) > b > a ) > ( ( b > a ) > b > a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    bNF_re1768220791201799059_a_b_b: ( product_unit > product_unit > $o ) > ( produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b > $o ) > ( product_unit > produc4558475209616630778_a_b_b ) > ( product_unit > produc4558475209616630778_a_b_b ) > $o ).

thf(sy_c_BNF__Def_OsndOp_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    bNF_sn6078974312152453525_a_b_b: ( dtree_a_b > dtree_a_b > $o ) > ( dtree_a_b > b > $o ) > produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b ).

thf(sy_c_BNF__Def_Ovimage2p_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J_001tf__b_001tf__b_001tf__a,type,
    bNF_vi9050661367211962233_b_b_a: ( ( b > a ) > b > a ) > ( b > b ) > ( ( b > a ) > b > a ) > ( b > a ) > b > a ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Nat__Onat_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    bNF_Gr8387754577466859481_a_b_b: set_nat > ( nat > dtree_a_b ) > ( nat > b ) > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Nat__Onat_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
    bNF_Gr8877520075124390378t_unit: set_nat > ( nat > product_unit ) > ( nat > product_unit ) > set_Pr5094982260447487303t_unit ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Nat__Onat_001tf__b_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    bNF_Gr2375466951317659983ee_a_b: set_nat > ( nat > b ) > ( nat > dtree_a_b ) > set_Pr6717515126349854430ee_a_b ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    bNF_Gr3881854498152092719_a_b_b: set_Pr3012420139608375472_a_b_b > ( produc4558475209616630778_a_b_b > dtree_a_b ) > ( produc4558475209616630778_a_b_b > b ) > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001tf__a_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    bNF_Gr5315966842453093087_a_b_b: set_a > ( a > dtree_a_b ) > ( a > b ) > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001tf__a_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
    bNF_Gr5172770309810061924t_unit: set_a > ( a > product_unit ) > ( a > product_unit ) > set_Pr5094982260447487303t_unit ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001tf__a_001tf__b_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    bNF_Gr8527051253158669397ee_a_b: set_a > ( a > b ) > ( a > dtree_a_b ) > set_Pr6717515126349854430ee_a_b ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001tf__b_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    bNF_Gr4676526542121276958_a_b_b: set_b > ( b > dtree_a_b ) > ( b > b ) > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001tf__b_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
    bNF_Gr2538028588435227621t_unit: set_b > ( b > product_unit ) > ( b > product_unit ) > set_Pr5094982260447487303t_unit ).

thf(sy_c_BNF__Greatest__Fixpoint_Oimage2_001tf__b_001tf__b_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    bNF_Gr7887610952826853268ee_a_b: set_b > ( b > b ) > ( b > dtree_a_b ) > set_Pr6717515126349854430ee_a_b ).

thf(sy_c_Basic__BNFs_Ofsts_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J,type,
    basic_fsts_b_a_b_a: product_prod_b_a_b_a > set_b_a ).

thf(sy_c_Basic__BNFs_Ofsts_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    basic_7578771248400840636_a_b_b: produc4558475209616630778_a_b_b > set_dtree_a_b ).

thf(sy_c_Basic__BNFs_Ofsts_001t__Nat__Onat_001t__Nat__Onat,type,
    basic_fsts_nat_nat: product_prod_nat_nat > set_nat ).

thf(sy_c_Basic__BNFs_Ofsts_001t__Nat__Onat_001tf__a,type,
    basic_fsts_nat_a: product_prod_nat_a > set_nat ).

thf(sy_c_Basic__BNFs_Ofsts_001t__Nat__Onat_001tf__b,type,
    basic_fsts_nat_b: product_prod_nat_b > set_nat ).

thf(sy_c_Basic__BNFs_Ofsts_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    basic_7126344468061175165_a_b_b: produc8908337785154950741_a_b_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Basic__BNFs_Ofsts_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
    basic_788101489561936839t_unit: produc8459935480633519975t_unit > set_Product_unit ).

thf(sy_c_Basic__BNFs_Ofsts_001tf__a_001t__Nat__Onat,type,
    basic_fsts_a_nat: product_prod_a_nat > set_a ).

thf(sy_c_Basic__BNFs_Ofsts_001tf__a_001tf__a,type,
    basic_fsts_a_a: product_prod_a_a > set_a ).

thf(sy_c_Basic__BNFs_Ofsts_001tf__a_001tf__b,type,
    basic_fsts_a_b: product_prod_a_b > set_a ).

thf(sy_c_Basic__BNFs_Ofsts_001tf__b_001t__Nat__Onat,type,
    basic_fsts_b_nat: product_prod_b_nat > set_b ).

thf(sy_c_Basic__BNFs_Ofsts_001tf__b_001tf__a,type,
    basic_fsts_b_a: product_prod_b_a > set_b ).

thf(sy_c_Basic__BNFs_Ofsts_001tf__b_001tf__b,type,
    basic_fsts_b_b: product_prod_b_b > set_b ).

thf(sy_c_Basic__BNFs_Osnds_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J,type,
    basic_snds_b_a_b_a: product_prod_b_a_b_a > set_b_a ).

thf(sy_c_Basic__BNFs_Osnds_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    basic_1877077703026942_a_b_b: produc4558475209616630778_a_b_b > set_b ).

thf(sy_c_Basic__BNFs_Osnds_001t__Nat__Onat_001t__Nat__Onat,type,
    basic_snds_nat_nat: product_prod_nat_nat > set_nat ).

thf(sy_c_Basic__BNFs_Osnds_001t__Nat__Onat_001tf__a,type,
    basic_snds_nat_a: product_prod_nat_a > set_a ).

thf(sy_c_Basic__BNFs_Osnds_001t__Nat__Onat_001tf__b,type,
    basic_snds_nat_b: product_prod_nat_b > set_b ).

thf(sy_c_Basic__BNFs_Osnds_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    basic_3365347479418424763_a_b_b: produc8908337785154950741_a_b_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Basic__BNFs_Osnds_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
    basic_1454403626444245253t_unit: produc8459935480633519975t_unit > set_Product_unit ).

thf(sy_c_Basic__BNFs_Osnds_001tf__a_001t__Nat__Onat,type,
    basic_snds_a_nat: product_prod_a_nat > set_nat ).

thf(sy_c_Basic__BNFs_Osnds_001tf__a_001tf__a,type,
    basic_snds_a_a: product_prod_a_a > set_a ).

thf(sy_c_Basic__BNFs_Osnds_001tf__a_001tf__b,type,
    basic_snds_a_b: product_prod_a_b > set_b ).

thf(sy_c_Basic__BNFs_Osnds_001tf__b_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    basic_3212961488408603252ee_a_b: produc3469756349985706280ee_a_b > set_dtree_a_b ).

thf(sy_c_Basic__BNFs_Osnds_001tf__b_001t__Nat__Onat,type,
    basic_snds_b_nat: product_prod_b_nat > set_nat ).

thf(sy_c_Basic__BNFs_Osnds_001tf__b_001tf__a,type,
    basic_snds_b_a: product_prod_b_a > set_a ).

thf(sy_c_Basic__BNFs_Osnds_001tf__b_001tf__b,type,
    basic_snds_b_b: product_prod_b_b > set_b ).

thf(sy_c_Dtree_Odtree_ONode_001tf__a_001tf__b,type,
    node_a_b: a > fset_P5281107635120001194_a_b_b > dtree_a_b ).

thf(sy_c_Dtree_Odtree_Odarcs_001tf__a_001tf__b,type,
    darcs_a_b: dtree_a_b > set_b ).

thf(sy_c_Dtree_Odtree_Odverts_001tf__a_001tf__b,type,
    dverts_a_b: dtree_a_b > set_a ).

thf(sy_c_Dtree_Odtree_Oroot_001tf__a_001tf__b,type,
    root_a_b: dtree_a_b > a ).

thf(sy_c_Dtree_Odtree_Osucs_001tf__a_001tf__b,type,
    sucs_a_b: dtree_a_b > fset_P5281107635120001194_a_b_b ).

thf(sy_c_Dtree_Owf__darcs_001tf__a_001tf__b,type,
    wf_darcs_a_b: dtree_a_b > $o ).

thf(sy_c_Dtree_Owf__dverts_001tf__a_001tf__b,type,
    wf_dverts_a_b: dtree_a_b > $o ).

thf(sy_c_FSet_Ofcard_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    fcard_7238254820230435945_a_b_b: fset_P5281107635120001194_a_b_b > nat ).

thf(sy_c_FSet_Ofcard_001t__Product____Type__Ounit,type,
    fcard_Product_unit: fset_Product_unit > nat ).

thf(sy_c_FSet_Offilter_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    ffilte5856148450850080273_a_b_b: ( produc4558475209616630778_a_b_b > $o ) > fset_P5281107635120001194_a_b_b > fset_P5281107635120001194_a_b_b ).

thf(sy_c_FSet_Ofinsert_001t__Nat__Onat,type,
    finsert_nat: nat > fset_nat > fset_nat ).

thf(sy_c_FSet_Ofinsert_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    finser8437519239679886002_a_b_b: produc4558475209616630778_a_b_b > fset_P5281107635120001194_a_b_b > fset_P5281107635120001194_a_b_b ).

thf(sy_c_FSet_Ofmember_001t__Nat__Onat,type,
    fmember_nat: nat > fset_nat > $o ).

thf(sy_c_FSet_Ofmember_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    fmembe3173364709796808819_a_b_b: produc4558475209616630778_a_b_b > fset_P5281107635120001194_a_b_b > $o ).

thf(sy_c_FSet_Ofset_Ofset_001t__Nat__Onat,type,
    fset_nat2: fset_nat > set_nat ).

thf(sy_c_FSet_Ofset_Ofset_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    fset_P783253628892185035_a_b_b: fset_P5281107635120001194_a_b_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_FSet_Ofset_Ofset_001t__Product____Type__Ounit,type,
    fset_Product_unit2: fset_Product_unit > set_Product_unit ).

thf(sy_c_FSet_Ofset_Ofset_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    fset_s6820437950863159900t_unit: fset_s2847261894197522515t_unit > set_set_Product_unit ).

thf(sy_c_FSet_Ofset_Ofset_001t__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
    fset_S3230643823001711158t_unit: fset_S6328958348615259029t_unit > set_Su4110612849109743515t_unit ).

thf(sy_c_FSet_Ofset_Ofset_001tf__a,type,
    fset_a2: fset_a > set_a ).

thf(sy_c_FSet_Ofset_Ofset_001tf__b,type,
    fset_b2: fset_b > set_b ).

thf(sy_c_FSet_Ofthe__elem_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    fthe_e7442499522476018237_a_b_b: fset_P5281107635120001194_a_b_b > produc4558475209616630778_a_b_b ).

thf(sy_c_FSet_Olinorder__class_OfMax_001t__Nat__Onat,type,
    linorder_fMax_nat: fset_nat > nat ).

thf(sy_c_FSet_Olinorder__class_OfMin_001t__Nat__Onat,type,
    linorder_fMin_nat: fset_nat > nat ).

thf(sy_c_Finite__Set_Ocard_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    finite2954864170529017298_a_b_b: set_Pr3012420139608375472_a_b_b > nat ).

thf(sy_c_Finite__Set_Ocard_001t__Product____Type__Ounit,type,
    finite410649719033368117t_unit: set_Product_unit > nat ).

thf(sy_c_Finite__Set_Ocomp__fun__commute__on_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001_062_Itf__b_Mtf__a_J,type,
    finite6564071228819977072_b_b_a: set_Pr3012420139608375472_a_b_b > ( produc4558475209616630778_a_b_b > ( b > a ) > b > a ) > $o ).

thf(sy_c_Finite__Set_Ocomp__fun__idem__on_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001_062_Itf__b_Mtf__a_J,type,
    finite582340075173961963_b_b_a: set_Pr3012420139608375472_a_b_b > ( produc4558475209616630778_a_b_b > ( b > a ) > b > a ) > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Nat__Onat,type,
    finite_finite_nat: set_nat > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    finite9145440207725541265_a_b_b: set_Pr3012420139608375472_a_b_b > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
    finite6816719414181127824t_unit: set_Pr5094982260447487303t_unit > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Ounit,type,
    finite4290736615968046902t_unit: set_Product_unit > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    finite1772178364199683094t_unit: set_set_Product_unit > $o ).

thf(sy_c_Finite__Set_Ofinite_001t__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
    finite3146551501593861116t_unit: set_Su4110612849109743515t_unit > $o ).

thf(sy_c_Fun_Ocomp_001_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J_001_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J_001_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J,type,
    comp_b3327941365615541530_a_b_a: ( ( ( b > a ) > b > a ) > ( b > a ) > b > a ) > ( ( ( b > a ) > b > a ) > ( b > a ) > b > a ) > ( ( b > a ) > b > a ) > ( b > a ) > b > a ).

thf(sy_c_Fun_Ocomp_001_062_I_062_Itf__b_Mtf__a_J_Mtf__a_J_001_062_I_062_Itf__b_Mtf__a_J_Mtf__a_J_001_062_I_062_Itf__b_Mtf__a_J_Mtf__a_J,type,
    comp_b1199615493944247470_b_a_a: ( ( ( b > a ) > a ) > ( b > a ) > a ) > ( ( ( b > a ) > a ) > ( b > a ) > a ) > ( ( b > a ) > a ) > ( b > a ) > a ).

thf(sy_c_Fun_Ocomp_001_062_I_062_Itf__b_Mtf__a_J_Mtf__b_J_001_062_I_062_Itf__b_Mtf__a_J_Mtf__b_J_001_062_I_062_Itf__b_Mtf__a_J_Mtf__b_J,type,
    comp_b1089415012269902447_b_a_b: ( ( ( b > a ) > b ) > ( b > a ) > b ) > ( ( ( b > a ) > b ) > ( b > a ) > b ) > ( ( b > a ) > b ) > ( b > a ) > b ).

thf(sy_c_Fun_Ocomp_001_062_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__a_J_001_062_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mtf__a_J_001_062_Itf__b_Mtf__a_J,type,
    comp_d7906738509105912391_a_b_a: ( ( dtree_a_b > a ) > produc4558475209616630778_a_b_b > a ) > ( ( b > a ) > dtree_a_b > a ) > ( b > a ) > produc4558475209616630778_a_b_b > a ).

thf(sy_c_Fun_Ocomp_001_062_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001_062_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mtf__b_J_001_062_Itf__b_Mtf__b_J,type,
    comp_d3764564436183338888_b_b_b: ( ( dtree_a_b > b ) > produc4558475209616630778_a_b_b > b ) > ( ( b > b ) > dtree_a_b > b ) > ( b > b ) > produc4558475209616630778_a_b_b > b ).

thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_M_Eo_J_001_062_It__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_M_Eo_J_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    comp_s7925026818889343833_a_b_b: ( ( set_Pr3012420139608375472_a_b_b > $o ) > fset_P5281107635120001194_a_b_b > $o ) > ( set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b > $o ) > set_Pr3012420139608375472_a_b_b > fset_P5281107635120001194_a_b_b > $o ).

thf(sy_c_Fun_Ocomp_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__a_J_001_062_Itf__a_Mtf__a_J,type,
    comp_a_a_a_a_a_a: ( ( a > a ) > a > a ) > ( ( a > a ) > a > a ) > ( a > a ) > a > a ).

thf(sy_c_Fun_Ocomp_001_062_Itf__a_Mtf__b_J_001_062_Itf__a_Mtf__b_J_001_062_Itf__a_Mtf__b_J,type,
    comp_a_b_a_b_a_b: ( ( a > b ) > a > b ) > ( ( a > b ) > a > b ) > ( a > b ) > a > b ).

thf(sy_c_Fun_Ocomp_001_062_Itf__b_M_062_Itf__b_Mtf__a_J_J_001_062_Itf__b_M_062_Itf__b_Mtf__a_J_J_001_062_Itf__b_M_062_Itf__b_Mtf__a_J_J,type,
    comp_b164129730918660337_b_b_a: ( ( b > b > a ) > b > b > a ) > ( ( b > b > a ) > b > b > a ) > ( b > b > a ) > b > b > a ).

thf(sy_c_Fun_Ocomp_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J,type,
    comp_b_a_b_a_b_a: ( ( b > a ) > b > a ) > ( ( b > a ) > b > a ) > ( b > a ) > b > a ).

thf(sy_c_Fun_Ocomp_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J_001t__Product____Type__Oprod_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J,type,
    comp_b1410776826426344764_a_b_a: ( ( b > a ) > b > a ) > ( product_prod_b_a_b_a > b > a ) > product_prod_b_a_b_a > b > a ).

thf(sy_c_Fun_Ocomp_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J_001t__Product____Type__Ounit,type,
    comp_b4751574389558959904t_unit: ( ( b > a ) > b > a ) > ( product_unit > b > a ) > product_unit > b > a ).

thf(sy_c_Fun_Ocomp_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    comp_b485742637902756864t_unit: ( ( b > a ) > b > a ) > ( set_Product_unit > b > a ) > set_Product_unit > b > a ).

thf(sy_c_Fun_Ocomp_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J_001t__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
    comp_b1962440982679487378t_unit: ( ( b > a ) > b > a ) > ( sum_su8719719018421925477t_unit > b > a ) > sum_su8719719018421925477t_unit > b > a ).

thf(sy_c_Fun_Ocomp_001_062_Itf__b_Mtf__a_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001_062_Itf__b_Mtf__a_J,type,
    comp_b3254671105061676455_b_b_a: ( ( b > a ) > dtree_a_b ) > ( ( b > a ) > b > a ) > ( b > a ) > dtree_a_b ).

thf(sy_c_Fun_Ocomp_001_062_Itf__b_Mtf__a_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    comp_b3926150692603505917_a_b_b: ( ( b > a ) > dtree_a_b ) > ( produc4558475209616630778_a_b_b > b > a ) > produc4558475209616630778_a_b_b > dtree_a_b ).

thf(sy_c_Fun_Ocomp_001_062_Itf__b_Mtf__a_J_001t__Product____Type__Oprod_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J_001_062_Itf__b_Mtf__a_J,type,
    comp_b7652884982158753286_a_b_a: ( ( b > a ) > product_prod_b_a_b_a ) > ( ( b > a ) > b > a ) > ( b > a ) > product_prod_b_a_b_a ).

thf(sy_c_Fun_Ocomp_001_062_Itf__b_Mtf__b_J_001_062_Itf__b_Mtf__b_J_001_062_Itf__b_Mtf__b_J,type,
    comp_b_b_b_b_b_b: ( ( b > b ) > b > b ) > ( ( b > b ) > b > b ) > ( b > b ) > b > b ).

thf(sy_c_Fun_Ocomp_001_Eo_001_Eo_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    comp_o3567036564971088019_a_b_b: ( $o > $o ) > ( set_Pr3012420139608375472_a_b_b > $o ) > set_Pr3012420139608375472_a_b_b > $o ).

thf(sy_c_Fun_Ocomp_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J,type,
    comp_d4284745388203020455_a_b_a: ( dtree_a_b > b > a ) > ( ( b > a ) > dtree_a_b ) > ( b > a ) > b > a ).

thf(sy_c_Fun_Ocomp_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001_062_Itf__b_Mtf__a_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    comp_d2537776500735531005_a_b_b: ( dtree_a_b > b > a ) > ( produc4558475209616630778_a_b_b > dtree_a_b ) > produc4558475209616630778_a_b_b > b > a ).

thf(sy_c_Fun_Ocomp_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    comp_d9193377603055859667_a_b_b: ( dtree_a_b > dtree_a_b ) > ( produc4558475209616630778_a_b_b > dtree_a_b ) > produc4558475209616630778_a_b_b > dtree_a_b ).

thf(sy_c_Fun_Ocomp_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_Itf__b_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    comp_d8104658743424935169ee_a_b: ( dtree_a_b > dtree_a_b ) > ( produc3469756349985706280ee_a_b > dtree_a_b ) > produc3469756349985706280ee_a_b > dtree_a_b ).

thf(sy_c_Fun_Ocomp_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_Itf__b_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    comp_d4253798619470020737_a_b_b: ( dtree_a_b > produc3469756349985706280ee_a_b ) > ( produc4558475209616630778_a_b_b > dtree_a_b ) > produc4558475209616630778_a_b_b > produc3469756349985706280ee_a_b ).

thf(sy_c_Fun_Ocomp_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    comp_d2161864785492113116ee_a_b: ( dtree_a_b > b ) > ( dtree_a_b > dtree_a_b ) > dtree_a_b > b ).

thf(sy_c_Fun_Ocomp_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    comp_d7292648224603294300_a_b_b: ( dtree_a_b > b ) > ( produc4558475209616630778_a_b_b > dtree_a_b ) > produc4558475209616630778_a_b_b > b ).

thf(sy_c_Fun_Ocomp_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b_001t__Product____Type__Oprod_Itf__b_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    comp_d6203929364972369802ee_a_b: ( dtree_a_b > b ) > ( produc3469756349985706280ee_a_b > dtree_a_b ) > produc3469756349985706280ee_a_b > b ).

thf(sy_c_Fun_Ocomp_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b_001tf__b,type,
    comp_dtree_a_b_b_b: ( dtree_a_b > b ) > ( b > dtree_a_b ) > b > b ).

thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Ounit,type,
    comp_n7656859423886344392t_unit: ( nat > nat ) > ( product_unit > nat ) > product_unit > nat ).

thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    comp_n162390648425316405_a_b_b: ( nat > nat ) > ( set_Pr3012420139608375472_a_b_b > nat ) > set_Pr3012420139608375472_a_b_b > nat ).

thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    comp_n1322525831489224104t_unit: ( nat > nat ) > ( set_Product_unit > nat ) > set_Product_unit > nat ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J,type,
    comp_P1653000078598994640_a_b_a: ( product_prod_b_a_b_a > b > a ) > ( ( b > a ) > product_prod_b_a_b_a ) > ( b > a ) > b > a ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J_001_062_Itf__b_Mtf__a_J_001t__Product____Type__Oprod_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J,type,
    comp_P8787221310571768189_a_b_a: ( product_prod_b_a_b_a > b > a ) > ( product_prod_b_a_b_a > product_prod_b_a_b_a ) > product_prod_b_a_b_a > b > a ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J_001t__Product____Type__Oprod_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J_001_062_Itf__b_Mtf__a_J,type,
    comp_P5805957429449400903_a_b_a: ( product_prod_b_a_b_a > product_prod_b_a_b_a ) > ( ( b > a ) > product_prod_b_a_b_a ) > ( b > a ) > product_prod_b_a_b_a ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J_001t__Product____Type__Oprod_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J_001t__Product____Type__Oprod_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J,type,
    comp_P929014663317004102_a_b_a: ( product_prod_b_a_b_a > product_prod_b_a_b_a ) > ( product_prod_b_a_b_a > product_prod_b_a_b_a ) > product_prod_b_a_b_a > product_prod_b_a_b_a ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_Itf__b_Mtf__a_J_Mtf__a_J_001t__Product____Type__Oprod_I_062_Itf__b_Mtf__a_J_Mtf__a_J_001t__Product____Type__Oprod_I_062_Itf__b_Mtf__a_J_Mtf__a_J,type,
    comp_P3579555031557280850_b_a_a: ( product_prod_b_a_a > product_prod_b_a_a ) > ( product_prod_b_a_a > product_prod_b_a_a ) > product_prod_b_a_a > product_prod_b_a_a ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_Itf__b_Mtf__a_J_Mtf__b_J_001t__Product____Type__Oprod_I_062_Itf__b_Mtf__a_J_Mtf__b_J_001t__Product____Type__Oprod_I_062_Itf__b_Mtf__a_J_Mtf__b_J,type,
    comp_P6265908536931808725_b_a_b: ( product_prod_b_a_b > product_prod_b_a_b ) > ( product_prod_b_a_b > product_prod_b_a_b ) > product_prod_b_a_b > product_prod_b_a_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__a_J_001t__Product____Type__Oprod_Itf__b_Mtf__a_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mtf__a_J,type,
    comp_P3369791497561358467_b_b_a: ( produc4558475205313401977_a_b_a > product_prod_b_a ) > ( produc6708371833713233913_b_b_a > produc4558475205313401977_a_b_a ) > produc6708371833713233913_b_b_a > product_prod_b_a ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J,type,
    comp_P5371444601569245991_a_b_a: ( produc4558475209616630778_a_b_b > b > a ) > ( ( b > a ) > produc4558475209616630778_a_b_b ) > ( b > a ) > b > a ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001_062_Itf__b_Mtf__a_J_001t__Product____Type__Oprod_Itf__b_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    comp_P7262450972268490667ee_a_b: ( produc4558475209616630778_a_b_b > b > a ) > ( produc3469756349985706280ee_a_b > produc4558475209616630778_a_b_b ) > produc3469756349985706280ee_a_b > b > a ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    comp_P2227990766219928147_a_b_b: ( produc4558475209616630778_a_b_b > dtree_a_b ) > ( produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b ) > produc4558475209616630778_a_b_b > dtree_a_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_Itf__b_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    comp_P1139271906589003649ee_a_b: ( produc4558475209616630778_a_b_b > dtree_a_b ) > ( produc3469756349985706280ee_a_b > produc4558475209616630778_a_b_b ) > produc3469756349985706280ee_a_b > dtree_a_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Ounit,type,
    comp_P7962621636793085684t_unit: ( produc4558475209616630778_a_b_b > dtree_a_b ) > ( product_unit > produc4558475209616630778_a_b_b ) > product_unit > dtree_a_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    comp_P338726295243193300t_unit: ( produc4558475209616630778_a_b_b > dtree_a_b ) > ( set_Product_unit > produc4558475209616630778_a_b_b ) > set_Product_unit > dtree_a_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    comp_P2960064163185208038_a_b_b: ( produc4558475209616630778_a_b_b > dtree_a_b ) > ( b > produc4558475209616630778_a_b_b ) > b > dtree_a_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    comp_P3357003996968799036_a_b_b: ( produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b ) > ( produc8908337785154950741_a_b_b > produc4558475209616630778_a_b_b ) > produc8908337785154950741_a_b_b > produc4558475209616630778_a_b_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Ounit,type,
    comp_P7633254161849120628t_unit: ( produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b ) > ( product_unit > produc4558475209616630778_a_b_b ) > product_unit > produc4558475209616630778_a_b_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_Itf__b_Mtf__b_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mtf__b_J,type,
    comp_P2381262878637464388_b_b_b: ( produc4558475209616630778_a_b_b > product_prod_b_b ) > ( produc6708371838016462714_b_b_b > produc4558475209616630778_a_b_b ) > produc6708371838016462714_b_b_b > product_prod_b_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001tf__b_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    comp_P7790946621747331036_a_b_b: ( produc4558475209616630778_a_b_b > b ) > ( produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b ) > produc4558475209616630778_a_b_b > b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001tf__b_001t__Product____Type__Oprod_Itf__b_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    comp_P6702227762116406538ee_a_b: ( produc4558475209616630778_a_b_b > b ) > ( produc3469756349985706280ee_a_b > produc4558475209616630778_a_b_b ) > produc3469756349985706280ee_a_b > b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001tf__b_001tf__b,type,
    comp_P1056441264483508125_b_b_b: ( produc4558475209616630778_a_b_b > b ) > ( b > produc4558475209616630778_a_b_b ) > b > b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    comp_P681776842046273447_a_b_b: ( produc8908337785154950741_a_b_b > produc4558475209616630778_a_b_b ) > ( produc8908337785154950741_a_b_b > produc8908337785154950741_a_b_b ) > produc8908337785154950741_a_b_b > produc4558475209616630778_a_b_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
    comp_P8863678191571823620t_unit: ( produc8459935480633519975t_unit > produc8459935480633519975t_unit ) > ( produc8459935480633519975t_unit > produc8459935480633519975t_unit ) > produc8459935480633519975t_unit > produc8459935480633519975t_unit ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_001t__Product____Type__Ounit_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
    comp_P6212367879010262750t_unit: ( produc8459935480633519975t_unit > product_unit ) > ( produc8459935480633519975t_unit > produc8459935480633519975t_unit ) > produc8459935480633519975t_unit > product_unit ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__a_Mtf__a_J_001t__Product____Type__Oprod_Itf__a_Mtf__a_J_001t__Product____Type__Oprod_Itf__a_Mtf__a_J,type,
    comp_P1279500999426142148od_a_a: ( product_prod_a_a > product_prod_a_a ) > ( product_prod_a_a > product_prod_a_a ) > product_prod_a_a > product_prod_a_a ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_Itf__a_Mtf__b_J,type,
    comp_P2392903256394990597od_a_b: ( product_prod_a_b > product_prod_a_b ) > ( product_prod_a_b > product_prod_a_b ) > product_prod_a_b > product_prod_a_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__b_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J,type,
    comp_P8523877797512642645_a_b_a: ( produc3469756349985706280ee_a_b > b > a ) > ( ( b > a ) > produc3469756349985706280ee_a_b ) > ( b > a ) > b > a ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__b_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_001_062_Itf__b_Mtf__a_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    comp_P1823700203131805611_a_b_b: ( produc3469756349985706280ee_a_b > b > a ) > ( produc4558475209616630778_a_b_b > produc3469756349985706280ee_a_b ) > produc4558475209616630778_a_b_b > b > a ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__b_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    comp_P5693690220181566849_a_b_b: ( produc3469756349985706280ee_a_b > dtree_a_b ) > ( produc4558475209616630778_a_b_b > produc3469756349985706280ee_a_b ) > produc4558475209616630778_a_b_b > dtree_a_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__b_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_Itf__b_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    comp_P4604971360550642351ee_a_b: ( produc3469756349985706280ee_a_b > dtree_a_b ) > ( produc3469756349985706280ee_a_b > produc3469756349985706280ee_a_b ) > produc3469756349985706280ee_a_b > dtree_a_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__b_Mtf__a_J_001t__Product____Type__Oprod_Itf__b_Mtf__a_J_001t__Product____Type__Oprod_Itf__b_Mtf__a_J,type,
    comp_P3995598562207432003od_b_a: ( product_prod_b_a > product_prod_b_a ) > ( product_prod_b_a > product_prod_b_a ) > product_prod_b_a > product_prod_b_a ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__b_Mtf__b_J_001t__Product____Type__Oprod_Itf__b_Mtf__b_J_001t__Product____Type__Oprod_Itf__b_Mtf__b_J,type,
    comp_P5109000819176280452od_b_b: ( product_prod_b_b > product_prod_b_b ) > ( product_prod_b_b > product_prod_b_b ) > product_prod_b_b > product_prod_b_b ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Ounit_001_062_Itf__b_Mtf__a_J_001t__Product____Type__Ounit,type,
    comp_P1897366385088438013t_unit: ( product_unit > b > a ) > ( product_unit > product_unit ) > product_unit > b > a ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
    comp_P6110245121441952900t_unit: ( product_unit > product_unit ) > ( produc8459935480633519975t_unit > product_unit ) > produc8459935480633519975t_unit > product_unit ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
    comp_P7645380973975430442t_unit: ( product_unit > product_unit ) > ( product_unit > product_unit ) > product_unit > product_unit ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    comp_P8826619440060422666t_unit: ( product_unit > product_unit ) > ( set_Product_unit > product_unit ) > set_Product_unit > product_unit ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Ounit_001t__Set__Oset_It__Product____Type__Ounit_J_001t__Product____Type__Ounit,type,
    comp_P5718741887063599178t_unit: ( product_unit > set_Product_unit ) > ( product_unit > product_unit ) > product_unit > set_Product_unit ).

thf(sy_c_Fun_Ocomp_001t__Product____Type__Ounit_001t__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_001t__Product____Type__Ounit,type,
    comp_P1827784402480779900t_unit: ( product_unit > sum_su8719719018421925477t_unit ) > ( product_unit > product_unit ) > product_unit > sum_su8719719018421925477t_unit ).

thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_001_062_It__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_M_Eo_J_001t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    comp_s4871757605105181180_a_b_b: ( set_Pr3012420139608375472_a_b_b > fset_P5281107635120001194_a_b_b > $o ) > ( fset_P5281107635120001194_a_b_b > set_Pr3012420139608375472_a_b_b ) > fset_P5281107635120001194_a_b_b > fset_P5281107635120001194_a_b_b > $o ).

thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_001_Eo_001t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    comp_s5789959651358644079_a_b_b: ( set_Pr3012420139608375472_a_b_b > $o ) > ( fset_P5281107635120001194_a_b_b > set_Pr3012420139608375472_a_b_b ) > fset_P5281107635120001194_a_b_b > $o ).

thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_001t__Nat__Onat_001t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    comp_s5024164508761875599_a_b_b: ( set_Pr3012420139608375472_a_b_b > nat ) > ( fset_P5281107635120001194_a_b_b > set_Pr3012420139608375472_a_b_b ) > fset_P5281107635120001194_a_b_b > nat ).

thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Product____Type__Ounit_J_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
    comp_s5463265027590662666t_unit: ( set_Product_unit > product_unit ) > ( product_unit > set_Product_unit ) > product_unit > product_unit ).

thf(sy_c_Fun_Ocomp_001t__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
    comp_S7963160314018604552t_unit: ( sum_su8719719018421925477t_unit > product_unit ) > ( product_unit > sum_su8719719018421925477t_unit ) > product_unit > product_unit ).

thf(sy_c_Fun_Ocomp_001tf__a_001tf__a_001t__Product____Type__Ounit,type,
    comp_a5016895688491196138t_unit: ( a > a ) > ( product_unit > a ) > product_unit > a ).

thf(sy_c_Fun_Ocomp_001tf__a_001tf__a_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    comp_a5037538144324670410t_unit: ( a > a ) > ( set_Product_unit > a ) > set_Product_unit > a ).

thf(sy_c_Fun_Ocomp_001tf__a_001tf__a_001tf__a,type,
    comp_a_a_a: ( a > a ) > ( a > a ) > a > a ).

thf(sy_c_Fun_Ocomp_001tf__a_001tf__a_001tf__b,type,
    comp_a_a_b: ( a > a ) > ( b > a ) > b > a ).

thf(sy_c_Fun_Ocomp_001tf__b_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    comp_b3128908137006596050_a_b_b: ( b > dtree_a_b ) > ( produc4558475209616630778_a_b_b > b ) > produc4558475209616630778_a_b_b > dtree_a_b ).

thf(sy_c_Fun_Ocomp_001tf__b_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    comp_b_dtree_a_b_b: ( b > dtree_a_b ) > ( b > b ) > b > dtree_a_b ).

thf(sy_c_Fun_Ocomp_001tf__b_001tf__a_001tf__b,type,
    comp_b_a_b: ( b > a ) > ( b > b ) > b > a ).

thf(sy_c_Fun_Ocomp_001tf__b_001tf__b_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    comp_b_b_dtree_a_b: ( b > b ) > ( dtree_a_b > b ) > dtree_a_b > b ).

thf(sy_c_Fun_Ocomp_001tf__b_001tf__b_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    comp_b4098124895279589661_a_b_b: ( b > b ) > ( produc4558475209616630778_a_b_b > b ) > produc4558475209616630778_a_b_b > b ).

thf(sy_c_Fun_Ocomp_001tf__b_001tf__b_001t__Product____Type__Ounit,type,
    comp_b5213037050122890410t_unit: ( b > b ) > ( product_unit > b ) > product_unit > b ).

thf(sy_c_Fun_Ocomp_001tf__b_001tf__b_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    comp_b8338046430617690506t_unit: ( b > b ) > ( set_Product_unit > b ) > set_Product_unit > b ).

thf(sy_c_Fun_Ocomp_001tf__b_001tf__b_001tf__b,type,
    comp_b_b_b: ( b > b ) > ( b > b ) > b > b ).

thf(sy_c_Fun_Oid_001_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J,type,
    id_b_a_b_a: ( ( b > a ) > b > a ) > ( b > a ) > b > a ).

thf(sy_c_Fun_Oid_001_062_Itf__b_Mtf__a_J,type,
    id_b_a: ( b > a ) > b > a ).

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

thf(sy_c_Fun_Oid_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    id_dtree_a_b: dtree_a_b > dtree_a_b ).

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

thf(sy_c_Fun_Oid_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    id_Pro6814982414164175945_a_b_b: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b ).

thf(sy_c_Fun_Oid_001t__Product____Type__Ounit,type,
    id_Product_unit: product_unit > product_unit ).

thf(sy_c_Fun_Omap__fun_001_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J_001_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J_001_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J_001_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J,type,
    map_fu7442569697125996214_a_b_a: ( ( ( b > a ) > b > a ) > ( b > a ) > b > a ) > ( ( ( b > a ) > b > a ) > ( b > a ) > b > a ) > ( ( ( b > a ) > b > a ) > ( b > a ) > b > a ) > ( ( b > a ) > b > a ) > ( b > a ) > b > a ).

thf(sy_c_Fun_Omap__fun_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J,type,
    map_fu6504469177912210346_a_b_a: ( ( b > a ) > b > a ) > ( ( b > a ) > b > a ) > ( ( b > a ) > b > a ) > ( b > a ) > b > a ).

thf(sy_c_Fun_Omap__fun_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J_001t__Product____Type__Oprod_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J,type,
    map_fu5601089516310178851_a_b_a: ( ( b > a ) > b > a ) > ( ( b > a ) > product_prod_b_a_b_a ) > ( ( b > a ) > b > a ) > ( b > a ) > product_prod_b_a_b_a ).

thf(sy_c_Fun_Omap__fun_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J_001tf__a_001tf__a,type,
    map_fun_b_a_b_a_a_a: ( ( b > a ) > b > a ) > ( a > a ) > ( ( b > a ) > a ) > ( b > a ) > a ).

thf(sy_c_Fun_Omap__fun_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J_001tf__b_001tf__b,type,
    map_fun_b_a_b_a_b_b: ( ( b > a ) > b > a ) > ( b > b ) > ( ( b > a ) > b ) > ( b > a ) > b ).

thf(sy_c_Fun_Omap__fun_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b_001tf__a_001tf__a,type,
    map_fu6616654539599832813_b_a_a: ( dtree_a_b > b ) > ( a > a ) > ( b > a ) > dtree_a_b > a ).

thf(sy_c_Fun_Omap__fun_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b_001tf__b_001tf__b,type,
    map_fu3829198957627156781_b_b_b: ( dtree_a_b > b ) > ( b > b ) > ( b > b ) > dtree_a_b > b ).

thf(sy_c_Fun_Omap__fun_001t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_M_Eo_J_001_062_It__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_M_Eo_J,type,
    map_fu8973901316717634488_b_b_o: ( fset_P5281107635120001194_a_b_b > set_Pr3012420139608375472_a_b_b ) > ( ( set_Pr3012420139608375472_a_b_b > $o ) > fset_P5281107635120001194_a_b_b > $o ) > ( set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b > $o ) > fset_P5281107635120001194_a_b_b > fset_P5281107635120001194_a_b_b > $o ).

thf(sy_c_Fun_Omap__fun_001t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_001_Eo_001_Eo,type,
    map_fu6922732985725783282_b_o_o: ( fset_P5281107635120001194_a_b_b > set_Pr3012420139608375472_a_b_b ) > ( $o > $o ) > ( set_Pr3012420139608375472_a_b_b > $o ) > fset_P5281107635120001194_a_b_b > $o ).

thf(sy_c_Fun_Omap__fun_001t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_001t__Nat__Onat_001t__Nat__Onat,type,
    map_fu8120312284176349332at_nat: ( fset_P5281107635120001194_a_b_b > set_Pr3012420139608375472_a_b_b ) > ( nat > nat ) > ( set_Pr3012420139608375472_a_b_b > nat ) > fset_P5281107635120001194_a_b_b > nat ).

thf(sy_c_Fun_Omap__fun_001t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    map_fu3200731890701411048_a_b_b: ( fset_P5281107635120001194_a_b_b > set_Pr3012420139608375472_a_b_b ) > ( produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b ) > ( set_Pr3012420139608375472_a_b_b > produc4558475209616630778_a_b_b ) > fset_P5281107635120001194_a_b_b > produc4558475209616630778_a_b_b ).

thf(sy_c_Fun_Omap__fun_001t__FSet__Ofset_It__Product____Type__Ounit_J_001t__Set__Oset_It__Product____Type__Ounit_J_001t__Nat__Onat_001t__Nat__Onat,type,
    map_fu3978117929841985266at_nat: ( fset_Product_unit > set_Product_unit ) > ( nat > nat ) > ( set_Product_unit > nat ) > fset_Product_unit > nat ).

thf(sy_c_Fun_Omap__fun_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__a_001tf__a,type,
    map_fu4331093424227850636_b_a_a: ( produc4558475209616630778_a_b_b > dtree_a_b ) > ( a > a ) > ( dtree_a_b > a ) > produc4558475209616630778_a_b_b > a ).

thf(sy_c_Fun_Omap__fun_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b_001tf__b,type,
    map_fu1543637842255174604_b_b_b: ( produc4558475209616630778_a_b_b > dtree_a_b ) > ( b > b ) > ( dtree_a_b > b ) > produc4558475209616630778_a_b_b > b ).

thf(sy_c_Fun_Omap__fun_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_M_Eo_J_001_062_It__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_M_Eo_J,type,
    map_fu8342389097230326738_b_b_o: ( produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b ) > ( ( set_Pr3012420139608375472_a_b_b > $o ) > fset_P5281107635120001194_a_b_b > $o ) > ( produc4558475209616630778_a_b_b > set_Pr3012420139608375472_a_b_b > $o ) > produc4558475209616630778_a_b_b > fset_P5281107635120001194_a_b_b > $o ).

thf(sy_c_Fun_Omap__fun_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001tf__b_001tf__a_001tf__a,type,
    map_fu4770936153506353261_b_a_a: ( produc4558475209616630778_a_b_b > b ) > ( a > a ) > ( b > a ) > produc4558475209616630778_a_b_b > a ).

thf(sy_c_Fun_Omap__fun_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001tf__b_001tf__b_001tf__b,type,
    map_fu1983480571533677229_b_b_b: ( produc4558475209616630778_a_b_b > b ) > ( b > b ) > ( b > b ) > produc4558475209616630778_a_b_b > b ).

thf(sy_c_Fun_Omap__fun_001tf__a_001tf__a_001tf__a_001tf__a,type,
    map_fun_a_a_a_a: ( a > a ) > ( a > a ) > ( a > a ) > a > a ).

thf(sy_c_Fun_Omap__fun_001tf__a_001tf__a_001tf__b_001tf__b,type,
    map_fun_a_a_b_b: ( a > a ) > ( b > b ) > ( a > b ) > a > b ).

thf(sy_c_Fun_Omap__fun_001tf__b_001tf__b_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J,type,
    map_fun_b_b_b_a_b_a: ( b > b ) > ( ( b > a ) > b > a ) > ( b > b > a ) > b > b > a ).

thf(sy_c_Fun_Omap__fun_001tf__b_001tf__b_001tf__a_001tf__a,type,
    map_fun_b_b_a_a: ( b > b ) > ( a > a ) > ( b > a ) > b > a ).

thf(sy_c_Fun_Omap__fun_001tf__b_001tf__b_001tf__b_001tf__b,type,
    map_fun_b_b_b_b: ( b > b ) > ( b > b ) > ( b > b ) > b > b ).

thf(sy_c_Fun__Def_Oin__rel_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    fun_in7817583439641278657_a_b_b: set_Pr3012420139608375472_a_b_b > dtree_a_b > b > $o ).

thf(sy_c_Fun__Def_Oin__rel_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    fun_in223410601938929720_a_b_b: set_Pr2755428042910921141_a_b_b > produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b > $o ).

thf(sy_c_Fun__Def_Oin__rel_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
    fun_in4492808859237503746t_unit: set_Pr5094982260447487303t_unit > product_unit > product_unit > $o ).

thf(sy_c_Fun__Def_Oin__rel_001tf__b_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    fun_in1805295813492079159ee_a_b: set_Pr6717515126349854430ee_a_b > b > dtree_a_b > $o ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    minus_1250967532242559235_a_b_b: fset_P5281107635120001194_a_b_b > fset_P5281107635120001194_a_b_b > fset_P5281107635120001194_a_b_b ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
    minus_minus_nat: nat > nat > nat ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    minus_1392386589478415753_a_b_b: set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    minus_6452836326544984404t_unit: set_Product_unit > set_Product_unit > set_Product_unit ).

thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
    one_one_nat: nat ).

thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_M_Eo_J,type,
    inf_in55627642082981827_b_b_o: ( produc4558475209616630778_a_b_b > $o ) > ( produc4558475209616630778_a_b_b > $o ) > produc4558475209616630778_a_b_b > $o ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    inf_in7138637532943773244_a_b_b: fset_P5281107635120001194_a_b_b > fset_P5281107635120001194_a_b_b > fset_P5281107635120001194_a_b_b ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_062_Itf__b_Mtf__a_J_J,type,
    inf_inf_set_b_a: set_b_a > set_b_a > set_b_a ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Nat__Onat_J,type,
    inf_inf_set_nat: set_nat > set_nat > set_nat ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    inf_in6138156342456174402_a_b_b: set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    inf_in4660618365625256667t_unit: set_Product_unit > set_Product_unit > set_Product_unit ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    inf_in3779707751953380600_a_b_b: set_se3183138701204633190_a_b_b > set_se3183138701204633190_a_b_b > set_se3183138701204633190_a_b_b ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Set__Oset_It__Product____Type__Ounit_J_J,type,
    inf_in2608933832725608379t_unit: set_set_Product_unit > set_set_Product_unit > set_set_Product_unit ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_J,type,
    inf_in5198890673353021997t_unit: set_Su4110612849109743515t_unit > set_Su4110612849109743515t_unit > set_Su4110612849109743515t_unit ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_Itf__a_J,type,
    inf_inf_set_a: set_a > set_a > set_a ).

thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_Itf__b_J,type,
    inf_inf_set_b: set_b > set_b > set_b ).

thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    semila4423693302617054363t_unit: ( set_Product_unit > set_Product_unit > set_Product_unit ) > set_Product_unit > ( set_Product_unit > set_Product_unit > $o ) > ( set_Product_unit > set_Product_unit > $o ) > $o ).

thf(sy_c_Lattices_Osup__class_Osup_001t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    sup_su860928060825958358_a_b_b: fset_P5281107635120001194_a_b_b > fset_P5281107635120001194_a_b_b > fset_P5281107635120001194_a_b_b ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    sup_su2887895092731772380_a_b_b: set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    sup_su793286257634532545t_unit: set_Product_unit > set_Product_unit > set_Product_unit ).

thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_Itf__b_J,type,
    sup_sup_set_b: set_b > set_b > set_b ).

thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
    lattic8265883725875713057ax_nat: set_nat > nat ).

thf(sy_c_Lattices__Big_Olinorder__class_OMin_001t__Nat__Onat,type,
    lattic8721135487736765967in_nat: set_nat > nat ).

thf(sy_c_Nat_Osize__class_Osize_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    size_size_dtree_a_b: dtree_a_b > nat ).

thf(sy_c_Order__Relation_Olinear__order__on_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    order_4468497924153950597_a_b_b: set_Pr3012420139608375472_a_b_b > set_Pr2755428042910921141_a_b_b > $o ).

thf(sy_c_Order__Relation_OunderS_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    order_2076638635254047924_a_b_b: set_Pr2755428042910921141_a_b_b > produc4558475209616630778_a_b_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Order__Relation_Ounder_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    order_443969674961680725_a_b_b: set_Pr2755428042910921141_a_b_b > produc4558475209616630778_a_b_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Order__Relation_Owell__order__on_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    order_3931594357693323740_a_b_b: set_Pr3012420139608375472_a_b_b > set_Pr2755428042910921141_a_b_b > $o ).

thf(sy_c_Order__Relation_Owell__order__on_001t__Product____Type__Ounit,type,
    order_3164716736300062379t_unit: set_Product_unit > set_Pr5094982260447487303t_unit > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Nat__Onat_M_Eo_J,type,
    bot_bot_nat_o: nat > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_M_Eo_J,type,
    bot_bo7321339186913516097_b_b_o: produc4558475209616630778_a_b_b > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Product____Type__Ounit_M_Eo_J,type,
    bot_bo4642748612307482820unit_o: product_unit > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_Itf__a_M_Eo_J,type,
    bot_bot_a_o: a > $o ).

thf(sy_c_Orderings_Obot__class_Obot_001_062_Itf__b_M_Eo_J,type,
    bot_bot_b_o: b > $o ).

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

thf(sy_c_Orderings_Obot__class_Obot_001t__FSet__Ofset_It__Nat__Onat_J,type,
    bot_bot_fset_nat: fset_nat ).

thf(sy_c_Orderings_Obot__class_Obot_001t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    bot_bo2895716411488905534_a_b_b: fset_P5281107635120001194_a_b_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__FSet__Ofset_It__Product____Type__Ounit_J,type,
    bot_bo7418305276487734239t_unit: fset_Product_unit ).

thf(sy_c_Orderings_Obot__class_Obot_001t__FSet__Ofset_Itf__a_J,type,
    bot_bot_fset_a: fset_a ).

thf(sy_c_Orderings_Obot__class_Obot_001t__FSet__Ofset_Itf__b_J,type,
    bot_bot_fset_b: fset_b ).

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_062_Itf__b_Mtf__a_J_J,type,
    bot_bot_set_b_a: set_b_a ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    bot_bo8730652382759064772ee_a_b: set_dtree_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_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    bot_bo3721250822024684356_a_b_b: set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    bot_bo3957492148770167129t_unit: set_Product_unit ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    bot_bo2537099559385417978_a_b_b: set_se3183138701204633190_a_b_b ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Set__Oset_It__Product____Type__Ounit_J_J,type,
    bot_bo6284674557190688313t_unit: set_set_Product_unit ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_J,type,
    bot_bo3448499826546176559t_unit: set_Su4110612849109743515t_unit ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
    bot_bot_set_a: set_a ).

thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__b_J,type,
    bot_bot_set_b: set_b ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
    ord_less_nat: nat > nat > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    ord_le3723863380492978948_a_b_b: set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    ord_le8056459307392131481t_unit: set_Product_unit > set_Product_unit > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__FSet__Ofset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    ord_le789900035998834954_a_b_b: fset_P5281107635120001194_a_b_b > fset_P5281107635120001194_a_b_b > $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_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    ord_le146215904626753808_a_b_b: set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    ord_le3507040750410214029t_unit: set_Product_unit > set_Product_unit > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
    ord_less_eq_set_a: set_a > set_a > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__b_J,type,
    ord_less_eq_set_b: set_b > set_b > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_I_062_Itf__b_Mtf__a_J_M_Eo_J,type,
    top_top_b_a_o: ( b > a ) > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_M_Eo_J,type,
    top_to762646584048855333_b_b_o: produc4558475209616630778_a_b_b > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Product____Type__Ounit_M_Eo_J,type,
    top_to2465898995584390880unit_o: product_unit > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Set__Oset_It__Product____Type__Ounit_J_M_Eo_J,type,
    top_to5616354022731438592unit_o: set_Product_unit > $o ).

thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_M_Eo_J,type,
    top_to8021728106141937658unit_o: sum_su8719719018421925477t_unit > $o ).

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

thf(sy_c_Orderings_Otop__class_Otop_001t__FSet__Ofset_It__Product____Type__Ounit_J,type,
    top_to4734357443822147779t_unit: fset_Product_unit ).

thf(sy_c_Orderings_Otop__class_Otop_001t__FSet__Ofset_It__Set__Oset_It__Product____Type__Ounit_J_J,type,
    top_to971128490267878819t_unit: fset_s2847261894197522515t_unit ).

thf(sy_c_Orderings_Otop__class_Otop_001t__FSet__Ofset_It__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_J,type,
    top_to5791472215405926981t_unit: fset_S6328958348615259029t_unit ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J_J,type,
    top_top_set_b_a_b_a: set_b_a_b_a ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_062_Itf__b_Mtf__a_J_J,type,
    top_top_set_b_a: set_b_a ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    top_to9008179178016042208ee_a_b: set_dtree_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__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    top_to7222684678772277088_a_b_b: set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_M_062_Itf__b_Mtf__a_J_J_J,type,
    top_to6155636102477775302it_b_a: set_Pr7494330017871143702it_b_a ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_J,type,
    top_to1835807148980544151t_unit: set_Pr5094982260447487303t_unit ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Set__Oset_It__Product____Type__Ounit_J_J_J,type,
    top_to233792371731913591t_unit: set_Pr217763282141584935t_unit ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_J_J,type,
    top_to5937313915539256967t_unit: set_Pr3091785439476234199t_unit ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Ounit_J_Mt__Product____Type__Ounit_J_J,type,
    top_to1243971000991123895t_unit: set_Pr1227941911400795239t_unit ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_J,type,
    top_to1704407628658980238ee_a_b: set_Pr6717515126349854430ee_a_b ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    top_to1996260823553986621t_unit: set_Product_unit ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_J,type,
    top_to1846739022409413910_a_b_b: set_se3183138701204633190_a_b_b ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_It__Product____Type__Ounit_J_J,type,
    top_to1767297665138865437t_unit: set_set_Product_unit ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_J,type,
    top_to2771918933716375115t_unit: set_Su4110612849109743515t_unit ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__a_J,type,
    top_top_set_a: set_a ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__b_J,type,
    top_top_set_b: set_b ).

thf(sy_c_Product__Type_OPair_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001_062_Itf__b_Mtf__a_J,type,
    produc1993688775741047735_b_b_a: dtree_a_b > ( b > a ) > produc1083523234014712191_b_b_a ).

thf(sy_c_Product__Type_OPair_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    produc7805419539522982029ee_a_b: dtree_a_b > dtree_a_b > produc5177672665255943253ee_a_b ).

thf(sy_c_Product__Type_OPair_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    produc331601717337510060_a_b_b: dtree_a_b > b > produc4558475209616630778_a_b_b ).

thf(sy_c_Product__Type_OPair_001t__Pair____Digraph__Opair____pre____digraph__Opair____pre____digraph____ext_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    produc5307704689474511050_a_b_b: pair_p3556638718232885427t_unit > produc6870677010558023550_a_b_b > produc7079444246281463442_a_b_b ).

thf(sy_c_Product__Type_OPair_001t__Pair____Digraph__Opair____pre____digraph__Opair____pre____digraph____ext_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_Mt__Product____Type__Ounit_J,type,
    produc2086944449173503016t_unit: pair_p7583798195187013628t_unit > produc6596653366452172941t_unit > produc2042437161806511672t_unit ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    produc6533307410877503629_a_b_b: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b > produc8908337785154950741_a_b_b ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    produc4872291942876762872_a_b_b: produc8908337785154950741_a_b_b > produc4558475209616630778_a_b_b > produc6870677010558023550_a_b_b ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_001t__Product____Type__Ounit,type,
    produc8155702538658622973t_unit: produc8459935480633519975t_unit > product_unit > produc6596653366452172941t_unit ).

thf(sy_c_Product__Type_OPair_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
    produc5692694829384537815t_unit: product_unit > product_unit > produc8459935480633519975t_unit ).

thf(sy_c_Product__Type_OPair_001tf__b_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    produc3542686128043086370ee_a_b: b > dtree_a_b > produc3469756349985706280ee_a_b ).

thf(sy_c_Product__Type_Oapfst_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    produc1844830993343419085_a_b_b: ( dtree_a_b > dtree_a_b ) > produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b ).

thf(sy_c_Product__Type_Oapsnd_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    produc3383614106744390411_a_b_b: ( dtree_a_b > dtree_a_b ) > produc3469756349985706280ee_a_b > produc3469756349985706280ee_a_b ).

thf(sy_c_Product__Type_Oapsnd_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    produc6388821566548385006_a_b_b: ( produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b ) > produc8908337785154950741_a_b_b > produc8908337785154950741_a_b_b ).

thf(sy_c_Product__Type_Oapsnd_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
    produc6120449539986271055t_unit: ( product_unit > product_unit ) > produc8459935480633519975t_unit > produc8459935480633519975t_unit ).

thf(sy_c_Product__Type_Oapsnd_001tf__b_001tf__b_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    produc7811666328248579896ee_a_b: ( b > b ) > produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b ).

thf(sy_c_Product__Type_Ocurry_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b_001_Eo,type,
    produc5550526150511291678_b_b_o: ( produc4558475209616630778_a_b_b > $o ) > dtree_a_b > b > $o ).

thf(sy_c_Product__Type_Ocurry_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    produc3315389081899078644_a_b_b: ( produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b ) > dtree_a_b > b > produc4558475209616630778_a_b_b ).

thf(sy_c_Product__Type_Ocurry_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    produc2895653412298819754_a_b_b: ( produc4558475209616630778_a_b_b > set_Pr3012420139608375472_a_b_b ) > dtree_a_b > b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Product__Type_Ocurry_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001_Eo,type,
    produc7211229566987185431_b_b_o: ( produc8908337785154950741_a_b_b > $o ) > produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b > $o ).

thf(sy_c_Product__Type_Ocurry_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001_Eo,type,
    produc7179068063668086733unit_o: ( produc8459935480633519975t_unit > $o ) > product_unit > product_unit > $o ).

thf(sy_c_Product__Type_Ocurry_001tf__b_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001_Eo,type,
    produc1826475430485498408_a_b_o: ( produc3469756349985706280ee_a_b > $o ) > b > dtree_a_b > $o ).

thf(sy_c_Product__Type_Ointernal__case__prod_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b_001_Eo,type,
    produc835642783053744213_b_b_o: ( dtree_a_b > b > $o ) > produc4558475209616630778_a_b_b > $o ).

thf(sy_c_Product__Type_Ointernal__case__prod_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    produc8719677615279257213_a_b_b: ( dtree_a_b > b > produc4558475209616630778_a_b_b ) > produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b ).

thf(sy_c_Product__Type_Ointernal__case__prod_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    produc6395705637274715955_a_b_b: ( dtree_a_b > b > set_Pr3012420139608375472_a_b_b ) > produc4558475209616630778_a_b_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Product__Type_Omap__prod_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J,type,
    produc1686386052851666058_a_b_a: ( ( b > a ) > b > a ) > ( ( b > a ) > b > a ) > product_prod_b_a_b_a > product_prod_b_a_b_a ).

thf(sy_c_Product__Type_Omap__prod_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J_001tf__a_001tf__a,type,
    produc2729404390646056256_a_a_a: ( ( b > a ) > b > a ) > ( a > a ) > product_prod_b_a_a > product_prod_b_a_a ).

thf(sy_c_Product__Type_Omap__prod_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J_001tf__b_001tf__b,type,
    produc9165320845528156032_a_b_b: ( ( b > a ) > b > a ) > ( b > b ) > product_prod_b_a_b > product_prod_b_a_b ).

thf(sy_c_Product__Type_Omap__prod_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b_001tf__b,type,
    produc2024282846164127276_b_b_b: ( dtree_a_b > dtree_a_b ) > ( b > b ) > produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b ).

thf(sy_c_Product__Type_Omap__prod_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001tf__b_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    produc1333424704237685261_a_b_b: ( dtree_a_b > produc4558475209616630778_a_b_b ) > ( b > produc4558475209616630778_a_b_b ) > produc4558475209616630778_a_b_b > produc8908337785154950741_a_b_b ).

thf(sy_c_Product__Type_Omap__prod_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Ounit_001tf__b_001t__Product____Type__Ounit,type,
    produc7457737578077058409t_unit: ( dtree_a_b > product_unit ) > ( b > product_unit ) > produc4558475209616630778_a_b_b > produc8459935480633519975t_unit ).

thf(sy_c_Product__Type_Omap__prod_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b_001tf__a_001tf__a,type,
    produc7039830289370142221_b_a_a: ( dtree_a_b > b ) > ( a > a ) > produc4558475205313401977_a_b_a > product_prod_b_a ).

thf(sy_c_Product__Type_Omap__prod_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b_001tf__b_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    produc2701657453118314412ee_a_b: ( dtree_a_b > b ) > ( b > dtree_a_b ) > produc4558475209616630778_a_b_b > produc3469756349985706280ee_a_b ).

thf(sy_c_Product__Type_Omap__prod_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b_001tf__b_001tf__b,type,
    produc4252374707397466189_b_b_b: ( dtree_a_b > b ) > ( b > b ) > produc4558475209616630778_a_b_b > product_prod_b_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_Omap__prod_001t__Nat__Onat_001t__Nat__Onat_001tf__a_001tf__a,type,
    produc7112430102003590552at_a_a: ( nat > nat ) > ( a > a ) > product_prod_nat_a > product_prod_nat_a ).

thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Nat__Onat_001tf__b_001tf__b,type,
    produc4324974520030914520at_b_b: ( nat > nat ) > ( b > b ) > product_prod_nat_b > product_prod_nat_b ).

thf(sy_c_Product__Type_Omap__prod_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001tf__b,type,
    produc9210843222980373143_b_b_b: ( produc4558475209616630778_a_b_b > dtree_a_b ) > ( produc4558475209616630778_a_b_b > b ) > produc8908337785154950741_a_b_b > produc4558475209616630778_a_b_b ).

thf(sy_c_Product__Type_Omap__prod_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__a_001tf__a,type,
    produc3482909109974950508_b_a_a: ( produc4558475209616630778_a_b_b > dtree_a_b ) > ( a > a ) > produc6708371833713233913_b_b_a > produc4558475205313401977_a_b_a ).

thf(sy_c_Product__Type_Omap__prod_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b_001tf__b,type,
    produc695453528002274476_b_b_b: ( produc4558475209616630778_a_b_b > dtree_a_b ) > ( b > b ) > produc6708371838016462714_b_b_b > produc4558475209616630778_a_b_b ).

thf(sy_c_Product__Type_Omap__prod_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    produc8659143532165282274_a_b_b: ( produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b ) > ( produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b ) > produc8908337785154950741_a_b_b > produc8908337785154950741_a_b_b ).

thf(sy_c_Product__Type_Omap__prod_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Ounit_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Ounit,type,
    produc1195185685987334582t_unit: ( produc4558475209616630778_a_b_b > product_unit ) > ( produc4558475209616630778_a_b_b > product_unit ) > produc8908337785154950741_a_b_b > produc8459935480633519975t_unit ).

thf(sy_c_Product__Type_Omap__prod_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001tf__b_001tf__a_001tf__a,type,
    produc4371205791216230285_b_a_a: ( produc4558475209616630778_a_b_b > b ) > ( a > a ) > produc6708371833713233913_b_b_a > product_prod_b_a ).

thf(sy_c_Product__Type_Omap__prod_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001tf__b_001tf__b_001tf__b,type,
    produc1583750209243554253_b_b_b: ( produc4558475209616630778_a_b_b > b ) > ( b > b ) > produc6708371838016462714_b_b_b > product_prod_b_b ).

thf(sy_c_Product__Type_Omap__prod_001t__Product____Type__Ounit_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Ounit_001tf__b,type,
    produc1291885961400238659unit_b: ( product_unit > dtree_a_b ) > ( product_unit > b ) > produc8459935480633519975t_unit > produc4558475209616630778_a_b_b ).

thf(sy_c_Product__Type_Omap__prod_001t__Product____Type__Ounit_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Ounit_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    produc8307554072185093430_a_b_b: ( product_unit > produc4558475209616630778_a_b_b ) > ( product_unit > produc4558475209616630778_a_b_b ) > produc8459935480633519975t_unit > produc8908337785154950741_a_b_b ).

thf(sy_c_Product__Type_Omap__prod_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001_062_Itf__b_Mtf__a_J_001t__Product____Type__Ounit,type,
    produc4508796588681953713t_unit: ( product_unit > product_unit ) > ( ( b > a ) > product_unit ) > produc5776317634898194272it_b_a > produc8459935480633519975t_unit ).

thf(sy_c_Product__Type_Omap__prod_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001_062_Itf__b_Mtf__a_J,type,
    produc5742360875550256123it_b_a: ( product_unit > product_unit ) > ( product_unit > b > a ) > produc8459935480633519975t_unit > produc5776317634898194272it_b_a ).

thf(sy_c_Product__Type_Omap__prod_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
    produc3941737999988548470t_unit: ( product_unit > product_unit ) > ( product_unit > product_unit ) > produc8459935480633519975t_unit > produc8459935480633519975t_unit ).

thf(sy_c_Product__Type_Omap__prod_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    produc5886246840336164950t_unit: ( product_unit > product_unit ) > ( product_unit > set_Product_unit ) > produc8459935480633519975t_unit > produc4787451486076709959t_unit ).

thf(sy_c_Product__Type_Omap__prod_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
    produc3239798823771121596t_unit: ( product_unit > product_unit ) > ( product_unit > sum_su8719719018421925477t_unit ) > produc8459935480633519975t_unit > produc1562073732673760929t_unit ).

thf(sy_c_Product__Type_Omap__prod_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Set__Oset_It__Product____Type__Ounit_J_001t__Product____Type__Ounit,type,
    produc2778369287339341462t_unit: ( product_unit > product_unit ) > ( set_Product_unit > product_unit ) > produc4787451486076709959t_unit > produc8459935480633519975t_unit ).

thf(sy_c_Product__Type_Omap__prod_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Set__Oset_It__Product____Type__Ounit_J_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    produc9113809635950836598t_unit: ( product_unit > product_unit ) > ( set_Product_unit > set_Product_unit ) > produc4787451486076709959t_unit > produc4787451486076709959t_unit ).

thf(sy_c_Product__Type_Omap__prod_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_001t__Product____Type__Ounit,type,
    produc6052776011906407728t_unit: ( product_unit > product_unit ) > ( sum_su8719719018421925477t_unit > product_unit ) > produc1562073732673760929t_unit > produc8459935480633519975t_unit ).

thf(sy_c_Product__Type_Omap__prod_001t__Product____Type__Ounit_001t__Set__Oset_It__Product____Type__Ounit_J_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
    produc2522892427866404950t_unit: ( product_unit > set_Product_unit ) > ( product_unit > product_unit ) > produc8459935480633519975t_unit > produc9013008050180029063t_unit ).

thf(sy_c_Product__Type_Omap__prod_001t__Product____Type__Ounit_001tf__b_001t__Product____Type__Ounit_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    produc4159773624399151967ee_a_b: ( product_unit > b ) > ( product_unit > dtree_a_b ) > produc8459935480633519975t_unit > produc3469756349985706280ee_a_b ).

thf(sy_c_Product__Type_Omap__prod_001t__Set__Oset_It__Product____Type__Ounit_J_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
    produc8516325191527966358t_unit: ( set_Product_unit > product_unit ) > ( product_unit > product_unit ) > produc9013008050180029063t_unit > produc8459935480633519975t_unit ).

thf(sy_c_Product__Type_Omap__prod_001tf__a_001tf__a_001t__Nat__Onat_001t__Nat__Onat,type,
    produc1377594951366540952at_nat: ( a > a ) > ( nat > nat ) > product_prod_a_nat > product_prod_a_nat ).

thf(sy_c_Product__Type_Omap__prod_001tf__a_001tf__a_001tf__a_001tf__a,type,
    produc4018698449564827638_a_a_a: ( a > a ) > ( a > a ) > product_prod_a_a > product_prod_a_a ).

thf(sy_c_Product__Type_Omap__prod_001tf__a_001tf__a_001tf__b_001tf__b,type,
    produc1231242867592151606_a_b_b: ( a > a ) > ( b > b ) > product_prod_a_b > product_prod_a_b ).

thf(sy_c_Product__Type_Omap__prod_001tf__b_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    produc5995436795640382528_a_b_b: ( b > dtree_a_b ) > ( dtree_a_b > b ) > produc3469756349985706280ee_a_b > produc4558475209616630778_a_b_b ).

thf(sy_c_Product__Type_Omap__prod_001tf__b_001t__Product____Type__Ounit_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Ounit,type,
    produc4430891178592075597t_unit: ( b > product_unit ) > ( dtree_a_b > product_unit ) > produc3469756349985706280ee_a_b > produc8459935480633519975t_unit ).

thf(sy_c_Product__Type_Omap__prod_001tf__b_001tf__b_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    produc4749355648339255596ee_a_b: ( b > b ) > ( dtree_a_b > dtree_a_b ) > produc3469756349985706280ee_a_b > produc3469756349985706280ee_a_b ).

thf(sy_c_Product__Type_Omap__prod_001tf__b_001tf__b_001t__Nat__Onat_001t__Nat__Onat,type,
    produc7117561280001982680at_nat: ( b > b ) > ( nat > nat ) > product_prod_b_nat > product_prod_b_nat ).

thf(sy_c_Product__Type_Omap__prod_001tf__b_001tf__b_001tf__a_001tf__a,type,
    produc1879507065192981046_b_a_a: ( b > b ) > ( a > a ) > product_prod_b_a > product_prod_b_a ).

thf(sy_c_Product__Type_Omap__prod_001tf__b_001tf__b_001tf__b_001tf__b,type,
    produc8315423520075080822_b_b_b: ( b > b ) > ( b > b ) > product_prod_b_b > product_prod_b_b ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b_001_Eo,type,
    produc1325217093046185599_b_b_o: ( dtree_a_b > b > $o ) > produc4558475209616630778_a_b_b > $o ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    produc5460679229782211283_a_b_b: ( dtree_a_b > b > produc4558475209616630778_a_b_b ) > produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b_001t__Set__Oset_It__Nat__Onat_J,type,
    produc6123424770501316703et_nat: ( dtree_a_b > b > set_nat ) > produc4558475209616630778_a_b_b > set_nat ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    produc2559767781221151625_a_b_b: ( dtree_a_b > b > set_Pr3012420139608375472_a_b_b ) > produc4558475209616630778_a_b_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b_001t__Set__Oset_Itf__a_J,type,
    produc5617419904392314821_set_a: ( dtree_a_b > b > set_a ) > produc4558475209616630778_a_b_b > set_a ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b_001t__Set__Oset_Itf__b_J,type,
    produc5617419908695543622_set_b: ( dtree_a_b > b > set_b ) > produc4558475209616630778_a_b_b > set_b ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Set__Oset_It__Nat__Onat_J,type,
    produc9075591806163244658et_nat: ( product_unit > product_unit > set_nat ) > produc8459935480633519975t_unit > set_nat ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Set__Oset_Itf__a_J,type,
    produc989992564485724274_set_a: ( product_unit > product_unit > set_a ) > produc8459935480633519975t_unit > set_a ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Set__Oset_Itf__b_J,type,
    produc989992568788953075_set_b: ( product_unit > product_unit > set_b ) > produc8459935480633519975t_unit > set_b ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Set__Oset_It__Nat__Onat_J,type,
    produc1571707150759354837et_nat: ( b > dtree_a_b > set_nat ) > produc3469756349985706280ee_a_b > set_nat ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Set__Oset_Itf__a_J,type,
    produc4685151519421980623_set_a: ( b > dtree_a_b > set_a ) > produc3469756349985706280ee_a_b > set_a ).

thf(sy_c_Product__Type_Oprod_Ocase__prod_001tf__b_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Set__Oset_Itf__b_J,type,
    produc4685151523725209424_set_b: ( b > dtree_a_b > set_b ) > produc3469756349985706280ee_a_b > set_b ).

thf(sy_c_Product__Type_Oprod_Ofst_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    produc697780174058963904_a_b_b: produc4558475209616630778_a_b_b > dtree_a_b ).

thf(sy_c_Product__Type_Oprod_Ofst_001tf__b_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    produc3908864584764540214ee_a_b: produc3469756349985706280ee_a_b > b ).

thf(sy_c_Product__Type_Oprod_Osnd_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J,type,
    product_snd_b_a_b_a: product_prod_b_a_b_a > b > a ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    produc5748100250121904638_a_b_b: produc4558475209616630778_a_b_b > b ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    produc8480234286567085243_a_b_b: produc8908337785154950741_a_b_b > produc4558475209616630778_a_b_b ).

thf(sy_c_Product__Type_Oprod_Osnd_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
    produc6786084904866402309t_unit: produc8459935480633519975t_unit > product_unit ).

thf(sy_c_Product__Type_Oprod_Osnd_001tf__b_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    produc8959184660827480948ee_a_b: produc3469756349985706280ee_a_b > dtree_a_b ).

thf(sy_c_Product__Type_Oprod_Oswap_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    produc2906148145665870604_a_b_b: produc4558475209616630778_a_b_b > produc3469756349985706280ee_a_b ).

thf(sy_c_Product__Type_Oprod_Oswap_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    produc9212635681174021677_a_b_b: produc8908337785154950741_a_b_b > produc8908337785154950741_a_b_b ).

thf(sy_c_Product__Type_Oprod_Oswap_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
    produc1940222046511404151t_unit: produc8459935480633519975t_unit > produc8459935480633519975t_unit ).

thf(sy_c_Product__Type_Oprod_Oswap_001tf__b_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    produc6117232556371446914ee_a_b: produc3469756349985706280ee_a_b > produc4558475209616630778_a_b_b ).

thf(sy_c_Relation_OField_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    field_2612910574630873453_a_b_b: set_Pr2755428042910921141_a_b_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Relation_OField_001t__Product____Type__Ounit,type,
    field_Product_unit: set_Pr5094982260447487303t_unit > set_Product_unit ).

thf(sy_c_Relation_ORange_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    range_dtree_a_b_b: set_Pr3012420139608375472_a_b_b > set_b ).

thf(sy_c_Relation_Orefl__on_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    refl_o6438828113603023419_a_b_b: set_Pr3012420139608375472_a_b_b > set_Pr2755428042910921141_a_b_b > $o ).

thf(sy_c_Relation_Orefl__on_001t__Product____Type__Ounit,type,
    refl_on_Product_unit: set_Product_unit > set_Pr5094982260447487303t_unit > $o ).

thf(sy_c_Relation_Orelcompp_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    relcom1818280762458196888_a_b_b: ( dtree_a_b > dtree_a_b > $o ) > ( dtree_a_b > b > $o ) > dtree_a_b > b > $o ).

thf(sy_c_Relation_Orelcompp_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b_001tf__b,type,
    relcom8461221429256392043_b_b_b: ( dtree_a_b > b > $o ) > ( b > b > $o ) > dtree_a_b > b > $o ).

thf(sy_c_Set_OCollect_001_062_Itf__b_Mtf__a_J,type,
    collect_b_a: ( ( b > a ) > $o ) > set_b_a ).

