%------------------------------------------------------------------------------
% File     : ITP216_3 : TPTP v8.2.0. Released v8.0.0.
% Domain   : Interactive Theorem Proving
% Problem  : Sledgehammer problem Time_Reasoning 00074_002979
% Version  : [Des22] axioms.
% English  :

% Refs     : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
%          : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% Source   : [Des22]
% Names    : 0029_Time_Reasoning_00074_002979 [Des22]

% Status   : Theorem
% Rating   : 0.00 v8.2.0, 0.33 v8.1.0
% Syntax   : Number of formulae    : 14526 (4371 unt;5761 typ;   0 def)
%            Number of atoms       : 18585 (8979 equ)
%            Maximal formula atoms :   38 (   2 avg)
%            Number of connectives : 11033 (1750   ~; 330   |; 857   &)
%                                         (1800 <=>;6296  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   4 avg)
%            Maximal term depth    :   38 (   2 avg)
%            Number of FOOLs       : 1729 ( 603 fml;1126 var)
%            Number of X terms     :  498 (   0  []; 472 ite;  26 let)
%            Number of types       : 1463 (1462 usr)
%            Number of type conns  : 6179 (3472   >;2707   *;   0   +;   0  <<)
%            Number of predicates  :  451 ( 448 usr;   3 prp; 0-6 aty)
%            Number of functors    : 3859 (3859 usr; 834 con; 0-8 aty)
%            Number of variables   : 21024 (20722   !; 302   ?;21024   :)
% SPC      : TX0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            from the van Emde Boas Trees session in the Archive of Formal
%            proofs - 
%            www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
%            2022-02-17 16:14:05.593
%------------------------------------------------------------------------------
% Could-be-implicit typings (1462)
tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J_J_J,type,
    fun_Pr386875378712213506et_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J_J,type,
    set_Pr7057080801110549565et_nat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J_J,type,
    fun_se2331804103973993189et_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_M_Eo_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J_J,type,
    fun_fu3515393148397969210et_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    produc505541996239113949et_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_M_Eo_J_J,type,
    fun_Pr3358449090565925198_nat_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J_Mt__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_J_J,type,
    fun_se4713689491525875926_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_J_Mt__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_M_Eo_J_J,type,
    fun_fu5983609555712719719_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_M_Eo_J_Mt__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_J_J,type,
    fun_fu4927615759029954091_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    fun_Pr6662792608368940153et_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    fun_Pr8630787502178681855et_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J_J,type,
    fun_fu3932451362284101085et_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_Mt__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J_J,type,
    fun_Pr8737872353715570297et_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_J_J,type,
    fun_Pr471679772948460611nteger: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_J,type,
    set_Pr6949033248718891245nteger: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_J,type,
    fun_se2190013347424485781nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_M_Eo_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_J,type,
    fun_fu5535353563232763194nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J_J,type,
    fun_fu951349246861503509et_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J_J,type,
    fun_Pr4147293223664569617et_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    produc7379341420752632205nteger: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_Mt__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J_J,type,
    fun_se6163777255337707072eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J_Mt__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_M_Eo_J_J,type,
    fun_fu7060041198443644797eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_M_Eo_J_Mt__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J_J,type,
    fun_fu4530937843762191077eger_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    fun_Pr2953255705995765467et_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    fun_Pr3978243888342905947et_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J_J,type,
    fun_Pr4459677240377800360et_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J_J,type,
    fun_Pr7963917038216275131nt_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    fun_Pr3905736301278533417nteger: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    fun_Pr6966570558394395095nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_J,type,
    fun_fu8946524575271555235nteger: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_J,type,
    fun_Pr8371818785129130299nteger: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
    set_Pr3767905878465553991nt_int: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
    fun_se1594822257893229295nt_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
    fun_fu4502062894868904186nt_int: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    produc881187336974765031nt_int: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_Mt__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J_J,type,
    fun_se5710315616867461632_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J_Mt__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J_J,type,
    fun_fu2458202332514215229_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J_Mt__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J_J,type,
    fun_fu4695829907076200203_int_o: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_J_J,type,
    fun_op291006984297869545at_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    fun_Pr5846521507401124227nt_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    fun_Pr5010838083610845651nt_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_J,type,
    fun_fu4173945377279696323nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
    fun_fu9160953773549289085nt_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
    fun_Pr8826142978676617911nt_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    fun_fu8902681562042749453nteger: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    fun_Pr4557384415951816845e_term: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    set_Pr9066344408807579265et_nat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    fun_se9157011578508667433et_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    fun_fu2239858650119588794et_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J_J,type,
    fun_fu5650763273978745334et_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    produc8893060842726229537et_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    fun_fu6196531292930346304et_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
    fun_Pr7618159474455865098_nat_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_Mt__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J_J,type,
    fun_se7509835969743050710_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J_Mt__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_J,type,
    fun_fu3464598166661278695_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_Mt__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J_J,type,
    fun_fu7582738562687708775_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    fun_Pr836988951548913597et_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    fun_Pr5416369060549219583et_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
    fun_fu60724386564609697nt_int: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J_J_J_J,type,
    fun_se1700271160720914596_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    fun_fu2265384587115734689et_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    fun_Pr5259258551928531321et_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_Mt__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_J_J,type,
    fun_fu7234567020521114219nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    fun_fu5813366174458671467nt_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    fun_Pr5872836680101629291e_term: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J_J_J_J,type,
    fun_se6980948925662697216_nat_o: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J_J,type,
    fun_op4112804339236761266it_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J_J,type,
    fun_Pr5088371826558493971nt_int: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J_J,type,
    set_Pr2514328457256655413e_term: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_Mt__fun_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J_J,type,
    fun_Pr3631287881653221602it_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    produc8529534078076073941e_term: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_Mt__fun_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    fun_Pr1003294667014919570it_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J_J,type,
    set_Pr257197284073945367e_term: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    fun_Pr6442729728054246170it_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    fun_fu2505754153367914865e_term: $tType ).

tff(ty_n_t__fun_It__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_Mt__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J_J,type,
    fun_fu2492676192234506515it_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_Mt__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J_J,type,
    fun_fu4233702620870981175it_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    produc9065761207657906103e_term: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_J,type,
    fun_se636550882185307767at_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J_J,type,
    set_se6059149423757001258et_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_J,type,
    fun_fu8543582513329703974nteger: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_J,type,
    fun_Pr894914116851403386nteger: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_M_Eo_J_J,type,
    set_fu4385504767878589843_nat_o: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
    set_Pr3703873761940759199nt_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J_M_Eo_J_J,type,
    fun_Pr6341106346053136302_nat_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
    fun_se2900878183379320647nt_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
    fun_fu9132409297049680378nt_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J_M_Eo_J_J,type,
    fun_Pr5911813565203289452_nat_o: $tType ).

tff(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    option5899113203645146382et_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    fun_fu836511555612062035e_term: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    set_Pr4040394263813967220et_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J_J,type,
    set_Pr7905283282039288826_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_M_Eo_J,type,
    fun_Pr1227177680593602867_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_Pr6160931176198666718nteger: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    fun_Pr2985126522952997572nteger: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    produc3192696172498486335nt_int: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_J_J,type,
    set_fu5576194784986904859_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J_J,type,
    fun_Pr886604116968709228_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J_Mt__fun_It__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_J_M_Eo_J_J,type,
    fun_fu7865199641817216212eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_J_Mt__fun_It__fun_It__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J_M_Eo_J_J,type,
    fun_fu8324349134136105556eger_o: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    produc4193628355235574503at_nat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J_J,type,
    fun_se5644990602862975744_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J_Mt__fun_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J_J,type,
    fun_fu5894409982295737917_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J_Mt__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J_J,type,
    fun_fu6286765928754279603_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    fun_fu1905361174868762994et_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    produc3112576180687729086et_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
    produc6858501863712832324_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    fun_fu8357309440898100312et_nat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J_J_J_J,type,
    fun_se3629081808164793780_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_Mt__Set__Oset_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J_J,type,
    fun_Pr7968690803259750408_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_J,type,
    fun_fu2611741329380808165_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_Mt__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_Eo_J_J,type,
    fun_Pr2647030239595059785at_o_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    fun_Pr5152393401594413531nt_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J_Mt__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    fun_Pr3284083897292419283nt_int: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_J,type,
    set_Pr7459493094073627847at_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    fun_fu5004560472337415769et_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    fun_Pr3017356861961520469et_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    fun_fu8710561278413400866et_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
    fun_Pr3233114924583728296_nat_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J_J_J_J,type,
    fun_se991814106188233920_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_J_Mt__fun_It__fun_It__fun_It__Int__Oint_Mt__Nat__Onat_J_Mt__fun_It__Int__Oint_Mt__Num__Onum_J_J_M_Eo_J_J,type,
    fun_fu6437682067762269056_num_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
    fun_fu465145433024125141nt_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
    fun_Pr4353654455642104759nt_int: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_J,type,
    fun_se7901873761543946185at_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    produc1319942482725812455at_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    fun_Pr2813956079162534559et_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    fun_Pr4885567672785483807et_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__fun_It__Product____Type__Oprod_It__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J_J,type,
    fun_Pr8463018485500633518_nat_o: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    set_Pr5564308138774400199at_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_M_Eo_J,type,
    fun_Pr5502292500389099060_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
    fun_fu4812223801888690549nt_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
    fun_Pr1547027809659849477nt_int: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    fun_se6846035212209387651at_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    fun_fu5127092707984472044at_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_J,type,
    set_se7873143835621700354nteger: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_M_Eo_J_J,type,
    set_fu6463009222652410043eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    fun_fu4688806437979560835nteger: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_Mt__fun_It__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_M_Eo_J_J,type,
    fun_op1633239139951409690_nat_o: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_Mt__fun_It__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_M_Eo_J_J,type,
    fun_op8703326495438967718_nat_o: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_Mt__fun_It__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_M_Eo_J_J,type,
    fun_op101698441058542546_nat_o: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_Mt__fun_It__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_M_Eo_J_J,type,
    fun_op2352717853092002798_nat_o: $tType ).

tff(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    option983905398058327270nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    fun_fu2531416508075921811et_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Set__Oset_It__Int__Oint_J_J_J,type,
    fun_fu6941240126142778863et_int: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    produc1906917888121415911at_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    fun_Pr1987159835869338959nt_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    fun_Pr4781553364444837327nt_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J_J,type,
    fun_Pr5947183769845927726_nat_o: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    set_Pr3486312109254157132nteger: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J_J,type,
    set_Pr3944325338781952762e_term: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    fun_fu2716251949043459987at_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_M_Eo_J,type,
    fun_Pr7015759342434529115eger_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J_J,type,
    fun_se8406536441587994090_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J_Mt__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J_J,type,
    fun_fu3198693465525813493_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Set__Oset_I_Eo_J_J_J,type,
    fun_fu6788480576040630871_set_o: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J_J,type,
    set_fu7224585531122448557eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J_J_J,type,
    fun_fu560856344546067396_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
    fun_fu6029888860018473377nt_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    fun_Pr6865292569827446866it_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J,type,
    fun_Pr8741579136290173250atural: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    fun_fu4835546211937200935e_term: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    fun_fu1176768540439120679e_term: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    fun_fu4810197545401214784nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Ounit_Mt__Heap____Time____Monad__OHeap_It__Product____Type__Ounit_J_J_Mt__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J_J,type,
    fun_fu2217603491152269828it_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    produc9140211490168418807atural: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    produc2453742332425399446nteger: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    produc592931078481472324e_term: $tType ).

tff(ty_n_t__fun_It__fun_It__Heap__Oarray_Itf__a_J_Mt__Heap____Time____Monad__OHeap_It__Product____Type__Ounit_J_J_Mt__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J_J,type,
    fun_fu5808343195260015654it_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Ounit_Mt__Heap____Time____Monad__OHeap_It__Heap__Oarray_Itf__a_J_J_J_Mt__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J_J,type,
    fun_fu1080234963260751190it_nat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J_J_J,type,
    fun_se5316394792625908170_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    fun_fu5971215405379524186nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Heap__Oarray_Itf__a_J_Mt__Heap____Time____Monad__OHeap_It__Heap__Oarray_Itf__a_J_J_J_Mt__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J_J,type,
    fun_fu7484024174323986552it_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Set__Oset_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J_J,type,
    fun_Pr5305228341155023582e_term: $tType ).

tff(ty_n_t__fun_It__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    fun_fu7445151911848907075at_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
    fun_fu7695273699059480439eger_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_Eo_J_J,type,
    fun_Pr4680327687137491167term_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    fun_fu4545303443005895275nt_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    fun_Pr7653582204007996523e_term: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    fun_Pr7644814098969791837it_nat: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    fun_op7765417307512062173it_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    fun_Pr7518090501403545819it_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    fun_Pr245379829043246639it_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    fun_Pr8118912048244921225it_nat: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    fun_op8917697677373047293it_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
    set_se2743246391971219311nt_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__fun_It__fun_It__Nat__Onat_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__fun_It__Nat__Onat_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    fun_fu695563712076452518at_nat: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J_J,type,
    set_fu5926610517471843470_int_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J_J_J,type,
    fun_se8716479205685501124_nat_o: $tType ).

tff(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    option1544258867535432659nt_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J_J,type,
    fun_Pr925140355916870337it_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J_J,type,
    fun_Pr2979129825601314957it_nat: $tType ).

tff(ty_n_t__fun_It__Heap__Oarray_Itf__a_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J_J,type,
    fun_ar4934926718671674165it_nat: $tType ).

tff(ty_n_t__fun_It__Heap__Oarray_Itf__a_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J_J,type,
    fun_ar7427004957847640857it_nat: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Onatural_Mt__fun_It__Code____Numeral__Onatural_Mt__fun_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J_J_J,type,
    fun_Co9168753396221475450atural: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__Int__Oint_Mt__Rat__Orat_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J_J_J,type,
    fun_fu61188948249169719_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__Rat__Orat_J_M_Eo_J_J_J,type,
    fun_fu3447610970239163469_rat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    fun_Pr1033138224055104269it_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    set_Pr6700895561065273913nt_int: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J_J,type,
    set_Pr3640028372902554249e_term: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J,type,
    fun_Pr3540825087398332590_int_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    fun_Pr3908927074708932117it_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    fun_Pr2014882013869309663it_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    fun_Pr3819237756034508227it_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_Mt__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
    fun_fu865538946246809014eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_M_Eo_J_J,type,
    fun_fu1909630106382427190eger_o: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J_J,type,
    set_fu1179388718870097536_int_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J_M_Eo_J_J_J_J,type,
    fun_se9209729713313069232_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    fun_fu4253467608928286509nt_int: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_Mt__Option__Ooption_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_J,type,
    fun_op7507520395135695063nteger: $tType ).

tff(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    set_se3290278062343509644et_nat: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_J,type,
    set_fu6830718107662835377_nat_o: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J_J,type,
    set_Pr2890355626087285447_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__fun_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J_J_J,type,
    fun_Pr5739084258597601403it_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    produc3043004577601930755nt_int: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    produc4155239895104388691e_term: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__fun_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J_J_J,type,
    fun_Pr2439654876356241257it_nat: $tType ).

tff(ty_n_t__fun_It__Heap__Oarray_Itf__a_J_Mt__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__fun_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J_J_J,type,
    fun_ar5851962999413977351it_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_J,type,
    fun_fu2039158179202302481nteger: $tType ).

tff(ty_n_t__fun_It__Heap__Oarray_Itf__a_J_Mt__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__fun_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J_J_J,type,
    fun_ar4667500465507062749it_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    fun_fu4219362280553733319nt_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_M_Eo_J_J,type,
    fun_fu7605985262670345913eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_Mt__fun_It__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
    fun_fu5480185501004512569eger_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Set__Oset_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J_J,type,
    fun_Pr4426623609552329069e_term: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    fun_fu6865642474282033866_int_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    fun_Pr6967485491430695501atural: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J,type,
    fun_Pr3377396784085331203atural: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_Eo_J_J,type,
    fun_Pr5526332658708858896term_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Code____Numeral__Onatural_J_J,type,
    fun_Pr4028877673837371139atural: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J,type,
    fun_Pr6891710885006071673atural: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J,type,
    fun_Pr3133360822718887225atural: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_J_J_J,type,
    fun_se7382040709525900966_nat_o: $tType ).

tff(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    option4955102875562834416et_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    fun_fu86038545275896455et_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__Set__Oset_It__Int__Oint_J_J_J,type,
    fun_fu4495862163342753507et_int: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J_J,type,
    set_Pr7847555563209246911e_term: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Code____Numeral__Ointeger_J,type,
    produc2402493665305094840nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
    fun_fu786557078278636193nt_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
    fun_Pr1951044811698827825nt_int: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    set_Pr1312406793078187350et_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J_J,type,
    set_Pr3013394129895136920_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J,type,
    fun_Pr2620521676128474833_nat_o: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
    produc6671579610312156647_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_Mt__Num__Onum_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_fu9089537617116752462nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__Set__Oset_I_Eo_J_J_J,type,
    fun_fu4934440599869564003_set_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Num__Onum_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_J,type,
    fun_fu5629128276443140046nteger: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    fun_Pr5651933991979716257it_nat: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J_J,type,
    set_fu3659417381080568633_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_Mt__fun_It__fun_It__Nat__Onat_Mt__Num__Onum_J_M_Eo_J_J,type,
    fun_fu5513256665162130182_num_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__Num__Onum_J_M_Eo_J_J,type,
    fun_fu7909047026757000106_num_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    fun_Pr192538292188806807it_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J_Mt__fun_It__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Rat__Orat_J_J_J_M_Eo_J_J,type,
    fun_fu2931456868620722337_rat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__fun_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J_J,type,
    fun_Pr3688637647703109351atural: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Onatural_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Code____Numeral__Onatural_J_J_J,type,
    fun_Co3643010573817537149atural: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Onatural_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J_J,type,
    fun_Co1105491363547889651atural: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Onatural_Mt__fun_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J_J,type,
    fun_Co1890133979025130057atural: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    produc7249898413471085407e_term: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_Mt__Rat__Orat_J_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__Rat__Orat_J_M_Eo_J_J_J,type,
    fun_fu8216932157852985630_rat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    fun_fu2352890940381120596et_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Code____Numeral__Ointeger_J,type,
    produc1284174907132067113nteger: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Int__Oint_J,type,
    produc8574895079301897479rm_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    fun_Pr1552678306225191715nt_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    fun_Pr8696298990344678139nt_int: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    set_Pr719794911490849221et_nat: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    fun_Co3668495603736800980e_term: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    produc8799533983703829792et_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
    produc2739566037923759970_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    fun_fu6029601804184707687at_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    fun_fu2890809920214373946et_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__Set__Oset_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J_J,type,
    fun_Pr8383423175210966566_nat_o: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J_J_J,type,
    set_Pr5070339090747523585at_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    set_Pr2072254264782222413at_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
    fun_fu8419763957888848259_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J_J_M_Eo_J,type,
    fun_Pr2493370495569891450_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_M_Eo_J,type,
    fun_Pr6861956506527726894_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_Eo_J_J,type,
    fun_Pr5843349257357397163at_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_J_Mt__fun_It__fun_It__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_J_M_Eo_J_J,type,
    fun_fu6544435175084778670_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_J_Mt__fun_It__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_J_M_Eo_J_J,type,
    fun_fu6282320651122755630at_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_J_Mt__fun_It__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_J_M_Eo_J_J,type,
    fun_fu783388071822146350nt_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_J_Mt__fun_It__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_J_M_Eo_J_J,type,
    fun_fu4429252470074529710_int_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    fun_se1551789852802198377at_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J,type,
    fun_fu3373238862511017284_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J_J,type,
    fun_fu5323616038969315652_int_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J_J,type,
    fun_se1934056669979388328_nat_o: $tType ).

tff(ty_n_t__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__fun_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J_J,type,
    fun_he8369595706569872389it_nat: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Code____Numeral__Ointeger_J_Mt__Option__Ooption_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_J,type,
    fun_op3037383146056310525nteger: $tType ).

tff(ty_n_t__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__fun_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J_J,type,
    fun_he2390400765173608009it_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J_J,type,
    fun_fu2847332191311216467_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J_J,type,
    fun_fu3528811849556752711nt_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    fun_fu4800041728187187127nteger: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Int__Oint_J,type,
    produc6693577919049233272rm_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    fun_fu4810317505167811835e_term: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    produc8111630337999740517et_nat: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    fun_in7158797356850311459e_term: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    fun_Co4988957157240174789e_term: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__fun_It__Code____Numeral__Onatural_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    produc7476732711998919211atural: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__fun_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    produc7509114972854644512nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J_Mt__fun_It__fun_It__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J_M_Eo_J_J,type,
    fun_fu9208662316977796352eger_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
    fun_Pr7920380315054183110_nat_o: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J_J,type,
    produc2087150632810049441at_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    produc2714363965264676845at_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    fun_Pr6212429452034653949at_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_J_Mt__fun_It__fun_It__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_J_M_Eo_J_J,type,
    fun_fu7998330801112555204at_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_J_Mt__fun_It__fun_It__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_J_M_Eo_J_J,type,
    fun_fu2720337172504440700nt_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_J_Mt__fun_It__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_J_M_Eo_J_J,type,
    fun_fu3364590669033493516at_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_J_Mt__fun_It__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_J_M_Eo_J_J,type,
    fun_fu7309969077280154820nt_o_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J_Mt__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J_M_Eo_J_J,type,
    fun_Pr5440946310329839626_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J_J,type,
    fun_Pr4146420783962613950_nat_o: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    set_fu8280898353253485872e_term: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_Eo_J,type,
    fun_fu4736795817735658359term_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J_J,type,
    fun_se6502775985981750992_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J_J_J,type,
    fun_fu6384561554008368101_nat_o: $tType ).

tff(ty_n_t__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    fun_he5234484606919320760it_nat: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    fun_in237891044757944084e_term: $tType ).

tff(ty_n_t__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    fun_he1504492240061592256it_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    fun_Pr7406272072912987266atural: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    fun_Pr6624299372562097772it_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    fun_Pr2136124334875798924atural: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Code____Numeral__Onatural_J_J,type,
    fun_Pr4906574453216509900atural: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J,type,
    fun_Pr7769407664385210434atural: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J,type,
    fun_Co5709460363461100952atural: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    produc8903623710181579841nteger: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    fun_Pr7091840695141096449et_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
    set_se4391686895574802075nt_int: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    produc714035400761762599atural: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_J_Mt__fun_It__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_J_M_Eo_J_J,type,
    fun_fu2657526370245387306_int_o: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J_J,type,
    set_fu5828550712561173602_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    fun_fu7448223259553364356at_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    fun_fu1039311746440044420at_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_Mt__fun_It__Code____Numeral__Ointeger_M_Eo_J_J,type,
    fun_fu8559083954280392170eger_o: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_M_Eo_J_J,type,
    fun_Co2466309612238040426eger_o: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_Mt__fun_It__Option__Ooption_It__Num__Onum_J_M_Eo_J_J,type,
    fun_op6018817604785332104_num_o: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Num__Onum_J_Mt__fun_It__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_M_Eo_J_J,type,
    fun_op298641349230941576_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_Mt__Rat__Orat_J_Mt__fun_It__Int__Oint_Mt__Rat__Orat_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__Rat__Orat_J_M_Eo_J_J_J,type,
    fun_fu2427765959047162121_rat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    fun_Pr285225112257423215e_term: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    fun_Pr5098669352780829690e_term: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_Mt__fun_It__Option__Ooption_It__Num__Onum_J_M_Eo_J_J,type,
    fun_op3129816456743790912_num_o: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Num__Onum_J_Mt__fun_It__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_M_Eo_J_J,type,
    fun_op261120641589640376_nat_o: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    set_fu5653557704672872225e_term: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_Eo_J,type,
    fun_fu6378075912484669126term_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    fun_fu6741006549690681129nt_int: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J_M_Eo_J_J_J,type,
    fun_se7979130632333208764_nat_o: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J_J_J,type,
    fun_na7109657165716327514_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_J,type,
    fun_Pr6721000092112975824et_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    produc6576344331059438605e_term: $tType ).

tff(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    option6186025235080601855nt_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    fun_fu9079770784915425324et_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Set__Oset_It__Int__Oint_J_J_J,type,
    fun_fu4266222366127506568et_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Option__Ooption_It__Product____Type__Ounit_J_J,type,
    fun_Pr5508761798988831599t_unit: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Nat__Onat_J_J,type,
    set_Pr552903133987017116at_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    set_Pr1625285437083415874at_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    set_Pr4166680992137330533nt_int: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J_J,type,
    set_Pr4417106977106297437e_term: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J_Mt__fun_It__fun_It__fun_It__Int__Oint_Mt__Nat__Onat_J_Mt__fun_It__Int__Oint_Mt__Num__Onum_J_J_M_Eo_J_J,type,
    fun_fu7828939442023433772_num_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_Mt__Nat__Onat_J_Mt__fun_It__Int__Oint_Mt__Num__Onum_J_J_Mt__fun_It__fun_It__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J_M_Eo_J_J,type,
    fun_fu867726335913497644eger_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J,type,
    fun_Pr1196100989263358594_int_o: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Onatural_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J,type,
    fun_Co1851440197950133416atural: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    fun_Co1561183069634336733nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_J_Mt__fun_It__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_J_M_Eo_J_J,type,
    fun_fu3188400912490975470at_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_J_Mt__fun_It__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_J_M_Eo_J_J,type,
    fun_fu6738731901453605870nt_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_Mt__fun_It__Num__Onum_M_Eo_J_J,type,
    fun_fu7485687605903516013_num_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J_J_J,type,
    fun_fu1617828088232643505_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J,type,
    fun_Pr1970694993525554974t_unit: $tType ).

tff(ty_n_t__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    fun_he4944555133437423336it_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Set__Oset_I_Eo_J_J_J,type,
    fun_fu4618385802829667198_set_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J,type,
    fun_Pr3456093102767711692t_unit: $tType ).

tff(ty_n_t__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    fun_he281446669002384250it_nat: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J_J,type,
    set_fu804515216739278420_int_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_Mt__Nat__Onat_J,type,
    fun_Pr8519750050727906972at_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__fun_It__Nat__Onat_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    fun_fu7433494735876822851at_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    fun_Pr7763680713840462443e_term: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    set_Pr1604112560894399303at_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    set_Pr5052581263052047815nteger: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    produc3911288613690379145it_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_M_Eo_J,type,
    fun_Pr7663348063272484276_nat_o: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    produc2867611627572283311it_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Option__Ooption_It__Num__Onum_J_J,type,
    fun_Pr6553355248451873380on_num: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
    fun_fu3898734532474705027nt_int: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_J_J,type,
    fun_se2918291395271296516_nat_o: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J_J_J,type,
    fun_na7330042712434367748_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    fun_fu5631754973857388633nt_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    fun_Pr6171258863536582648it_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    fun_Pr7425815736541306438et_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    set_Pr633603713510679705it_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    fun_Pr6764980218223570944et_nat: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    fun_na5670658592214072528at_nat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J_J,type,
    fun_se8417120708266284045_nat_o: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    produc4788131091073775919nt_int: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    produc5464280974217902119e_term: $tType ).