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

thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    collec1368399972772960719_a_b_b: ( produc4558475209616630778_a_b_b > $o ) > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Set_OCollect_001t__Product____Type__Ounit,type,
    collect_Product_unit: ( product_unit > $o ) > set_Product_unit ).

thf(sy_c_Set_OCollect_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    collec5997417077270831749_a_b_b: ( set_Pr3012420139608375472_a_b_b > $o ) > set_se3183138701204633190_a_b_b ).

thf(sy_c_Set_OCollect_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    collec7787489603430924120t_unit: ( set_Product_unit > $o ) > set_set_Product_unit ).

thf(sy_c_Set_OCollect_001t__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
    collec806072925662511674t_unit: ( sum_su8719719018421925477t_unit > $o ) > set_Su4110612849109743515t_unit ).

thf(sy_c_Set_OCollect_001tf__a,type,
    collect_a: ( a > $o ) > set_a ).

thf(sy_c_Set_OCollect_001tf__b,type,
    collect_b: ( b > $o ) > set_b ).

thf(sy_c_Set_Oimage_001_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J_001_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J,type,
    image_8714421494778392021_a_b_a: ( ( ( b > a ) > b > a ) > ( b > a ) > b > a ) > set_b_a_b_a > set_b_a_b_a ).

thf(sy_c_Set_Oimage_001_062_Itf__b_Mtf__a_J_001_062_Itf__b_Mtf__a_J,type,
    image_b_a_b_a: ( ( b > a ) > b > a ) > set_b_a > set_b_a ).

thf(sy_c_Set_Oimage_001_062_Itf__b_Mtf__a_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    image_b_a_dtree_a_b: ( ( b > a ) > dtree_a_b ) > set_b_a > set_dtree_a_b ).

thf(sy_c_Set_Oimage_001_062_Itf__b_Mtf__a_J_001t__Product____Type__Oprod_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J,type,
    image_3865962054164325950_a_b_a: ( ( b > a ) > product_prod_b_a_b_a ) > set_b_a > set_Pr5619283252532241417_a_b_a ).

thf(sy_c_Set_Oimage_001_062_Itf__b_Mtf__a_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    image_1791271310906730661_a_b_b: ( ( b > a ) > produc4558475209616630778_a_b_b ) > set_b_a > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Set_Oimage_001_062_Itf__b_Mtf__a_J_001t__Product____Type__Oprod_Itf__b_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    image_702552451275806163ee_a_b: ( ( b > a ) > produc3469756349985706280ee_a_b ) > set_b_a > set_Pr6717515126349854430ee_a_b ).

thf(sy_c_Set_Oimage_001_062_Itf__b_Mtf__a_J_001t__Product____Type__Ounit,type,
    image_2179813402173241122t_unit: ( ( b > a ) > product_unit ) > set_b_a > set_Product_unit ).

thf(sy_c_Set_Oimage_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    image_1160270813240538107ee_a_b: ( dtree_a_b > dtree_a_b ) > set_dtree_a_b > set_dtree_a_b ).

thf(sy_c_Set_Oimage_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    image_360604450665336955_a_b_b: ( dtree_a_b > produc4558475209616630778_a_b_b ) > set_dtree_a_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Set_Oimage_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001t__Product____Type__Oprod_Itf__b_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    image_8495257627889188265ee_a_b: ( dtree_a_b > produc3469756349985706280ee_a_b ) > set_dtree_a_b > set_Pr6717515126349854430ee_a_b ).

thf(sy_c_Set_Oimage_001t__Dtree__Odtree_Itf__a_Mtf__b_J_001tf__b,type,
    image_dtree_a_b_b: ( dtree_a_b > b ) > set_dtree_a_b > set_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_001tf__a,type,
    image_nat_a: ( nat > a ) > set_nat > set_a ).

thf(sy_c_Set_Oimage_001t__Nat__Onat_001tf__b,type,
    image_nat_b: ( nat > b ) > set_nat > set_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001_062_Itf__b_Mtf__a_J,type,
    image_7926328481751752869_b_b_a: ( produc4558475209616630778_a_b_b > b > a ) > set_Pr3012420139608375472_a_b_b > set_b_a ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    image_7065894828672115579ee_a_b: ( produc4558475209616630778_a_b_b > dtree_a_b ) > set_Pr3012420139608375472_a_b_b > set_dtree_a_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    image_6081965176830705659_a_b_b: ( produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b ) > set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
    image_4150594470010877606t_unit: ( produc4558475209616630778_a_b_b > produc8459935480633519975t_unit ) > set_Pr3012420139608375472_a_b_b > set_Pr5094982260447487303t_unit ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001t__Product____Type__Oprod_Itf__b_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    image_4993246317199781161ee_a_b: ( produc4558475209616630778_a_b_b > produc3469756349985706280ee_a_b ) > set_Pr3012420139608375472_a_b_b > set_Pr6717515126349854430ee_a_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_001tf__b,type,
    image_3908709015779211070_b_b_b: ( produc4558475209616630778_a_b_b > b ) > set_Pr3012420139608375472_a_b_b > set_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    image_8464404100643805253_a_b_b: ( produc8908337785154950741_a_b_b > produc8908337785154950741_a_b_b ) > set_Pr2755428042910921141_a_b_b > set_Pr2755428042910921141_a_b_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
    image_7356924584417892695t_unit: ( produc8908337785154950741_a_b_b > produc8459935480633519975t_unit ) > set_Pr2755428042910921141_a_b_b > set_Pr5094982260447487303t_unit ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Ounit_M_062_Itf__b_Mtf__a_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
    image_5329927176394305216t_unit: ( produc5776317634898194272it_b_a > produc8459935480633519975t_unit ) > set_Pr7494330017871143702it_b_a > set_Pr5094982260447487303t_unit ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    image_4720867526043783708_a_b_b: ( produc8459935480633519975t_unit > produc4558475209616630778_a_b_b ) > set_Pr5094982260447487303t_unit > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    image_7065570836208718259_a_b_b: ( produc8459935480633519975t_unit > produc8908337785154950741_a_b_b ) > set_Pr5094982260447487303t_unit > set_Pr2755428042910921141_a_b_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_M_062_Itf__b_Mtf__a_J_J,type,
    image_8908915882552613250it_b_a: ( produc8459935480633519975t_unit > produc5776317634898194272it_b_a ) > set_Pr5094982260447487303t_unit > set_Pr7494330017871143702it_b_a ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
    image_9149991759805673413t_unit: ( produc8459935480633519975t_unit > produc8459935480633519975t_unit ) > set_Pr5094982260447487303t_unit > set_Pr5094982260447487303t_unit ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Set__Oset_It__Product____Type__Ounit_J_J,type,
    image_4440353659548185765t_unit: ( produc8459935480633519975t_unit > produc4787451486076709959t_unit ) > set_Pr5094982260447487303t_unit > set_Pr217763282141584935t_unit ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_J,type,
    image_548699592699116739t_unit: ( produc8459935480633519975t_unit > produc1562073732673760929t_unit ) > set_Pr5094982260447487303t_unit > set_Pr3091785439476234199t_unit ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Ounit_J_Mt__Product____Type__Ounit_J,type,
    image_8665910223651504869t_unit: ( produc8459935480633519975t_unit > produc9013008050180029063t_unit ) > set_Pr5094982260447487303t_unit > set_Pr1227941911400795239t_unit ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_001t__Product____Type__Oprod_Itf__b_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    image_3632148666412859210ee_a_b: ( produc8459935480633519975t_unit > produc3469756349985706280ee_a_b ) > set_Pr5094982260447487303t_unit > set_Pr6717515126349854430ee_a_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Set__Oset_It__Product____Type__Ounit_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
    image_530514150481900261t_unit: ( produc4787451486076709959t_unit > produc8459935480633519975t_unit ) > set_Pr217763282141584935t_unit > set_Pr5094982260447487303t_unit ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Set__Oset_It__Product____Type__Ounit_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Set__Oset_It__Product____Type__Ounit_J_J,type,
    image_3652598542883616709t_unit: ( produc4787451486076709959t_unit > produc4787451486076709959t_unit ) > set_Pr217763282141584935t_unit > set_Pr217763282141584935t_unit ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
    image_1652486172545353919t_unit: ( produc1562073732673760929t_unit > produc8459935480633519975t_unit ) > set_Pr3091785439476234199t_unit > set_Pr5094982260447487303t_unit ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Ounit_J_Mt__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
    image_6812161408116896933t_unit: ( produc9013008050180029063t_unit > produc8459935480633519975t_unit ) > set_Pr1227941911400795239t_unit > set_Pr5094982260447487303t_unit ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__b_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_001_062_Itf__b_Mtf__a_J,type,
    image_4051856227524180435_b_b_a: ( produc3469756349985706280ee_a_b > b > a ) > set_Pr6717515126349854430ee_a_b > set_b_a ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__b_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    image_6364595536291967657ee_a_b: ( produc3469756349985706280ee_a_b > dtree_a_b ) > set_Pr6717515126349854430ee_a_b > set_dtree_a_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__b_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    image_3585698774939316521_a_b_b: ( produc3469756349985706280ee_a_b > produc4558475209616630778_a_b_b ) > set_Pr6717515126349854430ee_a_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__b_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
    image_198770111635725048t_unit: ( produc3469756349985706280ee_a_b > produc8459935480633519975t_unit ) > set_Pr6717515126349854430ee_a_b > set_Pr5094982260447487303t_unit ).

thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_Itf__b_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J_001t__Product____Type__Oprod_Itf__b_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    image_2496979915308392023ee_a_b: ( produc3469756349985706280ee_a_b > produc3469756349985706280ee_a_b ) > set_Pr6717515126349854430ee_a_b > set_Pr6717515126349854430ee_a_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Ounit_001_062_Itf__b_Mtf__a_J,type,
    image_3413377689041543532it_b_a: ( product_unit > b > a ) > set_Product_unit > set_b_a ).

thf(sy_c_Set_Oimage_001t__Product____Type__Ounit_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    image_5682477522529595202ee_a_b: ( product_unit > dtree_a_b ) > set_Product_unit > set_dtree_a_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Ounit_001t__Nat__Onat,type,
    image_875570014554754200it_nat: ( product_unit > nat ) > set_Product_unit > set_nat ).

thf(sy_c_Set_Oimage_001t__Product____Type__Ounit_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    image_2521969012719430850_a_b_b: ( product_unit > produc4558475209616630778_a_b_b ) > set_Product_unit > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Set_Oimage_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
    image_405062704495631173t_unit: ( product_unit > product_unit ) > set_Product_unit > set_Product_unit ).

thf(sy_c_Set_Oimage_001t__Product____Type__Ounit_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    image_7778121751606633509t_unit: ( product_unit > set_Product_unit ) > set_Product_unit > set_set_Product_unit ).

thf(sy_c_Set_Oimage_001t__Product____Type__Ounit_001t__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
    image_2037928093122670381t_unit: ( product_unit > sum_su8719719018421925477t_unit ) > set_Product_unit > set_Su4110612849109743515t_unit ).

thf(sy_c_Set_Oimage_001t__Product____Type__Ounit_001tf__a,type,
    image_Product_unit_a: ( product_unit > a ) > set_Product_unit > set_a ).

thf(sy_c_Set_Oimage_001t__Product____Type__Ounit_001tf__b,type,
    image_Product_unit_b: ( product_unit > b ) > set_Product_unit > set_b ).

thf(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    image_4903599603319290215_a_b_b: ( set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b ) > set_se3183138701204633190_a_b_b > set_se3183138701204633190_a_b_b ).

thf(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Ounit_J_001_062_Itf__b_Mtf__a_J,type,
    image_9176062692026671692it_b_a: ( set_Product_unit > b > a ) > set_set_Product_unit > set_b_a ).

thf(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Ounit_J_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    image_929270244206465058ee_a_b: ( set_Product_unit > dtree_a_b ) > set_set_Product_unit > set_dtree_a_b ).

thf(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Ounit_J_001t__Nat__Onat,type,
    image_4084087346006658424it_nat: ( set_Product_unit > nat ) > set_set_Product_unit > set_nat ).

thf(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    image_1948271130669936034_a_b_b: ( set_Product_unit > produc4558475209616630778_a_b_b ) > set_set_Product_unit > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Ounit_J_001t__Product____Type__Ounit,type,
    image_4670244198609810021t_unit: ( set_Product_unit > product_unit ) > set_set_Product_unit > set_Product_unit ).

thf(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Ounit_J_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    image_4019945301284682565t_unit: ( set_Product_unit > set_Product_unit ) > set_set_Product_unit > set_set_Product_unit ).

thf(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Ounit_J_001t__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
    image_5049393547324665869t_unit: ( set_Product_unit > sum_su8719719018421925477t_unit ) > set_set_Product_unit > set_Su4110612849109743515t_unit ).

thf(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Ounit_J_001tf__a,type,
    image_7680679895738368854unit_a: ( set_Product_unit > a ) > set_set_Product_unit > set_a ).

thf(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Ounit_J_001tf__b,type,
    image_7680679895738368855unit_b: ( set_Product_unit > b ) > set_set_Product_unit > set_b ).

thf(sy_c_Set_Oimage_001t__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_001_062_Itf__b_Mtf__a_J,type,
    image_3851727106056185104it_b_a: ( sum_su8719719018421925477t_unit > b > a ) > set_Su4110612849109743515t_unit > set_b_a ).

thf(sy_c_Set_Oimage_001t__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_001t__Nat__Onat,type,
    image_7724955480610936892it_nat: ( sum_su8719719018421925477t_unit > nat ) > set_Su4110612849109743515t_unit > set_nat ).

thf(sy_c_Set_Oimage_001t__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_001t__Product____Type__Ounit,type,
    image_4850905281257956513t_unit: ( sum_su8719719018421925477t_unit > product_unit ) > set_Su4110612849109743515t_unit > set_Product_unit ).

thf(sy_c_Set_Oimage_001t__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    image_1054766453263629697t_unit: ( sum_su8719719018421925477t_unit > set_Product_unit ) > set_Su4110612849109743515t_unit > set_set_Product_unit ).

thf(sy_c_Set_Oimage_001t__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_001tf__b,type,
    image_7415979216236306835unit_b: ( sum_su8719719018421925477t_unit > b ) > set_Su4110612849109743515t_unit > set_b ).

thf(sy_c_Set_Oimage_001tf__a_001t__Nat__Onat,type,
    image_a_nat: ( a > nat ) > set_a > set_nat ).

thf(sy_c_Set_Oimage_001tf__a_001tf__a,type,
    image_a_a: ( a > a ) > set_a > set_a ).

thf(sy_c_Set_Oimage_001tf__a_001tf__b,type,
    image_a_b: ( a > b ) > set_a > set_b ).

thf(sy_c_Set_Oimage_001tf__b_001t__Nat__Onat,type,
    image_b_nat: ( b > nat ) > set_b > set_nat ).

thf(sy_c_Set_Oimage_001tf__b_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    image_7642607452437185460_a_b_b: ( b > produc4558475209616630778_a_b_b ) > set_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Set_Oimage_001tf__b_001tf__a,type,
    image_b_a: ( b > a ) > set_b > set_a ).

thf(sy_c_Set_Oimage_001tf__b_001tf__b,type,
    image_b_b: ( b > b ) > set_b > set_b ).

thf(sy_c_Set_Oinsert_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    insert_dtree_a_b: dtree_a_b > set_dtree_a_b > set_dtree_a_b ).

thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
    insert_nat: nat > set_nat > set_nat ).

thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    insert1613891728210272810_a_b_b: produc4558475209616630778_a_b_b > set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Set_Oinsert_001t__Product____Type__Ounit,type,
    insert_Product_unit: product_unit > set_Product_unit > set_Product_unit ).

thf(sy_c_Set_Oinsert_001tf__b,type,
    insert_b: b > set_b > set_b ).

thf(sy_c_Set_Ois__singleton_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    is_sin1118336051388392454_a_b_b: set_Pr3012420139608375472_a_b_b > $o ).

thf(sy_c_Set_Oremove_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    remove1850832869696284629_a_b_b: produc4558475209616630778_a_b_b > set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b ).

thf(sy_c_Set_Othe__elem_001t__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    the_el4127461656392778949_a_b_b: set_Pr3012420139608375472_a_b_b > produc4558475209616630778_a_b_b ).

thf(sy_c_member_001_062_I_062_Itf__b_Mtf__a_J_M_062_Itf__b_Mtf__a_J_J,type,
    member_b_a_b_a: ( ( b > a ) > b > a ) > set_b_a_b_a > $o ).

thf(sy_c_member_001_062_Itf__b_Mtf__a_J,type,
    member_b_a: ( b > a ) > set_b_a > $o ).

thf(sy_c_member_001t__Dtree__Odtree_Itf__a_Mtf__b_J,type,
    member_dtree_a_b: dtree_a_b > set_dtree_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_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J,type,
    member4380921116106875537_a_b_b: produc4558475209616630778_a_b_b > set_Pr3012420139608375472_a_b_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_Mt__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    member9171970031259705598_a_b_b: produc8908337785154950741_a_b_b > set_Pr2755428042910921141_a_b_b > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
    member7821138191923116944t_unit: produc8459935480633519975t_unit > set_Pr5094982260447487303t_unit > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__b_Mt__Dtree__Odtree_Itf__a_Mtf__b_J_J,type,
    member3292202256475951039ee_a_b: produc3469756349985706280ee_a_b > set_Pr6717515126349854430ee_a_b > $o ).

thf(sy_c_member_001t__Product____Type__Ounit,type,
    member_Product_unit: product_unit > set_Product_unit > $o ).

thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Dtree__Odtree_Itf__a_Mtf__b_J_Mtf__b_J_J,type,
    member7431159781899395911_a_b_b: set_Pr3012420139608375472_a_b_b > set_se3183138701204633190_a_b_b > $o ).

thf(sy_c_member_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    member5877623283571906838t_unit: set_Product_unit > set_set_Product_unit > $o ).

thf(sy_c_member_001t__Sum____Type__Osum_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
    member1483886641279141628t_unit: sum_su8719719018421925477t_unit > set_Su4110612849109743515t_unit > $o ).

thf(sy_c_member_001tf__a,type,
    member_a: a > set_a > $o ).

thf(sy_c_member_001tf__b,type,
    member_b: b > set_b > $o ).

thf(sy_v_f,type,
    f: produc4558475209616630778_a_b_b > ( b > a ) > b > a ).

thf(sy_v_x,type,
    x: produc4558475209616630778_a_b_b ).

thf(sy_v_x1____,type,
    x1: dtree_a_b ).

thf(sy_v_x2____,type,
    x2: b ).

thf(sy_v_xs,type,
    xs: fset_P5281107635120001194_a_b_b ).

thf(sy_v_y,type,
    y: produc4558475209616630778_a_b_b ).

thf(sy_v_y1____,type,
    y1: dtree_a_b ).

thf(sy_v_y2____,type,
    y2: b ).

thf(sy_v_z,type,
    z: b > a ).

% Relevant facts (1277)
thf(fact_0_x__def,axiom,
    ( x
    = ( produc331601717337510060_a_b_b @ x1 @ x2 ) ) ).

% x_def
thf(fact_1_y__def,axiom,
    ( y
    = ( produc331601717337510060_a_b_b @ y1 @ y2 ) ) ).

% y_def
thf(fact_2__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062x1_Ax2_O_Ax_A_061_A_Ix1_M_Ax2_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
    ~ ! [X1: dtree_a_b,X2: b] :
        ( x
       != ( produc331601717337510060_a_b_b @ X1 @ X2 ) ) ).

% \<open>\<And>thesis. (\<And>x1 x2. x = (x1, x2) \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_3__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062y1_Ay2_O_Ay_A_061_A_Iy1_M_Ay2_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
    ~ ! [Y1: dtree_a_b,Y2: b] :
        ( y
       != ( produc331601717337510060_a_b_b @ Y1 @ Y2 ) ) ).

% \<open>\<And>thesis. (\<And>y1 y2. y = (y1, y2) \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_4_comp__apply,axiom,
    ( comp_d7292648224603294300_a_b_b
    = ( ^ [F: dtree_a_b > b,G: produc4558475209616630778_a_b_b > dtree_a_b,X: produc4558475209616630778_a_b_b] : ( F @ ( G @ X ) ) ) ) ).

% comp_apply
thf(fact_5_comp__apply,axiom,
    ( comp_b3327941365615541530_a_b_a
    = ( ^ [F: ( ( b > a ) > b > a ) > ( b > a ) > b > a,G: ( ( b > a ) > b > a ) > ( b > a ) > b > a,X: ( b > a ) > b > a] : ( F @ ( G @ X ) ) ) ) ).

% comp_apply
thf(fact_6_comp__apply,axiom,
    ( comp_b7652884982158753286_a_b_a
    = ( ^ [F: ( b > a ) > product_prod_b_a_b_a,G: ( b > a ) > b > a,X: b > a] : ( F @ ( G @ X ) ) ) ) ).

% comp_apply
thf(fact_7_comp__apply,axiom,
    ( comp_b_b_b
    = ( ^ [F: b > b,G: b > b,X: b] : ( F @ ( G @ X ) ) ) ) ).

% comp_apply
thf(fact_8_comp__apply,axiom,
    ( comp_a_a_a
    = ( ^ [F: a > a,G: a > a,X: a] : ( F @ ( G @ X ) ) ) ) ).

% comp_apply
thf(fact_9_comp__apply,axiom,
    ( comp_b_a_b_a_b_a
    = ( ^ [F: ( b > a ) > b > a,G: ( b > a ) > b > a,X: b > a] : ( F @ ( G @ X ) ) ) ) ).

% comp_apply
thf(fact_10_fun_Omap__comp,axiom,
    ! [G2: b > b,F2: dtree_a_b > b,V: produc4558475209616630778_a_b_b > dtree_a_b] :
      ( ( comp_b4098124895279589661_a_b_b @ G2 @ ( comp_d7292648224603294300_a_b_b @ F2 @ V ) )
      = ( comp_d7292648224603294300_a_b_b @ ( comp_b_b_dtree_a_b @ G2 @ F2 ) @ V ) ) ).

% fun.map_comp
thf(fact_11_fun_Omap__comp,axiom,
    ! [G2: product_prod_b_a_b_a > b > a,F2: ( b > a ) > product_prod_b_a_b_a,V: ( b > a ) > b > a] :
      ( ( comp_P1653000078598994640_a_b_a @ G2 @ ( comp_b7652884982158753286_a_b_a @ F2 @ V ) )
      = ( comp_b_a_b_a_b_a @ ( comp_P1653000078598994640_a_b_a @ G2 @ F2 ) @ V ) ) ).

% fun.map_comp
thf(fact_12_fun_Omap__comp,axiom,
    ! [G2: product_prod_b_a_b_a > product_prod_b_a_b_a,F2: ( b > a ) > product_prod_b_a_b_a,V: ( b > a ) > b > a] :
      ( ( comp_P5805957429449400903_a_b_a @ G2 @ ( comp_b7652884982158753286_a_b_a @ F2 @ V ) )
      = ( comp_b7652884982158753286_a_b_a @ ( comp_P5805957429449400903_a_b_a @ G2 @ F2 ) @ V ) ) ).

% fun.map_comp
thf(fact_13_fun_Omap__comp,axiom,
    ! [G2: dtree_a_b > b,F2: produc4558475209616630778_a_b_b > dtree_a_b,V: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b] :
      ( ( comp_d7292648224603294300_a_b_b @ G2 @ ( comp_P2227990766219928147_a_b_b @ F2 @ V ) )
      = ( comp_P7790946621747331036_a_b_b @ ( comp_d7292648224603294300_a_b_b @ G2 @ F2 ) @ V ) ) ).

% fun.map_comp
thf(fact_14_fun_Omap__comp,axiom,
    ! [G2: dtree_a_b > b,F2: dtree_a_b > dtree_a_b,V: produc4558475209616630778_a_b_b > dtree_a_b] :
      ( ( comp_d7292648224603294300_a_b_b @ G2 @ ( comp_d9193377603055859667_a_b_b @ F2 @ V ) )
      = ( comp_d7292648224603294300_a_b_b @ ( comp_d2161864785492113116ee_a_b @ G2 @ F2 ) @ V ) ) ).

% fun.map_comp
thf(fact_15_fun_Omap__comp,axiom,
    ! [G2: ( ( b > a ) > b > a ) > ( b > a ) > b > a,F2: ( ( b > a ) > b > a ) > ( b > a ) > b > a,V: ( ( b > a ) > b > a ) > ( b > a ) > b > a] :
      ( ( comp_b3327941365615541530_a_b_a @ G2 @ ( comp_b3327941365615541530_a_b_a @ F2 @ V ) )
      = ( comp_b3327941365615541530_a_b_a @ ( comp_b3327941365615541530_a_b_a @ G2 @ F2 ) @ V ) ) ).

% fun.map_comp
thf(fact_16_fun_Omap__comp,axiom,
    ! [G2: ( b > a ) > product_prod_b_a_b_a,F2: ( b > a ) > b > a,V: ( b > a ) > b > a] :
      ( ( comp_b7652884982158753286_a_b_a @ G2 @ ( comp_b_a_b_a_b_a @ F2 @ V ) )
      = ( comp_b7652884982158753286_a_b_a @ ( comp_b7652884982158753286_a_b_a @ G2 @ F2 ) @ V ) ) ).

% fun.map_comp
thf(fact_17_fun_Omap__comp,axiom,
    ! [G2: b > b,F2: b > b,V: b > b] :
      ( ( comp_b_b_b @ G2 @ ( comp_b_b_b @ F2 @ V ) )
      = ( comp_b_b_b @ ( comp_b_b_b @ G2 @ F2 ) @ V ) ) ).

% fun.map_comp
thf(fact_18_fun_Omap__comp,axiom,
    ! [G2: a > a,F2: a > a,V: a > a] :
      ( ( comp_a_a_a @ G2 @ ( comp_a_a_a @ F2 @ V ) )
      = ( comp_a_a_a @ ( comp_a_a_a @ G2 @ F2 ) @ V ) ) ).

% fun.map_comp
thf(fact_19_fun_Omap__comp,axiom,
    ! [G2: ( b > a ) > b > a,F2: ( b > a ) > b > a,V: ( b > a ) > b > a] :
      ( ( comp_b_a_b_a_b_a @ G2 @ ( comp_b_a_b_a_b_a @ F2 @ V ) )
      = ( comp_b_a_b_a_b_a @ ( comp_b_a_b_a_b_a @ G2 @ F2 ) @ V ) ) ).

% fun.map_comp
thf(fact_20_comp__def,axiom,
    ( comp_d7292648224603294300_a_b_b
    = ( ^ [F: dtree_a_b > b,G: produc4558475209616630778_a_b_b > dtree_a_b,X: produc4558475209616630778_a_b_b] : ( F @ ( G @ X ) ) ) ) ).

% comp_def
thf(fact_21_comp__def,axiom,
    ( comp_b3327941365615541530_a_b_a
    = ( ^ [F: ( ( b > a ) > b > a ) > ( b > a ) > b > a,G: ( ( b > a ) > b > a ) > ( b > a ) > b > a,X: ( b > a ) > b > a] : ( F @ ( G @ X ) ) ) ) ).

% comp_def
thf(fact_22_comp__def,axiom,
    ( comp_b7652884982158753286_a_b_a
    = ( ^ [F: ( b > a ) > product_prod_b_a_b_a,G: ( b > a ) > b > a,X: b > a] : ( F @ ( G @ X ) ) ) ) ).

% comp_def
thf(fact_23_comp__def,axiom,
    ( comp_b_b_b
    = ( ^ [F: b > b,G: b > b,X: b] : ( F @ ( G @ X ) ) ) ) ).

% comp_def
thf(fact_24_comp__def,axiom,
    ( comp_a_a_a
    = ( ^ [F: a > a,G: a > a,X: a] : ( F @ ( G @ X ) ) ) ) ).

% comp_def
thf(fact_25_comp__def,axiom,
    ( comp_b_a_b_a_b_a
    = ( ^ [F: ( b > a ) > b > a,G: ( b > a ) > b > a,X: b > a] : ( F @ ( G @ X ) ) ) ) ).

% comp_def
thf(fact_26_comp__assoc,axiom,
    ! [F2: dtree_a_b > b,G2: produc4558475209616630778_a_b_b > dtree_a_b,H: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b] :
      ( ( comp_P7790946621747331036_a_b_b @ ( comp_d7292648224603294300_a_b_b @ F2 @ G2 ) @ H )
      = ( comp_d7292648224603294300_a_b_b @ F2 @ ( comp_P2227990766219928147_a_b_b @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_27_comp__assoc,axiom,
    ! [F2: product_prod_b_a_b_a > b > a,G2: ( b > a ) > product_prod_b_a_b_a,H: ( b > a ) > b > a] :
      ( ( comp_b_a_b_a_b_a @ ( comp_P1653000078598994640_a_b_a @ F2 @ G2 ) @ H )
      = ( comp_P1653000078598994640_a_b_a @ F2 @ ( comp_b7652884982158753286_a_b_a @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_28_comp__assoc,axiom,
    ! [F2: b > b,G2: dtree_a_b > b,H: produc4558475209616630778_a_b_b > dtree_a_b] :
      ( ( comp_d7292648224603294300_a_b_b @ ( comp_b_b_dtree_a_b @ F2 @ G2 ) @ H )
      = ( comp_b4098124895279589661_a_b_b @ F2 @ ( comp_d7292648224603294300_a_b_b @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_29_comp__assoc,axiom,
    ! [F2: dtree_a_b > b,G2: dtree_a_b > dtree_a_b,H: produc4558475209616630778_a_b_b > dtree_a_b] :
      ( ( comp_d7292648224603294300_a_b_b @ ( comp_d2161864785492113116ee_a_b @ F2 @ G2 ) @ H )
      = ( comp_d7292648224603294300_a_b_b @ F2 @ ( comp_d9193377603055859667_a_b_b @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_30_comp__assoc,axiom,
    ! [F2: ( ( b > a ) > b > a ) > ( b > a ) > b > a,G2: ( ( b > a ) > b > a ) > ( b > a ) > b > a,H: ( ( b > a ) > b > a ) > ( b > a ) > b > a] :
      ( ( comp_b3327941365615541530_a_b_a @ ( comp_b3327941365615541530_a_b_a @ F2 @ G2 ) @ H )
      = ( comp_b3327941365615541530_a_b_a @ F2 @ ( comp_b3327941365615541530_a_b_a @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_31_comp__assoc,axiom,
    ! [F2: product_prod_b_a_b_a > product_prod_b_a_b_a,G2: ( b > a ) > product_prod_b_a_b_a,H: ( b > a ) > b > a] :
      ( ( comp_b7652884982158753286_a_b_a @ ( comp_P5805957429449400903_a_b_a @ F2 @ G2 ) @ H )
      = ( comp_P5805957429449400903_a_b_a @ F2 @ ( comp_b7652884982158753286_a_b_a @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_32_comp__assoc,axiom,
    ! [F2: ( b > a ) > product_prod_b_a_b_a,G2: ( b > a ) > b > a,H: ( b > a ) > b > a] :
      ( ( comp_b7652884982158753286_a_b_a @ ( comp_b7652884982158753286_a_b_a @ F2 @ G2 ) @ H )
      = ( comp_b7652884982158753286_a_b_a @ F2 @ ( comp_b_a_b_a_b_a @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_33_comp__assoc,axiom,
    ! [F2: b > b,G2: b > b,H: b > b] :
      ( ( comp_b_b_b @ ( comp_b_b_b @ F2 @ G2 ) @ H )
      = ( comp_b_b_b @ F2 @ ( comp_b_b_b @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_34_comp__assoc,axiom,
    ! [F2: a > a,G2: a > a,H: a > a] :
      ( ( comp_a_a_a @ ( comp_a_a_a @ F2 @ G2 ) @ H )
      = ( comp_a_a_a @ F2 @ ( comp_a_a_a @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_35_comp__assoc,axiom,
    ! [F2: ( b > a ) > b > a,G2: ( b > a ) > b > a,H: ( b > a ) > b > a] :
      ( ( comp_b_a_b_a_b_a @ ( comp_b_a_b_a_b_a @ F2 @ G2 ) @ H )
      = ( comp_b_a_b_a_b_a @ F2 @ ( comp_b_a_b_a_b_a @ G2 @ H ) ) ) ).

% comp_assoc
thf(fact_36_comp__eq__dest,axiom,
    ! [A: dtree_a_b > b,B: produc4558475209616630778_a_b_b > dtree_a_b,C: dtree_a_b > b,D: produc4558475209616630778_a_b_b > dtree_a_b,V: produc4558475209616630778_a_b_b] :
      ( ( ( comp_d7292648224603294300_a_b_b @ A @ B )
        = ( comp_d7292648224603294300_a_b_b @ C @ D ) )
     => ( ( A @ ( B @ V ) )
        = ( C @ ( D @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_37_comp__eq__dest,axiom,
    ! [A: ( ( b > a ) > b > a ) > ( b > a ) > b > a,B: ( ( b > a ) > b > a ) > ( b > a ) > b > a,C: ( ( b > a ) > b > a ) > ( b > a ) > b > a,D: ( ( b > a ) > b > a ) > ( b > a ) > b > a,V: ( b > a ) > b > a] :
      ( ( ( comp_b3327941365615541530_a_b_a @ A @ B )
        = ( comp_b3327941365615541530_a_b_a @ C @ D ) )
     => ( ( A @ ( B @ V ) )
        = ( C @ ( D @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_38_comp__eq__dest,axiom,
    ! [A: ( b > a ) > product_prod_b_a_b_a,B: ( b > a ) > b > a,C: ( b > a ) > product_prod_b_a_b_a,D: ( b > a ) > b > a,V: b > a] :
      ( ( ( comp_b7652884982158753286_a_b_a @ A @ B )
        = ( comp_b7652884982158753286_a_b_a @ C @ D ) )
     => ( ( A @ ( B @ V ) )
        = ( C @ ( D @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_39_comp__eq__dest,axiom,
    ! [A: b > b,B: b > b,C: b > b,D: b > b,V: b] :
      ( ( ( comp_b_b_b @ A @ B )
        = ( comp_b_b_b @ C @ D ) )
     => ( ( A @ ( B @ V ) )
        = ( C @ ( D @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_40_comp__eq__dest,axiom,
    ! [A: a > a,B: a > a,C: a > a,D: a > a,V: a] :
      ( ( ( comp_a_a_a @ A @ B )
        = ( comp_a_a_a @ C @ D ) )
     => ( ( A @ ( B @ V ) )
        = ( C @ ( D @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_41_comp__eq__dest,axiom,
    ! [A: ( b > a ) > b > a,B: ( b > a ) > b > a,C: ( b > a ) > b > a,D: ( b > a ) > b > a,V: b > a] :
      ( ( ( comp_b_a_b_a_b_a @ A @ B )
        = ( comp_b_a_b_a_b_a @ C @ D ) )
     => ( ( A @ ( B @ V ) )
        = ( C @ ( D @ V ) ) ) ) ).

% comp_eq_dest
thf(fact_42_comp__eq__elim,axiom,
    ! [A: dtree_a_b > b,B: produc4558475209616630778_a_b_b > dtree_a_b,C: dtree_a_b > b,D: produc4558475209616630778_a_b_b > dtree_a_b] :
      ( ( ( comp_d7292648224603294300_a_b_b @ A @ B )
        = ( comp_d7292648224603294300_a_b_b @ C @ D ) )
     => ! [V2: produc4558475209616630778_a_b_b] :
          ( ( A @ ( B @ V2 ) )
          = ( C @ ( D @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_43_comp__eq__elim,axiom,
    ! [A: ( ( b > a ) > b > a ) > ( b > a ) > b > a,B: ( ( b > a ) > b > a ) > ( b > a ) > b > a,C: ( ( b > a ) > b > a ) > ( b > a ) > b > a,D: ( ( b > a ) > b > a ) > ( b > a ) > b > a] :
      ( ( ( comp_b3327941365615541530_a_b_a @ A @ B )
        = ( comp_b3327941365615541530_a_b_a @ C @ D ) )
     => ! [V2: ( b > a ) > b > a] :
          ( ( A @ ( B @ V2 ) )
          = ( C @ ( D @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_44_comp__eq__elim,axiom,
    ! [A: ( b > a ) > product_prod_b_a_b_a,B: ( b > a ) > b > a,C: ( b > a ) > product_prod_b_a_b_a,D: ( b > a ) > b > a] :
      ( ( ( comp_b7652884982158753286_a_b_a @ A @ B )
        = ( comp_b7652884982158753286_a_b_a @ C @ D ) )
     => ! [V2: b > a] :
          ( ( A @ ( B @ V2 ) )
          = ( C @ ( D @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_45_comp__eq__elim,axiom,
    ! [A: b > b,B: b > b,C: b > b,D: b > b] :
      ( ( ( comp_b_b_b @ A @ B )
        = ( comp_b_b_b @ C @ D ) )
     => ! [V2: b] :
          ( ( A @ ( B @ V2 ) )
          = ( C @ ( D @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_46_comp__eq__elim,axiom,
    ! [A: a > a,B: a > a,C: a > a,D: a > a] :
      ( ( ( comp_a_a_a @ A @ B )
        = ( comp_a_a_a @ C @ D ) )
     => ! [V2: a] :
          ( ( A @ ( B @ V2 ) )
          = ( C @ ( D @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_47_comp__eq__elim,axiom,
    ! [A: ( b > a ) > b > a,B: ( b > a ) > b > a,C: ( b > a ) > b > a,D: ( b > a ) > b > a] :
      ( ( ( comp_b_a_b_a_b_a @ A @ B )
        = ( comp_b_a_b_a_b_a @ C @ D ) )
     => ! [V2: b > a] :
          ( ( A @ ( B @ V2 ) )
          = ( C @ ( D @ V2 ) ) ) ) ).

% comp_eq_elim
thf(fact_48_comp__cong,axiom,
    ! [F2: dtree_a_b > b,G2: produc4558475209616630778_a_b_b > dtree_a_b,X3: produc4558475209616630778_a_b_b,F3: dtree_a_b > b,G3: produc4558475209616630778_a_b_b > dtree_a_b,X4: produc4558475209616630778_a_b_b] :
      ( ( ( F2 @ ( G2 @ X3 ) )
        = ( F3 @ ( G3 @ X4 ) ) )
     => ( ( comp_d7292648224603294300_a_b_b @ F2 @ G2 @ X3 )
        = ( comp_d7292648224603294300_a_b_b @ F3 @ G3 @ X4 ) ) ) ).

% comp_cong
thf(fact_49_comp__cong,axiom,
    ! [F2: dtree_a_b > b,G2: produc4558475209616630778_a_b_b > dtree_a_b,X3: produc4558475209616630778_a_b_b,F3: b > b,G3: b > b,X4: b] :
      ( ( ( F2 @ ( G2 @ X3 ) )
        = ( F3 @ ( G3 @ X4 ) ) )
     => ( ( comp_d7292648224603294300_a_b_b @ F2 @ G2 @ X3 )
        = ( comp_b_b_b @ F3 @ G3 @ X4 ) ) ) ).

% comp_cong
thf(fact_50_comp__cong,axiom,
    ! [F2: ( ( b > a ) > b > a ) > ( b > a ) > b > a,G2: ( ( b > a ) > b > a ) > ( b > a ) > b > a,X3: ( b > a ) > b > a,F3: ( ( b > a ) > b > a ) > ( b > a ) > b > a,G3: ( ( b > a ) > b > a ) > ( b > a ) > b > a,X4: ( b > a ) > b > a] :
      ( ( ( F2 @ ( G2 @ X3 ) )
        = ( F3 @ ( G3 @ X4 ) ) )
     => ( ( comp_b3327941365615541530_a_b_a @ F2 @ G2 @ X3 )
        = ( comp_b3327941365615541530_a_b_a @ F3 @ G3 @ X4 ) ) ) ).

% comp_cong
thf(fact_51_comp__cong,axiom,
    ! [F2: ( b > a ) > product_prod_b_a_b_a,G2: ( b > a ) > b > a,X3: b > a,F3: ( b > a ) > product_prod_b_a_b_a,G3: ( b > a ) > b > a,X4: b > a] :
      ( ( ( F2 @ ( G2 @ X3 ) )
        = ( F3 @ ( G3 @ X4 ) ) )
     => ( ( comp_b7652884982158753286_a_b_a @ F2 @ G2 @ X3 )
        = ( comp_b7652884982158753286_a_b_a @ F3 @ G3 @ X4 ) ) ) ).

% comp_cong
thf(fact_52_comp__cong,axiom,
    ! [F2: b > b,G2: b > b,X3: b,F3: dtree_a_b > b,G3: produc4558475209616630778_a_b_b > dtree_a_b,X4: produc4558475209616630778_a_b_b] :
      ( ( ( F2 @ ( G2 @ X3 ) )
        = ( F3 @ ( G3 @ X4 ) ) )
     => ( ( comp_b_b_b @ F2 @ G2 @ X3 )
        = ( comp_d7292648224603294300_a_b_b @ F3 @ G3 @ X4 ) ) ) ).

% comp_cong
thf(fact_53_comp__cong,axiom,
    ! [F2: b > b,G2: b > b,X3: b,F3: b > b,G3: b > b,X4: b] :
      ( ( ( F2 @ ( G2 @ X3 ) )
        = ( F3 @ ( G3 @ X4 ) ) )
     => ( ( comp_b_b_b @ F2 @ G2 @ X3 )
        = ( comp_b_b_b @ F3 @ G3 @ X4 ) ) ) ).

% comp_cong
thf(fact_54_comp__cong,axiom,
    ! [F2: a > a,G2: a > a,X3: a,F3: a > a,G3: a > a,X4: a] :
      ( ( ( F2 @ ( G2 @ X3 ) )
        = ( F3 @ ( G3 @ X4 ) ) )
     => ( ( comp_a_a_a @ F2 @ G2 @ X3 )
        = ( comp_a_a_a @ F3 @ G3 @ X4 ) ) ) ).

% comp_cong
thf(fact_55_comp__cong,axiom,
    ! [F2: ( b > a ) > b > a,G2: ( b > a ) > b > a,X3: b > a,F3: ( b > a ) > b > a,G3: ( b > a ) > b > a,X4: b > a] :
      ( ( ( F2 @ ( G2 @ X3 ) )
        = ( F3 @ ( G3 @ X4 ) ) )
     => ( ( comp_b_a_b_a_b_a @ F2 @ G2 @ X3 )
        = ( comp_b_a_b_a_b_a @ F3 @ G3 @ X4 ) ) ) ).

% comp_cong
thf(fact_56_comp__eq__dest__lhs,axiom,
    ! [A: dtree_a_b > b,B: produc4558475209616630778_a_b_b > dtree_a_b,C: produc4558475209616630778_a_b_b > b,V: produc4558475209616630778_a_b_b] :
      ( ( ( comp_d7292648224603294300_a_b_b @ A @ B )
        = C )
     => ( ( A @ ( B @ V ) )
        = ( C @ V ) ) ) ).

% comp_eq_dest_lhs
thf(fact_57_comp__eq__dest__lhs,axiom,
    ! [A: ( ( b > a ) > b > a ) > ( b > a ) > b > a,B: ( ( b > a ) > b > a ) > ( b > a ) > b > a,C: ( ( b > a ) > b > a ) > ( b > a ) > b > a,V: ( b > a ) > b > a] :
      ( ( ( comp_b3327941365615541530_a_b_a @ A @ B )
        = C )
     => ( ( A @ ( B @ V ) )
        = ( C @ V ) ) ) ).

% comp_eq_dest_lhs
thf(fact_58_comp__eq__dest__lhs,axiom,
    ! [A: ( b > a ) > product_prod_b_a_b_a,B: ( b > a ) > b > a,C: ( b > a ) > product_prod_b_a_b_a,V: b > a] :
      ( ( ( comp_b7652884982158753286_a_b_a @ A @ B )
        = C )
     => ( ( A @ ( B @ V ) )
        = ( C @ V ) ) ) ).

% comp_eq_dest_lhs
thf(fact_59_comp__eq__dest__lhs,axiom,
    ! [A: b > b,B: b > b,C: b > b,V: b] :
      ( ( ( comp_b_b_b @ A @ B )
        = C )
     => ( ( A @ ( B @ V ) )
        = ( C @ V ) ) ) ).

% comp_eq_dest_lhs
thf(fact_60_comp__eq__dest__lhs,axiom,
    ! [A: a > a,B: a > a,C: a > a,V: a] :
      ( ( ( comp_a_a_a @ A @ B )
        = C )
     => ( ( A @ ( B @ V ) )
        = ( C @ V ) ) ) ).

% comp_eq_dest_lhs
thf(fact_61_comp__eq__dest__lhs,axiom,
    ! [A: ( b > a ) > b > a,B: ( b > a ) > b > a,C: ( b > a ) > b > a,V: b > a] :
      ( ( ( comp_b_a_b_a_b_a @ A @ B )
        = C )
     => ( ( A @ ( B @ V ) )
        = ( C @ V ) ) ) ).

% comp_eq_dest_lhs
thf(fact_62_comp__apply__eq,axiom,
    ! [F2: dtree_a_b > b,G2: produc4558475209616630778_a_b_b > dtree_a_b,X3: produc4558475209616630778_a_b_b,H: dtree_a_b > b,K: produc4558475209616630778_a_b_b > dtree_a_b] :
      ( ( ( F2 @ ( G2 @ X3 ) )
        = ( H @ ( K @ X3 ) ) )
     => ( ( comp_d7292648224603294300_a_b_b @ F2 @ G2 @ X3 )
        = ( comp_d7292648224603294300_a_b_b @ H @ K @ X3 ) ) ) ).

% comp_apply_eq
thf(fact_63_comp__apply__eq,axiom,
    ! [F2: ( ( b > a ) > b > a ) > ( b > a ) > b > a,G2: ( ( b > a ) > b > a ) > ( b > a ) > b > a,X3: ( b > a ) > b > a,H: ( ( b > a ) > b > a ) > ( b > a ) > b > a,K: ( ( b > a ) > b > a ) > ( b > a ) > b > a] :
      ( ( ( F2 @ ( G2 @ X3 ) )
        = ( H @ ( K @ X3 ) ) )
     => ( ( comp_b3327941365615541530_a_b_a @ F2 @ G2 @ X3 )
        = ( comp_b3327941365615541530_a_b_a @ H @ K @ X3 ) ) ) ).

% comp_apply_eq
thf(fact_64_comp__apply__eq,axiom,
    ! [F2: ( b > a ) > product_prod_b_a_b_a,G2: ( b > a ) > b > a,X3: b > a,H: ( b > a ) > product_prod_b_a_b_a,K: ( b > a ) > b > a] :
      ( ( ( F2 @ ( G2 @ X3 ) )
        = ( H @ ( K @ X3 ) ) )
     => ( ( comp_b7652884982158753286_a_b_a @ F2 @ G2 @ X3 )
        = ( comp_b7652884982158753286_a_b_a @ H @ K @ X3 ) ) ) ).

% comp_apply_eq
thf(fact_65_comp__apply__eq,axiom,
    ! [F2: b > b,G2: b > b,X3: b,H: b > b,K: b > b] :
      ( ( ( F2 @ ( G2 @ X3 ) )
        = ( H @ ( K @ X3 ) ) )
     => ( ( comp_b_b_b @ F2 @ G2 @ X3 )
        = ( comp_b_b_b @ H @ K @ X3 ) ) ) ).

% comp_apply_eq
thf(fact_66_comp__apply__eq,axiom,
    ! [F2: a > a,G2: a > a,X3: a,H: a > a,K: a > a] :
      ( ( ( F2 @ ( G2 @ X3 ) )
        = ( H @ ( K @ X3 ) ) )
     => ( ( comp_a_a_a @ F2 @ G2 @ X3 )
        = ( comp_a_a_a @ H @ K @ X3 ) ) ) ).

% comp_apply_eq
thf(fact_67_comp__apply__eq,axiom,
    ! [F2: ( b > a ) > b > a,G2: ( b > a ) > b > a,X3: b > a,H: ( b > a ) > b > a,K: ( b > a ) > b > a] :
      ( ( ( F2 @ ( G2 @ X3 ) )
        = ( H @ ( K @ X3 ) ) )
     => ( ( comp_b_a_b_a_b_a @ F2 @ G2 @ X3 )
        = ( comp_b_a_b_a_b_a @ H @ K @ X3 ) ) ) ).

% comp_apply_eq
thf(fact_68_function__factors__left,axiom,
    ! [G2: produc4558475209616630778_a_b_b > dtree_a_b,F2: produc4558475209616630778_a_b_b > b] :
      ( ( ! [X: produc4558475209616630778_a_b_b,Y: produc4558475209616630778_a_b_b] :
            ( ( ( G2 @ X )
              = ( G2 @ Y ) )
           => ( ( F2 @ X )
              = ( F2 @ Y ) ) ) )
      = ( ? [H2: dtree_a_b > b] :
            ( F2
            = ( comp_d7292648224603294300_a_b_b @ H2 @ G2 ) ) ) ) ).

% function_factors_left
thf(fact_69_function__factors__left,axiom,
    ! [G2: ( ( b > a ) > b > a ) > ( b > a ) > b > a,F2: ( ( b > a ) > b > a ) > ( b > a ) > b > a] :
      ( ( ! [X: ( b > a ) > b > a,Y: ( b > a ) > b > a] :
            ( ( ( G2 @ X )
              = ( G2 @ Y ) )
           => ( ( F2 @ X )
              = ( F2 @ Y ) ) ) )
      = ( ? [H2: ( ( b > a ) > b > a ) > ( b > a ) > b > a] :
            ( F2
            = ( comp_b3327941365615541530_a_b_a @ H2 @ G2 ) ) ) ) ).

% function_factors_left
thf(fact_70_function__factors__left,axiom,
    ! [G2: ( b > a ) > b > a,F2: ( b > a ) > product_prod_b_a_b_a] :
      ( ( ! [X: b > a,Y: b > a] :
            ( ( ( G2 @ X )
              = ( G2 @ Y ) )
           => ( ( F2 @ X )
              = ( F2 @ Y ) ) ) )
      = ( ? [H2: ( b > a ) > product_prod_b_a_b_a] :
            ( F2
            = ( comp_b7652884982158753286_a_b_a @ H2 @ G2 ) ) ) ) ).

% function_factors_left
thf(fact_71_function__factors__left,axiom,
    ! [G2: b > b,F2: b > b] :
      ( ( ! [X: b,Y: b] :
            ( ( ( G2 @ X )
              = ( G2 @ Y ) )
           => ( ( F2 @ X )
              = ( F2 @ Y ) ) ) )
      = ( ? [H2: b > b] :
            ( F2
            = ( comp_b_b_b @ H2 @ G2 ) ) ) ) ).

% function_factors_left
thf(fact_72_function__factors__left,axiom,
    ! [G2: a > a,F2: a > a] :
      ( ( ! [X: a,Y: a] :
            ( ( ( G2 @ X )
              = ( G2 @ Y ) )
           => ( ( F2 @ X )
              = ( F2 @ Y ) ) ) )
      = ( ? [H2: a > a] :
            ( F2
            = ( comp_a_a_a @ H2 @ G2 ) ) ) ) ).

% function_factors_left
thf(fact_73_function__factors__left,axiom,
    ! [G2: ( b > a ) > b > a,F2: ( b > a ) > b > a] :
      ( ( ! [X: b > a,Y: b > a] :
            ( ( ( G2 @ X )
              = ( G2 @ Y ) )
           => ( ( F2 @ X )
              = ( F2 @ Y ) ) ) )
      = ( ? [H2: ( b > a ) > b > a] :
            ( F2
            = ( comp_b_a_b_a_b_a @ H2 @ G2 ) ) ) ) ).

% function_factors_left
thf(fact_74_function__factors__right,axiom,
    ! [G2: dtree_a_b > b,F2: produc4558475209616630778_a_b_b > b] :
      ( ( ! [X: produc4558475209616630778_a_b_b] :
          ? [Y: dtree_a_b] :
            ( ( G2 @ Y )
            = ( F2 @ X ) ) )
      = ( ? [H2: produc4558475209616630778_a_b_b > dtree_a_b] :
            ( F2
            = ( comp_d7292648224603294300_a_b_b @ G2 @ H2 ) ) ) ) ).

% function_factors_right
thf(fact_75_function__factors__right,axiom,
    ! [G2: ( ( b > a ) > b > a ) > ( b > a ) > b > a,F2: ( ( b > a ) > b > a ) > ( b > a ) > b > a] :
      ( ( ! [X: ( b > a ) > b > a] :
          ? [Y: ( b > a ) > b > a] :
            ( ( G2 @ Y )
            = ( F2 @ X ) ) )
      = ( ? [H2: ( ( b > a ) > b > a ) > ( b > a ) > b > a] :
            ( F2
            = ( comp_b3327941365615541530_a_b_a @ G2 @ H2 ) ) ) ) ).

% function_factors_right
thf(fact_76_function__factors__right,axiom,
    ! [G2: ( b > a ) > product_prod_b_a_b_a,F2: ( b > a ) > product_prod_b_a_b_a] :
      ( ( ! [X: b > a] :
          ? [Y: b > a] :
            ( ( G2 @ Y )
            = ( F2 @ X ) ) )
      = ( ? [H2: ( b > a ) > b > a] :
            ( F2
            = ( comp_b7652884982158753286_a_b_a @ G2 @ H2 ) ) ) ) ).

% function_factors_right
thf(fact_77_function__factors__right,axiom,
    ! [G2: b > b,F2: b > b] :
      ( ( ! [X: b] :
          ? [Y: b] :
            ( ( G2 @ Y )
            = ( F2 @ X ) ) )
      = ( ? [H2: b > b] :
            ( F2
            = ( comp_b_b_b @ G2 @ H2 ) ) ) ) ).

% function_factors_right
thf(fact_78_function__factors__right,axiom,
    ! [G2: a > a,F2: a > a] :
      ( ( ! [X: a] :
          ? [Y: a] :
            ( ( G2 @ Y )
            = ( F2 @ X ) ) )
      = ( ? [H2: a > a] :
            ( F2
            = ( comp_a_a_a @ G2 @ H2 ) ) ) ) ).

% function_factors_right
thf(fact_79_function__factors__right,axiom,
    ! [G2: ( b > a ) > b > a,F2: ( b > a ) > b > a] :
      ( ( ! [X: b > a] :
          ? [Y: b > a] :
            ( ( G2 @ Y )
            = ( F2 @ X ) ) )
      = ( ? [H2: ( b > a ) > b > a] :
            ( F2
            = ( comp_b_a_b_a_b_a @ G2 @ H2 ) ) ) ) ).

% function_factors_right
thf(fact_80_type__copy__map__cong0,axiom,
    ! [M: ( b > a ) > b > a,G2: ( b > a ) > b > a,X3: b > a,N: ( b > a ) > b > a,H: ( b > a ) > b > a,F2: ( b > a ) > b > a] :
      ( ( ( M @ ( G2 @ X3 ) )
        = ( N @ ( H @ X3 ) ) )
     => ( ( comp_b_a_b_a_b_a @ ( comp_b_a_b_a_b_a @ F2 @ M ) @ G2 @ X3 )
        = ( comp_b_a_b_a_b_a @ ( comp_b_a_b_a_b_a @ F2 @ N ) @ H @ X3 ) ) ) ).

% type_copy_map_cong0
thf(fact_81_type__copy__map__cong0,axiom,
    ! [M: b > b,G2: b > b,X3: b,N: b > b,H: b > b,F2: b > b] :
      ( ( ( M @ ( G2 @ X3 ) )
        = ( N @ ( H @ X3 ) ) )
     => ( ( comp_b_b_b @ ( comp_b_b_b @ F2 @ M ) @ G2 @ X3 )
        = ( comp_b_b_b @ ( comp_b_b_b @ F2 @ N ) @ H @ X3 ) ) ) ).

% type_copy_map_cong0
thf(fact_82_type__copy__map__cong0,axiom,
    ! [M: a > a,G2: a > a,X3: a,N: a > a,H: a > a,F2: a > a] :
      ( ( ( M @ ( G2 @ X3 ) )
        = ( N @ ( H @ X3 ) ) )
     => ( ( comp_a_a_a @ ( comp_a_a_a @ F2 @ M ) @ G2 @ X3 )
        = ( comp_a_a_a @ ( comp_a_a_a @ F2 @ N ) @ H @ X3 ) ) ) ).

% type_copy_map_cong0
thf(fact_83_type__copy__map__cong0,axiom,
    ! [M: produc4558475209616630778_a_b_b > dtree_a_b,G2: b > produc4558475209616630778_a_b_b,X3: b,N: b > dtree_a_b,H: b > b,F2: dtree_a_b > b] :
      ( ( ( M @ ( G2 @ X3 ) )
        = ( N @ ( H @ X3 ) ) )
     => ( ( comp_P1056441264483508125_b_b_b @ ( comp_d7292648224603294300_a_b_b @ F2 @ M ) @ G2 @ X3 )
        = ( comp_b_b_b @ ( comp_dtree_a_b_b_b @ F2 @ N ) @ H @ X3 ) ) ) ).

% type_copy_map_cong0
thf(fact_84_type__copy__map__cong0,axiom,
    ! [M: b > b,G2: produc4558475209616630778_a_b_b > b,X3: produc4558475209616630778_a_b_b,N: dtree_a_b > b,H: produc4558475209616630778_a_b_b > dtree_a_b,F2: b > b] :
      ( ( ( M @ ( G2 @ X3 ) )
        = ( N @ ( H @ X3 ) ) )
     => ( ( comp_b4098124895279589661_a_b_b @ ( comp_b_b_b @ F2 @ M ) @ G2 @ X3 )
        = ( comp_d7292648224603294300_a_b_b @ ( comp_b_b_dtree_a_b @ F2 @ N ) @ H @ X3 ) ) ) ).

% type_copy_map_cong0
thf(fact_85_type__copy__map__cong0,axiom,
    ! [M: dtree_a_b > b,G2: produc4558475209616630778_a_b_b > dtree_a_b,X3: produc4558475209616630778_a_b_b,N: b > b,H: produc4558475209616630778_a_b_b > b,F2: b > b] :
      ( ( ( M @ ( G2 @ X3 ) )
        = ( N @ ( H @ X3 ) ) )
     => ( ( comp_d7292648224603294300_a_b_b @ ( comp_b_b_dtree_a_b @ F2 @ M ) @ G2 @ X3 )
        = ( comp_b4098124895279589661_a_b_b @ ( comp_b_b_b @ F2 @ N ) @ H @ X3 ) ) ) ).

% type_copy_map_cong0
thf(fact_86_type__copy__map__cong0,axiom,
    ! [M: b > dtree_a_b,G2: b > b,X3: b,N: produc4558475209616630778_a_b_b > dtree_a_b,H: b > produc4558475209616630778_a_b_b,F2: dtree_a_b > b] :
      ( ( ( M @ ( G2 @ X3 ) )
        = ( N @ ( H @ X3 ) ) )
     => ( ( comp_b_b_b @ ( comp_dtree_a_b_b_b @ F2 @ M ) @ G2 @ X3 )
        = ( comp_P1056441264483508125_b_b_b @ ( comp_d7292648224603294300_a_b_b @ F2 @ N ) @ H @ X3 ) ) ) ).

% type_copy_map_cong0
thf(fact_87_type__copy__map__cong0,axiom,
    ! [M: produc4558475209616630778_a_b_b > dtree_a_b,G2: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,X3: produc4558475209616630778_a_b_b,N: dtree_a_b > dtree_a_b,H: produc4558475209616630778_a_b_b > dtree_a_b,F2: dtree_a_b > b] :
      ( ( ( M @ ( G2 @ X3 ) )
        = ( N @ ( H @ X3 ) ) )
     => ( ( comp_P7790946621747331036_a_b_b @ ( comp_d7292648224603294300_a_b_b @ F2 @ M ) @ G2 @ X3 )
        = ( comp_d7292648224603294300_a_b_b @ ( comp_d2161864785492113116ee_a_b @ F2 @ N ) @ H @ X3 ) ) ) ).

% type_copy_map_cong0
thf(fact_88_type__copy__map__cong0,axiom,
    ! [M: dtree_a_b > dtree_a_b,G2: produc4558475209616630778_a_b_b > dtree_a_b,X3: produc4558475209616630778_a_b_b,N: produc4558475209616630778_a_b_b > dtree_a_b,H: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,F2: dtree_a_b > b] :
      ( ( ( M @ ( G2 @ X3 ) )
        = ( N @ ( H @ X3 ) ) )
     => ( ( comp_d7292648224603294300_a_b_b @ ( comp_d2161864785492113116ee_a_b @ F2 @ M ) @ G2 @ X3 )
        = ( comp_P7790946621747331036_a_b_b @ ( comp_d7292648224603294300_a_b_b @ F2 @ N ) @ H @ X3 ) ) ) ).

% type_copy_map_cong0
thf(fact_89_type__copy__map__cong0,axiom,
    ! [M: ( b > a ) > b > a,G2: ( b > a ) > b > a,X3: b > a,N: ( b > a ) > b > a,H: ( b > a ) > b > a,F2: ( b > a ) > product_prod_b_a_b_a] :
      ( ( ( M @ ( G2 @ X3 ) )
        = ( N @ ( H @ X3 ) ) )
     => ( ( comp_b7652884982158753286_a_b_a @ ( comp_b7652884982158753286_a_b_a @ F2 @ M ) @ G2 @ X3 )
        = ( comp_b7652884982158753286_a_b_a @ ( comp_b7652884982158753286_a_b_a @ F2 @ N ) @ H @ X3 ) ) ) ).

% type_copy_map_cong0
thf(fact_90__C0_C,axiom,
    ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ x1 @ x2 ) @ ( fset_P783253628892185035_a_b_b @ xs ) )
    & ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ y1 @ y2 ) @ ( fset_P783253628892185035_a_b_b @ xs ) ) ) ).

% "0"
thf(fact_91_prod_Oinject,axiom,
    ! [X12: b,X22: dtree_a_b,Y12: b,Y22: dtree_a_b] :
      ( ( ( produc3542686128043086370ee_a_b @ X12 @ X22 )
        = ( produc3542686128043086370ee_a_b @ Y12 @ Y22 ) )
      = ( ( X12 = Y12 )
        & ( X22 = Y22 ) ) ) ).

% prod.inject
thf(fact_92_prod_Oinject,axiom,
    ! [X12: produc4558475209616630778_a_b_b,X22: produc4558475209616630778_a_b_b,Y12: produc4558475209616630778_a_b_b,Y22: produc4558475209616630778_a_b_b] :
      ( ( ( produc6533307410877503629_a_b_b @ X12 @ X22 )
        = ( produc6533307410877503629_a_b_b @ Y12 @ Y22 ) )
      = ( ( X12 = Y12 )
        & ( X22 = Y22 ) ) ) ).

% prod.inject
thf(fact_93_prod_Oinject,axiom,
    ! [X12: product_unit,X22: product_unit,Y12: product_unit,Y22: product_unit] :
      ( ( ( produc5692694829384537815t_unit @ X12 @ X22 )
        = ( produc5692694829384537815t_unit @ Y12 @ Y22 ) )
      = ( ( X12 = Y12 )
        & ( X22 = Y22 ) ) ) ).

% prod.inject
thf(fact_94_prod_Oinject,axiom,
    ! [X12: dtree_a_b,X22: b,Y12: dtree_a_b,Y22: b] :
      ( ( ( produc331601717337510060_a_b_b @ X12 @ X22 )
        = ( produc331601717337510060_a_b_b @ Y12 @ Y22 ) )
      = ( ( X12 = Y12 )
        & ( X22 = Y22 ) ) ) ).

% prod.inject
thf(fact_95_old_Oprod_Oinject,axiom,
    ! [A: b,B: dtree_a_b,A2: b,B2: dtree_a_b] :
      ( ( ( produc3542686128043086370ee_a_b @ A @ B )
        = ( produc3542686128043086370ee_a_b @ A2 @ B2 ) )
      = ( ( A = A2 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_96_old_Oprod_Oinject,axiom,
    ! [A: produc4558475209616630778_a_b_b,B: produc4558475209616630778_a_b_b,A2: produc4558475209616630778_a_b_b,B2: produc4558475209616630778_a_b_b] :
      ( ( ( produc6533307410877503629_a_b_b @ A @ B )
        = ( produc6533307410877503629_a_b_b @ A2 @ B2 ) )
      = ( ( A = A2 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_97_old_Oprod_Oinject,axiom,
    ! [A: product_unit,B: product_unit,A2: product_unit,B2: product_unit] :
      ( ( ( produc5692694829384537815t_unit @ A @ B )
        = ( produc5692694829384537815t_unit @ A2 @ B2 ) )
      = ( ( A = A2 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_98_old_Oprod_Oinject,axiom,
    ! [A: dtree_a_b,B: b,A2: dtree_a_b,B2: b] :
      ( ( ( produc331601717337510060_a_b_b @ A @ B )
        = ( produc331601717337510060_a_b_b @ A2 @ B2 ) )
      = ( ( A = A2 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_99_rewriteR__comp__comp2,axiom,
    ! [G2: ( b > a ) > b > a,H: ( b > a ) > b > a,R1: ( b > a ) > b > a,R2: ( b > a ) > b > a,F2: ( b > a ) > b > a,L: ( b > a ) > b > a] :
      ( ( ( comp_b_a_b_a_b_a @ G2 @ H )
        = ( comp_b_a_b_a_b_a @ R1 @ R2 ) )
     => ( ( ( comp_b_a_b_a_b_a @ F2 @ R1 )
          = L )
       => ( ( comp_b_a_b_a_b_a @ ( comp_b_a_b_a_b_a @ F2 @ G2 ) @ H )
          = ( comp_b_a_b_a_b_a @ L @ R2 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_100_rewriteR__comp__comp2,axiom,
    ! [G2: b > b,H: b > b,R1: b > b,R2: b > b,F2: b > b,L: b > b] :
      ( ( ( comp_b_b_b @ G2 @ H )
        = ( comp_b_b_b @ R1 @ R2 ) )
     => ( ( ( comp_b_b_b @ F2 @ R1 )
          = L )
       => ( ( comp_b_b_b @ ( comp_b_b_b @ F2 @ G2 ) @ H )
          = ( comp_b_b_b @ L @ R2 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_101_rewriteR__comp__comp2,axiom,
    ! [G2: a > a,H: a > a,R1: a > a,R2: a > a,F2: a > a,L: a > a] :
      ( ( ( comp_a_a_a @ G2 @ H )
        = ( comp_a_a_a @ R1 @ R2 ) )
     => ( ( ( comp_a_a_a @ F2 @ R1 )
          = L )
       => ( ( comp_a_a_a @ ( comp_a_a_a @ F2 @ G2 ) @ H )
          = ( comp_a_a_a @ L @ R2 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_102_rewriteR__comp__comp2,axiom,
    ! [G2: produc4558475209616630778_a_b_b > dtree_a_b,H: b > produc4558475209616630778_a_b_b,R1: b > dtree_a_b,R2: b > b,F2: dtree_a_b > b,L: b > b] :
      ( ( ( comp_P2960064163185208038_a_b_b @ G2 @ H )
        = ( comp_b_dtree_a_b_b @ R1 @ R2 ) )
     => ( ( ( comp_dtree_a_b_b_b @ F2 @ R1 )
          = L )
       => ( ( comp_P1056441264483508125_b_b_b @ ( comp_d7292648224603294300_a_b_b @ F2 @ G2 ) @ H )
          = ( comp_b_b_b @ L @ R2 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_103_rewriteR__comp__comp2,axiom,
    ! [G2: b > dtree_a_b,H: b > b,R1: produc4558475209616630778_a_b_b > dtree_a_b,R2: b > produc4558475209616630778_a_b_b,F2: dtree_a_b > b,L: produc4558475209616630778_a_b_b > b] :
      ( ( ( comp_b_dtree_a_b_b @ G2 @ H )
        = ( comp_P2960064163185208038_a_b_b @ R1 @ R2 ) )
     => ( ( ( comp_d7292648224603294300_a_b_b @ F2 @ R1 )
          = L )
       => ( ( comp_b_b_b @ ( comp_dtree_a_b_b_b @ F2 @ G2 ) @ H )
          = ( comp_P1056441264483508125_b_b_b @ L @ R2 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_104_rewriteR__comp__comp2,axiom,
    ! [G2: b > b,H: produc4558475209616630778_a_b_b > b,R1: dtree_a_b > b,R2: produc4558475209616630778_a_b_b > dtree_a_b,F2: b > b,L: dtree_a_b > b] :
      ( ( ( comp_b4098124895279589661_a_b_b @ G2 @ H )
        = ( comp_d7292648224603294300_a_b_b @ R1 @ R2 ) )
     => ( ( ( comp_b_b_dtree_a_b @ F2 @ R1 )
          = L )
       => ( ( comp_b4098124895279589661_a_b_b @ ( comp_b_b_b @ F2 @ G2 ) @ H )
          = ( comp_d7292648224603294300_a_b_b @ L @ R2 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_105_rewriteR__comp__comp2,axiom,
    ! [G2: dtree_a_b > b,H: produc4558475209616630778_a_b_b > dtree_a_b,R1: b > b,R2: produc4558475209616630778_a_b_b > b,F2: b > b,L: b > b] :
      ( ( ( comp_d7292648224603294300_a_b_b @ G2 @ H )
        = ( comp_b4098124895279589661_a_b_b @ R1 @ R2 ) )
     => ( ( ( comp_b_b_b @ F2 @ R1 )
          = L )
       => ( ( comp_d7292648224603294300_a_b_b @ ( comp_b_b_dtree_a_b @ F2 @ G2 ) @ H )
          = ( comp_b4098124895279589661_a_b_b @ L @ R2 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_106_rewriteR__comp__comp2,axiom,
    ! [G2: dtree_a_b > b,H: produc4558475209616630778_a_b_b > dtree_a_b,R1: dtree_a_b > b,R2: produc4558475209616630778_a_b_b > dtree_a_b,F2: b > b,L: dtree_a_b > b] :
      ( ( ( comp_d7292648224603294300_a_b_b @ G2 @ H )
        = ( comp_d7292648224603294300_a_b_b @ R1 @ R2 ) )
     => ( ( ( comp_b_b_dtree_a_b @ F2 @ R1 )
          = L )
       => ( ( comp_d7292648224603294300_a_b_b @ ( comp_b_b_dtree_a_b @ F2 @ G2 ) @ H )
          = ( comp_d7292648224603294300_a_b_b @ L @ R2 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_107_rewriteR__comp__comp2,axiom,
    ! [G2: produc4558475209616630778_a_b_b > dtree_a_b,H: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,R1: dtree_a_b > dtree_a_b,R2: produc4558475209616630778_a_b_b > dtree_a_b,F2: dtree_a_b > b,L: dtree_a_b > b] :
      ( ( ( comp_P2227990766219928147_a_b_b @ G2 @ H )
        = ( comp_d9193377603055859667_a_b_b @ R1 @ R2 ) )
     => ( ( ( comp_d2161864785492113116ee_a_b @ F2 @ R1 )
          = L )
       => ( ( comp_P7790946621747331036_a_b_b @ ( comp_d7292648224603294300_a_b_b @ F2 @ G2 ) @ H )
          = ( comp_d7292648224603294300_a_b_b @ L @ R2 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_108_rewriteR__comp__comp2,axiom,
    ! [G2: dtree_a_b > dtree_a_b,H: produc4558475209616630778_a_b_b > dtree_a_b,R1: produc4558475209616630778_a_b_b > dtree_a_b,R2: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,F2: dtree_a_b > b,L: produc4558475209616630778_a_b_b > b] :
      ( ( ( comp_d9193377603055859667_a_b_b @ G2 @ H )
        = ( comp_P2227990766219928147_a_b_b @ R1 @ R2 ) )
     => ( ( ( comp_d7292648224603294300_a_b_b @ F2 @ R1 )
          = L )
       => ( ( comp_d7292648224603294300_a_b_b @ ( comp_d2161864785492113116ee_a_b @ F2 @ G2 ) @ H )
          = ( comp_P7790946621747331036_a_b_b @ L @ R2 ) ) ) ) ).

% rewriteR_comp_comp2
thf(fact_109_rewriteL__comp__comp2,axiom,
    ! [F2: ( b > a ) > b > a,G2: ( b > a ) > b > a,L1: ( b > a ) > b > a,L2: ( b > a ) > b > a,H: ( b > a ) > b > a,R: ( b > a ) > b > a] :
      ( ( ( comp_b_a_b_a_b_a @ F2 @ G2 )
        = ( comp_b_a_b_a_b_a @ L1 @ L2 ) )
     => ( ( ( comp_b_a_b_a_b_a @ L2 @ H )
          = R )
       => ( ( comp_b_a_b_a_b_a @ F2 @ ( comp_b_a_b_a_b_a @ G2 @ H ) )
          = ( comp_b_a_b_a_b_a @ L1 @ R ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_110_rewriteL__comp__comp2,axiom,
    ! [F2: b > b,G2: b > b,L1: b > b,L2: b > b,H: b > b,R: b > b] :
      ( ( ( comp_b_b_b @ F2 @ G2 )
        = ( comp_b_b_b @ L1 @ L2 ) )
     => ( ( ( comp_b_b_b @ L2 @ H )
          = R )
       => ( ( comp_b_b_b @ F2 @ ( comp_b_b_b @ G2 @ H ) )
          = ( comp_b_b_b @ L1 @ R ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_111_rewriteL__comp__comp2,axiom,
    ! [F2: a > a,G2: a > a,L1: a > a,L2: a > a,H: a > a,R: a > a] :
      ( ( ( comp_a_a_a @ F2 @ G2 )
        = ( comp_a_a_a @ L1 @ L2 ) )
     => ( ( ( comp_a_a_a @ L2 @ H )
          = R )
       => ( ( comp_a_a_a @ F2 @ ( comp_a_a_a @ G2 @ H ) )
          = ( comp_a_a_a @ L1 @ R ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_112_rewriteL__comp__comp2,axiom,
    ! [F2: b > b,G2: produc4558475209616630778_a_b_b > b,L1: dtree_a_b > b,L2: produc4558475209616630778_a_b_b > dtree_a_b,H: b > produc4558475209616630778_a_b_b,R: b > dtree_a_b] :
      ( ( ( comp_b4098124895279589661_a_b_b @ F2 @ G2 )
        = ( comp_d7292648224603294300_a_b_b @ L1 @ L2 ) )
     => ( ( ( comp_P2960064163185208038_a_b_b @ L2 @ H )
          = R )
       => ( ( comp_b_b_b @ F2 @ ( comp_P1056441264483508125_b_b_b @ G2 @ H ) )
          = ( comp_dtree_a_b_b_b @ L1 @ R ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_113_rewriteL__comp__comp2,axiom,
    ! [F2: dtree_a_b > b,G2: b > dtree_a_b,L1: b > b,L2: b > b,H: produc4558475209616630778_a_b_b > b,R: produc4558475209616630778_a_b_b > b] :
      ( ( ( comp_dtree_a_b_b_b @ F2 @ G2 )
        = ( comp_b_b_b @ L1 @ L2 ) )
     => ( ( ( comp_b4098124895279589661_a_b_b @ L2 @ H )
          = R )
       => ( ( comp_d7292648224603294300_a_b_b @ F2 @ ( comp_b3128908137006596050_a_b_b @ G2 @ H ) )
          = ( comp_b4098124895279589661_a_b_b @ L1 @ R ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_114_rewriteL__comp__comp2,axiom,
    ! [F2: dtree_a_b > b,G2: produc4558475209616630778_a_b_b > dtree_a_b,L1: b > b,L2: produc4558475209616630778_a_b_b > b,H: b > produc4558475209616630778_a_b_b,R: b > b] :
      ( ( ( comp_d7292648224603294300_a_b_b @ F2 @ G2 )
        = ( comp_b4098124895279589661_a_b_b @ L1 @ L2 ) )
     => ( ( ( comp_P1056441264483508125_b_b_b @ L2 @ H )
          = R )
       => ( ( comp_dtree_a_b_b_b @ F2 @ ( comp_P2960064163185208038_a_b_b @ G2 @ H ) )
          = ( comp_b_b_b @ L1 @ R ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_115_rewriteL__comp__comp2,axiom,
    ! [F2: b > b,G2: b > b,L1: dtree_a_b > b,L2: b > dtree_a_b,H: produc4558475209616630778_a_b_b > b,R: produc4558475209616630778_a_b_b > dtree_a_b] :
      ( ( ( comp_b_b_b @ F2 @ G2 )
        = ( comp_dtree_a_b_b_b @ L1 @ L2 ) )
     => ( ( ( comp_b3128908137006596050_a_b_b @ L2 @ H )
          = R )
       => ( ( comp_b4098124895279589661_a_b_b @ F2 @ ( comp_b4098124895279589661_a_b_b @ G2 @ H ) )
          = ( comp_d7292648224603294300_a_b_b @ L1 @ R ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_116_rewriteL__comp__comp2,axiom,
    ! [F2: b > b,G2: dtree_a_b > b,L1: dtree_a_b > b,L2: dtree_a_b > dtree_a_b,H: produc4558475209616630778_a_b_b > dtree_a_b,R: produc4558475209616630778_a_b_b > dtree_a_b] :
      ( ( ( comp_b_b_dtree_a_b @ F2 @ G2 )
        = ( comp_d2161864785492113116ee_a_b @ L1 @ L2 ) )
     => ( ( ( comp_d9193377603055859667_a_b_b @ L2 @ H )
          = R )
       => ( ( comp_b4098124895279589661_a_b_b @ F2 @ ( comp_d7292648224603294300_a_b_b @ G2 @ H ) )
          = ( comp_d7292648224603294300_a_b_b @ L1 @ R ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_117_rewriteL__comp__comp2,axiom,
    ! [F2: dtree_a_b > b,G2: dtree_a_b > dtree_a_b,L1: b > b,L2: dtree_a_b > b,H: produc4558475209616630778_a_b_b > dtree_a_b,R: produc4558475209616630778_a_b_b > b] :
      ( ( ( comp_d2161864785492113116ee_a_b @ F2 @ G2 )
        = ( comp_b_b_dtree_a_b @ L1 @ L2 ) )
     => ( ( ( comp_d7292648224603294300_a_b_b @ L2 @ H )
          = R )
       => ( ( comp_d7292648224603294300_a_b_b @ F2 @ ( comp_d9193377603055859667_a_b_b @ G2 @ H ) )
          = ( comp_b4098124895279589661_a_b_b @ L1 @ R ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_118_rewriteL__comp__comp2,axiom,
    ! [F2: dtree_a_b > b,G2: produc4558475209616630778_a_b_b > dtree_a_b,L1: dtree_a_b > b,L2: produc4558475209616630778_a_b_b > dtree_a_b,H: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,R: produc4558475209616630778_a_b_b > dtree_a_b] :
      ( ( ( comp_d7292648224603294300_a_b_b @ F2 @ G2 )
        = ( comp_d7292648224603294300_a_b_b @ L1 @ L2 ) )
     => ( ( ( comp_P2227990766219928147_a_b_b @ L2 @ H )
          = R )
       => ( ( comp_d7292648224603294300_a_b_b @ F2 @ ( comp_P2227990766219928147_a_b_b @ G2 @ H ) )
          = ( comp_d7292648224603294300_a_b_b @ L1 @ R ) ) ) ) ).

% rewriteL_comp_comp2
thf(fact_119_rewriteR__comp__comp,axiom,
    ! [G2: produc4558475209616630778_a_b_b > dtree_a_b,H: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,R: produc4558475209616630778_a_b_b > dtree_a_b,F2: dtree_a_b > b] :
      ( ( ( comp_P2227990766219928147_a_b_b @ G2 @ H )
        = R )
     => ( ( comp_P7790946621747331036_a_b_b @ ( comp_d7292648224603294300_a_b_b @ F2 @ G2 ) @ H )
        = ( comp_d7292648224603294300_a_b_b @ F2 @ R ) ) ) ).

% rewriteR_comp_comp
thf(fact_120_rewriteR__comp__comp,axiom,
    ! [G2: dtree_a_b > dtree_a_b,H: produc4558475209616630778_a_b_b > dtree_a_b,R: produc4558475209616630778_a_b_b > dtree_a_b,F2: dtree_a_b > b] :
      ( ( ( comp_d9193377603055859667_a_b_b @ G2 @ H )
        = R )
     => ( ( comp_d7292648224603294300_a_b_b @ ( comp_d2161864785492113116ee_a_b @ F2 @ G2 ) @ H )
        = ( comp_d7292648224603294300_a_b_b @ F2 @ R ) ) ) ).

% rewriteR_comp_comp
thf(fact_121_rewriteR__comp__comp,axiom,
    ! [G2: ( b > a ) > b > a,H: ( b > a ) > b > a,R: ( b > a ) > b > a,F2: ( b > a ) > product_prod_b_a_b_a] :
      ( ( ( comp_b_a_b_a_b_a @ G2 @ H )
        = R )
     => ( ( comp_b7652884982158753286_a_b_a @ ( comp_b7652884982158753286_a_b_a @ F2 @ G2 ) @ H )
        = ( comp_b7652884982158753286_a_b_a @ F2 @ R ) ) ) ).

% rewriteR_comp_comp
thf(fact_122_rewriteR__comp__comp,axiom,
    ! [G2: dtree_a_b > b,H: produc4558475209616630778_a_b_b > dtree_a_b,R: produc4558475209616630778_a_b_b > b,F2: b > b] :
      ( ( ( comp_d7292648224603294300_a_b_b @ G2 @ H )
        = R )
     => ( ( comp_d7292648224603294300_a_b_b @ ( comp_b_b_dtree_a_b @ F2 @ G2 ) @ H )
        = ( comp_b4098124895279589661_a_b_b @ F2 @ R ) ) ) ).

% rewriteR_comp_comp
thf(fact_123_rewriteR__comp__comp,axiom,
    ! [G2: ( ( b > a ) > b > a ) > ( b > a ) > b > a,H: ( ( b > a ) > b > a ) > ( b > a ) > b > a,R: ( ( b > a ) > b > a ) > ( b > a ) > b > a,F2: ( ( b > a ) > b > a ) > ( b > a ) > b > a] :
      ( ( ( comp_b3327941365615541530_a_b_a @ G2 @ H )
        = R )
     => ( ( comp_b3327941365615541530_a_b_a @ ( comp_b3327941365615541530_a_b_a @ F2 @ G2 ) @ H )
        = ( comp_b3327941365615541530_a_b_a @ F2 @ R ) ) ) ).

% rewriteR_comp_comp
thf(fact_124_rewriteR__comp__comp,axiom,
    ! [G2: ( b > a ) > product_prod_b_a_b_a,H: ( b > a ) > b > a,R: ( b > a ) > product_prod_b_a_b_a,F2: product_prod_b_a_b_a > b > a] :
      ( ( ( comp_b7652884982158753286_a_b_a @ G2 @ H )
        = R )
     => ( ( comp_b_a_b_a_b_a @ ( comp_P1653000078598994640_a_b_a @ F2 @ G2 ) @ H )
        = ( comp_P1653000078598994640_a_b_a @ F2 @ R ) ) ) ).

% rewriteR_comp_comp
thf(fact_125_rewriteR__comp__comp,axiom,
    ! [G2: ( b > a ) > product_prod_b_a_b_a,H: ( b > a ) > b > a,R: ( b > a ) > product_prod_b_a_b_a,F2: product_prod_b_a_b_a > product_prod_b_a_b_a] :
      ( ( ( comp_b7652884982158753286_a_b_a @ G2 @ H )
        = R )
     => ( ( comp_b7652884982158753286_a_b_a @ ( comp_P5805957429449400903_a_b_a @ F2 @ G2 ) @ H )
        = ( comp_P5805957429449400903_a_b_a @ F2 @ R ) ) ) ).

% rewriteR_comp_comp
thf(fact_126_rewriteR__comp__comp,axiom,
    ! [G2: b > b,H: b > b,R: b > b,F2: b > b] :
      ( ( ( comp_b_b_b @ G2 @ H )
        = R )
     => ( ( comp_b_b_b @ ( comp_b_b_b @ F2 @ G2 ) @ H )
        = ( comp_b_b_b @ F2 @ R ) ) ) ).

% rewriteR_comp_comp
thf(fact_127_rewriteR__comp__comp,axiom,
    ! [G2: a > a,H: a > a,R: a > a,F2: a > a] :
      ( ( ( comp_a_a_a @ G2 @ H )
        = R )
     => ( ( comp_a_a_a @ ( comp_a_a_a @ F2 @ G2 ) @ H )
        = ( comp_a_a_a @ F2 @ R ) ) ) ).

% rewriteR_comp_comp
thf(fact_128_rewriteR__comp__comp,axiom,
    ! [G2: ( b > a ) > b > a,H: ( b > a ) > b > a,R: ( b > a ) > b > a,F2: ( b > a ) > b > a] :
      ( ( ( comp_b_a_b_a_b_a @ G2 @ H )
        = R )
     => ( ( comp_b_a_b_a_b_a @ ( comp_b_a_b_a_b_a @ F2 @ G2 ) @ H )
        = ( comp_b_a_b_a_b_a @ F2 @ R ) ) ) ).

% rewriteR_comp_comp
thf(fact_129_rewriteL__comp__comp,axiom,
    ! [F2: b > b,G2: dtree_a_b > b,L: dtree_a_b > b,H: produc4558475209616630778_a_b_b > dtree_a_b] :
      ( ( ( comp_b_b_dtree_a_b @ F2 @ G2 )
        = L )
     => ( ( comp_b4098124895279589661_a_b_b @ F2 @ ( comp_d7292648224603294300_a_b_b @ G2 @ H ) )
        = ( comp_d7292648224603294300_a_b_b @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_130_rewriteL__comp__comp,axiom,
    ! [F2: product_prod_b_a_b_a > b > a,G2: ( b > a ) > product_prod_b_a_b_a,L: ( b > a ) > b > a,H: ( b > a ) > b > a] :
      ( ( ( comp_P1653000078598994640_a_b_a @ F2 @ G2 )
        = L )
     => ( ( comp_P1653000078598994640_a_b_a @ F2 @ ( comp_b7652884982158753286_a_b_a @ G2 @ H ) )
        = ( comp_b_a_b_a_b_a @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_131_rewriteL__comp__comp,axiom,
    ! [F2: product_prod_b_a_b_a > product_prod_b_a_b_a,G2: ( b > a ) > product_prod_b_a_b_a,L: ( b > a ) > product_prod_b_a_b_a,H: ( b > a ) > b > a] :
      ( ( ( comp_P5805957429449400903_a_b_a @ F2 @ G2 )
        = L )
     => ( ( comp_P5805957429449400903_a_b_a @ F2 @ ( comp_b7652884982158753286_a_b_a @ G2 @ H ) )
        = ( comp_b7652884982158753286_a_b_a @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_132_rewriteL__comp__comp,axiom,
    ! [F2: dtree_a_b > b,G2: dtree_a_b > dtree_a_b,L: dtree_a_b > b,H: produc4558475209616630778_a_b_b > dtree_a_b] :
      ( ( ( comp_d2161864785492113116ee_a_b @ F2 @ G2 )
        = L )
     => ( ( comp_d7292648224603294300_a_b_b @ F2 @ ( comp_d9193377603055859667_a_b_b @ G2 @ H ) )
        = ( comp_d7292648224603294300_a_b_b @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_133_rewriteL__comp__comp,axiom,
    ! [F2: dtree_a_b > b,G2: produc4558475209616630778_a_b_b > dtree_a_b,L: produc4558475209616630778_a_b_b > b,H: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b] :
      ( ( ( comp_d7292648224603294300_a_b_b @ F2 @ G2 )
        = L )
     => ( ( comp_d7292648224603294300_a_b_b @ F2 @ ( comp_P2227990766219928147_a_b_b @ G2 @ H ) )
        = ( comp_P7790946621747331036_a_b_b @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_134_rewriteL__comp__comp,axiom,
    ! [F2: ( ( b > a ) > b > a ) > ( b > a ) > b > a,G2: ( ( b > a ) > b > a ) > ( b > a ) > b > a,L: ( ( b > a ) > b > a ) > ( b > a ) > b > a,H: ( ( b > a ) > b > a ) > ( b > a ) > b > a] :
      ( ( ( comp_b3327941365615541530_a_b_a @ F2 @ G2 )
        = L )
     => ( ( comp_b3327941365615541530_a_b_a @ F2 @ ( comp_b3327941365615541530_a_b_a @ G2 @ H ) )
        = ( comp_b3327941365615541530_a_b_a @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_135_rewriteL__comp__comp,axiom,
    ! [F2: ( b > a ) > product_prod_b_a_b_a,G2: ( b > a ) > b > a,L: ( b > a ) > product_prod_b_a_b_a,H: ( b > a ) > b > a] :
      ( ( ( comp_b7652884982158753286_a_b_a @ F2 @ G2 )
        = L )
     => ( ( comp_b7652884982158753286_a_b_a @ F2 @ ( comp_b_a_b_a_b_a @ G2 @ H ) )
        = ( comp_b7652884982158753286_a_b_a @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_136_rewriteL__comp__comp,axiom,
    ! [F2: b > b,G2: b > b,L: b > b,H: b > b] :
      ( ( ( comp_b_b_b @ F2 @ G2 )
        = L )
     => ( ( comp_b_b_b @ F2 @ ( comp_b_b_b @ G2 @ H ) )
        = ( comp_b_b_b @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_137_rewriteL__comp__comp,axiom,
    ! [F2: a > a,G2: a > a,L: a > a,H: a > a] :
      ( ( ( comp_a_a_a @ F2 @ G2 )
        = L )
     => ( ( comp_a_a_a @ F2 @ ( comp_a_a_a @ G2 @ H ) )
        = ( comp_a_a_a @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_138_rewriteL__comp__comp,axiom,
    ! [F2: ( b > a ) > b > a,G2: ( b > a ) > b > a,L: ( b > a ) > b > a,H: ( b > a ) > b > a] :
      ( ( ( comp_b_a_b_a_b_a @ F2 @ G2 )
        = L )
     => ( ( comp_b_a_b_a_b_a @ F2 @ ( comp_b_a_b_a_b_a @ G2 @ H ) )
        = ( comp_b_a_b_a_b_a @ L @ H ) ) ) ).