tff(ty_n_t__Set__Oset_It__Option__Ooption_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    set_op989438649584373901at_nat: $tType ).

tff(ty_n_t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    option1583680563626158861at_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
    fun_fu353361380671289177nt_int: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_J_J,type,
    fun_fu2354122332637403079_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_M_Eo_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_J_J,type,
    fun_fu8897902691871853255_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
    fun_fu4482892469221626457nt_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_Mt__Num__Onum_J,type,
    fun_fu8347129338434488602er_num: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Ounit_J,type,
    fun_Pr8319229360018371625t_unit: $tType ).

tff(ty_n_t__fun_It__Num__Onum_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    fun_nu1379135015814352922nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    fun_fu3472058528428720115nt_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Set__Oset_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J_J,type,
    fun_Pr9081111800474865985e_term: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    set_Pr8551490117392284871at_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    fun_fu2978539155105838238_int_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_Eo_J_J,type,
    fun_Pr7145817153658775868term_o: $tType ).

tff(ty_n_t__Option__Ooption_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    option5210736251575913683nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J_J_J_J,type,
    fun_fu2677729659939697685_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J_J,type,
    fun_Pr7459525001844076368t_unit: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    set_Pr6777250647868329861it_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_M_Eo_J,type,
    fun_Pr914940982395022178_nat_o: $tType ).

tff(ty_n_t__fun_It__Heap__Oarray_Itf__a_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J_J,type,
    fun_ar121531768175530460t_unit: $tType ).

tff(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    set_se5479201105039950375at_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    produc7299876168958306407at_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    produc6756470014200349799atural: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    produc3334582477557816039nteger: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J_J,type,
    set_fu1867049230074397546_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Code____Numeral__Ointeger_M_Eo_J_J_J,type,
    fun_fu4083202260958266008eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_fu7390737412436561923nteger: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Num__Onum_J_J,type,
    fun_Pr1661544312997278575on_num: $tType ).

tff(ty_n_t__fun_It__Num__Onum_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    fun_nu8356290101743979119it_nat: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    fun_na5667031169817407269it_nat: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    fun_in8543325783774419841it_nat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__fun_It__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J_J,type,
    fun_se7001366092147120942_nat_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J_J_J,type,
    fun_se218054151627931304_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Num__Onum_J_J,type,
    fun_Pr2994431579521131585on_num: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_M_Eo_J_J,type,
    fun_Pr3592279944642289454ural_o: $tType ).

tff(ty_n_t__fun_It__Num__Onum_Mt__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    fun_nu5903705430729240393it_nat: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    fun_na4198017608689007891it_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_J,type,
    fun_fu6201336427292363868nteger: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J_J,type,
    set_fu2713250876831336446atural: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    produc3839731585411834681it_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J_M_Eo_J,type,
    fun_fu257250443624047805ural_o: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    fun_na1945018436707187408at_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Nat__Onat_J,type,
    fun_Pr1253225528153422666at_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Int__Oint_J,type,
    fun_Pr6298746545499001766at_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_fu2392828822626117773nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J_J,type,
    fun_fu5844746416483971737nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_Mt__Nat__Onat_J_Mt__fun_It__Int__Oint_Mt__Num__Onum_J_J_Mt__fun_It__fun_It__fun_It__Int__Oint_Mt__Nat__Onat_J_Mt__fun_It__Int__Oint_Mt__Num__Onum_J_J_M_Eo_J_J,type,
    fun_fu2275682760404419928_num_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J_J,type,
    fun_fu1677024581061081874_int_o: $tType ).

tff(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    option8699557107911914541at_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    set_op239864471688321678it_nat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J_J,type,
    fun_se5991283330978499451_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Ounit_J,type,
    fun_Pr7475791014719349342t_unit: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_M_Eo_J,type,
    fun_op479301348043730329_nat_o: $tType ).

tff(ty_n_t__fun_I_Eo_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    fun_o_7229649064035662211it_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    set_op3940070208846178154it_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc4166570645942440679at_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_J_J,type,
    fun_fu2253997797533952707_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_J_J,type,
    fun_fu8028891822603792907_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_J_J,type,
    fun_fu7618250142905304443_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_J_J,type,
    fun_fu4169772131120368835_int_o: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_M_Eo_J,type,
    fun_op4751157287140997969_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_Mt__Heap__Oarray_Itf__a_J_J,type,
    fun_Pr8833188457053967342rray_a: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    fun_fu4228150600790569371at_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J_J_J,type,
    fun_fu484727072080742171_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Rat__Orat_J_J_M_Eo_J_J,type,
    fun_fu1057420046263839031_rat_o: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Code____Numeral__Ointeger_J,type,
    produc3954786194548828667nteger: $tType ).

tff(ty_n_t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    produc2900562427881843919it_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    fun_Pr2477239776880934807at_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    fun_Pr1308109350235310159nt_int: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    set_Pr4329608150637261639at_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc9217583074051984497at_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J,type,
    fun_Pr3059359313727237556_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Assertions__Oassn_J_Mt__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Assertions__Oassn_J_Mt__fun_It__Code____Numeral__Ointeger_M_Eo_J_J_J,type,
    fun_fu4735791719682850818eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__List__Olist_It__Nat__Onat_J_Mt__fun_It__List__Olist_It__Nat__Onat_J_M_Eo_J_J_Mt__fun_It__List__Olist_It__Nat__Onat_J_Mt__fun_It__List__Olist_It__Nat__Onat_J_M_Eo_J_J_J,type,
    fun_fu4946532526548972611_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_Mt__Code____Numeral__Onatural_J,type,
    fun_Pr5131589689703537955atural: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    fun_Pr74676805955934211atural: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_Pr5876161306168176259nteger: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J,type,
    fun_Co4337079049361313443atural: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J_J,type,
    set_fu3555100300013713409atural: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J_J,type,
    set_fu2445755650934904413atural: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    fun_fu4638078822479986034_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__fun_It__Rat__Orat_Mt__Rat__Orat_J_M_Eo_J_J,type,
    fun_fu4306744791715064858_rat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J_M_Eo_J,type,
    fun_fu9211935013670480870ural_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J_J,type,
    fun_fu6699046866436802030_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J_M_Eo_J,type,
    fun_fu660488089777143946ural_o: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J_J,type,
    set_fu5472951507345886094_nat_o: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Code____Numeral__Ointeger_J,type,
    produc2752406535750279421nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    fun_fu7530206860547196985at_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_J_J_J,type,
    fun_fu8284676920001830735nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_J_J_J,type,
    fun_fu1188671613149117355nteger: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J,type,
    fun_Pr2548841491397842206atural: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J_J_J_J,type,
    fun_se3165749655728557022_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__Assertions__Oassn_J_Mt__fun_It__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J_Mt__Assertions__Oassn_J_J,type,
    fun_fu4821026654811345315r_assn: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_J_J,type,
    fun_fu6327154928193479288nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Rat__Orat_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Rat__Orat_J_J_J_J,type,
    fun_fu4582018930532246947nt_rat: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
    fun_fu3518228427392506443nt_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Rat__Orat_J_Mt__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Rat__Orat_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__Rat__Orat_J_J_J,type,
    fun_fu8767785434844327952er_rat: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_Mt__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_J_J,type,
    fun_fu2498091903632033272er_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_Mt__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_J_J,type,
    fun_fu1007793439646807308er_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_Mt__Num__Onum_J,type,
    fun_Pr1075626608990047775at_num: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J,type,
    fun_Pr367382672041210069at_nat: $tType ).

tff(ty_n_t__fun_It__Num__Onum_Mt__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    fun_nu5234077238548837151it_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_Mt__Num__Onum_J,type,
    fun_Pr1223581030874358257at_num: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J,type,
    fun_Pr515337093925520551at_nat: $tType ).

tff(ty_n_t__fun_It__Num__Onum_Mt__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    fun_nu2241728722996109699it_nat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J_J,type,
    fun_se7776568131818451942at_nat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Int__Oint_J_J,type,
    fun_se5286484986886725186at_int: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    fun_na8167864584424996432at_nat: $tType ).

tff(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    option8956607266484857688it_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J_J,type,
    fun_fu7344996400627858478_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_M_Eo_J_J,type,
    fun_fu4899062771603708206at_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_M_Eo_J_J_Mt__fun_It__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_M_Eo_J_J_M_Eo_J_J,type,
    fun_fu7590976836756945966nt_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J_J,type,
    fun_fu8074799898941972270_int_o: $tType ).

tff(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    option3216581401566546698it_nat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    fun_se5244420045238757833at_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    fun_fu717549361983437348nt_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
    fun_fu918106826131887214nt_int: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    produc5111566536631596683et_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    produc8299537390109905600et_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__Product____Type__Ounit_J_J,type,
    fun_Pr2049426570021530256t_unit: $tType ).

tff(ty_n_t__fun_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    fun_mu2328110650637990531at_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Int__Oint_J,type,
    produc217860453747927114_o_int: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc3843707927480180839at_nat: $tType ).

tff(ty_n_t__fun_It__Heap__Oarray_Itf__a_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__Heap__Oarray_Itf__a_J_J_J,type,
    fun_ar6017029185804945652rray_a: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    set_Pr1354866905816374718it_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Rat__Orat_J_Mt__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Rat__Orat_J_Mt__fun_It__Code____Numeral__Ointeger_M_Eo_J_J_J,type,
    fun_fu7141499545569947298eger_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_M_Eo_J,type,
    fun_Pr8032424337255632745_nat_o: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Onatural_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
    fun_Co2051191115980488992_nat_o: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
    fun_Co9016714620104711083_nat_o: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    set_Pr457366540195662369at_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    set_Pr5142436192348053284it_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Rat__Orat_J_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Rat__Orat_J_J,type,
    fun_fu3997796857297124035at_rat: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J,type,
    fun_fu3064074204415222357nt_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__Rat__Orat_Mt__Rat__Orat_J_J,type,
    fun_fu1098312133097393581at_rat: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    fun_fu3661779633992098115nt_int: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    fun_se953073389798102371at_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    fun_Pr557098546508347797at_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_M_Eo_J,type,
    fun_Pr7068637894315934487_nat_o: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    fun_na1668100129766719005at_nat: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J,type,
    fun_na2094359461478415435atural: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J,type,
    fun_in4857920871562217639atural: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J,type,
    fun_se5639961202347202350_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J,type,
    fun_Pr2419607445322970330t_unit: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Int__Oint_J,type,
    produc1164942017926883148rm_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_Mt__fun_It__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_M_Eo_J_J,type,
    fun_fu9045186299510176150at_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_J_J_J,type,
    fun_fu1723132215250845724er_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Int__Oint_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_J_J_J,type,
    fun_fu1491972344133157660er_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_J_J_J,type,
    fun_fu1895414074638732388er_int: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Code____Numeral__Ointeger_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    fun_Co2470855966376689427nteger: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Onatural_Mt__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    fun_Co298994598804093668e_term: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    fun_Co1966082167426949785e_term: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Num__Onum_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    fun_Pr8866567302531502864at_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Set__Oset_It__Int__Oint_J_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_fu2310701194077331499nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__Rat__Orat_J_Mt__fun_It__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J_Mt__Rat__Orat_J_J,type,
    fun_fu6017686703198564611er_rat: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_fu4961913266064405537nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Assertions__Oassn_J_Mt__fun_It__Assertions__Oassn_Mt__fun_It__Code____Numeral__Ointeger_Mt__Assertions__Oassn_J_J_J,type,
    fun_fu717556231145110950r_assn: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
    fun_fu4788845708739168348eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_J_J,type,
    fun_fu6802859072977114247_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_J_J,type,
    fun_fu14259429304446855_int_o: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J,type,
    set_Pr2352657477744078772atural: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__Nat__Onat_J_J,type,
    fun_Pr3587966566883452857at_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_M_Eo_J,type,
    fun_Pr513970351136536563ural_o: $tType ).