% rewriteL_comp_comp
thf(fact_139_subdivide_Ocases,axiom,
    ! [X3: produc7079444246281463442_a_b_b] :
      ~ ! [G4: pair_p3556638718232885427t_unit,U: produc4558475209616630778_a_b_b,V3: produc4558475209616630778_a_b_b,W: produc4558475209616630778_a_b_b] :
          ( X3
         != ( produc5307704689474511050_a_b_b @ G4 @ ( produc4872291942876762872_a_b_b @ ( produc6533307410877503629_a_b_b @ U @ V3 ) @ W ) ) ) ).

% subdivide.cases
thf(fact_140_subdivide_Ocases,axiom,
    ! [X3: produc2042437161806511672t_unit] :
      ~ ! [G4: pair_p7583798195187013628t_unit,U: product_unit,V3: product_unit,W: product_unit] :
          ( X3
         != ( produc2086944449173503016t_unit @ G4 @ ( produc8155702538658622973t_unit @ ( produc5692694829384537815t_unit @ U @ V3 ) @ W ) ) ) ).

% subdivide.cases
thf(fact_141_old_Oprod_Oexhaust,axiom,
    ! [Y3: produc3469756349985706280ee_a_b] :
      ~ ! [A3: b,B3: dtree_a_b] :
          ( Y3
         != ( produc3542686128043086370ee_a_b @ A3 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_142_old_Oprod_Oexhaust,axiom,
    ! [Y3: produc8908337785154950741_a_b_b] :
      ~ ! [A3: produc4558475209616630778_a_b_b,B3: produc4558475209616630778_a_b_b] :
          ( Y3
         != ( produc6533307410877503629_a_b_b @ A3 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_143_old_Oprod_Oexhaust,axiom,
    ! [Y3: produc8459935480633519975t_unit] :
      ~ ! [A3: product_unit,B3: product_unit] :
          ( Y3
         != ( produc5692694829384537815t_unit @ A3 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_144_old_Oprod_Oexhaust,axiom,
    ! [Y3: produc4558475209616630778_a_b_b] :
      ~ ! [A3: dtree_a_b,B3: b] :
          ( Y3
         != ( produc331601717337510060_a_b_b @ A3 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_145_surj__pair,axiom,
    ! [P: produc3469756349985706280ee_a_b] :
    ? [X5: b,Y4: dtree_a_b] :
      ( P
      = ( produc3542686128043086370ee_a_b @ X5 @ Y4 ) ) ).

% surj_pair
thf(fact_146_surj__pair,axiom,
    ! [P: produc8908337785154950741_a_b_b] :
    ? [X5: produc4558475209616630778_a_b_b,Y4: produc4558475209616630778_a_b_b] :
      ( P
      = ( produc6533307410877503629_a_b_b @ X5 @ Y4 ) ) ).

% surj_pair
thf(fact_147_surj__pair,axiom,
    ! [P: produc8459935480633519975t_unit] :
    ? [X5: product_unit,Y4: product_unit] :
      ( P
      = ( produc5692694829384537815t_unit @ X5 @ Y4 ) ) ).

% surj_pair
thf(fact_148_surj__pair,axiom,
    ! [P: produc4558475209616630778_a_b_b] :
    ? [X5: dtree_a_b,Y4: b] :
      ( P
      = ( produc331601717337510060_a_b_b @ X5 @ Y4 ) ) ).

% surj_pair
thf(fact_149_prod__cases,axiom,
    ! [P2: produc3469756349985706280ee_a_b > $o,P: produc3469756349985706280ee_a_b] :
      ( ! [A3: b,B3: dtree_a_b] : ( P2 @ ( produc3542686128043086370ee_a_b @ A3 @ B3 ) )
     => ( P2 @ P ) ) ).

% prod_cases
thf(fact_150_prod__cases,axiom,
    ! [P2: produc8908337785154950741_a_b_b > $o,P: produc8908337785154950741_a_b_b] :
      ( ! [A3: produc4558475209616630778_a_b_b,B3: produc4558475209616630778_a_b_b] : ( P2 @ ( produc6533307410877503629_a_b_b @ A3 @ B3 ) )
     => ( P2 @ P ) ) ).

% prod_cases
thf(fact_151_prod__cases,axiom,
    ! [P2: produc8459935480633519975t_unit > $o,P: produc8459935480633519975t_unit] :
      ( ! [A3: product_unit,B3: product_unit] : ( P2 @ ( produc5692694829384537815t_unit @ A3 @ B3 ) )
     => ( P2 @ P ) ) ).

% prod_cases
thf(fact_152_prod__cases,axiom,
    ! [P2: produc4558475209616630778_a_b_b > $o,P: produc4558475209616630778_a_b_b] :
      ( ! [A3: dtree_a_b,B3: b] : ( P2 @ ( produc331601717337510060_a_b_b @ A3 @ B3 ) )
     => ( P2 @ P ) ) ).

% prod_cases
thf(fact_153_prod__induct3,axiom,
    ! [P2: produc8908337785154950741_a_b_b > $o,X3: produc8908337785154950741_a_b_b] :
      ( ! [A3: produc4558475209616630778_a_b_b,B3: dtree_a_b,C2: b] : ( P2 @ ( produc6533307410877503629_a_b_b @ A3 @ ( produc331601717337510060_a_b_b @ B3 @ C2 ) ) )
     => ( P2 @ X3 ) ) ).

% prod_induct3
thf(fact_154_prod__cases3,axiom,
    ! [Y3: produc8908337785154950741_a_b_b] :
      ~ ! [A3: produc4558475209616630778_a_b_b,B3: dtree_a_b,C2: b] :
          ( Y3
         != ( produc6533307410877503629_a_b_b @ A3 @ ( produc331601717337510060_a_b_b @ B3 @ C2 ) ) ) ).

% prod_cases3
thf(fact_155_Pair__inject,axiom,
    ! [A: b,B: dtree_a_b,A2: b,B2: dtree_a_b] :
      ( ( ( produc3542686128043086370ee_a_b @ A @ B )
        = ( produc3542686128043086370ee_a_b @ A2 @ B2 ) )
     => ~ ( ( A = A2 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_156_Pair__inject,axiom,
    ! [A: produc4558475209616630778_a_b_b,B: produc4558475209616630778_a_b_b,A2: produc4558475209616630778_a_b_b,B2: produc4558475209616630778_a_b_b] :
      ( ( ( produc6533307410877503629_a_b_b @ A @ B )
        = ( produc6533307410877503629_a_b_b @ A2 @ B2 ) )
     => ~ ( ( A = A2 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_157_Pair__inject,axiom,
    ! [A: product_unit,B: product_unit,A2: product_unit,B2: product_unit] :
      ( ( ( produc5692694829384537815t_unit @ A @ B )
        = ( produc5692694829384537815t_unit @ A2 @ B2 ) )
     => ~ ( ( A = A2 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_158_Pair__inject,axiom,
    ! [A: dtree_a_b,B: b,A2: dtree_a_b,B2: b] :
      ( ( ( produc331601717337510060_a_b_b @ A @ B )
        = ( produc331601717337510060_a_b_b @ A2 @ B2 ) )
     => ~ ( ( A = A2 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_159_fset__cong,axiom,
    ! [X3: fset_Product_unit,Y3: fset_Product_unit] :
      ( ( ( fset_Product_unit2 @ X3 )
        = ( fset_Product_unit2 @ Y3 ) )
      = ( X3 = Y3 ) ) ).

% fset_cong
thf(fact_160_fset__cong,axiom,
    ! [X3: fset_P5281107635120001194_a_b_b,Y3: fset_P5281107635120001194_a_b_b] :
      ( ( ( fset_P783253628892185035_a_b_b @ X3 )
        = ( fset_P783253628892185035_a_b_b @ Y3 ) )
      = ( X3 = Y3 ) ) ).

% fset_cong
thf(fact_161_ssubst__Pair__rhs,axiom,
    ! [R: b,S: dtree_a_b,R3: set_Pr6717515126349854430ee_a_b,S2: dtree_a_b] :
      ( ( member3292202256475951039ee_a_b @ ( produc3542686128043086370ee_a_b @ R @ S ) @ R3 )
     => ( ( S2 = S )
       => ( member3292202256475951039ee_a_b @ ( produc3542686128043086370ee_a_b @ R @ S2 ) @ R3 ) ) ) ).

% ssubst_Pair_rhs
thf(fact_162_ssubst__Pair__rhs,axiom,
    ! [R: produc4558475209616630778_a_b_b,S: produc4558475209616630778_a_b_b,R3: set_Pr2755428042910921141_a_b_b,S2: produc4558475209616630778_a_b_b] :
      ( ( member9171970031259705598_a_b_b @ ( produc6533307410877503629_a_b_b @ R @ S ) @ R3 )
     => ( ( S2 = S )
       => ( member9171970031259705598_a_b_b @ ( produc6533307410877503629_a_b_b @ R @ S2 ) @ R3 ) ) ) ).

% ssubst_Pair_rhs
thf(fact_163_ssubst__Pair__rhs,axiom,
    ! [R: product_unit,S: product_unit,R3: set_Pr5094982260447487303t_unit,S2: product_unit] :
      ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ R @ S ) @ R3 )
     => ( ( S2 = S )
       => ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ R @ S2 ) @ R3 ) ) ) ).

% ssubst_Pair_rhs
thf(fact_164_ssubst__Pair__rhs,axiom,
    ! [R: dtree_a_b,S: b,R3: set_Pr3012420139608375472_a_b_b,S2: b] :
      ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ R @ S ) @ R3 )
     => ( ( S2 = S )
       => ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ R @ S2 ) @ R3 ) ) ) ).

% ssubst_Pair_rhs
thf(fact_165_curry__conv,axiom,
    ( produc5550526150511291678_b_b_o
    = ( ^ [F: produc4558475209616630778_a_b_b > $o,A4: dtree_a_b,B4: b] : ( F @ ( produc331601717337510060_a_b_b @ A4 @ B4 ) ) ) ) ).

% curry_conv
thf(fact_166_mem__Collect__eq,axiom,
    ! [A: set_Pr3012420139608375472_a_b_b,P2: set_Pr3012420139608375472_a_b_b > $o] :
      ( ( member7431159781899395911_a_b_b @ A @ ( collec5997417077270831749_a_b_b @ P2 ) )
      = ( P2 @ A ) ) ).

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

% mem_Collect_eq
thf(fact_168_mem__Collect__eq,axiom,
    ! [A: b > a,P2: ( b > a ) > $o] :
      ( ( member_b_a @ A @ ( collect_b_a @ P2 ) )
      = ( P2 @ A ) ) ).

% mem_Collect_eq
thf(fact_169_mem__Collect__eq,axiom,
    ! [A: b,P2: b > $o] :
      ( ( member_b @ A @ ( collect_b @ P2 ) )
      = ( P2 @ A ) ) ).

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

% mem_Collect_eq
thf(fact_171_mem__Collect__eq,axiom,
    ! [A: product_unit,P2: product_unit > $o] :
      ( ( member_Product_unit @ A @ ( collect_Product_unit @ P2 ) )
      = ( P2 @ A ) ) ).

% mem_Collect_eq
thf(fact_172_mem__Collect__eq,axiom,
    ! [A: produc4558475209616630778_a_b_b,P2: produc4558475209616630778_a_b_b > $o] :
      ( ( member4380921116106875537_a_b_b @ A @ ( collec1368399972772960719_a_b_b @ P2 ) )
      = ( P2 @ A ) ) ).

% mem_Collect_eq
thf(fact_173_Collect__mem__eq,axiom,
    ! [A5: set_se3183138701204633190_a_b_b] :
      ( ( collec5997417077270831749_a_b_b
        @ ^ [X: set_Pr3012420139608375472_a_b_b] : ( member7431159781899395911_a_b_b @ X @ A5 ) )
      = A5 ) ).

% Collect_mem_eq
thf(fact_174_Collect__mem__eq,axiom,
    ! [A5: set_nat] :
      ( ( collect_nat
        @ ^ [X: nat] : ( member_nat @ X @ A5 ) )
      = A5 ) ).

% Collect_mem_eq
thf(fact_175_Collect__mem__eq,axiom,
    ! [A5: set_b_a] :
      ( ( collect_b_a
        @ ^ [X: b > a] : ( member_b_a @ X @ A5 ) )
      = A5 ) ).

% Collect_mem_eq
thf(fact_176_Collect__mem__eq,axiom,
    ! [A5: set_b] :
      ( ( collect_b
        @ ^ [X: b] : ( member_b @ X @ A5 ) )
      = A5 ) ).

% Collect_mem_eq
thf(fact_177_Collect__mem__eq,axiom,
    ! [A5: set_a] :
      ( ( collect_a
        @ ^ [X: a] : ( member_a @ X @ A5 ) )
      = A5 ) ).

% Collect_mem_eq
thf(fact_178_Collect__mem__eq,axiom,
    ! [A5: set_Product_unit] :
      ( ( collect_Product_unit
        @ ^ [X: product_unit] : ( member_Product_unit @ X @ A5 ) )
      = A5 ) ).

% Collect_mem_eq
thf(fact_179_Collect__mem__eq,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b] :
      ( ( collec1368399972772960719_a_b_b
        @ ^ [X: produc4558475209616630778_a_b_b] : ( member4380921116106875537_a_b_b @ X @ A5 ) )
      = A5 ) ).

% Collect_mem_eq
thf(fact_180_Collect__cong,axiom,
    ! [P2: produc4558475209616630778_a_b_b > $o,Q: produc4558475209616630778_a_b_b > $o] :
      ( ! [X5: produc4558475209616630778_a_b_b] :
          ( ( P2 @ X5 )
          = ( Q @ X5 ) )
     => ( ( collec1368399972772960719_a_b_b @ P2 )
        = ( collec1368399972772960719_a_b_b @ Q ) ) ) ).

% Collect_cong
thf(fact_181_Collect__cong,axiom,
    ! [P2: product_unit > $o,Q: product_unit > $o] :
      ( ! [X5: product_unit] :
          ( ( P2 @ X5 )
          = ( Q @ X5 ) )
     => ( ( collect_Product_unit @ P2 )
        = ( collect_Product_unit @ Q ) ) ) ).

% Collect_cong
thf(fact_182_map__fun_Ocomp,axiom,
    ! [F2: b > b,G2: a > a,H: b > b,I: a > a] :
      ( ( comp_b_a_b_a_b_a @ ( map_fun_b_b_a_a @ F2 @ G2 ) @ ( map_fun_b_b_a_a @ H @ I ) )
      = ( map_fun_b_b_a_a @ ( comp_b_b_b @ H @ F2 ) @ ( comp_a_a_a @ G2 @ I ) ) ) ).

% map_fun.comp
thf(fact_183_map__fun_Ocomp,axiom,
    ! [F2: ( b > a ) > b > a,G2: ( b > a ) > b > a,H: ( b > a ) > b > a,I: ( b > a ) > b > a] :
      ( ( comp_b3327941365615541530_a_b_a @ ( map_fu6504469177912210346_a_b_a @ F2 @ G2 ) @ ( map_fu6504469177912210346_a_b_a @ H @ I ) )
      = ( map_fu6504469177912210346_a_b_a @ ( comp_b_a_b_a_b_a @ H @ F2 ) @ ( comp_b_a_b_a_b_a @ G2 @ I ) ) ) ).

% map_fun.comp
thf(fact_184_map__fun_Ocomp,axiom,
    ! [F2: b > b,G2: b > b,H: b > b,I: b > b] :
      ( ( comp_b_b_b_b_b_b @ ( map_fun_b_b_b_b @ F2 @ G2 ) @ ( map_fun_b_b_b_b @ H @ I ) )
      = ( map_fun_b_b_b_b @ ( comp_b_b_b @ H @ F2 ) @ ( comp_b_b_b @ G2 @ I ) ) ) ).

% map_fun.comp
thf(fact_185_map__fun_Ocomp,axiom,
    ! [F2: a > a,G2: b > b,H: a > a,I: b > b] :
      ( ( comp_a_b_a_b_a_b @ ( map_fun_a_a_b_b @ F2 @ G2 ) @ ( map_fun_a_a_b_b @ H @ I ) )
      = ( map_fun_a_a_b_b @ ( comp_a_a_a @ H @ F2 ) @ ( comp_b_b_b @ G2 @ I ) ) ) ).

% map_fun.comp
thf(fact_186_map__fun_Ocomp,axiom,
    ! [F2: a > a,G2: a > a,H: a > a,I: a > a] :
      ( ( comp_a_a_a_a_a_a @ ( map_fun_a_a_a_a @ F2 @ G2 ) @ ( map_fun_a_a_a_a @ H @ I ) )
      = ( map_fun_a_a_a_a @ ( comp_a_a_a @ H @ F2 ) @ ( comp_a_a_a @ G2 @ I ) ) ) ).

% map_fun.comp
thf(fact_187_map__fun_Ocomp,axiom,
    ! [F2: ( b > a ) > b > a,G2: b > b,H: ( b > a ) > b > a,I: b > b] :
      ( ( comp_b1089415012269902447_b_a_b @ ( map_fun_b_a_b_a_b_b @ F2 @ G2 ) @ ( map_fun_b_a_b_a_b_b @ H @ I ) )
      = ( map_fun_b_a_b_a_b_b @ ( comp_b_a_b_a_b_a @ H @ F2 ) @ ( comp_b_b_b @ G2 @ I ) ) ) ).

% map_fun.comp
thf(fact_188_map__fun_Ocomp,axiom,
    ! [F2: ( b > a ) > b > a,G2: a > a,H: ( b > a ) > b > a,I: a > a] :
      ( ( comp_b1199615493944247470_b_a_a @ ( map_fun_b_a_b_a_a_a @ F2 @ G2 ) @ ( map_fun_b_a_b_a_a_a @ H @ I ) )
      = ( map_fun_b_a_b_a_a_a @ ( comp_b_a_b_a_b_a @ H @ F2 ) @ ( comp_a_a_a @ G2 @ I ) ) ) ).

% map_fun.comp
thf(fact_189_map__fun_Ocomp,axiom,
    ! [F2: produc4558475209616630778_a_b_b > dtree_a_b,G2: b > b,H: dtree_a_b > b,I: b > b] :
      ( ( comp_d3764564436183338888_b_b_b @ ( map_fu1543637842255174604_b_b_b @ F2 @ G2 ) @ ( map_fu3829198957627156781_b_b_b @ H @ I ) )
      = ( map_fu1983480571533677229_b_b_b @ ( comp_d7292648224603294300_a_b_b @ H @ F2 ) @ ( comp_b_b_b @ G2 @ I ) ) ) ).

% map_fun.comp
thf(fact_190_map__fun_Ocomp,axiom,
    ! [F2: produc4558475209616630778_a_b_b > dtree_a_b,G2: a > a,H: dtree_a_b > b,I: a > a] :
      ( ( comp_d7906738509105912391_a_b_a @ ( map_fu4331093424227850636_b_a_a @ F2 @ G2 ) @ ( map_fu6616654539599832813_b_a_a @ H @ I ) )
      = ( map_fu4770936153506353261_b_a_a @ ( comp_d7292648224603294300_a_b_b @ H @ F2 ) @ ( comp_a_a_a @ G2 @ I ) ) ) ).

% map_fun.comp
thf(fact_191_map__fun_Ocomp,axiom,
    ! [F2: b > b,G2: ( b > a ) > b > a,H: b > b,I: ( b > a ) > b > a] :
      ( ( comp_b164129730918660337_b_b_a @ ( map_fun_b_b_b_a_b_a @ F2 @ G2 ) @ ( map_fun_b_b_b_a_b_a @ H @ I ) )
      = ( map_fun_b_b_b_a_b_a @ ( comp_b_b_b @ H @ F2 ) @ ( comp_b_a_b_a_b_a @ G2 @ I ) ) ) ).

% map_fun.comp
thf(fact_192_curryI,axiom,
    ! [F2: produc3469756349985706280ee_a_b > $o,A: b,B: dtree_a_b] :
      ( ( F2 @ ( produc3542686128043086370ee_a_b @ A @ B ) )
     => ( produc1826475430485498408_a_b_o @ F2 @ A @ B ) ) ).

% curryI
thf(fact_193_curryI,axiom,
    ! [F2: produc8908337785154950741_a_b_b > $o,A: produc4558475209616630778_a_b_b,B: produc4558475209616630778_a_b_b] :
      ( ( F2 @ ( produc6533307410877503629_a_b_b @ A @ B ) )
     => ( produc7211229566987185431_b_b_o @ F2 @ A @ B ) ) ).

% curryI
thf(fact_194_curryI,axiom,
    ! [F2: produc8459935480633519975t_unit > $o,A: product_unit,B: product_unit] :
      ( ( F2 @ ( produc5692694829384537815t_unit @ A @ B ) )
     => ( produc7179068063668086733unit_o @ F2 @ A @ B ) ) ).

% curryI
thf(fact_195_curryI,axiom,
    ! [F2: produc4558475209616630778_a_b_b > $o,A: dtree_a_b,B: b] :
      ( ( F2 @ ( produc331601717337510060_a_b_b @ A @ B ) )
     => ( produc5550526150511291678_b_b_o @ F2 @ A @ B ) ) ).

% curryI
thf(fact_196_vimage2p__comp,axiom,
    ! [F1: ( b > a ) > b > a,F22: ( b > a ) > b > a,G1: b > b,G22: b > b] :
      ( ( bNF_vi9050661367211962233_b_b_a @ ( comp_b_a_b_a_b_a @ F1 @ F22 ) @ ( comp_b_b_b @ G1 @ G22 ) )
      = ( comp_b3327941365615541530_a_b_a @ ( bNF_vi9050661367211962233_b_b_a @ F22 @ G22 ) @ ( bNF_vi9050661367211962233_b_b_a @ F1 @ G1 ) ) ) ).

% vimage2p_comp
thf(fact_197_swap__simp,axiom,
    ! [X3: produc4558475209616630778_a_b_b,Y3: produc4558475209616630778_a_b_b] :
      ( ( produc9212635681174021677_a_b_b @ ( produc6533307410877503629_a_b_b @ X3 @ Y3 ) )
      = ( produc6533307410877503629_a_b_b @ Y3 @ X3 ) ) ).

% swap_simp
thf(fact_198_swap__simp,axiom,
    ! [X3: product_unit,Y3: product_unit] :
      ( ( produc1940222046511404151t_unit @ ( produc5692694829384537815t_unit @ X3 @ Y3 ) )
      = ( produc5692694829384537815t_unit @ Y3 @ X3 ) ) ).

% swap_simp
thf(fact_199_swap__simp,axiom,
    ! [X3: b,Y3: dtree_a_b] :
      ( ( produc6117232556371446914ee_a_b @ ( produc3542686128043086370ee_a_b @ X3 @ Y3 ) )
      = ( produc331601717337510060_a_b_b @ Y3 @ X3 ) ) ).

% swap_simp
thf(fact_200_swap__simp,axiom,
    ! [X3: dtree_a_b,Y3: b] :
      ( ( produc2906148145665870604_a_b_b @ ( produc331601717337510060_a_b_b @ X3 @ Y3 ) )
      = ( produc3542686128043086370ee_a_b @ Y3 @ X3 ) ) ).

% swap_simp
thf(fact_201_map__fun__apply,axiom,
    ( map_fu6922732985725783282_b_o_o
    = ( ^ [F: fset_P5281107635120001194_a_b_b > set_Pr3012420139608375472_a_b_b,G: $o > $o,H2: set_Pr3012420139608375472_a_b_b > $o,X: fset_P5281107635120001194_a_b_b] : ( G @ ( H2 @ ( F @ X ) ) ) ) ) ).

% map_fun_apply
thf(fact_202_map__fun__apply,axiom,
    ( map_fu8120312284176349332at_nat
    = ( ^ [F: fset_P5281107635120001194_a_b_b > set_Pr3012420139608375472_a_b_b,G: nat > nat,H2: set_Pr3012420139608375472_a_b_b > nat,X: fset_P5281107635120001194_a_b_b] : ( G @ ( H2 @ ( F @ X ) ) ) ) ) ).

% map_fun_apply
thf(fact_203_map__fun__apply,axiom,
    ( map_fu8973901316717634488_b_b_o
    = ( ^ [F: fset_P5281107635120001194_a_b_b > set_Pr3012420139608375472_a_b_b,G: ( set_Pr3012420139608375472_a_b_b > $o ) > fset_P5281107635120001194_a_b_b > $o,H2: set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b > $o,X: fset_P5281107635120001194_a_b_b] : ( G @ ( H2 @ ( F @ X ) ) ) ) ) ).

% map_fun_apply
thf(fact_204_map__fun__apply,axiom,
    ( map_fu6504469177912210346_a_b_a
    = ( ^ [F: ( b > a ) > b > a,G: ( b > a ) > b > a,H2: ( b > a ) > b > a,X: b > a] : ( G @ ( H2 @ ( F @ X ) ) ) ) ) ).

% map_fun_apply
thf(fact_205_map__fun__apply,axiom,
    ( map_fun_b_b_a_a
    = ( ^ [F: b > b,G: a > a,H2: b > a,X: b] : ( G @ ( H2 @ ( F @ X ) ) ) ) ) ).

% map_fun_apply
thf(fact_206_dtree_Oinject,axiom,
    ! [X12: a,X22: fset_P5281107635120001194_a_b_b,Y12: a,Y22: fset_P5281107635120001194_a_b_b] :
      ( ( ( node_a_b @ X12 @ X22 )
        = ( node_a_b @ Y12 @ Y22 ) )
      = ( ( X12 = Y12 )
        & ( X22 = Y22 ) ) ) ).

% dtree.inject
thf(fact_207_swap__swap,axiom,
    ! [P: produc3469756349985706280ee_a_b] :
      ( ( produc2906148145665870604_a_b_b @ ( produc6117232556371446914ee_a_b @ P ) )
      = P ) ).

% swap_swap
thf(fact_208_swap__swap,axiom,
    ! [P: produc4558475209616630778_a_b_b] :
      ( ( produc6117232556371446914ee_a_b @ ( produc2906148145665870604_a_b_b @ P ) )
      = P ) ).

% swap_swap
thf(fact_209_dtail_Ocases,axiom,
    ! [X3: produc1083523234014712191_b_b_a] :
      ~ ! [R4: a,Xs: fset_P5281107635120001194_a_b_b,Def: b > a] :
          ( X3
         != ( produc1993688775741047735_b_b_a @ ( node_a_b @ R4 @ Xs ) @ Def ) ) ).

% dtail.cases
thf(fact_210_is__subtree_Ocases,axiom,
    ! [X3: produc5177672665255943253ee_a_b] :
      ~ ! [X5: dtree_a_b,R4: a,Xs: fset_P5281107635120001194_a_b_b] :
          ( X3
         != ( produc7805419539522982029ee_a_b @ X5 @ ( node_a_b @ R4 @ Xs ) ) ) ).

% is_subtree.cases
thf(fact_211_dtree_Oexhaust,axiom,
    ! [Y3: dtree_a_b] :
      ~ ! [X1: a,X2: fset_P5281107635120001194_a_b_b] :
          ( Y3
         != ( node_a_b @ X1 @ X2 ) ) ).

% dtree.exhaust
thf(fact_212_dverts__mset_Ocases,axiom,
    ! [X3: dtree_a_b] :
      ~ ! [R4: a,Xs: fset_P5281107635120001194_a_b_b] :
          ( X3
         != ( node_a_b @ R4 @ Xs ) ) ).

% dverts_mset.cases
thf(fact_213_map__fun__def,axiom,
    ( map_fu7442569697125996214_a_b_a
    = ( ^ [F: ( ( b > a ) > b > a ) > ( b > a ) > b > a,G: ( ( b > a ) > b > a ) > ( b > a ) > b > a,H2: ( ( b > a ) > b > a ) > ( b > a ) > b > a] : ( comp_b3327941365615541530_a_b_a @ ( comp_b3327941365615541530_a_b_a @ G @ H2 ) @ F ) ) ) ).

% map_fun_def
thf(fact_214_map__fun__def,axiom,
    ( map_fu5601089516310178851_a_b_a
    = ( ^ [F: ( b > a ) > b > a,G: ( b > a ) > product_prod_b_a_b_a,H2: ( b > a ) > b > a] : ( comp_b7652884982158753286_a_b_a @ ( comp_b7652884982158753286_a_b_a @ G @ H2 ) @ F ) ) ) ).

% map_fun_def
thf(fact_215_map__fun__def,axiom,
    ( map_fun_b_b_b_b
    = ( ^ [F: b > b,G: b > b,H2: b > b] : ( comp_b_b_b @ ( comp_b_b_b @ G @ H2 ) @ F ) ) ) ).

% map_fun_def
thf(fact_216_map__fun__def,axiom,
    ( map_fun_a_a_a_a
    = ( ^ [F: a > a,G: a > a,H2: a > a] : ( comp_a_a_a @ ( comp_a_a_a @ G @ H2 ) @ F ) ) ) ).

% map_fun_def
thf(fact_217_map__fun__def,axiom,
    ( map_fu6922732985725783282_b_o_o
    = ( ^ [F: fset_P5281107635120001194_a_b_b > set_Pr3012420139608375472_a_b_b,G: $o > $o,H2: set_Pr3012420139608375472_a_b_b > $o] : ( comp_s5789959651358644079_a_b_b @ ( comp_o3567036564971088019_a_b_b @ G @ H2 ) @ F ) ) ) ).

% map_fun_def
thf(fact_218_map__fun__def,axiom,
    ( map_fu8120312284176349332at_nat
    = ( ^ [F: fset_P5281107635120001194_a_b_b > set_Pr3012420139608375472_a_b_b,G: nat > nat,H2: set_Pr3012420139608375472_a_b_b > nat] : ( comp_s5024164508761875599_a_b_b @ ( comp_n162390648425316405_a_b_b @ G @ H2 ) @ F ) ) ) ).

% map_fun_def
thf(fact_219_map__fun__def,axiom,
    ( map_fu8973901316717634488_b_b_o
    = ( ^ [F: fset_P5281107635120001194_a_b_b > set_Pr3012420139608375472_a_b_b,G: ( set_Pr3012420139608375472_a_b_b > $o ) > fset_P5281107635120001194_a_b_b > $o,H2: set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b > $o] : ( comp_s4871757605105181180_a_b_b @ ( comp_s7925026818889343833_a_b_b @ G @ H2 ) @ F ) ) ) ).

% map_fun_def
thf(fact_220_map__fun__def,axiom,
    ( map_fun_b_b_a_a
    = ( ^ [F: b > b,G: a > a,H2: b > a] : ( comp_b_a_b @ ( comp_a_a_b @ G @ H2 ) @ F ) ) ) ).

% map_fun_def
thf(fact_221_map__fun__def,axiom,
    ( map_fu6504469177912210346_a_b_a
    = ( ^ [F: ( b > a ) > b > a,G: ( b > a ) > b > a,H2: ( b > a ) > b > a] : ( comp_b_a_b_a_b_a @ ( comp_b_a_b_a_b_a @ G @ H2 ) @ F ) ) ) ).

% map_fun_def
thf(fact_222_map__fun_Ocompositionality,axiom,
    ! [F2: ( b > a ) > b > a,G2: ( b > a ) > b > a,H: ( b > a ) > b > a,I: ( b > a ) > b > a,Fun: ( b > a ) > b > a] :
      ( ( map_fu6504469177912210346_a_b_a @ F2 @ G2 @ ( map_fu6504469177912210346_a_b_a @ H @ I @ Fun ) )
      = ( map_fu6504469177912210346_a_b_a @ ( comp_b_a_b_a_b_a @ H @ F2 ) @ ( comp_b_a_b_a_b_a @ G2 @ I ) @ Fun ) ) ).

% map_fun.compositionality
thf(fact_223_map__fun_Ocompositionality,axiom,
    ! [F2: b > b,G2: b > b,H: b > b,I: b > b,Fun: b > b] :
      ( ( map_fun_b_b_b_b @ F2 @ G2 @ ( map_fun_b_b_b_b @ H @ I @ Fun ) )
      = ( map_fun_b_b_b_b @ ( comp_b_b_b @ H @ F2 ) @ ( comp_b_b_b @ G2 @ I ) @ Fun ) ) ).

% map_fun.compositionality
thf(fact_224_map__fun_Ocompositionality,axiom,
    ! [F2: a > a,G2: b > b,H: a > a,I: b > b,Fun: a > b] :
      ( ( map_fun_a_a_b_b @ F2 @ G2 @ ( map_fun_a_a_b_b @ H @ I @ Fun ) )
      = ( map_fun_a_a_b_b @ ( comp_a_a_a @ H @ F2 ) @ ( comp_b_b_b @ G2 @ I ) @ Fun ) ) ).

% map_fun.compositionality
thf(fact_225_map__fun_Ocompositionality,axiom,
    ! [F2: a > a,G2: a > a,H: a > a,I: a > a,Fun: a > a] :
      ( ( map_fun_a_a_a_a @ F2 @ G2 @ ( map_fun_a_a_a_a @ H @ I @ Fun ) )
      = ( map_fun_a_a_a_a @ ( comp_a_a_a @ H @ F2 ) @ ( comp_a_a_a @ G2 @ I ) @ Fun ) ) ).

% map_fun.compositionality
thf(fact_226_map__fun_Ocompositionality,axiom,
    ! [F2: b > b,G2: a > a,H: b > b,I: a > a,Fun: b > a] :
      ( ( map_fun_b_b_a_a @ F2 @ G2 @ ( map_fun_b_b_a_a @ H @ I @ Fun ) )
      = ( map_fun_b_b_a_a @ ( comp_b_b_b @ H @ F2 ) @ ( comp_a_a_a @ G2 @ I ) @ Fun ) ) ).

% map_fun.compositionality
thf(fact_227_map__fun_Ocompositionality,axiom,
    ! [F2: ( b > a ) > b > a,G2: b > b,H: ( b > a ) > b > a,I: b > b,Fun: ( b > a ) > b] :
      ( ( map_fun_b_a_b_a_b_b @ F2 @ G2 @ ( map_fun_b_a_b_a_b_b @ H @ I @ Fun ) )
      = ( map_fun_b_a_b_a_b_b @ ( comp_b_a_b_a_b_a @ H @ F2 ) @ ( comp_b_b_b @ G2 @ I ) @ Fun ) ) ).

% map_fun.compositionality
thf(fact_228_map__fun_Ocompositionality,axiom,
    ! [F2: ( b > a ) > b > a,G2: a > a,H: ( b > a ) > b > a,I: a > a,Fun: ( b > a ) > a] :
      ( ( map_fun_b_a_b_a_a_a @ F2 @ G2 @ ( map_fun_b_a_b_a_a_a @ H @ I @ Fun ) )
      = ( map_fun_b_a_b_a_a_a @ ( comp_b_a_b_a_b_a @ H @ F2 ) @ ( comp_a_a_a @ G2 @ I ) @ Fun ) ) ).

% map_fun.compositionality
thf(fact_229_map__fun_Ocompositionality,axiom,
    ! [F2: produc4558475209616630778_a_b_b > dtree_a_b,G2: b > b,H: dtree_a_b > b,I: b > b,Fun: b > b] :
      ( ( map_fu1543637842255174604_b_b_b @ F2 @ G2 @ ( map_fu3829198957627156781_b_b_b @ H @ I @ Fun ) )
      = ( map_fu1983480571533677229_b_b_b @ ( comp_d7292648224603294300_a_b_b @ H @ F2 ) @ ( comp_b_b_b @ G2 @ I ) @ Fun ) ) ).

% map_fun.compositionality
thf(fact_230_map__fun_Ocompositionality,axiom,
    ! [F2: produc4558475209616630778_a_b_b > dtree_a_b,G2: a > a,H: dtree_a_b > b,I: a > a,Fun: b > a] :
      ( ( map_fu4331093424227850636_b_a_a @ F2 @ G2 @ ( map_fu6616654539599832813_b_a_a @ H @ I @ Fun ) )
      = ( map_fu4770936153506353261_b_a_a @ ( comp_d7292648224603294300_a_b_b @ H @ F2 ) @ ( comp_a_a_a @ G2 @ I ) @ Fun ) ) ).

% map_fun.compositionality
thf(fact_231_map__fun_Ocompositionality,axiom,
    ! [F2: b > b,G2: ( b > a ) > b > a,H: b > b,I: ( b > a ) > b > a,Fun: b > b > a] :
      ( ( map_fun_b_b_b_a_b_a @ F2 @ G2 @ ( map_fun_b_b_b_a_b_a @ H @ I @ Fun ) )
      = ( map_fun_b_b_b_a_b_a @ ( comp_b_b_b @ H @ F2 ) @ ( comp_b_a_b_a_b_a @ G2 @ I ) @ Fun ) ) ).

% map_fun.compositionality
thf(fact_232_curryD,axiom,
    ! [F2: produc3469756349985706280ee_a_b > $o,A: b,B: dtree_a_b] :
      ( ( produc1826475430485498408_a_b_o @ F2 @ A @ B )
     => ( F2 @ ( produc3542686128043086370ee_a_b @ A @ B ) ) ) ).

% curryD
thf(fact_233_curryD,axiom,
    ! [F2: produc8908337785154950741_a_b_b > $o,A: produc4558475209616630778_a_b_b,B: produc4558475209616630778_a_b_b] :
      ( ( produc7211229566987185431_b_b_o @ F2 @ A @ B )
     => ( F2 @ ( produc6533307410877503629_a_b_b @ A @ B ) ) ) ).

% curryD
thf(fact_234_curryD,axiom,
    ! [F2: produc8459935480633519975t_unit > $o,A: product_unit,B: product_unit] :
      ( ( produc7179068063668086733unit_o @ F2 @ A @ B )
     => ( F2 @ ( produc5692694829384537815t_unit @ A @ B ) ) ) ).

% curryD
thf(fact_235_curryD,axiom,
    ! [F2: produc4558475209616630778_a_b_b > $o,A: dtree_a_b,B: b] :
      ( ( produc5550526150511291678_b_b_o @ F2 @ A @ B )
     => ( F2 @ ( produc331601717337510060_a_b_b @ A @ B ) ) ) ).

% curryD
thf(fact_236_curryE,axiom,
    ! [F2: produc3469756349985706280ee_a_b > $o,A: b,B: dtree_a_b] :
      ( ( produc1826475430485498408_a_b_o @ F2 @ A @ B )
     => ( F2 @ ( produc3542686128043086370ee_a_b @ A @ B ) ) ) ).

% curryE
thf(fact_237_curryE,axiom,
    ! [F2: produc8908337785154950741_a_b_b > $o,A: produc4558475209616630778_a_b_b,B: produc4558475209616630778_a_b_b] :
      ( ( produc7211229566987185431_b_b_o @ F2 @ A @ B )
     => ( F2 @ ( produc6533307410877503629_a_b_b @ A @ B ) ) ) ).

% curryE
thf(fact_238_curryE,axiom,
    ! [F2: produc8459935480633519975t_unit > $o,A: product_unit,B: product_unit] :
      ( ( produc7179068063668086733unit_o @ F2 @ A @ B )
     => ( F2 @ ( produc5692694829384537815t_unit @ A @ B ) ) ) ).

% curryE
thf(fact_239_curryE,axiom,
    ! [F2: produc4558475209616630778_a_b_b > $o,A: dtree_a_b,B: b] :
      ( ( produc5550526150511291678_b_b_o @ F2 @ A @ B )
     => ( F2 @ ( produc331601717337510060_a_b_b @ A @ B ) ) ) ).

% curryE
thf(fact_240_disjoint__darcs__if__wf__aux4,axiom,
    ! [R: a,Xs2: fset_P5281107635120001194_a_b_b,T1: dtree_a_b,E1: b,T2: dtree_a_b,E2: b] :
      ( ( wf_darcs_a_b @ ( node_a_b @ R @ Xs2 ) )
     => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ T1 @ E1 ) @ ( fset_P783253628892185035_a_b_b @ Xs2 ) )
       => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ T2 @ E2 ) @ ( fset_P783253628892185035_a_b_b @ Xs2 ) )
         => ( ( ( produc331601717337510060_a_b_b @ T1 @ E1 )
             != ( produc331601717337510060_a_b_b @ T2 @ E2 ) )
           => ( E1 != E2 ) ) ) ) ) ).

% disjoint_darcs_if_wf_aux4
thf(fact_241_pair__in__swap__image,axiom,
    ! [Y3: produc4558475209616630778_a_b_b,X3: produc4558475209616630778_a_b_b,A5: set_Pr2755428042910921141_a_b_b] :
      ( ( member9171970031259705598_a_b_b @ ( produc6533307410877503629_a_b_b @ Y3 @ X3 ) @ ( image_8464404100643805253_a_b_b @ produc9212635681174021677_a_b_b @ A5 ) )
      = ( member9171970031259705598_a_b_b @ ( produc6533307410877503629_a_b_b @ X3 @ Y3 ) @ A5 ) ) ).

% pair_in_swap_image
thf(fact_242_pair__in__swap__image,axiom,
    ! [Y3: product_unit,X3: product_unit,A5: set_Pr5094982260447487303t_unit] :
      ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ Y3 @ X3 ) @ ( image_9149991759805673413t_unit @ produc1940222046511404151t_unit @ A5 ) )
      = ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X3 @ Y3 ) @ A5 ) ) ).

% pair_in_swap_image
thf(fact_243_pair__in__swap__image,axiom,
    ! [Y3: b,X3: dtree_a_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( member3292202256475951039ee_a_b @ ( produc3542686128043086370ee_a_b @ Y3 @ X3 ) @ ( image_4993246317199781161ee_a_b @ produc2906148145665870604_a_b_b @ A5 ) )
      = ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ X3 @ Y3 ) @ A5 ) ) ).

% pair_in_swap_image
thf(fact_244_pair__in__swap__image,axiom,
    ! [Y3: dtree_a_b,X3: b,A5: set_Pr6717515126349854430ee_a_b] :
      ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ Y3 @ X3 ) @ ( image_3585698774939316521_a_b_b @ produc6117232556371446914ee_a_b @ A5 ) )
      = ( member3292202256475951039ee_a_b @ ( produc3542686128043086370ee_a_b @ X3 @ Y3 ) @ A5 ) ) ).

% pair_in_swap_image
thf(fact_245_internal__case__prod__def,axiom,
    produc6395705637274715955_a_b_b = produc2559767781221151625_a_b_b ).

% internal_case_prod_def
thf(fact_246_internal__case__prod__def,axiom,
    produc8719677615279257213_a_b_b = produc5460679229782211283_a_b_b ).

% internal_case_prod_def
thf(fact_247_internal__case__prod__def,axiom,
    produc835642783053744213_b_b_o = produc1325217093046185599_b_b_o ).

% internal_case_prod_def
thf(fact_248_in__rel__def,axiom,
    ( fun_in1805295813492079159ee_a_b
    = ( ^ [R5: set_Pr6717515126349854430ee_a_b,X: b,Y: dtree_a_b] : ( member3292202256475951039ee_a_b @ ( produc3542686128043086370ee_a_b @ X @ Y ) @ R5 ) ) ) ).

% in_rel_def
thf(fact_249_in__rel__def,axiom,
    ( fun_in223410601938929720_a_b_b
    = ( ^ [R5: set_Pr2755428042910921141_a_b_b,X: produc4558475209616630778_a_b_b,Y: produc4558475209616630778_a_b_b] : ( member9171970031259705598_a_b_b @ ( produc6533307410877503629_a_b_b @ X @ Y ) @ R5 ) ) ) ).

% in_rel_def
thf(fact_250_in__rel__def,axiom,
    ( fun_in4492808859237503746t_unit
    = ( ^ [R5: set_Pr5094982260447487303t_unit,X: product_unit,Y: product_unit] : ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X @ Y ) @ R5 ) ) ) ).

% in_rel_def
thf(fact_251_in__rel__def,axiom,
    ( fun_in7817583439641278657_a_b_b
    = ( ^ [R5: set_Pr3012420139608375472_a_b_b,X: dtree_a_b,Y: b] : ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ X @ Y ) @ R5 ) ) ) ).

% in_rel_def
thf(fact_252_apsnd__conv,axiom,
    ! [F2: dtree_a_b > dtree_a_b,X3: b,Y3: dtree_a_b] :
      ( ( produc3383614106744390411_a_b_b @ F2 @ ( produc3542686128043086370ee_a_b @ X3 @ Y3 ) )
      = ( produc3542686128043086370ee_a_b @ X3 @ ( F2 @ Y3 ) ) ) ).

% apsnd_conv
thf(fact_253_apsnd__conv,axiom,
    ! [F2: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,X3: produc4558475209616630778_a_b_b,Y3: produc4558475209616630778_a_b_b] :
      ( ( produc6388821566548385006_a_b_b @ F2 @ ( produc6533307410877503629_a_b_b @ X3 @ Y3 ) )
      = ( produc6533307410877503629_a_b_b @ X3 @ ( F2 @ Y3 ) ) ) ).

% apsnd_conv
thf(fact_254_apsnd__conv,axiom,
    ! [F2: product_unit > product_unit,X3: product_unit,Y3: product_unit] :
      ( ( produc6120449539986271055t_unit @ F2 @ ( produc5692694829384537815t_unit @ X3 @ Y3 ) )
      = ( produc5692694829384537815t_unit @ X3 @ ( F2 @ Y3 ) ) ) ).

% apsnd_conv
thf(fact_255_apsnd__conv,axiom,
    ! [F2: b > b,X3: dtree_a_b,Y3: b] :
      ( ( produc7811666328248579896ee_a_b @ F2 @ ( produc331601717337510060_a_b_b @ X3 @ Y3 ) )
      = ( produc331601717337510060_a_b_b @ X3 @ ( F2 @ Y3 ) ) ) ).

% apsnd_conv
thf(fact_256_case__prod__curry,axiom,
    ! [F2: produc4558475209616630778_a_b_b > set_Pr3012420139608375472_a_b_b] :
      ( ( produc2559767781221151625_a_b_b @ ( produc2895653412298819754_a_b_b @ F2 ) )
      = F2 ) ).

% case_prod_curry
thf(fact_257_case__prod__curry,axiom,
    ! [F2: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b] :
      ( ( produc5460679229782211283_a_b_b @ ( produc3315389081899078644_a_b_b @ F2 ) )
      = F2 ) ).

% case_prod_curry
thf(fact_258_case__prod__curry,axiom,
    ! [F2: produc4558475209616630778_a_b_b > $o] :
      ( ( produc1325217093046185599_b_b_o @ ( produc5550526150511291678_b_b_o @ F2 ) )
      = F2 ) ).

% case_prod_curry
thf(fact_259_curry__case__prod,axiom,
    ! [F2: dtree_a_b > b > set_Pr3012420139608375472_a_b_b] :
      ( ( produc2895653412298819754_a_b_b @ ( produc2559767781221151625_a_b_b @ F2 ) )
      = F2 ) ).

% curry_case_prod
thf(fact_260_curry__case__prod,axiom,
    ! [F2: dtree_a_b > b > produc4558475209616630778_a_b_b] :
      ( ( produc3315389081899078644_a_b_b @ ( produc5460679229782211283_a_b_b @ F2 ) )
      = F2 ) ).

% curry_case_prod
thf(fact_261_curry__case__prod,axiom,
    ! [F2: dtree_a_b > b > $o] :
      ( ( produc5550526150511291678_b_b_o @ ( produc1325217093046185599_b_b_o @ F2 ) )
      = F2 ) ).

% curry_case_prod
thf(fact_262_mem__case__prodE,axiom,
    ! [Z: produc4558475209616630778_a_b_b,C: dtree_a_b > b > set_Pr3012420139608375472_a_b_b,P: produc4558475209616630778_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ Z @ ( produc2559767781221151625_a_b_b @ C @ P ) )
     => ~ ! [X5: dtree_a_b,Y4: b] :
            ( ( P
              = ( produc331601717337510060_a_b_b @ X5 @ Y4 ) )
           => ~ ( member4380921116106875537_a_b_b @ Z @ ( C @ X5 @ Y4 ) ) ) ) ).

% mem_case_prodE
thf(fact_263_mem__case__prodE,axiom,
    ! [Z: nat,C: product_unit > product_unit > set_nat,P: produc8459935480633519975t_unit] :
      ( ( member_nat @ Z @ ( produc9075591806163244658et_nat @ C @ P ) )
     => ~ ! [X5: product_unit,Y4: product_unit] :
            ( ( P
              = ( produc5692694829384537815t_unit @ X5 @ Y4 ) )
           => ~ ( member_nat @ Z @ ( C @ X5 @ Y4 ) ) ) ) ).

% mem_case_prodE
thf(fact_264_mem__case__prodE,axiom,
    ! [Z: b,C: product_unit > product_unit > set_b,P: produc8459935480633519975t_unit] :
      ( ( member_b @ Z @ ( produc989992568788953075_set_b @ C @ P ) )
     => ~ ! [X5: product_unit,Y4: product_unit] :
            ( ( P
              = ( produc5692694829384537815t_unit @ X5 @ Y4 ) )
           => ~ ( member_b @ Z @ ( C @ X5 @ Y4 ) ) ) ) ).

% mem_case_prodE
thf(fact_265_mem__case__prodE,axiom,
    ! [Z: a,C: product_unit > product_unit > set_a,P: produc8459935480633519975t_unit] :
      ( ( member_a @ Z @ ( produc989992564485724274_set_a @ C @ P ) )
     => ~ ! [X5: product_unit,Y4: product_unit] :
            ( ( P
              = ( produc5692694829384537815t_unit @ X5 @ Y4 ) )
           => ~ ( member_a @ Z @ ( C @ X5 @ Y4 ) ) ) ) ).

% mem_case_prodE
thf(fact_266_mem__case__prodE,axiom,
    ! [Z: nat,C: dtree_a_b > b > set_nat,P: produc4558475209616630778_a_b_b] :
      ( ( member_nat @ Z @ ( produc6123424770501316703et_nat @ C @ P ) )
     => ~ ! [X5: dtree_a_b,Y4: b] :
            ( ( P
              = ( produc331601717337510060_a_b_b @ X5 @ Y4 ) )
           => ~ ( member_nat @ Z @ ( C @ X5 @ Y4 ) ) ) ) ).

% mem_case_prodE
thf(fact_267_mem__case__prodE,axiom,
    ! [Z: b,C: dtree_a_b > b > set_b,P: produc4558475209616630778_a_b_b] :
      ( ( member_b @ Z @ ( produc5617419908695543622_set_b @ C @ P ) )
     => ~ ! [X5: dtree_a_b,Y4: b] :
            ( ( P
              = ( produc331601717337510060_a_b_b @ X5 @ Y4 ) )
           => ~ ( member_b @ Z @ ( C @ X5 @ Y4 ) ) ) ) ).

% mem_case_prodE
thf(fact_268_mem__case__prodE,axiom,
    ! [Z: a,C: dtree_a_b > b > set_a,P: produc4558475209616630778_a_b_b] :
      ( ( member_a @ Z @ ( produc5617419904392314821_set_a @ C @ P ) )
     => ~ ! [X5: dtree_a_b,Y4: b] :
            ( ( P
              = ( produc331601717337510060_a_b_b @ X5 @ Y4 ) )
           => ~ ( member_a @ Z @ ( C @ X5 @ Y4 ) ) ) ) ).

% mem_case_prodE
thf(fact_269_mem__case__prodE,axiom,
    ! [Z: nat,C: b > dtree_a_b > set_nat,P: produc3469756349985706280ee_a_b] :
      ( ( member_nat @ Z @ ( produc1571707150759354837et_nat @ C @ P ) )
     => ~ ! [X5: b,Y4: dtree_a_b] :
            ( ( P
              = ( produc3542686128043086370ee_a_b @ X5 @ Y4 ) )
           => ~ ( member_nat @ Z @ ( C @ X5 @ Y4 ) ) ) ) ).

% mem_case_prodE
thf(fact_270_mem__case__prodE,axiom,
    ! [Z: b,C: b > dtree_a_b > set_b,P: produc3469756349985706280ee_a_b] :
      ( ( member_b @ Z @ ( produc4685151523725209424_set_b @ C @ P ) )
     => ~ ! [X5: b,Y4: dtree_a_b] :
            ( ( P
              = ( produc3542686128043086370ee_a_b @ X5 @ Y4 ) )
           => ~ ( member_b @ Z @ ( C @ X5 @ Y4 ) ) ) ) ).

% mem_case_prodE
thf(fact_271_mem__case__prodE,axiom,
    ! [Z: a,C: b > dtree_a_b > set_a,P: produc3469756349985706280ee_a_b] :
      ( ( member_a @ Z @ ( produc4685151519421980623_set_a @ C @ P ) )
     => ~ ! [X5: b,Y4: dtree_a_b] :
            ( ( P
              = ( produc3542686128043086370ee_a_b @ X5 @ Y4 ) )
           => ~ ( member_a @ Z @ ( C @ X5 @ Y4 ) ) ) ) ).

% mem_case_prodE
thf(fact_272_image__comp,axiom,
    ! [F2: ( b > a ) > b > a,G2: ( b > a ) > b > a,R: set_b_a] :
      ( ( image_b_a_b_a @ F2 @ ( image_b_a_b_a @ G2 @ R ) )
      = ( image_b_a_b_a @ ( comp_b_a_b_a_b_a @ F2 @ G2 ) @ R ) ) ).

% image_comp
thf(fact_273_image__comp,axiom,
    ! [F2: b > b,G2: b > b,R: set_b] :
      ( ( image_b_b @ F2 @ ( image_b_b @ G2 @ R ) )
      = ( image_b_b @ ( comp_b_b_b @ F2 @ G2 ) @ R ) ) ).

% image_comp
thf(fact_274_image__comp,axiom,
    ! [F2: a > a,G2: a > a,R: set_a] :
      ( ( image_a_a @ F2 @ ( image_a_a @ G2 @ R ) )
      = ( image_a_a @ ( comp_a_a_a @ F2 @ G2 ) @ R ) ) ).

% image_comp
thf(fact_275_image__comp,axiom,
    ! [F2: dtree_a_b > b,G2: produc4558475209616630778_a_b_b > dtree_a_b,R: set_Pr3012420139608375472_a_b_b] :
      ( ( image_dtree_a_b_b @ F2 @ ( image_7065894828672115579ee_a_b @ G2 @ R ) )
      = ( image_3908709015779211070_b_b_b @ ( comp_d7292648224603294300_a_b_b @ F2 @ G2 ) @ R ) ) ).

% image_comp
thf(fact_276_image__comp,axiom,
    ! [F2: dtree_a_b > dtree_a_b,G2: produc4558475209616630778_a_b_b > dtree_a_b,R: set_Pr3012420139608375472_a_b_b] :
      ( ( image_1160270813240538107ee_a_b @ F2 @ ( image_7065894828672115579ee_a_b @ G2 @ R ) )
      = ( image_7065894828672115579ee_a_b @ ( comp_d9193377603055859667_a_b_b @ F2 @ G2 ) @ R ) ) ).

% image_comp
thf(fact_277_image__comp,axiom,
    ! [F2: produc3469756349985706280ee_a_b > dtree_a_b,G2: produc4558475209616630778_a_b_b > produc3469756349985706280ee_a_b,R: set_Pr3012420139608375472_a_b_b] :
      ( ( image_6364595536291967657ee_a_b @ F2 @ ( image_4993246317199781161ee_a_b @ G2 @ R ) )
      = ( image_7065894828672115579ee_a_b @ ( comp_P5693690220181566849_a_b_b @ F2 @ G2 ) @ R ) ) ).

% image_comp
thf(fact_278_image__comp,axiom,
    ! [F2: dtree_a_b > produc3469756349985706280ee_a_b,G2: produc4558475209616630778_a_b_b > dtree_a_b,R: set_Pr3012420139608375472_a_b_b] :
      ( ( image_8495257627889188265ee_a_b @ F2 @ ( image_7065894828672115579ee_a_b @ G2 @ R ) )
      = ( image_4993246317199781161ee_a_b @ ( comp_d4253798619470020737_a_b_b @ F2 @ G2 ) @ R ) ) ).

% image_comp
thf(fact_279_image__comp,axiom,
    ! [F2: ( b > a ) > product_prod_b_a_b_a,G2: ( b > a ) > b > a,R: set_b_a] :
      ( ( image_3865962054164325950_a_b_a @ F2 @ ( image_b_a_b_a @ G2 @ R ) )
      = ( image_3865962054164325950_a_b_a @ ( comp_b7652884982158753286_a_b_a @ F2 @ G2 ) @ R ) ) ).

% image_comp
thf(fact_280_image__comp,axiom,
    ! [F2: produc4558475209616630778_a_b_b > dtree_a_b,G2: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,R: set_Pr3012420139608375472_a_b_b] :
      ( ( image_7065894828672115579ee_a_b @ F2 @ ( image_6081965176830705659_a_b_b @ G2 @ R ) )
      = ( image_7065894828672115579ee_a_b @ ( comp_P2227990766219928147_a_b_b @ F2 @ G2 ) @ R ) ) ).

% image_comp
thf(fact_281_image__comp,axiom,
    ! [F2: produc4558475209616630778_a_b_b > dtree_a_b,G2: produc3469756349985706280ee_a_b > produc4558475209616630778_a_b_b,R: set_Pr6717515126349854430ee_a_b] :
      ( ( image_7065894828672115579ee_a_b @ F2 @ ( image_3585698774939316521_a_b_b @ G2 @ R ) )
      = ( image_6364595536291967657ee_a_b @ ( comp_P1139271906589003649ee_a_b @ F2 @ G2 ) @ R ) ) ).

% image_comp
thf(fact_282_image__eq__imp__comp,axiom,
    ! [F2: ( b > a ) > b > a,A5: set_b_a,G2: ( b > a ) > b > a,B5: set_b_a,H: ( b > a ) > b > a] :
      ( ( ( image_b_a_b_a @ F2 @ A5 )
        = ( image_b_a_b_a @ G2 @ B5 ) )
     => ( ( image_b_a_b_a @ ( comp_b_a_b_a_b_a @ H @ F2 ) @ A5 )
        = ( image_b_a_b_a @ ( comp_b_a_b_a_b_a @ H @ G2 ) @ B5 ) ) ) ).

% image_eq_imp_comp
thf(fact_283_image__eq__imp__comp,axiom,
    ! [F2: b > b,A5: set_b,G2: b > b,B5: set_b,H: b > b] :
      ( ( ( image_b_b @ F2 @ A5 )
        = ( image_b_b @ G2 @ B5 ) )
     => ( ( image_b_b @ ( comp_b_b_b @ H @ F2 ) @ A5 )
        = ( image_b_b @ ( comp_b_b_b @ H @ G2 ) @ B5 ) ) ) ).

% image_eq_imp_comp
thf(fact_284_image__eq__imp__comp,axiom,
    ! [F2: a > a,A5: set_a,G2: a > a,B5: set_a,H: a > a] :
      ( ( ( image_a_a @ F2 @ A5 )
        = ( image_a_a @ G2 @ B5 ) )
     => ( ( image_a_a @ ( comp_a_a_a @ H @ F2 ) @ A5 )
        = ( image_a_a @ ( comp_a_a_a @ H @ G2 ) @ B5 ) ) ) ).

% image_eq_imp_comp
thf(fact_285_image__eq__imp__comp,axiom,
    ! [F2: ( b > a ) > dtree_a_b,A5: set_b_a,G2: produc4558475209616630778_a_b_b > dtree_a_b,B5: set_Pr3012420139608375472_a_b_b,H: dtree_a_b > b > a] :
      ( ( ( image_b_a_dtree_a_b @ F2 @ A5 )
        = ( image_7065894828672115579ee_a_b @ G2 @ B5 ) )
     => ( ( image_b_a_b_a @ ( comp_d4284745388203020455_a_b_a @ H @ F2 ) @ A5 )
        = ( image_7926328481751752869_b_b_a @ ( comp_d2537776500735531005_a_b_b @ H @ G2 ) @ B5 ) ) ) ).

% image_eq_imp_comp
thf(fact_286_image__eq__imp__comp,axiom,
    ! [F2: produc4558475209616630778_a_b_b > b > a,A5: set_Pr3012420139608375472_a_b_b,G2: ( b > a ) > b > a,B5: set_b_a,H: ( b > a ) > dtree_a_b] :
      ( ( ( image_7926328481751752869_b_b_a @ F2 @ A5 )
        = ( image_b_a_b_a @ G2 @ B5 ) )
     => ( ( image_7065894828672115579ee_a_b @ ( comp_b3926150692603505917_a_b_b @ H @ F2 ) @ A5 )
        = ( image_b_a_dtree_a_b @ ( comp_b3254671105061676455_b_b_a @ H @ G2 ) @ B5 ) ) ) ).

% image_eq_imp_comp
thf(fact_287_image__eq__imp__comp,axiom,
    ! [F2: produc4558475209616630778_a_b_b > dtree_a_b,A5: set_Pr3012420139608375472_a_b_b,G2: ( b > a ) > dtree_a_b,B5: set_b_a,H: dtree_a_b > b > a] :
      ( ( ( image_7065894828672115579ee_a_b @ F2 @ A5 )
        = ( image_b_a_dtree_a_b @ G2 @ B5 ) )
     => ( ( image_7926328481751752869_b_b_a @ ( comp_d2537776500735531005_a_b_b @ H @ F2 ) @ A5 )
        = ( image_b_a_b_a @ ( comp_d4284745388203020455_a_b_a @ H @ G2 ) @ B5 ) ) ) ).

% image_eq_imp_comp
thf(fact_288_image__eq__imp__comp,axiom,
    ! [F2: produc4558475209616630778_a_b_b > dtree_a_b,A5: set_Pr3012420139608375472_a_b_b,G2: produc4558475209616630778_a_b_b > dtree_a_b,B5: set_Pr3012420139608375472_a_b_b,H: dtree_a_b > b] :
      ( ( ( image_7065894828672115579ee_a_b @ F2 @ A5 )
        = ( image_7065894828672115579ee_a_b @ G2 @ B5 ) )
     => ( ( image_3908709015779211070_b_b_b @ ( comp_d7292648224603294300_a_b_b @ H @ F2 ) @ A5 )
        = ( image_3908709015779211070_b_b_b @ ( comp_d7292648224603294300_a_b_b @ H @ G2 ) @ B5 ) ) ) ).

% image_eq_imp_comp
thf(fact_289_image__eq__imp__comp,axiom,
    ! [F2: ( b > a ) > b > a,A5: set_b_a,G2: produc4558475209616630778_a_b_b > b > a,B5: set_Pr3012420139608375472_a_b_b,H: ( b > a ) > dtree_a_b] :
      ( ( ( image_b_a_b_a @ F2 @ A5 )
        = ( image_7926328481751752869_b_b_a @ G2 @ B5 ) )
     => ( ( image_b_a_dtree_a_b @ ( comp_b3254671105061676455_b_b_a @ H @ F2 ) @ A5 )
        = ( image_7065894828672115579ee_a_b @ ( comp_b3926150692603505917_a_b_b @ H @ G2 ) @ B5 ) ) ) ).

% image_eq_imp_comp
thf(fact_290_image__eq__imp__comp,axiom,
    ! [F2: ( b > a ) > produc3469756349985706280ee_a_b,A5: set_b_a,G2: produc4558475209616630778_a_b_b > produc3469756349985706280ee_a_b,B5: set_Pr3012420139608375472_a_b_b,H: produc3469756349985706280ee_a_b > b > a] :
      ( ( ( image_702552451275806163ee_a_b @ F2 @ A5 )
        = ( image_4993246317199781161ee_a_b @ G2 @ B5 ) )
     => ( ( image_b_a_b_a @ ( comp_P8523877797512642645_a_b_a @ H @ F2 ) @ A5 )
        = ( image_7926328481751752869_b_b_a @ ( comp_P1823700203131805611_a_b_b @ H @ G2 ) @ B5 ) ) ) ).

% image_eq_imp_comp
thf(fact_291_image__eq__imp__comp,axiom,
    ! [F2: ( b > a ) > produc4558475209616630778_a_b_b,A5: set_b_a,G2: produc3469756349985706280ee_a_b > produc4558475209616630778_a_b_b,B5: set_Pr6717515126349854430ee_a_b,H: produc4558475209616630778_a_b_b > b > a] :
      ( ( ( image_1791271310906730661_a_b_b @ F2 @ A5 )
        = ( image_3585698774939316521_a_b_b @ G2 @ B5 ) )
     => ( ( image_b_a_b_a @ ( comp_P5371444601569245991_a_b_a @ H @ F2 ) @ A5 )
        = ( image_4051856227524180435_b_b_a @ ( comp_P7262450972268490667ee_a_b @ H @ G2 ) @ B5 ) ) ) ).

% image_eq_imp_comp
thf(fact_292_old_Oprod_Ocase,axiom,
    ! [F2: dtree_a_b > b > set_Pr3012420139608375472_a_b_b,X12: dtree_a_b,X22: b] :
      ( ( produc2559767781221151625_a_b_b @ F2 @ ( produc331601717337510060_a_b_b @ X12 @ X22 ) )
      = ( F2 @ X12 @ X22 ) ) ).

% old.prod.case
thf(fact_293_old_Oprod_Ocase,axiom,
    ! [F2: dtree_a_b > b > produc4558475209616630778_a_b_b,X12: dtree_a_b,X22: b] :
      ( ( produc5460679229782211283_a_b_b @ F2 @ ( produc331601717337510060_a_b_b @ X12 @ X22 ) )
      = ( F2 @ X12 @ X22 ) ) ).

% old.prod.case
thf(fact_294_old_Oprod_Ocase,axiom,
    ! [F2: dtree_a_b > b > $o,X12: dtree_a_b,X22: b] :
      ( ( produc1325217093046185599_b_b_o @ F2 @ ( produc331601717337510060_a_b_b @ X12 @ X22 ) )
      = ( F2 @ X12 @ X22 ) ) ).

% old.prod.case
thf(fact_295_split__cong,axiom,
    ! [Q2: produc4558475209616630778_a_b_b,F2: dtree_a_b > b > set_Pr3012420139608375472_a_b_b,G2: dtree_a_b > b > set_Pr3012420139608375472_a_b_b,P: produc4558475209616630778_a_b_b] :
      ( ! [X5: dtree_a_b,Y4: b] :
          ( ( ( produc331601717337510060_a_b_b @ X5 @ Y4 )
            = Q2 )
         => ( ( F2 @ X5 @ Y4 )
            = ( G2 @ X5 @ Y4 ) ) )
     => ( ( P = Q2 )
       => ( ( produc2559767781221151625_a_b_b @ F2 @ P )
          = ( produc2559767781221151625_a_b_b @ G2 @ Q2 ) ) ) ) ).

% split_cong
thf(fact_296_split__cong,axiom,
    ! [Q2: produc4558475209616630778_a_b_b,F2: dtree_a_b > b > produc4558475209616630778_a_b_b,G2: dtree_a_b > b > produc4558475209616630778_a_b_b,P: produc4558475209616630778_a_b_b] :
      ( ! [X5: dtree_a_b,Y4: b] :
          ( ( ( produc331601717337510060_a_b_b @ X5 @ Y4 )
            = Q2 )
         => ( ( F2 @ X5 @ Y4 )
            = ( G2 @ X5 @ Y4 ) ) )
     => ( ( P = Q2 )
       => ( ( produc5460679229782211283_a_b_b @ F2 @ P )
          = ( produc5460679229782211283_a_b_b @ G2 @ Q2 ) ) ) ) ).

% split_cong
thf(fact_297_split__cong,axiom,
    ! [Q2: produc4558475209616630778_a_b_b,F2: dtree_a_b > b > $o,G2: dtree_a_b > b > $o,P: produc4558475209616630778_a_b_b] :
      ( ! [X5: dtree_a_b,Y4: b] :
          ( ( ( produc331601717337510060_a_b_b @ X5 @ Y4 )
            = Q2 )
         => ( ( F2 @ X5 @ Y4 )
            = ( G2 @ X5 @ Y4 ) ) )
     => ( ( P = Q2 )
       => ( ( produc1325217093046185599_b_b_o @ F2 @ P )
          = ( produc1325217093046185599_b_b_o @ G2 @ Q2 ) ) ) ) ).

% split_cong
thf(fact_298_apsnd__compose,axiom,
    ! [F2: b > b,G2: b > b,X3: produc4558475209616630778_a_b_b] :
      ( ( produc7811666328248579896ee_a_b @ F2 @ ( produc7811666328248579896ee_a_b @ G2 @ X3 ) )
      = ( produc7811666328248579896ee_a_b @ ( comp_b_b_b @ F2 @ G2 ) @ X3 ) ) ).

% apsnd_compose
thf(fact_299_image__eqI,axiom,
    ! [B: produc4558475209616630778_a_b_b,F2: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,X3: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( ( member4380921116106875537_a_b_b @ X3 @ A5 )
       => ( member4380921116106875537_a_b_b @ B @ ( image_6081965176830705659_a_b_b @ F2 @ A5 ) ) ) ) ).

% image_eqI
thf(fact_300_image__eqI,axiom,
    ! [B: nat,F2: nat > nat,X3: nat,A5: set_nat] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( ( member_nat @ X3 @ A5 )
       => ( member_nat @ B @ ( image_nat_nat @ F2 @ A5 ) ) ) ) ).

% image_eqI
thf(fact_301_image__eqI,axiom,
    ! [B: b,F2: nat > b,X3: nat,A5: set_nat] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( ( member_nat @ X3 @ A5 )
       => ( member_b @ B @ ( image_nat_b @ F2 @ A5 ) ) ) ) ).

% image_eqI
thf(fact_302_image__eqI,axiom,
    ! [B: a,F2: nat > a,X3: nat,A5: set_nat] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( ( member_nat @ X3 @ A5 )
       => ( member_a @ B @ ( image_nat_a @ F2 @ A5 ) ) ) ) ).

% image_eqI
thf(fact_303_image__eqI,axiom,
    ! [B: nat,F2: b > nat,X3: b,A5: set_b] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( ( member_b @ X3 @ A5 )
       => ( member_nat @ B @ ( image_b_nat @ F2 @ A5 ) ) ) ) ).

% image_eqI
thf(fact_304_image__eqI,axiom,
    ! [B: b,F2: b > b,X3: b,A5: set_b] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( ( member_b @ X3 @ A5 )
       => ( member_b @ B @ ( image_b_b @ F2 @ A5 ) ) ) ) ).

% image_eqI
thf(fact_305_image__eqI,axiom,
    ! [B: a,F2: b > a,X3: b,A5: set_b] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( ( member_b @ X3 @ A5 )
       => ( member_a @ B @ ( image_b_a @ F2 @ A5 ) ) ) ) ).

% image_eqI
thf(fact_306_image__eqI,axiom,
    ! [B: nat,F2: a > nat,X3: a,A5: set_a] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( ( member_a @ X3 @ A5 )
       => ( member_nat @ B @ ( image_a_nat @ F2 @ A5 ) ) ) ) ).

% image_eqI
thf(fact_307_image__eqI,axiom,
    ! [B: b,F2: a > b,X3: a,A5: set_a] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( ( member_a @ X3 @ A5 )
       => ( member_b @ B @ ( image_a_b @ F2 @ A5 ) ) ) ) ).

% image_eqI
thf(fact_308_image__eqI,axiom,
    ! [B: a,F2: a > a,X3: a,A5: set_a] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( ( member_a @ X3 @ A5 )
       => ( member_a @ B @ ( image_a_a @ F2 @ A5 ) ) ) ) ).

% image_eqI
thf(fact_309_bot__apply,axiom,
    ( bot_bo7321339186913516097_b_b_o
    = ( ^ [X: produc4558475209616630778_a_b_b] : bot_bot_o ) ) ).

% bot_apply
thf(fact_310_Inf_OINF__image,axiom,
    ! [Inf: set_b_a > b > a,G2: ( b > a ) > b > a,F2: ( b > a ) > b > a,A5: set_b_a] :
      ( ( Inf @ ( image_b_a_b_a @ G2 @ ( image_b_a_b_a @ F2 @ A5 ) ) )
      = ( Inf @ ( image_b_a_b_a @ ( comp_b_a_b_a_b_a @ G2 @ F2 ) @ A5 ) ) ) ).

% Inf.INF_image
thf(fact_311_Inf_OINF__image,axiom,
    ! [Inf: set_b > b,G2: b > b,F2: b > b,A5: set_b] :
      ( ( Inf @ ( image_b_b @ G2 @ ( image_b_b @ F2 @ A5 ) ) )
      = ( Inf @ ( image_b_b @ ( comp_b_b_b @ G2 @ F2 ) @ A5 ) ) ) ).

% Inf.INF_image
thf(fact_312_Inf_OINF__image,axiom,
    ! [Inf: set_a > a,G2: a > a,F2: a > a,A5: set_a] :
      ( ( Inf @ ( image_a_a @ G2 @ ( image_a_a @ F2 @ A5 ) ) )
      = ( Inf @ ( image_a_a @ ( comp_a_a_a @ G2 @ F2 ) @ A5 ) ) ) ).

% Inf.INF_image
thf(fact_313_Inf_OINF__image,axiom,
    ! [Inf: set_b > b,G2: dtree_a_b > b,F2: produc4558475209616630778_a_b_b > dtree_a_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( Inf @ ( image_dtree_a_b_b @ G2 @ ( image_7065894828672115579ee_a_b @ F2 @ A5 ) ) )
      = ( Inf @ ( image_3908709015779211070_b_b_b @ ( comp_d7292648224603294300_a_b_b @ G2 @ F2 ) @ A5 ) ) ) ).

% Inf.INF_image
thf(fact_314_Inf_OINF__image,axiom,
    ! [Inf: set_dtree_a_b > dtree_a_b,G2: dtree_a_b > dtree_a_b,F2: produc4558475209616630778_a_b_b > dtree_a_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( Inf @ ( image_1160270813240538107ee_a_b @ G2 @ ( image_7065894828672115579ee_a_b @ F2 @ A5 ) ) )
      = ( Inf @ ( image_7065894828672115579ee_a_b @ ( comp_d9193377603055859667_a_b_b @ G2 @ F2 ) @ A5 ) ) ) ).

% Inf.INF_image
thf(fact_315_Inf_OINF__image,axiom,
    ! [Inf: set_dtree_a_b > dtree_a_b,G2: produc3469756349985706280ee_a_b > dtree_a_b,F2: produc4558475209616630778_a_b_b > produc3469756349985706280ee_a_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( Inf @ ( image_6364595536291967657ee_a_b @ G2 @ ( image_4993246317199781161ee_a_b @ F2 @ A5 ) ) )
      = ( Inf @ ( image_7065894828672115579ee_a_b @ ( comp_P5693690220181566849_a_b_b @ G2 @ F2 ) @ A5 ) ) ) ).

% Inf.INF_image
thf(fact_316_Inf_OINF__image,axiom,
    ! [Inf: set_Pr6717515126349854430ee_a_b > produc3469756349985706280ee_a_b,G2: dtree_a_b > produc3469756349985706280ee_a_b,F2: produc4558475209616630778_a_b_b > dtree_a_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( Inf @ ( image_8495257627889188265ee_a_b @ G2 @ ( image_7065894828672115579ee_a_b @ F2 @ A5 ) ) )
      = ( Inf @ ( image_4993246317199781161ee_a_b @ ( comp_d4253798619470020737_a_b_b @ G2 @ F2 ) @ A5 ) ) ) ).

% Inf.INF_image
thf(fact_317_Inf_OINF__image,axiom,
    ! [Inf: set_Pr5619283252532241417_a_b_a > product_prod_b_a_b_a,G2: ( b > a ) > product_prod_b_a_b_a,F2: ( b > a ) > b > a,A5: set_b_a] :
      ( ( Inf @ ( image_3865962054164325950_a_b_a @ G2 @ ( image_b_a_b_a @ F2 @ A5 ) ) )
      = ( Inf @ ( image_3865962054164325950_a_b_a @ ( comp_b7652884982158753286_a_b_a @ G2 @ F2 ) @ A5 ) ) ) ).

% Inf.INF_image
thf(fact_318_Inf_OINF__image,axiom,
    ! [Inf: set_dtree_a_b > dtree_a_b,G2: produc4558475209616630778_a_b_b > dtree_a_b,F2: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( Inf @ ( image_7065894828672115579ee_a_b @ G2 @ ( image_6081965176830705659_a_b_b @ F2 @ A5 ) ) )
      = ( Inf @ ( image_7065894828672115579ee_a_b @ ( comp_P2227990766219928147_a_b_b @ G2 @ F2 ) @ A5 ) ) ) ).

% Inf.INF_image
thf(fact_319_Inf_OINF__image,axiom,
    ! [Inf: set_dtree_a_b > dtree_a_b,G2: produc4558475209616630778_a_b_b > dtree_a_b,F2: produc3469756349985706280ee_a_b > produc4558475209616630778_a_b_b,A5: set_Pr6717515126349854430ee_a_b] :
      ( ( Inf @ ( image_7065894828672115579ee_a_b @ G2 @ ( image_3585698774939316521_a_b_b @ F2 @ A5 ) ) )
      = ( Inf @ ( image_6364595536291967657ee_a_b @ ( comp_P1139271906589003649ee_a_b @ G2 @ F2 ) @ A5 ) ) ) ).

% Inf.INF_image
thf(fact_320_Sup_OSUP__image,axiom,
    ! [Sup: set_b_a > b > a,G2: ( b > a ) > b > a,F2: ( b > a ) > b > a,A5: set_b_a] :
      ( ( Sup @ ( image_b_a_b_a @ G2 @ ( image_b_a_b_a @ F2 @ A5 ) ) )
      = ( Sup @ ( image_b_a_b_a @ ( comp_b_a_b_a_b_a @ G2 @ F2 ) @ A5 ) ) ) ).

% Sup.SUP_image
thf(fact_321_Sup_OSUP__image,axiom,
    ! [Sup: set_b > b,G2: b > b,F2: b > b,A5: set_b] :
      ( ( Sup @ ( image_b_b @ G2 @ ( image_b_b @ F2 @ A5 ) ) )
      = ( Sup @ ( image_b_b @ ( comp_b_b_b @ G2 @ F2 ) @ A5 ) ) ) ).

% Sup.SUP_image
thf(fact_322_Sup_OSUP__image,axiom,
    ! [Sup: set_a > a,G2: a > a,F2: a > a,A5: set_a] :
      ( ( Sup @ ( image_a_a @ G2 @ ( image_a_a @ F2 @ A5 ) ) )
      = ( Sup @ ( image_a_a @ ( comp_a_a_a @ G2 @ F2 ) @ A5 ) ) ) ).

% Sup.SUP_image
thf(fact_323_Sup_OSUP__image,axiom,
    ! [Sup: set_b > b,G2: dtree_a_b > b,F2: produc4558475209616630778_a_b_b > dtree_a_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( Sup @ ( image_dtree_a_b_b @ G2 @ ( image_7065894828672115579ee_a_b @ F2 @ A5 ) ) )
      = ( Sup @ ( image_3908709015779211070_b_b_b @ ( comp_d7292648224603294300_a_b_b @ G2 @ F2 ) @ A5 ) ) ) ).