tff(ty_n_t__fun_It__Heap__Oarray_Itf__a_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__Nat__Onat_J_J,type,
    fun_ar8857663332695973421at_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_M_Eo_J_J,type,
    fun_fu7456240966027273028at_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__fun_It__Nat__Onat_M_Eo_J_M_Eo_J_J_J,type,
    fun_fu4957514873648614724at_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J_Mt__fun_It__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J_M_Eo_J_J,type,
    fun_fu6215369687776649212nt_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_M_Eo_J_J,type,
    fun_fu5378497120668327052at_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J_Mt__fun_It__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J_M_Eo_J_J,type,
    fun_fu4137625842417703236nt_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J_Mt__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__fun_It__Int__Oint_M_Eo_J_M_Eo_J_J_J,type,
    fun_fu7129310890971069252nt_o_o: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Int__Oint_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    produc8065447618272157327et_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Ounit_Mt__Assertions__Oassn_J_Mt__fun_It__Assertions__Oassn_Mt__fun_It__Product____Type__Ounit_Mt__Assertions__Oassn_J_J_J,type,
    fun_fu7405491065986884212t_assn: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    set_Pr8693737435421807431at_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    set_Pr2560585780119916871nt_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_Mt__fun_It__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_Mt__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_J_J,type,
    fun_fu3959123160307459545t_assn: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J,type,
    fun_Pr363642936170290612_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    fun_Pr3337834798857116037et_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__Set__Oset_It__Int__Oint_J_J,type,
    fun_Pr847751653925389281et_int: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    fun_Co4803750647967840348et_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    produc8664842809031399944it_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    fun_fu8532066432991188095_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__fun_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Int__Oint_M_Eo_J_J_J,type,
    fun_fu63825462011493995_int_o: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
    fun_in1927439276604979228_nat_o: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc732395585841259969at_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    produc6714399278180371524it_nat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    fun_se320340636488258563at_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    fun_Pr5733170697710890607et_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_Pr5056853159479207325nteger: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    fun_Pr5596209257725365771nt_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    fun_fu381918921314004384at_nat: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J_M_Eo_J_J,type,
    fun_na8508211072120413978_nat_o: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J_J,type,
    set_Pr1932065953672099015od_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J,type,
    fun_fu3275390434952296369_nat_o: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Nat__Onat_J_Mt__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    fun_op386870758422531628et_nat: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Code____Numeral__Ointeger_J_Mt__Option__Ooption_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    fun_op8756596739451609009nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_J,type,
    fun_fu5660447535128473811at_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    fun_fu7012516915885544207at_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J_J_J_J,type,
    fun_fu2668056085831081835nt_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Int__Oint_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_J_J_J,type,
    fun_fu3125320701163054607at_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Int__Oint_J_J,type,
    fun_fu5207212825597307859nt_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_J_J_J,type,
    fun_fu4152238915952267095at_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__fun_It__List__Olist_It__Nat__Onat_J_M_Eo_J_J_Mt__fun_It__Nat__Onat_Mt__fun_It__List__Olist_It__Nat__Onat_J_M_Eo_J_J_J,type,
    fun_fu6714502955005156803_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__List__Olist_It__Nat__Onat_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__List__Olist_It__Nat__Onat_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    fun_fu4568065243339218371_nat_o: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    fun_in94812177438132456e_term: $tType ).

tff(ty_n_t__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__fun_It__Nat__Onat_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J_J,type,
    fun_he6845747896722556172t_unit: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Onatural_Mt__Option__Ooption_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J,type,
    fun_Co7921331830460615208atural: $tType ).

tff(ty_n_t__fun_It__fun_It__Set__Oset_It__Int__Oint_J_Mt__Assertions__Oassn_J_Mt__fun_It__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_Mt__Assertions__Oassn_J_J,type,
    fun_fu7925354201654153025t_assn: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_fu1763652423599918571nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Assertions__Oassn_J_Mt__fun_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__Assertions__Oassn_J_J,type,
    fun_fu727159081937814839r_assn: $tType ).

tff(ty_n_t__fun_It__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
    fun_fu1832432239164473695eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J_J,type,
    fun_fu6471771360118961870_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
    fun_fu6011537917091710943eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__fun_It__Assertions__Oassn_Mt__Assertions__Oassn_J_M_Eo_J_J,type,
    fun_fu8741070064424208326assn_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Assertions__Oassn_Mt__Assertions__Oassn_J_Mt__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
    fun_fu2770652263662631110eger_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__Set__Oset_I_Eo_J_J,type,
    fun_Pr5633121574208248783_set_o: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
    set_fu3555266933746557007_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Set__Oset_I_Eo_J_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Set__Oset_It__Set__Oset_I_Eo_J_J_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_fu1045876692016343459nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J,type,
    fun_fu1413608398870722896at_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_Eo_J,type,
    fun_fu5135969500543783852at_o_o: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    fun_na8713714802964096592at_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Code____Numeral__Onatural_J,type,
    produc3981471736659609608atural: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    produc5835291356934675326atural: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    produc3346328345660746739nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__List__Olist_It__Nat__Onat_J_M_Eo_J_Mt__fun_It__List__Olist_It__Nat__Onat_J_Mt__fun_It__List__Olist_It__Nat__Onat_J_M_Eo_J_J_J,type,
    fun_fu9062970525541950460_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    fun_Pr7804344347641417161at_nat: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Product____Type__Ounit_J_Mt__fun_It__Product____Type__Ounit_Mt__Option__Ooption_It__Product____Type__Ounit_J_J_J,type,
    fun_op5903753652030861359t_unit: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Onatural_Mt__Set__Oset_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J,type,
    fun_Co2944084857415636034atural: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__Rat__Orat_J_M_Eo_J_J,type,
    fun_fu7677565902479959693_rat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__fun_It__Code____Numeral__Onatural_M_Eo_J_J,type,
    fun_Pr3928691295121555099ural_o: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Onatural_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_M_Eo_J_J,type,
    fun_Co9066792663755620495ural_o: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Onatural_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    fun_Co6386927884524458043e_term: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Code____Numeral__Ointeger_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_J_J,type,
    fun_Co3544761417380347684eger_o: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    fun_Co3460408610320954864e_term: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    set_fu3629540756087427317e_term: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_Eo_J,type,
    fun_fu3265955482920998386term_o: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    produc859450856879609959at_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    produc1219242969750017639nt_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Rat__Orat_J_Mt__fun_It__Rat__Orat_Mt__fun_It__Code____Numeral__Ointeger_Mt__Rat__Orat_J_J_J,type,
    fun_fu3744699754670041014er_rat: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    fun_in4666789911842550827et_nat: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    set_fu2374436075715859015nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_M_Eo_J,type,
    fun_fu4285281161728579104eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_Mt__fun_It__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    fun_fu3109912920687205353_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Assertions__Oassn_J_Mt__fun_It__fun_It__Int__Oint_Mt__Assertions__Oassn_J_Mt__fun_It__Int__Oint_M_Eo_J_J_J,type,
    fun_fu607692679349591509_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Set__Oset_It__Code____Numeral__Ointeger_J_J_Mt__fun_It__Code____Numeral__Ointeger_M_Eo_J_J,type,
    fun_fu5766609707292941056eger_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    fun_Pr1469247711798767971at_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_Pr5243970527273625488nteger: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_Pr2029408141414424556nteger: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_J,type,
    fun_Pr2600655309230267920er_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_J,type,
    fun_Pr110572164298541164er_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_J,type,
    fun_Pr3118124138693225744er_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    fun_Pr5398690294390750379at_nat: $tType ).

tff(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    option936205604648967762et_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J,type,
    fun_fu8391177546919232046_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J,type,
    fun_fu7503566767892366382_int_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J_Mt__fun_It__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J_M_Eo_J_J,type,
    fun_Pr4799464687642144302_num_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J,type,
    fun_Pr2028404973800837934_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    fun_Pr9018117161326028078_int_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__Product____Type__Ounit_J,type,
    fun_Pr9045474026565384218t_unit: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    produc2934264451710624999od_o_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__Heap__Oarray_Itf__a_J_J,type,
    fun_Pr8777304358194983264rray_a: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    fun_na5644505769342238765nteger: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__Set__Oset_It__Code____Numeral__Ointeger_J_J_J,type,
    set_Pr7577011563204128103nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Ounit_Mt__Rat__Orat_J_Mt__fun_It__Rat__Orat_Mt__fun_It__Product____Type__Ounit_Mt__Rat__Orat_J_J_J,type,
    fun_fu1171974497074579908it_rat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    fun_se4014881416909572940_nat_o: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    fun_na3424944204176166544_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J,type,
    fun_fu6778223257468740055_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Set__Oset_It__Int__Oint_J_Mt__Rat__Orat_J_Mt__fun_It__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_Mt__Rat__Orat_J_J,type,
    fun_fu8704076394632857761nt_rat: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    fun_fu1217771548038759377at_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Rat__Orat_J_Mt__fun_It__fun_It__Nat__Onat_Mt__Rat__Orat_J_Mt__fun_It__Nat__Onat_Mt__Rat__Orat_J_J_J,type,
    fun_fu6579618355643354601at_rat: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Num__Onum_J_Mt__fun_It__fun_It__Int__Oint_Mt__Nat__Onat_J_Mt__fun_It__Int__Oint_Mt__Num__Onum_J_J_J,type,
    fun_fu3670889464739865373nt_num: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__fun_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    fun_fu5935951186182374353at_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Int__Oint_J_Mt__fun_It__fun_It__Nat__Onat_Mt__Int__Oint_J_Mt__fun_It__Nat__Onat_Mt__Int__Oint_J_J_J,type,
    fun_fu960360787657196261at_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_Mt__fun_It__Assertions__Oassn_Mt__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_J_J,type,
    fun_fu1995072252941043084t_assn: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    fun_fu6092417073193843705nt_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Rat__Orat_J_Mt__fun_It__fun_It__Int__Oint_Mt__Rat__Orat_J_Mt__fun_It__Int__Oint_Mt__Rat__Orat_J_J_J,type,
    fun_fu1617438229336688381nt_rat: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Nat__Onat_J_Mt__fun_It__fun_It__Int__Oint_Mt__Nat__Onat_J_Mt__fun_It__Int__Oint_Mt__Nat__Onat_J_J_J,type,
    fun_fu973771059875708133nt_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Set__Oset_It__Int__Oint_J_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_fu7510501037550790335nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Assertions__Oassn_J_Mt__fun_It__Assertions__Oassn_Mt__fun_It__Int__Oint_Mt__Assertions__Oassn_J_J_J,type,
    fun_fu4482299812767249988t_assn: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Rat__Orat_J_Mt__fun_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__Rat__Orat_J_J,type,
    fun_fu8198789307943805079er_rat: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Num__Onum_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_fu1714096010366225192nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_fu2219603532186391848nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Assertions__Oassn_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__Assertions__Oassn_J_J,type,
    fun_fu5082522747898945281r_assn: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    set_Pr3948176798113811640et_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Rat__Orat_Mt__Rat__Orat_J_Mt__fun_It__fun_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_M_Eo_J_J,type,
    fun_fu2627094579170320592ural_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Rat__Orat_Mt__Rat__Orat_J_Mt__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
    fun_fu841611025618976102eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
    fun_fu3131294797999541474eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Num__Onum_J_Mt__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
    fun_fu5877413357861189036eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__fun_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_M_Eo_J_J,type,
    fun_fu2034268335391280352ural_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
    fun_fu248784781839935862eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
    fun_fu6536794386266229110eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__fun_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_M_Eo_J_J,type,
    fun_fu2512357375982829608ural_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
    fun_fu726873822431485118eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__fun_It__Rat__Orat_Mt__Rat__Orat_J_M_Eo_J_J,type,
    fun_fu1378022486368508006_rat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__fun_It__Nat__Onat_Mt__Num__Onum_J_M_Eo_J_J,type,
    fun_fu5250823318952805804_num_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__fun_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J,type,
    fun_fu4924233495492459638_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__fun_It__Int__Oint_Mt__Nat__Onat_J_M_Eo_J_J,type,
    fun_fu7320023857087329562_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    fun_fu7391974349310290878_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Assertions__Oassn_Mt__Assertions__Oassn_J_Mt__fun_It__fun_It__Assertions__Oassn_Mt__Assertions__Oassn_J_M_Eo_J_J,type,
    fun_fu829217510089154608assn_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
    fun_Pr6460944699146269935_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Set__Oset_I_Eo_J_Mt__Assertions__Oassn_J_Mt__fun_It__Set__Oset_It__Set__Oset_I_Eo_J_J_Mt__Assertions__Oassn_J_J,type,
    fun_fu3743863873453506915o_assn: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Int__Oint_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    produc6162884466328367972nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_M_Eo_J_J,type,
    fun_fu1853282479105234414at_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_M_Eo_J_J,type,
    fun_fu3604077110225719534nt_o_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J_M_Eo_J,type,
    fun_Pr1057819736042215569_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J,type,
    fun_Pr8338385031646565611_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Num__Onum_Mt__Option__Ooption_It__Num__Onum_J_J_Mt__fun_It__Num__Onum_Mt__Option__Ooption_It__Num__Onum_J_J_J,type,
    fun_fu2987389051837124479on_num: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__fun_I_Eo_Mt__Code____Numeral__Ointeger_J_Mt__fun_I_Eo_M_Eo_J_J_J,type,
    fun_fu8716660765737269145un_o_o: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Assertions__Oassn_J_Mt__fun_It__Assertions__Oassn_Mt__Option__Ooption_It__Assertions__Oassn_J_J_J,type,
    fun_op4146996366486250514n_assn: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Rat__Orat_J_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    fun_fu4522195968571808382nt_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__Int__Oint_Mt__Rat__Orat_J_J,type,
    fun_fu7460908759652350970nt_rat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    fun_Pr6405077315951356852et_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Set__Oset_It__Int__Oint_J_J,type,
    fun_Pr3914994171019630096et_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Code____Numeral__Ointeger_J,type,
    fun_Pr6596356882939945227nteger: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    fun_na4143055713577223196at_nat: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
    fun_in2204242111582549184nt_int: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_Co6597186368970283863nteger: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    set_fu4273546686648440324nteger: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    set_fu2873095257816804008nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_M_Eo_J,type,
    fun_fu5503004773767123511eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__List__Olist_It__Nat__Onat_J_M_Eo_J_Mt__fun_It__Nat__Onat_Mt__fun_It__List__Olist_It__Nat__Onat_J_M_Eo_J_J_J,type,
    fun_fu2721382957917623308_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_M_Eo_J,type,
    fun_fu7325869825756301971eger_o: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    fun_in5730379987311621695e_term: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_J_J,type,
    set_fu1437006448190940916_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_Mt__fun_It__fun_It__Int__Oint_M_Eo_J_M_Eo_J_J,type,
    fun_fu9090758901314268781nt_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    fun_fu5650529485467354185_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_J_M_Eo_J,type,
    fun_fu6749285349733798471at_o_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Nat__Onat_J_Mt__fun_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    fun_se8125625266612218818et_nat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Nat__Onat_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__Set__Oset_It__Code____Numeral__Ointeger_J_J_J,type,
    fun_se3841591170510310256nteger: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    fun_Pr3616673511947161127atural: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_Pr864343514034809617nteger: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    fun_Pr8136591464420530493_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__Nat__Onat_J,type,
    fun_Pr4343998633453697049at_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Rat__Orat_J_Mt__fun_It__fun_It__Nat__Onat_Mt__Rat__Orat_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    fun_fu1806770557662746761_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__fun_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    fun_fu6075382464776002713_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_M_Eo_J_J,type,
    fun_fu4239617643652599019assn_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_Mt__fun_It__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
    fun_fu5719784276005855083eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Rat__Orat_J_Mt__fun_It__fun_It__Int__Oint_Mt__Rat__Orat_J_Mt__fun_It__Int__Oint_M_Eo_J_J_J,type,
    fun_fu7714913403879666293_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Code____Numeral__Ointeger_M_Eo_J_J,type,
    fun_fu855086506144988854eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_M_Eo_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_fu2729256655946442782nteger: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    fun_Pr2118491707810114563at_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_J,type,
    fun_Pr8851780599733163615at_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J_J,type,
    fun_Pr4305413282503136351nt_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    fun_Pr1815330137571409595nt_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_J,type,
    fun_Pr7754697619089165059at_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    fun_Pr2478283820680522243nt_int: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    fun_na1790740735814032627at_nat: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_J_J,type,
    fun_na3504973565017656480nteger: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_J_J,type,
    fun_na5353050896416397052nteger: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_J_J,type,
    fun_na2743204842065625888er_nat: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_J_J,type,
    fun_na7153028460132482940er_int: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_J_J,type,
    fun_na937208397672391712er_int: $tType ).