% Sup.SUP_image
thf(fact_324_Sup_OSUP__image,axiom,
    ! [Sup: set_dtree_a_b > dtree_a_b,G2: dtree_a_b > dtree_a_b,F2: produc4558475209616630778_a_b_b > dtree_a_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( Sup @ ( image_1160270813240538107ee_a_b @ G2 @ ( image_7065894828672115579ee_a_b @ F2 @ A5 ) ) )
      = ( Sup @ ( image_7065894828672115579ee_a_b @ ( comp_d9193377603055859667_a_b_b @ G2 @ F2 ) @ A5 ) ) ) ).

% Sup.SUP_image
thf(fact_325_Sup_OSUP__image,axiom,
    ! [Sup: set_dtree_a_b > dtree_a_b,G2: produc3469756349985706280ee_a_b > dtree_a_b,F2: produc4558475209616630778_a_b_b > produc3469756349985706280ee_a_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( Sup @ ( image_6364595536291967657ee_a_b @ G2 @ ( image_4993246317199781161ee_a_b @ F2 @ A5 ) ) )
      = ( Sup @ ( image_7065894828672115579ee_a_b @ ( comp_P5693690220181566849_a_b_b @ G2 @ F2 ) @ A5 ) ) ) ).

% Sup.SUP_image
thf(fact_326_Sup_OSUP__image,axiom,
    ! [Sup: set_Pr6717515126349854430ee_a_b > produc3469756349985706280ee_a_b,G2: dtree_a_b > produc3469756349985706280ee_a_b,F2: produc4558475209616630778_a_b_b > dtree_a_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( Sup @ ( image_8495257627889188265ee_a_b @ G2 @ ( image_7065894828672115579ee_a_b @ F2 @ A5 ) ) )
      = ( Sup @ ( image_4993246317199781161ee_a_b @ ( comp_d4253798619470020737_a_b_b @ G2 @ F2 ) @ A5 ) ) ) ).

% Sup.SUP_image
thf(fact_327_Sup_OSUP__image,axiom,
    ! [Sup: set_Pr5619283252532241417_a_b_a > product_prod_b_a_b_a,G2: ( b > a ) > product_prod_b_a_b_a,F2: ( b > a ) > b > a,A5: set_b_a] :
      ( ( Sup @ ( image_3865962054164325950_a_b_a @ G2 @ ( image_b_a_b_a @ F2 @ A5 ) ) )
      = ( Sup @ ( image_3865962054164325950_a_b_a @ ( comp_b7652884982158753286_a_b_a @ G2 @ F2 ) @ A5 ) ) ) ).

% Sup.SUP_image
thf(fact_328_Sup_OSUP__image,axiom,
    ! [Sup: set_dtree_a_b > dtree_a_b,G2: produc4558475209616630778_a_b_b > dtree_a_b,F2: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( Sup @ ( image_7065894828672115579ee_a_b @ G2 @ ( image_6081965176830705659_a_b_b @ F2 @ A5 ) ) )
      = ( Sup @ ( image_7065894828672115579ee_a_b @ ( comp_P2227990766219928147_a_b_b @ G2 @ F2 ) @ A5 ) ) ) ).

% Sup.SUP_image
thf(fact_329_Sup_OSUP__image,axiom,
    ! [Sup: set_dtree_a_b > dtree_a_b,G2: produc4558475209616630778_a_b_b > dtree_a_b,F2: produc3469756349985706280ee_a_b > produc4558475209616630778_a_b_b,A5: set_Pr6717515126349854430ee_a_b] :
      ( ( Sup @ ( image_7065894828672115579ee_a_b @ G2 @ ( image_3585698774939316521_a_b_b @ F2 @ A5 ) ) )
      = ( Sup @ ( image_6364595536291967657ee_a_b @ ( comp_P1139271906589003649ee_a_b @ G2 @ F2 ) @ A5 ) ) ) ).

% Sup.SUP_image
thf(fact_330_in__rel__Collect__case__prod__eq,axiom,
    ! [X6: dtree_a_b > b > $o] :
      ( ( fun_in7817583439641278657_a_b_b @ ( collec1368399972772960719_a_b_b @ ( produc1325217093046185599_b_b_o @ X6 ) ) )
      = X6 ) ).

% in_rel_Collect_case_prod_eq
thf(fact_331_disjoint__darcs__if__wf__aux1,axiom,
    ! [R: a,Xs2: fset_P5281107635120001194_a_b_b,T1: dtree_a_b,E1: b] :
      ( ( wf_darcs_a_b @ ( node_a_b @ R @ Xs2 ) )
     => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ T1 @ E1 ) @ ( fset_P783253628892185035_a_b_b @ Xs2 ) )
       => ~ ( member_b @ E1 @ ( darcs_a_b @ T1 ) ) ) ) ).

% disjoint_darcs_if_wf_aux1
thf(fact_332_disjoint__darcs__if__wf__aux3,axiom,
    ! [R: a,Xs2: fset_P5281107635120001194_a_b_b,T1: dtree_a_b,E1: b,T2: dtree_a_b,E2: b] :
      ( ( wf_darcs_a_b @ ( node_a_b @ R @ Xs2 ) )
     => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ T1 @ E1 ) @ ( fset_P783253628892185035_a_b_b @ Xs2 ) )
       => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ T2 @ E2 ) @ ( fset_P783253628892185035_a_b_b @ Xs2 ) )
         => ~ ( member_b @ E2 @ ( darcs_a_b @ T1 ) ) ) ) ) ).

% disjoint_darcs_if_wf_aux3
thf(fact_333_surj__swap,axiom,
    ( ( image_4993246317199781161ee_a_b @ produc2906148145665870604_a_b_b @ top_to7222684678772277088_a_b_b )
    = top_to1704407628658980238ee_a_b ) ).

% surj_swap
thf(fact_334_surj__swap,axiom,
    ( ( image_3585698774939316521_a_b_b @ produc6117232556371446914ee_a_b @ top_to1704407628658980238ee_a_b )
    = top_to7222684678772277088_a_b_b ) ).

% surj_swap
thf(fact_335_dtree_Oset__cases_I1_J,axiom,
    ! [E: a,A: dtree_a_b] :
      ( ( member_a @ E @ ( dverts_a_b @ A ) )
     => ( ! [Z2: fset_P5281107635120001194_a_b_b] :
            ( A
           != ( node_a_b @ E @ Z2 ) )
       => ~ ! [Z1: a,Z2: fset_P5281107635120001194_a_b_b] :
              ( ( A
                = ( node_a_b @ Z1 @ Z2 ) )
             => ! [X5: produc4558475209616630778_a_b_b] :
                  ( ( member4380921116106875537_a_b_b @ X5 @ ( fset_P783253628892185035_a_b_b @ Z2 ) )
                 => ! [Xa: dtree_a_b] :
                      ( ( member_dtree_a_b @ Xa @ ( basic_7578771248400840636_a_b_b @ X5 ) )
                     => ~ ( member_a @ E @ ( dverts_a_b @ Xa ) ) ) ) ) ) ) ).

% dtree.set_cases(1)
thf(fact_336_dtree_Oset__intros_I2_J,axiom,
    ! [Y3: produc4558475209616630778_a_b_b,X22: fset_P5281107635120001194_a_b_b,Ya: dtree_a_b,Yb: a,X12: a] :
      ( ( member4380921116106875537_a_b_b @ Y3 @ ( fset_P783253628892185035_a_b_b @ X22 ) )
     => ( ( member_dtree_a_b @ Ya @ ( basic_7578771248400840636_a_b_b @ Y3 ) )
       => ( ( member_a @ Yb @ ( dverts_a_b @ Ya ) )
         => ( member_a @ Yb @ ( dverts_a_b @ ( node_a_b @ X12 @ X22 ) ) ) ) ) ) ).

% dtree.set_intros(2)
thf(fact_337_top__apply,axiom,
    ( top_to2465898995584390880unit_o
    = ( ^ [X: product_unit] : top_top_o ) ) ).

% top_apply
thf(fact_338_top__apply,axiom,
    ( top_to762646584048855333_b_b_o
    = ( ^ [X: produc4558475209616630778_a_b_b] : top_top_o ) ) ).

% top_apply
thf(fact_339_UNIV__I,axiom,
    ! [X3: set_Pr3012420139608375472_a_b_b] : ( member7431159781899395911_a_b_b @ X3 @ top_to1846739022409413910_a_b_b ) ).

% UNIV_I
thf(fact_340_UNIV__I,axiom,
    ! [X3: nat] : ( member_nat @ X3 @ top_top_set_nat ) ).

% UNIV_I
thf(fact_341_UNIV__I,axiom,
    ! [X3: b] : ( member_b @ X3 @ top_top_set_b ) ).

% UNIV_I
thf(fact_342_UNIV__I,axiom,
    ! [X3: a] : ( member_a @ X3 @ top_top_set_a ) ).

% UNIV_I
thf(fact_343_UNIV__I,axiom,
    ! [X3: sum_su8719719018421925477t_unit] : ( member1483886641279141628t_unit @ X3 @ top_to2771918933716375115t_unit ) ).

% UNIV_I
thf(fact_344_UNIV__I,axiom,
    ! [X3: set_Product_unit] : ( member5877623283571906838t_unit @ X3 @ top_to1767297665138865437t_unit ) ).

% UNIV_I
thf(fact_345_UNIV__I,axiom,
    ! [X3: b > a] : ( member_b_a @ X3 @ top_top_set_b_a ) ).

% UNIV_I
thf(fact_346_UNIV__I,axiom,
    ! [X3: produc4558475209616630778_a_b_b] : ( member4380921116106875537_a_b_b @ X3 @ top_to7222684678772277088_a_b_b ) ).

% UNIV_I
thf(fact_347_UNIV__I,axiom,
    ! [X3: product_unit] : ( member_Product_unit @ X3 @ top_to1996260823553986621t_unit ) ).

% UNIV_I
thf(fact_348_image__empty,axiom,
    ! [F2: nat > nat] :
      ( ( image_nat_nat @ F2 @ bot_bot_set_nat )
      = bot_bot_set_nat ) ).

% image_empty
thf(fact_349_image__empty,axiom,
    ! [F2: nat > b] :
      ( ( image_nat_b @ F2 @ bot_bot_set_nat )
      = bot_bot_set_b ) ).

% image_empty
thf(fact_350_image__empty,axiom,
    ! [F2: nat > a] :
      ( ( image_nat_a @ F2 @ bot_bot_set_nat )
      = bot_bot_set_a ) ).

% image_empty
thf(fact_351_image__empty,axiom,
    ! [F2: b > nat] :
      ( ( image_b_nat @ F2 @ bot_bot_set_b )
      = bot_bot_set_nat ) ).

% image_empty
thf(fact_352_image__empty,axiom,
    ! [F2: b > b] :
      ( ( image_b_b @ F2 @ bot_bot_set_b )
      = bot_bot_set_b ) ).

% image_empty
thf(fact_353_image__empty,axiom,
    ! [F2: b > a] :
      ( ( image_b_a @ F2 @ bot_bot_set_b )
      = bot_bot_set_a ) ).

% image_empty
thf(fact_354_image__empty,axiom,
    ! [F2: a > nat] :
      ( ( image_a_nat @ F2 @ bot_bot_set_a )
      = bot_bot_set_nat ) ).

% image_empty
thf(fact_355_image__empty,axiom,
    ! [F2: a > b] :
      ( ( image_a_b @ F2 @ bot_bot_set_a )
      = bot_bot_set_b ) ).

% image_empty
thf(fact_356_image__empty,axiom,
    ! [F2: a > a] :
      ( ( image_a_a @ F2 @ bot_bot_set_a )
      = bot_bot_set_a ) ).

% image_empty
thf(fact_357_image__empty,axiom,
    ! [F2: ( b > a ) > b > a] :
      ( ( image_b_a_b_a @ F2 @ bot_bot_set_b_a )
      = bot_bot_set_b_a ) ).

% image_empty
thf(fact_358_empty__is__image,axiom,
    ! [F2: nat > nat,A5: set_nat] :
      ( ( bot_bot_set_nat
        = ( image_nat_nat @ F2 @ A5 ) )
      = ( A5 = bot_bot_set_nat ) ) ).

% empty_is_image
thf(fact_359_empty__is__image,axiom,
    ! [F2: b > nat,A5: set_b] :
      ( ( bot_bot_set_nat
        = ( image_b_nat @ F2 @ A5 ) )
      = ( A5 = bot_bot_set_b ) ) ).

% empty_is_image
thf(fact_360_empty__is__image,axiom,
    ! [F2: a > nat,A5: set_a] :
      ( ( bot_bot_set_nat
        = ( image_a_nat @ F2 @ A5 ) )
      = ( A5 = bot_bot_set_a ) ) ).

% empty_is_image
thf(fact_361_empty__is__image,axiom,
    ! [F2: nat > b,A5: set_nat] :
      ( ( bot_bot_set_b
        = ( image_nat_b @ F2 @ A5 ) )
      = ( A5 = bot_bot_set_nat ) ) ).

% empty_is_image
thf(fact_362_empty__is__image,axiom,
    ! [F2: b > b,A5: set_b] :
      ( ( bot_bot_set_b
        = ( image_b_b @ F2 @ A5 ) )
      = ( A5 = bot_bot_set_b ) ) ).

% empty_is_image
thf(fact_363_empty__is__image,axiom,
    ! [F2: a > b,A5: set_a] :
      ( ( bot_bot_set_b
        = ( image_a_b @ F2 @ A5 ) )
      = ( A5 = bot_bot_set_a ) ) ).

% empty_is_image
thf(fact_364_empty__is__image,axiom,
    ! [F2: nat > a,A5: set_nat] :
      ( ( bot_bot_set_a
        = ( image_nat_a @ F2 @ A5 ) )
      = ( A5 = bot_bot_set_nat ) ) ).

% empty_is_image
thf(fact_365_empty__is__image,axiom,
    ! [F2: b > a,A5: set_b] :
      ( ( bot_bot_set_a
        = ( image_b_a @ F2 @ A5 ) )
      = ( A5 = bot_bot_set_b ) ) ).

% empty_is_image
thf(fact_366_empty__is__image,axiom,
    ! [F2: a > a,A5: set_a] :
      ( ( bot_bot_set_a
        = ( image_a_a @ F2 @ A5 ) )
      = ( A5 = bot_bot_set_a ) ) ).

% empty_is_image
thf(fact_367_empty__is__image,axiom,
    ! [F2: ( b > a ) > b > a,A5: set_b_a] :
      ( ( bot_bot_set_b_a
        = ( image_b_a_b_a @ F2 @ A5 ) )
      = ( A5 = bot_bot_set_b_a ) ) ).

% empty_is_image
thf(fact_368_image__is__empty,axiom,
    ! [F2: nat > nat,A5: set_nat] :
      ( ( ( image_nat_nat @ F2 @ A5 )
        = bot_bot_set_nat )
      = ( A5 = bot_bot_set_nat ) ) ).

% image_is_empty
thf(fact_369_image__is__empty,axiom,
    ! [F2: b > nat,A5: set_b] :
      ( ( ( image_b_nat @ F2 @ A5 )
        = bot_bot_set_nat )
      = ( A5 = bot_bot_set_b ) ) ).

% image_is_empty
thf(fact_370_image__is__empty,axiom,
    ! [F2: a > nat,A5: set_a] :
      ( ( ( image_a_nat @ F2 @ A5 )
        = bot_bot_set_nat )
      = ( A5 = bot_bot_set_a ) ) ).

% image_is_empty
thf(fact_371_image__is__empty,axiom,
    ! [F2: nat > b,A5: set_nat] :
      ( ( ( image_nat_b @ F2 @ A5 )
        = bot_bot_set_b )
      = ( A5 = bot_bot_set_nat ) ) ).

% image_is_empty
thf(fact_372_image__is__empty,axiom,
    ! [F2: b > b,A5: set_b] :
      ( ( ( image_b_b @ F2 @ A5 )
        = bot_bot_set_b )
      = ( A5 = bot_bot_set_b ) ) ).

% image_is_empty
thf(fact_373_image__is__empty,axiom,
    ! [F2: a > b,A5: set_a] :
      ( ( ( image_a_b @ F2 @ A5 )
        = bot_bot_set_b )
      = ( A5 = bot_bot_set_a ) ) ).

% image_is_empty
thf(fact_374_image__is__empty,axiom,
    ! [F2: nat > a,A5: set_nat] :
      ( ( ( image_nat_a @ F2 @ A5 )
        = bot_bot_set_a )
      = ( A5 = bot_bot_set_nat ) ) ).

% image_is_empty
thf(fact_375_image__is__empty,axiom,
    ! [F2: b > a,A5: set_b] :
      ( ( ( image_b_a @ F2 @ A5 )
        = bot_bot_set_a )
      = ( A5 = bot_bot_set_b ) ) ).

% image_is_empty
thf(fact_376_image__is__empty,axiom,
    ! [F2: a > a,A5: set_a] :
      ( ( ( image_a_a @ F2 @ A5 )
        = bot_bot_set_a )
      = ( A5 = bot_bot_set_a ) ) ).

% image_is_empty
thf(fact_377_image__is__empty,axiom,
    ! [F2: ( b > a ) > b > a,A5: set_b_a] :
      ( ( ( image_b_a_b_a @ F2 @ A5 )
        = bot_bot_set_b_a )
      = ( A5 = bot_bot_set_b_a ) ) ).

% image_is_empty
thf(fact_378_bot__fset_Orep__eq,axiom,
    ( ( fset_Product_unit2 @ bot_bo7418305276487734239t_unit )
    = bot_bo3957492148770167129t_unit ) ).

% bot_fset.rep_eq
thf(fact_379_bot__fset_Orep__eq,axiom,
    ( ( fset_nat2 @ bot_bot_fset_nat )
    = bot_bot_set_nat ) ).

% bot_fset.rep_eq
thf(fact_380_bot__fset_Orep__eq,axiom,
    ( ( fset_b2 @ bot_bot_fset_b )
    = bot_bot_set_b ) ).

% bot_fset.rep_eq
thf(fact_381_bot__fset_Orep__eq,axiom,
    ( ( fset_a2 @ bot_bot_fset_a )
    = bot_bot_set_a ) ).

% bot_fset.rep_eq
thf(fact_382_bot__fset_Orep__eq,axiom,
    ( ( fset_P783253628892185035_a_b_b @ bot_bo2895716411488905534_a_b_b )
    = bot_bo3721250822024684356_a_b_b ) ).

% bot_fset.rep_eq
thf(fact_383_empty__not__UNIV,axiom,
    bot_bot_set_nat != top_top_set_nat ).

% empty_not_UNIV
thf(fact_384_empty__not__UNIV,axiom,
    bot_bot_set_b != top_top_set_b ).

% empty_not_UNIV
thf(fact_385_empty__not__UNIV,axiom,
    bot_bot_set_a != top_top_set_a ).

% empty_not_UNIV
thf(fact_386_empty__not__UNIV,axiom,
    bot_bo3448499826546176559t_unit != top_to2771918933716375115t_unit ).

% empty_not_UNIV
thf(fact_387_empty__not__UNIV,axiom,
    bot_bo6284674557190688313t_unit != top_to1767297665138865437t_unit ).

% empty_not_UNIV
thf(fact_388_empty__not__UNIV,axiom,
    bot_bot_set_b_a != top_top_set_b_a ).

% empty_not_UNIV
thf(fact_389_empty__not__UNIV,axiom,
    bot_bo3957492148770167129t_unit != top_to1996260823553986621t_unit ).

% empty_not_UNIV
thf(fact_390_UNIV__eq__I,axiom,
    ! [A5: set_se3183138701204633190_a_b_b] :
      ( ! [X5: set_Pr3012420139608375472_a_b_b] : ( member7431159781899395911_a_b_b @ X5 @ A5 )
     => ( top_to1846739022409413910_a_b_b = A5 ) ) ).

% UNIV_eq_I
thf(fact_391_UNIV__eq__I,axiom,
    ! [A5: set_nat] :
      ( ! [X5: nat] : ( member_nat @ X5 @ A5 )
     => ( top_top_set_nat = A5 ) ) ).

% UNIV_eq_I
thf(fact_392_UNIV__eq__I,axiom,
    ! [A5: set_b] :
      ( ! [X5: b] : ( member_b @ X5 @ A5 )
     => ( top_top_set_b = A5 ) ) ).

% UNIV_eq_I
thf(fact_393_UNIV__eq__I,axiom,
    ! [A5: set_a] :
      ( ! [X5: a] : ( member_a @ X5 @ A5 )
     => ( top_top_set_a = A5 ) ) ).

% UNIV_eq_I
thf(fact_394_UNIV__eq__I,axiom,
    ! [A5: set_Su4110612849109743515t_unit] :
      ( ! [X5: sum_su8719719018421925477t_unit] : ( member1483886641279141628t_unit @ X5 @ A5 )
     => ( top_to2771918933716375115t_unit = A5 ) ) ).

% UNIV_eq_I
thf(fact_395_UNIV__eq__I,axiom,
    ! [A5: set_set_Product_unit] :
      ( ! [X5: set_Product_unit] : ( member5877623283571906838t_unit @ X5 @ A5 )
     => ( top_to1767297665138865437t_unit = A5 ) ) ).

% UNIV_eq_I
thf(fact_396_UNIV__eq__I,axiom,
    ! [A5: set_b_a] :
      ( ! [X5: b > a] : ( member_b_a @ X5 @ A5 )
     => ( top_top_set_b_a = A5 ) ) ).

% UNIV_eq_I
thf(fact_397_UNIV__eq__I,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b] :
      ( ! [X5: produc4558475209616630778_a_b_b] : ( member4380921116106875537_a_b_b @ X5 @ A5 )
     => ( top_to7222684678772277088_a_b_b = A5 ) ) ).

% UNIV_eq_I
thf(fact_398_UNIV__eq__I,axiom,
    ! [A5: set_Product_unit] :
      ( ! [X5: product_unit] : ( member_Product_unit @ X5 @ A5 )
     => ( top_to1996260823553986621t_unit = A5 ) ) ).

% UNIV_eq_I
thf(fact_399_UNIV__witness,axiom,
    ? [X5: set_Pr3012420139608375472_a_b_b] : ( member7431159781899395911_a_b_b @ X5 @ top_to1846739022409413910_a_b_b ) ).

% UNIV_witness
thf(fact_400_UNIV__witness,axiom,
    ? [X5: nat] : ( member_nat @ X5 @ top_top_set_nat ) ).

% UNIV_witness
thf(fact_401_UNIV__witness,axiom,
    ? [X5: b] : ( member_b @ X5 @ top_top_set_b ) ).

% UNIV_witness
thf(fact_402_UNIV__witness,axiom,
    ? [X5: a] : ( member_a @ X5 @ top_top_set_a ) ).

% UNIV_witness
thf(fact_403_UNIV__witness,axiom,
    ? [X5: sum_su8719719018421925477t_unit] : ( member1483886641279141628t_unit @ X5 @ top_to2771918933716375115t_unit ) ).

% UNIV_witness
thf(fact_404_UNIV__witness,axiom,
    ? [X5: set_Product_unit] : ( member5877623283571906838t_unit @ X5 @ top_to1767297665138865437t_unit ) ).

% UNIV_witness
thf(fact_405_UNIV__witness,axiom,
    ? [X5: b > a] : ( member_b_a @ X5 @ top_top_set_b_a ) ).

% UNIV_witness
thf(fact_406_UNIV__witness,axiom,
    ? [X5: produc4558475209616630778_a_b_b] : ( member4380921116106875537_a_b_b @ X5 @ top_to7222684678772277088_a_b_b ) ).

% UNIV_witness
thf(fact_407_UNIV__witness,axiom,
    ? [X5: product_unit] : ( member_Product_unit @ X5 @ top_to1996260823553986621t_unit ) ).

% UNIV_witness
thf(fact_408_rangeI,axiom,
    ! [F2: product_unit > produc4558475209616630778_a_b_b,X3: product_unit] : ( member4380921116106875537_a_b_b @ ( F2 @ X3 ) @ ( image_2521969012719430850_a_b_b @ F2 @ top_to1996260823553986621t_unit ) ) ).

% rangeI
thf(fact_409_rangeI,axiom,
    ! [F2: product_unit > nat,X3: product_unit] : ( member_nat @ ( F2 @ X3 ) @ ( image_875570014554754200it_nat @ F2 @ top_to1996260823553986621t_unit ) ) ).

% rangeI
thf(fact_410_rangeI,axiom,
    ! [F2: product_unit > b,X3: product_unit] : ( member_b @ ( F2 @ X3 ) @ ( image_Product_unit_b @ F2 @ top_to1996260823553986621t_unit ) ) ).

% rangeI
thf(fact_411_rangeI,axiom,
    ! [F2: product_unit > a,X3: product_unit] : ( member_a @ ( F2 @ X3 ) @ ( image_Product_unit_a @ F2 @ top_to1996260823553986621t_unit ) ) ).

% rangeI
thf(fact_412_rangeI,axiom,
    ! [F2: set_Product_unit > nat,X3: set_Product_unit] : ( member_nat @ ( F2 @ X3 ) @ ( image_4084087346006658424it_nat @ F2 @ top_to1767297665138865437t_unit ) ) ).

% rangeI
thf(fact_413_rangeI,axiom,
    ! [F2: set_Product_unit > b,X3: set_Product_unit] : ( member_b @ ( F2 @ X3 ) @ ( image_7680679895738368855unit_b @ F2 @ top_to1767297665138865437t_unit ) ) ).

% rangeI
thf(fact_414_rangeI,axiom,
    ! [F2: set_Product_unit > a,X3: set_Product_unit] : ( member_a @ ( F2 @ X3 ) @ ( image_7680679895738368854unit_a @ F2 @ top_to1767297665138865437t_unit ) ) ).

% rangeI
thf(fact_415_rangeI,axiom,
    ! [F2: product_unit > b > a,X3: product_unit] : ( member_b_a @ ( F2 @ X3 ) @ ( image_3413377689041543532it_b_a @ F2 @ top_to1996260823553986621t_unit ) ) ).

% rangeI
thf(fact_416_rangeI,axiom,
    ! [F2: sum_su8719719018421925477t_unit > nat,X3: sum_su8719719018421925477t_unit] : ( member_nat @ ( F2 @ X3 ) @ ( image_7724955480610936892it_nat @ F2 @ top_to2771918933716375115t_unit ) ) ).

% rangeI
thf(fact_417_rangeI,axiom,
    ! [F2: sum_su8719719018421925477t_unit > b,X3: sum_su8719719018421925477t_unit] : ( member_b @ ( F2 @ X3 ) @ ( image_7415979216236306835unit_b @ F2 @ top_to2771918933716375115t_unit ) ) ).

% rangeI
thf(fact_418_range__eqI,axiom,
    ! [B: produc4558475209616630778_a_b_b,F2: product_unit > produc4558475209616630778_a_b_b,X3: product_unit] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( member4380921116106875537_a_b_b @ B @ ( image_2521969012719430850_a_b_b @ F2 @ top_to1996260823553986621t_unit ) ) ) ).

% range_eqI
thf(fact_419_range__eqI,axiom,
    ! [B: nat,F2: product_unit > nat,X3: product_unit] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( member_nat @ B @ ( image_875570014554754200it_nat @ F2 @ top_to1996260823553986621t_unit ) ) ) ).

% range_eqI
thf(fact_420_range__eqI,axiom,
    ! [B: b,F2: product_unit > b,X3: product_unit] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( member_b @ B @ ( image_Product_unit_b @ F2 @ top_to1996260823553986621t_unit ) ) ) ).

% range_eqI
thf(fact_421_range__eqI,axiom,
    ! [B: a,F2: product_unit > a,X3: product_unit] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( member_a @ B @ ( image_Product_unit_a @ F2 @ top_to1996260823553986621t_unit ) ) ) ).

% range_eqI
thf(fact_422_range__eqI,axiom,
    ! [B: nat,F2: set_Product_unit > nat,X3: set_Product_unit] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( member_nat @ B @ ( image_4084087346006658424it_nat @ F2 @ top_to1767297665138865437t_unit ) ) ) ).

% range_eqI
thf(fact_423_range__eqI,axiom,
    ! [B: b,F2: set_Product_unit > b,X3: set_Product_unit] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( member_b @ B @ ( image_7680679895738368855unit_b @ F2 @ top_to1767297665138865437t_unit ) ) ) ).

% range_eqI
thf(fact_424_range__eqI,axiom,
    ! [B: a,F2: set_Product_unit > a,X3: set_Product_unit] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( member_a @ B @ ( image_7680679895738368854unit_a @ F2 @ top_to1767297665138865437t_unit ) ) ) ).

% range_eqI
thf(fact_425_range__eqI,axiom,
    ! [B: b > a,F2: product_unit > b > a,X3: product_unit] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( member_b_a @ B @ ( image_3413377689041543532it_b_a @ F2 @ top_to1996260823553986621t_unit ) ) ) ).

% range_eqI
thf(fact_426_range__eqI,axiom,
    ! [B: nat,F2: sum_su8719719018421925477t_unit > nat,X3: sum_su8719719018421925477t_unit] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( member_nat @ B @ ( image_7724955480610936892it_nat @ F2 @ top_to2771918933716375115t_unit ) ) ) ).

% range_eqI
thf(fact_427_range__eqI,axiom,
    ! [B: b,F2: sum_su8719719018421925477t_unit > b,X3: sum_su8719719018421925477t_unit] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( member_b @ B @ ( image_7415979216236306835unit_b @ F2 @ top_to2771918933716375115t_unit ) ) ) ).

% range_eqI
thf(fact_428_dtree_Oset__intros_I1_J,axiom,
    ! [X12: a,X22: fset_P5281107635120001194_a_b_b] : ( member_a @ X12 @ ( dverts_a_b @ ( node_a_b @ X12 @ X22 ) ) ) ).

% dtree.set_intros(1)
thf(fact_429_surj__def,axiom,
    ! [F2: product_unit > product_unit] :
      ( ( ( image_405062704495631173t_unit @ F2 @ top_to1996260823553986621t_unit )
        = top_to1996260823553986621t_unit )
      = ( ! [Y: product_unit] :
          ? [X: product_unit] :
            ( Y
            = ( F2 @ X ) ) ) ) ).

% surj_def
thf(fact_430_surj__def,axiom,
    ! [F2: product_unit > set_Product_unit] :
      ( ( ( image_7778121751606633509t_unit @ F2 @ top_to1996260823553986621t_unit )
        = top_to1767297665138865437t_unit )
      = ( ! [Y: set_Product_unit] :
          ? [X: product_unit] :
            ( Y
            = ( F2 @ X ) ) ) ) ).

% surj_def
thf(fact_431_surj__def,axiom,
    ! [F2: set_Product_unit > product_unit] :
      ( ( ( image_4670244198609810021t_unit @ F2 @ top_to1767297665138865437t_unit )
        = top_to1996260823553986621t_unit )
      = ( ! [Y: product_unit] :
          ? [X: set_Product_unit] :
            ( Y
            = ( F2 @ X ) ) ) ) ).

% surj_def
thf(fact_432_surj__def,axiom,
    ! [F2: product_unit > sum_su8719719018421925477t_unit] :
      ( ( ( image_2037928093122670381t_unit @ F2 @ top_to1996260823553986621t_unit )
        = top_to2771918933716375115t_unit )
      = ( ! [Y: sum_su8719719018421925477t_unit] :
          ? [X: product_unit] :
            ( Y
            = ( F2 @ X ) ) ) ) ).

% surj_def
thf(fact_433_surj__def,axiom,
    ! [F2: product_unit > b > a] :
      ( ( ( image_3413377689041543532it_b_a @ F2 @ top_to1996260823553986621t_unit )
        = top_top_set_b_a )
      = ( ! [Y: b > a] :
          ? [X: product_unit] :
            ( Y
            = ( F2 @ X ) ) ) ) ).

% surj_def
thf(fact_434_surj__def,axiom,
    ! [F2: sum_su8719719018421925477t_unit > product_unit] :
      ( ( ( image_4850905281257956513t_unit @ F2 @ top_to2771918933716375115t_unit )
        = top_to1996260823553986621t_unit )
      = ( ! [Y: product_unit] :
          ? [X: sum_su8719719018421925477t_unit] :
            ( Y
            = ( F2 @ X ) ) ) ) ).

% surj_def
thf(fact_435_surj__def,axiom,
    ! [F2: set_Product_unit > set_Product_unit] :
      ( ( ( image_4019945301284682565t_unit @ F2 @ top_to1767297665138865437t_unit )
        = top_to1767297665138865437t_unit )
      = ( ! [Y: set_Product_unit] :
          ? [X: set_Product_unit] :
            ( Y
            = ( F2 @ X ) ) ) ) ).

% surj_def
thf(fact_436_surj__def,axiom,
    ! [F2: ( b > a ) > product_unit] :
      ( ( ( image_2179813402173241122t_unit @ F2 @ top_top_set_b_a )
        = top_to1996260823553986621t_unit )
      = ( ! [Y: product_unit] :
          ? [X: b > a] :
            ( Y
            = ( F2 @ X ) ) ) ) ).

% surj_def
thf(fact_437_surj__def,axiom,
    ! [F2: sum_su8719719018421925477t_unit > set_Product_unit] :
      ( ( ( image_1054766453263629697t_unit @ F2 @ top_to2771918933716375115t_unit )
        = top_to1767297665138865437t_unit )
      = ( ! [Y: set_Product_unit] :
          ? [X: sum_su8719719018421925477t_unit] :
            ( Y
            = ( F2 @ X ) ) ) ) ).

% surj_def
thf(fact_438_surj__def,axiom,
    ! [F2: set_Product_unit > sum_su8719719018421925477t_unit] :
      ( ( ( image_5049393547324665869t_unit @ F2 @ top_to1767297665138865437t_unit )
        = top_to2771918933716375115t_unit )
      = ( ! [Y: sum_su8719719018421925477t_unit] :
          ? [X: set_Product_unit] :
            ( Y
            = ( F2 @ X ) ) ) ) ).

% surj_def
thf(fact_439_surjI,axiom,
    ! [G2: product_unit > product_unit,F2: product_unit > product_unit] :
      ( ! [X5: product_unit] :
          ( ( G2 @ ( F2 @ X5 ) )
          = X5 )
     => ( ( image_405062704495631173t_unit @ G2 @ top_to1996260823553986621t_unit )
        = top_to1996260823553986621t_unit ) ) ).

% surjI
thf(fact_440_surjI,axiom,
    ! [G2: product_unit > set_Product_unit,F2: set_Product_unit > product_unit] :
      ( ! [X5: set_Product_unit] :
          ( ( G2 @ ( F2 @ X5 ) )
          = X5 )
     => ( ( image_7778121751606633509t_unit @ G2 @ top_to1996260823553986621t_unit )
        = top_to1767297665138865437t_unit ) ) ).

% surjI
thf(fact_441_surjI,axiom,
    ! [G2: set_Product_unit > product_unit,F2: product_unit > set_Product_unit] :
      ( ! [X5: product_unit] :
          ( ( G2 @ ( F2 @ X5 ) )
          = X5 )
     => ( ( image_4670244198609810021t_unit @ G2 @ top_to1767297665138865437t_unit )
        = top_to1996260823553986621t_unit ) ) ).

% surjI
thf(fact_442_surjI,axiom,
    ! [G2: product_unit > sum_su8719719018421925477t_unit,F2: sum_su8719719018421925477t_unit > product_unit] :
      ( ! [X5: sum_su8719719018421925477t_unit] :
          ( ( G2 @ ( F2 @ X5 ) )
          = X5 )
     => ( ( image_2037928093122670381t_unit @ G2 @ top_to1996260823553986621t_unit )
        = top_to2771918933716375115t_unit ) ) ).

% surjI
thf(fact_443_surjI,axiom,
    ! [G2: product_unit > b > a,F2: ( b > a ) > product_unit] :
      ( ! [X5: b > a] :
          ( ( G2 @ ( F2 @ X5 ) )
          = X5 )
     => ( ( image_3413377689041543532it_b_a @ G2 @ top_to1996260823553986621t_unit )
        = top_top_set_b_a ) ) ).

% surjI
thf(fact_444_surjI,axiom,
    ! [G2: sum_su8719719018421925477t_unit > product_unit,F2: product_unit > sum_su8719719018421925477t_unit] :
      ( ! [X5: product_unit] :
          ( ( G2 @ ( F2 @ X5 ) )
          = X5 )
     => ( ( image_4850905281257956513t_unit @ G2 @ top_to2771918933716375115t_unit )
        = top_to1996260823553986621t_unit ) ) ).

% surjI
thf(fact_445_surjI,axiom,
    ! [G2: set_Product_unit > set_Product_unit,F2: set_Product_unit > set_Product_unit] :
      ( ! [X5: set_Product_unit] :
          ( ( G2 @ ( F2 @ X5 ) )
          = X5 )
     => ( ( image_4019945301284682565t_unit @ G2 @ top_to1767297665138865437t_unit )
        = top_to1767297665138865437t_unit ) ) ).

% surjI
thf(fact_446_surjI,axiom,
    ! [G2: ( b > a ) > product_unit,F2: product_unit > b > a] :
      ( ! [X5: product_unit] :
          ( ( G2 @ ( F2 @ X5 ) )
          = X5 )
     => ( ( image_2179813402173241122t_unit @ G2 @ top_top_set_b_a )
        = top_to1996260823553986621t_unit ) ) ).

% surjI
thf(fact_447_surjI,axiom,
    ! [G2: sum_su8719719018421925477t_unit > set_Product_unit,F2: set_Product_unit > sum_su8719719018421925477t_unit] :
      ( ! [X5: set_Product_unit] :
          ( ( G2 @ ( F2 @ X5 ) )
          = X5 )
     => ( ( image_1054766453263629697t_unit @ G2 @ top_to2771918933716375115t_unit )
        = top_to1767297665138865437t_unit ) ) ).

% surjI
thf(fact_448_surjI,axiom,
    ! [G2: set_Product_unit > sum_su8719719018421925477t_unit,F2: sum_su8719719018421925477t_unit > set_Product_unit] :
      ( ! [X5: sum_su8719719018421925477t_unit] :
          ( ( G2 @ ( F2 @ X5 ) )
          = X5 )
     => ( ( image_5049393547324665869t_unit @ G2 @ top_to1767297665138865437t_unit )
        = top_to2771918933716375115t_unit ) ) ).

% surjI
thf(fact_449_surjE,axiom,
    ! [F2: product_unit > product_unit,Y3: product_unit] :
      ( ( ( image_405062704495631173t_unit @ F2 @ top_to1996260823553986621t_unit )
        = top_to1996260823553986621t_unit )
     => ~ ! [X5: product_unit] :
            ( Y3
           != ( F2 @ X5 ) ) ) ).

% surjE
thf(fact_450_surjE,axiom,
    ! [F2: product_unit > set_Product_unit,Y3: set_Product_unit] :
      ( ( ( image_7778121751606633509t_unit @ F2 @ top_to1996260823553986621t_unit )
        = top_to1767297665138865437t_unit )
     => ~ ! [X5: product_unit] :
            ( Y3
           != ( F2 @ X5 ) ) ) ).

% surjE
thf(fact_451_surjE,axiom,
    ! [F2: set_Product_unit > product_unit,Y3: product_unit] :
      ( ( ( image_4670244198609810021t_unit @ F2 @ top_to1767297665138865437t_unit )
        = top_to1996260823553986621t_unit )
     => ~ ! [X5: set_Product_unit] :
            ( Y3
           != ( F2 @ X5 ) ) ) ).

% surjE
thf(fact_452_surjE,axiom,
    ! [F2: product_unit > sum_su8719719018421925477t_unit,Y3: sum_su8719719018421925477t_unit] :
      ( ( ( image_2037928093122670381t_unit @ F2 @ top_to1996260823553986621t_unit )
        = top_to2771918933716375115t_unit )
     => ~ ! [X5: product_unit] :
            ( Y3
           != ( F2 @ X5 ) ) ) ).

% surjE
thf(fact_453_surjE,axiom,
    ! [F2: product_unit > b > a,Y3: b > a] :
      ( ( ( image_3413377689041543532it_b_a @ F2 @ top_to1996260823553986621t_unit )
        = top_top_set_b_a )
     => ~ ! [X5: product_unit] :
            ( Y3
           != ( F2 @ X5 ) ) ) ).

% surjE
thf(fact_454_surjE,axiom,
    ! [F2: sum_su8719719018421925477t_unit > product_unit,Y3: product_unit] :
      ( ( ( image_4850905281257956513t_unit @ F2 @ top_to2771918933716375115t_unit )
        = top_to1996260823553986621t_unit )
     => ~ ! [X5: sum_su8719719018421925477t_unit] :
            ( Y3
           != ( F2 @ X5 ) ) ) ).

% surjE
thf(fact_455_surjE,axiom,
    ! [F2: set_Product_unit > set_Product_unit,Y3: set_Product_unit] :
      ( ( ( image_4019945301284682565t_unit @ F2 @ top_to1767297665138865437t_unit )
        = top_to1767297665138865437t_unit )
     => ~ ! [X5: set_Product_unit] :
            ( Y3
           != ( F2 @ X5 ) ) ) ).

% surjE
thf(fact_456_surjE,axiom,
    ! [F2: ( b > a ) > product_unit,Y3: product_unit] :
      ( ( ( image_2179813402173241122t_unit @ F2 @ top_top_set_b_a )
        = top_to1996260823553986621t_unit )
     => ~ ! [X5: b > a] :
            ( Y3
           != ( F2 @ X5 ) ) ) ).

% surjE
thf(fact_457_surjE,axiom,
    ! [F2: sum_su8719719018421925477t_unit > set_Product_unit,Y3: set_Product_unit] :
      ( ( ( image_1054766453263629697t_unit @ F2 @ top_to2771918933716375115t_unit )
        = top_to1767297665138865437t_unit )
     => ~ ! [X5: sum_su8719719018421925477t_unit] :
            ( Y3
           != ( F2 @ X5 ) ) ) ).

% surjE
thf(fact_458_surjE,axiom,
    ! [F2: set_Product_unit > sum_su8719719018421925477t_unit,Y3: sum_su8719719018421925477t_unit] :
      ( ( ( image_5049393547324665869t_unit @ F2 @ top_to1767297665138865437t_unit )
        = top_to2771918933716375115t_unit )
     => ~ ! [X5: set_Product_unit] :
            ( Y3
           != ( F2 @ X5 ) ) ) ).

% surjE
thf(fact_459_surjD,axiom,
    ! [F2: product_unit > product_unit,Y3: product_unit] :
      ( ( ( image_405062704495631173t_unit @ F2 @ top_to1996260823553986621t_unit )
        = top_to1996260823553986621t_unit )
     => ? [X5: product_unit] :
          ( Y3
          = ( F2 @ X5 ) ) ) ).

% surjD
thf(fact_460_surjD,axiom,
    ! [F2: product_unit > set_Product_unit,Y3: set_Product_unit] :
      ( ( ( image_7778121751606633509t_unit @ F2 @ top_to1996260823553986621t_unit )
        = top_to1767297665138865437t_unit )
     => ? [X5: product_unit] :
          ( Y3
          = ( F2 @ X5 ) ) ) ).

% surjD
thf(fact_461_surjD,axiom,
    ! [F2: set_Product_unit > product_unit,Y3: product_unit] :
      ( ( ( image_4670244198609810021t_unit @ F2 @ top_to1767297665138865437t_unit )
        = top_to1996260823553986621t_unit )
     => ? [X5: set_Product_unit] :
          ( Y3
          = ( F2 @ X5 ) ) ) ).

% surjD
thf(fact_462_surjD,axiom,
    ! [F2: product_unit > sum_su8719719018421925477t_unit,Y3: sum_su8719719018421925477t_unit] :
      ( ( ( image_2037928093122670381t_unit @ F2 @ top_to1996260823553986621t_unit )
        = top_to2771918933716375115t_unit )
     => ? [X5: product_unit] :
          ( Y3
          = ( F2 @ X5 ) ) ) ).

% surjD
thf(fact_463_surjD,axiom,
    ! [F2: product_unit > b > a,Y3: b > a] :
      ( ( ( image_3413377689041543532it_b_a @ F2 @ top_to1996260823553986621t_unit )
        = top_top_set_b_a )
     => ? [X5: product_unit] :
          ( Y3
          = ( F2 @ X5 ) ) ) ).

% surjD
thf(fact_464_surjD,axiom,
    ! [F2: sum_su8719719018421925477t_unit > product_unit,Y3: product_unit] :
      ( ( ( image_4850905281257956513t_unit @ F2 @ top_to2771918933716375115t_unit )
        = top_to1996260823553986621t_unit )
     => ? [X5: sum_su8719719018421925477t_unit] :
          ( Y3
          = ( F2 @ X5 ) ) ) ).

% surjD
thf(fact_465_surjD,axiom,
    ! [F2: set_Product_unit > set_Product_unit,Y3: set_Product_unit] :
      ( ( ( image_4019945301284682565t_unit @ F2 @ top_to1767297665138865437t_unit )
        = top_to1767297665138865437t_unit )
     => ? [X5: set_Product_unit] :
          ( Y3
          = ( F2 @ X5 ) ) ) ).

% surjD
thf(fact_466_surjD,axiom,
    ! [F2: ( b > a ) > product_unit,Y3: product_unit] :
      ( ( ( image_2179813402173241122t_unit @ F2 @ top_top_set_b_a )
        = top_to1996260823553986621t_unit )
     => ? [X5: b > a] :
          ( Y3
          = ( F2 @ X5 ) ) ) ).

% surjD
thf(fact_467_surjD,axiom,
    ! [F2: sum_su8719719018421925477t_unit > set_Product_unit,Y3: set_Product_unit] :
      ( ( ( image_1054766453263629697t_unit @ F2 @ top_to2771918933716375115t_unit )
        = top_to1767297665138865437t_unit )
     => ? [X5: sum_su8719719018421925477t_unit] :
          ( Y3
          = ( F2 @ X5 ) ) ) ).

% surjD
thf(fact_468_surjD,axiom,
    ! [F2: set_Product_unit > sum_su8719719018421925477t_unit,Y3: sum_su8719719018421925477t_unit] :
      ( ( ( image_5049393547324665869t_unit @ F2 @ top_to1767297665138865437t_unit )
        = top_to2771918933716375115t_unit )
     => ? [X5: set_Product_unit] :
          ( Y3
          = ( F2 @ X5 ) ) ) ).

% surjD
thf(fact_469_surj__fun__eq,axiom,
    ! [F2: ( ( b > a ) > b > a ) > ( b > a ) > b > a,X6: set_b_a_b_a,G1: ( ( b > a ) > b > a ) > ( b > a ) > b > a,G22: ( ( b > a ) > b > a ) > ( b > a ) > b > a] :
      ( ( ( image_8714421494778392021_a_b_a @ F2 @ X6 )
        = top_top_set_b_a_b_a )
     => ( ! [X5: ( b > a ) > b > a] :
            ( ( member_b_a_b_a @ X5 @ X6 )
           => ( ( comp_b3327941365615541530_a_b_a @ G1 @ F2 @ X5 )
              = ( comp_b3327941365615541530_a_b_a @ G22 @ F2 @ X5 ) ) )
       => ( G1 = G22 ) ) ) ).

% surj_fun_eq
thf(fact_470_surj__fun__eq,axiom,
    ! [F2: b > b,X6: set_b,G1: b > b,G22: b > b] :
      ( ( ( image_b_b @ F2 @ X6 )
        = top_top_set_b )
     => ( ! [X5: b] :
            ( ( member_b @ X5 @ X6 )
           => ( ( comp_b_b_b @ G1 @ F2 @ X5 )
              = ( comp_b_b_b @ G22 @ F2 @ X5 ) ) )
       => ( G1 = G22 ) ) ) ).

% surj_fun_eq
thf(fact_471_surj__fun__eq,axiom,
    ! [F2: a > a,X6: set_a,G1: a > a,G22: a > a] :
      ( ( ( image_a_a @ F2 @ X6 )
        = top_top_set_a )
     => ( ! [X5: a] :
            ( ( member_a @ X5 @ X6 )
           => ( ( comp_a_a_a @ G1 @ F2 @ X5 )
              = ( comp_a_a_a @ G22 @ F2 @ X5 ) ) )
       => ( G1 = G22 ) ) ) ).

% surj_fun_eq
thf(fact_472_surj__fun__eq,axiom,
    ! [F2: produc4558475209616630778_a_b_b > dtree_a_b,X6: set_Pr3012420139608375472_a_b_b,G1: dtree_a_b > b,G22: dtree_a_b > b] :
      ( ( ( image_7065894828672115579ee_a_b @ F2 @ X6 )
        = top_to9008179178016042208ee_a_b )
     => ( ! [X5: produc4558475209616630778_a_b_b] :
            ( ( member4380921116106875537_a_b_b @ X5 @ X6 )
           => ( ( comp_d7292648224603294300_a_b_b @ G1 @ F2 @ X5 )
              = ( comp_d7292648224603294300_a_b_b @ G22 @ F2 @ X5 ) ) )
       => ( G1 = G22 ) ) ) ).

% surj_fun_eq
thf(fact_473_surj__fun__eq,axiom,
    ! [F2: ( b > a ) > b > a,X6: set_b_a,G1: ( b > a ) > product_prod_b_a_b_a,G22: ( b > a ) > product_prod_b_a_b_a] :
      ( ( ( image_b_a_b_a @ F2 @ X6 )
        = top_top_set_b_a )
     => ( ! [X5: b > a] :
            ( ( member_b_a @ X5 @ X6 )
           => ( ( comp_b7652884982158753286_a_b_a @ G1 @ F2 @ X5 )
              = ( comp_b7652884982158753286_a_b_a @ G22 @ F2 @ X5 ) ) )
       => ( G1 = G22 ) ) ) ).

% surj_fun_eq
thf(fact_474_surj__fun__eq,axiom,
    ! [F2: ( b > a ) > b > a,X6: set_b_a,G1: ( b > a ) > b > a,G22: ( b > a ) > b > a] :
      ( ( ( image_b_a_b_a @ F2 @ X6 )
        = top_top_set_b_a )
     => ( ! [X5: b > a] :
            ( ( member_b_a @ X5 @ X6 )
           => ( ( comp_b_a_b_a_b_a @ G1 @ F2 @ X5 )
              = ( comp_b_a_b_a_b_a @ G22 @ F2 @ X5 ) ) )
       => ( G1 = G22 ) ) ) ).

% surj_fun_eq
thf(fact_475_fun_Oset__map,axiom,
    ! [F2: ( b > a ) > b > a,V: ( b > a ) > b > a] :
      ( ( image_b_a_b_a @ ( comp_b_a_b_a_b_a @ F2 @ V ) @ top_top_set_b_a )
      = ( image_b_a_b_a @ F2 @ ( image_b_a_b_a @ V @ top_top_set_b_a ) ) ) ).

% fun.set_map
thf(fact_476_fun_Oset__map,axiom,
    ! [F2: b > b,V: b > b] :
      ( ( image_b_b @ ( comp_b_b_b @ F2 @ V ) @ top_top_set_b )
      = ( image_b_b @ F2 @ ( image_b_b @ V @ top_top_set_b ) ) ) ).

% fun.set_map
thf(fact_477_fun_Oset__map,axiom,
    ! [F2: a > a,V: a > a] :
      ( ( image_a_a @ ( comp_a_a_a @ F2 @ V ) @ top_top_set_a )
      = ( image_a_a @ F2 @ ( image_a_a @ V @ top_top_set_a ) ) ) ).

% fun.set_map
thf(fact_478_fun_Oset__map,axiom,
    ! [F2: ( b > a ) > b > a,V: product_unit > b > a] :
      ( ( image_3413377689041543532it_b_a @ ( comp_b4751574389558959904t_unit @ F2 @ V ) @ top_to1996260823553986621t_unit )
      = ( image_b_a_b_a @ F2 @ ( image_3413377689041543532it_b_a @ V @ top_to1996260823553986621t_unit ) ) ) ).

% fun.set_map
thf(fact_479_fun_Oset__map,axiom,
    ! [F2: ( b > a ) > b > a,V: set_Product_unit > b > a] :
      ( ( image_9176062692026671692it_b_a @ ( comp_b485742637902756864t_unit @ F2 @ V ) @ top_to1767297665138865437t_unit )
      = ( image_b_a_b_a @ F2 @ ( image_9176062692026671692it_b_a @ V @ top_to1767297665138865437t_unit ) ) ) ).

% fun.set_map
thf(fact_480_fun_Oset__map,axiom,
    ! [F2: dtree_a_b > b,V: produc4558475209616630778_a_b_b > dtree_a_b] :
      ( ( image_3908709015779211070_b_b_b @ ( comp_d7292648224603294300_a_b_b @ F2 @ V ) @ top_to7222684678772277088_a_b_b )
      = ( image_dtree_a_b_b @ F2 @ ( image_7065894828672115579ee_a_b @ V @ top_to7222684678772277088_a_b_b ) ) ) ).

% fun.set_map
thf(fact_481_fun_Oset__map,axiom,
    ! [F2: produc4558475209616630778_a_b_b > dtree_a_b,V: product_unit > produc4558475209616630778_a_b_b] :
      ( ( image_5682477522529595202ee_a_b @ ( comp_P7962621636793085684t_unit @ F2 @ V ) @ top_to1996260823553986621t_unit )
      = ( image_7065894828672115579ee_a_b @ F2 @ ( image_2521969012719430850_a_b_b @ V @ top_to1996260823553986621t_unit ) ) ) ).

% fun.set_map
thf(fact_482_fun_Oset__map,axiom,
    ! [F2: ( b > a ) > b > a,V: sum_su8719719018421925477t_unit > b > a] :
      ( ( image_3851727106056185104it_b_a @ ( comp_b1962440982679487378t_unit @ F2 @ V ) @ top_to2771918933716375115t_unit )
      = ( image_b_a_b_a @ F2 @ ( image_3851727106056185104it_b_a @ V @ top_to2771918933716375115t_unit ) ) ) ).

% fun.set_map
thf(fact_483_fun_Oset__map,axiom,
    ! [F2: produc4558475209616630778_a_b_b > dtree_a_b,V: set_Product_unit > produc4558475209616630778_a_b_b] :
      ( ( image_929270244206465058ee_a_b @ ( comp_P338726295243193300t_unit @ F2 @ V ) @ top_to1767297665138865437t_unit )
      = ( image_7065894828672115579ee_a_b @ F2 @ ( image_1948271130669936034_a_b_b @ V @ top_to1767297665138865437t_unit ) ) ) ).

% fun.set_map
thf(fact_484_fun_Oset__map,axiom,
    ! [F2: dtree_a_b > dtree_a_b,V: produc4558475209616630778_a_b_b > dtree_a_b] :
      ( ( image_7065894828672115579ee_a_b @ ( comp_d9193377603055859667_a_b_b @ F2 @ V ) @ top_to7222684678772277088_a_b_b )
      = ( image_1160270813240538107ee_a_b @ F2 @ ( image_7065894828672115579ee_a_b @ V @ top_to7222684678772277088_a_b_b ) ) ) ).

% fun.set_map
thf(fact_485_fun_Omap__cong,axiom,
    ! [X3: ( ( b > a ) > b > a ) > ( b > a ) > b > a,Ya: ( ( b > a ) > b > a ) > ( b > a ) > b > a,F2: ( ( b > a ) > b > a ) > ( b > a ) > b > a,G2: ( ( b > a ) > b > a ) > ( b > a ) > b > a] :
      ( ( X3 = Ya )
     => ( ! [Z3: ( b > a ) > b > a] :
            ( ( member_b_a_b_a @ Z3 @ ( image_8714421494778392021_a_b_a @ Ya @ top_top_set_b_a_b_a ) )
           => ( ( F2 @ Z3 )
              = ( G2 @ Z3 ) ) )
       => ( ( comp_b3327941365615541530_a_b_a @ F2 @ X3 )
          = ( comp_b3327941365615541530_a_b_a @ G2 @ Ya ) ) ) ) ).

% fun.map_cong
thf(fact_486_fun_Omap__cong,axiom,
    ! [X3: produc4558475209616630778_a_b_b > dtree_a_b,Ya: produc4558475209616630778_a_b_b > dtree_a_b,F2: dtree_a_b > b,G2: dtree_a_b > b] :
      ( ( X3 = Ya )
     => ( ! [Z3: dtree_a_b] :
            ( ( member_dtree_a_b @ Z3 @ ( image_7065894828672115579ee_a_b @ Ya @ top_to7222684678772277088_a_b_b ) )
           => ( ( F2 @ Z3 )
              = ( G2 @ Z3 ) ) )
       => ( ( comp_d7292648224603294300_a_b_b @ F2 @ X3 )
          = ( comp_d7292648224603294300_a_b_b @ G2 @ Ya ) ) ) ) ).

% fun.map_cong
thf(fact_487_fun_Omap__cong,axiom,
    ! [X3: b > b,Ya: b > b,F2: b > b,G2: b > b] :
      ( ( X3 = Ya )
     => ( ! [Z3: b] :
            ( ( member_b @ Z3 @ ( image_b_b @ Ya @ top_top_set_b ) )
           => ( ( F2 @ Z3 )
              = ( G2 @ Z3 ) ) )
       => ( ( comp_b_b_b @ F2 @ X3 )
          = ( comp_b_b_b @ G2 @ Ya ) ) ) ) ).

% fun.map_cong
thf(fact_488_fun_Omap__cong,axiom,
    ! [X3: a > a,Ya: a > a,F2: a > a,G2: a > a] :
      ( ( X3 = Ya )
     => ( ! [Z3: a] :
            ( ( member_a @ Z3 @ ( image_a_a @ Ya @ top_top_set_a ) )
           => ( ( F2 @ Z3 )
              = ( G2 @ Z3 ) ) )
       => ( ( comp_a_a_a @ F2 @ X3 )
          = ( comp_a_a_a @ G2 @ Ya ) ) ) ) ).

% fun.map_cong
thf(fact_489_fun_Omap__cong,axiom,
    ! [X3: ( b > a ) > b > a,Ya: ( b > a ) > b > a,F2: ( b > a ) > product_prod_b_a_b_a,G2: ( b > a ) > product_prod_b_a_b_a] :
      ( ( X3 = Ya )
     => ( ! [Z3: b > a] :
            ( ( member_b_a @ Z3 @ ( image_b_a_b_a @ Ya @ top_top_set_b_a ) )
           => ( ( F2 @ Z3 )
              = ( G2 @ Z3 ) ) )
       => ( ( comp_b7652884982158753286_a_b_a @ F2 @ X3 )
          = ( comp_b7652884982158753286_a_b_a @ G2 @ Ya ) ) ) ) ).

% fun.map_cong
thf(fact_490_fun_Omap__cong,axiom,
    ! [X3: ( b > a ) > b > a,Ya: ( b > a ) > b > a,F2: ( b > a ) > b > a,G2: ( b > a ) > b > a] :
      ( ( X3 = Ya )
     => ( ! [Z3: b > a] :
            ( ( member_b_a @ Z3 @ ( image_b_a_b_a @ Ya @ top_top_set_b_a ) )
           => ( ( F2 @ Z3 )
              = ( G2 @ Z3 ) ) )
       => ( ( comp_b_a_b_a_b_a @ F2 @ X3 )
          = ( comp_b_a_b_a_b_a @ G2 @ Ya ) ) ) ) ).

% fun.map_cong
thf(fact_491_fun_Omap__cong0,axiom,
    ! [X3: ( ( b > a ) > b > a ) > ( b > a ) > b > a,F2: ( ( b > a ) > b > a ) > ( b > a ) > b > a,G2: ( ( b > a ) > b > a ) > ( b > a ) > b > a] :
      ( ! [Z3: ( b > a ) > b > a] :
          ( ( member_b_a_b_a @ Z3 @ ( image_8714421494778392021_a_b_a @ X3 @ top_top_set_b_a_b_a ) )
         => ( ( F2 @ Z3 )
            = ( G2 @ Z3 ) ) )
     => ( ( comp_b3327941365615541530_a_b_a @ F2 @ X3 )
        = ( comp_b3327941365615541530_a_b_a @ G2 @ X3 ) ) ) ).

% fun.map_cong0
thf(fact_492_fun_Omap__cong0,axiom,
    ! [X3: produc4558475209616630778_a_b_b > dtree_a_b,F2: dtree_a_b > b,G2: dtree_a_b > b] :
      ( ! [Z3: dtree_a_b] :
          ( ( member_dtree_a_b @ Z3 @ ( image_7065894828672115579ee_a_b @ X3 @ top_to7222684678772277088_a_b_b ) )
         => ( ( F2 @ Z3 )
            = ( G2 @ Z3 ) ) )
     => ( ( comp_d7292648224603294300_a_b_b @ F2 @ X3 )
        = ( comp_d7292648224603294300_a_b_b @ G2 @ X3 ) ) ) ).

% fun.map_cong0
thf(fact_493_fun_Omap__cong0,axiom,
    ! [X3: b > b,F2: b > b,G2: b > b] :
      ( ! [Z3: b] :
          ( ( member_b @ Z3 @ ( image_b_b @ X3 @ top_top_set_b ) )
         => ( ( F2 @ Z3 )
            = ( G2 @ Z3 ) ) )
     => ( ( comp_b_b_b @ F2 @ X3 )
        = ( comp_b_b_b @ G2 @ X3 ) ) ) ).

% fun.map_cong0
thf(fact_494_fun_Omap__cong0,axiom,
    ! [X3: a > a,F2: a > a,G2: a > a] :
      ( ! [Z3: a] :
          ( ( member_a @ Z3 @ ( image_a_a @ X3 @ top_top_set_a ) )
         => ( ( F2 @ Z3 )
            = ( G2 @ Z3 ) ) )
     => ( ( comp_a_a_a @ F2 @ X3 )
        = ( comp_a_a_a @ G2 @ X3 ) ) ) ).

% fun.map_cong0
thf(fact_495_fun_Omap__cong0,axiom,
    ! [X3: ( b > a ) > b > a,F2: ( b > a ) > product_prod_b_a_b_a,G2: ( b > a ) > product_prod_b_a_b_a] :
      ( ! [Z3: b > a] :
          ( ( member_b_a @ Z3 @ ( image_b_a_b_a @ X3 @ top_top_set_b_a ) )
         => ( ( F2 @ Z3 )
            = ( G2 @ Z3 ) ) )
     => ( ( comp_b7652884982158753286_a_b_a @ F2 @ X3 )
        = ( comp_b7652884982158753286_a_b_a @ G2 @ X3 ) ) ) ).

% fun.map_cong0
thf(fact_496_fun_Omap__cong0,axiom,
    ! [X3: ( b > a ) > b > a,F2: ( b > a ) > b > a,G2: ( b > a ) > b > a] :
      ( ! [Z3: b > a] :
          ( ( member_b_a @ Z3 @ ( image_b_a_b_a @ X3 @ top_top_set_b_a ) )
         => ( ( F2 @ Z3 )
            = ( G2 @ Z3 ) ) )
     => ( ( comp_b_a_b_a_b_a @ F2 @ X3 )
        = ( comp_b_a_b_a_b_a @ G2 @ X3 ) ) ) ).

% fun.map_cong0
thf(fact_497_fun_Oinj__map__strong,axiom,
    ! [X3: ( ( b > a ) > b > a ) > ( b > a ) > b > a,Xa2: ( ( b > a ) > b > a ) > ( b > a ) > b > a,F2: ( ( b > a ) > b > a ) > ( b > a ) > b > a,Fa: ( ( b > a ) > b > a ) > ( b > a ) > b > a] :
      ( ! [Z3: ( b > a ) > b > a,Za: ( b > a ) > b > a] :
          ( ( member_b_a_b_a @ Z3 @ ( image_8714421494778392021_a_b_a @ X3 @ top_top_set_b_a_b_a ) )
         => ( ( member_b_a_b_a @ Za @ ( image_8714421494778392021_a_b_a @ Xa2 @ top_top_set_b_a_b_a ) )
           => ( ( ( F2 @ Z3 )
                = ( Fa @ Za ) )
             => ( Z3 = Za ) ) ) )
     => ( ( ( comp_b3327941365615541530_a_b_a @ F2 @ X3 )
          = ( comp_b3327941365615541530_a_b_a @ Fa @ Xa2 ) )
       => ( X3 = Xa2 ) ) ) ).

% fun.inj_map_strong
thf(fact_498_fun_Oinj__map__strong,axiom,
    ! [X3: produc4558475209616630778_a_b_b > dtree_a_b,Xa2: produc4558475209616630778_a_b_b > dtree_a_b,F2: dtree_a_b > b,Fa: dtree_a_b > b] :
      ( ! [Z3: dtree_a_b,Za: dtree_a_b] :
          ( ( member_dtree_a_b @ Z3 @ ( image_7065894828672115579ee_a_b @ X3 @ top_to7222684678772277088_a_b_b ) )
         => ( ( member_dtree_a_b @ Za @ ( image_7065894828672115579ee_a_b @ Xa2 @ top_to7222684678772277088_a_b_b ) )
           => ( ( ( F2 @ Z3 )
                = ( Fa @ Za ) )
             => ( Z3 = Za ) ) ) )
     => ( ( ( comp_d7292648224603294300_a_b_b @ F2 @ X3 )
          = ( comp_d7292648224603294300_a_b_b @ Fa @ Xa2 ) )
       => ( X3 = Xa2 ) ) ) ).

% fun.inj_map_strong
thf(fact_499_fun_Oinj__map__strong,axiom,
    ! [X3: b > b,Xa2: b > b,F2: b > b,Fa: b > b] :
      ( ! [Z3: b,Za: b] :
          ( ( member_b @ Z3 @ ( image_b_b @ X3 @ top_top_set_b ) )
         => ( ( member_b @ Za @ ( image_b_b @ Xa2 @ top_top_set_b ) )
           => ( ( ( F2 @ Z3 )
                = ( Fa @ Za ) )
             => ( Z3 = Za ) ) ) )
     => ( ( ( comp_b_b_b @ F2 @ X3 )
          = ( comp_b_b_b @ Fa @ Xa2 ) )
       => ( X3 = Xa2 ) ) ) ).

% fun.inj_map_strong
thf(fact_500_fun_Oinj__map__strong,axiom,
    ! [X3: a > a,Xa2: a > a,F2: a > a,Fa: a > a] :
      ( ! [Z3: a,Za: a] :
          ( ( member_a @ Z3 @ ( image_a_a @ X3 @ top_top_set_a ) )
         => ( ( member_a @ Za @ ( image_a_a @ Xa2 @ top_top_set_a ) )
           => ( ( ( F2 @ Z3 )
                = ( Fa @ Za ) )
             => ( Z3 = Za ) ) ) )
     => ( ( ( comp_a_a_a @ F2 @ X3 )
          = ( comp_a_a_a @ Fa @ Xa2 ) )
       => ( X3 = Xa2 ) ) ) ).

% fun.inj_map_strong
thf(fact_501_fun_Oinj__map__strong,axiom,
    ! [X3: ( b > a ) > b > a,Xa2: ( b > a ) > b > a,F2: ( b > a ) > product_prod_b_a_b_a,Fa: ( b > a ) > product_prod_b_a_b_a] :
      ( ! [Z3: b > a,Za: b > a] :
          ( ( member_b_a @ Z3 @ ( image_b_a_b_a @ X3 @ top_top_set_b_a ) )
         => ( ( member_b_a @ Za @ ( image_b_a_b_a @ Xa2 @ top_top_set_b_a ) )
           => ( ( ( F2 @ Z3 )
                = ( Fa @ Za ) )
             => ( Z3 = Za ) ) ) )
     => ( ( ( comp_b7652884982158753286_a_b_a @ F2 @ X3 )
          = ( comp_b7652884982158753286_a_b_a @ Fa @ Xa2 ) )
       => ( X3 = Xa2 ) ) ) ).

% fun.inj_map_strong
thf(fact_502_fun_Oinj__map__strong,axiom,
    ! [X3: ( b > a ) > b > a,Xa2: ( b > a ) > b > a,F2: ( b > a ) > b > a,Fa: ( b > a ) > b > a] :
      ( ! [Z3: b > a,Za: b > a] :
          ( ( member_b_a @ Z3 @ ( image_b_a_b_a @ X3 @ top_top_set_b_a ) )
         => ( ( member_b_a @ Za @ ( image_b_a_b_a @ Xa2 @ top_top_set_b_a ) )
           => ( ( ( F2 @ Z3 )
                = ( Fa @ Za ) )
             => ( Z3 = Za ) ) ) )
     => ( ( ( comp_b_a_b_a_b_a @ F2 @ X3 )
          = ( comp_b_a_b_a_b_a @ Fa @ Xa2 ) )
       => ( X3 = Xa2 ) ) ) ).

% fun.inj_map_strong
thf(fact_503_fun_Omap__ident__strong,axiom,
    ! [T: ( b > a ) > b > a,F2: ( b > a ) > b > a] :
      ( ! [Z3: b > a] :
          ( ( member_b_a @ Z3 @ ( image_b_a_b_a @ T @ top_top_set_b_a ) )
         => ( ( F2 @ Z3 )
            = Z3 ) )
     => ( ( comp_b_a_b_a_b_a @ F2 @ T )
        = T ) ) ).

% fun.map_ident_strong
thf(fact_504_fun_Omap__ident__strong,axiom,
    ! [T: product_unit > produc4558475209616630778_a_b_b,F2: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b] :
      ( ! [Z3: produc4558475209616630778_a_b_b] :
          ( ( member4380921116106875537_a_b_b @ Z3 @ ( image_2521969012719430850_a_b_b @ T @ top_to1996260823553986621t_unit ) )
         => ( ( F2 @ Z3 )
            = Z3 ) )
     => ( ( comp_P7633254161849120628t_unit @ F2 @ T )
        = T ) ) ).

% fun.map_ident_strong
thf(fact_505_fun_Omap__ident__strong,axiom,
    ! [T: b > b,F2: b > b] :
      ( ! [Z3: b] :
          ( ( member_b @ Z3 @ ( image_b_b @ T @ top_top_set_b ) )
         => ( ( F2 @ Z3 )
            = Z3 ) )
     => ( ( comp_b_b_b @ F2 @ T )
        = T ) ) ).

% fun.map_ident_strong
thf(fact_506_fun_Omap__ident__strong,axiom,
    ! [T: a > a,F2: a > a] :
      ( ! [Z3: a] :
          ( ( member_a @ Z3 @ ( image_a_a @ T @ top_top_set_a ) )
         => ( ( F2 @ Z3 )
            = Z3 ) )
     => ( ( comp_a_a_a @ F2 @ T )
        = T ) ) ).

% fun.map_ident_strong
thf(fact_507_fun_Omap__ident__strong,axiom,
    ! [T: product_unit > nat,F2: nat > nat] :
      ( ! [Z3: nat] :
          ( ( member_nat @ Z3 @ ( image_875570014554754200it_nat @ T @ top_to1996260823553986621t_unit ) )
         => ( ( F2 @ Z3 )
            = Z3 ) )
     => ( ( comp_n7656859423886344392t_unit @ F2 @ T )
        = T ) ) ).

% fun.map_ident_strong
thf(fact_508_fun_Omap__ident__strong,axiom,
    ! [T: product_unit > b,F2: b > b] :
      ( ! [Z3: b] :
          ( ( member_b @ Z3 @ ( image_Product_unit_b @ T @ top_to1996260823553986621t_unit ) )
         => ( ( F2 @ Z3 )
            = Z3 ) )
     => ( ( comp_b5213037050122890410t_unit @ F2 @ T )
        = T ) ) ).

% fun.map_ident_strong
thf(fact_509_fun_Omap__ident__strong,axiom,
    ! [T: product_unit > a,F2: a > a] :
      ( ! [Z3: a] :
          ( ( member_a @ Z3 @ ( image_Product_unit_a @ T @ top_to1996260823553986621t_unit ) )
         => ( ( F2 @ Z3 )
            = Z3 ) )
     => ( ( comp_a5016895688491196138t_unit @ F2 @ T )
        = T ) ) ).

% fun.map_ident_strong
thf(fact_510_fun_Omap__ident__strong,axiom,
    ! [T: set_Product_unit > nat,F2: nat > nat] :
      ( ! [Z3: nat] :
          ( ( member_nat @ Z3 @ ( image_4084087346006658424it_nat @ T @ top_to1767297665138865437t_unit ) )
         => ( ( F2 @ Z3 )
            = Z3 ) )
     => ( ( comp_n1322525831489224104t_unit @ F2 @ T )
        = T ) ) ).

% fun.map_ident_strong
thf(fact_511_fun_Omap__ident__strong,axiom,
    ! [T: set_Product_unit > b,F2: b > b] :
      ( ! [Z3: b] :
          ( ( member_b @ Z3 @ ( image_7680679895738368855unit_b @ T @ top_to1767297665138865437t_unit ) )
         => ( ( F2 @ Z3 )
            = Z3 ) )
     => ( ( comp_b8338046430617690506t_unit @ F2 @ T )
        = T ) ) ).

% fun.map_ident_strong
thf(fact_512_fun_Omap__ident__strong,axiom,
    ! [T: set_Product_unit > a,F2: a > a] :
      ( ! [Z3: a] :
          ( ( member_a @ Z3 @ ( image_7680679895738368854unit_a @ T @ top_to1767297665138865437t_unit ) )
         => ( ( F2 @ Z3 )
            = Z3 ) )
     => ( ( comp_a5037538144324670410t_unit @ F2 @ T )
        = T ) ) ).

% fun.map_ident_strong
thf(fact_513_comp__surj,axiom,
    ! [F2: product_unit > product_unit,G2: product_unit > product_unit] :
      ( ( ( image_405062704495631173t_unit @ F2 @ top_to1996260823553986621t_unit )
        = top_to1996260823553986621t_unit )
     => ( ( ( image_405062704495631173t_unit @ G2 @ top_to1996260823553986621t_unit )
          = top_to1996260823553986621t_unit )
       => ( ( image_405062704495631173t_unit @ ( comp_P7645380973975430442t_unit @ G2 @ F2 ) @ top_to1996260823553986621t_unit )
          = top_to1996260823553986621t_unit ) ) ) ).

% comp_surj
thf(fact_514_comp__surj,axiom,
    ! [F2: ( b > a ) > b > a,G2: ( b > a ) > b > a] :
      ( ( ( image_b_a_b_a @ F2 @ top_top_set_b_a )
        = top_top_set_b_a )
     => ( ( ( image_b_a_b_a @ G2 @ top_top_set_b_a )
          = top_top_set_b_a )
       => ( ( image_b_a_b_a @ ( comp_b_a_b_a_b_a @ G2 @ F2 ) @ top_top_set_b_a )
          = top_top_set_b_a ) ) ) ).

% comp_surj
thf(fact_515_comp__surj,axiom,
    ! [F2: b > b,G2: b > b] :
      ( ( ( image_b_b @ F2 @ top_top_set_b )
        = top_top_set_b )
     => ( ( ( image_b_b @ G2 @ top_top_set_b )
          = top_top_set_b )
       => ( ( image_b_b @ ( comp_b_b_b @ G2 @ F2 ) @ top_top_set_b )
          = top_top_set_b ) ) ) ).

% comp_surj
thf(fact_516_comp__surj,axiom,
    ! [F2: a > a,G2: a > a] :
      ( ( ( image_a_a @ F2 @ top_top_set_a )
        = top_top_set_a )
     => ( ( ( image_a_a @ G2 @ top_top_set_a )
          = top_top_set_a )
       => ( ( image_a_a @ ( comp_a_a_a @ G2 @ F2 ) @ top_top_set_a )
          = top_top_set_a ) ) ) ).

% comp_surj
thf(fact_517_comp__surj,axiom,
    ! [F2: product_unit > product_unit,G2: product_unit > set_Product_unit] :
      ( ( ( image_405062704495631173t_unit @ F2 @ top_to1996260823553986621t_unit )
        = top_to1996260823553986621t_unit )
     => ( ( ( image_7778121751606633509t_unit @ G2 @ top_to1996260823553986621t_unit )
          = top_to1767297665138865437t_unit )
       => ( ( image_7778121751606633509t_unit @ ( comp_P5718741887063599178t_unit @ G2 @ F2 ) @ top_to1996260823553986621t_unit )
          = top_to1767297665138865437t_unit ) ) ) ).

% comp_surj
thf(fact_518_comp__surj,axiom,
    ! [F2: product_unit > set_Product_unit,G2: set_Product_unit > product_unit] :
      ( ( ( image_7778121751606633509t_unit @ F2 @ top_to1996260823553986621t_unit )
        = top_to1767297665138865437t_unit )
     => ( ( ( image_4670244198609810021t_unit @ G2 @ top_to1767297665138865437t_unit )
          = top_to1996260823553986621t_unit )
       => ( ( image_405062704495631173t_unit @ ( comp_s5463265027590662666t_unit @ G2 @ F2 ) @ top_to1996260823553986621t_unit )
          = top_to1996260823553986621t_unit ) ) ) ).

% comp_surj
thf(fact_519_comp__surj,axiom,
    ! [F2: set_Product_unit > product_unit,G2: product_unit > product_unit] :
      ( ( ( image_4670244198609810021t_unit @ F2 @ top_to1767297665138865437t_unit )
        = top_to1996260823553986621t_unit )
     => ( ( ( image_405062704495631173t_unit @ G2 @ top_to1996260823553986621t_unit )
          = top_to1996260823553986621t_unit )
       => ( ( image_4670244198609810021t_unit @ ( comp_P8826619440060422666t_unit @ G2 @ F2 ) @ top_to1767297665138865437t_unit )
          = top_to1996260823553986621t_unit ) ) ) ).

% comp_surj
thf(fact_520_comp__surj,axiom,
    ! [F2: product_unit > product_unit,G2: product_unit > sum_su8719719018421925477t_unit] :
      ( ( ( image_405062704495631173t_unit @ F2 @ top_to1996260823553986621t_unit )
        = top_to1996260823553986621t_unit )
     => ( ( ( image_2037928093122670381t_unit @ G2 @ top_to1996260823553986621t_unit )
          = top_to2771918933716375115t_unit )
       => ( ( image_2037928093122670381t_unit @ ( comp_P1827784402480779900t_unit @ G2 @ F2 ) @ top_to1996260823553986621t_unit )
          = top_to2771918933716375115t_unit ) ) ) ).

% comp_surj
thf(fact_521_comp__surj,axiom,
    ! [F2: product_unit > product_unit,G2: product_unit > b > a] :
      ( ( ( image_405062704495631173t_unit @ F2 @ top_to1996260823553986621t_unit )
        = top_to1996260823553986621t_unit )
     => ( ( ( image_3413377689041543532it_b_a @ G2 @ top_to1996260823553986621t_unit )
          = top_top_set_b_a )
       => ( ( image_3413377689041543532it_b_a @ ( comp_P1897366385088438013t_unit @ G2 @ F2 ) @ top_to1996260823553986621t_unit )
          = top_top_set_b_a ) ) ) ).

% comp_surj
thf(fact_522_comp__surj,axiom,
    ! [F2: product_unit > sum_su8719719018421925477t_unit,G2: sum_su8719719018421925477t_unit > product_unit] :
      ( ( ( image_2037928093122670381t_unit @ F2 @ top_to1996260823553986621t_unit )
        = top_to2771918933716375115t_unit )
     => ( ( ( image_4850905281257956513t_unit @ G2 @ top_to2771918933716375115t_unit )
          = top_to1996260823553986621t_unit )
       => ( ( image_405062704495631173t_unit @ ( comp_S7963160314018604552t_unit @ G2 @ F2 ) @ top_to1996260823553986621t_unit )
          = top_to1996260823553986621t_unit ) ) ) ).

% comp_surj
thf(fact_523_bot__fun__def,axiom,
    ( bot_bo7321339186913516097_b_b_o
    = ( ^ [X: produc4558475209616630778_a_b_b] : bot_bot_o ) ) ).

% bot_fun_def
thf(fact_524_Inf_OINF__cong,axiom,
    ! [A5: set_Pr6717515126349854430ee_a_b,B5: set_Pr6717515126349854430ee_a_b,C3: produc3469756349985706280ee_a_b > produc4558475209616630778_a_b_b,D2: produc3469756349985706280ee_a_b > produc4558475209616630778_a_b_b,Inf: set_Pr3012420139608375472_a_b_b > produc4558475209616630778_a_b_b] :
      ( ( A5 = B5 )
     => ( ! [X5: produc3469756349985706280ee_a_b] :
            ( ( member3292202256475951039ee_a_b @ X5 @ B5 )
           => ( ( C3 @ X5 )
              = ( D2 @ X5 ) ) )
       => ( ( Inf @ ( image_3585698774939316521_a_b_b @ C3 @ A5 ) )
          = ( Inf @ ( image_3585698774939316521_a_b_b @ D2 @ B5 ) ) ) ) ) ).

% Inf.INF_cong
thf(fact_525_Inf_OINF__cong,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b,C3: produc4558475209616630778_a_b_b > produc3469756349985706280ee_a_b,D2: produc4558475209616630778_a_b_b > produc3469756349985706280ee_a_b,Inf: set_Pr6717515126349854430ee_a_b > produc3469756349985706280ee_a_b] :
      ( ( A5 = B5 )
     => ( ! [X5: produc4558475209616630778_a_b_b] :
            ( ( member4380921116106875537_a_b_b @ X5 @ B5 )
           => ( ( C3 @ X5 )
              = ( D2 @ X5 ) ) )
       => ( ( Inf @ ( image_4993246317199781161ee_a_b @ C3 @ A5 ) )
          = ( Inf @ ( image_4993246317199781161ee_a_b @ D2 @ B5 ) ) ) ) ) ).

% Inf.INF_cong
thf(fact_526_Inf_OINF__cong,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b,C3: produc4558475209616630778_a_b_b > dtree_a_b,D2: produc4558475209616630778_a_b_b > dtree_a_b,Inf: set_dtree_a_b > dtree_a_b] :
      ( ( A5 = B5 )
     => ( ! [X5: produc4558475209616630778_a_b_b] :
            ( ( member4380921116106875537_a_b_b @ X5 @ B5 )
           => ( ( C3 @ X5 )
              = ( D2 @ X5 ) ) )
       => ( ( Inf @ ( image_7065894828672115579ee_a_b @ C3 @ A5 ) )
          = ( Inf @ ( image_7065894828672115579ee_a_b @ D2 @ B5 ) ) ) ) ) ).

% Inf.INF_cong
thf(fact_527_Inf_OINF__cong,axiom,
    ! [A5: set_se3183138701204633190_a_b_b,B5: set_se3183138701204633190_a_b_b,C3: set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b,D2: set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b,Inf: set_se3183138701204633190_a_b_b > set_Pr3012420139608375472_a_b_b] :
      ( ( A5 = B5 )
     => ( ! [X5: set_Pr3012420139608375472_a_b_b] :
            ( ( member7431159781899395911_a_b_b @ X5 @ B5 )
           => ( ( C3 @ X5 )
              = ( D2 @ X5 ) ) )
       => ( ( Inf @ ( image_4903599603319290215_a_b_b @ C3 @ A5 ) )
          = ( Inf @ ( image_4903599603319290215_a_b_b @ D2 @ B5 ) ) ) ) ) ).

% Inf.INF_cong
thf(fact_528_Inf_OINF__cong,axiom,
    ! [A5: set_b_a,B5: set_b_a,C3: ( b > a ) > b > a,D2: ( b > a ) > b > a,Inf: set_b_a > b > a] :
      ( ( A5 = B5 )
     => ( ! [X5: b > a] :
            ( ( member_b_a @ X5 @ B5 )
           => ( ( C3 @ X5 )
              = ( D2 @ X5 ) ) )
       => ( ( Inf @ ( image_b_a_b_a @ C3 @ A5 ) )
          = ( Inf @ ( image_b_a_b_a @ D2 @ B5 ) ) ) ) ) ).

% Inf.INF_cong
thf(fact_529_Sup_OSUP__cong,axiom,
    ! [A5: set_Pr6717515126349854430ee_a_b,B5: set_Pr6717515126349854430ee_a_b,C3: produc3469756349985706280ee_a_b > produc4558475209616630778_a_b_b,D2: produc3469756349985706280ee_a_b > produc4558475209616630778_a_b_b,Sup: set_Pr3012420139608375472_a_b_b > produc4558475209616630778_a_b_b] :
      ( ( A5 = B5 )
     => ( ! [X5: produc3469756349985706280ee_a_b] :
            ( ( member3292202256475951039ee_a_b @ X5 @ B5 )
           => ( ( C3 @ X5 )
              = ( D2 @ X5 ) ) )
       => ( ( Sup @ ( image_3585698774939316521_a_b_b @ C3 @ A5 ) )
          = ( Sup @ ( image_3585698774939316521_a_b_b @ D2 @ B5 ) ) ) ) ) ).

% Sup.SUP_cong
thf(fact_530_Sup_OSUP__cong,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b,C3: produc4558475209616630778_a_b_b > produc3469756349985706280ee_a_b,D2: produc4558475209616630778_a_b_b > produc3469756349985706280ee_a_b,Sup: set_Pr6717515126349854430ee_a_b > produc3469756349985706280ee_a_b] :
      ( ( A5 = B5 )
     => ( ! [X5: produc4558475209616630778_a_b_b] :
            ( ( member4380921116106875537_a_b_b @ X5 @ B5 )
           => ( ( C3 @ X5 )
              = ( D2 @ X5 ) ) )
       => ( ( Sup @ ( image_4993246317199781161ee_a_b @ C3 @ A5 ) )
          = ( Sup @ ( image_4993246317199781161ee_a_b @ D2 @ B5 ) ) ) ) ) ).

% Sup.SUP_cong
thf(fact_531_Sup_OSUP__cong,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b,C3: produc4558475209616630778_a_b_b > dtree_a_b,D2: produc4558475209616630778_a_b_b > dtree_a_b,Sup: set_dtree_a_b > dtree_a_b] :
      ( ( A5 = B5 )
     => ( ! [X5: produc4558475209616630778_a_b_b] :
            ( ( member4380921116106875537_a_b_b @ X5 @ B5 )
           => ( ( C3 @ X5 )
              = ( D2 @ X5 ) ) )
       => ( ( Sup @ ( image_7065894828672115579ee_a_b @ C3 @ A5 ) )
          = ( Sup @ ( image_7065894828672115579ee_a_b @ D2 @ B5 ) ) ) ) ) ).

% Sup.SUP_cong
thf(fact_532_Sup_OSUP__cong,axiom,
    ! [A5: set_se3183138701204633190_a_b_b,B5: set_se3183138701204633190_a_b_b,C3: set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b,D2: set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b,Sup: set_se3183138701204633190_a_b_b > set_Pr3012420139608375472_a_b_b] :
      ( ( A5 = B5 )
     => ( ! [X5: set_Pr3012420139608375472_a_b_b] :
            ( ( member7431159781899395911_a_b_b @ X5 @ B5 )
           => ( ( C3 @ X5 )
              = ( D2 @ X5 ) ) )
       => ( ( Sup @ ( image_4903599603319290215_a_b_b @ C3 @ A5 ) )
          = ( Sup @ ( image_4903599603319290215_a_b_b @ D2 @ B5 ) ) ) ) ) ).

% Sup.SUP_cong
thf(fact_533_Sup_OSUP__cong,axiom,
    ! [A5: set_b_a,B5: set_b_a,C3: ( b > a ) > b > a,D2: ( b > a ) > b > a,Sup: set_b_a > b > a] :
      ( ( A5 = B5 )
     => ( ! [X5: b > a] :
            ( ( member_b_a @ X5 @ B5 )
           => ( ( C3 @ X5 )
              = ( D2 @ X5 ) ) )
       => ( ( Sup @ ( image_b_a_b_a @ C3 @ A5 ) )
          = ( Sup @ ( image_b_a_b_a @ D2 @ B5 ) ) ) ) ) ).

% Sup.SUP_cong
thf(fact_534_imageI,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b,F2: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ X3 @ A5 )
     => ( member4380921116106875537_a_b_b @ ( F2 @ X3 ) @ ( image_6081965176830705659_a_b_b @ F2 @ A5 ) ) ) ).

% imageI
thf(fact_535_imageI,axiom,
    ! [X3: nat,A5: set_nat,F2: nat > nat] :
      ( ( member_nat @ X3 @ A5 )
     => ( member_nat @ ( F2 @ X3 ) @ ( image_nat_nat @ F2 @ A5 ) ) ) ).

% imageI
thf(fact_536_imageI,axiom,
    ! [X3: nat,A5: set_nat,F2: nat > b] :
      ( ( member_nat @ X3 @ A5 )
     => ( member_b @ ( F2 @ X3 ) @ ( image_nat_b @ F2 @ A5 ) ) ) ).

% imageI
thf(fact_537_imageI,axiom,
    ! [X3: nat,A5: set_nat,F2: nat > a] :
      ( ( member_nat @ X3 @ A5 )
     => ( member_a @ ( F2 @ X3 ) @ ( image_nat_a @ F2 @ A5 ) ) ) ).

% imageI
thf(fact_538_imageI,axiom,
    ! [X3: b,A5: set_b,F2: b > nat] :
      ( ( member_b @ X3 @ A5 )
     => ( member_nat @ ( F2 @ X3 ) @ ( image_b_nat @ F2 @ A5 ) ) ) ).

% imageI
thf(fact_539_imageI,axiom,
    ! [X3: b,A5: set_b,F2: b > b] :
      ( ( member_b @ X3 @ A5 )
     => ( member_b @ ( F2 @ X3 ) @ ( image_b_b @ F2 @ A5 ) ) ) ).

% imageI
thf(fact_540_imageI,axiom,
    ! [X3: b,A5: set_b,F2: b > a] :
      ( ( member_b @ X3 @ A5 )
     => ( member_a @ ( F2 @ X3 ) @ ( image_b_a @ F2 @ A5 ) ) ) ).

% imageI
thf(fact_541_imageI,axiom,
    ! [X3: a,A5: set_a,F2: a > nat] :
      ( ( member_a @ X3 @ A5 )
     => ( member_nat @ ( F2 @ X3 ) @ ( image_a_nat @ F2 @ A5 ) ) ) ).

% imageI
thf(fact_542_imageI,axiom,
    ! [X3: a,A5: set_a,F2: a > b] :
      ( ( member_a @ X3 @ A5 )
     => ( member_b @ ( F2 @ X3 ) @ ( image_a_b @ F2 @ A5 ) ) ) ).

% imageI
thf(fact_543_imageI,axiom,
    ! [X3: a,A5: set_a,F2: a > a] :
      ( ( member_a @ X3 @ A5 )
     => ( member_a @ ( F2 @ X3 ) @ ( image_a_a @ F2 @ A5 ) ) ) ).

% imageI
thf(fact_544_image__iff,axiom,
    ! [Z: produc3469756349985706280ee_a_b,F2: produc4558475209616630778_a_b_b > produc3469756349985706280ee_a_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( member3292202256475951039ee_a_b @ Z @ ( image_4993246317199781161ee_a_b @ F2 @ A5 ) )
      = ( ? [X: produc4558475209616630778_a_b_b] :
            ( ( member4380921116106875537_a_b_b @ X @ A5 )
            & ( Z
              = ( F2 @ X ) ) ) ) ) ).

% image_iff
thf(fact_545_image__iff,axiom,
    ! [Z: dtree_a_b,F2: produc4558475209616630778_a_b_b > dtree_a_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( member_dtree_a_b @ Z @ ( image_7065894828672115579ee_a_b @ F2 @ A5 ) )
      = ( ? [X: produc4558475209616630778_a_b_b] :
            ( ( member4380921116106875537_a_b_b @ X @ A5 )
            & ( Z
              = ( F2 @ X ) ) ) ) ) ).

% image_iff
thf(fact_546_image__iff,axiom,
    ! [Z: produc4558475209616630778_a_b_b,F2: produc3469756349985706280ee_a_b > produc4558475209616630778_a_b_b,A5: set_Pr6717515126349854430ee_a_b] :
      ( ( member4380921116106875537_a_b_b @ Z @ ( image_3585698774939316521_a_b_b @ F2 @ A5 ) )
      = ( ? [X: produc3469756349985706280ee_a_b] :
            ( ( member3292202256475951039ee_a_b @ X @ A5 )
            & ( Z
              = ( F2 @ X ) ) ) ) ) ).

% image_iff
thf(fact_547_image__iff,axiom,
    ! [Z: set_Pr3012420139608375472_a_b_b,F2: set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b,A5: set_se3183138701204633190_a_b_b] :
      ( ( member7431159781899395911_a_b_b @ Z @ ( image_4903599603319290215_a_b_b @ F2 @ A5 ) )
      = ( ? [X: set_Pr3012420139608375472_a_b_b] :
            ( ( member7431159781899395911_a_b_b @ X @ A5 )
            & ( Z
              = ( F2 @ X ) ) ) ) ) ).

% image_iff
thf(fact_548_image__iff,axiom,
    ! [Z: b > a,F2: ( b > a ) > b > a,A5: set_b_a] :
      ( ( member_b_a @ Z @ ( image_b_a_b_a @ F2 @ A5 ) )
      = ( ? [X: b > a] :
            ( ( member_b_a @ X @ A5 )
            & ( Z
              = ( F2 @ X ) ) ) ) ) ).

% image_iff
thf(fact_549_bex__imageD,axiom,
    ! [F2: produc4558475209616630778_a_b_b > produc3469756349985706280ee_a_b,A5: set_Pr3012420139608375472_a_b_b,P2: produc3469756349985706280ee_a_b > $o] :
      ( ? [X7: produc3469756349985706280ee_a_b] :
          ( ( member3292202256475951039ee_a_b @ X7 @ ( image_4993246317199781161ee_a_b @ F2 @ A5 ) )
          & ( P2 @ X7 ) )
     => ? [X5: produc4558475209616630778_a_b_b] :
          ( ( member4380921116106875537_a_b_b @ X5 @ A5 )
          & ( P2 @ ( F2 @ X5 ) ) ) ) ).

% bex_imageD
thf(fact_550_bex__imageD,axiom,
    ! [F2: produc4558475209616630778_a_b_b > dtree_a_b,A5: set_Pr3012420139608375472_a_b_b,P2: dtree_a_b > $o] :
      ( ? [X7: dtree_a_b] :
          ( ( member_dtree_a_b @ X7 @ ( image_7065894828672115579ee_a_b @ F2 @ A5 ) )
          & ( P2 @ X7 ) )
     => ? [X5: produc4558475209616630778_a_b_b] :
          ( ( member4380921116106875537_a_b_b @ X5 @ A5 )
          & ( P2 @ ( F2 @ X5 ) ) ) ) ).

% bex_imageD
thf(fact_551_bex__imageD,axiom,
    ! [F2: produc3469756349985706280ee_a_b > produc4558475209616630778_a_b_b,A5: set_Pr6717515126349854430ee_a_b,P2: produc4558475209616630778_a_b_b > $o] :
      ( ? [X7: produc4558475209616630778_a_b_b] :
          ( ( member4380921116106875537_a_b_b @ X7 @ ( image_3585698774939316521_a_b_b @ F2 @ A5 ) )
          & ( P2 @ X7 ) )
     => ? [X5: produc3469756349985706280ee_a_b] :
          ( ( member3292202256475951039ee_a_b @ X5 @ A5 )
          & ( P2 @ ( F2 @ X5 ) ) ) ) ).

% bex_imageD
thf(fact_552_bex__imageD,axiom,
    ! [F2: set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b,A5: set_se3183138701204633190_a_b_b,P2: set_Pr3012420139608375472_a_b_b > $o] :
      ( ? [X7: set_Pr3012420139608375472_a_b_b] :
          ( ( member7431159781899395911_a_b_b @ X7 @ ( image_4903599603319290215_a_b_b @ F2 @ A5 ) )
          & ( P2 @ X7 ) )
     => ? [X5: set_Pr3012420139608375472_a_b_b] :
          ( ( member7431159781899395911_a_b_b @ X5 @ A5 )
          & ( P2 @ ( F2 @ X5 ) ) ) ) ).

% bex_imageD
thf(fact_553_bex__imageD,axiom,
    ! [F2: ( b > a ) > b > a,A5: set_b_a,P2: ( b > a ) > $o] :
      ( ? [X7: b > a] :
          ( ( member_b_a @ X7 @ ( image_b_a_b_a @ F2 @ A5 ) )
          & ( P2 @ X7 ) )
     => ? [X5: b > a] :
          ( ( member_b_a @ X5 @ A5 )
          & ( P2 @ ( F2 @ X5 ) ) ) ) ).

% bex_imageD
thf(fact_554_image__cong,axiom,
    ! [M: set_Pr6717515126349854430ee_a_b,N: set_Pr6717515126349854430ee_a_b,F2: produc3469756349985706280ee_a_b > produc4558475209616630778_a_b_b,G2: produc3469756349985706280ee_a_b > produc4558475209616630778_a_b_b] :
      ( ( M = N )
     => ( ! [X5: produc3469756349985706280ee_a_b] :
            ( ( member3292202256475951039ee_a_b @ X5 @ N )
           => ( ( F2 @ X5 )
              = ( G2 @ X5 ) ) )
       => ( ( image_3585698774939316521_a_b_b @ F2 @ M )
          = ( image_3585698774939316521_a_b_b @ G2 @ N ) ) ) ) ).

% image_cong
thf(fact_555_image__cong,axiom,
    ! [M: set_Pr3012420139608375472_a_b_b,N: set_Pr3012420139608375472_a_b_b,F2: produc4558475209616630778_a_b_b > produc3469756349985706280ee_a_b,G2: produc4558475209616630778_a_b_b > produc3469756349985706280ee_a_b] :
      ( ( M = N )
     => ( ! [X5: produc4558475209616630778_a_b_b] :
            ( ( member4380921116106875537_a_b_b @ X5 @ N )
           => ( ( F2 @ X5 )
              = ( G2 @ X5 ) ) )
       => ( ( image_4993246317199781161ee_a_b @ F2 @ M )
          = ( image_4993246317199781161ee_a_b @ G2 @ N ) ) ) ) ).

% image_cong
thf(fact_556_image__cong,axiom,
    ! [M: set_Pr3012420139608375472_a_b_b,N: set_Pr3012420139608375472_a_b_b,F2: produc4558475209616630778_a_b_b > dtree_a_b,G2: produc4558475209616630778_a_b_b > dtree_a_b] :
      ( ( M = N )
     => ( ! [X5: produc4558475209616630778_a_b_b] :
            ( ( member4380921116106875537_a_b_b @ X5 @ N )
           => ( ( F2 @ X5 )
              = ( G2 @ X5 ) ) )
       => ( ( image_7065894828672115579ee_a_b @ F2 @ M )
          = ( image_7065894828672115579ee_a_b @ G2 @ N ) ) ) ) ).

% image_cong
thf(fact_557_image__cong,axiom,
    ! [M: set_se3183138701204633190_a_b_b,N: set_se3183138701204633190_a_b_b,F2: set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b,G2: set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b] :
      ( ( M = N )
     => ( ! [X5: set_Pr3012420139608375472_a_b_b] :
            ( ( member7431159781899395911_a_b_b @ X5 @ N )
           => ( ( F2 @ X5 )
              = ( G2 @ X5 ) ) )
       => ( ( image_4903599603319290215_a_b_b @ F2 @ M )
          = ( image_4903599603319290215_a_b_b @ G2 @ N ) ) ) ) ).

% image_cong
thf(fact_558_image__cong,axiom,
    ! [M: set_b_a,N: set_b_a,F2: ( b > a ) > b > a,G2: ( b > a ) > b > a] :
      ( ( M = N )
     => ( ! [X5: b > a] :
            ( ( member_b_a @ X5 @ N )
           => ( ( F2 @ X5 )
              = ( G2 @ X5 ) ) )
       => ( ( image_b_a_b_a @ F2 @ M )
          = ( image_b_a_b_a @ G2 @ N ) ) ) ) ).

% image_cong
thf(fact_559_ball__imageD,axiom,
    ! [F2: produc4558475209616630778_a_b_b > produc3469756349985706280ee_a_b,A5: set_Pr3012420139608375472_a_b_b,P2: produc3469756349985706280ee_a_b > $o] :
      ( ! [X5: produc3469756349985706280ee_a_b] :
          ( ( member3292202256475951039ee_a_b @ X5 @ ( image_4993246317199781161ee_a_b @ F2 @ A5 ) )
         => ( P2 @ X5 ) )
     => ! [X7: produc4558475209616630778_a_b_b] :
          ( ( member4380921116106875537_a_b_b @ X7 @ A5 )
         => ( P2 @ ( F2 @ X7 ) ) ) ) ).

% ball_imageD
thf(fact_560_ball__imageD,axiom,
    ! [F2: produc4558475209616630778_a_b_b > dtree_a_b,A5: set_Pr3012420139608375472_a_b_b,P2: dtree_a_b > $o] :
      ( ! [X5: dtree_a_b] :
          ( ( member_dtree_a_b @ X5 @ ( image_7065894828672115579ee_a_b @ F2 @ A5 ) )
         => ( P2 @ X5 ) )
     => ! [X7: produc4558475209616630778_a_b_b] :
          ( ( member4380921116106875537_a_b_b @ X7 @ A5 )
         => ( P2 @ ( F2 @ X7 ) ) ) ) ).

% ball_imageD
thf(fact_561_ball__imageD,axiom,
    ! [F2: produc3469756349985706280ee_a_b > produc4558475209616630778_a_b_b,A5: set_Pr6717515126349854430ee_a_b,P2: produc4558475209616630778_a_b_b > $o] :
      ( ! [X5: produc4558475209616630778_a_b_b] :
          ( ( member4380921116106875537_a_b_b @ X5 @ ( image_3585698774939316521_a_b_b @ F2 @ A5 ) )
         => ( P2 @ X5 ) )
     => ! [X7: produc3469756349985706280ee_a_b] :
          ( ( member3292202256475951039ee_a_b @ X7 @ A5 )
         => ( P2 @ ( F2 @ X7 ) ) ) ) ).

% ball_imageD
thf(fact_562_ball__imageD,axiom,
    ! [F2: set_Pr3012420139608375472_a_b_b > set_Pr3012420139608375472_a_b_b,A5: set_se3183138701204633190_a_b_b,P2: set_Pr3012420139608375472_a_b_b > $o] :
      ( ! [X5: set_Pr3012420139608375472_a_b_b] :
          ( ( member7431159781899395911_a_b_b @ X5 @ ( image_4903599603319290215_a_b_b @ F2 @ A5 ) )
         => ( P2 @ X5 ) )
     => ! [X7: set_Pr3012420139608375472_a_b_b] :
          ( ( member7431159781899395911_a_b_b @ X7 @ A5 )
         => ( P2 @ ( F2 @ X7 ) ) ) ) ).

% ball_imageD
thf(fact_563_ball__imageD,axiom,
    ! [F2: ( b > a ) > b > a,A5: set_b_a,P2: ( b > a ) > $o] :
      ( ! [X5: b > a] :
          ( ( member_b_a @ X5 @ ( image_b_a_b_a @ F2 @ A5 ) )
         => ( P2 @ X5 ) )
     => ! [X7: b > a] :
          ( ( member_b_a @ X7 @ A5 )
         => ( P2 @ ( F2 @ X7 ) ) ) ) ).

% ball_imageD
thf(fact_564_rev__image__eqI,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b,B: produc4558475209616630778_a_b_b,F2: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ X3 @ A5 )
     => ( ( B
          = ( F2 @ X3 ) )
       => ( member4380921116106875537_a_b_b @ B @ ( image_6081965176830705659_a_b_b @ F2 @ A5 ) ) ) ) ).

% rev_image_eqI
thf(fact_565_rev__image__eqI,axiom,
    ! [X3: nat,A5: set_nat,B: nat,F2: nat > nat] :
      ( ( member_nat @ X3 @ A5 )
     => ( ( B
          = ( F2 @ X3 ) )
       => ( member_nat @ B @ ( image_nat_nat @ F2 @ A5 ) ) ) ) ).

% rev_image_eqI
thf(fact_566_rev__image__eqI,axiom,
    ! [X3: nat,A5: set_nat,B: b,F2: nat > b] :
      ( ( member_nat @ X3 @ A5 )
     => ( ( B
          = ( F2 @ X3 ) )
       => ( member_b @ B @ ( image_nat_b @ F2 @ A5 ) ) ) ) ).

% rev_image_eqI
thf(fact_567_rev__image__eqI,axiom,
    ! [X3: nat,A5: set_nat,B: a,F2: nat > a] :
      ( ( member_nat @ X3 @ A5 )
     => ( ( B
          = ( F2 @ X3 ) )
       => ( member_a @ B @ ( image_nat_a @ F2 @ A5 ) ) ) ) ).

% rev_image_eqI
thf(fact_568_rev__image__eqI,axiom,
    ! [X3: b,A5: set_b,B: nat,F2: b > nat] :
      ( ( member_b @ X3 @ A5 )
     => ( ( B
          = ( F2 @ X3 ) )
       => ( member_nat @ B @ ( image_b_nat @ F2 @ A5 ) ) ) ) ).

% rev_image_eqI
thf(fact_569_rev__image__eqI,axiom,
    ! [X3: b,A5: set_b,B: b,F2: b > b] :
      ( ( member_b @ X3 @ A5 )
     => ( ( B
          = ( F2 @ X3 ) )
       => ( member_b @ B @ ( image_b_b @ F2 @ A5 ) ) ) ) ).

% rev_image_eqI
thf(fact_570_rev__image__eqI,axiom,
    ! [X3: b,A5: set_b,B: a,F2: b > a] :
      ( ( member_b @ X3 @ A5 )
     => ( ( B
          = ( F2 @ X3 ) )
       => ( member_a @ B @ ( image_b_a @ F2 @ A5 ) ) ) ) ).

% rev_image_eqI
thf(fact_571_rev__image__eqI,axiom,
    ! [X3: a,A5: set_a,B: nat,F2: a > nat] :
      ( ( member_a @ X3 @ A5 )
     => ( ( B
          = ( F2 @ X3 ) )
       => ( member_nat @ B @ ( image_a_nat @ F2 @ A5 ) ) ) ) ).

% rev_image_eqI
thf(fact_572_rev__image__eqI,axiom,
    ! [X3: a,A5: set_a,B: b,F2: a > b] :
      ( ( member_a @ X3 @ A5 )
     => ( ( B
          = ( F2 @ X3 ) )
       => ( member_b @ B @ ( image_a_b @ F2 @ A5 ) ) ) ) ).

% rev_image_eqI
thf(fact_573_rev__image__eqI,axiom,
    ! [X3: a,A5: set_a,B: a,F2: a > a] :
      ( ( member_a @ X3 @ A5 )
     => ( ( B
          = ( F2 @ X3 ) )
       => ( member_a @ B @ ( image_a_a @ F2 @ A5 ) ) ) ) ).

% rev_image_eqI
thf(fact_574_dtree_Oset__intros_I3_J,axiom,
    ! [Ye: produc4558475209616630778_a_b_b,X22: fset_P5281107635120001194_a_b_b,Yf: dtree_a_b,Yh: b,X12: a] :
      ( ( member4380921116106875537_a_b_b @ Ye @ ( fset_P783253628892185035_a_b_b @ X22 ) )
     => ( ( member_dtree_a_b @ Yf @ ( basic_7578771248400840636_a_b_b @ Ye ) )
       => ( ( member_b @ Yh @ ( darcs_a_b @ Yf ) )
         => ( member_b @ Yh @ ( darcs_a_b @ ( node_a_b @ X12 @ X22 ) ) ) ) ) ) ).

% dtree.set_intros(3)
thf(fact_575_iso__tuple__UNIV__I,axiom,
    ! [X3: set_Pr3012420139608375472_a_b_b] : ( member7431159781899395911_a_b_b @ X3 @ top_to1846739022409413910_a_b_b ) ).

% iso_tuple_UNIV_I
thf(fact_576_iso__tuple__UNIV__I,axiom,
    ! [X3: nat] : ( member_nat @ X3 @ top_top_set_nat ) ).

% iso_tuple_UNIV_I
thf(fact_577_iso__tuple__UNIV__I,axiom,
    ! [X3: b] : ( member_b @ X3 @ top_top_set_b ) ).

% iso_tuple_UNIV_I
thf(fact_578_iso__tuple__UNIV__I,axiom,
    ! [X3: a] : ( member_a @ X3 @ top_top_set_a ) ).

% iso_tuple_UNIV_I
thf(fact_579_iso__tuple__UNIV__I,axiom,
    ! [X3: sum_su8719719018421925477t_unit] : ( member1483886641279141628t_unit @ X3 @ top_to2771918933716375115t_unit ) ).

% iso_tuple_UNIV_I
thf(fact_580_iso__tuple__UNIV__I,axiom,
    ! [X3: set_Product_unit] : ( member5877623283571906838t_unit @ X3 @ top_to1767297665138865437t_unit ) ).

% iso_tuple_UNIV_I
thf(fact_581_iso__tuple__UNIV__I,axiom,
    ! [X3: b > a] : ( member_b_a @ X3 @ top_top_set_b_a ) ).

% iso_tuple_UNIV_I
thf(fact_582_iso__tuple__UNIV__I,axiom,
    ! [X3: produc4558475209616630778_a_b_b] : ( member4380921116106875537_a_b_b @ X3 @ top_to7222684678772277088_a_b_b ) ).

% iso_tuple_UNIV_I
thf(fact_583_iso__tuple__UNIV__I,axiom,
    ! [X3: product_unit] : ( member_Product_unit @ X3 @ top_to1996260823553986621t_unit ) ).

% iso_tuple_UNIV_I
thf(fact_584_root__not__child__if__wf__dverts,axiom,
    ! [R: a,Xs2: fset_P5281107635120001194_a_b_b,T1: dtree_a_b,E1: b] :
      ( ( wf_dverts_a_b @ ( node_a_b @ R @ Xs2 ) )
     => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ T1 @ E1 ) @ ( fset_P783253628892185035_a_b_b @ Xs2 ) )
       => ~ ( member_a @ R @ ( dverts_a_b @ T1 ) ) ) ) ).

% root_not_child_if_wf_dverts
thf(fact_585_dtree_Oset__cases_I2_J,axiom,
    ! [E: b,A: dtree_a_b] :
      ( ( member_b @ E @ ( darcs_a_b @ A ) )
     => ( ! [Z1: a,Z2: fset_P5281107635120001194_a_b_b] :
            ( ( A
              = ( node_a_b @ Z1 @ Z2 ) )
           => ! [X5: produc4558475209616630778_a_b_b] :
                ( ( member4380921116106875537_a_b_b @ X5 @ ( fset_P783253628892185035_a_b_b @ Z2 ) )
               => ! [Xa: dtree_a_b] :
                    ( ( member_dtree_a_b @ Xa @ ( basic_7578771248400840636_a_b_b @ X5 ) )
                   => ~ ( member_b @ E @ ( darcs_a_b @ Xa ) ) ) ) )
       => ~ ! [Z1: a,Z2: fset_P5281107635120001194_a_b_b] :
              ( ( A
                = ( node_a_b @ Z1 @ Z2 ) )
             => ! [X5: produc4558475209616630778_a_b_b] :
                  ( ( member4380921116106875537_a_b_b @ X5 @ ( fset_P783253628892185035_a_b_b @ Z2 ) )
                 => ~ ( member_b @ E @ ( basic_1877077703026942_a_b_b @ X5 ) ) ) ) ) ) ).

% dtree.set_cases(2)
thf(fact_586_disjoint__darcs__if__wf__aux2,axiom,
    ! [R: a,Xs2: fset_P5281107635120001194_a_b_b,T1: dtree_a_b,E1: b,T2: dtree_a_b,E2: b] :
      ( ( wf_darcs_a_b @ ( node_a_b @ R @ Xs2 ) )
     => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ T1 @ E1 ) @ ( fset_P783253628892185035_a_b_b @ Xs2 ) )
       => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ T2 @ E2 ) @ ( fset_P783253628892185035_a_b_b @ Xs2 ) )
         => ( ( ( produc331601717337510060_a_b_b @ T1 @ E1 )
             != ( produc331601717337510060_a_b_b @ T2 @ E2 ) )
           => ( ( inf_inf_set_b @ ( darcs_a_b @ T1 ) @ ( darcs_a_b @ T2 ) )
              = bot_bot_set_b ) ) ) ) ) ).

% disjoint_darcs_if_wf_aux2
thf(fact_587_map__prod__surj,axiom,
    ! [F2: product_unit > product_unit,G2: product_unit > product_unit] :
      ( ( ( image_405062704495631173t_unit @ F2 @ top_to1996260823553986621t_unit )
        = top_to1996260823553986621t_unit )
     => ( ( ( image_405062704495631173t_unit @ G2 @ top_to1996260823553986621t_unit )
          = top_to1996260823553986621t_unit )
       => ( ( image_9149991759805673413t_unit @ ( produc3941737999988548470t_unit @ F2 @ G2 ) @ top_to1835807148980544151t_unit )
          = top_to1835807148980544151t_unit ) ) ) ).

% map_prod_surj
thf(fact_588_map__prod__surj,axiom,
    ! [F2: product_unit > product_unit,G2: product_unit > set_Product_unit] :
      ( ( ( image_405062704495631173t_unit @ F2 @ top_to1996260823553986621t_unit )
        = top_to1996260823553986621t_unit )
     => ( ( ( image_7778121751606633509t_unit @ G2 @ top_to1996260823553986621t_unit )
          = top_to1767297665138865437t_unit )
       => ( ( image_4440353659548185765t_unit @ ( produc5886246840336164950t_unit @ F2 @ G2 ) @ top_to1835807148980544151t_unit )
          = top_to233792371731913591t_unit ) ) ) ).

% map_prod_surj
thf(fact_589_map__prod__surj,axiom,
    ! [F2: product_unit > product_unit,G2: set_Product_unit > product_unit] :
      ( ( ( image_405062704495631173t_unit @ F2 @ top_to1996260823553986621t_unit )
        = top_to1996260823553986621t_unit )
     => ( ( ( image_4670244198609810021t_unit @ G2 @ top_to1767297665138865437t_unit )
          = top_to1996260823553986621t_unit )
       => ( ( image_530514150481900261t_unit @ ( produc2778369287339341462t_unit @ F2 @ G2 ) @ top_to233792371731913591t_unit )
          = top_to1835807148980544151t_unit ) ) ) ).

% map_prod_surj
thf(fact_590_map__prod__surj,axiom,
    ! [F2: product_unit > set_Product_unit,G2: product_unit > product_unit] :
      ( ( ( image_7778121751606633509t_unit @ F2 @ top_to1996260823553986621t_unit )
        = top_to1767297665138865437t_unit )
     => ( ( ( image_405062704495631173t_unit @ G2 @ top_to1996260823553986621t_unit )
          = top_to1996260823553986621t_unit )
       => ( ( image_8665910223651504869t_unit @ ( produc2522892427866404950t_unit @ F2 @ G2 ) @ top_to1835807148980544151t_unit )
          = top_to1243971000991123895t_unit ) ) ) ).

% map_prod_surj
thf(fact_591_map__prod__surj,axiom,
    ! [F2: set_Product_unit > product_unit,G2: product_unit > product_unit] :
      ( ( ( image_4670244198609810021t_unit @ F2 @ top_to1767297665138865437t_unit )
        = top_to1996260823553986621t_unit )
     => ( ( ( image_405062704495631173t_unit @ G2 @ top_to1996260823553986621t_unit )
          = top_to1996260823553986621t_unit )
       => ( ( image_6812161408116896933t_unit @ ( produc8516325191527966358t_unit @ F2 @ G2 ) @ top_to1243971000991123895t_unit )
          = top_to1835807148980544151t_unit ) ) ) ).

% map_prod_surj
thf(fact_592_map__prod__surj,axiom,
    ! [F2: product_unit > product_unit,G2: product_unit > sum_su8719719018421925477t_unit] :
      ( ( ( image_405062704495631173t_unit @ F2 @ top_to1996260823553986621t_unit )
        = top_to1996260823553986621t_unit )
     => ( ( ( image_2037928093122670381t_unit @ G2 @ top_to1996260823553986621t_unit )
          = top_to2771918933716375115t_unit )
       => ( ( image_548699592699116739t_unit @ ( produc3239798823771121596t_unit @ F2 @ G2 ) @ top_to1835807148980544151t_unit )
          = top_to5937313915539256967t_unit ) ) ) ).

% map_prod_surj
thf(fact_593_map__prod__surj,axiom,
    ! [F2: product_unit > product_unit,G2: product_unit > b > a] :
      ( ( ( image_405062704495631173t_unit @ F2 @ top_to1996260823553986621t_unit )
        = top_to1996260823553986621t_unit )
     => ( ( ( image_3413377689041543532it_b_a @ G2 @ top_to1996260823553986621t_unit )
          = top_top_set_b_a )
       => ( ( image_8908915882552613250it_b_a @ ( produc5742360875550256123it_b_a @ F2 @ G2 ) @ top_to1835807148980544151t_unit )
          = top_to6155636102477775302it_b_a ) ) ) ).

% map_prod_surj
thf(fact_594_map__prod__surj,axiom,
    ! [F2: product_unit > product_unit,G2: sum_su8719719018421925477t_unit > product_unit] :
      ( ( ( image_405062704495631173t_unit @ F2 @ top_to1996260823553986621t_unit )
        = top_to1996260823553986621t_unit )
     => ( ( ( image_4850905281257956513t_unit @ G2 @ top_to2771918933716375115t_unit )
          = top_to1996260823553986621t_unit )
       => ( ( image_1652486172545353919t_unit @ ( produc6052776011906407728t_unit @ F2 @ G2 ) @ top_to5937313915539256967t_unit )
          = top_to1835807148980544151t_unit ) ) ) ).

% map_prod_surj
thf(fact_595_map__prod__surj,axiom,
    ! [F2: product_unit > product_unit,G2: set_Product_unit > set_Product_unit] :
      ( ( ( image_405062704495631173t_unit @ F2 @ top_to1996260823553986621t_unit )
        = top_to1996260823553986621t_unit )
     => ( ( ( image_4019945301284682565t_unit @ G2 @ top_to1767297665138865437t_unit )
          = top_to1767297665138865437t_unit )
       => ( ( image_3652598542883616709t_unit @ ( produc9113809635950836598t_unit @ F2 @ G2 ) @ top_to233792371731913591t_unit )
          = top_to233792371731913591t_unit ) ) ) ).

% map_prod_surj
thf(fact_596_map__prod__surj,axiom,
    ! [F2: product_unit > product_unit,G2: ( b > a ) > product_unit] :
      ( ( ( image_405062704495631173t_unit @ F2 @ top_to1996260823553986621t_unit )
        = top_to1996260823553986621t_unit )
     => ( ( ( image_2179813402173241122t_unit @ G2 @ top_top_set_b_a )
          = top_to1996260823553986621t_unit )
       => ( ( image_5329927176394305216t_unit @ ( produc4508796588681953713t_unit @ F2 @ G2 ) @ top_to6155636102477775302it_b_a )
          = top_to1835807148980544151t_unit ) ) ) ).

% map_prod_surj
thf(fact_597_dtree_Oset__intros_I4_J,axiom,
    ! [Ye: produc4558475209616630778_a_b_b,X22: fset_P5281107635120001194_a_b_b,Yi: b,X12: a] :
      ( ( member4380921116106875537_a_b_b @ Ye @ ( fset_P783253628892185035_a_b_b @ X22 ) )
     => ( ( member_b @ Yi @ ( basic_1877077703026942_a_b_b @ Ye ) )
       => ( member_b @ Yi @ ( darcs_a_b @ ( node_a_b @ X12 @ X22 ) ) ) ) ) ).

% dtree.set_intros(4)
thf(fact_598_dtree_Oset__sel_I2_J,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A: dtree_a_b,Xa2: dtree_a_b,Xb: a] :
      ( ( member4380921116106875537_a_b_b @ X3 @ ( fset_P783253628892185035_a_b_b @ ( sucs_a_b @ A ) ) )
     => ( ( member_dtree_a_b @ Xa2 @ ( basic_7578771248400840636_a_b_b @ X3 ) )
       => ( ( member_a @ Xb @ ( dverts_a_b @ Xa2 ) )
         => ( member_a @ Xb @ ( dverts_a_b @ A ) ) ) ) ) ).

% dtree.set_sel(2)
thf(fact_599_dtree_Oset__sel_I3_J,axiom,
    ! [Xe: produc4558475209616630778_a_b_b,A: dtree_a_b,Xf: dtree_a_b,Xh: b] :
      ( ( member4380921116106875537_a_b_b @ Xe @ ( fset_P783253628892185035_a_b_b @ ( sucs_a_b @ A ) ) )
     => ( ( member_dtree_a_b @ Xf @ ( basic_7578771248400840636_a_b_b @ Xe ) )
       => ( ( member_b @ Xh @ ( darcs_a_b @ Xf ) )
         => ( member_b @ Xh @ ( darcs_a_b @ A ) ) ) ) ) ).

% dtree.set_sel(3)
thf(fact_600_image2__eqI,axiom,
    ! [B: dtree_a_b,F2: produc4558475209616630778_a_b_b > dtree_a_b,X3: produc4558475209616630778_a_b_b,C: b,G2: produc4558475209616630778_a_b_b > b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( ( C
          = ( G2 @ X3 ) )
       => ( ( member4380921116106875537_a_b_b @ X3 @ A5 )
         => ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ B @ C ) @ ( bNF_Gr3881854498152092719_a_b_b @ A5 @ F2 @ G2 ) ) ) ) ) ).

% image2_eqI
thf(fact_601_image2__eqI,axiom,
    ! [B: product_unit,F2: nat > product_unit,X3: nat,C: product_unit,G2: nat > product_unit,A5: set_nat] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( ( C
          = ( G2 @ X3 ) )
       => ( ( member_nat @ X3 @ A5 )
         => ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ B @ C ) @ ( bNF_Gr8877520075124390378t_unit @ A5 @ F2 @ G2 ) ) ) ) ) ).

% image2_eqI
thf(fact_602_image2__eqI,axiom,
    ! [B: product_unit,F2: b > product_unit,X3: b,C: product_unit,G2: b > product_unit,A5: set_b] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( ( C
          = ( G2 @ X3 ) )
       => ( ( member_b @ X3 @ A5 )
         => ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ B @ C ) @ ( bNF_Gr2538028588435227621t_unit @ A5 @ F2 @ G2 ) ) ) ) ) ).

% image2_eqI
thf(fact_603_image2__eqI,axiom,
    ! [B: product_unit,F2: a > product_unit,X3: a,C: product_unit,G2: a > product_unit,A5: set_a] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( ( C
          = ( G2 @ X3 ) )
       => ( ( member_a @ X3 @ A5 )
         => ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ B @ C ) @ ( bNF_Gr5172770309810061924t_unit @ A5 @ F2 @ G2 ) ) ) ) ) ).

% image2_eqI
thf(fact_604_image2__eqI,axiom,
    ! [B: dtree_a_b,F2: nat > dtree_a_b,X3: nat,C: b,G2: nat > b,A5: set_nat] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( ( C
          = ( G2 @ X3 ) )
       => ( ( member_nat @ X3 @ A5 )
         => ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ B @ C ) @ ( bNF_Gr8387754577466859481_a_b_b @ A5 @ F2 @ G2 ) ) ) ) ) ).

% image2_eqI
thf(fact_605_image2__eqI,axiom,
    ! [B: dtree_a_b,F2: b > dtree_a_b,X3: b,C: b,G2: b > b,A5: set_b] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( ( C
          = ( G2 @ X3 ) )
       => ( ( member_b @ X3 @ A5 )
         => ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ B @ C ) @ ( bNF_Gr4676526542121276958_a_b_b @ A5 @ F2 @ G2 ) ) ) ) ) ).

% image2_eqI
thf(fact_606_image2__eqI,axiom,
    ! [B: dtree_a_b,F2: a > dtree_a_b,X3: a,C: b,G2: a > b,A5: set_a] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( ( C
          = ( G2 @ X3 ) )
       => ( ( member_a @ X3 @ A5 )
         => ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ B @ C ) @ ( bNF_Gr5315966842453093087_a_b_b @ A5 @ F2 @ G2 ) ) ) ) ) ).

% image2_eqI
thf(fact_607_image2__eqI,axiom,
    ! [B: b,F2: nat > b,X3: nat,C: dtree_a_b,G2: nat > dtree_a_b,A5: set_nat] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( ( C
          = ( G2 @ X3 ) )
       => ( ( member_nat @ X3 @ A5 )
         => ( member3292202256475951039ee_a_b @ ( produc3542686128043086370ee_a_b @ B @ C ) @ ( bNF_Gr2375466951317659983ee_a_b @ A5 @ F2 @ G2 ) ) ) ) ) ).

% image2_eqI
thf(fact_608_image2__eqI,axiom,
    ! [B: b,F2: b > b,X3: b,C: dtree_a_b,G2: b > dtree_a_b,A5: set_b] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( ( C
          = ( G2 @ X3 ) )
       => ( ( member_b @ X3 @ A5 )
         => ( member3292202256475951039ee_a_b @ ( produc3542686128043086370ee_a_b @ B @ C ) @ ( bNF_Gr7887610952826853268ee_a_b @ A5 @ F2 @ G2 ) ) ) ) ) ).

% image2_eqI
thf(fact_609_image2__eqI,axiom,
    ! [B: b,F2: a > b,X3: a,C: dtree_a_b,G2: a > dtree_a_b,A5: set_a] :
      ( ( B
        = ( F2 @ X3 ) )
     => ( ( C
          = ( G2 @ X3 ) )
       => ( ( member_a @ X3 @ A5 )
         => ( member3292202256475951039ee_a_b @ ( produc3542686128043086370ee_a_b @ B @ C ) @ ( bNF_Gr8527051253158669397ee_a_b @ A5 @ F2 @ G2 ) ) ) ) ) ).

% image2_eqI
thf(fact_610_empty__Collect__eq,axiom,
    ! [P2: produc4558475209616630778_a_b_b > $o] :
      ( ( bot_bo3721250822024684356_a_b_b
        = ( collec1368399972772960719_a_b_b @ P2 ) )
      = ( ! [X: produc4558475209616630778_a_b_b] :
            ~ ( P2 @ X ) ) ) ).

% empty_Collect_eq
thf(fact_611_empty__Collect__eq,axiom,
    ! [P2: product_unit > $o] :
      ( ( bot_bo3957492148770167129t_unit
        = ( collect_Product_unit @ P2 ) )
      = ( ! [X: product_unit] :
            ~ ( P2 @ X ) ) ) ).

% empty_Collect_eq
thf(fact_612_empty__Collect__eq,axiom,
    ! [P2: nat > $o] :
      ( ( bot_bot_set_nat
        = ( collect_nat @ P2 ) )
      = ( ! [X: nat] :
            ~ ( P2 @ X ) ) ) ).

% empty_Collect_eq
thf(fact_613_empty__Collect__eq,axiom,
    ! [P2: b > $o] :
      ( ( bot_bot_set_b
        = ( collect_b @ P2 ) )
      = ( ! [X: b] :
            ~ ( P2 @ X ) ) ) ).

% empty_Collect_eq
thf(fact_614_empty__Collect__eq,axiom,
    ! [P2: a > $o] :
      ( ( bot_bot_set_a
        = ( collect_a @ P2 ) )
      = ( ! [X: a] :
            ~ ( P2 @ X ) ) ) ).

% empty_Collect_eq
thf(fact_615_Collect__empty__eq,axiom,
    ! [P2: produc4558475209616630778_a_b_b > $o] :
      ( ( ( collec1368399972772960719_a_b_b @ P2 )
        = bot_bo3721250822024684356_a_b_b )
      = ( ! [X: produc4558475209616630778_a_b_b] :
            ~ ( P2 @ X ) ) ) ).

% Collect_empty_eq
thf(fact_616_Collect__empty__eq,axiom,
    ! [P2: product_unit > $o] :
      ( ( ( collect_Product_unit @ P2 )
        = bot_bo3957492148770167129t_unit )
      = ( ! [X: product_unit] :
            ~ ( P2 @ X ) ) ) ).

% Collect_empty_eq
thf(fact_617_Collect__empty__eq,axiom,
    ! [P2: nat > $o] :
      ( ( ( collect_nat @ P2 )
        = bot_bot_set_nat )
      = ( ! [X: nat] :
            ~ ( P2 @ X ) ) ) ).

% Collect_empty_eq
thf(fact_618_Collect__empty__eq,axiom,
    ! [P2: b > $o] :
      ( ( ( collect_b @ P2 )
        = bot_bot_set_b )
      = ( ! [X: b] :
            ~ ( P2 @ X ) ) ) ).

% Collect_empty_eq
thf(fact_619_Collect__empty__eq,axiom,
    ! [P2: a > $o] :
      ( ( ( collect_a @ P2 )
        = bot_bot_set_a )
      = ( ! [X: a] :
            ~ ( P2 @ X ) ) ) ).

% Collect_empty_eq
thf(fact_620_all__not__in__conv,axiom,
    ! [A5: set_se3183138701204633190_a_b_b] :
      ( ( ! [X: set_Pr3012420139608375472_a_b_b] :
            ~ ( member7431159781899395911_a_b_b @ X @ A5 ) )
      = ( A5 = bot_bo2537099559385417978_a_b_b ) ) ).

% all_not_in_conv
thf(fact_621_all__not__in__conv,axiom,
    ! [A5: set_b_a] :
      ( ( ! [X: b > a] :
            ~ ( member_b_a @ X @ A5 ) )
      = ( A5 = bot_bot_set_b_a ) ) ).

% all_not_in_conv
thf(fact_622_all__not__in__conv,axiom,
    ! [A5: set_nat] :
      ( ( ! [X: nat] :
            ~ ( member_nat @ X @ A5 ) )
      = ( A5 = bot_bot_set_nat ) ) ).

% all_not_in_conv
thf(fact_623_all__not__in__conv,axiom,
    ! [A5: set_b] :
      ( ( ! [X: b] :
            ~ ( member_b @ X @ A5 ) )
      = ( A5 = bot_bot_set_b ) ) ).

% all_not_in_conv
thf(fact_624_all__not__in__conv,axiom,
    ! [A5: set_a] :
      ( ( ! [X: a] :
            ~ ( member_a @ X @ A5 ) )
      = ( A5 = bot_bot_set_a ) ) ).

% all_not_in_conv
thf(fact_625_all__not__in__conv,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b] :
      ( ( ! [X: produc4558475209616630778_a_b_b] :
            ~ ( member4380921116106875537_a_b_b @ X @ A5 ) )
      = ( A5 = bot_bo3721250822024684356_a_b_b ) ) ).

% all_not_in_conv
thf(fact_626_empty__iff,axiom,
    ! [C: set_Pr3012420139608375472_a_b_b] :
      ~ ( member7431159781899395911_a_b_b @ C @ bot_bo2537099559385417978_a_b_b ) ).

% empty_iff
thf(fact_627_empty__iff,axiom,
    ! [C: b > a] :
      ~ ( member_b_a @ C @ bot_bot_set_b_a ) ).

% empty_iff
thf(fact_628_empty__iff,axiom,
    ! [C: nat] :
      ~ ( member_nat @ C @ bot_bot_set_nat ) ).

% empty_iff
thf(fact_629_empty__iff,axiom,
    ! [C: b] :
      ~ ( member_b @ C @ bot_bot_set_b ) ).

% empty_iff
thf(fact_630_empty__iff,axiom,
    ! [C: a] :
      ~ ( member_a @ C @ bot_bot_set_a ) ).

% empty_iff
thf(fact_631_empty__iff,axiom,
    ! [C: produc4558475209616630778_a_b_b] :
      ~ ( member4380921116106875537_a_b_b @ C @ bot_bo3721250822024684356_a_b_b ) ).

% empty_iff
thf(fact_632_IntI,axiom,
    ! [C: set_Pr3012420139608375472_a_b_b,A5: set_se3183138701204633190_a_b_b,B5: set_se3183138701204633190_a_b_b] :
      ( ( member7431159781899395911_a_b_b @ C @ A5 )
     => ( ( member7431159781899395911_a_b_b @ C @ B5 )
       => ( member7431159781899395911_a_b_b @ C @ ( inf_in3779707751953380600_a_b_b @ A5 @ B5 ) ) ) ) ).

% IntI
thf(fact_633_IntI,axiom,
    ! [C: nat,A5: set_nat,B5: set_nat] :
      ( ( member_nat @ C @ A5 )
     => ( ( member_nat @ C @ B5 )
       => ( member_nat @ C @ ( inf_inf_set_nat @ A5 @ B5 ) ) ) ) ).

% IntI
thf(fact_634_IntI,axiom,
    ! [C: b > a,A5: set_b_a,B5: set_b_a] :
      ( ( member_b_a @ C @ A5 )
     => ( ( member_b_a @ C @ B5 )
       => ( member_b_a @ C @ ( inf_inf_set_b_a @ A5 @ B5 ) ) ) ) ).

% IntI
thf(fact_635_IntI,axiom,
    ! [C: b,A5: set_b,B5: set_b] :
      ( ( member_b @ C @ A5 )
     => ( ( member_b @ C @ B5 )
       => ( member_b @ C @ ( inf_inf_set_b @ A5 @ B5 ) ) ) ) ).

% IntI
thf(fact_636_IntI,axiom,
    ! [C: product_unit,A5: set_Product_unit,B5: set_Product_unit] :
      ( ( member_Product_unit @ C @ A5 )
     => ( ( member_Product_unit @ C @ B5 )
       => ( member_Product_unit @ C @ ( inf_in4660618365625256667t_unit @ A5 @ B5 ) ) ) ) ).

% IntI
thf(fact_637_IntI,axiom,
    ! [C: a,A5: set_a,B5: set_a] :
      ( ( member_a @ C @ A5 )
     => ( ( member_a @ C @ B5 )
       => ( member_a @ C @ ( inf_inf_set_a @ A5 @ B5 ) ) ) ) ).

% IntI
thf(fact_638_IntI,axiom,
    ! [C: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ A5 )
     => ( ( member4380921116106875537_a_b_b @ C @ B5 )
       => ( member4380921116106875537_a_b_b @ C @ ( inf_in6138156342456174402_a_b_b @ A5 @ B5 ) ) ) ) ).

% IntI
thf(fact_639_Int__iff,axiom,
    ! [C: set_Pr3012420139608375472_a_b_b,A5: set_se3183138701204633190_a_b_b,B5: set_se3183138701204633190_a_b_b] :
      ( ( member7431159781899395911_a_b_b @ C @ ( inf_in3779707751953380600_a_b_b @ A5 @ B5 ) )
      = ( ( member7431159781899395911_a_b_b @ C @ A5 )
        & ( member7431159781899395911_a_b_b @ C @ B5 ) ) ) ).

% Int_iff
thf(fact_640_Int__iff,axiom,
    ! [C: nat,A5: set_nat,B5: set_nat] :
      ( ( member_nat @ C @ ( inf_inf_set_nat @ A5 @ B5 ) )
      = ( ( member_nat @ C @ A5 )
        & ( member_nat @ C @ B5 ) ) ) ).

% Int_iff
thf(fact_641_Int__iff,axiom,
    ! [C: b > a,A5: set_b_a,B5: set_b_a] :
      ( ( member_b_a @ C @ ( inf_inf_set_b_a @ A5 @ B5 ) )
      = ( ( member_b_a @ C @ A5 )
        & ( member_b_a @ C @ B5 ) ) ) ).

% Int_iff
thf(fact_642_Int__iff,axiom,
    ! [C: b,A5: set_b,B5: set_b] :
      ( ( member_b @ C @ ( inf_inf_set_b @ A5 @ B5 ) )
      = ( ( member_b @ C @ A5 )
        & ( member_b @ C @ B5 ) ) ) ).

% Int_iff
thf(fact_643_Int__iff,axiom,
    ! [C: product_unit,A5: set_Product_unit,B5: set_Product_unit] :
      ( ( member_Product_unit @ C @ ( inf_in4660618365625256667t_unit @ A5 @ B5 ) )
      = ( ( member_Product_unit @ C @ A5 )
        & ( member_Product_unit @ C @ B5 ) ) ) ).

% Int_iff
thf(fact_644_Int__iff,axiom,
    ! [C: a,A5: set_a,B5: set_a] :
      ( ( member_a @ C @ ( inf_inf_set_a @ A5 @ B5 ) )
      = ( ( member_a @ C @ A5 )
        & ( member_a @ C @ B5 ) ) ) ).

% Int_iff
thf(fact_645_Int__iff,axiom,
    ! [C: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ ( inf_in6138156342456174402_a_b_b @ A5 @ B5 ) )
      = ( ( member4380921116106875537_a_b_b @ C @ A5 )
        & ( member4380921116106875537_a_b_b @ C @ B5 ) ) ) ).

% Int_iff
thf(fact_646_Int__UNIV,axiom,
    ! [A5: set_b,B5: set_b] :
      ( ( ( inf_inf_set_b @ A5 @ B5 )
        = top_top_set_b )
      = ( ( A5 = top_top_set_b )
        & ( B5 = top_top_set_b ) ) ) ).

% Int_UNIV
thf(fact_647_Int__UNIV,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ( ( inf_in6138156342456174402_a_b_b @ A5 @ B5 )
        = top_to7222684678772277088_a_b_b )
      = ( ( A5 = top_to7222684678772277088_a_b_b )
        & ( B5 = top_to7222684678772277088_a_b_b ) ) ) ).

% Int_UNIV
thf(fact_648_Int__UNIV,axiom,
    ! [A5: set_a,B5: set_a] :
      ( ( ( inf_inf_set_a @ A5 @ B5 )
        = top_top_set_a )
      = ( ( A5 = top_top_set_a )
        & ( B5 = top_top_set_a ) ) ) ).

% Int_UNIV
thf(fact_649_Int__UNIV,axiom,
    ! [A5: set_Su4110612849109743515t_unit,B5: set_Su4110612849109743515t_unit] :
      ( ( ( inf_in5198890673353021997t_unit @ A5 @ B5 )
        = top_to2771918933716375115t_unit )
      = ( ( A5 = top_to2771918933716375115t_unit )
        & ( B5 = top_to2771918933716375115t_unit ) ) ) ).

% Int_UNIV
thf(fact_650_Int__UNIV,axiom,
    ! [A5: set_set_Product_unit,B5: set_set_Product_unit] :
      ( ( ( inf_in2608933832725608379t_unit @ A5 @ B5 )
        = top_to1767297665138865437t_unit )
      = ( ( A5 = top_to1767297665138865437t_unit )
        & ( B5 = top_to1767297665138865437t_unit ) ) ) ).

% Int_UNIV
thf(fact_651_Int__UNIV,axiom,
    ! [A5: set_b_a,B5: set_b_a] :
      ( ( ( inf_inf_set_b_a @ A5 @ B5 )
        = top_top_set_b_a )
      = ( ( A5 = top_top_set_b_a )
        & ( B5 = top_top_set_b_a ) ) ) ).

% Int_UNIV
thf(fact_652_Int__UNIV,axiom,
    ! [A5: set_Product_unit,B5: set_Product_unit] :
      ( ( ( inf_in4660618365625256667t_unit @ A5 @ B5 )
        = top_to1996260823553986621t_unit )
      = ( ( A5 = top_to1996260823553986621t_unit )
        & ( B5 = top_to1996260823553986621t_unit ) ) ) ).

% Int_UNIV
thf(fact_653_top__fset_Orep__eq,axiom,
    ( ( fset_S3230643823001711158t_unit @ top_to5791472215405926981t_unit )
    = top_to2771918933716375115t_unit ) ).

% top_fset.rep_eq
thf(fact_654_top__fset_Orep__eq,axiom,
    ( ( fset_s6820437950863159900t_unit @ top_to971128490267878819t_unit )
    = top_to1767297665138865437t_unit ) ).

% top_fset.rep_eq
thf(fact_655_top__fset_Orep__eq,axiom,
    ( ( fset_Product_unit2 @ top_to4734357443822147779t_unit )
    = top_to1996260823553986621t_unit ) ).

% top_fset.rep_eq
thf(fact_656_map__prod__simp,axiom,
    ! [F2: dtree_a_b > dtree_a_b,G2: b > b,A: dtree_a_b,B: b] :
      ( ( produc2024282846164127276_b_b_b @ F2 @ G2 @ ( produc331601717337510060_a_b_b @ A @ B ) )
      = ( produc331601717337510060_a_b_b @ ( F2 @ A ) @ ( G2 @ B ) ) ) ).

% map_prod_simp
thf(fact_657_map__prod__simp,axiom,
    ! [F2: product_unit > product_unit,G2: product_unit > product_unit,A: product_unit,B: product_unit] :
      ( ( produc3941737999988548470t_unit @ F2 @ G2 @ ( produc5692694829384537815t_unit @ A @ B ) )
      = ( produc5692694829384537815t_unit @ ( F2 @ A ) @ ( G2 @ B ) ) ) ).

% map_prod_simp
thf(fact_658_map__prod__simp,axiom,
    ! [F2: dtree_a_b > product_unit,G2: b > product_unit,A: dtree_a_b,B: b] :
      ( ( produc7457737578077058409t_unit @ F2 @ G2 @ ( produc331601717337510060_a_b_b @ A @ B ) )
      = ( produc5692694829384537815t_unit @ ( F2 @ A ) @ ( G2 @ B ) ) ) ).

% map_prod_simp
thf(fact_659_map__prod__simp,axiom,
    ! [F2: b > product_unit,G2: dtree_a_b > product_unit,A: b,B: dtree_a_b] :
      ( ( produc4430891178592075597t_unit @ F2 @ G2 @ ( produc3542686128043086370ee_a_b @ A @ B ) )
      = ( produc5692694829384537815t_unit @ ( F2 @ A ) @ ( G2 @ B ) ) ) ).

% map_prod_simp
thf(fact_660_map__prod__simp,axiom,
    ! [F2: product_unit > dtree_a_b,G2: product_unit > b,A: product_unit,B: product_unit] :
      ( ( produc1291885961400238659unit_b @ F2 @ G2 @ ( produc5692694829384537815t_unit @ A @ B ) )
      = ( produc331601717337510060_a_b_b @ ( F2 @ A ) @ ( G2 @ B ) ) ) ).

% map_prod_simp
thf(fact_661_map__prod__simp,axiom,
    ! [F2: product_unit > b,G2: product_unit > dtree_a_b,A: product_unit,B: product_unit] :
      ( ( produc4159773624399151967ee_a_b @ F2 @ G2 @ ( produc5692694829384537815t_unit @ A @ B ) )
      = ( produc3542686128043086370ee_a_b @ ( F2 @ A ) @ ( G2 @ B ) ) ) ).

% map_prod_simp
thf(fact_662_map__prod__simp,axiom,
    ! [F2: dtree_a_b > b,G2: b > dtree_a_b,A: dtree_a_b,B: b] :
      ( ( produc2701657453118314412ee_a_b @ F2 @ G2 @ ( produc331601717337510060_a_b_b @ A @ B ) )
      = ( produc3542686128043086370ee_a_b @ ( F2 @ A ) @ ( G2 @ B ) ) ) ).

% map_prod_simp
thf(fact_663_map__prod__simp,axiom,
    ! [F2: b > dtree_a_b,G2: dtree_a_b > b,A: b,B: dtree_a_b] :
      ( ( produc5995436795640382528_a_b_b @ F2 @ G2 @ ( produc3542686128043086370ee_a_b @ A @ B ) )
      = ( produc331601717337510060_a_b_b @ ( F2 @ A ) @ ( G2 @ B ) ) ) ).

% map_prod_simp
thf(fact_664_map__prod__simp,axiom,
    ! [F2: b > b,G2: dtree_a_b > dtree_a_b,A: b,B: dtree_a_b] :
      ( ( produc4749355648339255596ee_a_b @ F2 @ G2 @ ( produc3542686128043086370ee_a_b @ A @ B ) )
      = ( produc3542686128043086370ee_a_b @ ( F2 @ A ) @ ( G2 @ B ) ) ) ).

% map_prod_simp
thf(fact_665_map__prod__simp,axiom,
    ! [F2: produc4558475209616630778_a_b_b > product_unit,G2: produc4558475209616630778_a_b_b > product_unit,A: produc4558475209616630778_a_b_b,B: produc4558475209616630778_a_b_b] :
      ( ( produc1195185685987334582t_unit @ F2 @ G2 @ ( produc6533307410877503629_a_b_b @ A @ B ) )
      = ( produc5692694829384537815t_unit @ ( F2 @ A ) @ ( G2 @ B ) ) ) ).

% map_prod_simp
thf(fact_666_snd__comp__map__prod,axiom,
    ! [F2: product_unit > product_unit,G2: product_unit > product_unit] :
      ( ( comp_P6212367879010262750t_unit @ produc6786084904866402309t_unit @ ( produc3941737999988548470t_unit @ F2 @ G2 ) )
      = ( comp_P6110245121441952900t_unit @ G2 @ produc6786084904866402309t_unit ) ) ).

% snd_comp_map_prod
thf(fact_667_snd__comp__map__prod,axiom,
    ! [F2: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,G2: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b] :
      ( ( comp_P681776842046273447_a_b_b @ produc8480234286567085243_a_b_b @ ( produc8659143532165282274_a_b_b @ F2 @ G2 ) )
      = ( comp_P3357003996968799036_a_b_b @ G2 @ produc8480234286567085243_a_b_b ) ) ).

% snd_comp_map_prod
thf(fact_668_snd__comp__map__prod,axiom,
    ! [F2: ( b > a ) > b > a,G2: ( b > a ) > b > a] :
      ( ( comp_P8787221310571768189_a_b_a @ product_snd_b_a_b_a @ ( produc1686386052851666058_a_b_a @ F2 @ G2 ) )
      = ( comp_b1410776826426344764_a_b_a @ G2 @ product_snd_b_a_b_a ) ) ).

% snd_comp_map_prod
thf(fact_669_snd__comp__map__prod,axiom,
    ! [F2: dtree_a_b > dtree_a_b,G2: b > b] :
      ( ( comp_P7790946621747331036_a_b_b @ produc5748100250121904638_a_b_b @ ( produc2024282846164127276_b_b_b @ F2 @ G2 ) )
      = ( comp_b4098124895279589661_a_b_b @ G2 @ produc5748100250121904638_a_b_b ) ) ).

% snd_comp_map_prod
thf(fact_670_snd__comp__map__prod,axiom,
    ! [F2: b > dtree_a_b,G2: dtree_a_b > b] :
      ( ( comp_P6702227762116406538ee_a_b @ produc5748100250121904638_a_b_b @ ( produc5995436795640382528_a_b_b @ F2 @ G2 ) )
      = ( comp_d6203929364972369802ee_a_b @ G2 @ produc8959184660827480948ee_a_b ) ) ).

% snd_comp_map_prod
thf(fact_671_snd__comp__map__prod,axiom,
    ! [F2: dtree_a_b > b,G2: b > dtree_a_b] :
      ( ( comp_P5693690220181566849_a_b_b @ produc8959184660827480948ee_a_b @ ( produc2701657453118314412ee_a_b @ F2 @ G2 ) )
      = ( comp_b3128908137006596050_a_b_b @ G2 @ produc5748100250121904638_a_b_b ) ) ).

% snd_comp_map_prod
thf(fact_672_snd__comp__map__prod,axiom,
    ! [F2: b > b,G2: dtree_a_b > dtree_a_b] :
      ( ( comp_P4604971360550642351ee_a_b @ produc8959184660827480948ee_a_b @ ( produc4749355648339255596ee_a_b @ F2 @ G2 ) )
      = ( comp_d8104658743424935169ee_a_b @ G2 @ produc8959184660827480948ee_a_b ) ) ).

% snd_comp_map_prod
thf(fact_673_snd__map__prod,axiom,
    ! [F2: product_unit > product_unit,G2: product_unit > product_unit,X3: produc8459935480633519975t_unit] :
      ( ( produc6786084904866402309t_unit @ ( produc3941737999988548470t_unit @ F2 @ G2 @ X3 ) )
      = ( G2 @ ( produc6786084904866402309t_unit @ X3 ) ) ) ).

% snd_map_prod
thf(fact_674_snd__map__prod,axiom,
    ! [F2: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,G2: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,X3: produc8908337785154950741_a_b_b] :
      ( ( produc8480234286567085243_a_b_b @ ( produc8659143532165282274_a_b_b @ F2 @ G2 @ X3 ) )
      = ( G2 @ ( produc8480234286567085243_a_b_b @ X3 ) ) ) ).

% snd_map_prod
thf(fact_675_snd__map__prod,axiom,
    ! [F2: ( b > a ) > b > a,G2: ( b > a ) > b > a,X3: product_prod_b_a_b_a] :
      ( ( product_snd_b_a_b_a @ ( produc1686386052851666058_a_b_a @ F2 @ G2 @ X3 ) )
      = ( G2 @ ( product_snd_b_a_b_a @ X3 ) ) ) ).

% snd_map_prod
thf(fact_676_snd__map__prod,axiom,
    ! [F2: dtree_a_b > dtree_a_b,G2: b > b,X3: produc4558475209616630778_a_b_b] :
      ( ( produc5748100250121904638_a_b_b @ ( produc2024282846164127276_b_b_b @ F2 @ G2 @ X3 ) )
      = ( G2 @ ( produc5748100250121904638_a_b_b @ X3 ) ) ) ).

% snd_map_prod
thf(fact_677_snd__map__prod,axiom,
    ! [F2: b > dtree_a_b,G2: dtree_a_b > b,X3: produc3469756349985706280ee_a_b] :
      ( ( produc5748100250121904638_a_b_b @ ( produc5995436795640382528_a_b_b @ F2 @ G2 @ X3 ) )
      = ( G2 @ ( produc8959184660827480948ee_a_b @ X3 ) ) ) ).

% snd_map_prod
thf(fact_678_snd__map__prod,axiom,
    ! [F2: dtree_a_b > b,G2: b > dtree_a_b,X3: produc4558475209616630778_a_b_b] :
      ( ( produc8959184660827480948ee_a_b @ ( produc2701657453118314412ee_a_b @ F2 @ G2 @ X3 ) )
      = ( G2 @ ( produc5748100250121904638_a_b_b @ X3 ) ) ) ).

% snd_map_prod
thf(fact_679_snd__map__prod,axiom,
    ! [F2: b > b,G2: dtree_a_b > dtree_a_b,X3: produc3469756349985706280ee_a_b] :
      ( ( produc8959184660827480948ee_a_b @ ( produc4749355648339255596ee_a_b @ F2 @ G2 @ X3 ) )
      = ( G2 @ ( produc8959184660827480948ee_a_b @ X3 ) ) ) ).

% snd_map_prod
thf(fact_680_snd__comp__apsnd,axiom,
    ! [F2: b > b] :
      ( ( comp_P7790946621747331036_a_b_b @ produc5748100250121904638_a_b_b @ ( produc7811666328248579896ee_a_b @ F2 ) )
      = ( comp_b4098124895279589661_a_b_b @ F2 @ produc5748100250121904638_a_b_b ) ) ).

% snd_comp_apsnd
thf(fact_681_snd__comp__apsnd,axiom,
    ! [F2: dtree_a_b > dtree_a_b] :
      ( ( comp_P4604971360550642351ee_a_b @ produc8959184660827480948ee_a_b @ ( produc3383614106744390411_a_b_b @ F2 ) )
      = ( comp_d8104658743424935169ee_a_b @ F2 @ produc8959184660827480948ee_a_b ) ) ).

% snd_comp_apsnd
thf(fact_682_snd__apsnd,axiom,
    ! [F2: b > b,X3: produc4558475209616630778_a_b_b] :
      ( ( produc5748100250121904638_a_b_b @ ( produc7811666328248579896ee_a_b @ F2 @ X3 ) )
      = ( F2 @ ( produc5748100250121904638_a_b_b @ X3 ) ) ) ).

% snd_apsnd
thf(fact_683_snd__apsnd,axiom,
    ! [F2: dtree_a_b > dtree_a_b,X3: produc3469756349985706280ee_a_b] :
      ( ( produc8959184660827480948ee_a_b @ ( produc3383614106744390411_a_b_b @ F2 @ X3 ) )
      = ( F2 @ ( produc8959184660827480948ee_a_b @ X3 ) ) ) ).

% snd_apsnd
thf(fact_684_apsnd__eq__conv,axiom,
    ! [F2: b > b,X3: produc4558475209616630778_a_b_b,G2: b > b] :
      ( ( ( produc7811666328248579896ee_a_b @ F2 @ X3 )
        = ( produc7811666328248579896ee_a_b @ G2 @ X3 ) )
      = ( ( F2 @ ( produc5748100250121904638_a_b_b @ X3 ) )
        = ( G2 @ ( produc5748100250121904638_a_b_b @ X3 ) ) ) ) ).

% apsnd_eq_conv
thf(fact_685_map__prod__imageI,axiom,
    ! [A: dtree_a_b,B: b,R3: set_Pr3012420139608375472_a_b_b,F2: dtree_a_b > dtree_a_b,G2: b > b] :
      ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ A @ B ) @ R3 )
     => ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ ( F2 @ A ) @ ( G2 @ B ) ) @ ( image_6081965176830705659_a_b_b @ ( produc2024282846164127276_b_b_b @ F2 @ G2 ) @ R3 ) ) ) ).

% map_prod_imageI
thf(fact_686_map__prod__imageI,axiom,
    ! [A: product_unit,B: product_unit,R3: set_Pr5094982260447487303t_unit,F2: product_unit > product_unit,G2: product_unit > product_unit] :
      ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ A @ B ) @ R3 )
     => ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ ( F2 @ A ) @ ( G2 @ B ) ) @ ( image_9149991759805673413t_unit @ ( produc3941737999988548470t_unit @ F2 @ G2 ) @ R3 ) ) ) ).

% map_prod_imageI
thf(fact_687_map__prod__imageI,axiom,
    ! [A: dtree_a_b,B: b,R3: set_Pr3012420139608375472_a_b_b,F2: dtree_a_b > product_unit,G2: b > product_unit] :
      ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ A @ B ) @ R3 )
     => ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ ( F2 @ A ) @ ( G2 @ B ) ) @ ( image_4150594470010877606t_unit @ ( produc7457737578077058409t_unit @ F2 @ G2 ) @ R3 ) ) ) ).

% map_prod_imageI
thf(fact_688_map__prod__imageI,axiom,
    ! [A: b,B: dtree_a_b,R3: set_Pr6717515126349854430ee_a_b,F2: b > product_unit,G2: dtree_a_b > product_unit] :
      ( ( member3292202256475951039ee_a_b @ ( produc3542686128043086370ee_a_b @ A @ B ) @ R3 )
     => ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ ( F2 @ A ) @ ( G2 @ B ) ) @ ( image_198770111635725048t_unit @ ( produc4430891178592075597t_unit @ F2 @ G2 ) @ R3 ) ) ) ).

% map_prod_imageI
thf(fact_689_map__prod__imageI,axiom,
    ! [A: product_unit,B: product_unit,R3: set_Pr5094982260447487303t_unit,F2: product_unit > dtree_a_b,G2: product_unit > b] :
      ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ A @ B ) @ R3 )
     => ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ ( F2 @ A ) @ ( G2 @ B ) ) @ ( image_4720867526043783708_a_b_b @ ( produc1291885961400238659unit_b @ F2 @ G2 ) @ R3 ) ) ) ).

% map_prod_imageI
thf(fact_690_map__prod__imageI,axiom,
    ! [A: product_unit,B: product_unit,R3: set_Pr5094982260447487303t_unit,F2: product_unit > b,G2: product_unit > dtree_a_b] :
      ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ A @ B ) @ R3 )
     => ( member3292202256475951039ee_a_b @ ( produc3542686128043086370ee_a_b @ ( F2 @ A ) @ ( G2 @ B ) ) @ ( image_3632148666412859210ee_a_b @ ( produc4159773624399151967ee_a_b @ F2 @ G2 ) @ R3 ) ) ) ).

% map_prod_imageI
thf(fact_691_map__prod__imageI,axiom,
    ! [A: dtree_a_b,B: b,R3: set_Pr3012420139608375472_a_b_b,F2: dtree_a_b > b,G2: b > dtree_a_b] :
      ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ A @ B ) @ R3 )
     => ( member3292202256475951039ee_a_b @ ( produc3542686128043086370ee_a_b @ ( F2 @ A ) @ ( G2 @ B ) ) @ ( image_4993246317199781161ee_a_b @ ( produc2701657453118314412ee_a_b @ F2 @ G2 ) @ R3 ) ) ) ).

% map_prod_imageI
thf(fact_692_map__prod__imageI,axiom,
    ! [A: b,B: dtree_a_b,R3: set_Pr6717515126349854430ee_a_b,F2: b > dtree_a_b,G2: dtree_a_b > b] :
      ( ( member3292202256475951039ee_a_b @ ( produc3542686128043086370ee_a_b @ A @ B ) @ R3 )
     => ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ ( F2 @ A ) @ ( G2 @ B ) ) @ ( image_3585698774939316521_a_b_b @ ( produc5995436795640382528_a_b_b @ F2 @ G2 ) @ R3 ) ) ) ).

% map_prod_imageI
thf(fact_693_map__prod__imageI,axiom,
    ! [A: b,B: dtree_a_b,R3: set_Pr6717515126349854430ee_a_b,F2: b > b,G2: dtree_a_b > dtree_a_b] :
      ( ( member3292202256475951039ee_a_b @ ( produc3542686128043086370ee_a_b @ A @ B ) @ R3 )
     => ( member3292202256475951039ee_a_b @ ( produc3542686128043086370ee_a_b @ ( F2 @ A ) @ ( G2 @ B ) ) @ ( image_2496979915308392023ee_a_b @ ( produc4749355648339255596ee_a_b @ F2 @ G2 ) @ R3 ) ) ) ).

% map_prod_imageI
thf(fact_694_map__prod__imageI,axiom,
    ! [A: produc4558475209616630778_a_b_b,B: produc4558475209616630778_a_b_b,R3: set_Pr2755428042910921141_a_b_b,F2: produc4558475209616630778_a_b_b > product_unit,G2: produc4558475209616630778_a_b_b > product_unit] :
      ( ( member9171970031259705598_a_b_b @ ( produc6533307410877503629_a_b_b @ A @ B ) @ R3 )
     => ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ ( F2 @ A ) @ ( G2 @ B ) ) @ ( image_7356924584417892695t_unit @ ( produc1195185685987334582t_unit @ F2 @ G2 ) @ R3 ) ) ) ).

% map_prod_imageI
thf(fact_695_disjoint__iff__not__equal,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ( ( inf_in6138156342456174402_a_b_b @ A5 @ B5 )
        = bot_bo3721250822024684356_a_b_b )
      = ( ! [X: produc4558475209616630778_a_b_b] :
            ( ( member4380921116106875537_a_b_b @ X @ A5 )
           => ! [Y: produc4558475209616630778_a_b_b] :
                ( ( member4380921116106875537_a_b_b @ Y @ B5 )
               => ( X != Y ) ) ) ) ) ).

% disjoint_iff_not_equal
thf(fact_696_disjoint__iff__not__equal,axiom,
    ! [A5: set_Product_unit,B5: set_Product_unit] :
      ( ( ( inf_in4660618365625256667t_unit @ A5 @ B5 )
        = bot_bo3957492148770167129t_unit )
      = ( ! [X: product_unit] :
            ( ( member_Product_unit @ X @ A5 )
           => ! [Y: product_unit] :
                ( ( member_Product_unit @ Y @ B5 )
               => ( X != Y ) ) ) ) ) ).

% disjoint_iff_not_equal
thf(fact_697_disjoint__iff__not__equal,axiom,
    ! [A5: set_nat,B5: set_nat] :
      ( ( ( inf_inf_set_nat @ A5 @ B5 )
        = bot_bot_set_nat )
      = ( ! [X: nat] :
            ( ( member_nat @ X @ A5 )
           => ! [Y: nat] :
                ( ( member_nat @ Y @ B5 )
               => ( X != Y ) ) ) ) ) ).

% disjoint_iff_not_equal
thf(fact_698_disjoint__iff__not__equal,axiom,
    ! [A5: set_b,B5: set_b] :
      ( ( ( inf_inf_set_b @ A5 @ B5 )
        = bot_bot_set_b )
      = ( ! [X: b] :
            ( ( member_b @ X @ A5 )
           => ! [Y: b] :
                ( ( member_b @ Y @ B5 )
               => ( X != Y ) ) ) ) ) ).

% disjoint_iff_not_equal
thf(fact_699_disjoint__iff__not__equal,axiom,
    ! [A5: set_a,B5: set_a] :
      ( ( ( inf_inf_set_a @ A5 @ B5 )
        = bot_bot_set_a )
      = ( ! [X: a] :
            ( ( member_a @ X @ A5 )
           => ! [Y: a] :
                ( ( member_a @ Y @ B5 )
               => ( X != Y ) ) ) ) ) ).

% disjoint_iff_not_equal
thf(fact_700_Int__empty__right,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b] :
      ( ( inf_in6138156342456174402_a_b_b @ A5 @ bot_bo3721250822024684356_a_b_b )
      = bot_bo3721250822024684356_a_b_b ) ).

% Int_empty_right
thf(fact_701_Int__empty__right,axiom,
    ! [A5: set_Product_unit] :
      ( ( inf_in4660618365625256667t_unit @ A5 @ bot_bo3957492148770167129t_unit )
      = bot_bo3957492148770167129t_unit ) ).

% Int_empty_right
thf(fact_702_Int__empty__right,axiom,
    ! [A5: set_nat] :
      ( ( inf_inf_set_nat @ A5 @ bot_bot_set_nat )
      = bot_bot_set_nat ) ).

% Int_empty_right
thf(fact_703_Int__empty__right,axiom,
    ! [A5: set_b] :
      ( ( inf_inf_set_b @ A5 @ bot_bot_set_b )
      = bot_bot_set_b ) ).

% Int_empty_right
thf(fact_704_Int__empty__right,axiom,
    ! [A5: set_a] :
      ( ( inf_inf_set_a @ A5 @ bot_bot_set_a )
      = bot_bot_set_a ) ).