tff(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J,type,
    set_se3372686590935047281atural: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__Set__Oset_It__Code____Numeral__Ointeger_J_J,type,
    produc6491284506569428743nteger: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    fun_Pr3455331679158536364_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Set__Oset_I_Eo_J_J,type,
    fun_Pr1817902730575146976_set_o: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J_J,type,
    fun_na5914473681949881652_nat_o: $tType ).

tff(ty_n_t__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__fun_It__Nat__Onat_Mt__Product____Type__Ounit_J_J,type,
    fun_he8708342781048922188t_unit: $tType ).

tff(ty_n_t__fun_It__Set__Oset_I_Eo_J_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Set__Oset_I_Eo_J_J_J,type,
    fun_se7283963663803345157_set_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_J,type,
    fun_Pr2088208266900590058et_nat: $tType ).

tff(ty_n_t__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__fun_It__Nat__Onat_Mt__Heap__Oarray_Itf__a_J_J_J,type,
    fun_he4035479571739904452rray_a: $tType ).

tff(ty_n_t__fun_It__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_fu552866168194876645nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    fun_fu6924846375782198887atural: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_fu2499394402704830801nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_fu8508204053700405677nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_fu6921880696561781257nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_fu3628599891403802633nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Assertions__Oassn_J_Mt__fun_It__Set__Oset_It__Int__Oint_J_Mt__Assertions__Oassn_J_J,type,
    fun_fu6757290529232567765t_assn: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Rat__Orat_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__Rat__Orat_J_J,type,
    fun_fu722387130092441185er_rat: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Num__Onum_J_Mt__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_fu9168018664657815141nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_J,type,
    fun_fu7724909810345500241er_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_J,type,
    fun_fu2894000772521619117er_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_J,type,
    fun_fu403917627589892361er_int: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_J_J,type,
    fun_na8856381646659805649nteger: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Onatural_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Code____Numeral__Onatural_J_J_J,type,
    fun_Co200561849269645671atural: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_J_J,type,
    fun_Co5080488584548667985nteger: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    produc3658429121746597890et_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Num__Onum_Mt__Int__Oint_J_Mt__fun_It__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
    fun_fu6196024946523381971eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__fun_It__Int__Oint_Mt__Num__Onum_J_M_Eo_J_J,type,
    fun_fu9167764846409469779_num_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__fun_It__Int__Oint_Mt__Nat__Onat_J_M_Eo_J_J,type,
    fun_fu8841175022949123613_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__fun_It__Nat__Onat_Mt__Rat__Orat_J_M_Eo_J_J,type,
    fun_fu5056201337121744443_rat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__fun_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J,type,
    fun_fu3689012285533931075_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__fun_It__Nat__Onat_Mt__Int__Oint_J_M_Eo_J_J,type,
    fun_fu3760962777756892391_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_Mt__fun_It__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_M_Eo_J_J,type,
    fun_fu6461175078876253408assn_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Num__Onum_J_Mt__fun_It__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
    fun_fu914036251014348755eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Nat__Onat_J_Mt__fun_It__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
    fun_fu5133016914843556765eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Assertions__Oassn_J_Mt__fun_It__Code____Numeral__Ointeger_M_Eo_J_J,type,
    fun_fu4844139638962010283eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_M_Eo_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__Assertions__Oassn_J_J,type,
    fun_fu1898041513128675305r_assn: $tType ).

tff(ty_n_t__fun_It__fun_It__Assertions__Oassn_Mt__Assertions__Oassn_J_Mt__fun_It__fun_It__Rat__Orat_Mt__Rat__Orat_J_M_Eo_J_J,type,
    fun_fu2448905236868045008_rat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Assertions__Oassn_Mt__Assertions__Oassn_J_Mt__fun_It__fun_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J,type,
    fun_fu5995116245991996640_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Assertions__Oassn_Mt__Assertions__Oassn_J_Mt__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    fun_fu8462857099809827880_int_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__fun_It__Set__Oset_It__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
    fun_se5529282185252607396eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Set__Oset_I_Eo_J_Mt__Rat__Orat_J_Mt__fun_It__Set__Oset_It__Set__Oset_I_Eo_J_J_Mt__Rat__Orat_J_J,type,
    fun_fu6849062756650152291_o_rat: $tType ).

tff(ty_n_t__fun_It__fun_It__Set__Oset_I_Eo_J_Mt__Nat__Onat_J_Mt__fun_It__Set__Oset_It__Set__Oset_I_Eo_J_J_Mt__Nat__Onat_J_J,type,
    fun_fu1060865441899640675_o_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    fun_fu6436183194761443139_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    fun_fu927436805355353155_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_J,type,
    fun_fu138107234227827011_int_o: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Set__Oset_I_Eo_J_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_fu6303754889700780451nteger: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_Mt__Assertions__Oassn_J_Mt__fun_It__Assertions__Oassn_Mt__fun_I_Eo_Mt__Assertions__Oassn_J_J_J,type,
    fun_fu1324339541976909620o_assn: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Option__Ooption_It__Product____Type__Ounit_J_J,type,
    fun_Pr648072847990616533t_unit: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Num__Onum_J_J,type,
    set_Pr7477759153910077568at_num: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_J,type,
    set_Pr2539167527615954998at_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    set_Pr7717912310451564380at_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J,type,
    produc366245978424229472at_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc3313772616054891654at_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    produc5665947927044467078nt_int: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    produc382792921321436433nt_int: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_Mt__Assertions__Oassn_J_Mt__fun_It__fun_I_Eo_Mt__Assertions__Oassn_J_Mt__fun_I_Eo_M_Eo_J_J_J,type,
    fun_fu5861359551626625881un_o_o: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Code____Numeral__Ointeger_J_Mt__Option__Ooption_It__Code____Numeral__Ointeger_J_J,type,
    fun_op1637087682669155543nteger: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Int__Oint_J,type,
    fun_se8575562297434572672at_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_Mt__Code____Numeral__Ointeger_J,type,
    fun_Pr4523587930069869694nteger: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_Mt__Code____Numeral__Ointeger_J,type,
    fun_Pr3662307866719382234nteger: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Nat__Onat_J,type,
    fun_Pr2804840792690441492al_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_Mt__Code____Numeral__Ointeger_J,type,
    fun_Pr5940403383236205310nteger: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_Mt__Code____Numeral__Ointeger_J,type,
    fun_Pr2725840997377004378nteger: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    fun_na6574806417004769082atural: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_na3822476419092417572nteger: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    fun_in7496697025202066910atural: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_in4744367027289715400nteger: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    fun_se7755072775241076291_nat_o: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__fun_It__Nat__Onat_M_Eo_J_J_Mt__Option__Ooption_It__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    fun_op3284592519439835779_nat_o: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J,type,
    fun_na4518284863240432007_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    fun_fu7075445697382584196_int_o: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    fun_in7664021439913478804_nat_o: $tType ).

tff(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    option5403585828896915703atural: $tType ).

tff(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    option2651255830984564193nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Rat__Orat_J_Mt__fun_It__Rat__Orat_Mt__fun_It__Nat__Onat_Mt__Rat__Orat_J_J_J,type,
    fun_fu4710970720072501148at_rat: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__List__Olist_It__Nat__Onat_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    fun_fu2312272580554962172_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Rat__Orat_J_Mt__fun_It__Rat__Orat_Mt__fun_It__Int__Oint_Mt__Rat__Orat_J_J_J,type,
    fun_fu114989186063767636nt_rat: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Rat__Orat_J_J_J,type,
    fun_fu5158109473865063676nt_rat: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    fun_fu923337204662071120nt_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Code____Numeral__Ointeger_J,type,
    fun_fu5689865433563736081nteger: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Nat__Onat_J_Mt__fun_It__Nat__Onat_Mt__Set__Oset_It__Code____Numeral__Ointeger_J_J_J,type,
    fun_se2951167709562549603nteger: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Nat__Onat_J_Mt__fun_It__Int__Oint_Mt__Set__Oset_It__Code____Numeral__Ointeger_J_J_J,type,
    fun_se8949688400205348287nteger: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Nat__Onat_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    fun_se8450096479846816355et_nat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Nat__Onat_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__Set__Oset_It__Int__Oint_J_J_J,type,
    fun_se3636548061058897599et_int: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Int__Oint_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__Set__Oset_It__Int__Oint_J_J_J,type,
    fun_se2042144505192658715et_int: $tType ).

tff(ty_n_t__fun_It__Rat__Orat_Mt__fun_It__Rat__Orat_Mt__fun_It__Rat__Orat_Mt__fun_It__Nat__Onat_Mt__Rat__Orat_J_J_J_J,type,
    fun_ra8505079968215247908at_rat: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Onatural_Mt__fun_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    fun_Co6813818151677833714atural: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_Co1981900195452921617nteger: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    set_fu6863465268813640805nt_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J,type,
    fun_fu4509100218321815938_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_Mt__fun_It__fun_It__Nat__Onat_Mt__Rat__Orat_J_M_Eo_J_J,type,
    fun_fu3204908904631799856_rat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_Mt__fun_It__fun_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J,type,
    fun_fu1837719853043986488_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_Mt__fun_It__fun_It__Nat__Onat_Mt__Int__Oint_J_M_Eo_J_J,type,
    fun_fu1909670345266947804_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Rat__Orat_J_Mt__fun_It__Code____Numeral__Ointeger_M_Eo_J_J,type,
    fun_fu4523568072766896123eger_o: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Nat__Onat_J_J_J,type,
    set_Pr3451248702717554689st_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Num__Onum_Mt__Option__Ooption_It__Num__Onum_J_J_Mt__fun_It__Num__Onum_Mt__Num__Onum_J_J,type,
    fun_fu152868422178311599um_num: $tType ).

tff(ty_n_t__fun_It__fun_It__Num__Onum_Mt__Option__Ooption_It__Num__Onum_J_J_Mt__fun_It__Num__Onum_Mt__Int__Oint_J_J,type,
    fun_fu1947565687807238081um_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Num__Onum_Mt__Num__Onum_J_Mt__fun_It__Num__Onum_Mt__Option__Ooption_It__Num__Onum_J_J_J,type,
    fun_fu4719417816141531311on_num: $tType ).

tff(ty_n_t__fun_It__fun_It__Num__Onum_Mt__Int__Oint_J_Mt__fun_It__Num__Onum_Mt__Option__Ooption_It__Num__Onum_J_J_J,type,
    fun_fu7964671872712412353on_num: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Nat__Onat_J_J_M_Eo_J,type,
    fun_Pr5375745717004158586_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_Mt__Rat__Orat_J_Mt__fun_It__fun_I_Eo_Mt__Rat__Orat_J_Mt__fun_I_Eo_Mt__Rat__Orat_J_J_J,type,
    fun_fu9039538216874201369_o_rat: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_Mt__Nat__Onat_J_Mt__fun_It__fun_I_Eo_Mt__Nat__Onat_J_Mt__fun_I_Eo_Mt__Nat__Onat_J_J_J,type,
    fun_fu3581538110357139729_o_nat: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_Mt__Int__Oint_J_Mt__fun_It__fun_I_Eo_Mt__Int__Oint_J_Mt__fun_I_Eo_Mt__Int__Oint_J_J_J,type,
    fun_fu9026017786105829997_o_int: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    fun_na2338080690716861136at_nat: $tType ).

tff(ty_n_t__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__fun_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    fun_he5369522480449343229at_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J,type,
    set_Pr6558897299634722526_nat_o: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Num__Onum_J_Mt__fun_It__Num__Onum_Mt__Option__Ooption_It__Num__Onum_J_J_J,type,
    fun_op3323321805596408808on_num: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J,type,
    fun_Pr7267779425873451369nt_int: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    fun_na4138050610385705875at_nat: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_J_J,type,
    fun_na8547874228452562927at_int: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J_J_J,type,
    fun_na7356754204550075887nt_nat: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_J_J,type,
    fun_na7450791247808564371at_int: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    fun_in1696471567231710611nt_int: $tType ).