% Int_empty_right
thf(fact_705_Int__empty__left,axiom,
    ! [B5: set_Pr3012420139608375472_a_b_b] :
      ( ( inf_in6138156342456174402_a_b_b @ bot_bo3721250822024684356_a_b_b @ B5 )
      = bot_bo3721250822024684356_a_b_b ) ).

% Int_empty_left
thf(fact_706_Int__empty__left,axiom,
    ! [B5: set_Product_unit] :
      ( ( inf_in4660618365625256667t_unit @ bot_bo3957492148770167129t_unit @ B5 )
      = bot_bo3957492148770167129t_unit ) ).

% Int_empty_left
thf(fact_707_Int__empty__left,axiom,
    ! [B5: set_nat] :
      ( ( inf_inf_set_nat @ bot_bot_set_nat @ B5 )
      = bot_bot_set_nat ) ).

% Int_empty_left
thf(fact_708_Int__empty__left,axiom,
    ! [B5: set_b] :
      ( ( inf_inf_set_b @ bot_bot_set_b @ B5 )
      = bot_bot_set_b ) ).

% Int_empty_left
thf(fact_709_Int__empty__left,axiom,
    ! [B5: set_a] :
      ( ( inf_inf_set_a @ bot_bot_set_a @ B5 )
      = bot_bot_set_a ) ).

% Int_empty_left
thf(fact_710_disjoint__iff,axiom,
    ! [A5: set_se3183138701204633190_a_b_b,B5: set_se3183138701204633190_a_b_b] :
      ( ( ( inf_in3779707751953380600_a_b_b @ A5 @ B5 )
        = bot_bo2537099559385417978_a_b_b )
      = ( ! [X: set_Pr3012420139608375472_a_b_b] :
            ( ( member7431159781899395911_a_b_b @ X @ A5 )
           => ~ ( member7431159781899395911_a_b_b @ X @ B5 ) ) ) ) ).

% disjoint_iff
thf(fact_711_disjoint__iff,axiom,
    ! [A5: set_b_a,B5: set_b_a] :
      ( ( ( inf_inf_set_b_a @ A5 @ B5 )
        = bot_bot_set_b_a )
      = ( ! [X: b > a] :
            ( ( member_b_a @ X @ A5 )
           => ~ ( member_b_a @ X @ B5 ) ) ) ) ).

% disjoint_iff
thf(fact_712_disjoint__iff,axiom,
    ! [A5: set_Product_unit,B5: set_Product_unit] :
      ( ( ( inf_in4660618365625256667t_unit @ A5 @ B5 )
        = bot_bo3957492148770167129t_unit )
      = ( ! [X: product_unit] :
            ( ( member_Product_unit @ X @ A5 )
           => ~ ( member_Product_unit @ X @ B5 ) ) ) ) ).

% disjoint_iff
thf(fact_713_disjoint__iff,axiom,
    ! [A5: set_nat,B5: set_nat] :
      ( ( ( inf_inf_set_nat @ A5 @ B5 )
        = bot_bot_set_nat )
      = ( ! [X: nat] :
            ( ( member_nat @ X @ A5 )
           => ~ ( member_nat @ X @ B5 ) ) ) ) ).

% disjoint_iff
thf(fact_714_disjoint__iff,axiom,
    ! [A5: set_b,B5: set_b] :
      ( ( ( inf_inf_set_b @ A5 @ B5 )
        = bot_bot_set_b )
      = ( ! [X: b] :
            ( ( member_b @ X @ A5 )
           => ~ ( member_b @ X @ B5 ) ) ) ) ).

% disjoint_iff
thf(fact_715_disjoint__iff,axiom,
    ! [A5: set_a,B5: set_a] :
      ( ( ( inf_inf_set_a @ A5 @ B5 )
        = bot_bot_set_a )
      = ( ! [X: a] :
            ( ( member_a @ X @ A5 )
           => ~ ( member_a @ X @ B5 ) ) ) ) ).

% disjoint_iff
thf(fact_716_disjoint__iff,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ( ( inf_in6138156342456174402_a_b_b @ A5 @ B5 )
        = bot_bo3721250822024684356_a_b_b )
      = ( ! [X: produc4558475209616630778_a_b_b] :
            ( ( member4380921116106875537_a_b_b @ X @ A5 )
           => ~ ( member4380921116106875537_a_b_b @ X @ B5 ) ) ) ) ).

% disjoint_iff
thf(fact_717_bot__set__def,axiom,
    ( bot_bo3957492148770167129t_unit
    = ( collect_Product_unit @ bot_bo4642748612307482820unit_o ) ) ).

% bot_set_def
thf(fact_718_bot__set__def,axiom,
    ( bot_bo3721250822024684356_a_b_b
    = ( collec1368399972772960719_a_b_b @ bot_bo7321339186913516097_b_b_o ) ) ).

% bot_set_def
thf(fact_719_bot__set__def,axiom,
    ( bot_bot_set_nat
    = ( collect_nat @ bot_bot_nat_o ) ) ).

% bot_set_def
thf(fact_720_bot__set__def,axiom,
    ( bot_bot_set_b
    = ( collect_b @ bot_bot_b_o ) ) ).

% bot_set_def
thf(fact_721_bot__set__def,axiom,
    ( bot_bot_set_a
    = ( collect_a @ bot_bot_a_o ) ) ).

% bot_set_def
thf(fact_722_ex__in__conv,axiom,
    ! [A5: set_se3183138701204633190_a_b_b] :
      ( ( ? [X: set_Pr3012420139608375472_a_b_b] : ( member7431159781899395911_a_b_b @ X @ A5 ) )
      = ( A5 != bot_bo2537099559385417978_a_b_b ) ) ).

% ex_in_conv
thf(fact_723_ex__in__conv,axiom,
    ! [A5: set_b_a] :
      ( ( ? [X: b > a] : ( member_b_a @ X @ A5 ) )
      = ( A5 != bot_bot_set_b_a ) ) ).

% ex_in_conv
thf(fact_724_ex__in__conv,axiom,
    ! [A5: set_nat] :
      ( ( ? [X: nat] : ( member_nat @ X @ A5 ) )
      = ( A5 != bot_bot_set_nat ) ) ).

% ex_in_conv
thf(fact_725_ex__in__conv,axiom,
    ! [A5: set_b] :
      ( ( ? [X: b] : ( member_b @ X @ A5 ) )
      = ( A5 != bot_bot_set_b ) ) ).

% ex_in_conv
thf(fact_726_ex__in__conv,axiom,
    ! [A5: set_a] :
      ( ( ? [X: a] : ( member_a @ X @ A5 ) )
      = ( A5 != bot_bot_set_a ) ) ).

% ex_in_conv
thf(fact_727_ex__in__conv,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b] :
      ( ( ? [X: produc4558475209616630778_a_b_b] : ( member4380921116106875537_a_b_b @ X @ A5 ) )
      = ( A5 != bot_bo3721250822024684356_a_b_b ) ) ).

% ex_in_conv
thf(fact_728_Int__emptyI,axiom,
    ! [A5: set_se3183138701204633190_a_b_b,B5: set_se3183138701204633190_a_b_b] :
      ( ! [X5: set_Pr3012420139608375472_a_b_b] :
          ( ( member7431159781899395911_a_b_b @ X5 @ A5 )
         => ~ ( member7431159781899395911_a_b_b @ X5 @ B5 ) )
     => ( ( inf_in3779707751953380600_a_b_b @ A5 @ B5 )
        = bot_bo2537099559385417978_a_b_b ) ) ).

% Int_emptyI
thf(fact_729_Int__emptyI,axiom,
    ! [A5: set_b_a,B5: set_b_a] :
      ( ! [X5: b > a] :
          ( ( member_b_a @ X5 @ A5 )
         => ~ ( member_b_a @ X5 @ B5 ) )
     => ( ( inf_inf_set_b_a @ A5 @ B5 )
        = bot_bot_set_b_a ) ) ).

% Int_emptyI
thf(fact_730_Int__emptyI,axiom,
    ! [A5: set_Product_unit,B5: set_Product_unit] :
      ( ! [X5: product_unit] :
          ( ( member_Product_unit @ X5 @ A5 )
         => ~ ( member_Product_unit @ X5 @ B5 ) )
     => ( ( inf_in4660618365625256667t_unit @ A5 @ B5 )
        = bot_bo3957492148770167129t_unit ) ) ).

% Int_emptyI
thf(fact_731_Int__emptyI,axiom,
    ! [A5: set_nat,B5: set_nat] :
      ( ! [X5: nat] :
          ( ( member_nat @ X5 @ A5 )
         => ~ ( member_nat @ X5 @ B5 ) )
     => ( ( inf_inf_set_nat @ A5 @ B5 )
        = bot_bot_set_nat ) ) ).

% Int_emptyI
thf(fact_732_Int__emptyI,axiom,
    ! [A5: set_b,B5: set_b] :
      ( ! [X5: b] :
          ( ( member_b @ X5 @ A5 )
         => ~ ( member_b @ X5 @ B5 ) )
     => ( ( inf_inf_set_b @ A5 @ B5 )
        = bot_bot_set_b ) ) ).

% Int_emptyI
thf(fact_733_Int__emptyI,axiom,
    ! [A5: set_a,B5: set_a] :
      ( ! [X5: a] :
          ( ( member_a @ X5 @ A5 )
         => ~ ( member_a @ X5 @ B5 ) )
     => ( ( inf_inf_set_a @ A5 @ B5 )
        = bot_bot_set_a ) ) ).

% Int_emptyI
thf(fact_734_Int__emptyI,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ! [X5: produc4558475209616630778_a_b_b] :
          ( ( member4380921116106875537_a_b_b @ X5 @ A5 )
         => ~ ( member4380921116106875537_a_b_b @ X5 @ B5 ) )
     => ( ( inf_in6138156342456174402_a_b_b @ A5 @ B5 )
        = bot_bo3721250822024684356_a_b_b ) ) ).

% Int_emptyI
thf(fact_735_equals0I,axiom,
    ! [A5: set_se3183138701204633190_a_b_b] :
      ( ! [Y4: set_Pr3012420139608375472_a_b_b] :
          ~ ( member7431159781899395911_a_b_b @ Y4 @ A5 )
     => ( A5 = bot_bo2537099559385417978_a_b_b ) ) ).

% equals0I
thf(fact_736_equals0I,axiom,
    ! [A5: set_b_a] :
      ( ! [Y4: b > a] :
          ~ ( member_b_a @ Y4 @ A5 )
     => ( A5 = bot_bot_set_b_a ) ) ).

% equals0I
thf(fact_737_equals0I,axiom,
    ! [A5: set_nat] :
      ( ! [Y4: nat] :
          ~ ( member_nat @ Y4 @ A5 )
     => ( A5 = bot_bot_set_nat ) ) ).

% equals0I
thf(fact_738_equals0I,axiom,
    ! [A5: set_b] :
      ( ! [Y4: b] :
          ~ ( member_b @ Y4 @ A5 )
     => ( A5 = bot_bot_set_b ) ) ).

% equals0I
thf(fact_739_equals0I,axiom,
    ! [A5: set_a] :
      ( ! [Y4: a] :
          ~ ( member_a @ Y4 @ A5 )
     => ( A5 = bot_bot_set_a ) ) ).

% equals0I
thf(fact_740_equals0I,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b] :
      ( ! [Y4: produc4558475209616630778_a_b_b] :
          ~ ( member4380921116106875537_a_b_b @ Y4 @ A5 )
     => ( A5 = bot_bo3721250822024684356_a_b_b ) ) ).

% equals0I
thf(fact_741_equals0D,axiom,
    ! [A5: set_se3183138701204633190_a_b_b,A: set_Pr3012420139608375472_a_b_b] :
      ( ( A5 = bot_bo2537099559385417978_a_b_b )
     => ~ ( member7431159781899395911_a_b_b @ A @ A5 ) ) ).

% equals0D
thf(fact_742_equals0D,axiom,
    ! [A5: set_b_a,A: b > a] :
      ( ( A5 = bot_bot_set_b_a )
     => ~ ( member_b_a @ A @ A5 ) ) ).

% equals0D
thf(fact_743_equals0D,axiom,
    ! [A5: set_nat,A: nat] :
      ( ( A5 = bot_bot_set_nat )
     => ~ ( member_nat @ A @ A5 ) ) ).

% equals0D
thf(fact_744_equals0D,axiom,
    ! [A5: set_b,A: b] :
      ( ( A5 = bot_bot_set_b )
     => ~ ( member_b @ A @ A5 ) ) ).

% equals0D
thf(fact_745_equals0D,axiom,
    ! [A5: set_a,A: a] :
      ( ( A5 = bot_bot_set_a )
     => ~ ( member_a @ A @ A5 ) ) ).

% equals0D
thf(fact_746_equals0D,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,A: produc4558475209616630778_a_b_b] :
      ( ( A5 = bot_bo3721250822024684356_a_b_b )
     => ~ ( member4380921116106875537_a_b_b @ A @ A5 ) ) ).

% equals0D
thf(fact_747_emptyE,axiom,
    ! [A: set_Pr3012420139608375472_a_b_b] :
      ~ ( member7431159781899395911_a_b_b @ A @ bot_bo2537099559385417978_a_b_b ) ).

% emptyE
thf(fact_748_emptyE,axiom,
    ! [A: b > a] :
      ~ ( member_b_a @ A @ bot_bot_set_b_a ) ).

% emptyE
thf(fact_749_emptyE,axiom,
    ! [A: nat] :
      ~ ( member_nat @ A @ bot_bot_set_nat ) ).

% emptyE
thf(fact_750_emptyE,axiom,
    ! [A: b] :
      ~ ( member_b @ A @ bot_bot_set_b ) ).

% emptyE
thf(fact_751_emptyE,axiom,
    ! [A: a] :
      ~ ( member_a @ A @ bot_bot_set_a ) ).

% emptyE
thf(fact_752_emptyE,axiom,
    ! [A: produc4558475209616630778_a_b_b] :
      ~ ( member4380921116106875537_a_b_b @ A @ bot_bo3721250822024684356_a_b_b ) ).

% emptyE
thf(fact_753_IntE,axiom,
    ! [C: set_Pr3012420139608375472_a_b_b,A5: set_se3183138701204633190_a_b_b,B5: set_se3183138701204633190_a_b_b] :
      ( ( member7431159781899395911_a_b_b @ C @ ( inf_in3779707751953380600_a_b_b @ A5 @ B5 ) )
     => ~ ( ( member7431159781899395911_a_b_b @ C @ A5 )
         => ~ ( member7431159781899395911_a_b_b @ C @ B5 ) ) ) ).

% IntE
thf(fact_754_IntE,axiom,
    ! [C: nat,A5: set_nat,B5: set_nat] :
      ( ( member_nat @ C @ ( inf_inf_set_nat @ A5 @ B5 ) )
     => ~ ( ( member_nat @ C @ A5 )
         => ~ ( member_nat @ C @ B5 ) ) ) ).

% IntE
thf(fact_755_IntE,axiom,
    ! [C: b > a,A5: set_b_a,B5: set_b_a] :
      ( ( member_b_a @ C @ ( inf_inf_set_b_a @ A5 @ B5 ) )
     => ~ ( ( member_b_a @ C @ A5 )
         => ~ ( member_b_a @ C @ B5 ) ) ) ).

% IntE
thf(fact_756_IntE,axiom,
    ! [C: b,A5: set_b,B5: set_b] :
      ( ( member_b @ C @ ( inf_inf_set_b @ A5 @ B5 ) )
     => ~ ( ( member_b @ C @ A5 )
         => ~ ( member_b @ C @ B5 ) ) ) ).

% IntE
thf(fact_757_IntE,axiom,
    ! [C: product_unit,A5: set_Product_unit,B5: set_Product_unit] :
      ( ( member_Product_unit @ C @ ( inf_in4660618365625256667t_unit @ A5 @ B5 ) )
     => ~ ( ( member_Product_unit @ C @ A5 )
         => ~ ( member_Product_unit @ C @ B5 ) ) ) ).

% IntE
thf(fact_758_IntE,axiom,
    ! [C: a,A5: set_a,B5: set_a] :
      ( ( member_a @ C @ ( inf_inf_set_a @ A5 @ B5 ) )
     => ~ ( ( member_a @ C @ A5 )
         => ~ ( member_a @ C @ B5 ) ) ) ).

% IntE
thf(fact_759_IntE,axiom,
    ! [C: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ ( inf_in6138156342456174402_a_b_b @ A5 @ B5 ) )
     => ~ ( ( member4380921116106875537_a_b_b @ C @ A5 )
         => ~ ( member4380921116106875537_a_b_b @ C @ B5 ) ) ) ).

% IntE
thf(fact_760_IntD1,axiom,
    ! [C: set_Pr3012420139608375472_a_b_b,A5: set_se3183138701204633190_a_b_b,B5: set_se3183138701204633190_a_b_b] :
      ( ( member7431159781899395911_a_b_b @ C @ ( inf_in3779707751953380600_a_b_b @ A5 @ B5 ) )
     => ( member7431159781899395911_a_b_b @ C @ A5 ) ) ).

% IntD1
thf(fact_761_IntD1,axiom,
    ! [C: nat,A5: set_nat,B5: set_nat] :
      ( ( member_nat @ C @ ( inf_inf_set_nat @ A5 @ B5 ) )
     => ( member_nat @ C @ A5 ) ) ).

% IntD1
thf(fact_762_IntD1,axiom,
    ! [C: b > a,A5: set_b_a,B5: set_b_a] :
      ( ( member_b_a @ C @ ( inf_inf_set_b_a @ A5 @ B5 ) )
     => ( member_b_a @ C @ A5 ) ) ).

% IntD1
thf(fact_763_IntD1,axiom,
    ! [C: b,A5: set_b,B5: set_b] :
      ( ( member_b @ C @ ( inf_inf_set_b @ A5 @ B5 ) )
     => ( member_b @ C @ A5 ) ) ).

% IntD1
thf(fact_764_IntD1,axiom,
    ! [C: product_unit,A5: set_Product_unit,B5: set_Product_unit] :
      ( ( member_Product_unit @ C @ ( inf_in4660618365625256667t_unit @ A5 @ B5 ) )
     => ( member_Product_unit @ C @ A5 ) ) ).

% IntD1
thf(fact_765_IntD1,axiom,
    ! [C: a,A5: set_a,B5: set_a] :
      ( ( member_a @ C @ ( inf_inf_set_a @ A5 @ B5 ) )
     => ( member_a @ C @ A5 ) ) ).

% IntD1
thf(fact_766_IntD1,axiom,
    ! [C: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ ( inf_in6138156342456174402_a_b_b @ A5 @ B5 ) )
     => ( member4380921116106875537_a_b_b @ C @ A5 ) ) ).

% IntD1
thf(fact_767_IntD2,axiom,
    ! [C: set_Pr3012420139608375472_a_b_b,A5: set_se3183138701204633190_a_b_b,B5: set_se3183138701204633190_a_b_b] :
      ( ( member7431159781899395911_a_b_b @ C @ ( inf_in3779707751953380600_a_b_b @ A5 @ B5 ) )
     => ( member7431159781899395911_a_b_b @ C @ B5 ) ) ).

% IntD2
thf(fact_768_IntD2,axiom,
    ! [C: nat,A5: set_nat,B5: set_nat] :
      ( ( member_nat @ C @ ( inf_inf_set_nat @ A5 @ B5 ) )
     => ( member_nat @ C @ B5 ) ) ).

% IntD2
thf(fact_769_IntD2,axiom,
    ! [C: b > a,A5: set_b_a,B5: set_b_a] :
      ( ( member_b_a @ C @ ( inf_inf_set_b_a @ A5 @ B5 ) )
     => ( member_b_a @ C @ B5 ) ) ).

% IntD2
thf(fact_770_IntD2,axiom,
    ! [C: b,A5: set_b,B5: set_b] :
      ( ( member_b @ C @ ( inf_inf_set_b @ A5 @ B5 ) )
     => ( member_b @ C @ B5 ) ) ).

% IntD2
thf(fact_771_IntD2,axiom,
    ! [C: product_unit,A5: set_Product_unit,B5: set_Product_unit] :
      ( ( member_Product_unit @ C @ ( inf_in4660618365625256667t_unit @ A5 @ B5 ) )
     => ( member_Product_unit @ C @ B5 ) ) ).

% IntD2
thf(fact_772_IntD2,axiom,
    ! [C: a,A5: set_a,B5: set_a] :
      ( ( member_a @ C @ ( inf_inf_set_a @ A5 @ B5 ) )
     => ( member_a @ C @ B5 ) ) ).

% IntD2
thf(fact_773_IntD2,axiom,
    ! [C: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ ( inf_in6138156342456174402_a_b_b @ A5 @ B5 ) )
     => ( member4380921116106875537_a_b_b @ C @ B5 ) ) ).

% IntD2
thf(fact_774_Int__assoc,axiom,
    ! [A5: set_b,B5: set_b,C3: set_b] :
      ( ( inf_inf_set_b @ ( inf_inf_set_b @ A5 @ B5 ) @ C3 )
      = ( inf_inf_set_b @ A5 @ ( inf_inf_set_b @ B5 @ C3 ) ) ) ).

% Int_assoc
thf(fact_775_Int__assoc,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b,C3: set_Pr3012420139608375472_a_b_b] :
      ( ( inf_in6138156342456174402_a_b_b @ ( inf_in6138156342456174402_a_b_b @ A5 @ B5 ) @ C3 )
      = ( inf_in6138156342456174402_a_b_b @ A5 @ ( inf_in6138156342456174402_a_b_b @ B5 @ C3 ) ) ) ).

% Int_assoc
thf(fact_776_Int__assoc,axiom,
    ! [A5: set_Product_unit,B5: set_Product_unit,C3: set_Product_unit] :
      ( ( inf_in4660618365625256667t_unit @ ( inf_in4660618365625256667t_unit @ A5 @ B5 ) @ C3 )
      = ( inf_in4660618365625256667t_unit @ A5 @ ( inf_in4660618365625256667t_unit @ B5 @ C3 ) ) ) ).

% Int_assoc
thf(fact_777_Int__assoc,axiom,
    ! [A5: set_a,B5: set_a,C3: set_a] :
      ( ( inf_inf_set_a @ ( inf_inf_set_a @ A5 @ B5 ) @ C3 )
      = ( inf_inf_set_a @ A5 @ ( inf_inf_set_a @ B5 @ C3 ) ) ) ).

% Int_assoc
thf(fact_778_Int__absorb,axiom,
    ! [A5: set_b] :
      ( ( inf_inf_set_b @ A5 @ A5 )
      = A5 ) ).

% Int_absorb
thf(fact_779_Int__absorb,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b] :
      ( ( inf_in6138156342456174402_a_b_b @ A5 @ A5 )
      = A5 ) ).

% Int_absorb
thf(fact_780_Int__absorb,axiom,
    ! [A5: set_Product_unit] :
      ( ( inf_in4660618365625256667t_unit @ A5 @ A5 )
      = A5 ) ).

% Int_absorb
thf(fact_781_Int__absorb,axiom,
    ! [A5: set_a] :
      ( ( inf_inf_set_a @ A5 @ A5 )
      = A5 ) ).

% Int_absorb
thf(fact_782_Int__commute,axiom,
    ( inf_inf_set_b
    = ( ^ [A6: set_b,B6: set_b] : ( inf_inf_set_b @ B6 @ A6 ) ) ) ).

% Int_commute
thf(fact_783_Int__commute,axiom,
    ( inf_in6138156342456174402_a_b_b
    = ( ^ [A6: set_Pr3012420139608375472_a_b_b,B6: set_Pr3012420139608375472_a_b_b] : ( inf_in6138156342456174402_a_b_b @ B6 @ A6 ) ) ) ).

% Int_commute
thf(fact_784_Int__commute,axiom,
    ( inf_in4660618365625256667t_unit
    = ( ^ [A6: set_Product_unit,B6: set_Product_unit] : ( inf_in4660618365625256667t_unit @ B6 @ A6 ) ) ) ).

% Int_commute
thf(fact_785_Int__commute,axiom,
    ( inf_inf_set_a
    = ( ^ [A6: set_a,B6: set_a] : ( inf_inf_set_a @ B6 @ A6 ) ) ) ).

% Int_commute
thf(fact_786_Int__left__absorb,axiom,
    ! [A5: set_b,B5: set_b] :
      ( ( inf_inf_set_b @ A5 @ ( inf_inf_set_b @ A5 @ B5 ) )
      = ( inf_inf_set_b @ A5 @ B5 ) ) ).

% Int_left_absorb
thf(fact_787_Int__left__absorb,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ( inf_in6138156342456174402_a_b_b @ A5 @ ( inf_in6138156342456174402_a_b_b @ A5 @ B5 ) )
      = ( inf_in6138156342456174402_a_b_b @ A5 @ B5 ) ) ).

% Int_left_absorb
thf(fact_788_Int__left__absorb,axiom,
    ! [A5: set_Product_unit,B5: set_Product_unit] :
      ( ( inf_in4660618365625256667t_unit @ A5 @ ( inf_in4660618365625256667t_unit @ A5 @ B5 ) )
      = ( inf_in4660618365625256667t_unit @ A5 @ B5 ) ) ).

% Int_left_absorb
thf(fact_789_Int__left__absorb,axiom,
    ! [A5: set_a,B5: set_a] :
      ( ( inf_inf_set_a @ A5 @ ( inf_inf_set_a @ A5 @ B5 ) )
      = ( inf_inf_set_a @ A5 @ B5 ) ) ).

% Int_left_absorb
thf(fact_790_Int__left__commute,axiom,
    ! [A5: set_b,B5: set_b,C3: set_b] :
      ( ( inf_inf_set_b @ A5 @ ( inf_inf_set_b @ B5 @ C3 ) )
      = ( inf_inf_set_b @ B5 @ ( inf_inf_set_b @ A5 @ C3 ) ) ) ).

% Int_left_commute
thf(fact_791_Int__left__commute,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b,C3: set_Pr3012420139608375472_a_b_b] :
      ( ( inf_in6138156342456174402_a_b_b @ A5 @ ( inf_in6138156342456174402_a_b_b @ B5 @ C3 ) )
      = ( inf_in6138156342456174402_a_b_b @ B5 @ ( inf_in6138156342456174402_a_b_b @ A5 @ C3 ) ) ) ).

% Int_left_commute
thf(fact_792_Int__left__commute,axiom,
    ! [A5: set_Product_unit,B5: set_Product_unit,C3: set_Product_unit] :
      ( ( inf_in4660618365625256667t_unit @ A5 @ ( inf_in4660618365625256667t_unit @ B5 @ C3 ) )
      = ( inf_in4660618365625256667t_unit @ B5 @ ( inf_in4660618365625256667t_unit @ A5 @ C3 ) ) ) ).

% Int_left_commute
thf(fact_793_Int__left__commute,axiom,
    ! [A5: set_a,B5: set_a,C3: set_a] :
      ( ( inf_inf_set_a @ A5 @ ( inf_inf_set_a @ B5 @ C3 ) )
      = ( inf_inf_set_a @ B5 @ ( inf_inf_set_a @ A5 @ C3 ) ) ) ).

% Int_left_commute
thf(fact_794_snds_Ocases,axiom,
    ! [A: produc4558475209616630778_a_b_b,P: produc8908337785154950741_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ A @ ( basic_3365347479418424763_a_b_b @ P ) )
     => ( A
        = ( produc8480234286567085243_a_b_b @ P ) ) ) ).

% snds.cases
thf(fact_795_snds_Ocases,axiom,
    ! [A: b,P: produc4558475209616630778_a_b_b] :
      ( ( member_b @ A @ ( basic_1877077703026942_a_b_b @ P ) )
     => ( A
        = ( produc5748100250121904638_a_b_b @ P ) ) ) ).

% snds.cases
thf(fact_796_snds_Ocases,axiom,
    ! [A: dtree_a_b,P: produc3469756349985706280ee_a_b] :
      ( ( member_dtree_a_b @ A @ ( basic_3212961488408603252ee_a_b @ P ) )
     => ( A
        = ( produc8959184660827480948ee_a_b @ P ) ) ) ).

% snds.cases
thf(fact_797_snds_Osimps,axiom,
    ! [A: produc4558475209616630778_a_b_b,P: produc8908337785154950741_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ A @ ( basic_3365347479418424763_a_b_b @ P ) )
      = ( A
        = ( produc8480234286567085243_a_b_b @ P ) ) ) ).

% snds.simps
thf(fact_798_snds_Osimps,axiom,
    ! [A: b,P: produc4558475209616630778_a_b_b] :
      ( ( member_b @ A @ ( basic_1877077703026942_a_b_b @ P ) )
      = ( A
        = ( produc5748100250121904638_a_b_b @ P ) ) ) ).

% snds.simps
thf(fact_799_snds_Osimps,axiom,
    ! [A: dtree_a_b,P: produc3469756349985706280ee_a_b] :
      ( ( member_dtree_a_b @ A @ ( basic_3212961488408603252ee_a_b @ P ) )
      = ( A
        = ( produc8959184660827480948ee_a_b @ P ) ) ) ).

% snds.simps
thf(fact_800_snds_Ointros,axiom,
    ! [P: produc8908337785154950741_a_b_b] : ( member4380921116106875537_a_b_b @ ( produc8480234286567085243_a_b_b @ P ) @ ( basic_3365347479418424763_a_b_b @ P ) ) ).

% snds.intros
thf(fact_801_snds_Ointros,axiom,
    ! [P: produc4558475209616630778_a_b_b] : ( member_b @ ( produc5748100250121904638_a_b_b @ P ) @ ( basic_1877077703026942_a_b_b @ P ) ) ).

% snds.intros
thf(fact_802_snds_Ointros,axiom,
    ! [P: produc3469756349985706280ee_a_b] : ( member_dtree_a_b @ ( produc8959184660827480948ee_a_b @ P ) @ ( basic_3212961488408603252ee_a_b @ P ) ) ).

% snds.intros
thf(fact_803_prod_Oset__map_I2_J,axiom,
    ! [F1: produc4558475209616630778_a_b_b > dtree_a_b,F22: produc4558475209616630778_a_b_b > b,V: produc8908337785154950741_a_b_b] :
      ( ( basic_1877077703026942_a_b_b @ ( produc9210843222980373143_b_b_b @ F1 @ F22 @ V ) )
      = ( image_3908709015779211070_b_b_b @ F22 @ ( basic_3365347479418424763_a_b_b @ V ) ) ) ).

% prod.set_map(2)
thf(fact_804_prod_Oset__map_I2_J,axiom,
    ! [F1: dtree_a_b > produc4558475209616630778_a_b_b,F22: b > produc4558475209616630778_a_b_b,V: produc4558475209616630778_a_b_b] :
      ( ( basic_3365347479418424763_a_b_b @ ( produc1333424704237685261_a_b_b @ F1 @ F22 @ V ) )
      = ( image_7642607452437185460_a_b_b @ F22 @ ( basic_1877077703026942_a_b_b @ V ) ) ) ).

% prod.set_map(2)
thf(fact_805_prod_Oset__map_I2_J,axiom,
    ! [F1: product_unit > product_unit,F22: product_unit > product_unit,V: produc8459935480633519975t_unit] :
      ( ( basic_1454403626444245253t_unit @ ( produc3941737999988548470t_unit @ F1 @ F22 @ V ) )
      = ( image_405062704495631173t_unit @ F22 @ ( basic_1454403626444245253t_unit @ V ) ) ) ).

% prod.set_map(2)
thf(fact_806_prod_Oset__map_I2_J,axiom,
    ! [F1: dtree_a_b > dtree_a_b,F22: b > b,V: produc4558475209616630778_a_b_b] :
      ( ( basic_1877077703026942_a_b_b @ ( produc2024282846164127276_b_b_b @ F1 @ F22 @ V ) )
      = ( image_b_b @ F22 @ ( basic_1877077703026942_a_b_b @ V ) ) ) ).

% prod.set_map(2)
thf(fact_807_prod_Oset__map_I2_J,axiom,
    ! [F1: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,F22: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,V: produc8908337785154950741_a_b_b] :
      ( ( basic_3365347479418424763_a_b_b @ ( produc8659143532165282274_a_b_b @ F1 @ F22 @ V ) )
      = ( image_6081965176830705659_a_b_b @ F22 @ ( basic_3365347479418424763_a_b_b @ V ) ) ) ).

% prod.set_map(2)
thf(fact_808_prod_Oset__map_I2_J,axiom,
    ! [F1: ( b > a ) > b > a,F22: ( b > a ) > b > a,V: product_prod_b_a_b_a] :
      ( ( basic_snds_b_a_b_a @ ( produc1686386052851666058_a_b_a @ F1 @ F22 @ V ) )
      = ( image_b_a_b_a @ F22 @ ( basic_snds_b_a_b_a @ V ) ) ) ).

% prod.set_map(2)
thf(fact_809_prod_Omap__cong,axiom,
    ! [X3: produc8459935480633519975t_unit,Ya: produc8459935480633519975t_unit,F1: product_unit > product_unit,G1: product_unit > product_unit,F22: product_unit > product_unit,G22: product_unit > product_unit] :
      ( ( X3 = Ya )
     => ( ! [Z1: product_unit] :
            ( ( member_Product_unit @ Z1 @ ( basic_788101489561936839t_unit @ Ya ) )
           => ( ( F1 @ Z1 )
              = ( G1 @ Z1 ) ) )
       => ( ! [Z2: product_unit] :
              ( ( member_Product_unit @ Z2 @ ( basic_1454403626444245253t_unit @ Ya ) )
             => ( ( F22 @ Z2 )
                = ( G22 @ Z2 ) ) )
         => ( ( produc3941737999988548470t_unit @ F1 @ F22 @ X3 )
            = ( produc3941737999988548470t_unit @ G1 @ G22 @ Ya ) ) ) ) ) ).

% prod.map_cong
thf(fact_810_prod_Omap__cong,axiom,
    ! [X3: produc4558475209616630778_a_b_b,Ya: produc4558475209616630778_a_b_b,F1: dtree_a_b > dtree_a_b,G1: dtree_a_b > dtree_a_b,F22: b > b,G22: b > b] :
      ( ( X3 = Ya )
     => ( ! [Z1: dtree_a_b] :
            ( ( member_dtree_a_b @ Z1 @ ( basic_7578771248400840636_a_b_b @ Ya ) )
           => ( ( F1 @ Z1 )
              = ( G1 @ Z1 ) ) )
       => ( ! [Z2: b] :
              ( ( member_b @ Z2 @ ( basic_1877077703026942_a_b_b @ Ya ) )
             => ( ( F22 @ Z2 )
                = ( G22 @ Z2 ) ) )
         => ( ( produc2024282846164127276_b_b_b @ F1 @ F22 @ X3 )
            = ( produc2024282846164127276_b_b_b @ G1 @ G22 @ Ya ) ) ) ) ) ).

% prod.map_cong
thf(fact_811_prod_Omap__cong,axiom,
    ! [X3: produc8908337785154950741_a_b_b,Ya: produc8908337785154950741_a_b_b,F1: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,G1: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,F22: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,G22: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b] :
      ( ( X3 = Ya )
     => ( ! [Z1: produc4558475209616630778_a_b_b] :
            ( ( member4380921116106875537_a_b_b @ Z1 @ ( basic_7126344468061175165_a_b_b @ Ya ) )
           => ( ( F1 @ Z1 )
              = ( G1 @ Z1 ) ) )
       => ( ! [Z2: produc4558475209616630778_a_b_b] :
              ( ( member4380921116106875537_a_b_b @ Z2 @ ( basic_3365347479418424763_a_b_b @ Ya ) )
             => ( ( F22 @ Z2 )
                = ( G22 @ Z2 ) ) )
         => ( ( produc8659143532165282274_a_b_b @ F1 @ F22 @ X3 )
            = ( produc8659143532165282274_a_b_b @ G1 @ G22 @ Ya ) ) ) ) ) ).

% prod.map_cong
thf(fact_812_prod_Omap__cong,axiom,
    ! [X3: product_prod_b_a_b_a,Ya: product_prod_b_a_b_a,F1: ( b > a ) > b > a,G1: ( b > a ) > b > a,F22: ( b > a ) > b > a,G22: ( b > a ) > b > a] :
      ( ( X3 = Ya )
     => ( ! [Z1: b > a] :
            ( ( member_b_a @ Z1 @ ( basic_fsts_b_a_b_a @ Ya ) )
           => ( ( F1 @ Z1 )
              = ( G1 @ Z1 ) ) )
       => ( ! [Z2: b > a] :
              ( ( member_b_a @ Z2 @ ( basic_snds_b_a_b_a @ Ya ) )
             => ( ( F22 @ Z2 )
                = ( G22 @ Z2 ) ) )
         => ( ( produc1686386052851666058_a_b_a @ F1 @ F22 @ X3 )
            = ( produc1686386052851666058_a_b_a @ G1 @ G22 @ Ya ) ) ) ) ) ).

% prod.map_cong
thf(fact_813_prod_Omap__cong0,axiom,
    ! [X3: produc8459935480633519975t_unit,F1: product_unit > product_unit,G1: product_unit > product_unit,F22: product_unit > product_unit,G22: product_unit > product_unit] :
      ( ! [Z1: product_unit] :
          ( ( member_Product_unit @ Z1 @ ( basic_788101489561936839t_unit @ X3 ) )
         => ( ( F1 @ Z1 )
            = ( G1 @ Z1 ) ) )
     => ( ! [Z2: product_unit] :
            ( ( member_Product_unit @ Z2 @ ( basic_1454403626444245253t_unit @ X3 ) )
           => ( ( F22 @ Z2 )
              = ( G22 @ Z2 ) ) )
       => ( ( produc3941737999988548470t_unit @ F1 @ F22 @ X3 )
          = ( produc3941737999988548470t_unit @ G1 @ G22 @ X3 ) ) ) ) ).

% prod.map_cong0
thf(fact_814_prod_Omap__cong0,axiom,
    ! [X3: produc4558475209616630778_a_b_b,F1: dtree_a_b > dtree_a_b,G1: dtree_a_b > dtree_a_b,F22: b > b,G22: b > b] :
      ( ! [Z1: dtree_a_b] :
          ( ( member_dtree_a_b @ Z1 @ ( basic_7578771248400840636_a_b_b @ X3 ) )
         => ( ( F1 @ Z1 )
            = ( G1 @ Z1 ) ) )
     => ( ! [Z2: b] :
            ( ( member_b @ Z2 @ ( basic_1877077703026942_a_b_b @ X3 ) )
           => ( ( F22 @ Z2 )
              = ( G22 @ Z2 ) ) )
       => ( ( produc2024282846164127276_b_b_b @ F1 @ F22 @ X3 )
          = ( produc2024282846164127276_b_b_b @ G1 @ G22 @ X3 ) ) ) ) ).

% prod.map_cong0
thf(fact_815_prod_Omap__cong0,axiom,
    ! [X3: produc8908337785154950741_a_b_b,F1: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,G1: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,F22: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,G22: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b] :
      ( ! [Z1: produc4558475209616630778_a_b_b] :
          ( ( member4380921116106875537_a_b_b @ Z1 @ ( basic_7126344468061175165_a_b_b @ X3 ) )
         => ( ( F1 @ Z1 )
            = ( G1 @ Z1 ) ) )
     => ( ! [Z2: produc4558475209616630778_a_b_b] :
            ( ( member4380921116106875537_a_b_b @ Z2 @ ( basic_3365347479418424763_a_b_b @ X3 ) )
           => ( ( F22 @ Z2 )
              = ( G22 @ Z2 ) ) )
       => ( ( produc8659143532165282274_a_b_b @ F1 @ F22 @ X3 )
          = ( produc8659143532165282274_a_b_b @ G1 @ G22 @ X3 ) ) ) ) ).

% prod.map_cong0
thf(fact_816_prod_Omap__cong0,axiom,
    ! [X3: product_prod_b_a_b_a,F1: ( b > a ) > b > a,G1: ( b > a ) > b > a,F22: ( b > a ) > b > a,G22: ( b > a ) > b > a] :
      ( ! [Z1: b > a] :
          ( ( member_b_a @ Z1 @ ( basic_fsts_b_a_b_a @ X3 ) )
         => ( ( F1 @ Z1 )
            = ( G1 @ Z1 ) ) )
     => ( ! [Z2: b > a] :
            ( ( member_b_a @ Z2 @ ( basic_snds_b_a_b_a @ X3 ) )
           => ( ( F22 @ Z2 )
              = ( G22 @ Z2 ) ) )
       => ( ( produc1686386052851666058_a_b_a @ F1 @ F22 @ X3 )
          = ( produc1686386052851666058_a_b_a @ G1 @ G22 @ X3 ) ) ) ) ).

% prod.map_cong0
thf(fact_817_prod_Oinj__map__strong,axiom,
    ! [X3: produc8459935480633519975t_unit,Xa2: produc8459935480633519975t_unit,F1: product_unit > product_unit,F1a: product_unit > product_unit,F22: product_unit > product_unit,F2a: product_unit > product_unit] :
      ( ! [Z1: product_unit,Z1a: product_unit] :
          ( ( member_Product_unit @ Z1 @ ( basic_788101489561936839t_unit @ X3 ) )
         => ( ( member_Product_unit @ Z1a @ ( basic_788101489561936839t_unit @ Xa2 ) )
           => ( ( ( F1 @ Z1 )
                = ( F1a @ Z1a ) )
             => ( Z1 = Z1a ) ) ) )
     => ( ! [Z2: product_unit,Z2a: product_unit] :
            ( ( member_Product_unit @ Z2 @ ( basic_1454403626444245253t_unit @ X3 ) )
           => ( ( member_Product_unit @ Z2a @ ( basic_1454403626444245253t_unit @ Xa2 ) )
             => ( ( ( F22 @ Z2 )
                  = ( F2a @ Z2a ) )
               => ( Z2 = Z2a ) ) ) )
       => ( ( ( produc3941737999988548470t_unit @ F1 @ F22 @ X3 )
            = ( produc3941737999988548470t_unit @ F1a @ F2a @ Xa2 ) )
         => ( X3 = Xa2 ) ) ) ) ).

% prod.inj_map_strong
thf(fact_818_prod_Oinj__map__strong,axiom,
    ! [X3: produc4558475209616630778_a_b_b,Xa2: produc4558475209616630778_a_b_b,F1: dtree_a_b > dtree_a_b,F1a: dtree_a_b > dtree_a_b,F22: b > b,F2a: b > b] :
      ( ! [Z1: dtree_a_b,Z1a: dtree_a_b] :
          ( ( member_dtree_a_b @ Z1 @ ( basic_7578771248400840636_a_b_b @ X3 ) )
         => ( ( member_dtree_a_b @ Z1a @ ( basic_7578771248400840636_a_b_b @ Xa2 ) )
           => ( ( ( F1 @ Z1 )
                = ( F1a @ Z1a ) )
             => ( Z1 = Z1a ) ) ) )
     => ( ! [Z2: b,Z2a: b] :
            ( ( member_b @ Z2 @ ( basic_1877077703026942_a_b_b @ X3 ) )
           => ( ( member_b @ Z2a @ ( basic_1877077703026942_a_b_b @ Xa2 ) )
             => ( ( ( F22 @ Z2 )
                  = ( F2a @ Z2a ) )
               => ( Z2 = Z2a ) ) ) )
       => ( ( ( produc2024282846164127276_b_b_b @ F1 @ F22 @ X3 )
            = ( produc2024282846164127276_b_b_b @ F1a @ F2a @ Xa2 ) )
         => ( X3 = Xa2 ) ) ) ) ).

% prod.inj_map_strong
thf(fact_819_prod_Oinj__map__strong,axiom,
    ! [X3: produc8908337785154950741_a_b_b,Xa2: produc8908337785154950741_a_b_b,F1: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,F1a: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,F22: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,F2a: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b] :
      ( ! [Z1: produc4558475209616630778_a_b_b,Z1a: produc4558475209616630778_a_b_b] :
          ( ( member4380921116106875537_a_b_b @ Z1 @ ( basic_7126344468061175165_a_b_b @ X3 ) )
         => ( ( member4380921116106875537_a_b_b @ Z1a @ ( basic_7126344468061175165_a_b_b @ Xa2 ) )
           => ( ( ( F1 @ Z1 )
                = ( F1a @ Z1a ) )
             => ( Z1 = Z1a ) ) ) )
     => ( ! [Z2: produc4558475209616630778_a_b_b,Z2a: produc4558475209616630778_a_b_b] :
            ( ( member4380921116106875537_a_b_b @ Z2 @ ( basic_3365347479418424763_a_b_b @ X3 ) )
           => ( ( member4380921116106875537_a_b_b @ Z2a @ ( basic_3365347479418424763_a_b_b @ Xa2 ) )
             => ( ( ( F22 @ Z2 )
                  = ( F2a @ Z2a ) )
               => ( Z2 = Z2a ) ) ) )
       => ( ( ( produc8659143532165282274_a_b_b @ F1 @ F22 @ X3 )
            = ( produc8659143532165282274_a_b_b @ F1a @ F2a @ Xa2 ) )
         => ( X3 = Xa2 ) ) ) ) ).

% prod.inj_map_strong
thf(fact_820_prod_Oinj__map__strong,axiom,
    ! [X3: product_prod_b_a_b_a,Xa2: product_prod_b_a_b_a,F1: ( b > a ) > b > a,F1a: ( b > a ) > b > a,F22: ( b > a ) > b > a,F2a: ( b > a ) > b > a] :
      ( ! [Z1: b > a,Z1a: b > a] :
          ( ( member_b_a @ Z1 @ ( basic_fsts_b_a_b_a @ X3 ) )
         => ( ( member_b_a @ Z1a @ ( basic_fsts_b_a_b_a @ Xa2 ) )
           => ( ( ( F1 @ Z1 )
                = ( F1a @ Z1a ) )
             => ( Z1 = Z1a ) ) ) )
     => ( ! [Z2: b > a,Z2a: b > a] :
            ( ( member_b_a @ Z2 @ ( basic_snds_b_a_b_a @ X3 ) )
           => ( ( member_b_a @ Z2a @ ( basic_snds_b_a_b_a @ Xa2 ) )
             => ( ( ( F22 @ Z2 )
                  = ( F2a @ Z2a ) )
               => ( Z2 = Z2a ) ) ) )
       => ( ( ( produc1686386052851666058_a_b_a @ F1 @ F22 @ X3 )
            = ( produc1686386052851666058_a_b_a @ F1a @ F2a @ Xa2 ) )
         => ( X3 = Xa2 ) ) ) ) ).

% prod.inj_map_strong
thf(fact_821_prod_Omap__ident__strong,axiom,
    ! [T: produc8908337785154950741_a_b_b,F1: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,F22: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b] :
      ( ! [Z1: produc4558475209616630778_a_b_b] :
          ( ( member4380921116106875537_a_b_b @ Z1 @ ( basic_7126344468061175165_a_b_b @ T ) )
         => ( ( F1 @ Z1 )
            = Z1 ) )
     => ( ! [Z2: produc4558475209616630778_a_b_b] :
            ( ( member4380921116106875537_a_b_b @ Z2 @ ( basic_3365347479418424763_a_b_b @ T ) )
           => ( ( F22 @ Z2 )
              = Z2 ) )
       => ( ( produc8659143532165282274_a_b_b @ F1 @ F22 @ T )
          = T ) ) ) ).

% prod.map_ident_strong
thf(fact_822_prod_Omap__ident__strong,axiom,
    ! [T: product_prod_nat_nat,F1: nat > nat,F22: nat > nat] :
      ( ! [Z1: nat] :
          ( ( member_nat @ Z1 @ ( basic_fsts_nat_nat @ T ) )
         => ( ( F1 @ Z1 )
            = Z1 ) )
     => ( ! [Z2: nat] :
            ( ( member_nat @ Z2 @ ( basic_snds_nat_nat @ T ) )
           => ( ( F22 @ Z2 )
              = Z2 ) )
       => ( ( produc6977886695330630970at_nat @ F1 @ F22 @ T )
          = T ) ) ) ).

% prod.map_ident_strong
thf(fact_823_prod_Omap__ident__strong,axiom,
    ! [T: product_prod_nat_b,F1: nat > nat,F22: b > b] :
      ( ! [Z1: nat] :
          ( ( member_nat @ Z1 @ ( basic_fsts_nat_b @ T ) )
         => ( ( F1 @ Z1 )
            = Z1 ) )
     => ( ! [Z2: b] :
            ( ( member_b @ Z2 @ ( basic_snds_nat_b @ T ) )
           => ( ( F22 @ Z2 )
              = Z2 ) )
       => ( ( produc4324974520030914520at_b_b @ F1 @ F22 @ T )
          = T ) ) ) ).

% prod.map_ident_strong
thf(fact_824_prod_Omap__ident__strong,axiom,
    ! [T: product_prod_nat_a,F1: nat > nat,F22: a > a] :
      ( ! [Z1: nat] :
          ( ( member_nat @ Z1 @ ( basic_fsts_nat_a @ T ) )
         => ( ( F1 @ Z1 )
            = Z1 ) )
     => ( ! [Z2: a] :
            ( ( member_a @ Z2 @ ( basic_snds_nat_a @ T ) )
           => ( ( F22 @ Z2 )
              = Z2 ) )
       => ( ( produc7112430102003590552at_a_a @ F1 @ F22 @ T )
          = T ) ) ) ).

% prod.map_ident_strong
thf(fact_825_prod_Omap__ident__strong,axiom,
    ! [T: product_prod_b_nat,F1: b > b,F22: nat > nat] :
      ( ! [Z1: b] :
          ( ( member_b @ Z1 @ ( basic_fsts_b_nat @ T ) )
         => ( ( F1 @ Z1 )
            = Z1 ) )
     => ( ! [Z2: nat] :
            ( ( member_nat @ Z2 @ ( basic_snds_b_nat @ T ) )
           => ( ( F22 @ Z2 )
              = Z2 ) )
       => ( ( produc7117561280001982680at_nat @ F1 @ F22 @ T )
          = T ) ) ) ).

% prod.map_ident_strong
thf(fact_826_prod_Omap__ident__strong,axiom,
    ! [T: product_prod_b_b,F1: b > b,F22: b > b] :
      ( ! [Z1: b] :
          ( ( member_b @ Z1 @ ( basic_fsts_b_b @ T ) )
         => ( ( F1 @ Z1 )
            = Z1 ) )
     => ( ! [Z2: b] :
            ( ( member_b @ Z2 @ ( basic_snds_b_b @ T ) )
           => ( ( F22 @ Z2 )
              = Z2 ) )
       => ( ( produc8315423520075080822_b_b_b @ F1 @ F22 @ T )
          = T ) ) ) ).

% prod.map_ident_strong
thf(fact_827_prod_Omap__ident__strong,axiom,
    ! [T: product_prod_b_a,F1: b > b,F22: a > a] :
      ( ! [Z1: b] :
          ( ( member_b @ Z1 @ ( basic_fsts_b_a @ T ) )
         => ( ( F1 @ Z1 )
            = Z1 ) )
     => ( ! [Z2: a] :
            ( ( member_a @ Z2 @ ( basic_snds_b_a @ T ) )
           => ( ( F22 @ Z2 )
              = Z2 ) )
       => ( ( produc1879507065192981046_b_a_a @ F1 @ F22 @ T )
          = T ) ) ) ).

% prod.map_ident_strong
thf(fact_828_prod_Omap__ident__strong,axiom,
    ! [T: product_prod_a_nat,F1: a > a,F22: nat > nat] :
      ( ! [Z1: a] :
          ( ( member_a @ Z1 @ ( basic_fsts_a_nat @ T ) )
         => ( ( F1 @ Z1 )
            = Z1 ) )
     => ( ! [Z2: nat] :
            ( ( member_nat @ Z2 @ ( basic_snds_a_nat @ T ) )
           => ( ( F22 @ Z2 )
              = Z2 ) )
       => ( ( produc1377594951366540952at_nat @ F1 @ F22 @ T )
          = T ) ) ) ).

% prod.map_ident_strong
thf(fact_829_prod_Omap__ident__strong,axiom,
    ! [T: product_prod_a_b,F1: a > a,F22: b > b] :
      ( ! [Z1: a] :
          ( ( member_a @ Z1 @ ( basic_fsts_a_b @ T ) )
         => ( ( F1 @ Z1 )
            = Z1 ) )
     => ( ! [Z2: b] :
            ( ( member_b @ Z2 @ ( basic_snds_a_b @ T ) )
           => ( ( F22 @ Z2 )
              = Z2 ) )
       => ( ( produc1231242867592151606_a_b_b @ F1 @ F22 @ T )
          = T ) ) ) ).

% prod.map_ident_strong
thf(fact_830_prod_Omap__ident__strong,axiom,
    ! [T: product_prod_a_a,F1: a > a,F22: a > a] :
      ( ! [Z1: a] :
          ( ( member_a @ Z1 @ ( basic_fsts_a_a @ T ) )
         => ( ( F1 @ Z1 )
            = Z1 ) )
     => ( ! [Z2: a] :
            ( ( member_a @ Z2 @ ( basic_snds_a_a @ T ) )
           => ( ( F22 @ Z2 )
              = Z2 ) )
       => ( ( produc4018698449564827638_a_a_a @ F1 @ F22 @ T )
          = T ) ) ) ).

% prod.map_ident_strong
thf(fact_831_top__set__def,axiom,
    ( top_to7222684678772277088_a_b_b
    = ( collec1368399972772960719_a_b_b @ top_to762646584048855333_b_b_o ) ) ).

% top_set_def
thf(fact_832_top__set__def,axiom,
    ( top_to2771918933716375115t_unit
    = ( collec806072925662511674t_unit @ top_to8021728106141937658unit_o ) ) ).

% top_set_def
thf(fact_833_top__set__def,axiom,
    ( top_to1767297665138865437t_unit
    = ( collec7787489603430924120t_unit @ top_to5616354022731438592unit_o ) ) ).

% top_set_def
thf(fact_834_top__set__def,axiom,
    ( top_top_set_b_a
    = ( collect_b_a @ top_top_b_a_o ) ) ).

% top_set_def
thf(fact_835_top__set__def,axiom,
    ( top_to1996260823553986621t_unit
    = ( collect_Product_unit @ top_to2465898995584390880unit_o ) ) ).

% top_set_def
thf(fact_836_snd__conv,axiom,
    ! [X12: produc4558475209616630778_a_b_b,X22: produc4558475209616630778_a_b_b] :
      ( ( produc8480234286567085243_a_b_b @ ( produc6533307410877503629_a_b_b @ X12 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_837_snd__conv,axiom,
    ! [X12: product_unit,X22: product_unit] :
      ( ( produc6786084904866402309t_unit @ ( produc5692694829384537815t_unit @ X12 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_838_snd__conv,axiom,
    ! [X12: b,X22: dtree_a_b] :
      ( ( produc8959184660827480948ee_a_b @ ( produc3542686128043086370ee_a_b @ X12 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_839_snd__conv,axiom,
    ! [X12: dtree_a_b,X22: b] :
      ( ( produc5748100250121904638_a_b_b @ ( produc331601717337510060_a_b_b @ X12 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_840_snd__eqD,axiom,
    ! [X3: produc4558475209616630778_a_b_b,Y3: produc4558475209616630778_a_b_b,A: produc4558475209616630778_a_b_b] :
      ( ( ( produc8480234286567085243_a_b_b @ ( produc6533307410877503629_a_b_b @ X3 @ Y3 ) )
        = A )
     => ( Y3 = A ) ) ).

% snd_eqD
thf(fact_841_snd__eqD,axiom,
    ! [X3: product_unit,Y3: product_unit,A: product_unit] :
      ( ( ( produc6786084904866402309t_unit @ ( produc5692694829384537815t_unit @ X3 @ Y3 ) )
        = A )
     => ( Y3 = A ) ) ).

% snd_eqD
thf(fact_842_snd__eqD,axiom,
    ! [X3: b,Y3: dtree_a_b,A: dtree_a_b] :
      ( ( ( produc8959184660827480948ee_a_b @ ( produc3542686128043086370ee_a_b @ X3 @ Y3 ) )
        = A )
     => ( Y3 = A ) ) ).

% snd_eqD
thf(fact_843_snd__eqD,axiom,
    ! [X3: dtree_a_b,Y3: b,A: b] :
      ( ( ( produc5748100250121904638_a_b_b @ ( produc331601717337510060_a_b_b @ X3 @ Y3 ) )
        = A )
     => ( Y3 = A ) ) ).

% snd_eqD
thf(fact_844_sndI,axiom,
    ! [X3: produc8908337785154950741_a_b_b,Y3: produc4558475209616630778_a_b_b,Z: produc4558475209616630778_a_b_b] :
      ( ( X3
        = ( produc6533307410877503629_a_b_b @ Y3 @ Z ) )
     => ( ( produc8480234286567085243_a_b_b @ X3 )
        = Z ) ) ).

% sndI
thf(fact_845_sndI,axiom,
    ! [X3: produc8459935480633519975t_unit,Y3: product_unit,Z: product_unit] :
      ( ( X3
        = ( produc5692694829384537815t_unit @ Y3 @ Z ) )
     => ( ( produc6786084904866402309t_unit @ X3 )
        = Z ) ) ).

% sndI
thf(fact_846_sndI,axiom,
    ! [X3: produc3469756349985706280ee_a_b,Y3: b,Z: dtree_a_b] :
      ( ( X3
        = ( produc3542686128043086370ee_a_b @ Y3 @ Z ) )
     => ( ( produc8959184660827480948ee_a_b @ X3 )
        = Z ) ) ).

% sndI
thf(fact_847_sndI,axiom,
    ! [X3: produc4558475209616630778_a_b_b,Y3: dtree_a_b,Z: b] :
      ( ( X3
        = ( produc331601717337510060_a_b_b @ Y3 @ Z ) )
     => ( ( produc5748100250121904638_a_b_b @ X3 )
        = Z ) ) ).

% sndI
thf(fact_848_map__prod_Ocomp,axiom,
    ! [F2: ( b > a ) > b > a,G2: ( b > a ) > b > a,H: ( b > a ) > b > a,I: ( b > a ) > b > a] :
      ( ( comp_P929014663317004102_a_b_a @ ( produc1686386052851666058_a_b_a @ F2 @ G2 ) @ ( produc1686386052851666058_a_b_a @ H @ I ) )
      = ( produc1686386052851666058_a_b_a @ ( comp_b_a_b_a_b_a @ F2 @ H ) @ ( comp_b_a_b_a_b_a @ G2 @ I ) ) ) ).

% map_prod.comp
thf(fact_849_map__prod_Ocomp,axiom,
    ! [F2: b > b,G2: b > b,H: b > b,I: b > b] :
      ( ( comp_P5109000819176280452od_b_b @ ( produc8315423520075080822_b_b_b @ F2 @ G2 ) @ ( produc8315423520075080822_b_b_b @ H @ I ) )
      = ( produc8315423520075080822_b_b_b @ ( comp_b_b_b @ F2 @ H ) @ ( comp_b_b_b @ G2 @ I ) ) ) ).

% map_prod.comp
thf(fact_850_map__prod_Ocomp,axiom,
    ! [F2: b > b,G2: a > a,H: b > b,I: a > a] :
      ( ( comp_P3995598562207432003od_b_a @ ( produc1879507065192981046_b_a_a @ F2 @ G2 ) @ ( produc1879507065192981046_b_a_a @ H @ I ) )
      = ( produc1879507065192981046_b_a_a @ ( comp_b_b_b @ F2 @ H ) @ ( comp_a_a_a @ G2 @ I ) ) ) ).

% map_prod.comp
thf(fact_851_map__prod_Ocomp,axiom,
    ! [F2: a > a,G2: b > b,H: a > a,I: b > b] :
      ( ( comp_P2392903256394990597od_a_b @ ( produc1231242867592151606_a_b_b @ F2 @ G2 ) @ ( produc1231242867592151606_a_b_b @ H @ I ) )
      = ( produc1231242867592151606_a_b_b @ ( comp_a_a_a @ F2 @ H ) @ ( comp_b_b_b @ G2 @ I ) ) ) ).

% map_prod.comp
thf(fact_852_map__prod_Ocomp,axiom,
    ! [F2: a > a,G2: a > a,H: a > a,I: a > a] :
      ( ( comp_P1279500999426142148od_a_a @ ( produc4018698449564827638_a_a_a @ F2 @ G2 ) @ ( produc4018698449564827638_a_a_a @ H @ I ) )
      = ( produc4018698449564827638_a_a_a @ ( comp_a_a_a @ F2 @ H ) @ ( comp_a_a_a @ G2 @ I ) ) ) ).

% map_prod.comp
thf(fact_853_map__prod_Ocomp,axiom,
    ! [F2: product_unit > product_unit,G2: product_unit > product_unit,H: product_unit > product_unit,I: product_unit > product_unit] :
      ( ( comp_P8863678191571823620t_unit @ ( produc3941737999988548470t_unit @ F2 @ G2 ) @ ( produc3941737999988548470t_unit @ H @ I ) )
      = ( produc3941737999988548470t_unit @ ( comp_P7645380973975430442t_unit @ F2 @ H ) @ ( comp_P7645380973975430442t_unit @ G2 @ I ) ) ) ).

% map_prod.comp
thf(fact_854_map__prod_Ocomp,axiom,
    ! [F2: ( b > a ) > b > a,G2: b > b,H: ( b > a ) > b > a,I: b > b] :
      ( ( comp_P6265908536931808725_b_a_b @ ( produc9165320845528156032_a_b_b @ F2 @ G2 ) @ ( produc9165320845528156032_a_b_b @ H @ I ) )
      = ( produc9165320845528156032_a_b_b @ ( comp_b_a_b_a_b_a @ F2 @ H ) @ ( comp_b_b_b @ G2 @ I ) ) ) ).

% map_prod.comp
thf(fact_855_map__prod_Ocomp,axiom,
    ! [F2: ( b > a ) > b > a,G2: a > a,H: ( b > a ) > b > a,I: a > a] :
      ( ( comp_P3579555031557280850_b_a_a @ ( produc2729404390646056256_a_a_a @ F2 @ G2 ) @ ( produc2729404390646056256_a_a_a @ H @ I ) )
      = ( produc2729404390646056256_a_a_a @ ( comp_b_a_b_a_b_a @ F2 @ H ) @ ( comp_a_a_a @ G2 @ I ) ) ) ).

% map_prod.comp
thf(fact_856_map__prod_Ocomp,axiom,
    ! [F2: dtree_a_b > b,G2: b > b,H: produc4558475209616630778_a_b_b > dtree_a_b,I: b > b] :
      ( ( comp_P2381262878637464388_b_b_b @ ( produc4252374707397466189_b_b_b @ F2 @ G2 ) @ ( produc695453528002274476_b_b_b @ H @ I ) )
      = ( produc1583750209243554253_b_b_b @ ( comp_d7292648224603294300_a_b_b @ F2 @ H ) @ ( comp_b_b_b @ G2 @ I ) ) ) ).

% map_prod.comp
thf(fact_857_map__prod_Ocomp,axiom,
    ! [F2: dtree_a_b > b,G2: a > a,H: produc4558475209616630778_a_b_b > dtree_a_b,I: a > a] :
      ( ( comp_P3369791497561358467_b_b_a @ ( produc7039830289370142221_b_a_a @ F2 @ G2 ) @ ( produc3482909109974950508_b_a_a @ H @ I ) )
      = ( produc4371205791216230285_b_a_a @ ( comp_d7292648224603294300_a_b_b @ F2 @ H ) @ ( comp_a_a_a @ G2 @ I ) ) ) ).

% map_prod.comp
thf(fact_858_map__prod_Ocompositionality,axiom,
    ! [F2: ( b > a ) > b > a,G2: ( b > a ) > b > a,H: ( b > a ) > b > a,I: ( b > a ) > b > a,Prod: product_prod_b_a_b_a] :
      ( ( produc1686386052851666058_a_b_a @ F2 @ G2 @ ( produc1686386052851666058_a_b_a @ H @ I @ Prod ) )
      = ( produc1686386052851666058_a_b_a @ ( comp_b_a_b_a_b_a @ F2 @ H ) @ ( comp_b_a_b_a_b_a @ G2 @ I ) @ Prod ) ) ).

% map_prod.compositionality
thf(fact_859_map__prod_Ocompositionality,axiom,
    ! [F2: b > b,G2: b > b,H: b > b,I: b > b,Prod: product_prod_b_b] :
      ( ( produc8315423520075080822_b_b_b @ F2 @ G2 @ ( produc8315423520075080822_b_b_b @ H @ I @ Prod ) )
      = ( produc8315423520075080822_b_b_b @ ( comp_b_b_b @ F2 @ H ) @ ( comp_b_b_b @ G2 @ I ) @ Prod ) ) ).

% map_prod.compositionality
thf(fact_860_map__prod_Ocompositionality,axiom,
    ! [F2: b > b,G2: a > a,H: b > b,I: a > a,Prod: product_prod_b_a] :
      ( ( produc1879507065192981046_b_a_a @ F2 @ G2 @ ( produc1879507065192981046_b_a_a @ H @ I @ Prod ) )
      = ( produc1879507065192981046_b_a_a @ ( comp_b_b_b @ F2 @ H ) @ ( comp_a_a_a @ G2 @ I ) @ Prod ) ) ).

% map_prod.compositionality
thf(fact_861_map__prod_Ocompositionality,axiom,
    ! [F2: a > a,G2: b > b,H: a > a,I: b > b,Prod: product_prod_a_b] :
      ( ( produc1231242867592151606_a_b_b @ F2 @ G2 @ ( produc1231242867592151606_a_b_b @ H @ I @ Prod ) )
      = ( produc1231242867592151606_a_b_b @ ( comp_a_a_a @ F2 @ H ) @ ( comp_b_b_b @ G2 @ I ) @ Prod ) ) ).

% map_prod.compositionality
thf(fact_862_map__prod_Ocompositionality,axiom,
    ! [F2: a > a,G2: a > a,H: a > a,I: a > a,Prod: product_prod_a_a] :
      ( ( produc4018698449564827638_a_a_a @ F2 @ G2 @ ( produc4018698449564827638_a_a_a @ H @ I @ Prod ) )
      = ( produc4018698449564827638_a_a_a @ ( comp_a_a_a @ F2 @ H ) @ ( comp_a_a_a @ G2 @ I ) @ Prod ) ) ).

% map_prod.compositionality
thf(fact_863_map__prod_Ocompositionality,axiom,
    ! [F2: product_unit > product_unit,G2: product_unit > product_unit,H: product_unit > product_unit,I: product_unit > product_unit,Prod: produc8459935480633519975t_unit] :
      ( ( produc3941737999988548470t_unit @ F2 @ G2 @ ( produc3941737999988548470t_unit @ H @ I @ Prod ) )
      = ( produc3941737999988548470t_unit @ ( comp_P7645380973975430442t_unit @ F2 @ H ) @ ( comp_P7645380973975430442t_unit @ G2 @ I ) @ Prod ) ) ).

% map_prod.compositionality
thf(fact_864_map__prod_Ocompositionality,axiom,
    ! [F2: ( b > a ) > b > a,G2: b > b,H: ( b > a ) > b > a,I: b > b,Prod: product_prod_b_a_b] :
      ( ( produc9165320845528156032_a_b_b @ F2 @ G2 @ ( produc9165320845528156032_a_b_b @ H @ I @ Prod ) )
      = ( produc9165320845528156032_a_b_b @ ( comp_b_a_b_a_b_a @ F2 @ H ) @ ( comp_b_b_b @ G2 @ I ) @ Prod ) ) ).

% map_prod.compositionality
thf(fact_865_map__prod_Ocompositionality,axiom,
    ! [F2: ( b > a ) > b > a,G2: a > a,H: ( b > a ) > b > a,I: a > a,Prod: product_prod_b_a_a] :
      ( ( produc2729404390646056256_a_a_a @ F2 @ G2 @ ( produc2729404390646056256_a_a_a @ H @ I @ Prod ) )
      = ( produc2729404390646056256_a_a_a @ ( comp_b_a_b_a_b_a @ F2 @ H ) @ ( comp_a_a_a @ G2 @ I ) @ Prod ) ) ).

% map_prod.compositionality
thf(fact_866_map__prod_Ocompositionality,axiom,
    ! [F2: dtree_a_b > b,G2: b > b,H: produc4558475209616630778_a_b_b > dtree_a_b,I: b > b,Prod: produc6708371838016462714_b_b_b] :
      ( ( produc4252374707397466189_b_b_b @ F2 @ G2 @ ( produc695453528002274476_b_b_b @ H @ I @ Prod ) )
      = ( produc1583750209243554253_b_b_b @ ( comp_d7292648224603294300_a_b_b @ F2 @ H ) @ ( comp_b_b_b @ G2 @ I ) @ Prod ) ) ).

% map_prod.compositionality
thf(fact_867_map__prod_Ocompositionality,axiom,
    ! [F2: dtree_a_b > b,G2: a > a,H: produc4558475209616630778_a_b_b > dtree_a_b,I: a > a,Prod: produc6708371833713233913_b_b_a] :
      ( ( produc7039830289370142221_b_a_a @ F2 @ G2 @ ( produc3482909109974950508_b_a_a @ H @ I @ Prod ) )
      = ( produc4371205791216230285_b_a_a @ ( comp_d7292648224603294300_a_b_b @ F2 @ H ) @ ( comp_a_a_a @ G2 @ I ) @ Prod ) ) ).

% map_prod.compositionality
thf(fact_868_map__prod__compose,axiom,
    ! [F1: ( b > a ) > b > a,F22: ( b > a ) > b > a,G1: ( b > a ) > b > a,G22: ( b > a ) > b > a] :
      ( ( produc1686386052851666058_a_b_a @ ( comp_b_a_b_a_b_a @ F1 @ F22 ) @ ( comp_b_a_b_a_b_a @ G1 @ G22 ) )
      = ( comp_P929014663317004102_a_b_a @ ( produc1686386052851666058_a_b_a @ F1 @ G1 ) @ ( produc1686386052851666058_a_b_a @ F22 @ G22 ) ) ) ).

% map_prod_compose
thf(fact_869_map__prod__compose,axiom,
    ! [F1: b > b,F22: b > b,G1: b > b,G22: b > b] :
      ( ( produc8315423520075080822_b_b_b @ ( comp_b_b_b @ F1 @ F22 ) @ ( comp_b_b_b @ G1 @ G22 ) )
      = ( comp_P5109000819176280452od_b_b @ ( produc8315423520075080822_b_b_b @ F1 @ G1 ) @ ( produc8315423520075080822_b_b_b @ F22 @ G22 ) ) ) ).

% map_prod_compose
thf(fact_870_map__prod__compose,axiom,
    ! [F1: b > b,F22: b > b,G1: a > a,G22: a > a] :
      ( ( produc1879507065192981046_b_a_a @ ( comp_b_b_b @ F1 @ F22 ) @ ( comp_a_a_a @ G1 @ G22 ) )
      = ( comp_P3995598562207432003od_b_a @ ( produc1879507065192981046_b_a_a @ F1 @ G1 ) @ ( produc1879507065192981046_b_a_a @ F22 @ G22 ) ) ) ).

% map_prod_compose
thf(fact_871_map__prod__compose,axiom,
    ! [F1: a > a,F22: a > a,G1: b > b,G22: b > b] :
      ( ( produc1231242867592151606_a_b_b @ ( comp_a_a_a @ F1 @ F22 ) @ ( comp_b_b_b @ G1 @ G22 ) )
      = ( comp_P2392903256394990597od_a_b @ ( produc1231242867592151606_a_b_b @ F1 @ G1 ) @ ( produc1231242867592151606_a_b_b @ F22 @ G22 ) ) ) ).

% map_prod_compose
thf(fact_872_map__prod__compose,axiom,
    ! [F1: a > a,F22: a > a,G1: a > a,G22: a > a] :
      ( ( produc4018698449564827638_a_a_a @ ( comp_a_a_a @ F1 @ F22 ) @ ( comp_a_a_a @ G1 @ G22 ) )
      = ( comp_P1279500999426142148od_a_a @ ( produc4018698449564827638_a_a_a @ F1 @ G1 ) @ ( produc4018698449564827638_a_a_a @ F22 @ G22 ) ) ) ).

% map_prod_compose
thf(fact_873_map__prod__compose,axiom,
    ! [F1: product_unit > product_unit,F22: product_unit > product_unit,G1: product_unit > product_unit,G22: product_unit > product_unit] :
      ( ( produc3941737999988548470t_unit @ ( comp_P7645380973975430442t_unit @ F1 @ F22 ) @ ( comp_P7645380973975430442t_unit @ G1 @ G22 ) )
      = ( comp_P8863678191571823620t_unit @ ( produc3941737999988548470t_unit @ F1 @ G1 ) @ ( produc3941737999988548470t_unit @ F22 @ G22 ) ) ) ).

% map_prod_compose
thf(fact_874_map__prod__compose,axiom,
    ! [F1: ( b > a ) > b > a,F22: ( b > a ) > b > a,G1: b > b,G22: b > b] :
      ( ( produc9165320845528156032_a_b_b @ ( comp_b_a_b_a_b_a @ F1 @ F22 ) @ ( comp_b_b_b @ G1 @ G22 ) )
      = ( comp_P6265908536931808725_b_a_b @ ( produc9165320845528156032_a_b_b @ F1 @ G1 ) @ ( produc9165320845528156032_a_b_b @ F22 @ G22 ) ) ) ).

% map_prod_compose
thf(fact_875_map__prod__compose,axiom,
    ! [F1: ( b > a ) > b > a,F22: ( b > a ) > b > a,G1: a > a,G22: a > a] :
      ( ( produc2729404390646056256_a_a_a @ ( comp_b_a_b_a_b_a @ F1 @ F22 ) @ ( comp_a_a_a @ G1 @ G22 ) )
      = ( comp_P3579555031557280850_b_a_a @ ( produc2729404390646056256_a_a_a @ F1 @ G1 ) @ ( produc2729404390646056256_a_a_a @ F22 @ G22 ) ) ) ).

% map_prod_compose
thf(fact_876_map__prod__compose,axiom,
    ! [F1: dtree_a_b > b,F22: produc4558475209616630778_a_b_b > dtree_a_b,G1: b > b,G22: b > b] :
      ( ( produc1583750209243554253_b_b_b @ ( comp_d7292648224603294300_a_b_b @ F1 @ F22 ) @ ( comp_b_b_b @ G1 @ G22 ) )
      = ( comp_P2381262878637464388_b_b_b @ ( produc4252374707397466189_b_b_b @ F1 @ G1 ) @ ( produc695453528002274476_b_b_b @ F22 @ G22 ) ) ) ).

% map_prod_compose
thf(fact_877_map__prod__compose,axiom,
    ! [F1: dtree_a_b > b,F22: produc4558475209616630778_a_b_b > dtree_a_b,G1: a > a,G22: a > a] :
      ( ( produc4371205791216230285_b_a_a @ ( comp_d7292648224603294300_a_b_b @ F1 @ F22 ) @ ( comp_a_a_a @ G1 @ G22 ) )
      = ( comp_P3369791497561358467_b_b_a @ ( produc7039830289370142221_b_a_a @ F1 @ G1 ) @ ( produc3482909109974950508_b_a_a @ F22 @ G22 ) ) ) ).

% map_prod_compose
thf(fact_878_prod_Omap__comp,axiom,
    ! [G1: ( b > a ) > b > a,G22: ( b > a ) > b > a,F1: ( b > a ) > b > a,F22: ( b > a ) > b > a,V: product_prod_b_a_b_a] :
      ( ( produc1686386052851666058_a_b_a @ G1 @ G22 @ ( produc1686386052851666058_a_b_a @ F1 @ F22 @ V ) )
      = ( produc1686386052851666058_a_b_a @ ( comp_b_a_b_a_b_a @ G1 @ F1 ) @ ( comp_b_a_b_a_b_a @ G22 @ F22 ) @ V ) ) ).

% prod.map_comp
thf(fact_879_prod_Omap__comp,axiom,
    ! [G1: b > b,G22: b > b,F1: b > b,F22: b > b,V: product_prod_b_b] :
      ( ( produc8315423520075080822_b_b_b @ G1 @ G22 @ ( produc8315423520075080822_b_b_b @ F1 @ F22 @ V ) )
      = ( produc8315423520075080822_b_b_b @ ( comp_b_b_b @ G1 @ F1 ) @ ( comp_b_b_b @ G22 @ F22 ) @ V ) ) ).

% prod.map_comp
thf(fact_880_prod_Omap__comp,axiom,
    ! [G1: b > b,G22: a > a,F1: b > b,F22: a > a,V: product_prod_b_a] :
      ( ( produc1879507065192981046_b_a_a @ G1 @ G22 @ ( produc1879507065192981046_b_a_a @ F1 @ F22 @ V ) )
      = ( produc1879507065192981046_b_a_a @ ( comp_b_b_b @ G1 @ F1 ) @ ( comp_a_a_a @ G22 @ F22 ) @ V ) ) ).

% prod.map_comp
thf(fact_881_prod_Omap__comp,axiom,
    ! [G1: a > a,G22: b > b,F1: a > a,F22: b > b,V: product_prod_a_b] :
      ( ( produc1231242867592151606_a_b_b @ G1 @ G22 @ ( produc1231242867592151606_a_b_b @ F1 @ F22 @ V ) )
      = ( produc1231242867592151606_a_b_b @ ( comp_a_a_a @ G1 @ F1 ) @ ( comp_b_b_b @ G22 @ F22 ) @ V ) ) ).

% prod.map_comp
thf(fact_882_prod_Omap__comp,axiom,
    ! [G1: a > a,G22: a > a,F1: a > a,F22: a > a,V: product_prod_a_a] :
      ( ( produc4018698449564827638_a_a_a @ G1 @ G22 @ ( produc4018698449564827638_a_a_a @ F1 @ F22 @ V ) )
      = ( produc4018698449564827638_a_a_a @ ( comp_a_a_a @ G1 @ F1 ) @ ( comp_a_a_a @ G22 @ F22 ) @ V ) ) ).

% prod.map_comp
thf(fact_883_prod_Omap__comp,axiom,
    ! [G1: product_unit > product_unit,G22: product_unit > product_unit,F1: product_unit > product_unit,F22: product_unit > product_unit,V: produc8459935480633519975t_unit] :
      ( ( produc3941737999988548470t_unit @ G1 @ G22 @ ( produc3941737999988548470t_unit @ F1 @ F22 @ V ) )
      = ( produc3941737999988548470t_unit @ ( comp_P7645380973975430442t_unit @ G1 @ F1 ) @ ( comp_P7645380973975430442t_unit @ G22 @ F22 ) @ V ) ) ).

% prod.map_comp
thf(fact_884_prod_Omap__comp,axiom,
    ! [G1: ( b > a ) > b > a,G22: b > b,F1: ( b > a ) > b > a,F22: b > b,V: product_prod_b_a_b] :
      ( ( produc9165320845528156032_a_b_b @ G1 @ G22 @ ( produc9165320845528156032_a_b_b @ F1 @ F22 @ V ) )
      = ( produc9165320845528156032_a_b_b @ ( comp_b_a_b_a_b_a @ G1 @ F1 ) @ ( comp_b_b_b @ G22 @ F22 ) @ V ) ) ).

% prod.map_comp
thf(fact_885_prod_Omap__comp,axiom,
    ! [G1: ( b > a ) > b > a,G22: a > a,F1: ( b > a ) > b > a,F22: a > a,V: product_prod_b_a_a] :
      ( ( produc2729404390646056256_a_a_a @ G1 @ G22 @ ( produc2729404390646056256_a_a_a @ F1 @ F22 @ V ) )
      = ( produc2729404390646056256_a_a_a @ ( comp_b_a_b_a_b_a @ G1 @ F1 ) @ ( comp_a_a_a @ G22 @ F22 ) @ V ) ) ).

% prod.map_comp
thf(fact_886_prod_Omap__comp,axiom,
    ! [G1: dtree_a_b > b,G22: b > b,F1: produc4558475209616630778_a_b_b > dtree_a_b,F22: b > b,V: produc6708371838016462714_b_b_b] :
      ( ( produc4252374707397466189_b_b_b @ G1 @ G22 @ ( produc695453528002274476_b_b_b @ F1 @ F22 @ V ) )
      = ( produc1583750209243554253_b_b_b @ ( comp_d7292648224603294300_a_b_b @ G1 @ F1 ) @ ( comp_b_b_b @ G22 @ F22 ) @ V ) ) ).

% prod.map_comp
thf(fact_887_prod_Omap__comp,axiom,
    ! [G1: dtree_a_b > b,G22: a > a,F1: produc4558475209616630778_a_b_b > dtree_a_b,F22: a > a,V: produc6708371833713233913_b_b_a] :
      ( ( produc7039830289370142221_b_a_a @ G1 @ G22 @ ( produc3482909109974950508_b_a_a @ F1 @ F22 @ V ) )
      = ( produc4371205791216230285_b_a_a @ ( comp_d7292648224603294300_a_b_b @ G1 @ F1 ) @ ( comp_a_a_a @ G22 @ F22 ) @ V ) ) ).

% prod.map_comp
thf(fact_888_Int__UNIV__right,axiom,
    ! [A5: set_b] :
      ( ( inf_inf_set_b @ A5 @ top_top_set_b )
      = A5 ) ).