tff(ty_n_t__Set__Oset_It__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    set_se5158245632345848097at_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    set_Pr5488025237498180813et_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Int__Oint_J_Mt__Set__Oset_It__Int__Oint_J_J_J,type,
    set_Pr2522554150109002629et_int: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    set_Pr7564037697178849041atural: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    set_Pr4811707699266497531nteger: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J,type,
    fun_se7504237348027150170_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
    fun_Pr3947133745332865710_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_M_Eo_J,type,
    fun_Pr8359263388657976682ural_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J,type,
    fun_Pr7211993375558241536eger_o: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_J,type,
    fun_Co1766037875893669450eger_o: $tType ).

tff(ty_n_t__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J,type,
    option6357759511663192854e_term: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Option__Ooption_It__Num__Onum_J_J,type,
    fun_Pr7397166214287566974on_num: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    set_Pr2929610433303031111_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Num__Onum_Mt__Num__Onum_J_Mt__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_fu2252611666013297880nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Num__Onum_Mt__Num__Onum_J_Mt__fun_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_fu8261421317008872756nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Num__Onum_Mt__Int__Oint_J_Mt__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_fu3380082687118895412nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_Mt__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_J,type,
    fun_fu2995346897264222311t_assn: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Rat__Orat_J_Mt__fun_It__Set__Oset_It__Int__Oint_J_Mt__Rat__Orat_J_J,type,
    fun_fu3579422585476231989nt_rat: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Assertions__Oassn_J_Mt__fun_It__Int__Oint_Mt__Assertions__Oassn_J_J,type,
    fun_fu6568868615275847455t_assn: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_Mt__fun_It__Num__Onum_Mt__Num__Onum_J_J,type,
    fun_fu5315010139097431512um_num: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_Mt__fun_It__Num__Onum_Mt__Num__Onum_J_J,type,
    fun_fu43082730658364980um_num: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J_Mt__Code____Numeral__Ointeger_J,type,
    fun_se1218973151702474915nteger: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_M_Eo_J,type,
    fun_Pr6629464623532871604at_o_o: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
    produc6653097349344004940it_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Rat__Orat_Mt__Rat__Orat_J_Mt__fun_It__fun_It__Rat__Orat_Mt__Rat__Orat_J_M_Eo_J_J,type,
    fun_fu4201227159558561136_rat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Rat__Orat_Mt__Rat__Orat_J_Mt__fun_It__fun_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J,type,
    fun_fu7747438168682512768_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Rat__Orat_Mt__Rat__Orat_J_Mt__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    fun_fu991806985645568200_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Num__Onum_Mt__Int__Oint_J_Mt__fun_It__fun_It__Num__Onum_Mt__Int__Oint_J_M_Eo_J_J,type,
    fun_fu5908277796454533188_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Num__Onum_J_Mt__fun_It__fun_It__Nat__Onat_Mt__Num__Onum_J_M_Eo_J_J,type,
    fun_fu223923076992463612_num_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__fun_It__Rat__Orat_Mt__Rat__Orat_J_M_Eo_J_J,type,
    fun_fu5655606085901093248_rat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__fun_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J,type,
    fun_fu9201817095025044880_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    fun_fu2446185911988100312_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Num__Onum_J_Mt__fun_It__fun_It__Int__Oint_Mt__Num__Onum_J_M_Eo_J_J,type,
    fun_fu6636849678353221188_num_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Nat__Onat_J_Mt__fun_It__fun_It__Int__Oint_Mt__Nat__Onat_J_M_Eo_J_J,type,
    fun_fu6391371659531026648_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__fun_It__Rat__Orat_Mt__Rat__Orat_J_M_Eo_J_J,type,
    fun_fu7417829167477406920_rat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__fun_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J,type,
    fun_fu1740668139746582744_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    fun_fu4208408993564413984_int_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__fun_It__Code____Numeral__Ointeger_M_Eo_J_J,type,
    fun_se4239619783102168410eger_o: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J_J_J,type,
    fun_na927404270896789692_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_M_Eo_J_Mt__fun_It__Code____Numeral__Ointeger_M_Eo_J_J,type,
    fun_fu8094397175230428611eger_o: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_Mt__Code____Numeral__Ointeger_J_Mt__fun_I_Eo_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_fu2786480252100984515nteger: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_Mt__Assertions__Oassn_J_Mt__fun_It__Set__Oset_I_Eo_J_Mt__Assertions__Oassn_J_J,type,
    fun_fu5561970054461773155o_assn: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__fun_It__Nat__Onat_M_Eo_J_J_Mt__Set__Oset_It__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    fun_se2106923200977956867_nat_o: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Num__Onum_J,type,
    produc9082142974458947146at_num: $tType ).

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

tff(ty_n_t__Product____Type__Oprod_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    produc759720530913461378nt_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__fun_It__Code____Numeral__Onatural_M_Eo_J_M_Eo_J_J,type,
    fun_fu1622112948621879430al_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__fun_It__Code____Numeral__Ointeger_M_Eo_J_M_Eo_J_J,type,
    fun_fu4168831735773172575er_o_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__Heap____Time____Monad__OHeap_It__Product____Type__Ounit_J_J,type,
    fun_Pr292408699144966967t_unit: $tType ).

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

tff(ty_n_t__Set__Oset_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    set_mu2057375006010111271at_nat: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_Mt__Rat__Orat_J_Mt__fun_It__fun_I_Eo_Mt__Rat__Orat_J_Mt__fun_I_Eo_M_Eo_J_J_J,type,
    fun_fu2641566564518291801un_o_o: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_Mt__Nat__Onat_J_Mt__fun_It__fun_I_Eo_Mt__Nat__Onat_J_Mt__fun_I_Eo_M_Eo_J_J_J,type,
    fun_fu5915781709770235737un_o_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__Heap____Time____Monad__OHeap_It__Heap__Oarray_Itf__a_J_J_J,type,
    fun_Pr5924905948197006361rray_a: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Code____Numeral__Ointeger_J_J,type,
    fun_op4521932154746760340nteger: $tType ).

tff(ty_n_t__fun_It__Heap__Oarray_Itf__a_J_Mt__Heap____Time____Monad__OHeap_It__Product____Type__Ounit_J_J,type,
    fun_ar1074044450438384043t_unit: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J,type,
    fun_se4097146774670233028at_nat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Int__Oint_J,type,
    fun_se9142667792015812128at_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    fun_Pr9038118721296872730et_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Set__Oset_It__Int__Oint_J_J,type,
    fun_Pr6548035576365145974et_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Code____Numeral__Ointeger_J,type,
    fun_Pr6026251430685297nteger: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_Mt__Nat__Onat_J,type,
    fun_Pr7395487658768111217er_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    fun_Pr3513738403344720850et_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Set__Oset_It__Int__Oint_J_J,type,
    fun_Pr1023655258412994094et_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_Mt__Int__Oint_J,type,
    fun_Pr907818707165963561er_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_Mt__Nat__Onat_J,type,
    fun_Pr1791375292569619697at_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_Mt__Int__Oint_J,type,
    fun_Pr9023817884608220585nt_int: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Num__Onum_J_Mt__fun_It__Option__Ooption_It__Num__Onum_J_M_Eo_J_J,type,
    fun_op493924057549976310_num_o: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    fun_na7044673412300895210at_nat: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_na1596024190920976919nteger: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_na7604833841916551795nteger: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_J,type,
    fun_na8176081009732395159er_nat: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_J,type,
    fun_na5685997864800668403er_int: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_J,type,
    fun_in7446034528553779607er_int: $tType ).

tff(ty_n_t__fun_It__Heap__Oarray_Itf__a_J_Mt__Heap____Time____Monad__OHeap_It__Heap__Oarray_Itf__a_J_J_J,type,
    fun_ar3891948820113774757rray_a: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    fun_Co4113693717567439989nt_int: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    set_fu360863049907232802nt_int: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    set_fu8487152106118010054nt_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_Mt__Nat__Onat_J,type,
    fun_fu1115759055147092071_o_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J,type,
    fun_fu6598048713889201561_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J,type,
    fun_fu8565479202776651253_int_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    fun_Pr4738963024209204295_int_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Rat__Orat_M_Eo_J_J,type,
    fun_Pr7537129237977221859_rat_o: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J,type,
    fun_na3970208099681795815_nat_o: $tType ).

tff(ty_n_t__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Product____Type__Ounit_J,type,
    fun_he5123621388056232515t_unit: $tType ).

tff(ty_n_t__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Heap__Oarray_Itf__a_J_J,type,
    fun_he7369252872201260279rray_a: $tType ).

tff(ty_n_t__Set__Oset_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    set_op4508134149509766951at_nat: $tType ).

tff(ty_n_t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    option8963830502488799655at_nat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J_Mt__Assertions__Oassn_J,type,
    fun_se704019859950278126r_assn: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Nat__Onat_J_Mt__fun_It__Nat__Onat_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    fun_se3395149180098744406et_nat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Nat__Onat_J_Mt__fun_It__Nat__Onat_Mt__Set__Oset_It__Int__Oint_J_J_J,type,
    fun_se7804972798165601458et_int: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Nat__Onat_J_Mt__fun_It__Int__Oint_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    fun_se180586794239543474et_nat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Nat__Onat_J_Mt__fun_It__Int__Oint_Mt__Set__Oset_It__Int__Oint_J_J_J,type,
    fun_se4590410412306400526et_int: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Int__Oint_J_Mt__fun_It__Nat__Onat_Mt__Set__Oset_It__Int__Oint_J_J_J,type,
    fun_se2974063760341720334et_int: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__Set__Oset_It__Int__Oint_J_J_J,type,
    fun_se8982873411337295210et_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    fun_Pr7036769738611282295at_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    fun_Pr6733608168372577327nt_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Ounit_J,type,
    fun_Pr2481279687482350479t_unit: $tType ).

tff(ty_n_t__fun_It__Num__Onum_Mt__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_nu1287335591331657422nteger: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    fun_na607345901702507418atural: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_na7078387940644931716nteger: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Onatural_Mt__fun_It__Nat__Onat_Mt__Code____Numeral__Onatural_J_J,type,
    fun_Co740390889742897050atural: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_Co6226381647958292740nteger: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Code____Numeral__Ointeger_Mt__Num__Onum_J_J,type,
    fun_Co8521658056209057742er_num: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_J,type,
    fun_Co3583066429914935172er_nat: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_J,type,
    fun_Co1092983284983208416er_int: $tType ).

tff(ty_n_t__fun_It__Assertions__Oassn_Mt__fun_It__Code____Numeral__Ointeger_Mt__Assertions__Oassn_J_J,type,
    fun_as4904527345752988583r_assn: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    fun_fu4467818495196037351_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Set__Oset_It__Int__Oint_J_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    fun_fu6344747128213397387_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    fun_fu5838931486547983824_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_fu7898940055406642654nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    fun_fu3900186759307340847_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Set__Oset_It__Int__Oint_J_J_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    fun_fu5777115392324700883_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    fun_fu5271299750659287320_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_fu6361890901329191134nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J,type,
    fun_fu5852520550942320402_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_M_Eo_J,type,
    fun_fu325614617715050166at_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_M_Eo_J_J_M_Eo_J,type,
    fun_fu1324968329616104722nt_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J,type,
    fun_fu7060637683870700398_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    fun_fu2106003848923686156_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_Mt__Rat__Orat_J_Mt__fun_It__Rat__Orat_Mt__fun_I_Eo_Mt__Rat__Orat_J_J_J,type,
    fun_fu8716238685137547908_o_rat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Nat__Onat_J_Mt__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_J,type,
    fun_se7316093745529328985et_nat: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Code____Numeral__Ointeger_J_J,type,
    fun_Co8029881127924365703nteger: $tType ).

tff(ty_n_t__Option__Ooption_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    option8886115935005447431nteger: $tType ).

tff(ty_n_t__fun_It__Assertions__Oassn_Mt__fun_It__Product____Type__Ounit_Mt__Assertions__Oassn_J_J,type,
    fun_as4019953064511417593t_assn: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__Nat__Onat_J_J_J,type,
    set_Pr698032948827214833st_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__Nat__Onat_J_J,type,
    set_Pr7549493975000385137at_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
    produc652263959640188542_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__Option__Ooption_It__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    fun_fu5368785673109833417_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__Nat__Onat_J_J_M_Eo_J,type,
    fun_Pr961374740995693450_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__Nat__Onat_J_M_Eo_J,type,
    fun_Pr7575312783043447050_nat_o: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    fun_op9036024853803066045_nat_o: $tType ).

tff(ty_n_t__fun_It__List__Olist_It__Nat__Onat_J_Mt__Set__Oset_It__List__Olist_It__Nat__Onat_J_J_J,type,
    fun_li1191372448985611379st_nat: $tType ).

tff(ty_n_t__fun_It__List__Olist_It__Nat__Onat_J_Mt__fun_It__List__Olist_It__Nat__Onat_J_M_Eo_J_J,type,
    fun_li1025265955262268170_nat_o: $tType ).