% Int_UNIV_right
thf(fact_889_Int__UNIV__right,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b] :
      ( ( inf_in6138156342456174402_a_b_b @ A5 @ top_to7222684678772277088_a_b_b )
      = A5 ) ).

% Int_UNIV_right
thf(fact_890_Int__UNIV__right,axiom,
    ! [A5: set_a] :
      ( ( inf_inf_set_a @ A5 @ top_top_set_a )
      = A5 ) ).

% Int_UNIV_right
thf(fact_891_Int__UNIV__right,axiom,
    ! [A5: set_Su4110612849109743515t_unit] :
      ( ( inf_in5198890673353021997t_unit @ A5 @ top_to2771918933716375115t_unit )
      = A5 ) ).

% Int_UNIV_right
thf(fact_892_Int__UNIV__right,axiom,
    ! [A5: set_set_Product_unit] :
      ( ( inf_in2608933832725608379t_unit @ A5 @ top_to1767297665138865437t_unit )
      = A5 ) ).

% Int_UNIV_right
thf(fact_893_Int__UNIV__right,axiom,
    ! [A5: set_b_a] :
      ( ( inf_inf_set_b_a @ A5 @ top_top_set_b_a )
      = A5 ) ).

% Int_UNIV_right
thf(fact_894_Int__UNIV__right,axiom,
    ! [A5: set_Product_unit] :
      ( ( inf_in4660618365625256667t_unit @ A5 @ top_to1996260823553986621t_unit )
      = A5 ) ).

% Int_UNIV_right
thf(fact_895_Int__UNIV__left,axiom,
    ! [B5: set_b] :
      ( ( inf_inf_set_b @ top_top_set_b @ B5 )
      = B5 ) ).

% Int_UNIV_left
thf(fact_896_Int__UNIV__left,axiom,
    ! [B5: set_Pr3012420139608375472_a_b_b] :
      ( ( inf_in6138156342456174402_a_b_b @ top_to7222684678772277088_a_b_b @ B5 )
      = B5 ) ).

% Int_UNIV_left
thf(fact_897_Int__UNIV__left,axiom,
    ! [B5: set_a] :
      ( ( inf_inf_set_a @ top_top_set_a @ B5 )
      = B5 ) ).

% Int_UNIV_left
thf(fact_898_Int__UNIV__left,axiom,
    ! [B5: set_Su4110612849109743515t_unit] :
      ( ( inf_in5198890673353021997t_unit @ top_to2771918933716375115t_unit @ B5 )
      = B5 ) ).

% Int_UNIV_left
thf(fact_899_Int__UNIV__left,axiom,
    ! [B5: set_set_Product_unit] :
      ( ( inf_in2608933832725608379t_unit @ top_to1767297665138865437t_unit @ B5 )
      = B5 ) ).

% Int_UNIV_left
thf(fact_900_Int__UNIV__left,axiom,
    ! [B5: set_b_a] :
      ( ( inf_inf_set_b_a @ top_top_set_b_a @ B5 )
      = B5 ) ).

% Int_UNIV_left
thf(fact_901_Int__UNIV__left,axiom,
    ! [B5: set_Product_unit] :
      ( ( inf_in4660618365625256667t_unit @ top_to1996260823553986621t_unit @ B5 )
      = B5 ) ).

% Int_UNIV_left
thf(fact_902_dtree_Oset__sel_I4_J,axiom,
    ! [Xe: produc4558475209616630778_a_b_b,A: dtree_a_b,Xi: b] :
      ( ( member4380921116106875537_a_b_b @ Xe @ ( fset_P783253628892185035_a_b_b @ ( sucs_a_b @ A ) ) )
     => ( ( member_b @ Xi @ ( basic_1877077703026942_a_b_b @ Xe ) )
       => ( member_b @ Xi @ ( darcs_a_b @ A ) ) ) ) ).

% dtree.set_sel(4)
thf(fact_903_dtree_Osel_I2_J,axiom,
    ! [X12: a,X22: fset_P5281107635120001194_a_b_b] :
      ( ( sucs_a_b @ ( node_a_b @ X12 @ X22 ) )
      = X22 ) ).

% dtree.sel(2)
thf(fact_904_prod_Oset__map_I1_J,axiom,
    ! [F1: produc4558475209616630778_a_b_b > dtree_a_b,F22: produc4558475209616630778_a_b_b > b,V: produc8908337785154950741_a_b_b] :
      ( ( basic_7578771248400840636_a_b_b @ ( produc9210843222980373143_b_b_b @ F1 @ F22 @ V ) )
      = ( image_7065894828672115579ee_a_b @ F1 @ ( basic_7126344468061175165_a_b_b @ V ) ) ) ).

% prod.set_map(1)
thf(fact_905_prod_Oset__map_I1_J,axiom,
    ! [F1: dtree_a_b > produc4558475209616630778_a_b_b,F22: b > produc4558475209616630778_a_b_b,V: produc4558475209616630778_a_b_b] :
      ( ( basic_7126344468061175165_a_b_b @ ( produc1333424704237685261_a_b_b @ F1 @ F22 @ V ) )
      = ( image_360604450665336955_a_b_b @ F1 @ ( basic_7578771248400840636_a_b_b @ V ) ) ) ).

% prod.set_map(1)
thf(fact_906_prod_Oset__map_I1_J,axiom,
    ! [F1: product_unit > product_unit,F22: product_unit > product_unit,V: produc8459935480633519975t_unit] :
      ( ( basic_788101489561936839t_unit @ ( produc3941737999988548470t_unit @ F1 @ F22 @ V ) )
      = ( image_405062704495631173t_unit @ F1 @ ( basic_788101489561936839t_unit @ V ) ) ) ).

% prod.set_map(1)
thf(fact_907_prod_Oset__map_I1_J,axiom,
    ! [F1: dtree_a_b > dtree_a_b,F22: b > b,V: produc4558475209616630778_a_b_b] :
      ( ( basic_7578771248400840636_a_b_b @ ( produc2024282846164127276_b_b_b @ F1 @ F22 @ V ) )
      = ( image_1160270813240538107ee_a_b @ F1 @ ( basic_7578771248400840636_a_b_b @ V ) ) ) ).

% prod.set_map(1)
thf(fact_908_prod_Oset__map_I1_J,axiom,
    ! [F1: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,F22: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,V: produc8908337785154950741_a_b_b] :
      ( ( basic_7126344468061175165_a_b_b @ ( produc8659143532165282274_a_b_b @ F1 @ F22 @ V ) )
      = ( image_6081965176830705659_a_b_b @ F1 @ ( basic_7126344468061175165_a_b_b @ V ) ) ) ).

% prod.set_map(1)
thf(fact_909_prod_Oset__map_I1_J,axiom,
    ! [F1: ( b > a ) > b > a,F22: ( b > a ) > b > a,V: product_prod_b_a_b_a] :
      ( ( basic_fsts_b_a_b_a @ ( produc1686386052851666058_a_b_a @ F1 @ F22 @ V ) )
      = ( image_b_a_b_a @ F1 @ ( basic_fsts_b_a_b_a @ V ) ) ) ).

% prod.set_map(1)
thf(fact_910_prod__fun__imageE,axiom,
    ! [C: produc4558475209616630778_a_b_b,F2: dtree_a_b > dtree_a_b,G2: b > b,R3: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ ( image_6081965176830705659_a_b_b @ ( produc2024282846164127276_b_b_b @ F2 @ G2 ) @ R3 ) )
     => ~ ! [X5: dtree_a_b,Y4: b] :
            ( ( C
              = ( produc331601717337510060_a_b_b @ ( F2 @ X5 ) @ ( G2 @ Y4 ) ) )
           => ~ ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ X5 @ Y4 ) @ R3 ) ) ) ).

% prod_fun_imageE
thf(fact_911_prod__fun__imageE,axiom,
    ! [C: produc8459935480633519975t_unit,F2: product_unit > product_unit,G2: product_unit > product_unit,R3: set_Pr5094982260447487303t_unit] :
      ( ( member7821138191923116944t_unit @ C @ ( image_9149991759805673413t_unit @ ( produc3941737999988548470t_unit @ F2 @ G2 ) @ R3 ) )
     => ~ ! [X5: product_unit,Y4: product_unit] :
            ( ( C
              = ( produc5692694829384537815t_unit @ ( F2 @ X5 ) @ ( G2 @ Y4 ) ) )
           => ~ ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X5 @ Y4 ) @ R3 ) ) ) ).

% prod_fun_imageE
thf(fact_912_prod__fun__imageE,axiom,
    ! [C: produc4558475209616630778_a_b_b,F2: product_unit > dtree_a_b,G2: product_unit > b,R3: set_Pr5094982260447487303t_unit] :
      ( ( member4380921116106875537_a_b_b @ C @ ( image_4720867526043783708_a_b_b @ ( produc1291885961400238659unit_b @ F2 @ G2 ) @ R3 ) )
     => ~ ! [X5: product_unit,Y4: product_unit] :
            ( ( C
              = ( produc331601717337510060_a_b_b @ ( F2 @ X5 ) @ ( G2 @ Y4 ) ) )
           => ~ ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X5 @ Y4 ) @ R3 ) ) ) ).

% prod_fun_imageE
thf(fact_913_prod__fun__imageE,axiom,
    ! [C: produc3469756349985706280ee_a_b,F2: product_unit > b,G2: product_unit > dtree_a_b,R3: set_Pr5094982260447487303t_unit] :
      ( ( member3292202256475951039ee_a_b @ C @ ( image_3632148666412859210ee_a_b @ ( produc4159773624399151967ee_a_b @ F2 @ G2 ) @ R3 ) )
     => ~ ! [X5: product_unit,Y4: product_unit] :
            ( ( C
              = ( produc3542686128043086370ee_a_b @ ( F2 @ X5 ) @ ( G2 @ Y4 ) ) )
           => ~ ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X5 @ Y4 ) @ R3 ) ) ) ).

% prod_fun_imageE
thf(fact_914_prod__fun__imageE,axiom,
    ! [C: produc8459935480633519975t_unit,F2: dtree_a_b > product_unit,G2: b > product_unit,R3: set_Pr3012420139608375472_a_b_b] :
      ( ( member7821138191923116944t_unit @ C @ ( image_4150594470010877606t_unit @ ( produc7457737578077058409t_unit @ F2 @ G2 ) @ R3 ) )
     => ~ ! [X5: dtree_a_b,Y4: b] :
            ( ( C
              = ( produc5692694829384537815t_unit @ ( F2 @ X5 ) @ ( G2 @ Y4 ) ) )
           => ~ ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ X5 @ Y4 ) @ R3 ) ) ) ).

% prod_fun_imageE
thf(fact_915_prod__fun__imageE,axiom,
    ! [C: produc8459935480633519975t_unit,F2: b > product_unit,G2: dtree_a_b > product_unit,R3: set_Pr6717515126349854430ee_a_b] :
      ( ( member7821138191923116944t_unit @ C @ ( image_198770111635725048t_unit @ ( produc4430891178592075597t_unit @ F2 @ G2 ) @ R3 ) )
     => ~ ! [X5: b,Y4: dtree_a_b] :
            ( ( C
              = ( produc5692694829384537815t_unit @ ( F2 @ X5 ) @ ( G2 @ Y4 ) ) )
           => ~ ( member3292202256475951039ee_a_b @ ( produc3542686128043086370ee_a_b @ X5 @ Y4 ) @ R3 ) ) ) ).

% prod_fun_imageE
thf(fact_916_prod__fun__imageE,axiom,
    ! [C: produc4558475209616630778_a_b_b,F2: b > dtree_a_b,G2: dtree_a_b > b,R3: set_Pr6717515126349854430ee_a_b] :
      ( ( member4380921116106875537_a_b_b @ C @ ( image_3585698774939316521_a_b_b @ ( produc5995436795640382528_a_b_b @ F2 @ G2 ) @ R3 ) )
     => ~ ! [X5: b,Y4: dtree_a_b] :
            ( ( C
              = ( produc331601717337510060_a_b_b @ ( F2 @ X5 ) @ ( G2 @ Y4 ) ) )
           => ~ ( member3292202256475951039ee_a_b @ ( produc3542686128043086370ee_a_b @ X5 @ Y4 ) @ R3 ) ) ) ).

% prod_fun_imageE
thf(fact_917_prod__fun__imageE,axiom,
    ! [C: produc3469756349985706280ee_a_b,F2: dtree_a_b > b,G2: b > dtree_a_b,R3: set_Pr3012420139608375472_a_b_b] :
      ( ( member3292202256475951039ee_a_b @ C @ ( image_4993246317199781161ee_a_b @ ( produc2701657453118314412ee_a_b @ F2 @ G2 ) @ R3 ) )
     => ~ ! [X5: dtree_a_b,Y4: b] :
            ( ( C
              = ( produc3542686128043086370ee_a_b @ ( F2 @ X5 ) @ ( G2 @ Y4 ) ) )
           => ~ ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ X5 @ Y4 ) @ R3 ) ) ) ).

% prod_fun_imageE
thf(fact_918_prod__fun__imageE,axiom,
    ! [C: produc3469756349985706280ee_a_b,F2: b > b,G2: dtree_a_b > dtree_a_b,R3: set_Pr6717515126349854430ee_a_b] :
      ( ( member3292202256475951039ee_a_b @ C @ ( image_2496979915308392023ee_a_b @ ( produc4749355648339255596ee_a_b @ F2 @ G2 ) @ R3 ) )
     => ~ ! [X5: b,Y4: dtree_a_b] :
            ( ( C
              = ( produc3542686128043086370ee_a_b @ ( F2 @ X5 ) @ ( G2 @ Y4 ) ) )
           => ~ ( member3292202256475951039ee_a_b @ ( produc3542686128043086370ee_a_b @ X5 @ Y4 ) @ R3 ) ) ) ).

% prod_fun_imageE
thf(fact_919_prod__fun__imageE,axiom,
    ! [C: produc8908337785154950741_a_b_b,F2: product_unit > produc4558475209616630778_a_b_b,G2: product_unit > produc4558475209616630778_a_b_b,R3: set_Pr5094982260447487303t_unit] :
      ( ( member9171970031259705598_a_b_b @ C @ ( image_7065570836208718259_a_b_b @ ( produc8307554072185093430_a_b_b @ F2 @ G2 ) @ R3 ) )
     => ~ ! [X5: product_unit,Y4: product_unit] :
            ( ( C
              = ( produc6533307410877503629_a_b_b @ ( F2 @ X5 ) @ ( G2 @ Y4 ) ) )
           => ~ ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X5 @ Y4 ) @ R3 ) ) ) ).

% prod_fun_imageE
thf(fact_920_disjoint__dverts__if__wf__aux,axiom,
    ! [R: a,Xs2: fset_P5281107635120001194_a_b_b,T1: dtree_a_b,E1: b,T2: dtree_a_b,E2: b] :
      ( ( wf_dverts_a_b @ ( node_a_b @ R @ Xs2 ) )
     => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ T1 @ E1 ) @ ( fset_P783253628892185035_a_b_b @ Xs2 ) )
       => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ T2 @ E2 ) @ ( fset_P783253628892185035_a_b_b @ Xs2 ) )
         => ( ( ( produc331601717337510060_a_b_b @ T1 @ E1 )
             != ( produc331601717337510060_a_b_b @ T2 @ E2 ) )
           => ( ( inf_inf_set_a @ ( dverts_a_b @ T1 ) @ ( dverts_a_b @ T2 ) )
              = bot_bot_set_a ) ) ) ) ) ).

% disjoint_dverts_if_wf_aux
thf(fact_921_range__snd,axiom,
    ( ( image_3908709015779211070_b_b_b @ produc5748100250121904638_a_b_b @ top_to7222684678772277088_a_b_b )
    = top_top_set_b ) ).

% range_snd
thf(fact_922_range__snd,axiom,
    ( ( image_6364595536291967657ee_a_b @ produc8959184660827480948ee_a_b @ top_to1704407628658980238ee_a_b )
    = top_to9008179178016042208ee_a_b ) ).

% range_snd
thf(fact_923_boolean__algebra_Oconj__zero__right,axiom,
    ! [X3: set_Pr3012420139608375472_a_b_b] :
      ( ( inf_in6138156342456174402_a_b_b @ X3 @ bot_bo3721250822024684356_a_b_b )
      = bot_bo3721250822024684356_a_b_b ) ).

% boolean_algebra.conj_zero_right
thf(fact_924_boolean__algebra_Oconj__zero__right,axiom,
    ! [X3: set_Product_unit] :
      ( ( inf_in4660618365625256667t_unit @ X3 @ bot_bo3957492148770167129t_unit )
      = bot_bo3957492148770167129t_unit ) ).

% boolean_algebra.conj_zero_right
thf(fact_925_boolean__algebra_Oconj__zero__right,axiom,
    ! [X3: set_nat] :
      ( ( inf_inf_set_nat @ X3 @ bot_bot_set_nat )
      = bot_bot_set_nat ) ).

% boolean_algebra.conj_zero_right
thf(fact_926_boolean__algebra_Oconj__zero__right,axiom,
    ! [X3: set_b] :
      ( ( inf_inf_set_b @ X3 @ bot_bot_set_b )
      = bot_bot_set_b ) ).

% boolean_algebra.conj_zero_right
thf(fact_927_boolean__algebra_Oconj__zero__right,axiom,
    ! [X3: set_a] :
      ( ( inf_inf_set_a @ X3 @ bot_bot_set_a )
      = bot_bot_set_a ) ).

% boolean_algebra.conj_zero_right
thf(fact_928_boolean__algebra_Oconj__zero__right,axiom,
    ! [X3: produc4558475209616630778_a_b_b > $o] :
      ( ( inf_in55627642082981827_b_b_o @ X3 @ bot_bo7321339186913516097_b_b_o )
      = bot_bo7321339186913516097_b_b_o ) ).

% boolean_algebra.conj_zero_right
thf(fact_929_boolean__algebra_Oconj__zero__left,axiom,
    ! [X3: set_b] :
      ( ( inf_inf_set_b @ bot_bot_set_b @ X3 )
      = bot_bot_set_b ) ).

% boolean_algebra.conj_zero_left
thf(fact_930_boolean__algebra_Oconj__zero__left,axiom,
    ! [X3: set_a] :
      ( ( inf_inf_set_a @ bot_bot_set_a @ X3 )
      = bot_bot_set_a ) ).

% boolean_algebra.conj_zero_left
thf(fact_931_boolean__algebra_Oconj__zero__left,axiom,
    ! [X3: produc4558475209616630778_a_b_b > $o] :
      ( ( inf_in55627642082981827_b_b_o @ bot_bo7321339186913516097_b_b_o @ X3 )
      = bot_bo7321339186913516097_b_b_o ) ).

% boolean_algebra.conj_zero_left
thf(fact_932_inf__top_Oright__neutral,axiom,
    ! [A: set_Product_unit] :
      ( ( inf_in4660618365625256667t_unit @ A @ top_to1996260823553986621t_unit )
      = A ) ).

% inf_top.right_neutral
thf(fact_933_inf__top_Oneutr__eq__iff,axiom,
    ! [A: set_Product_unit,B: set_Product_unit] :
      ( ( top_to1996260823553986621t_unit
        = ( inf_in4660618365625256667t_unit @ A @ B ) )
      = ( ( A = top_to1996260823553986621t_unit )
        & ( B = top_to1996260823553986621t_unit ) ) ) ).

% inf_top.neutr_eq_iff
thf(fact_934_inf__top_Oleft__neutral,axiom,
    ! [A: set_Product_unit] :
      ( ( inf_in4660618365625256667t_unit @ top_to1996260823553986621t_unit @ A )
      = A ) ).

% inf_top.left_neutral
thf(fact_935_inf__top_Oeq__neutr__iff,axiom,
    ! [A: set_Product_unit,B: set_Product_unit] :
      ( ( ( inf_in4660618365625256667t_unit @ A @ B )
        = top_to1996260823553986621t_unit )
      = ( ( A = top_to1996260823553986621t_unit )
        & ( B = top_to1996260823553986621t_unit ) ) ) ).

% inf_top.eq_neutr_iff
thf(fact_936_inf__top__left,axiom,
    ! [X3: set_Product_unit] :
      ( ( inf_in4660618365625256667t_unit @ top_to1996260823553986621t_unit @ X3 )
      = X3 ) ).

% inf_top_left
thf(fact_937_inf__top__right,axiom,
    ! [X3: set_Product_unit] :
      ( ( inf_in4660618365625256667t_unit @ X3 @ top_to1996260823553986621t_unit )
      = X3 ) ).

% inf_top_right
thf(fact_938_inf__eq__top__iff,axiom,
    ! [X3: set_Product_unit,Y3: set_Product_unit] :
      ( ( ( inf_in4660618365625256667t_unit @ X3 @ Y3 )
        = top_to1996260823553986621t_unit )
      = ( ( X3 = top_to1996260823553986621t_unit )
        & ( Y3 = top_to1996260823553986621t_unit ) ) ) ).

% inf_eq_top_iff
thf(fact_939_top__eq__inf__iff,axiom,
    ! [X3: set_Product_unit,Y3: set_Product_unit] :
      ( ( top_to1996260823553986621t_unit
        = ( inf_in4660618365625256667t_unit @ X3 @ Y3 ) )
      = ( ( X3 = top_to1996260823553986621t_unit )
        & ( Y3 = top_to1996260823553986621t_unit ) ) ) ).

% top_eq_inf_iff
thf(fact_940_inter__fset,axiom,
    ! [X3: fset_P5281107635120001194_a_b_b,Xa2: fset_P5281107635120001194_a_b_b] :
      ( ( fset_P783253628892185035_a_b_b @ ( inf_in7138637532943773244_a_b_b @ X3 @ Xa2 ) )
      = ( inf_in6138156342456174402_a_b_b @ ( fset_P783253628892185035_a_b_b @ X3 ) @ ( fset_P783253628892185035_a_b_b @ Xa2 ) ) ) ).

% inter_fset
thf(fact_941_top__empty__eq,axiom,
    ( top_to762646584048855333_b_b_o
    = ( ^ [X: produc4558475209616630778_a_b_b] : ( member4380921116106875537_a_b_b @ X @ top_to7222684678772277088_a_b_b ) ) ) ).

% top_empty_eq
thf(fact_942_top__empty__eq,axiom,
    ( top_to2465898995584390880unit_o
    = ( ^ [X: product_unit] : ( member_Product_unit @ X @ top_to1996260823553986621t_unit ) ) ) ).

% top_empty_eq
thf(fact_943_bot__empty__eq,axiom,
    ( bot_bo7321339186913516097_b_b_o
    = ( ^ [X: produc4558475209616630778_a_b_b] : ( member4380921116106875537_a_b_b @ X @ bot_bo3721250822024684356_a_b_b ) ) ) ).

% bot_empty_eq
thf(fact_944_boolean__algebra_Oconj__one__right,axiom,
    ! [X3: set_Product_unit] :
      ( ( inf_in4660618365625256667t_unit @ X3 @ top_to1996260823553986621t_unit )
      = X3 ) ).

% boolean_algebra.conj_one_right
thf(fact_945_eq__snd__iff,axiom,
    ! [B: b,P: produc4558475209616630778_a_b_b] :
      ( ( B
        = ( produc5748100250121904638_a_b_b @ P ) )
      = ( ? [A4: dtree_a_b] :
            ( P
            = ( produc331601717337510060_a_b_b @ A4 @ B ) ) ) ) ).

% eq_snd_iff
thf(fact_946_wf__darcs__sucs,axiom,
    ! [T: dtree_a_b,X3: produc4558475209616630778_a_b_b,R: a] :
      ( ( wf_darcs_a_b @ T )
     => ( ( member4380921116106875537_a_b_b @ X3 @ ( fset_P783253628892185035_a_b_b @ ( sucs_a_b @ T ) ) )
       => ( wf_darcs_a_b @ ( node_a_b @ R @ ( finser8437519239679886002_a_b_b @ X3 @ bot_bo2895716411488905534_a_b_b ) ) ) ) ) ).

% wf_darcs_sucs
thf(fact_947_map__prod__o__convol,axiom,
    ! [H1: ( b > a ) > b > a,H22: ( b > a ) > b > a,F2: ( b > a ) > b > a,G2: ( b > a ) > b > a] :
      ( ( comp_P5805957429449400903_a_b_a @ ( produc1686386052851666058_a_b_a @ H1 @ H22 ) @ ( bNF_co7059620845615007703_a_b_a @ F2 @ G2 ) )
      = ( bNF_co7059620845615007703_a_b_a @ ( comp_b_a_b_a_b_a @ H1 @ F2 ) @ ( comp_b_a_b_a_b_a @ H22 @ G2 ) ) ) ).

% map_prod_o_convol
thf(fact_948_singleton__uneq,axiom,
    ! [R: a,T: dtree_a_b,E: b] :
      ( ( node_a_b @ R @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T @ E ) @ bot_bo2895716411488905534_a_b_b ) )
     != T ) ).

% singleton_uneq
thf(fact_949_convol__o,axiom,
    ! [F2: ( b > a ) > b > a,G2: ( b > a ) > b > a,H: ( b > a ) > b > a] :
      ( ( comp_b7652884982158753286_a_b_a @ ( bNF_co7059620845615007703_a_b_a @ F2 @ G2 ) @ H )
      = ( bNF_co7059620845615007703_a_b_a @ ( comp_b_a_b_a_b_a @ F2 @ H ) @ ( comp_b_a_b_a_b_a @ G2 @ H ) ) ) ).

% convol_o
thf(fact_950_singleton__uneq_H,axiom,
    ! [R: a,T: dtree_a_b,E: b,V: a] :
      ( ( node_a_b @ R @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T @ E ) @ bot_bo2895716411488905534_a_b_b ) )
     != ( node_a_b @ V @ ( sucs_a_b @ T ) ) ) ).

% singleton_uneq'
thf(fact_951_singleton__suc,axiom,
    ! [T: dtree_a_b,R: a,E: b] : ( member_dtree_a_b @ T @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ ( sucs_a_b @ ( node_a_b @ R @ ( finser8437519239679886002_a_b_b @ ( produc331601717337510060_a_b_b @ T @ E ) @ bot_bo2895716411488905534_a_b_b ) ) ) ) ) ) ).

% singleton_suc
thf(fact_952_dverts__suc__if__not__root,axiom,
    ! [V: a,T: dtree_a_b] :
      ( ( member_a @ V @ ( dverts_a_b @ T ) )
     => ( ( V
         != ( root_a_b @ T ) )
       => ? [X5: dtree_a_b] :
            ( ( member_dtree_a_b @ X5 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ ( sucs_a_b @ T ) ) ) )
            & ( member_a @ V @ ( dverts_a_b @ X5 ) ) ) ) ) ).

% dverts_suc_if_not_root
thf(fact_953_case__prod__Pair,axiom,
    ( ( produc5460679229782211283_a_b_b @ produc331601717337510060_a_b_b )
    = id_Pro6814982414164175945_a_b_b ) ).

% case_prod_Pair
thf(fact_954_fun_Omap__id,axiom,
    ! [T: ( b > a ) > b > a] :
      ( ( comp_b_a_b_a_b_a @ id_b_a @ T )
      = T ) ).

% fun.map_id
thf(fact_955_id__comp,axiom,
    ! [G2: ( b > a ) > b > a] :
      ( ( comp_b_a_b_a_b_a @ id_b_a @ G2 )
      = G2 ) ).

% id_comp
thf(fact_956_comp__id,axiom,
    ! [F2: ( b > a ) > b > a] :
      ( ( comp_b_a_b_a_b_a @ F2 @ id_b_a )
      = F2 ) ).

% comp_id
thf(fact_957_prod_Ocollapse,axiom,
    ! [Prod: produc4558475209616630778_a_b_b] :
      ( ( produc331601717337510060_a_b_b @ ( produc697780174058963904_a_b_b @ Prod ) @ ( produc5748100250121904638_a_b_b @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_958_fun_Omap__id0,axiom,
    ( ( comp_b_a_b_a_b_a @ id_b_a )
    = id_b_a_b_a ) ).

% fun.map_id0
thf(fact_959_DEADID_Oin__rel,axiom,
    ( ( ^ [Y5: produc4558475209616630778_a_b_b,Z4: produc4558475209616630778_a_b_b] : ( Y5 = Z4 ) )
    = ( ^ [A4: produc4558475209616630778_a_b_b,B4: produc4558475209616630778_a_b_b] :
        ? [Z5: produc4558475209616630778_a_b_b] :
          ( ( member4380921116106875537_a_b_b @ Z5 @ top_to7222684678772277088_a_b_b )
          & ( ( id_Pro6814982414164175945_a_b_b @ Z5 )
            = A4 )
          & ( ( id_Pro6814982414164175945_a_b_b @ Z5 )
            = B4 ) ) ) ) ).

% DEADID.in_rel
thf(fact_960_DEADID_Oin__rel,axiom,
    ( ( ^ [Y5: product_unit,Z4: product_unit] : ( Y5 = Z4 ) )
    = ( ^ [A4: product_unit,B4: product_unit] :
        ? [Z5: product_unit] :
          ( ( member_Product_unit @ Z5 @ top_to1996260823553986621t_unit )
          & ( ( id_Product_unit @ Z5 )
            = A4 )
          & ( ( id_Product_unit @ Z5 )
            = B4 ) ) ) ) ).

% DEADID.in_rel
thf(fact_961_fstI,axiom,
    ! [X3: produc4558475209616630778_a_b_b,Y3: dtree_a_b,Z: b] :
      ( ( X3
        = ( produc331601717337510060_a_b_b @ Y3 @ Z ) )
     => ( ( produc697780174058963904_a_b_b @ X3 )
        = Y3 ) ) ).

% fstI
thf(fact_962_fst__eqD,axiom,
    ! [X3: dtree_a_b,Y3: b,A: dtree_a_b] :
      ( ( ( produc697780174058963904_a_b_b @ ( produc331601717337510060_a_b_b @ X3 @ Y3 ) )
        = A )
     => ( X3 = A ) ) ).

% fst_eqD
thf(fact_963_fst__conv,axiom,
    ! [X12: dtree_a_b,X22: b] :
      ( ( produc697780174058963904_a_b_b @ ( produc331601717337510060_a_b_b @ X12 @ X22 ) )
      = X12 ) ).

% fst_conv
thf(fact_964_eq__fst__iff,axiom,
    ! [A: dtree_a_b,P: produc4558475209616630778_a_b_b] :
      ( ( A
        = ( produc697780174058963904_a_b_b @ P ) )
      = ( ? [B4: b] :
            ( P
            = ( produc331601717337510060_a_b_b @ A @ B4 ) ) ) ) ).

% eq_fst_iff
thf(fact_965_comp__eq__id__dest,axiom,
    ! [A: ( b > a ) > b > a,B: ( b > a ) > b > a,C: ( b > a ) > b > a,V: b > a] :
      ( ( ( comp_b_a_b_a_b_a @ A @ B )
        = ( comp_b_a_b_a_b_a @ id_b_a @ C ) )
     => ( ( A @ ( B @ V ) )
        = ( C @ V ) ) ) ).

% comp_eq_id_dest
thf(fact_966_pointfree__idE,axiom,
    ! [F2: ( b > a ) > b > a,G2: ( b > a ) > b > a,X3: b > a] :
      ( ( ( comp_b_a_b_a_b_a @ F2 @ G2 )
        = id_b_a )
     => ( ( F2 @ ( G2 @ X3 ) )
        = X3 ) ) ).

% pointfree_idE
thf(fact_967_surj__id,axiom,
    ( ( image_405062704495631173t_unit @ id_Product_unit @ top_to1996260823553986621t_unit )
    = top_to1996260823553986621t_unit ) ).

% surj_id
thf(fact_968_surjective__pairing,axiom,
    ! [T: produc4558475209616630778_a_b_b] :
      ( T
      = ( produc331601717337510060_a_b_b @ ( produc697780174058963904_a_b_b @ T ) @ ( produc5748100250121904638_a_b_b @ T ) ) ) ).

% surjective_pairing
thf(fact_969_prod_Oexhaust__sel,axiom,
    ! [Prod: produc4558475209616630778_a_b_b] :
      ( Prod
      = ( produc331601717337510060_a_b_b @ ( produc697780174058963904_a_b_b @ Prod ) @ ( produc5748100250121904638_a_b_b @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_970_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P2: dtree_a_b > b > $o,X3: dtree_a_b,Y3: b,A: produc4558475209616630778_a_b_b] :
      ( ( P2 @ X3 @ Y3 )
     => ( ( A
          = ( produc331601717337510060_a_b_b @ X3 @ Y3 ) )
       => ( P2 @ ( produc697780174058963904_a_b_b @ A ) @ ( produc5748100250121904638_a_b_b @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_971_Product__Type_OCollect__case__prodD,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A5: dtree_a_b > b > $o] :
      ( ( member4380921116106875537_a_b_b @ X3 @ ( collec1368399972772960719_a_b_b @ ( produc1325217093046185599_b_b_o @ A5 ) ) )
     => ( A5 @ ( produc697780174058963904_a_b_b @ X3 ) @ ( produc5748100250121904638_a_b_b @ X3 ) ) ) ).

% Product_Type.Collect_case_prodD
thf(fact_972_child__uneq,axiom,
    ! [T: dtree_a_b,Xs2: fset_P5281107635120001194_a_b_b,R: a] :
      ( ( member_dtree_a_b @ T @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ Xs2 ) ) )
     => ( ( node_a_b @ R @ Xs2 )
       != T ) ) ).

% child_uneq
thf(fact_973_suc__uneq,axiom,
    ! [T1: dtree_a_b,T: dtree_a_b] :
      ( ( member_dtree_a_b @ T1 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ ( sucs_a_b @ T ) ) ) )
     => ( T != T1 ) ) ).

% suc_uneq
thf(fact_974_dverts__child__if__not__root,axiom,
    ! [V: a,R: a,Xs2: fset_P5281107635120001194_a_b_b] :
      ( ( member_a @ V @ ( dverts_a_b @ ( node_a_b @ R @ Xs2 ) ) )
     => ( ( V != R )
       => ? [X5: dtree_a_b] :
            ( ( member_dtree_a_b @ X5 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ Xs2 ) ) )
            & ( member_a @ V @ ( dverts_a_b @ X5 ) ) ) ) ) ).

% dverts_child_if_not_root
thf(fact_975_prod_Oswap__def,axiom,
    ( produc6117232556371446914ee_a_b
    = ( ^ [P3: produc3469756349985706280ee_a_b] : ( produc331601717337510060_a_b_b @ ( produc8959184660827480948ee_a_b @ P3 ) @ ( produc3908864584764540214ee_a_b @ P3 ) ) ) ) ).

% prod.swap_def
thf(fact_976_child__uneq_H,axiom,
    ! [T: dtree_a_b,Xs2: fset_P5281107635120001194_a_b_b,R: a,V: a] :
      ( ( member_dtree_a_b @ T @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ Xs2 ) ) )
     => ( ( node_a_b @ R @ Xs2 )
       != ( node_a_b @ V @ ( sucs_a_b @ T ) ) ) ) ).

% child_uneq'
thf(fact_977_suc__uneq_H,axiom,
    ! [T1: dtree_a_b,T: dtree_a_b,V: a] :
      ( ( member_dtree_a_b @ T1 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ ( sucs_a_b @ T ) ) ) )
     => ( T
       != ( node_a_b @ V @ ( sucs_a_b @ T1 ) ) ) ) ).

% suc_uneq'
thf(fact_978_wf__darcs__rec,axiom,
    ! [R: a,Xs2: fset_P5281107635120001194_a_b_b,T1: dtree_a_b] :
      ( ( wf_darcs_a_b @ ( node_a_b @ R @ Xs2 ) )
     => ( ( member_dtree_a_b @ T1 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ Xs2 ) ) )
       => ( wf_darcs_a_b @ T1 ) ) ) ).

% wf_darcs_rec
thf(fact_979_wf__dverts__rec,axiom,
    ! [R: a,Xs2: fset_P5281107635120001194_a_b_b,T1: dtree_a_b] :
      ( ( wf_dverts_a_b @ ( node_a_b @ R @ Xs2 ) )
     => ( ( member_dtree_a_b @ T1 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ Xs2 ) ) )
       => ( wf_dverts_a_b @ T1 ) ) ) ).

% wf_dverts_rec
thf(fact_980_exI__realizer,axiom,
    ! [P2: b > dtree_a_b > $o,Y3: b,X3: dtree_a_b] :
      ( ( P2 @ Y3 @ X3 )
     => ( P2 @ ( produc5748100250121904638_a_b_b @ ( produc331601717337510060_a_b_b @ X3 @ Y3 ) ) @ ( produc697780174058963904_a_b_b @ ( produc331601717337510060_a_b_b @ X3 @ Y3 ) ) ) ) ).

% exI_realizer
thf(fact_981_conjI__realizer,axiom,
    ! [P2: dtree_a_b > $o,P: dtree_a_b,Q: b > $o,Q2: b] :
      ( ( P2 @ P )
     => ( ( Q @ Q2 )
       => ( ( P2 @ ( produc697780174058963904_a_b_b @ ( produc331601717337510060_a_b_b @ P @ Q2 ) ) )
          & ( Q @ ( produc5748100250121904638_a_b_b @ ( produc331601717337510060_a_b_b @ P @ Q2 ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_982_isomorphism__expand,axiom,
    ! [F2: ( b > a ) > b > a,G2: ( b > a ) > b > a] :
      ( ( ( ( comp_b_a_b_a_b_a @ F2 @ G2 )
          = id_b_a )
        & ( ( comp_b_a_b_a_b_a @ G2 @ F2 )
          = id_b_a ) )
      = ( ! [X: b > a] :
            ( ( F2 @ ( G2 @ X ) )
            = X )
        & ! [X: b > a] :
            ( ( G2 @ ( F2 @ X ) )
            = X ) ) ) ).

% isomorphism_expand
thf(fact_983_left__right__inverse__eq,axiom,
    ! [F2: ( b > a ) > b > a,G2: ( b > a ) > b > a,H: ( b > a ) > b > a] :
      ( ( ( comp_b_a_b_a_b_a @ F2 @ G2 )
        = id_b_a )
     => ( ( ( comp_b_a_b_a_b_a @ G2 @ H )
          = id_b_a )
       => ( F2 = H ) ) ) ).

% left_right_inverse_eq
thf(fact_984_apfst__conv,axiom,
    ! [F2: dtree_a_b > dtree_a_b,X3: dtree_a_b,Y3: b] :
      ( ( produc1844830993343419085_a_b_b @ F2 @ ( produc331601717337510060_a_b_b @ X3 @ Y3 ) )
      = ( produc331601717337510060_a_b_b @ ( F2 @ X3 ) @ Y3 ) ) ).

% apfst_conv
thf(fact_985_apfst__convE,axiom,
    ! [Q2: produc4558475209616630778_a_b_b,F2: dtree_a_b > dtree_a_b,P: produc4558475209616630778_a_b_b] :
      ( ( Q2
        = ( produc1844830993343419085_a_b_b @ F2 @ P ) )
     => ~ ! [X5: dtree_a_b,Y4: b] :
            ( ( P
              = ( produc331601717337510060_a_b_b @ X5 @ Y4 ) )
           => ( Q2
             != ( produc331601717337510060_a_b_b @ ( F2 @ X5 ) @ Y4 ) ) ) ) ).

% apfst_convE
thf(fact_986_fthe__elem__def,axiom,
    ( fthe_e7442499522476018237_a_b_b
    = ( map_fu3200731890701411048_a_b_b @ fset_P783253628892185035_a_b_b @ id_Pro6814982414164175945_a_b_b @ the_el4127461656392778949_a_b_b ) ) ).

% fthe_elem_def
thf(fact_987_dverts__suc__subseteq,axiom,
    ! [X3: dtree_a_b,T: dtree_a_b] :
      ( ( member_dtree_a_b @ X3 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ ( sucs_a_b @ T ) ) ) )
     => ( ord_less_eq_set_a @ ( dverts_a_b @ X3 ) @ ( dverts_a_b @ T ) ) ) ).

% dverts_suc_subseteq
thf(fact_988_dverts__child__subseteq,axiom,
    ! [X3: dtree_a_b,Xs2: fset_P5281107635120001194_a_b_b,R: a] :
      ( ( member_dtree_a_b @ X3 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ Xs2 ) ) )
     => ( ord_less_eq_set_a @ ( dverts_a_b @ X3 ) @ ( dverts_a_b @ ( node_a_b @ R @ Xs2 ) ) ) ) ).

% dverts_child_subseteq
thf(fact_989_dual__order_Orefl,axiom,
    ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).

% dual_order.refl
thf(fact_990_order__refl,axiom,
    ! [X3: nat] : ( ord_less_eq_nat @ X3 @ X3 ) ).

% order_refl
thf(fact_991_subsetI,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ! [X5: produc4558475209616630778_a_b_b] :
          ( ( member4380921116106875537_a_b_b @ X5 @ A5 )
         => ( member4380921116106875537_a_b_b @ X5 @ B5 ) )
     => ( ord_le146215904626753808_a_b_b @ A5 @ B5 ) ) ).

% subsetI
thf(fact_992_order__antisym__conv,axiom,
    ! [Y3: nat,X3: nat] :
      ( ( ord_less_eq_nat @ Y3 @ X3 )
     => ( ( ord_less_eq_nat @ X3 @ Y3 )
        = ( X3 = Y3 ) ) ) ).

% order_antisym_conv
thf(fact_993_linorder__le__cases,axiom,
    ! [X3: nat,Y3: nat] :
      ( ~ ( ord_less_eq_nat @ X3 @ Y3 )
     => ( ord_less_eq_nat @ Y3 @ X3 ) ) ).

% linorder_le_cases
thf(fact_994_ord__le__eq__subst,axiom,
    ! [A: nat,B: nat,F2: nat > nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ( F2 @ B )
          = C )
       => ( ! [X5: nat,Y4: nat] :
              ( ( ord_less_eq_nat @ X5 @ Y4 )
             => ( ord_less_eq_nat @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) )
         => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).

% ord_le_eq_subst
thf(fact_995_ord__eq__le__subst,axiom,
    ! [A: nat,F2: nat > nat,B: nat,C: nat] :
      ( ( A
        = ( F2 @ B ) )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ! [X5: nat,Y4: nat] :
              ( ( ord_less_eq_nat @ X5 @ Y4 )
             => ( ord_less_eq_nat @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) )
         => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_996_linorder__linear,axiom,
    ! [X3: nat,Y3: nat] :
      ( ( ord_less_eq_nat @ X3 @ Y3 )
      | ( ord_less_eq_nat @ Y3 @ X3 ) ) ).

% linorder_linear
thf(fact_997_order__eq__refl,axiom,
    ! [X3: nat,Y3: nat] :
      ( ( X3 = Y3 )
     => ( ord_less_eq_nat @ X3 @ Y3 ) ) ).

% order_eq_refl
thf(fact_998_order__subst2,axiom,
    ! [A: nat,B: nat,F2: nat > nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ ( F2 @ B ) @ C )
       => ( ! [X5: nat,Y4: nat] :
              ( ( ord_less_eq_nat @ X5 @ Y4 )
             => ( ord_less_eq_nat @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) )
         => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).

% order_subst2
thf(fact_999_order__subst1,axiom,
    ! [A: nat,F2: nat > nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ! [X5: nat,Y4: nat] :
              ( ( ord_less_eq_nat @ X5 @ Y4 )
             => ( ord_less_eq_nat @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) )
         => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).

% order_subst1
thf(fact_1000_Orderings_Oorder__eq__iff,axiom,
    ( ( ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
    = ( ^ [A4: nat,B4: nat] :
          ( ( ord_less_eq_nat @ A4 @ B4 )
          & ( ord_less_eq_nat @ B4 @ A4 ) ) ) ) ).

% Orderings.order_eq_iff
thf(fact_1001_antisym,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ A )
       => ( A = B ) ) ) ).

% antisym
thf(fact_1002_subset__iff,axiom,
    ( ord_le146215904626753808_a_b_b
    = ( ^ [A6: set_Pr3012420139608375472_a_b_b,B6: set_Pr3012420139608375472_a_b_b] :
        ! [T3: produc4558475209616630778_a_b_b] :
          ( ( member4380921116106875537_a_b_b @ T3 @ A6 )
         => ( member4380921116106875537_a_b_b @ T3 @ B6 ) ) ) ) ).

% subset_iff
thf(fact_1003_subset__eq,axiom,
    ( ord_le146215904626753808_a_b_b
    = ( ^ [A6: set_Pr3012420139608375472_a_b_b,B6: set_Pr3012420139608375472_a_b_b] :
        ! [X: produc4558475209616630778_a_b_b] :
          ( ( member4380921116106875537_a_b_b @ X @ A6 )
         => ( member4380921116106875537_a_b_b @ X @ B6 ) ) ) ) ).

% subset_eq
thf(fact_1004_subsetD,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b,C: produc4558475209616630778_a_b_b] :
      ( ( ord_le146215904626753808_a_b_b @ A5 @ B5 )
     => ( ( member4380921116106875537_a_b_b @ C @ A5 )
       => ( member4380921116106875537_a_b_b @ C @ B5 ) ) ) ).

% subsetD
thf(fact_1005_in__mono,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b,X3: produc4558475209616630778_a_b_b] :
      ( ( ord_le146215904626753808_a_b_b @ A5 @ B5 )
     => ( ( member4380921116106875537_a_b_b @ X3 @ A5 )
       => ( member4380921116106875537_a_b_b @ X3 @ B5 ) ) ) ).

% in_mono
thf(fact_1006_dual__order_Otrans,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( ( ord_less_eq_nat @ B @ A )
     => ( ( ord_less_eq_nat @ C @ B )
       => ( ord_less_eq_nat @ C @ A ) ) ) ).

% dual_order.trans
thf(fact_1007_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_1008_dual__order_Oeq__iff,axiom,
    ( ( ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
    = ( ^ [A4: nat,B4: nat] :
          ( ( ord_less_eq_nat @ B4 @ A4 )
          & ( ord_less_eq_nat @ A4 @ B4 ) ) ) ) ).

% dual_order.eq_iff
thf(fact_1009_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_1010_order__trans,axiom,
    ! [X3: nat,Y3: nat,Z: nat] :
      ( ( ord_less_eq_nat @ X3 @ Y3 )
     => ( ( ord_less_eq_nat @ Y3 @ Z )
       => ( ord_less_eq_nat @ X3 @ Z ) ) ) ).

% order_trans
thf(fact_1011_order_Otrans,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_eq_nat @ A @ C ) ) ) ).

% order.trans
thf(fact_1012_order__antisym,axiom,
    ! [X3: nat,Y3: nat] :
      ( ( ord_less_eq_nat @ X3 @ Y3 )
     => ( ( ord_less_eq_nat @ Y3 @ X3 )
       => ( X3 = Y3 ) ) ) ).

% order_antisym
thf(fact_1013_ord__le__eq__trans,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( B = C )
       => ( ord_less_eq_nat @ A @ C ) ) ) ).

% ord_le_eq_trans
thf(fact_1014_ord__eq__le__trans,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( A = B )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_eq_nat @ A @ C ) ) ) ).

% ord_eq_le_trans
thf(fact_1015_order__class_Oorder__eq__iff,axiom,
    ( ( ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
    = ( ^ [X: nat,Y: nat] :
          ( ( ord_less_eq_nat @ X @ Y )
          & ( ord_less_eq_nat @ Y @ X ) ) ) ) ).

% order_class.order_eq_iff
thf(fact_1016_le__cases3,axiom,
    ! [X3: nat,Y3: nat,Z: nat] :
      ( ( ( ord_less_eq_nat @ X3 @ Y3 )
       => ~ ( ord_less_eq_nat @ Y3 @ Z ) )
     => ( ( ( ord_less_eq_nat @ Y3 @ X3 )
         => ~ ( ord_less_eq_nat @ X3 @ Z ) )
       => ( ( ( ord_less_eq_nat @ X3 @ Z )
           => ~ ( ord_less_eq_nat @ Z @ Y3 ) )
         => ( ( ( ord_less_eq_nat @ Z @ Y3 )
             => ~ ( ord_less_eq_nat @ Y3 @ X3 ) )
           => ( ( ( ord_less_eq_nat @ Y3 @ Z )
               => ~ ( ord_less_eq_nat @ Z @ X3 ) )
             => ~ ( ( ord_less_eq_nat @ Z @ X3 )
                 => ~ ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ) ) ) ) ).

% le_cases3
thf(fact_1017_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_1018_top__greatest,axiom,
    ! [A: set_Product_unit] : ( ord_le3507040750410214029t_unit @ A @ top_to1996260823553986621t_unit ) ).

% top_greatest
thf(fact_1019_top_Oextremum__unique,axiom,
    ! [A: set_Product_unit] :
      ( ( ord_le3507040750410214029t_unit @ top_to1996260823553986621t_unit @ A )
      = ( A = top_to1996260823553986621t_unit ) ) ).

% top.extremum_unique
thf(fact_1020_top_Oextremum__uniqueI,axiom,
    ! [A: set_Product_unit] :
      ( ( ord_le3507040750410214029t_unit @ top_to1996260823553986621t_unit @ A )
     => ( A = top_to1996260823553986621t_unit ) ) ).

% top.extremum_uniqueI
thf(fact_1021_bot_Oextremum,axiom,
    ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).

% bot.extremum
thf(fact_1022_bot_Oextremum__unique,axiom,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ A @ bot_bot_nat )
      = ( A = bot_bot_nat ) ) ).

% bot.extremum_unique
thf(fact_1023_bot_Oextremum__uniqueI,axiom,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ A @ bot_bot_nat )
     => ( A = bot_bot_nat ) ) ).

% bot.extremum_uniqueI
thf(fact_1024_subrelI,axiom,
    ! [R: set_Pr3012420139608375472_a_b_b,S: set_Pr3012420139608375472_a_b_b] :
      ( ! [X5: dtree_a_b,Y4: b] :
          ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ X5 @ Y4 ) @ R )
         => ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ X5 @ Y4 ) @ S ) )
     => ( ord_le146215904626753808_a_b_b @ R @ S ) ) ).

% subrelI
thf(fact_1025_subset__UNIV,axiom,
    ! [A5: set_Product_unit] : ( ord_le3507040750410214029t_unit @ A5 @ top_to1996260823553986621t_unit ) ).

% subset_UNIV
thf(fact_1026_image__subsetI,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,F2: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ! [X5: produc4558475209616630778_a_b_b] :
          ( ( member4380921116106875537_a_b_b @ X5 @ A5 )
         => ( member4380921116106875537_a_b_b @ ( F2 @ X5 ) @ B5 ) )
     => ( ord_le146215904626753808_a_b_b @ ( image_6081965176830705659_a_b_b @ F2 @ A5 ) @ B5 ) ) ).

% image_subsetI
thf(fact_1027_subset__emptyI,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b] :
      ( ! [X5: produc4558475209616630778_a_b_b] :
          ~ ( member4380921116106875537_a_b_b @ X5 @ A5 )
     => ( ord_le146215904626753808_a_b_b @ A5 @ bot_bo3721250822024684356_a_b_b ) ) ).

% subset_emptyI
thf(fact_1028_Int__Collect__mono,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b,P2: produc4558475209616630778_a_b_b > $o,Q: produc4558475209616630778_a_b_b > $o] :
      ( ( ord_le146215904626753808_a_b_b @ A5 @ B5 )
     => ( ! [X5: produc4558475209616630778_a_b_b] :
            ( ( member4380921116106875537_a_b_b @ X5 @ A5 )
           => ( ( P2 @ X5 )
             => ( Q @ X5 ) ) )
       => ( ord_le146215904626753808_a_b_b @ ( inf_in6138156342456174402_a_b_b @ A5 @ ( collec1368399972772960719_a_b_b @ P2 ) ) @ ( inf_in6138156342456174402_a_b_b @ B5 @ ( collec1368399972772960719_a_b_b @ Q ) ) ) ) ) ).

% Int_Collect_mono
thf(fact_1029_range__subsetD,axiom,
    ! [F2: product_unit > produc4558475209616630778_a_b_b,B5: set_Pr3012420139608375472_a_b_b,I: product_unit] :
      ( ( ord_le146215904626753808_a_b_b @ ( image_2521969012719430850_a_b_b @ F2 @ top_to1996260823553986621t_unit ) @ B5 )
     => ( member4380921116106875537_a_b_b @ ( F2 @ I ) @ B5 ) ) ).

% range_subsetD
thf(fact_1030_fthe__elem_Orep__eq,axiom,
    ( fthe_e7442499522476018237_a_b_b
    = ( ^ [X: fset_P5281107635120001194_a_b_b] : ( the_el4127461656392778949_a_b_b @ ( fset_P783253628892185035_a_b_b @ X ) ) ) ) ).

% fthe_elem.rep_eq
thf(fact_1031_darcs__child__subseteq,axiom,
    ! [X3: dtree_a_b,Xs2: fset_P5281107635120001194_a_b_b,R: a] :
      ( ( member_dtree_a_b @ X3 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ Xs2 ) ) )
     => ( ord_less_eq_set_b @ ( darcs_a_b @ X3 ) @ ( darcs_a_b @ ( node_a_b @ R @ Xs2 ) ) ) ) ).

% darcs_child_subseteq
thf(fact_1032_Collect__case__prod__Grp__eqD,axiom,
    ! [Z: produc4558475209616630778_a_b_b,A5: set_dtree_a_b,F2: dtree_a_b > b] :
      ( ( member4380921116106875537_a_b_b @ Z @ ( collec1368399972772960719_a_b_b @ ( produc1325217093046185599_b_b_o @ ( bNF_Grp_dtree_a_b_b @ A5 @ F2 ) ) ) )
     => ( ( comp_d7292648224603294300_a_b_b @ F2 @ produc697780174058963904_a_b_b @ Z )
        = ( produc5748100250121904638_a_b_b @ Z ) ) ) ).

% Collect_case_prod_Grp_eqD
thf(fact_1033_filter__fset,axiom,
    ! [P2: produc4558475209616630778_a_b_b > $o,Xs2: fset_P5281107635120001194_a_b_b] :
      ( ( fset_P783253628892185035_a_b_b @ ( ffilte5856148450850080273_a_b_b @ P2 @ Xs2 ) )
      = ( inf_in6138156342456174402_a_b_b @ ( collec1368399972772960719_a_b_b @ P2 ) @ ( fset_P783253628892185035_a_b_b @ Xs2 ) ) ) ).

% filter_fset
thf(fact_1034_less__eq__fset_Orep__eq,axiom,
    ( ord_le789900035998834954_a_b_b
    = ( ^ [X: fset_P5281107635120001194_a_b_b,Xa3: fset_P5281107635120001194_a_b_b] : ( ord_le146215904626753808_a_b_b @ ( fset_P783253628892185035_a_b_b @ X ) @ ( fset_P783253628892185035_a_b_b @ Xa3 ) ) ) ) ).

% less_eq_fset.rep_eq
thf(fact_1035_less__eq__fset__def,axiom,
    ( ord_le789900035998834954_a_b_b
    = ( map_fu8973901316717634488_b_b_o @ fset_P783253628892185035_a_b_b @ ( map_fu6922732985725783282_b_o_o @ fset_P783253628892185035_a_b_b @ id_o ) @ ord_le146215904626753808_a_b_b ) ) ).

% less_eq_fset_def
thf(fact_1036_Grp__UNIV__idI,axiom,
    ! [X3: product_unit,Y3: product_unit] :
      ( ( X3 = Y3 )
     => ( bNF_Gr2512511087679822862t_unit @ top_to1996260823553986621t_unit @ id_Product_unit @ X3 @ Y3 ) ) ).

% Grp_UNIV_idI
thf(fact_1037_eq__alt,axiom,
    ( ( ^ [Y5: product_unit,Z4: product_unit] : ( Y5 = Z4 ) )
    = ( bNF_Gr2512511087679822862t_unit @ top_to1996260823553986621t_unit @ id_Product_unit ) ) ).

% eq_alt
thf(fact_1038_Collect__case__prod__Grp__in,axiom,
    ! [Z: produc4558475209616630778_a_b_b,A5: set_dtree_a_b,F2: dtree_a_b > b] :
      ( ( member4380921116106875537_a_b_b @ Z @ ( collec1368399972772960719_a_b_b @ ( produc1325217093046185599_b_b_o @ ( bNF_Grp_dtree_a_b_b @ A5 @ F2 ) ) ) )
     => ( member_dtree_a_b @ ( produc697780174058963904_a_b_b @ Z ) @ A5 ) ) ).

% Collect_case_prod_Grp_in
thf(fact_1039_sndOp__in,axiom,
    ! [Ac: produc4558475209616630778_a_b_b,P2: dtree_a_b > dtree_a_b > $o,Q: dtree_a_b > b > $o] :
      ( ( member4380921116106875537_a_b_b @ Ac @ ( collec1368399972772960719_a_b_b @ ( produc1325217093046185599_b_b_o @ ( relcom1818280762458196888_a_b_b @ P2 @ Q ) ) ) )
     => ( member4380921116106875537_a_b_b @ ( bNF_sn6078974312152453525_a_b_b @ P2 @ Q @ Ac ) @ ( collec1368399972772960719_a_b_b @ ( produc1325217093046185599_b_b_o @ Q ) ) ) ) ).

% sndOp_in
thf(fact_1040_fstOp__in,axiom,
    ! [Ac: produc4558475209616630778_a_b_b,P2: dtree_a_b > b > $o,Q: b > b > $o] :
      ( ( member4380921116106875537_a_b_b @ Ac @ ( collec1368399972772960719_a_b_b @ ( produc1325217093046185599_b_b_o @ ( relcom8461221429256392043_b_b_b @ P2 @ Q ) ) ) )
     => ( member4380921116106875537_a_b_b @ ( bNF_fs7198647118416170860_b_b_b @ P2 @ Q @ Ac ) @ ( collec1368399972772960719_a_b_b @ ( produc1325217093046185599_b_b_o @ P2 ) ) ) ) ).

% fstOp_in
thf(fact_1041_convol__mem__GrpI,axiom,
    ! [X3: dtree_a_b,A5: set_dtree_a_b,G2: dtree_a_b > b] :
      ( ( member_dtree_a_b @ X3 @ A5 )
     => ( member4380921116106875537_a_b_b @ ( bNF_co684571163256649440_a_b_b @ id_dtree_a_b @ G2 @ X3 ) @ ( collec1368399972772960719_a_b_b @ ( produc1325217093046185599_b_b_o @ ( bNF_Grp_dtree_a_b_b @ A5 @ G2 ) ) ) ) ) ).

% convol_mem_GrpI
thf(fact_1042_prod__set__simps_I2_J,axiom,
    ! [X3: dtree_a_b,Y3: b] :
      ( ( basic_1877077703026942_a_b_b @ ( produc331601717337510060_a_b_b @ X3 @ Y3 ) )
      = ( insert_b @ Y3 @ bot_bot_set_b ) ) ).

% prod_set_simps(2)
thf(fact_1043_insert__iff,axiom,
    ! [A: produc4558475209616630778_a_b_b,B: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ A @ ( insert1613891728210272810_a_b_b @ B @ A5 ) )
      = ( ( A = B )
        | ( member4380921116106875537_a_b_b @ A @ A5 ) ) ) ).

% insert_iff
thf(fact_1044_insertCI,axiom,
    ! [A: produc4558475209616630778_a_b_b,B5: set_Pr3012420139608375472_a_b_b,B: produc4558475209616630778_a_b_b] :
      ( ( ~ ( member4380921116106875537_a_b_b @ A @ B5 )
       => ( A = B ) )
     => ( member4380921116106875537_a_b_b @ A @ ( insert1613891728210272810_a_b_b @ B @ B5 ) ) ) ).

% insertCI
thf(fact_1045_singletonI,axiom,
    ! [A: produc4558475209616630778_a_b_b] : ( member4380921116106875537_a_b_b @ A @ ( insert1613891728210272810_a_b_b @ A @ bot_bo3721250822024684356_a_b_b ) ) ).

% singletonI
thf(fact_1046_insert__subset,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ( ord_le146215904626753808_a_b_b @ ( insert1613891728210272810_a_b_b @ X3 @ A5 ) @ B5 )
      = ( ( member4380921116106875537_a_b_b @ X3 @ B5 )
        & ( ord_le146215904626753808_a_b_b @ A5 @ B5 ) ) ) ).

% insert_subset
thf(fact_1047_Int__insert__right__if1,axiom,
    ! [A: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ A @ A5 )
     => ( ( inf_in6138156342456174402_a_b_b @ A5 @ ( insert1613891728210272810_a_b_b @ A @ B5 ) )
        = ( insert1613891728210272810_a_b_b @ A @ ( inf_in6138156342456174402_a_b_b @ A5 @ B5 ) ) ) ) ).

% Int_insert_right_if1
thf(fact_1048_Int__insert__right__if0,axiom,
    ! [A: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ~ ( member4380921116106875537_a_b_b @ A @ A5 )
     => ( ( inf_in6138156342456174402_a_b_b @ A5 @ ( insert1613891728210272810_a_b_b @ A @ B5 ) )
        = ( inf_in6138156342456174402_a_b_b @ A5 @ B5 ) ) ) ).

% Int_insert_right_if0
thf(fact_1049_Int__insert__left__if1,axiom,
    ! [A: produc4558475209616630778_a_b_b,C3: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ A @ C3 )
     => ( ( inf_in6138156342456174402_a_b_b @ ( insert1613891728210272810_a_b_b @ A @ B5 ) @ C3 )
        = ( insert1613891728210272810_a_b_b @ A @ ( inf_in6138156342456174402_a_b_b @ B5 @ C3 ) ) ) ) ).

% Int_insert_left_if1
thf(fact_1050_Int__insert__left__if0,axiom,
    ! [A: produc4558475209616630778_a_b_b,C3: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ~ ( member4380921116106875537_a_b_b @ A @ C3 )
     => ( ( inf_in6138156342456174402_a_b_b @ ( insert1613891728210272810_a_b_b @ A @ B5 ) @ C3 )
        = ( inf_in6138156342456174402_a_b_b @ B5 @ C3 ) ) ) ).

% Int_insert_left_if0
thf(fact_1051_disjoint__insert_I2_J,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,B: produc4558475209616630778_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ( bot_bo3721250822024684356_a_b_b
        = ( inf_in6138156342456174402_a_b_b @ A5 @ ( insert1613891728210272810_a_b_b @ B @ B5 ) ) )
      = ( ~ ( member4380921116106875537_a_b_b @ B @ A5 )
        & ( bot_bo3721250822024684356_a_b_b
          = ( inf_in6138156342456174402_a_b_b @ A5 @ B5 ) ) ) ) ).

% disjoint_insert(2)
thf(fact_1052_disjoint__insert_I1_J,axiom,
    ! [B5: set_Pr3012420139608375472_a_b_b,A: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( ( inf_in6138156342456174402_a_b_b @ B5 @ ( insert1613891728210272810_a_b_b @ A @ A5 ) )
        = bot_bo3721250822024684356_a_b_b )
      = ( ~ ( member4380921116106875537_a_b_b @ A @ B5 )
        & ( ( inf_in6138156342456174402_a_b_b @ B5 @ A5 )
          = bot_bo3721250822024684356_a_b_b ) ) ) ).

% disjoint_insert(1)
thf(fact_1053_insert__disjoint_I2_J,axiom,
    ! [A: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ( bot_bo3721250822024684356_a_b_b
        = ( inf_in6138156342456174402_a_b_b @ ( insert1613891728210272810_a_b_b @ A @ A5 ) @ B5 ) )
      = ( ~ ( member4380921116106875537_a_b_b @ A @ B5 )
        & ( bot_bo3721250822024684356_a_b_b
          = ( inf_in6138156342456174402_a_b_b @ A5 @ B5 ) ) ) ) ).

% insert_disjoint(2)
thf(fact_1054_insert__disjoint_I1_J,axiom,
    ! [A: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ( ( inf_in6138156342456174402_a_b_b @ ( insert1613891728210272810_a_b_b @ A @ A5 ) @ B5 )
        = bot_bo3721250822024684356_a_b_b )
      = ( ~ ( member4380921116106875537_a_b_b @ A @ B5 )
        & ( ( inf_in6138156342456174402_a_b_b @ A5 @ B5 )
          = bot_bo3721250822024684356_a_b_b ) ) ) ).

% insert_disjoint(1)
thf(fact_1055_finsert_Orep__eq,axiom,
    ! [X3: produc4558475209616630778_a_b_b,Xa2: fset_P5281107635120001194_a_b_b] :
      ( ( fset_P783253628892185035_a_b_b @ ( finser8437519239679886002_a_b_b @ X3 @ Xa2 ) )
      = ( insert1613891728210272810_a_b_b @ X3 @ ( fset_P783253628892185035_a_b_b @ Xa2 ) ) ) ).

% finsert.rep_eq
thf(fact_1056_prod__set__simps_I1_J,axiom,
    ! [X3: dtree_a_b,Y3: b] :
      ( ( basic_7578771248400840636_a_b_b @ ( produc331601717337510060_a_b_b @ X3 @ Y3 ) )
      = ( insert_dtree_a_b @ X3 @ bot_bo8730652382759064772ee_a_b ) ) ).

% prod_set_simps(1)
thf(fact_1057_insert__UNIV,axiom,
    ! [X3: product_unit] :
      ( ( insert_Product_unit @ X3 @ top_to1996260823553986621t_unit )
      = top_to1996260823553986621t_unit ) ).

% insert_UNIV
thf(fact_1058_singleton__iff,axiom,
    ! [B: produc4558475209616630778_a_b_b,A: produc4558475209616630778_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ B @ ( insert1613891728210272810_a_b_b @ A @ bot_bo3721250822024684356_a_b_b ) )
      = ( B = A ) ) ).

% singleton_iff
thf(fact_1059_singletonD,axiom,
    ! [B: produc4558475209616630778_a_b_b,A: produc4558475209616630778_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ B @ ( insert1613891728210272810_a_b_b @ A @ bot_bo3721250822024684356_a_b_b ) )
     => ( B = A ) ) ).

% singletonD
thf(fact_1060_subset__insert,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ~ ( member4380921116106875537_a_b_b @ X3 @ A5 )
     => ( ( ord_le146215904626753808_a_b_b @ A5 @ ( insert1613891728210272810_a_b_b @ X3 @ B5 ) )
        = ( ord_le146215904626753808_a_b_b @ A5 @ B5 ) ) ) ).

% subset_insert
thf(fact_1061_insert__subsetI,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b,X6: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ X3 @ A5 )
     => ( ( ord_le146215904626753808_a_b_b @ X6 @ A5 )
       => ( ord_le146215904626753808_a_b_b @ ( insert1613891728210272810_a_b_b @ X3 @ X6 ) @ A5 ) ) ) ).

% insert_subsetI
thf(fact_1062_Int__insert__left,axiom,
    ! [A: produc4558475209616630778_a_b_b,C3: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ( ( member4380921116106875537_a_b_b @ A @ C3 )
       => ( ( inf_in6138156342456174402_a_b_b @ ( insert1613891728210272810_a_b_b @ A @ B5 ) @ C3 )
          = ( insert1613891728210272810_a_b_b @ A @ ( inf_in6138156342456174402_a_b_b @ B5 @ C3 ) ) ) )
      & ( ~ ( member4380921116106875537_a_b_b @ A @ C3 )
       => ( ( inf_in6138156342456174402_a_b_b @ ( insert1613891728210272810_a_b_b @ A @ B5 ) @ C3 )
          = ( inf_in6138156342456174402_a_b_b @ B5 @ C3 ) ) ) ) ).

% Int_insert_left
thf(fact_1063_Int__insert__right,axiom,
    ! [A: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ( ( member4380921116106875537_a_b_b @ A @ A5 )
       => ( ( inf_in6138156342456174402_a_b_b @ A5 @ ( insert1613891728210272810_a_b_b @ A @ B5 ) )
          = ( insert1613891728210272810_a_b_b @ A @ ( inf_in6138156342456174402_a_b_b @ A5 @ B5 ) ) ) )
      & ( ~ ( member4380921116106875537_a_b_b @ A @ A5 )
       => ( ( inf_in6138156342456174402_a_b_b @ A5 @ ( insert1613891728210272810_a_b_b @ A @ B5 ) )
          = ( inf_in6138156342456174402_a_b_b @ A5 @ B5 ) ) ) ) ).

% Int_insert_right
thf(fact_1064_mk__disjoint__insert,axiom,
    ! [A: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ A @ A5 )
     => ? [B7: set_Pr3012420139608375472_a_b_b] :
          ( ( A5
            = ( insert1613891728210272810_a_b_b @ A @ B7 ) )
          & ~ ( member4380921116106875537_a_b_b @ A @ B7 ) ) ) ).

% mk_disjoint_insert
thf(fact_1065_insert__eq__iff,axiom,
    ! [A: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b,B: produc4558475209616630778_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ~ ( member4380921116106875537_a_b_b @ A @ A5 )
     => ( ~ ( member4380921116106875537_a_b_b @ B @ B5 )
       => ( ( ( insert1613891728210272810_a_b_b @ A @ A5 )
            = ( insert1613891728210272810_a_b_b @ B @ B5 ) )
          = ( ( ( A = B )
             => ( A5 = B5 ) )
            & ( ( A != B )
             => ? [C4: set_Pr3012420139608375472_a_b_b] :
                  ( ( A5
                    = ( insert1613891728210272810_a_b_b @ B @ C4 ) )
                  & ~ ( member4380921116106875537_a_b_b @ B @ C4 )
                  & ( B5
                    = ( insert1613891728210272810_a_b_b @ A @ C4 ) )
                  & ~ ( member4380921116106875537_a_b_b @ A @ C4 ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_1066_insert__absorb,axiom,
    ! [A: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ A @ A5 )
     => ( ( insert1613891728210272810_a_b_b @ A @ A5 )
        = A5 ) ) ).

% insert_absorb
thf(fact_1067_insert__ident,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ~ ( member4380921116106875537_a_b_b @ X3 @ A5 )
     => ( ~ ( member4380921116106875537_a_b_b @ X3 @ B5 )
       => ( ( ( insert1613891728210272810_a_b_b @ X3 @ A5 )
            = ( insert1613891728210272810_a_b_b @ X3 @ B5 ) )
          = ( A5 = B5 ) ) ) ) ).

% insert_ident
thf(fact_1068_Set_Oset__insert,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ X3 @ A5 )
     => ~ ! [B7: set_Pr3012420139608375472_a_b_b] :
            ( ( A5
              = ( insert1613891728210272810_a_b_b @ X3 @ B7 ) )
           => ( member4380921116106875537_a_b_b @ X3 @ B7 ) ) ) ).

% Set.set_insert
thf(fact_1069_insertI2,axiom,
    ! [A: produc4558475209616630778_a_b_b,B5: set_Pr3012420139608375472_a_b_b,B: produc4558475209616630778_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ A @ B5 )
     => ( member4380921116106875537_a_b_b @ A @ ( insert1613891728210272810_a_b_b @ B @ B5 ) ) ) ).

% insertI2
thf(fact_1070_insertI1,axiom,
    ! [A: produc4558475209616630778_a_b_b,B5: set_Pr3012420139608375472_a_b_b] : ( member4380921116106875537_a_b_b @ A @ ( insert1613891728210272810_a_b_b @ A @ B5 ) ) ).

% insertI1
thf(fact_1071_insertE,axiom,
    ! [A: produc4558475209616630778_a_b_b,B: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ A @ ( insert1613891728210272810_a_b_b @ B @ A5 ) )
     => ( ( A != B )
       => ( member4380921116106875537_a_b_b @ A @ A5 ) ) ) ).

% insertE
thf(fact_1072_comp__transfer,axiom,
    ! [B5: ( b > a ) > ( b > a ) > $o,C3: ( b > a ) > ( b > a ) > $o,A5: ( b > a ) > ( b > a ) > $o] : ( bNF_re1473080822477210889_a_b_a @ ( bNF_re7432613075280381681_a_b_a @ B5 @ C3 ) @ ( bNF_re5527643775196010493_a_b_a @ ( bNF_re7432613075280381681_a_b_a @ A5 @ B5 ) @ ( bNF_re7432613075280381681_a_b_a @ A5 @ C3 ) ) @ comp_b_a_b_a_b_a @ comp_b_a_b_a_b_a ) ).

% comp_transfer
thf(fact_1073_fun_Omap__transfer,axiom,
    ! [Rb: ( b > a ) > ( b > a ) > $o,Sd: ( b > a ) > ( b > a ) > $o] :
      ( bNF_re1473080822477210889_a_b_a @ ( bNF_re7432613075280381681_a_b_a @ Rb @ Sd )
      @ ( bNF_re5527643775196010493_a_b_a
        @ ( bNF_re7432613075280381681_a_b_a
          @ ^ [Y5: b > a,Z4: b > a] : ( Y5 = Z4 )
          @ Rb )
        @ ( bNF_re7432613075280381681_a_b_a
          @ ^ [Y5: b > a,Z4: b > a] : ( Y5 = Z4 )
          @ Sd ) )
      @ comp_b_a_b_a_b_a
      @ comp_b_a_b_a_b_a ) ).

% fun.map_transfer
thf(fact_1074_comp__fun__commute__on_Ointro,axiom,
    ! [S3: set_Pr3012420139608375472_a_b_b,F2: produc4558475209616630778_a_b_b > ( b > a ) > b > a] :
      ( ! [X5: produc4558475209616630778_a_b_b,Y4: produc4558475209616630778_a_b_b] :
          ( ( member4380921116106875537_a_b_b @ X5 @ S3 )
         => ( ( member4380921116106875537_a_b_b @ Y4 @ S3 )
           => ( ( comp_b_a_b_a_b_a @ ( F2 @ Y4 ) @ ( F2 @ X5 ) )
              = ( comp_b_a_b_a_b_a @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) ) ) )
     => ( finite6564071228819977072_b_b_a @ S3 @ F2 ) ) ).

% comp_fun_commute_on.intro
thf(fact_1075_comp__fun__commute__on_Ocommute__left__comp,axiom,
    ! [S3: set_Pr3012420139608375472_a_b_b,F2: produc4558475209616630778_a_b_b > ( b > a ) > b > a,X3: produc4558475209616630778_a_b_b,Y3: produc4558475209616630778_a_b_b,G2: ( b > a ) > b > a] :
      ( ( finite6564071228819977072_b_b_a @ S3 @ F2 )
     => ( ( member4380921116106875537_a_b_b @ X3 @ S3 )
       => ( ( member4380921116106875537_a_b_b @ Y3 @ S3 )
         => ( ( comp_b_a_b_a_b_a @ ( F2 @ Y3 ) @ ( comp_b_a_b_a_b_a @ ( F2 @ X3 ) @ G2 ) )
            = ( comp_b_a_b_a_b_a @ ( F2 @ X3 ) @ ( comp_b_a_b_a_b_a @ ( F2 @ Y3 ) @ G2 ) ) ) ) ) ) ).

% comp_fun_commute_on.commute_left_comp
thf(fact_1076_comp__fun__commute__on_Ocomp__fun__commute__on,axiom,
    ! [S3: set_Pr3012420139608375472_a_b_b,F2: produc4558475209616630778_a_b_b > ( b > a ) > b > a,X3: produc4558475209616630778_a_b_b,Y3: produc4558475209616630778_a_b_b] :
      ( ( finite6564071228819977072_b_b_a @ S3 @ F2 )
     => ( ( member4380921116106875537_a_b_b @ X3 @ S3 )
       => ( ( member4380921116106875537_a_b_b @ Y3 @ S3 )
         => ( ( comp_b_a_b_a_b_a @ ( F2 @ Y3 ) @ ( F2 @ X3 ) )
            = ( comp_b_a_b_a_b_a @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) ) ) ) ) ).

% comp_fun_commute_on.comp_fun_commute_on
thf(fact_1077_comp__fun__commute__on__def,axiom,
    ( finite6564071228819977072_b_b_a
    = ( ^ [S4: set_Pr3012420139608375472_a_b_b,F: produc4558475209616630778_a_b_b > ( b > a ) > b > a] :
        ! [X: produc4558475209616630778_a_b_b,Y: produc4558475209616630778_a_b_b] :
          ( ( member4380921116106875537_a_b_b @ X @ S4 )
         => ( ( member4380921116106875537_a_b_b @ Y @ S4 )
           => ( ( comp_b_a_b_a_b_a @ ( F @ Y ) @ ( F @ X ) )
              = ( comp_b_a_b_a_b_a @ ( F @ X ) @ ( F @ Y ) ) ) ) ) ) ) ).

% comp_fun_commute_on_def
thf(fact_1078_fun_Orel__cong,axiom,
    ! [X3: product_unit > produc4558475209616630778_a_b_b,Ya: product_unit > produc4558475209616630778_a_b_b,Y3: product_unit > produc4558475209616630778_a_b_b,Xa2: product_unit > produc4558475209616630778_a_b_b,R3: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b > $o,Ra: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b > $o] :
      ( ( X3 = Ya )
     => ( ( Y3 = Xa2 )
       => ( ! [Z3: produc4558475209616630778_a_b_b,Yb2: produc4558475209616630778_a_b_b] :
              ( ( member4380921116106875537_a_b_b @ Z3 @ ( image_2521969012719430850_a_b_b @ Ya @ top_to1996260823553986621t_unit ) )
             => ( ( member4380921116106875537_a_b_b @ Yb2 @ ( image_2521969012719430850_a_b_b @ Xa2 @ top_to1996260823553986621t_unit ) )
               => ( ( R3 @ Z3 @ Yb2 )
                  = ( Ra @ Z3 @ Yb2 ) ) ) )
         => ( ( bNF_re1768220791201799059_a_b_b
              @ ^ [Y5: product_unit,Z4: product_unit] : ( Y5 = Z4 )
              @ R3
              @ X3
              @ Y3 )
            = ( bNF_re1768220791201799059_a_b_b
              @ ^ [Y5: product_unit,Z4: product_unit] : ( Y5 = Z4 )
              @ Ra
              @ Ya
              @ Xa2 ) ) ) ) ) ).

% fun.rel_cong
thf(fact_1079_fun_Orel__mono__strong,axiom,
    ! [R3: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b > $o,X3: product_unit > produc4558475209616630778_a_b_b,Y3: product_unit > produc4558475209616630778_a_b_b,Ra: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b > $o] :
      ( ( bNF_re1768220791201799059_a_b_b
        @ ^ [Y5: product_unit,Z4: product_unit] : ( Y5 = Z4 )
        @ R3
        @ X3
        @ Y3 )
     => ( ! [Z3: produc4558475209616630778_a_b_b,Yb2: produc4558475209616630778_a_b_b] :
            ( ( member4380921116106875537_a_b_b @ Z3 @ ( image_2521969012719430850_a_b_b @ X3 @ top_to1996260823553986621t_unit ) )
           => ( ( member4380921116106875537_a_b_b @ Yb2 @ ( image_2521969012719430850_a_b_b @ Y3 @ top_to1996260823553986621t_unit ) )
             => ( ( R3 @ Z3 @ Yb2 )
               => ( Ra @ Z3 @ Yb2 ) ) ) )
       => ( bNF_re1768220791201799059_a_b_b
          @ ^ [Y5: product_unit,Z4: product_unit] : ( Y5 = Z4 )
          @ Ra
          @ X3
          @ Y3 ) ) ) ).

% fun.rel_mono_strong
thf(fact_1080_fun_Orel__refl__strong,axiom,
    ! [X3: product_unit > produc4558475209616630778_a_b_b,Ra: produc4558475209616630778_a_b_b > produc4558475209616630778_a_b_b > $o] :
      ( ! [Z3: produc4558475209616630778_a_b_b] :
          ( ( member4380921116106875537_a_b_b @ Z3 @ ( image_2521969012719430850_a_b_b @ X3 @ top_to1996260823553986621t_unit ) )
         => ( Ra @ Z3 @ Z3 ) )
     => ( bNF_re1768220791201799059_a_b_b
        @ ^ [Y5: product_unit,Z4: product_unit] : ( Y5 = Z4 )
        @ Ra
        @ X3
        @ X3 ) ) ).

% fun.rel_refl_strong
thf(fact_1081_GrD1,axiom,
    ! [X3: dtree_a_b,Fx: b,A5: set_dtree_a_b,F2: dtree_a_b > b] :
      ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ X3 @ Fx ) @ ( bNF_Gr_dtree_a_b_b @ A5 @ F2 ) )
     => ( member_dtree_a_b @ X3 @ A5 ) ) ).

% GrD1
thf(fact_1082_GrD2,axiom,
    ! [X3: dtree_a_b,Fx: b,A5: set_dtree_a_b,F2: dtree_a_b > b] :
      ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ X3 @ Fx ) @ ( bNF_Gr_dtree_a_b_b @ A5 @ F2 ) )
     => ( ( F2 @ X3 )
        = Fx ) ) ).

% GrD2
thf(fact_1083_comp__fun__idem__on_Ocomp__fun__idem__on,axiom,
    ! [S3: set_Pr3012420139608375472_a_b_b,F2: produc4558475209616630778_a_b_b > ( b > a ) > b > a,X3: produc4558475209616630778_a_b_b] :
      ( ( finite582340075173961963_b_b_a @ S3 @ F2 )
     => ( ( member4380921116106875537_a_b_b @ X3 @ S3 )
       => ( ( comp_b_a_b_a_b_a @ ( F2 @ X3 ) @ ( F2 @ X3 ) )
          = ( F2 @ X3 ) ) ) ) ).