tff(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    set_se7855581050983116737at_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_J,type,
    set_Pr2406931829603198446nteger: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_J,type,
    set_Pr8415741480598773322nteger: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_J,type,
    set_Pr8986988648414616686er_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_J,type,
    set_Pr6496905503482889930er_int: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    produc7819656566062154093et_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Int__Oint_J_Mt__Set__Oset_It__Int__Oint_J_J,type,
    produc2115011035271226405et_int: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    produc7822875418678951345atural: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    produc8923325533196201883nteger: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Set__Oset_It__List__Olist_It__Nat__Onat_J_J_J_Mt__Int__Oint_J,type,
    fun_se1018900654481025269at_int: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J,type,
    fun_se4782206882984618170_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Set__Oset_I_Eo_J_J,type,
    fun_Pr8467005832278515962_set_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Set__Oset_I_Eo_J_J,type,
    fun_Pr5150627949553849410_set_o: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J,type,
    set_fu8838435424971791696_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_M_Eo_J,type,
    fun_fu6891447142836604759at_o_o: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_I_Eo_J_Mt__Set__Oset_I_Eo_J_J_J,type,
    set_Pr4577759397028426247_set_o: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    produc7704145150520151143_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Num__Onum_Mt__Num__Onum_J_Mt__fun_It__Num__Onum_Mt__Num__Onum_J_J,type,
    fun_fu8155524643419131615um_num: $tType ).

tff(ty_n_t__fun_It__fun_It__Num__Onum_Mt__Num__Onum_J_Mt__fun_It__Num__Onum_Mt__Int__Oint_J_J,type,
    fun_fu726849872193282289um_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Num__Onum_Mt__Int__Oint_J_Mt__fun_It__Num__Onum_Mt__Num__Onum_J_J,type,
    fun_fu5322398707847370225um_num: $tType ).

tff(ty_n_t__fun_It__fun_It__Num__Onum_Mt__Int__Oint_J_Mt__fun_It__Num__Onum_Mt__Int__Oint_J_J,type,
    fun_fu7117095973476296707um_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Num__Onum_Mt__Int__Oint_J_Mt__fun_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    fun_fu7588784024441849949at_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Num__Onum_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__Num__Onum_J_J,type,
    fun_fu5490925188574218499nt_num: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Rat__Orat_J_Mt__fun_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
    fun_fu8328862064278946247at_rat: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    fun_fu7002938529518989751at_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__Int__Oint_Mt__Num__Onum_J_J,type,
    fun_fu4905079693651358301nt_num: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Int__Oint_J_Mt__fun_It__Nat__Onat_Mt__Int__Oint_J_J,type,
    fun_fu8464300013002972271at_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Rat__Orat_J_Mt__fun_It__Int__Oint_Mt__Rat__Orat_J_J,type,
    fun_fu1008360527747082367nt_rat: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Nat__Onat_J_Mt__fun_It__Int__Oint_Mt__Num__Onum_J_J,type,
    fun_fu4621028619281248441nt_num: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Nat__Onat_J_Mt__fun_It__Int__Oint_Mt__Nat__Onat_J_J,type,
    fun_fu8905809029841901679nt_nat: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J,type,
    fun_fu1143798476471108391nt_int: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_Mt__Code____Numeral__Ointeger_J,type,
    fun_se8304080770522320754nteger: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J_Mt__Rat__Orat_J,type,
    fun_se1173871648619632798er_rat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J_Mt__Int__Oint_J,type,
    fun_se504249187503832818er_int: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J_J,type,
    fun_se3362872515591026879et_nat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__Code____Numeral__Ointeger_J,type,
    fun_se3773019727686582893nteger: $tType ).

tff(ty_n_t__fun_It__Rat__Orat_Mt__fun_It__Rat__Orat_Mt__fun_It__Nat__Onat_Mt__Rat__Orat_J_J_J,type,
    fun_ra3995598502166916815at_rat: $tType ).

tff(ty_n_t__fun_It__Rat__Orat_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Rat__Orat_J_J_J,type,
    fun_ra5513060666784058567at_rat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__Option__Ooption_It__Product____Type__Ounit_J_J,type,
    fun_Pr8303579546892975945t_unit: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Rat__Orat_Mt__fun_It__Nat__Onat_Mt__Rat__Orat_J_J_J,type,
    fun_na1148497095348402375at_rat: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    fun_na3244735409550470327at_nat: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Int__Oint_J_J_J,type,
    fun_na7654559027617327379at_int: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_Mt__Int__Oint_J_J_J,type,
    fun_na2382631619178260847at_int: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Int__Oint_J_J_J,type,
    fun_in6793278964266839919at_int: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__Set__Oset_It__Code____Numeral__Ointeger_J_J,type,
    fun_Co744628173305925485nteger: $tType ).

tff(ty_n_t__fun_It__Assertions__Oassn_Mt__fun_It__Assertions__Oassn_Mt__Assertions__Oassn_J_J,type,
    fun_as3983628580203722482n_assn: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    set_fu5818728815147633517nteger: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Nat__Onat_J_J,type,
    set_Pr1763845938948868674it_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Int__Oint_J_J,type,
    set_Pr8497134830871917726it_int: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Ounit_J_J,type,
    set_Pr4334478416066269672t_unit: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Product____Type__Ounit_J_J,type,
    set_Pr5889264611543340172t_unit: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    fun_fu1116345184836134341_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_J,type,
    fun_fu2792963925203051945t_assn: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Assertions__Oassn_J_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    fun_fu2934462529731303693_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_Mt__Assertions__Oassn_J_J,type,
    fun_fu2048648494261043369t_assn: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_M_Eo_J,type,
    fun_fu2916398056546941156ural_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J,type,
    fun_fu1769128043447206010eger_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Nat__Onat_J_Mt__fun_It__Set__Oset_It__Nat__Onat_J_M_Eo_J_J,type,
    fun_se2170385732985038782_nat_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Nat__Onat_J_Mt__fun_I_Eo_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    fun_se5245582867311637764et_nat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Int__Oint_J_Mt__fun_It__Set__Oset_It__Int__Oint_J_M_Eo_J_J,type,
    fun_se2051630309975736070_int_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Int__Oint_J_Mt__fun_I_Eo_Mt__Set__Oset_It__Int__Oint_J_J_J,type,
    fun_se241328533291454980et_int: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Onatural_Mt__fun_It__Code____Numeral__Onatural_M_Eo_J_J,type,
    fun_Co7302518231560758906ural_o: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Code____Numeral__Ointeger_M_Eo_J_J,type,
    fun_Co2081214437782444048eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Set__Oset_I_Eo_J_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    fun_fu8708304106554588451_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Code____Numeral__Onatural_M_Eo_J_J,type,
    fun_fu2969420921405070251ural_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Set__Oset_I_Eo_J_J_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    fun_fu7671276271812522531_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Code____Numeral__Ointeger_M_Eo_J_J,type,
    fun_fu8256284588060503314eger_o: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_Mt__Rat__Orat_J_Mt__fun_It__Set__Oset_I_Eo_J_Mt__Rat__Orat_J_J,type,
    fun_fu4803769369665013091_o_rat: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_Mt__Nat__Onat_J_Mt__fun_It__Set__Oset_I_Eo_J_Mt__Nat__Onat_J_J,type,
    fun_fu8843157277860572003_o_nat: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_Mt__Assertions__Oassn_J_Mt__fun_I_Eo_Mt__Assertions__Oassn_J_J,type,
    fun_fu704708528062463619o_assn: $tType ).

tff(ty_n_t__fun_It__Num__Onum_Mt__fun_It__Num__Onum_Mt__Option__Ooption_It__Num__Onum_J_J_J,type,
    fun_nu1049378303802735384on_num: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Num__Onum_Mt__Option__Ooption_It__Num__Onum_J_J_J,type,
    fun_na7595719129879163854on_num: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_M_Eo_J,type,
    fun_fu182496756620222510at_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J_M_Eo_J,type,
    fun_fu1181850468521277066nt_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_M_Eo_J,type,
    fun_fu4016735857504249042at_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J_M_Eo_J,type,
    fun_fu5016089569405303598nt_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__fun_It__Nat__Onat_M_Eo_J_M_Eo_J_J,type,
    fun_fu7564235448449272366at_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__fun_It__Int__Oint_M_Eo_J_M_Eo_J_J,type,
    fun_fu6971708032831053102nt_o_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Set__Oset_It__Product____Type__Ounit_J_J_Mt__Int__Oint_J,type,
    fun_se1823139391991869964it_int: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J,type,
    fun_na8669532458821385046t_unit: $tType ).

tff(ty_n_t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    multis2468970476368604999at_nat: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J,type,
    fun_op8989173174992673105on_num: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Num__Onum_J_J,type,
    fun_op6210678640266353415on_num: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J,type,
    fun_op1272087013972230845on_nat: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Int__Oint_J_Mt__Option__Ooption_It__Num__Onum_J_J,type,
    fun_op2398388785115040099on_num: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Int__Oint_J_Mt__Option__Ooption_It__Nat__Onat_J_J,type,
    fun_op6683169195675693337on_nat: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Int__Oint_J_Mt__Option__Ooption_It__Int__Oint_J_J,type,
    fun_op4193086050743966581on_int: $tType ).

tff(ty_n_t__fun_It__Rat__Orat_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    fun_ra4503298312962071866nt_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J_Mt__Num__Onum_J,type,
    fun_Pr3269564255357226306um_num: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J_Mt__Nat__Onat_J,type,
    fun_Pr4620512490437729710um_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Rat__Orat_J,type,
    fun_Pr8317260874932935276at_rat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J,type,
    fun_Pr2602117396471556196at_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Int__Oint_J,type,
    fun_Pr7647638413817135296at_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_Mt__Nat__Onat_J,type,
    fun_Pr4789038971164577984nt_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_Mt__Int__Oint_J,type,
    fun_Pr611187951655381276nt_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Num__Onum_J_Mt__Int__Oint_J,type,
    fun_Pr814315031165377638um_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J_Mt__Nat__Onat_J,type,
    fun_Pr2973770956708400832at_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J_Mt__Int__Oint_J,type,
    fun_Pr8019291974053979932at_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Rat__Orat_J,type,
    fun_Pr1652463973008025892nt_rat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Int__Oint_J,type,
    fun_Pr982841511892225912nt_int: $tType ).

tff(ty_n_t__fun_It__Num__Onum_Mt__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J_J,type,
    fun_nu5148503272595741012um_num: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    fun_na1476630412504255114at_nat: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_J,type,
    fun_na8209919304427304166at_int: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J_J,type,
    fun_na3663551987197276902nt_nat: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    fun_na1173468842265550146nt_int: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    fun_in4514472496968388910at_nat: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_J,type,
    fun_in2024389352036662154at_int: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    fun_in4211310926729683942nt_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__Set__Oset_It__Product____Type__Ounit_J_J,type,
    fun_Pr3013102738158121955t_unit: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__List__Olist_It__Nat__Onat_J_J_J,type,
    fun_na819858167508000762st_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Set__Oset_It__Set__Oset_It__List__Olist_It__Nat__Onat_J_J_J_J,type,
    set_set_set_list_nat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Set__Oset_It__List__Olist_It__Nat__Onat_J_J_J_M_Eo_J,type,
    fun_se5048694460222551717_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__fun_It__Product____Type__Ounit_M_Eo_J_J,type,
    fun_Pr1520749766685617582unit_o: $tType ).

tff(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    option4927543243414619207at_nat: $tType ).

tff(ty_n_t__Option__Ooption_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    option4624381673175914239nt_int: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_Mt__Assertions__Oassn_J,type,
    fun_set_set_int_assn: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__Assertions__Oassn_J,type,
    fun_se244736854054144952r_assn: $tType ).

tff(ty_n_t__fun_It__Rat__Orat_Mt__fun_It__Code____Numeral__Ointeger_Mt__Rat__Orat_J_J,type,
    fun_ra3321464020636160263er_rat: $tType ).

tff(ty_n_t__fun_It__Num__Onum_Mt__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_nu2537414170016844299nteger: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    fun_na6128946301132549280et_nat: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Code____Numeral__Onatural_J_J,type,
    fun_na3365689438791330114atural: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_na8135612474337863287nteger: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Assertions__Oassn_Mt__Assertions__Oassn_J_J,type,
    fun_na2454419004871237530n_assn: $tType ).

tff(ty_n_t__fun_It__Assertions__Oassn_Mt__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_J,type,
    fun_as8240436605320707994t_assn: $tType ).

tff(ty_n_t__fun_It__Assertions__Oassn_Mt__fun_It__Int__Oint_Mt__Assertions__Oassn_J_J,type,
    fun_as3432858861813084150t_assn: $tType ).

tff(ty_n_t__Set__Oset_It__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J_J,type,
    set_se8531188866349061887nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Rat__Orat_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    fun_fu7145897819039579925_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    fun_fu5477517762487726877_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
    fun_fu3162257917499486297at_rat: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J,type,
    fun_fu15710647883683081nt_int: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Rat__Orat_J_J_M_Eo_J,type,
    fun_fu8658704570366206279_rat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J,type,
    fun_fu7363466011001354227_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Rat__Orat_J_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    fun_fu3473604023002724957_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    fun_fu6779973503720134245_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    fun_fu4534828536049688329_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J,type,
    fun_fu7811933856372049837nt_int: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J_M_Eo_J,type,
    fun_se1103039064484435816eger_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Set__Oset_I_Eo_J_J_Mt__Code____Numeral__Ointeger_J,type,
    fun_se5062308858318814664nteger: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    fun_na7928631014926962227_nat_o: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Assertions__Oassn_M_Eo_J_J,type,
    fun_Co4819230592921789445assn_o: $tType ).

tff(ty_n_t__fun_It__Assertions__Oassn_Mt__fun_It__Code____Numeral__Ointeger_M_Eo_J_J,type,
    fun_as7521517929205406341eger_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_I_Eo_J_Mt__fun_It__Nat__Onat_Mt__Set__Oset_I_Eo_J_J_J,type,
    fun_se5315385049746747468_set_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_I_Eo_J_Mt__fun_It__Int__Oint_Mt__Set__Oset_I_Eo_J_J_J,type,
    fun_se7711175411341617392_set_o: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_J,type,
    fun_na896109329399166627et_nat: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_J,type,
    fun_in2104226462327546623et_nat: $tType ).

tff(ty_n_t__fun_It__Assertions__Oassn_Mt__Option__Ooption_It__Assertions__Oassn_J_J,type,
    fun_assn_option_assn: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__fun_I_Eo_M_Eo_J_J,type,
    fun_fu4049601875756261639un_o_o: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_Mt__Set__Oset_It__Int__Oint_J_J_Mt__fun_I_Eo_M_Eo_J_J,type,
    fun_fu8465396169103413603un_o_o: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_Mt__Code____Numeral__Ointeger_J_Mt__fun_I_Eo_M_Eo_J_J,type,
    fun_fu3819205551299168222un_o_o: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_M_Eo_J_Mt__fun_I_Eo_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_fu7181763470137098718nteger: $tType ).

tff(ty_n_t__fun_It__Rat__Orat_Mt__fun_It__Product____Type__Ounit_Mt__Rat__Orat_J_J,type,
    fun_ra5613769993463817465it_rat: $tType ).

tff(ty_n_t__Set__Oset_It__Set__Oset_It__Set__Oset_It__Product____Type__Ounit_J_J_J,type,
    set_se7118615804146677933t_unit: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Set__Oset_It__Product____Type__Ounit_J_J_M_Eo_J,type,
    fun_se2288280263375636942unit_o: $tType ).

tff(ty_n_t__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_M_Eo_J,type,
    fun_he8413527710729349838unit_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__Option__Ooption_It__Num__Onum_J_J,type,
    fun_Pr792663941044724234on_num: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Ounit_J_J,type,
    fun_na5635918068280204892t_unit: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Ounit_J_J,type,
    fun_in5873495209930779904t_unit: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J_J,type,
    set_Pr6200539531224447659at_num: $tType ).