% comp_fun_idem_on.comp_fun_idem_on
thf(fact_1084_disjoint__darcs__if__wf__aux5,axiom,
    ! [R: a,Xs2: fset_P5281107635120001194_a_b_b,T1: dtree_a_b,E1: b,T2: dtree_a_b,E2: b] :
      ( ( wf_darcs_a_b @ ( node_a_b @ R @ Xs2 ) )
     => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ T1 @ E1 ) @ ( fset_P783253628892185035_a_b_b @ Xs2 ) )
       => ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ T2 @ E2 ) @ ( fset_P783253628892185035_a_b_b @ Xs2 ) )
         => ( ( ( produc331601717337510060_a_b_b @ T1 @ E1 )
             != ( produc331601717337510060_a_b_b @ T2 @ E2 ) )
           => ( ( inf_inf_set_b @ ( sup_sup_set_b @ ( darcs_a_b @ T1 ) @ ( insert_b @ E1 @ bot_bot_set_b ) ) @ ( sup_sup_set_b @ ( darcs_a_b @ T2 ) @ ( insert_b @ E2 @ bot_bot_set_b ) ) )
              = bot_bot_set_b ) ) ) ) ) ).

% disjoint_darcs_if_wf_aux5
thf(fact_1085_UnCI,axiom,
    ! [C: produc4558475209616630778_a_b_b,B5: set_Pr3012420139608375472_a_b_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( ~ ( member4380921116106875537_a_b_b @ C @ B5 )
       => ( member4380921116106875537_a_b_b @ C @ A5 ) )
     => ( member4380921116106875537_a_b_b @ C @ ( sup_su2887895092731772380_a_b_b @ A5 @ B5 ) ) ) ).

% UnCI
thf(fact_1086_Un__iff,axiom,
    ! [C: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ ( sup_su2887895092731772380_a_b_b @ A5 @ B5 ) )
      = ( ( member4380921116106875537_a_b_b @ C @ A5 )
        | ( member4380921116106875537_a_b_b @ C @ B5 ) ) ) ).

% Un_iff
thf(fact_1087_sup__top__left,axiom,
    ! [X3: set_Product_unit] :
      ( ( sup_su793286257634532545t_unit @ top_to1996260823553986621t_unit @ X3 )
      = top_to1996260823553986621t_unit ) ).

% sup_top_left
thf(fact_1088_sup__top__right,axiom,
    ! [X3: set_Product_unit] :
      ( ( sup_su793286257634532545t_unit @ X3 @ top_to1996260823553986621t_unit )
      = top_to1996260823553986621t_unit ) ).

% sup_top_right
thf(fact_1089_boolean__algebra_Odisj__one__left,axiom,
    ! [X3: set_Product_unit] :
      ( ( sup_su793286257634532545t_unit @ top_to1996260823553986621t_unit @ X3 )
      = top_to1996260823553986621t_unit ) ).

% boolean_algebra.disj_one_left
thf(fact_1090_boolean__algebra_Odisj__one__right,axiom,
    ! [X3: set_Product_unit] :
      ( ( sup_su793286257634532545t_unit @ X3 @ top_to1996260823553986621t_unit )
      = top_to1996260823553986621t_unit ) ).

% boolean_algebra.disj_one_right
thf(fact_1091_UnE,axiom,
    ! [C: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ ( sup_su2887895092731772380_a_b_b @ A5 @ B5 ) )
     => ( ~ ( member4380921116106875537_a_b_b @ C @ A5 )
       => ( member4380921116106875537_a_b_b @ C @ B5 ) ) ) ).

% UnE
thf(fact_1092_UnI1,axiom,
    ! [C: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ A5 )
     => ( member4380921116106875537_a_b_b @ C @ ( sup_su2887895092731772380_a_b_b @ A5 @ B5 ) ) ) ).

% UnI1
thf(fact_1093_UnI2,axiom,
    ! [C: produc4558475209616630778_a_b_b,B5: set_Pr3012420139608375472_a_b_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ B5 )
     => ( member4380921116106875537_a_b_b @ C @ ( sup_su2887895092731772380_a_b_b @ A5 @ B5 ) ) ) ).

% UnI2
thf(fact_1094_Un__UNIV__left,axiom,
    ! [B5: set_Product_unit] :
      ( ( sup_su793286257634532545t_unit @ top_to1996260823553986621t_unit @ B5 )
      = top_to1996260823553986621t_unit ) ).

% Un_UNIV_left
thf(fact_1095_Un__UNIV__right,axiom,
    ! [A5: set_Product_unit] :
      ( ( sup_su793286257634532545t_unit @ A5 @ top_to1996260823553986621t_unit )
      = top_to1996260823553986621t_unit ) ).

% Un_UNIV_right
thf(fact_1096_boolean__algebra_Ocomplement__unique,axiom,
    ! [A: set_Product_unit,X3: set_Product_unit,Y3: set_Product_unit] :
      ( ( ( inf_in4660618365625256667t_unit @ A @ X3 )
        = bot_bo3957492148770167129t_unit )
     => ( ( ( sup_su793286257634532545t_unit @ A @ X3 )
          = top_to1996260823553986621t_unit )
       => ( ( ( inf_in4660618365625256667t_unit @ A @ Y3 )
            = bot_bo3957492148770167129t_unit )
         => ( ( ( sup_su793286257634532545t_unit @ A @ Y3 )
              = top_to1996260823553986621t_unit )
           => ( X3 = Y3 ) ) ) ) ) ).

% boolean_algebra.complement_unique
thf(fact_1097_o__rsp_I2_J,axiom,
    ! [R12: ( b > a ) > ( b > a ) > $o] :
      ( bNF_re1473080822477210889_a_b_a
      @ ^ [Y5: ( b > a ) > b > a,Z4: ( b > a ) > b > a] : ( Y5 = Z4 )
      @ ( bNF_re5527643775196010493_a_b_a
        @ ( bNF_re7432613075280381681_a_b_a @ R12
          @ ^ [Y5: b > a,Z4: b > a] : ( Y5 = Z4 ) )
        @ ( bNF_re7432613075280381681_a_b_a @ R12
          @ ^ [Y5: b > a,Z4: b > a] : ( Y5 = Z4 ) ) )
      @ comp_b_a_b_a_b_a
      @ comp_b_a_b_a_b_a ) ).

% o_rsp(2)
thf(fact_1098_o__rsp_I1_J,axiom,
    ! [R22: ( b > a ) > ( b > a ) > $o,R32: ( b > a ) > ( b > a ) > $o,R12: ( b > a ) > ( b > a ) > $o] : ( bNF_re1473080822477210889_a_b_a @ ( bNF_re7432613075280381681_a_b_a @ R22 @ R32 ) @ ( bNF_re5527643775196010493_a_b_a @ ( bNF_re7432613075280381681_a_b_a @ R12 @ R22 ) @ ( bNF_re7432613075280381681_a_b_a @ R12 @ R32 ) ) @ comp_b_a_b_a_b_a @ comp_b_a_b_a_b_a ) ).

% o_rsp(1)
thf(fact_1099_union__fset,axiom,
    ! [X3: fset_P5281107635120001194_a_b_b,Xa2: fset_P5281107635120001194_a_b_b] :
      ( ( fset_P783253628892185035_a_b_b @ ( sup_su860928060825958358_a_b_b @ X3 @ Xa2 ) )
      = ( sup_su2887895092731772380_a_b_b @ ( fset_P783253628892185035_a_b_b @ X3 ) @ ( fset_P783253628892185035_a_b_b @ Xa2 ) ) ) ).

% union_fset
thf(fact_1100_is__singletonI_H,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b] :
      ( ( A5 != bot_bo3721250822024684356_a_b_b )
     => ( ! [X5: produc4558475209616630778_a_b_b,Y4: produc4558475209616630778_a_b_b] :
            ( ( member4380921116106875537_a_b_b @ X5 @ A5 )
           => ( ( member4380921116106875537_a_b_b @ Y4 @ A5 )
             => ( X5 = Y4 ) ) )
       => ( is_sin1118336051388392454_a_b_b @ A5 ) ) ) ).

% is_singletonI'
thf(fact_1101_fmember__def,axiom,
    ( fmembe3173364709796808819_a_b_b
    = ( map_fu8342389097230326738_b_b_o @ id_Pro6814982414164175945_a_b_b @ ( map_fu6922732985725783282_b_o_o @ fset_P783253628892185035_a_b_b @ id_o ) @ member4380921116106875537_a_b_b ) ) ).

% fmember_def
thf(fact_1102_FieldI2,axiom,
    ! [I: produc4558475209616630778_a_b_b,J: produc4558475209616630778_a_b_b,R3: set_Pr2755428042910921141_a_b_b] :
      ( ( member9171970031259705598_a_b_b @ ( produc6533307410877503629_a_b_b @ I @ J ) @ R3 )
     => ( member4380921116106875537_a_b_b @ J @ ( field_2612910574630873453_a_b_b @ R3 ) ) ) ).

% FieldI2
thf(fact_1103_FieldI1,axiom,
    ! [I: produc4558475209616630778_a_b_b,J: produc4558475209616630778_a_b_b,R3: set_Pr2755428042910921141_a_b_b] :
      ( ( member9171970031259705598_a_b_b @ ( produc6533307410877503629_a_b_b @ I @ J ) @ R3 )
     => ( member4380921116106875537_a_b_b @ I @ ( field_2612910574630873453_a_b_b @ R3 ) ) ) ).

% FieldI1
thf(fact_1104_fmember_Orep__eq,axiom,
    ( fmembe3173364709796808819_a_b_b
    = ( ^ [X: produc4558475209616630778_a_b_b,Xa3: fset_P5281107635120001194_a_b_b] : ( member4380921116106875537_a_b_b @ X @ ( fset_P783253628892185035_a_b_b @ Xa3 ) ) ) ) ).

% fmember.rep_eq
thf(fact_1105_notin__fset,axiom,
    ! [X3: produc4558475209616630778_a_b_b,S3: fset_P5281107635120001194_a_b_b] :
      ( ( ~ ( fmembe3173364709796808819_a_b_b @ X3 @ S3 ) )
      = ( ~ ( member4380921116106875537_a_b_b @ X3 @ ( fset_P783253628892185035_a_b_b @ S3 ) ) ) ) ).

% notin_fset
thf(fact_1106_fmember__iff__member__fset,axiom,
    ( fmembe3173364709796808819_a_b_b
    = ( ^ [X: produc4558475209616630778_a_b_b,A6: fset_P5281107635120001194_a_b_b] : ( member4380921116106875537_a_b_b @ X @ ( fset_P783253628892185035_a_b_b @ A6 ) ) ) ) ).

% fmember_iff_member_fset
thf(fact_1107_fMin__eqI,axiom,
    ! [A5: fset_nat,X3: nat] :
      ( ! [Y4: nat] :
          ( ( fmember_nat @ Y4 @ A5 )
         => ( ord_less_eq_nat @ X3 @ Y4 ) )
     => ( ( fmember_nat @ X3 @ A5 )
       => ( ( linorder_fMin_nat @ A5 )
          = X3 ) ) ) ).

% fMin_eqI
thf(fact_1108_fMax__eqI,axiom,
    ! [A5: fset_nat,X3: nat] :
      ( ! [Y4: nat] :
          ( ( fmember_nat @ Y4 @ A5 )
         => ( ord_less_eq_nat @ Y4 @ X3 ) )
     => ( ( fmember_nat @ X3 @ A5 )
       => ( ( linorder_fMax_nat @ A5 )
          = X3 ) ) ) ).

% fMax_eqI
thf(fact_1109_fMin__le,axiom,
    ! [X3: nat,A5: fset_nat] :
      ( ( fmember_nat @ X3 @ A5 )
     => ( ord_less_eq_nat @ ( linorder_fMin_nat @ A5 ) @ X3 ) ) ).

% fMin_le
thf(fact_1110_fMax__ge,axiom,
    ! [X3: nat,A5: fset_nat] :
      ( ( fmember_nat @ X3 @ A5 )
     => ( ord_less_eq_nat @ X3 @ ( linorder_fMax_nat @ A5 ) ) ) ).

% fMax_ge
thf(fact_1111_Range__insert,axiom,
    ! [A: dtree_a_b,B: b,R: set_Pr3012420139608375472_a_b_b] :
      ( ( range_dtree_a_b_b @ ( insert1613891728210272810_a_b_b @ ( produc331601717337510060_a_b_b @ A @ B ) @ R ) )
      = ( insert_b @ B @ ( range_dtree_a_b_b @ R ) ) ) ).

% Range_insert
thf(fact_1112_refl__onD,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,R: set_Pr2755428042910921141_a_b_b,A: produc4558475209616630778_a_b_b] :
      ( ( refl_o6438828113603023419_a_b_b @ A5 @ R )
     => ( ( member4380921116106875537_a_b_b @ A @ A5 )
       => ( member9171970031259705598_a_b_b @ ( produc6533307410877503629_a_b_b @ A @ A ) @ R ) ) ) ).

% refl_onD
thf(fact_1113_refl__onD1,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,R: set_Pr2755428042910921141_a_b_b,X3: produc4558475209616630778_a_b_b,Y3: produc4558475209616630778_a_b_b] :
      ( ( refl_o6438828113603023419_a_b_b @ A5 @ R )
     => ( ( member9171970031259705598_a_b_b @ ( produc6533307410877503629_a_b_b @ X3 @ Y3 ) @ R )
       => ( member4380921116106875537_a_b_b @ X3 @ A5 ) ) ) ).

% refl_onD1
thf(fact_1114_refl__onD2,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,R: set_Pr2755428042910921141_a_b_b,X3: produc4558475209616630778_a_b_b,Y3: produc4558475209616630778_a_b_b] :
      ( ( refl_o6438828113603023419_a_b_b @ A5 @ R )
     => ( ( member9171970031259705598_a_b_b @ ( produc6533307410877503629_a_b_b @ X3 @ Y3 ) @ R )
       => ( member4380921116106875537_a_b_b @ Y3 @ A5 ) ) ) ).

% refl_onD2
thf(fact_1115_refl__on__domain,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,R: set_Pr2755428042910921141_a_b_b,A: produc4558475209616630778_a_b_b,B: produc4558475209616630778_a_b_b] :
      ( ( refl_o6438828113603023419_a_b_b @ A5 @ R )
     => ( ( member9171970031259705598_a_b_b @ ( produc6533307410877503629_a_b_b @ A @ B ) @ R )
       => ( ( member4380921116106875537_a_b_b @ A @ A5 )
          & ( member4380921116106875537_a_b_b @ B @ A5 ) ) ) ) ).

% refl_on_domain
thf(fact_1116_Range__iff,axiom,
    ! [A: b,R: set_Pr3012420139608375472_a_b_b] :
      ( ( member_b @ A @ ( range_dtree_a_b_b @ R ) )
      = ( ? [Y: dtree_a_b] : ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ Y @ A ) @ R ) ) ) ).

% Range_iff
thf(fact_1117_RangeE,axiom,
    ! [B: b,R: set_Pr3012420139608375472_a_b_b] :
      ( ( member_b @ B @ ( range_dtree_a_b_b @ R ) )
     => ~ ! [A3: dtree_a_b] :
            ~ ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ A3 @ B ) @ R ) ) ).

% RangeE
thf(fact_1118_Range_Ointros,axiom,
    ! [A: dtree_a_b,B: b,R: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ A @ B ) @ R )
     => ( member_b @ B @ ( range_dtree_a_b_b @ R ) ) ) ).

% Range.intros
thf(fact_1119_Range_Osimps,axiom,
    ! [A: b,R: set_Pr3012420139608375472_a_b_b] :
      ( ( member_b @ A @ ( range_dtree_a_b_b @ R ) )
      = ( ? [A4: dtree_a_b,B4: b] :
            ( ( A = B4 )
            & ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ A4 @ B4 ) @ R ) ) ) ) ).

% Range.simps
thf(fact_1120_Range_Ocases,axiom,
    ! [A: b,R: set_Pr3012420139608375472_a_b_b] :
      ( ( member_b @ A @ ( range_dtree_a_b_b @ R ) )
     => ~ ! [A3: dtree_a_b] :
            ~ ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ A3 @ A ) @ R ) ) ).

% Range.cases
thf(fact_1121_reflD,axiom,
    ! [R: set_Pr5094982260447487303t_unit,A: product_unit] :
      ( ( refl_on_Product_unit @ top_to1996260823553986621t_unit @ R )
     => ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ A @ A ) @ R ) ) ).

% reflD
thf(fact_1122_reflI,axiom,
    ! [R: set_Pr5094982260447487303t_unit] :
      ( ! [X5: product_unit] : ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X5 @ X5 ) @ R )
     => ( refl_on_Product_unit @ top_to1996260823553986621t_unit @ R ) ) ).

% reflI
thf(fact_1123_underS__incl__iff,axiom,
    ! [R: set_Pr2755428042910921141_a_b_b,A: produc4558475209616630778_a_b_b,B: produc4558475209616630778_a_b_b] :
      ( ( order_4468497924153950597_a_b_b @ ( field_2612910574630873453_a_b_b @ R ) @ R )
     => ( ( member4380921116106875537_a_b_b @ A @ ( field_2612910574630873453_a_b_b @ R ) )
       => ( ( member4380921116106875537_a_b_b @ B @ ( field_2612910574630873453_a_b_b @ R ) )
         => ( ( ord_le146215904626753808_a_b_b @ ( order_2076638635254047924_a_b_b @ R @ A ) @ ( order_2076638635254047924_a_b_b @ R @ B ) )
            = ( member9171970031259705598_a_b_b @ ( produc6533307410877503629_a_b_b @ A @ B ) @ R ) ) ) ) ) ).

% underS_incl_iff
thf(fact_1124_well__order__on__domain,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,R: set_Pr2755428042910921141_a_b_b,A: produc4558475209616630778_a_b_b,B: produc4558475209616630778_a_b_b] :
      ( ( order_3931594357693323740_a_b_b @ A5 @ R )
     => ( ( member9171970031259705598_a_b_b @ ( produc6533307410877503629_a_b_b @ A @ B ) @ R )
       => ( ( member4380921116106875537_a_b_b @ A @ A5 )
          & ( member4380921116106875537_a_b_b @ B @ A5 ) ) ) ) ).

% well_order_on_domain
thf(fact_1125_underS__E,axiom,
    ! [I: produc4558475209616630778_a_b_b,R3: set_Pr2755428042910921141_a_b_b,J: produc4558475209616630778_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ I @ ( order_2076638635254047924_a_b_b @ R3 @ J ) )
     => ( ( I != J )
        & ( member9171970031259705598_a_b_b @ ( produc6533307410877503629_a_b_b @ I @ J ) @ R3 ) ) ) ).

% underS_E
thf(fact_1126_underS__I,axiom,
    ! [I: produc4558475209616630778_a_b_b,J: produc4558475209616630778_a_b_b,R3: set_Pr2755428042910921141_a_b_b] :
      ( ( I != J )
     => ( ( member9171970031259705598_a_b_b @ ( produc6533307410877503629_a_b_b @ I @ J ) @ R3 )
       => ( member4380921116106875537_a_b_b @ I @ ( order_2076638635254047924_a_b_b @ R3 @ J ) ) ) ) ).

% underS_I
thf(fact_1127_BNF__Least__Fixpoint_OunderS__Field,axiom,
    ! [I: produc4558475209616630778_a_b_b,R3: set_Pr2755428042910921141_a_b_b,J: produc4558475209616630778_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ I @ ( order_2076638635254047924_a_b_b @ R3 @ J ) )
     => ( member4380921116106875537_a_b_b @ I @ ( field_2612910574630873453_a_b_b @ R3 ) ) ) ).

% BNF_Least_Fixpoint.underS_Field
thf(fact_1128_underS__empty,axiom,
    ! [A: produc4558475209616630778_a_b_b,R: set_Pr2755428042910921141_a_b_b] :
      ( ~ ( member4380921116106875537_a_b_b @ A @ ( field_2612910574630873453_a_b_b @ R ) )
     => ( ( order_2076638635254047924_a_b_b @ R @ A )
        = bot_bo3721250822024684356_a_b_b ) ) ).

% underS_empty
thf(fact_1129_well__ordering,axiom,
    ? [R4: set_Pr5094982260447487303t_unit] :
      ( ( order_3164716736300062379t_unit @ ( field_Product_unit @ R4 ) @ R4 )
      & ( ( field_Product_unit @ R4 )
        = top_to1996260823553986621t_unit ) ) ).

% well_ordering
thf(fact_1130_Refl__under__underS,axiom,
    ! [R: set_Pr2755428042910921141_a_b_b,A: produc4558475209616630778_a_b_b] :
      ( ( refl_o6438828113603023419_a_b_b @ ( field_2612910574630873453_a_b_b @ R ) @ R )
     => ( ( member4380921116106875537_a_b_b @ A @ ( field_2612910574630873453_a_b_b @ R ) )
       => ( ( order_443969674961680725_a_b_b @ R @ A )
          = ( sup_su2887895092731772380_a_b_b @ ( order_2076638635254047924_a_b_b @ R @ A ) @ ( insert1613891728210272810_a_b_b @ A @ bot_bo3721250822024684356_a_b_b ) ) ) ) ) ).

% Refl_under_underS
thf(fact_1131_Diff__insert0,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ~ ( member4380921116106875537_a_b_b @ X3 @ A5 )
     => ( ( minus_1392386589478415753_a_b_b @ A5 @ ( insert1613891728210272810_a_b_b @ X3 @ B5 ) )
        = ( minus_1392386589478415753_a_b_b @ A5 @ B5 ) ) ) ).

% Diff_insert0
thf(fact_1132_insert__Diff1,axiom,
    ! [X3: produc4558475209616630778_a_b_b,B5: set_Pr3012420139608375472_a_b_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ X3 @ B5 )
     => ( ( minus_1392386589478415753_a_b_b @ ( insert1613891728210272810_a_b_b @ X3 @ A5 ) @ B5 )
        = ( minus_1392386589478415753_a_b_b @ A5 @ B5 ) ) ) ).

% insert_Diff1
thf(fact_1133_Diff__UNIV,axiom,
    ! [A5: set_Product_unit] :
      ( ( minus_6452836326544984404t_unit @ A5 @ top_to1996260823553986621t_unit )
      = bot_bo3957492148770167129t_unit ) ).

% Diff_UNIV
thf(fact_1134_minus__fset,axiom,
    ! [X3: fset_P5281107635120001194_a_b_b,Xa2: fset_P5281107635120001194_a_b_b] :
      ( ( fset_P783253628892185035_a_b_b @ ( minus_1250967532242559235_a_b_b @ X3 @ Xa2 ) )
      = ( minus_1392386589478415753_a_b_b @ ( fset_P783253628892185035_a_b_b @ X3 ) @ ( fset_P783253628892185035_a_b_b @ Xa2 ) ) ) ).

% minus_fset
thf(fact_1135_insert__Diff,axiom,
    ! [A: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ A @ A5 )
     => ( ( insert1613891728210272810_a_b_b @ A @ ( minus_1392386589478415753_a_b_b @ A5 @ ( insert1613891728210272810_a_b_b @ A @ bot_bo3721250822024684356_a_b_b ) ) )
        = A5 ) ) ).

% insert_Diff
thf(fact_1136_Diff__insert__absorb,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ~ ( member4380921116106875537_a_b_b @ X3 @ A5 )
     => ( ( minus_1392386589478415753_a_b_b @ ( insert1613891728210272810_a_b_b @ X3 @ A5 ) @ ( insert1613891728210272810_a_b_b @ X3 @ bot_bo3721250822024684356_a_b_b ) )
        = A5 ) ) ).

% Diff_insert_absorb
thf(fact_1137_in__image__insert__iff,axiom,
    ! [B5: set_se3183138701204633190_a_b_b,X3: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ! [C5: set_Pr3012420139608375472_a_b_b] :
          ( ( member7431159781899395911_a_b_b @ C5 @ B5 )
         => ~ ( member4380921116106875537_a_b_b @ X3 @ C5 ) )
     => ( ( member7431159781899395911_a_b_b @ A5 @ ( image_4903599603319290215_a_b_b @ ( insert1613891728210272810_a_b_b @ X3 ) @ B5 ) )
        = ( ( member4380921116106875537_a_b_b @ X3 @ A5 )
          & ( member7431159781899395911_a_b_b @ ( minus_1392386589478415753_a_b_b @ A5 @ ( insert1613891728210272810_a_b_b @ X3 @ bot_bo3721250822024684356_a_b_b ) ) @ B5 ) ) ) ) ).

% in_image_insert_iff
thf(fact_1138_subset__Diff__insert,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b,X3: produc4558475209616630778_a_b_b,C3: set_Pr3012420139608375472_a_b_b] :
      ( ( ord_le146215904626753808_a_b_b @ A5 @ ( minus_1392386589478415753_a_b_b @ B5 @ ( insert1613891728210272810_a_b_b @ X3 @ C3 ) ) )
      = ( ( ord_le146215904626753808_a_b_b @ A5 @ ( minus_1392386589478415753_a_b_b @ B5 @ C3 ) )
        & ~ ( member4380921116106875537_a_b_b @ X3 @ A5 ) ) ) ).

% subset_Diff_insert
thf(fact_1139_insert__Diff__if,axiom,
    ! [X3: produc4558475209616630778_a_b_b,B5: set_Pr3012420139608375472_a_b_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( ( member4380921116106875537_a_b_b @ X3 @ B5 )
       => ( ( minus_1392386589478415753_a_b_b @ ( insert1613891728210272810_a_b_b @ X3 @ A5 ) @ B5 )
          = ( minus_1392386589478415753_a_b_b @ A5 @ B5 ) ) )
      & ( ~ ( member4380921116106875537_a_b_b @ X3 @ B5 )
       => ( ( minus_1392386589478415753_a_b_b @ ( insert1613891728210272810_a_b_b @ X3 @ A5 ) @ B5 )
          = ( insert1613891728210272810_a_b_b @ X3 @ ( minus_1392386589478415753_a_b_b @ A5 @ B5 ) ) ) ) ) ).

% insert_Diff_if
thf(fact_1140_subset__insert__iff,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,X3: produc4558475209616630778_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ( ord_le146215904626753808_a_b_b @ A5 @ ( insert1613891728210272810_a_b_b @ X3 @ B5 ) )
      = ( ( ( member4380921116106875537_a_b_b @ X3 @ A5 )
         => ( ord_le146215904626753808_a_b_b @ ( minus_1392386589478415753_a_b_b @ A5 @ ( insert1613891728210272810_a_b_b @ X3 @ bot_bo3721250822024684356_a_b_b ) ) @ B5 ) )
        & ( ~ ( member4380921116106875537_a_b_b @ X3 @ A5 )
         => ( ord_le146215904626753808_a_b_b @ A5 @ B5 ) ) ) ) ).

% subset_insert_iff
thf(fact_1141_DiffI,axiom,
    ! [C: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ A5 )
     => ( ~ ( member4380921116106875537_a_b_b @ C @ B5 )
       => ( member4380921116106875537_a_b_b @ C @ ( minus_1392386589478415753_a_b_b @ A5 @ B5 ) ) ) ) ).

% DiffI
thf(fact_1142_Diff__iff,axiom,
    ! [C: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ ( minus_1392386589478415753_a_b_b @ A5 @ B5 ) )
      = ( ( member4380921116106875537_a_b_b @ C @ A5 )
        & ~ ( member4380921116106875537_a_b_b @ C @ B5 ) ) ) ).

% Diff_iff
thf(fact_1143_DiffE,axiom,
    ! [C: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ ( minus_1392386589478415753_a_b_b @ A5 @ B5 ) )
     => ~ ( ( member4380921116106875537_a_b_b @ C @ A5 )
         => ( member4380921116106875537_a_b_b @ C @ B5 ) ) ) ).

% DiffE
thf(fact_1144_DiffD1,axiom,
    ! [C: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ ( minus_1392386589478415753_a_b_b @ A5 @ B5 ) )
     => ( member4380921116106875537_a_b_b @ C @ A5 ) ) ).

% DiffD1
thf(fact_1145_DiffD2,axiom,
    ! [C: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ C @ ( minus_1392386589478415753_a_b_b @ A5 @ B5 ) )
     => ~ ( member4380921116106875537_a_b_b @ C @ B5 ) ) ).

% DiffD2
thf(fact_1146_bot_Onot__eq__extremum,axiom,
    ! [A: nat] :
      ( ( A != bot_bot_nat )
      = ( ord_less_nat @ bot_bot_nat @ A ) ) ).

% bot.not_eq_extremum
thf(fact_1147_bot_Oextremum__strict,axiom,
    ! [A: nat] :
      ~ ( ord_less_nat @ A @ bot_bot_nat ) ).

% bot.extremum_strict
thf(fact_1148_gt__ex,axiom,
    ! [X3: nat] :
    ? [X_1: nat] : ( ord_less_nat @ X3 @ X_1 ) ).

% gt_ex
thf(fact_1149_less__imp__neq,axiom,
    ! [X3: nat,Y3: nat] :
      ( ( ord_less_nat @ X3 @ Y3 )
     => ( X3 != Y3 ) ) ).

% less_imp_neq
thf(fact_1150_order_Oasym,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ~ ( ord_less_nat @ B @ A ) ) ).

% order.asym
thf(fact_1151_ord__eq__less__trans,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( A = B )
     => ( ( ord_less_nat @ B @ C )
       => ( ord_less_nat @ A @ C ) ) ) ).

% ord_eq_less_trans
thf(fact_1152_ord__less__eq__trans,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( B = C )
       => ( ord_less_nat @ A @ C ) ) ) ).

% ord_less_eq_trans
thf(fact_1153_less__induct,axiom,
    ! [P2: nat > $o,A: nat] :
      ( ! [X5: nat] :
          ( ! [Y6: nat] :
              ( ( ord_less_nat @ Y6 @ X5 )
             => ( P2 @ Y6 ) )
         => ( P2 @ X5 ) )
     => ( P2 @ A ) ) ).

% less_induct
thf(fact_1154_antisym__conv3,axiom,
    ! [Y3: nat,X3: nat] :
      ( ~ ( ord_less_nat @ Y3 @ X3 )
     => ( ( ~ ( ord_less_nat @ X3 @ Y3 ) )
        = ( X3 = Y3 ) ) ) ).

% antisym_conv3
thf(fact_1155_linorder__cases,axiom,
    ! [X3: nat,Y3: nat] :
      ( ~ ( ord_less_nat @ X3 @ Y3 )
     => ( ( X3 != Y3 )
       => ( ord_less_nat @ Y3 @ X3 ) ) ) ).

% linorder_cases
thf(fact_1156_dual__order_Oasym,axiom,
    ! [B: nat,A: nat] :
      ( ( ord_less_nat @ B @ A )
     => ~ ( ord_less_nat @ A @ B ) ) ).

% dual_order.asym
thf(fact_1157_dual__order_Oirrefl,axiom,
    ! [A: nat] :
      ~ ( ord_less_nat @ A @ A ) ).

% dual_order.irrefl
thf(fact_1158_exists__least__iff,axiom,
    ( ( ^ [P4: nat > $o] :
        ? [X8: nat] : ( P4 @ X8 ) )
    = ( ^ [P5: nat > $o] :
        ? [N2: nat] :
          ( ( P5 @ N2 )
          & ! [M2: nat] :
              ( ( ord_less_nat @ M2 @ N2 )
             => ~ ( P5 @ M2 ) ) ) ) ) ).

% exists_least_iff
thf(fact_1159_linorder__less__wlog,axiom,
    ! [P2: nat > nat > $o,A: nat,B: nat] :
      ( ! [A3: nat,B3: nat] :
          ( ( ord_less_nat @ A3 @ B3 )
         => ( P2 @ A3 @ B3 ) )
     => ( ! [A3: nat] : ( P2 @ A3 @ A3 )
       => ( ! [A3: nat,B3: nat] :
              ( ( P2 @ B3 @ A3 )
             => ( P2 @ A3 @ B3 ) )
         => ( P2 @ A @ B ) ) ) ) ).

% linorder_less_wlog
thf(fact_1160_order_Ostrict__trans,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_nat @ B @ C )
       => ( ord_less_nat @ A @ C ) ) ) ).

% order.strict_trans
thf(fact_1161_not__less__iff__gr__or__eq,axiom,
    ! [X3: nat,Y3: nat] :
      ( ( ~ ( ord_less_nat @ X3 @ Y3 ) )
      = ( ( ord_less_nat @ Y3 @ X3 )
        | ( X3 = Y3 ) ) ) ).

% not_less_iff_gr_or_eq
thf(fact_1162_dual__order_Ostrict__trans,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( ( ord_less_nat @ B @ A )
     => ( ( ord_less_nat @ C @ B )
       => ( ord_less_nat @ C @ A ) ) ) ).

% dual_order.strict_trans
thf(fact_1163_order_Ostrict__implies__not__eq,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( A != B ) ) ).

% order.strict_implies_not_eq
thf(fact_1164_dual__order_Ostrict__implies__not__eq,axiom,
    ! [B: nat,A: nat] :
      ( ( ord_less_nat @ B @ A )
     => ( A != B ) ) ).

% dual_order.strict_implies_not_eq
thf(fact_1165_linorder__neqE,axiom,
    ! [X3: nat,Y3: nat] :
      ( ( X3 != Y3 )
     => ( ~ ( ord_less_nat @ X3 @ Y3 )
       => ( ord_less_nat @ Y3 @ X3 ) ) ) ).

% linorder_neqE
thf(fact_1166_order__less__asym,axiom,
    ! [X3: nat,Y3: nat] :
      ( ( ord_less_nat @ X3 @ Y3 )
     => ~ ( ord_less_nat @ Y3 @ X3 ) ) ).

% order_less_asym
thf(fact_1167_linorder__neq__iff,axiom,
    ! [X3: nat,Y3: nat] :
      ( ( X3 != Y3 )
      = ( ( ord_less_nat @ X3 @ Y3 )
        | ( ord_less_nat @ Y3 @ X3 ) ) ) ).

% linorder_neq_iff
thf(fact_1168_order__less__asym_H,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ~ ( ord_less_nat @ B @ A ) ) ).

% order_less_asym'
thf(fact_1169_order__less__trans,axiom,
    ! [X3: nat,Y3: nat,Z: nat] :
      ( ( ord_less_nat @ X3 @ Y3 )
     => ( ( ord_less_nat @ Y3 @ Z )
       => ( ord_less_nat @ X3 @ Z ) ) ) ).

% order_less_trans
thf(fact_1170_ord__eq__less__subst,axiom,
    ! [A: nat,F2: nat > nat,B: nat,C: nat] :
      ( ( A
        = ( F2 @ B ) )
     => ( ( ord_less_nat @ B @ C )
       => ( ! [X5: nat,Y4: nat] :
              ( ( ord_less_nat @ X5 @ Y4 )
             => ( ord_less_nat @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) )
         => ( ord_less_nat @ A @ ( F2 @ C ) ) ) ) ) ).

% ord_eq_less_subst
thf(fact_1171_ord__less__eq__subst,axiom,
    ! [A: nat,B: nat,F2: nat > nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ( F2 @ B )
          = C )
       => ( ! [X5: nat,Y4: nat] :
              ( ( ord_less_nat @ X5 @ Y4 )
             => ( ord_less_nat @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) )
         => ( ord_less_nat @ ( F2 @ A ) @ C ) ) ) ) ).

% ord_less_eq_subst
thf(fact_1172_order__less__irrefl,axiom,
    ! [X3: nat] :
      ~ ( ord_less_nat @ X3 @ X3 ) ).

% order_less_irrefl
thf(fact_1173_order__less__subst1,axiom,
    ! [A: nat,F2: nat > nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ ( F2 @ B ) )
     => ( ( ord_less_nat @ B @ C )
       => ( ! [X5: nat,Y4: nat] :
              ( ( ord_less_nat @ X5 @ Y4 )
             => ( ord_less_nat @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) )
         => ( ord_less_nat @ A @ ( F2 @ C ) ) ) ) ) ).

% order_less_subst1
thf(fact_1174_order__less__subst2,axiom,
    ! [A: nat,B: nat,F2: nat > nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_nat @ ( F2 @ B ) @ C )
       => ( ! [X5: nat,Y4: nat] :
              ( ( ord_less_nat @ X5 @ Y4 )
             => ( ord_less_nat @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) )
         => ( ord_less_nat @ ( F2 @ A ) @ C ) ) ) ) ).

% order_less_subst2
thf(fact_1175_order__less__not__sym,axiom,
    ! [X3: nat,Y3: nat] :
      ( ( ord_less_nat @ X3 @ Y3 )
     => ~ ( ord_less_nat @ Y3 @ X3 ) ) ).

% order_less_not_sym
thf(fact_1176_order__less__imp__triv,axiom,
    ! [X3: nat,Y3: nat,P2: $o] :
      ( ( ord_less_nat @ X3 @ Y3 )
     => ( ( ord_less_nat @ Y3 @ X3 )
       => P2 ) ) ).

% order_less_imp_triv
thf(fact_1177_linorder__less__linear,axiom,
    ! [X3: nat,Y3: nat] :
      ( ( ord_less_nat @ X3 @ Y3 )
      | ( X3 = Y3 )
      | ( ord_less_nat @ Y3 @ X3 ) ) ).

% linorder_less_linear
thf(fact_1178_order__less__imp__not__eq,axiom,
    ! [X3: nat,Y3: nat] :
      ( ( ord_less_nat @ X3 @ Y3 )
     => ( X3 != Y3 ) ) ).

% order_less_imp_not_eq
thf(fact_1179_order__less__imp__not__eq2,axiom,
    ! [X3: nat,Y3: nat] :
      ( ( ord_less_nat @ X3 @ Y3 )
     => ( Y3 != X3 ) ) ).

% order_less_imp_not_eq2
thf(fact_1180_order__less__imp__not__less,axiom,
    ! [X3: nat,Y3: nat] :
      ( ( ord_less_nat @ X3 @ Y3 )
     => ~ ( ord_less_nat @ Y3 @ X3 ) ) ).

% order_less_imp_not_less
thf(fact_1181_top_Oextremum__strict,axiom,
    ! [A: set_Product_unit] :
      ~ ( ord_le8056459307392131481t_unit @ top_to1996260823553986621t_unit @ A ) ).

% top.extremum_strict
thf(fact_1182_top_Onot__eq__extremum,axiom,
    ! [A: set_Product_unit] :
      ( ( A != top_to1996260823553986621t_unit )
      = ( ord_le8056459307392131481t_unit @ A @ top_to1996260823553986621t_unit ) ) ).

% top.not_eq_extremum
thf(fact_1183_order__le__imp__less__or__eq,axiom,
    ! [X3: nat,Y3: nat] :
      ( ( ord_less_eq_nat @ X3 @ Y3 )
     => ( ( ord_less_nat @ X3 @ Y3 )
        | ( X3 = Y3 ) ) ) ).

% order_le_imp_less_or_eq
thf(fact_1184_linorder__le__less__linear,axiom,
    ! [X3: nat,Y3: nat] :
      ( ( ord_less_eq_nat @ X3 @ Y3 )
      | ( ord_less_nat @ Y3 @ X3 ) ) ).

% linorder_le_less_linear
thf(fact_1185_order__less__le__subst2,axiom,
    ! [A: nat,B: nat,F2: nat > nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_eq_nat @ ( F2 @ B ) @ C )
       => ( ! [X5: nat,Y4: nat] :
              ( ( ord_less_nat @ X5 @ Y4 )
             => ( ord_less_nat @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) )
         => ( ord_less_nat @ ( F2 @ A ) @ C ) ) ) ) ).

% order_less_le_subst2
thf(fact_1186_order__less__le__subst1,axiom,
    ! [A: nat,F2: nat > nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ ( F2 @ B ) )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ! [X5: nat,Y4: nat] :
              ( ( ord_less_eq_nat @ X5 @ Y4 )
             => ( ord_less_eq_nat @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) )
         => ( ord_less_nat @ A @ ( F2 @ C ) ) ) ) ) ).

% order_less_le_subst1
thf(fact_1187_order__le__less__subst2,axiom,
    ! [A: nat,B: nat,F2: nat > nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_nat @ ( F2 @ B ) @ C )
       => ( ! [X5: nat,Y4: nat] :
              ( ( ord_less_eq_nat @ X5 @ Y4 )
             => ( ord_less_eq_nat @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) )
         => ( ord_less_nat @ ( F2 @ A ) @ C ) ) ) ) ).

% order_le_less_subst2
thf(fact_1188_order__le__less__subst1,axiom,
    ! [A: nat,F2: nat > nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
     => ( ( ord_less_nat @ B @ C )
       => ( ! [X5: nat,Y4: nat] :
              ( ( ord_less_nat @ X5 @ Y4 )
             => ( ord_less_nat @ ( F2 @ X5 ) @ ( F2 @ Y4 ) ) )
         => ( ord_less_nat @ A @ ( F2 @ C ) ) ) ) ) ).

% order_le_less_subst1
thf(fact_1189_order__less__le__trans,axiom,
    ! [X3: nat,Y3: nat,Z: nat] :
      ( ( ord_less_nat @ X3 @ Y3 )
     => ( ( ord_less_eq_nat @ Y3 @ Z )
       => ( ord_less_nat @ X3 @ Z ) ) ) ).

% order_less_le_trans
thf(fact_1190_order__le__less__trans,axiom,
    ! [X3: nat,Y3: nat,Z: nat] :
      ( ( ord_less_eq_nat @ X3 @ Y3 )
     => ( ( ord_less_nat @ Y3 @ Z )
       => ( ord_less_nat @ X3 @ Z ) ) ) ).

% order_le_less_trans
thf(fact_1191_order__neq__le__trans,axiom,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ( ord_less_eq_nat @ A @ B )
       => ( ord_less_nat @ A @ B ) ) ) ).

% order_neq_le_trans
thf(fact_1192_order__le__neq__trans,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( A != B )
       => ( ord_less_nat @ A @ B ) ) ) ).

% order_le_neq_trans
thf(fact_1193_order__less__imp__le,axiom,
    ! [X3: nat,Y3: nat] :
      ( ( ord_less_nat @ X3 @ Y3 )
     => ( ord_less_eq_nat @ X3 @ Y3 ) ) ).

% order_less_imp_le
thf(fact_1194_linorder__not__less,axiom,
    ! [X3: nat,Y3: nat] :
      ( ( ~ ( ord_less_nat @ X3 @ Y3 ) )
      = ( ord_less_eq_nat @ Y3 @ X3 ) ) ).

% linorder_not_less
thf(fact_1195_linorder__not__le,axiom,
    ! [X3: nat,Y3: nat] :
      ( ( ~ ( ord_less_eq_nat @ X3 @ Y3 ) )
      = ( ord_less_nat @ Y3 @ X3 ) ) ).

% linorder_not_le
thf(fact_1196_order__less__le,axiom,
    ( ord_less_nat
    = ( ^ [X: nat,Y: nat] :
          ( ( ord_less_eq_nat @ X @ Y )
          & ( X != Y ) ) ) ) ).

% order_less_le
thf(fact_1197_order__le__less,axiom,
    ( ord_less_eq_nat
    = ( ^ [X: nat,Y: nat] :
          ( ( ord_less_nat @ X @ Y )
          | ( X = Y ) ) ) ) ).

% order_le_less
thf(fact_1198_dual__order_Ostrict__implies__order,axiom,
    ! [B: nat,A: nat] :
      ( ( ord_less_nat @ B @ A )
     => ( ord_less_eq_nat @ B @ A ) ) ).

% dual_order.strict_implies_order
thf(fact_1199_order_Ostrict__implies__order,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ord_less_eq_nat @ A @ B ) ) ).

% order.strict_implies_order
thf(fact_1200_dual__order_Ostrict__iff__not,axiom,
    ( ord_less_nat
    = ( ^ [B4: nat,A4: nat] :
          ( ( ord_less_eq_nat @ B4 @ A4 )
          & ~ ( ord_less_eq_nat @ A4 @ B4 ) ) ) ) ).

% dual_order.strict_iff_not
thf(fact_1201_dual__order_Ostrict__trans2,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( ( ord_less_nat @ B @ A )
     => ( ( ord_less_eq_nat @ C @ B )
       => ( ord_less_nat @ C @ A ) ) ) ).

% dual_order.strict_trans2
thf(fact_1202_dual__order_Ostrict__trans1,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( ( ord_less_eq_nat @ B @ A )
     => ( ( ord_less_nat @ C @ B )
       => ( ord_less_nat @ C @ A ) ) ) ).

% dual_order.strict_trans1
thf(fact_1203_dual__order_Ostrict__iff__order,axiom,
    ( ord_less_nat
    = ( ^ [B4: nat,A4: nat] :
          ( ( ord_less_eq_nat @ B4 @ A4 )
          & ( A4 != B4 ) ) ) ) ).

% dual_order.strict_iff_order
thf(fact_1204_dual__order_Oorder__iff__strict,axiom,
    ( ord_less_eq_nat
    = ( ^ [B4: nat,A4: nat] :
          ( ( ord_less_nat @ B4 @ A4 )
          | ( A4 = B4 ) ) ) ) ).

% dual_order.order_iff_strict
thf(fact_1205_order_Ostrict__iff__not,axiom,
    ( ord_less_nat
    = ( ^ [A4: nat,B4: nat] :
          ( ( ord_less_eq_nat @ A4 @ B4 )
          & ~ ( ord_less_eq_nat @ B4 @ A4 ) ) ) ) ).

% order.strict_iff_not
thf(fact_1206_order_Ostrict__trans2,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_eq_nat @ B @ C )
       => ( ord_less_nat @ A @ C ) ) ) ).

% order.strict_trans2
thf(fact_1207_order_Ostrict__trans1,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_nat @ B @ C )
       => ( ord_less_nat @ A @ C ) ) ) ).

% order.strict_trans1
thf(fact_1208_order_Ostrict__iff__order,axiom,
    ( ord_less_nat
    = ( ^ [A4: nat,B4: nat] :
          ( ( ord_less_eq_nat @ A4 @ B4 )
          & ( A4 != B4 ) ) ) ) ).

% order.strict_iff_order
thf(fact_1209_order_Oorder__iff__strict,axiom,
    ( ord_less_eq_nat
    = ( ^ [A4: nat,B4: nat] :
          ( ( ord_less_nat @ A4 @ B4 )
          | ( A4 = B4 ) ) ) ) ).

% order.order_iff_strict
thf(fact_1210_not__le__imp__less,axiom,
    ! [Y3: nat,X3: nat] :
      ( ~ ( ord_less_eq_nat @ Y3 @ X3 )
     => ( ord_less_nat @ X3 @ Y3 ) ) ).

% not_le_imp_less
thf(fact_1211_less__le__not__le,axiom,
    ( ord_less_nat
    = ( ^ [X: nat,Y: nat] :
          ( ( ord_less_eq_nat @ X @ Y )
          & ~ ( ord_less_eq_nat @ Y @ X ) ) ) ) ).

% less_le_not_le
thf(fact_1212_antisym__conv2,axiom,
    ! [X3: nat,Y3: nat] :
      ( ( ord_less_eq_nat @ X3 @ Y3 )
     => ( ( ~ ( ord_less_nat @ X3 @ Y3 ) )
        = ( X3 = Y3 ) ) ) ).

% antisym_conv2
thf(fact_1213_antisym__conv1,axiom,
    ! [X3: nat,Y3: nat] :
      ( ~ ( ord_less_nat @ X3 @ Y3 )
     => ( ( ord_less_eq_nat @ X3 @ Y3 )
        = ( X3 = Y3 ) ) ) ).

% antisym_conv1
thf(fact_1214_nless__le,axiom,
    ! [A: nat,B: nat] :
      ( ( ~ ( ord_less_nat @ A @ B ) )
      = ( ~ ( ord_less_eq_nat @ A @ B )
        | ( A = B ) ) ) ).

% nless_le
thf(fact_1215_leI,axiom,
    ! [X3: nat,Y3: nat] :
      ( ~ ( ord_less_nat @ X3 @ Y3 )
     => ( ord_less_eq_nat @ Y3 @ X3 ) ) ).

% leI
thf(fact_1216_leD,axiom,
    ! [Y3: nat,X3: nat] :
      ( ( ord_less_eq_nat @ Y3 @ X3 )
     => ~ ( ord_less_nat @ X3 @ Y3 ) ) ).

% leD
thf(fact_1217_fset__linorder__max__induct,axiom,
    ! [P2: fset_nat > $o,S3: fset_nat] :
      ( ( P2 @ bot_bot_fset_nat )
     => ( ! [X5: nat,S5: fset_nat] :
            ( ! [Y6: nat] :
                ( ( fmember_nat @ Y6 @ S5 )
               => ( ord_less_nat @ Y6 @ X5 ) )
           => ( ( P2 @ S5 )
             => ( P2 @ ( finsert_nat @ X5 @ S5 ) ) ) )
       => ( P2 @ S3 ) ) ) ).

% fset_linorder_max_induct
thf(fact_1218_fset__linorder__min__induct,axiom,
    ! [P2: fset_nat > $o,S3: fset_nat] :
      ( ( P2 @ bot_bot_fset_nat )
     => ( ! [X5: nat,S5: fset_nat] :
            ( ! [Y6: nat] :
                ( ( fmember_nat @ Y6 @ S5 )
               => ( ord_less_nat @ X5 @ Y6 ) )
           => ( ( P2 @ S5 )
             => ( P2 @ ( finsert_nat @ X5 @ S5 ) ) ) )
       => ( P2 @ S3 ) ) ) ).

% fset_linorder_min_induct
thf(fact_1219_inf__top_Osemilattice__neutr__order__axioms,axiom,
    semila4423693302617054363t_unit @ inf_in4660618365625256667t_unit @ top_to1996260823553986621t_unit @ ord_le3507040750410214029t_unit @ ord_le8056459307392131481t_unit ).

% inf_top.semilattice_neutr_order_axioms
thf(fact_1220_member__remove,axiom,
    ! [X3: produc4558475209616630778_a_b_b,Y3: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ X3 @ ( remove1850832869696284629_a_b_b @ Y3 @ A5 ) )
      = ( ( member4380921116106875537_a_b_b @ X3 @ A5 )
        & ( X3 != Y3 ) ) ) ).

% member_remove
thf(fact_1221_psubset__imp__ex__mem,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ( ord_le3723863380492978948_a_b_b @ A5 @ B5 )
     => ? [B3: produc4558475209616630778_a_b_b] : ( member4380921116106875537_a_b_b @ B3 @ ( minus_1392386589478415753_a_b_b @ B5 @ A5 ) ) ) ).

% psubset_imp_ex_mem
thf(fact_1222_psubset__insert__iff,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,X3: produc4558475209616630778_a_b_b,B5: set_Pr3012420139608375472_a_b_b] :
      ( ( ord_le3723863380492978948_a_b_b @ A5 @ ( insert1613891728210272810_a_b_b @ X3 @ B5 ) )
      = ( ( ( member4380921116106875537_a_b_b @ X3 @ B5 )
         => ( ord_le3723863380492978948_a_b_b @ A5 @ B5 ) )
        & ( ~ ( member4380921116106875537_a_b_b @ X3 @ B5 )
         => ( ( ( member4380921116106875537_a_b_b @ X3 @ A5 )
             => ( ord_le3723863380492978948_a_b_b @ ( minus_1392386589478415753_a_b_b @ A5 @ ( insert1613891728210272810_a_b_b @ X3 @ bot_bo3721250822024684356_a_b_b ) ) @ B5 ) )
            & ( ~ ( member4380921116106875537_a_b_b @ X3 @ A5 )
             => ( ord_le146215904626753808_a_b_b @ A5 @ B5 ) ) ) ) ) ) ).

% psubset_insert_iff
thf(fact_1223_dtree__size__decr__aux_H,axiom,
    ! [T1: dtree_a_b,Xs2: fset_P5281107635120001194_a_b_b,R: a] :
      ( ( member_dtree_a_b @ T1 @ ( image_7065894828672115579ee_a_b @ produc697780174058963904_a_b_b @ ( fset_P783253628892185035_a_b_b @ Xs2 ) ) )
     => ( ord_less_nat @ ( size_size_dtree_a_b @ T1 ) @ ( size_size_dtree_a_b @ ( node_a_b @ R @ Xs2 ) ) ) ) ).

% dtree_size_decr_aux'
thf(fact_1224_psubsetD,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,B5: set_Pr3012420139608375472_a_b_b,C: produc4558475209616630778_a_b_b] :
      ( ( ord_le3723863380492978948_a_b_b @ A5 @ B5 )
     => ( ( member4380921116106875537_a_b_b @ C @ A5 )
       => ( member4380921116106875537_a_b_b @ C @ B5 ) ) ) ).

% psubsetD
thf(fact_1225_nat__descend__induct,axiom,
    ! [N3: nat,P2: nat > $o,M3: nat] :
      ( ! [K2: nat] :
          ( ( ord_less_nat @ N3 @ K2 )
         => ( P2 @ K2 ) )
     => ( ! [K2: nat] :
            ( ( ord_less_eq_nat @ K2 @ N3 )
           => ( ! [I2: nat] :
                  ( ( ord_less_nat @ K2 @ I2 )
                 => ( P2 @ I2 ) )
             => ( P2 @ K2 ) ) )
       => ( P2 @ M3 ) ) ) ).

% nat_descend_induct
thf(fact_1226_dtree__size__decr__aux,axiom,
    ! [X3: dtree_a_b,Y3: b,Xs2: fset_P5281107635120001194_a_b_b,R: a] :
      ( ( member4380921116106875537_a_b_b @ ( produc331601717337510060_a_b_b @ X3 @ Y3 ) @ ( fset_P783253628892185035_a_b_b @ Xs2 ) )
     => ( ord_less_nat @ ( size_size_dtree_a_b @ X3 ) @ ( size_size_dtree_a_b @ ( node_a_b @ R @ Xs2 ) ) ) ) ).

% dtree_size_decr_aux
thf(fact_1227_card__Diff__singleton,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ X3 @ A5 )
     => ( ( finite2954864170529017298_a_b_b @ ( minus_1392386589478415753_a_b_b @ A5 @ ( insert1613891728210272810_a_b_b @ X3 @ bot_bo3721250822024684356_a_b_b ) ) )
        = ( minus_minus_nat @ ( finite2954864170529017298_a_b_b @ A5 ) @ one_one_nat ) ) ) ).

% card_Diff_singleton
thf(fact_1228_card__Diff__singleton,axiom,
    ! [X3: product_unit,A5: set_Product_unit] :
      ( ( member_Product_unit @ X3 @ A5 )
     => ( ( finite410649719033368117t_unit @ ( minus_6452836326544984404t_unit @ A5 @ ( insert_Product_unit @ X3 @ bot_bo3957492148770167129t_unit ) ) )
        = ( minus_minus_nat @ ( finite410649719033368117t_unit @ A5 ) @ one_one_nat ) ) ) ).

% card_Diff_singleton
thf(fact_1229_card__UNIV__unit,axiom,
    ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
    = one_one_nat ) ).

% card_UNIV_unit
thf(fact_1230_card__1__singletonE,axiom,
    ! [A5: set_Product_unit] :
      ( ( ( finite410649719033368117t_unit @ A5 )
        = one_one_nat )
     => ~ ! [X5: product_unit] :
            ( A5
           != ( insert_Product_unit @ X5 @ bot_bo3957492148770167129t_unit ) ) ) ).

% card_1_singletonE
thf(fact_1231_fcard_Orep__eq,axiom,
    ( fcard_7238254820230435945_a_b_b
    = ( ^ [X: fset_P5281107635120001194_a_b_b] : ( finite2954864170529017298_a_b_b @ ( fset_P783253628892185035_a_b_b @ X ) ) ) ) ).

% fcard.rep_eq
thf(fact_1232_fcard_Orep__eq,axiom,
    ( fcard_Product_unit
    = ( ^ [X: fset_Product_unit] : ( finite410649719033368117t_unit @ ( fset_Product_unit2 @ X ) ) ) ) ).

% fcard.rep_eq
thf(fact_1233_fcard__def,axiom,
    ( fcard_7238254820230435945_a_b_b
    = ( map_fu8120312284176349332at_nat @ fset_P783253628892185035_a_b_b @ id_nat @ finite2954864170529017298_a_b_b ) ) ).

% fcard_def
thf(fact_1234_fcard__def,axiom,
    ( fcard_Product_unit
    = ( map_fu3978117929841985266at_nat @ fset_Product_unit2 @ id_nat @ finite410649719033368117t_unit ) ) ).

% fcard_def
thf(fact_1235_card__Diff1__le,axiom,
    ! [A5: set_Product_unit,X3: product_unit] : ( ord_less_eq_nat @ ( finite410649719033368117t_unit @ ( minus_6452836326544984404t_unit @ A5 @ ( insert_Product_unit @ X3 @ bot_bo3957492148770167129t_unit ) ) ) @ ( finite410649719033368117t_unit @ A5 ) ) ).

% card_Diff1_le
thf(fact_1236_card__Diff__singleton__if,axiom,
    ! [X3: produc4558475209616630778_a_b_b,A5: set_Pr3012420139608375472_a_b_b] :
      ( ( ( member4380921116106875537_a_b_b @ X3 @ A5 )
       => ( ( finite2954864170529017298_a_b_b @ ( minus_1392386589478415753_a_b_b @ A5 @ ( insert1613891728210272810_a_b_b @ X3 @ bot_bo3721250822024684356_a_b_b ) ) )
          = ( minus_minus_nat @ ( finite2954864170529017298_a_b_b @ A5 ) @ one_one_nat ) ) )
      & ( ~ ( member4380921116106875537_a_b_b @ X3 @ A5 )
       => ( ( finite2954864170529017298_a_b_b @ ( minus_1392386589478415753_a_b_b @ A5 @ ( insert1613891728210272810_a_b_b @ X3 @ bot_bo3721250822024684356_a_b_b ) ) )
          = ( finite2954864170529017298_a_b_b @ A5 ) ) ) ) ).

% card_Diff_singleton_if
thf(fact_1237_card__Diff__singleton__if,axiom,
    ! [X3: product_unit,A5: set_Product_unit] :
      ( ( ( member_Product_unit @ X3 @ A5 )
       => ( ( finite410649719033368117t_unit @ ( minus_6452836326544984404t_unit @ A5 @ ( insert_Product_unit @ X3 @ bot_bo3957492148770167129t_unit ) ) )
          = ( minus_minus_nat @ ( finite410649719033368117t_unit @ A5 ) @ one_one_nat ) ) )
      & ( ~ ( member_Product_unit @ X3 @ A5 )
       => ( ( finite410649719033368117t_unit @ ( minus_6452836326544984404t_unit @ A5 @ ( insert_Product_unit @ X3 @ bot_bo3957492148770167129t_unit ) ) )
          = ( finite410649719033368117t_unit @ A5 ) ) ) ) ).

% card_Diff_singleton_if
thf(fact_1238_mem__card1__singleton,axiom,
    ! [U2: produc4558475209616630778_a_b_b,U3: set_Pr3012420139608375472_a_b_b] :
      ( ( member4380921116106875537_a_b_b @ U2 @ U3 )
     => ( ( ( finite2954864170529017298_a_b_b @ U3 )
          = one_one_nat )
       => ( U3
          = ( insert1613891728210272810_a_b_b @ U2 @ bot_bo3721250822024684356_a_b_b ) ) ) ) ).

% mem_card1_singleton
thf(fact_1239_mem__card1__singleton,axiom,
    ! [U2: product_unit,U3: set_Product_unit] :
      ( ( member_Product_unit @ U2 @ U3 )
     => ( ( ( finite410649719033368117t_unit @ U3 )
          = one_one_nat )
       => ( U3
          = ( insert_Product_unit @ U2 @ bot_bo3957492148770167129t_unit ) ) ) ) ).

% mem_card1_singleton
thf(fact_1240_card__Diff1__less,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b,X3: produc4558475209616630778_a_b_b] :
      ( ( finite9145440207725541265_a_b_b @ A5 )
     => ( ( member4380921116106875537_a_b_b @ X3 @ A5 )
       => ( ord_less_nat @ ( finite2954864170529017298_a_b_b @ ( minus_1392386589478415753_a_b_b @ A5 @ ( insert1613891728210272810_a_b_b @ X3 @ bot_bo3721250822024684356_a_b_b ) ) ) @ ( finite2954864170529017298_a_b_b @ A5 ) ) ) ) ).

% card_Diff1_less
thf(fact_1241_card__Diff1__less,axiom,
    ! [A5: set_Product_unit,X3: product_unit] :
      ( ( finite4290736615968046902t_unit @ A5 )
     => ( ( member_Product_unit @ X3 @ A5 )
       => ( ord_less_nat @ ( finite410649719033368117t_unit @ ( minus_6452836326544984404t_unit @ A5 @ ( insert_Product_unit @ X3 @ bot_bo3957492148770167129t_unit ) ) ) @ ( finite410649719033368117t_unit @ A5 ) ) ) ) ).

% card_Diff1_less
thf(fact_1242_finite__Plus__UNIV__iff,axiom,
    ( ( finite3146551501593861116t_unit @ top_to2771918933716375115t_unit )
    = ( ( finite4290736615968046902t_unit @ top_to1996260823553986621t_unit )
      & ( finite4290736615968046902t_unit @ top_to1996260823553986621t_unit ) ) ) ).

% finite_Plus_UNIV_iff
thf(fact_1243_Max_Obounded__iff,axiom,
    ! [A5: set_nat,X3: nat] :
      ( ( finite_finite_nat @ A5 )
     => ( ( A5 != bot_bot_set_nat )
       => ( ( ord_less_eq_nat @ ( lattic8265883725875713057ax_nat @ A5 ) @ X3 )
          = ( ! [X: nat] :
                ( ( member_nat @ X @ A5 )
               => ( ord_less_eq_nat @ X @ X3 ) ) ) ) ) ) ).

% Max.bounded_iff
thf(fact_1244_Min_Obounded__iff,axiom,
    ! [A5: set_nat,X3: nat] :
      ( ( finite_finite_nat @ A5 )
     => ( ( A5 != bot_bot_set_nat )
       => ( ( ord_less_eq_nat @ X3 @ ( lattic8721135487736765967in_nat @ A5 ) )
          = ( ! [X: nat] :
                ( ( member_nat @ X @ A5 )
               => ( ord_less_eq_nat @ X3 @ X ) ) ) ) ) ) ).

% Min.bounded_iff
thf(fact_1245_Max__less__iff,axiom,
    ! [A5: set_nat,X3: nat] :
      ( ( finite_finite_nat @ A5 )
     => ( ( A5 != bot_bot_set_nat )
       => ( ( ord_less_nat @ ( lattic8265883725875713057ax_nat @ A5 ) @ X3 )
          = ( ! [X: nat] :
                ( ( member_nat @ X @ A5 )
               => ( ord_less_nat @ X @ X3 ) ) ) ) ) ) ).

% Max_less_iff
thf(fact_1246_Min__gr__iff,axiom,
    ! [A5: set_nat,X3: nat] :
      ( ( finite_finite_nat @ A5 )
     => ( ( A5 != bot_bot_set_nat )
       => ( ( ord_less_nat @ X3 @ ( lattic8721135487736765967in_nat @ A5 ) )
          = ( ! [X: nat] :
                ( ( member_nat @ X @ A5 )
               => ( ord_less_nat @ X3 @ X ) ) ) ) ) ) ).

% Min_gr_iff
thf(fact_1247_card__eq__UNIV__imp__eq__UNIV,axiom,
    ! [A5: set_Product_unit] :
      ( ( finite4290736615968046902t_unit @ top_to1996260823553986621t_unit )
     => ( ( ( finite410649719033368117t_unit @ A5 )
          = ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit ) )
       => ( A5 = top_to1996260823553986621t_unit ) ) ) ).

% card_eq_UNIV_imp_eq_UNIV
thf(fact_1248_card__image__le,axiom,
    ! [A5: set_Product_unit,F2: product_unit > product_unit] :
      ( ( finite4290736615968046902t_unit @ A5 )
     => ( ord_less_eq_nat @ ( finite410649719033368117t_unit @ ( image_405062704495631173t_unit @ F2 @ A5 ) ) @ ( finite410649719033368117t_unit @ A5 ) ) ) ).

% card_image_le
thf(fact_1249_ex__min__if__finite,axiom,
    ! [S3: set_nat] :
      ( ( finite_finite_nat @ S3 )
     => ( ( S3 != bot_bot_set_nat )
       => ? [X5: nat] :
            ( ( member_nat @ X5 @ S3 )
            & ~ ? [Xa4: nat] :
                  ( ( member_nat @ Xa4 @ S3 )
                  & ( ord_less_nat @ Xa4 @ X5 ) ) ) ) ) ).

% ex_min_if_finite
thf(fact_1250_infinite__growing,axiom,
    ! [X6: set_nat] :
      ( ( X6 != bot_bot_set_nat )
     => ( ! [X5: nat] :
            ( ( member_nat @ X5 @ X6 )
           => ? [Xa4: nat] :
                ( ( member_nat @ Xa4 @ X6 )
                & ( ord_less_nat @ X5 @ Xa4 ) ) )
       => ~ ( finite_finite_nat @ X6 ) ) ) ).

% infinite_growing
thf(fact_1251_finite__has__maximal,axiom,
    ! [A5: set_nat] :
      ( ( finite_finite_nat @ A5 )
     => ( ( A5 != bot_bot_set_nat )
       => ? [X5: nat] :
            ( ( member_nat @ X5 @ A5 )
            & ! [Xa4: nat] :
                ( ( member_nat @ Xa4 @ A5 )
               => ( ( ord_less_eq_nat @ X5 @ Xa4 )
                 => ( X5 = Xa4 ) ) ) ) ) ) ).

% finite_has_maximal
thf(fact_1252_finite__has__minimal,axiom,
    ! [A5: set_nat] :
      ( ( finite_finite_nat @ A5 )
     => ( ( A5 != bot_bot_set_nat )
       => ? [X5: nat] :
            ( ( member_nat @ X5 @ A5 )
            & ! [Xa4: nat] :
                ( ( member_nat @ Xa4 @ A5 )
               => ( ( ord_less_eq_nat @ Xa4 @ X5 )
                 => ( X5 = Xa4 ) ) ) ) ) ) ).

% finite_has_minimal
thf(fact_1253_finite__ranking__induct,axiom,
    ! [S3: set_Pr3012420139608375472_a_b_b,P2: set_Pr3012420139608375472_a_b_b > $o,F2: produc4558475209616630778_a_b_b > nat] :
      ( ( finite9145440207725541265_a_b_b @ S3 )
     => ( ( P2 @ bot_bo3721250822024684356_a_b_b )
       => ( ! [X5: produc4558475209616630778_a_b_b,S5: set_Pr3012420139608375472_a_b_b] :
              ( ( finite9145440207725541265_a_b_b @ S5 )
             => ( ! [Y6: produc4558475209616630778_a_b_b] :
                    ( ( member4380921116106875537_a_b_b @ Y6 @ S5 )
                   => ( ord_less_eq_nat @ ( F2 @ Y6 ) @ ( F2 @ X5 ) ) )
               => ( ( P2 @ S5 )
                 => ( P2 @ ( insert1613891728210272810_a_b_b @ X5 @ S5 ) ) ) ) )
         => ( P2 @ S3 ) ) ) ) ).

% finite_ranking_induct
thf(fact_1254_finite__linorder__max__induct,axiom,
    ! [A5: set_nat,P2: set_nat > $o] :
      ( ( finite_finite_nat @ A5 )
     => ( ( P2 @ bot_bot_set_nat )
       => ( ! [B3: nat,A7: set_nat] :
              ( ( finite_finite_nat @ A7 )
             => ( ! [X7: nat] :
                    ( ( member_nat @ X7 @ A7 )
                   => ( ord_less_nat @ X7 @ B3 ) )
               => ( ( P2 @ A7 )
                 => ( P2 @ ( insert_nat @ B3 @ A7 ) ) ) ) )
         => ( P2 @ A5 ) ) ) ) ).

% finite_linorder_max_induct
thf(fact_1255_finite__linorder__min__induct,axiom,
    ! [A5: set_nat,P2: set_nat > $o] :
      ( ( finite_finite_nat @ A5 )
     => ( ( P2 @ bot_bot_set_nat )
       => ( ! [B3: nat,A7: set_nat] :
              ( ( finite_finite_nat @ A7 )
             => ( ! [X7: nat] :
                    ( ( member_nat @ X7 @ A7 )
                   => ( ord_less_nat @ B3 @ X7 ) )
               => ( ( P2 @ A7 )
                 => ( P2 @ ( insert_nat @ B3 @ A7 ) ) ) ) )
         => ( P2 @ A5 ) ) ) ) ).

% finite_linorder_min_induct
thf(fact_1256_finite__subset__induct_H,axiom,
    ! [F4: set_Pr3012420139608375472_a_b_b,A5: set_Pr3012420139608375472_a_b_b,P2: set_Pr3012420139608375472_a_b_b > $o] :
      ( ( finite9145440207725541265_a_b_b @ F4 )
     => ( ( ord_le146215904626753808_a_b_b @ F4 @ A5 )
       => ( ( P2 @ bot_bo3721250822024684356_a_b_b )
         => ( ! [A3: produc4558475209616630778_a_b_b,F5: set_Pr3012420139608375472_a_b_b] :
                ( ( finite9145440207725541265_a_b_b @ F5 )
               => ( ( member4380921116106875537_a_b_b @ A3 @ A5 )
                 => ( ( ord_le146215904626753808_a_b_b @ F5 @ A5 )
                   => ( ~ ( member4380921116106875537_a_b_b @ A3 @ F5 )
                     => ( ( P2 @ F5 )
                       => ( P2 @ ( insert1613891728210272810_a_b_b @ A3 @ F5 ) ) ) ) ) ) )
           => ( P2 @ F4 ) ) ) ) ) ).

% finite_subset_induct'
thf(fact_1257_finite__subset__induct,axiom,
    ! [F4: set_Pr3012420139608375472_a_b_b,A5: set_Pr3012420139608375472_a_b_b,P2: set_Pr3012420139608375472_a_b_b > $o] :
      ( ( finite9145440207725541265_a_b_b @ F4 )
     => ( ( ord_le146215904626753808_a_b_b @ F4 @ A5 )
       => ( ( P2 @ bot_bo3721250822024684356_a_b_b )
         => ( ! [A3: produc4558475209616630778_a_b_b,F5: set_Pr3012420139608375472_a_b_b] :
                ( ( finite9145440207725541265_a_b_b @ F5 )
               => ( ( member4380921116106875537_a_b_b @ A3 @ A5 )
                 => ( ~ ( member4380921116106875537_a_b_b @ A3 @ F5 )
                   => ( ( P2 @ F5 )
                     => ( P2 @ ( insert1613891728210272810_a_b_b @ A3 @ F5 ) ) ) ) ) )
           => ( P2 @ F4 ) ) ) ) ) ).

% finite_subset_induct
thf(fact_1258_finite__induct,axiom,
    ! [F4: set_Pr3012420139608375472_a_b_b,P2: set_Pr3012420139608375472_a_b_b > $o] :
      ( ( finite9145440207725541265_a_b_b @ F4 )
     => ( ( P2 @ bot_bo3721250822024684356_a_b_b )
       => ( ! [X5: produc4558475209616630778_a_b_b,F5: set_Pr3012420139608375472_a_b_b] :
              ( ( finite9145440207725541265_a_b_b @ F5 )
             => ( ~ ( member4380921116106875537_a_b_b @ X5 @ F5 )
               => ( ( P2 @ F5 )
                 => ( P2 @ ( insert1613891728210272810_a_b_b @ X5 @ F5 ) ) ) ) )
         => ( P2 @ F4 ) ) ) ) ).

% finite_induct
thf(fact_1259_finite__ne__induct,axiom,
    ! [F4: set_Pr3012420139608375472_a_b_b,P2: set_Pr3012420139608375472_a_b_b > $o] :
      ( ( finite9145440207725541265_a_b_b @ F4 )
     => ( ( F4 != bot_bo3721250822024684356_a_b_b )
       => ( ! [X5: produc4558475209616630778_a_b_b] : ( P2 @ ( insert1613891728210272810_a_b_b @ X5 @ bot_bo3721250822024684356_a_b_b ) )
         => ( ! [X5: produc4558475209616630778_a_b_b,F5: set_Pr3012420139608375472_a_b_b] :
                ( ( finite9145440207725541265_a_b_b @ F5 )
               => ( ( F5 != bot_bo3721250822024684356_a_b_b )
                 => ( ~ ( member4380921116106875537_a_b_b @ X5 @ F5 )
                   => ( ( P2 @ F5 )
                     => ( P2 @ ( insert1613891728210272810_a_b_b @ X5 @ F5 ) ) ) ) ) )
           => ( P2 @ F4 ) ) ) ) ) ).

% finite_ne_induct
thf(fact_1260_infinite__finite__induct,axiom,
    ! [P2: set_Pr3012420139608375472_a_b_b > $o,A5: set_Pr3012420139608375472_a_b_b] :
      ( ! [A7: set_Pr3012420139608375472_a_b_b] :
          ( ~ ( finite9145440207725541265_a_b_b @ A7 )
         => ( P2 @ A7 ) )
     => ( ( P2 @ bot_bo3721250822024684356_a_b_b )
       => ( ! [X5: produc4558475209616630778_a_b_b,F5: set_Pr3012420139608375472_a_b_b] :
              ( ( finite9145440207725541265_a_b_b @ F5 )
             => ( ~ ( member4380921116106875537_a_b_b @ X5 @ F5 )
               => ( ( P2 @ F5 )
                 => ( P2 @ ( insert1613891728210272810_a_b_b @ X5 @ F5 ) ) ) ) )
         => ( P2 @ A5 ) ) ) ) ).

% infinite_finite_induct
thf(fact_1261_finite__fset,axiom,
    ! [S3: fset_P5281107635120001194_a_b_b] : ( finite9145440207725541265_a_b_b @ ( fset_P783253628892185035_a_b_b @ S3 ) ) ).

% finite_fset
thf(fact_1262_finite__Prod__UNIV,axiom,
    ( ( finite4290736615968046902t_unit @ top_to1996260823553986621t_unit )
   => ( ( finite4290736615968046902t_unit @ top_to1996260823553986621t_unit )
     => ( finite6816719414181127824t_unit @ top_to1835807148980544151t_unit ) ) ) ).

% finite_Prod_UNIV
thf(fact_1263_finite__prod,axiom,
    ( ( finite6816719414181127824t_unit @ top_to1835807148980544151t_unit )
    = ( ( finite4290736615968046902t_unit @ top_to1996260823553986621t_unit )
      & ( finite4290736615968046902t_unit @ top_to1996260823553986621t_unit ) ) ) ).

% finite_prod
thf(fact_1264_finite__UNIV,axiom,
    finite4290736615968046902t_unit @ top_to1996260823553986621t_unit ).

% finite_UNIV
thf(fact_1265_ex__new__if__finite,axiom,
    ! [A5: set_Pr3012420139608375472_a_b_b] :
      ( ~ ( finite9145440207725541265_a_b_b @ top_to7222684678772277088_a_b_b )
     => ( ( finite9145440207725541265_a_b_b @ A5 )
       => ? [A3: produc4558475209616630778_a_b_b] :
            ~ ( member4380921116106875537_a_b_b @ A3 @ A5 ) ) ) ).

% ex_new_if_finite
thf(fact_1266_ex__new__if__finite,axiom,
    ! [A5: set_Product_unit] :
      ( ~ ( finite4290736615968046902t_unit @ top_to1996260823553986621t_unit )
     => ( ( finite4290736615968046902t_unit @ A5 )
       => ? [A3: product_unit] :
            ~ ( member_Product_unit @ A3 @ A5 ) ) ) ).

% ex_new_if_finite
thf(fact_1267_Finite__Set_Ofinite__set,axiom,
    ( ( finite1772178364199683094t_unit @ top_to1767297665138865437t_unit )
    = ( finite4290736615968046902t_unit @ top_to1996260823553986621t_unit ) ) ).

% Finite_Set.finite_set
thf(fact_1268_Min__less__iff,axiom,
    ! [A5: set_nat,X3: nat] :
      ( ( finite_finite_nat @ A5 )
     => ( ( A5 != bot_bot_set_nat )
       => ( ( ord_less_nat @ ( lattic8721135487736765967in_nat @ A5 ) @ X3 )
          = ( ? [X: nat] :
                ( ( member_nat @ X @ A5 )
                & ( ord_less_nat @ X @ X3 ) ) ) ) ) ) ).

% Min_less_iff
thf(fact_1269_Max__gr__iff,axiom,
    ! [A5: set_nat,X3: nat] :
      ( ( finite_finite_nat @ A5 )
     => ( ( A5 != bot_bot_set_nat )
       => ( ( ord_less_nat @ X3 @ ( lattic8265883725875713057ax_nat @ A5 ) )
          = ( ? [X: nat] :
                ( ( member_nat @ X @ A5 )
                & ( ord_less_nat @ X3 @ X ) ) ) ) ) ) ).

% Max_gr_iff
thf(fact_1270_Min_OboundedI,axiom,
    ! [A5: set_nat,X3: nat] :
      ( ( finite_finite_nat @ A5 )
     => ( ( A5 != bot_bot_set_nat )
       => ( ! [A3: nat] :
              ( ( member_nat @ A3 @ A5 )
             => ( ord_less_eq_nat @ X3 @ A3 ) )
         => ( ord_less_eq_nat @ X3 @ ( lattic8721135487736765967in_nat @ A5 ) ) ) ) ) ).

% Min.boundedI
thf(fact_1271_Min_OboundedE,axiom,
    ! [A5: set_nat,X3: nat] :
      ( ( finite_finite_nat @ A5 )
     => ( ( A5 != bot_bot_set_nat )
       => ( ( ord_less_eq_nat @ X3 @ ( lattic8721135487736765967in_nat @ A5 ) )
         => ! [A8: nat] :
              ( ( member_nat @ A8 @ A5 )
             => ( ord_less_eq_nat @ X3 @ A8 ) ) ) ) ) ).

% Min.boundedE
thf(fact_1272_eq__Min__iff,axiom,
    ! [A5: set_nat,M3: nat] :
      ( ( finite_finite_nat @ A5 )
     => ( ( A5 != bot_bot_set_nat )
       => ( ( M3
            = ( lattic8721135487736765967in_nat @ A5 ) )
          = ( ( member_nat @ M3 @ A5 )
            & ! [X: nat] :
                ( ( member_nat @ X @ A5 )
               => ( ord_less_eq_nat @ M3 @ X ) ) ) ) ) ) ).

% eq_Min_iff
thf(fact_1273_Min__le__iff,axiom,
    ! [A5: set_nat,X3: nat] :
      ( ( finite_finite_nat @ A5 )
     => ( ( A5 != bot_bot_set_nat )
       => ( ( ord_less_eq_nat @ ( lattic8721135487736765967in_nat @ A5 ) @ X3 )
          = ( ? [X: nat] :
                ( ( member_nat @ X @ A5 )
                & ( ord_less_eq_nat @ X @ X3 ) ) ) ) ) ) ).

% Min_le_iff
thf(fact_1274_Min__eq__iff,axiom,
    ! [A5: set_nat,M3: nat] :
      ( ( finite_finite_nat @ A5 )
     => ( ( A5 != bot_bot_set_nat )
       => ( ( ( lattic8721135487736765967in_nat @ A5 )
            = M3 )
          = ( ( member_nat @ M3 @ A5 )
            & ! [X: nat] :
                ( ( member_nat @ X @ A5 )
               => ( ord_less_eq_nat @ M3 @ X ) ) ) ) ) ) ).

% Min_eq_iff
thf(fact_1275_Max_OboundedI,axiom,
    ! [A5: set_nat,X3: nat] :
      ( ( finite_finite_nat @ A5 )
     => ( ( A5 != bot_bot_set_nat )
       => ( ! [A3: nat] :
              ( ( member_nat @ A3 @ A5 )
             => ( ord_less_eq_nat @ A3 @ X3 ) )
         => ( ord_less_eq_nat @ ( lattic8265883725875713057ax_nat @ A5 ) @ X3 ) ) ) ) ).

% Max.boundedI
thf(fact_1276_Max_OboundedE,axiom,
    ! [A5: set_nat,X3: nat] :
      ( ( finite_finite_nat @ A5 )
     => ( ( A5 != bot_bot_set_nat )
       => ( ( ord_less_eq_nat @ ( lattic8265883725875713057ax_nat @ A5 ) @ X3 )
         => ! [A8: nat] :
              ( ( member_nat @ A8 @ A5 )
             => ( ord_less_eq_nat @ A8 @ X3 ) ) ) ) ) ).

% Max.boundedE

% Conjectures (1)
thf(conj_0,conjecture,
    ( ( comp_b_a_b_a_b_a @ ( f @ y ) @ ( f @ x ) @ z )
    = ( comp_b_a_b_a_b_a @ ( f @ x ) @ ( f @ y ) @ z ) ) ).

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