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

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_J,type,
    set_Pr7995236796853374141at_int: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Num__Onum_J_J,type,
    set_Pr8387461105917469447nt_num: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J_J,type,
    set_Pr3448869479623346877nt_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    set_Pr958786334691620121nt_int: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J,type,
    produc2591615631378489102nteger: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Int__Oint_Mt__Code____Numeral__Ointeger_J,type,
    produc2963269191615333738nteger: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Num__Onum_J,type,
    produc7142191362829087448er_num: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J,type,
    produc6433947425880249742er_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J,type,
    produc2256096406371053034er_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
    fun_Pr4796943543331071514_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_Mt__Nat__Onat_J,type,
    fun_Pr103879662602641546_o_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
    fun_Pr3238374608701176162_int_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_M_Eo_J_Mt__Int__Oint_J,type,
    fun_Pr5835976712988771210_o_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_Mt__Nat__Onat_J,type,
    fun_Pr5585980272307166948at_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_Mt__Int__Oint_J,type,
    fun_Pr3595050827490992028nt_int: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Set__Oset_It__List__Olist_It__Nat__Onat_J_J_J,type,
    fun_nat_set_list_nat: $tType ).

tff(ty_n_t__fun_It__List__Olist_It__Nat__Onat_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    fun_list_nat_set_nat: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__List__Olist_It__Nat__Onat_J_M_Eo_J_J,type,
    fun_na7234455742697417626_nat_o: $tType ).

tff(ty_n_t__fun_It__List__Olist_It__Nat__Onat_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    fun_li2421049240157457050_nat_o: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Set__Oset_I_Eo_J_Mt__Set__Oset_I_Eo_J_J,type,
    produc7369051934464679207_set_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J_Mt__Int__Oint_J,type,
    fun_set_set_nat_int: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_Mt__Rat__Orat_J,type,
    fun_set_set_int_rat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_Mt__Int__Oint_J,type,
    fun_set_set_int_int: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Num__Onum_J_Mt__Set__Oset_It__Num__Onum_J_J,type,
    fun_set_num_set_num: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    fun_set_nat_set_nat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Int__Oint_J_Mt__Set__Oset_It__Int__Oint_J_J,type,
    fun_set_int_set_int: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Int__Oint_J_Mt__Code____Numeral__Ointeger_J,type,
    fun_se4372286887653997756nteger: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__Rat__Orat_J,type,
    fun_se2244710085602452072er_rat: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Set__Oset_It__Code____Numeral__Ointeger_J_J,type,
    fun_na9118744110877893344nteger: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__Set__Oset_It__Code____Numeral__Ointeger_J_J,type,
    fun_in6808926178784942396nteger: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    fun_Co7398788559141407565atural: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Onatural_Mt__Code____Numeral__Ointeger_J,type,
    fun_Co2940338738630218498nteger: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    fun_Co8307959106670069728et_nat: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__Set__Oset_It__Int__Oint_J_J,type,
    fun_Co5817875961738342972et_int: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Onatural_J,type,
    fun_Co3734316457315071362atural: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    fun_Co8499238673658658103nteger: $tType ).

tff(ty_n_t__fun_It__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_M_Eo_J,type,
    fun_fu3961712701602788733eger_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_M_Eo_J,type,
    fun_fu2893655071357150791eger_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Set__Oset_I_Eo_J_J_Mt__Assertions__Oassn_J,type,
    fun_set_set_o_assn: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Nat__Onat_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    fun_se382663106265794036_nat_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Int__Oint_J_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    fun_se867122708194164540_int_o: $tType ).

tff(ty_n_t__fun_It__Rat__Orat_Mt__fun_It__Code____Numeral__Onatural_M_Eo_J_J,type,
    fun_ra6546579167043500746ural_o: $tType ).

tff(ty_n_t__fun_It__Rat__Orat_Mt__fun_It__Code____Numeral__Ointeger_M_Eo_J_J,type,
    fun_ra1401953663915778005eger_o: $tType ).

tff(ty_n_t__fun_It__Num__Onum_Mt__fun_It__Code____Numeral__Ointeger_M_Eo_J_J,type,
    fun_nu5413996832991386387eger_o: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Code____Numeral__Onatural_M_Eo_J_J,type,
    fun_na2240068485812228818ural_o: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Code____Numeral__Ointeger_M_Eo_J_J,type,
    fun_na6318815019539281885eger_o: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__fun_It__Code____Numeral__Onatural_M_Eo_J_J,type,
    fun_in812919657445819766ural_o: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__fun_It__Code____Numeral__Ointeger_M_Eo_J_J,type,
    fun_in4891666191172872833eger_o: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Onatural_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    fun_Co196715998180962002_nat_o: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Rat__Orat_M_Eo_J_J,type,
    fun_Co625613742390903637_rat_o: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Num__Onum_M_Eo_J_J,type,
    fun_Co2133228800495250323_num_o: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    fun_Co1375048237525739357_nat_o: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    fun_Co8353275306710069249_int_o: $tType ).

tff(ty_n_t__fun_It__Assertions__Oassn_Mt__fun_It__Assertions__Oassn_M_Eo_J_J,type,
    fun_assn_fun_assn_o: $tType ).

tff(ty_n_t__fun_It__Assertions__Oassn_Mt__fun_I_Eo_Mt__Assertions__Oassn_J_J,type,
    fun_assn_fun_o_assn: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    set_fu7727944524835118346_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    fun_fu4001317426178549763_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    fun_fu1756172458508103847_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_M_Eo_J,type,
    fun_fu4354239228518319373at_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_M_Eo_J,type,
    fun_fu5353592940419373929nt_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    fun_fu6128684156180612191_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    fun_fu3883539188510166275_int_o: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_Mt__Rat__Orat_J_Mt__fun_I_Eo_Mt__Rat__Orat_J_J,type,
    fun_fu1989461620956114563_o_rat: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_Mt__Nat__Onat_J_Mt__fun_I_Eo_Mt__Nat__Onat_J_J,type,
    fun_fu6701067901881939075_o_nat: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_Mt__Int__Oint_J_Mt__fun_I_Eo_Mt__Int__Oint_J_J,type,
    fun_fu6940589326549028739_o_int: $tType ).

tff(ty_n_t__Set__Oset_It__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_J,type,
    set_option_set_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Option__Ooption_It__Code____Numeral__Ointeger_J_J,type,
    set_op687863988967635939nteger: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_Mt__Assertions__Oassn_J_Mt__fun_I_Eo_M_Eo_J_J,type,
    fun_fu3143923321121214633un_o_o: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_M_Eo_J_Mt__fun_I_Eo_Mt__Assertions__Oassn_J_J,type,
    fun_fu7714003655882793385o_assn: $tType ).

tff(ty_n_t__fun_It__Set__Oset_I_Eo_J_Mt__fun_I_Eo_Mt__Set__Oset_I_Eo_J_J_J,type,
    fun_se3315603611433934638_set_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    fun_Pr1628945989756059814et_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__Set__Oset_It__Int__Oint_J_J,type,
    fun_Pr8362234881679108866et_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__Code____Numeral__Onatural_J,type,
    fun_Pr6278675377255837256atural: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__Code____Numeral__Ointeger_J,type,
    fun_Pr1820225556744648189nteger: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Ounit_J_J,type,
    fun_na896991816813928310t_unit: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__Set__Oset_It__Product____Type__Ounit_J_J,type,
    fun_in4731230917697954842t_unit: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__Product____Type__Ounit_J,type,
    fun_Co1365676809456677961t_unit: $tType ).

tff(ty_n_t__fun_I_Eo_Mt__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_J,type,
    fun_o_option_set_nat: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_Mt__Set__Oset_I_Eo_J_J_Mt__fun_I_Eo_M_Eo_J_J,type,
    fun_fu5370137289309429475un_o_o: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Ounit_M_Eo_J_J,type,
    fun_na5971062356810558811unit_o: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_M_Eo_J_J,type,
    fun_in8984369272479023031unit_o: $tType ).

tff(ty_n_t__Set__Oset_It__Option__Ooption_It__Product____Type__Ounit_J_J,type,
    set_op3165557761946182707t_unit: $tType ).

tff(ty_n_t__Option__Ooption_It__Set__Oset_It__Product____Type__Ounit_J_J,type,
    option8137458692691377843t_unit: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J,type,
    fun_Pr2191293291710260995t_unit: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_I_Eo_J_Mt__Option__Ooption_I_Eo_J_J,type,
    fun_op5853259939270031811tion_o: $tType ).

tff(ty_n_t__fun_I_Eo_Mt__Option__Ooption_It__Product____Type__Ounit_J_J,type,
    fun_o_6261137236491177342t_unit: $tType ).

tff(ty_n_t__Set__Oset_It__Set__Oset_It__List__Olist_It__Nat__Onat_J_J_J,type,
    set_set_list_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J,type,
    set_Pr3149072824959771635_nat_o: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_M_Eo_J_J,type,
    set_Pr903927857289325719_int_o: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_Eo_Mt__Num__Onum_J_J,type,
    set_Pr7040061329075590551_o_num: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
    set_Pr2101469702781467981_o_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_J,type,
    set_Pr8834758594704517033_o_int: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
    produc6271795597528267376eger_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_M_Eo_J,type,
    fun_Pr2976697613021001844at_o_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_It__Int__Oint_M_Eo_J_M_Eo_J,type,
    fun_Pr1059884994059025616nt_o_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_I_Eo_Mt__Num__Onum_J_M_Eo_J,type,
    fun_Pr4362196099282670544_num_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_M_Eo_J,type,
    fun_Pr3604015536313159578_nat_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_M_Eo_J,type,
    fun_Pr1358870568642713662_int_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Int__Oint_J_Mt__Assertions__Oassn_J,type,
    fun_set_int_assn: $tType ).

tff(ty_n_t__fun_It__Rat__Orat_Mt__fun_It__Rat__Orat_Mt__Rat__Orat_J_J,type,
    fun_rat_fun_rat_rat: $tType ).

tff(ty_n_t__fun_It__Rat__Orat_Mt__fun_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
    fun_rat_fun_nat_rat: $tType ).

tff(ty_n_t__fun_It__Rat__Orat_Mt__fun_It__Int__Oint_Mt__Rat__Orat_J_J,type,
    fun_rat_fun_int_rat: $tType ).

tff(ty_n_t__fun_It__Num__Onum_Mt__fun_It__Num__Onum_Mt__Num__Onum_J_J,type,
    fun_num_fun_num_num: $tType ).

tff(ty_n_t__fun_It__Num__Onum_Mt__fun_It__Num__Onum_Mt__Int__Oint_J_J,type,
    fun_num_fun_num_int: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Rat__Orat_Mt__Rat__Orat_J_J,type,
    fun_nat_fun_rat_rat: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
    fun_nat_fun_nat_rat: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    fun_nat_fun_nat_nat: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Int__Oint_J_J,type,
    fun_nat_fun_nat_int: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J,type,
    fun_nat_fun_int_int: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_Mt__Int__Oint_J_J,type,
    fun_int_fun_nat_int: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Rat__Orat_J_J,type,
    fun_int_fun_int_rat: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J,type,
    fun_int_fun_int_int: $tType ).

tff(ty_n_t__fun_It__Heap__Oarray_Itf__a_J_Mt__Heap__Oarray_Itf__a_J_J,type,
    fun_array_a_array_a: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__Assertions__Oassn_J,type,
    fun_Co4490034186337852034r_assn: $tType ).

tff(ty_n_t__Set__Oset_It__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J_J,type,
    set_set_set_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_J,type,
    set_set_set_int: $tType ).

tff(ty_n_t__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J,type,
    set_set_Code_integer: $tType ).

tff(ty_n_t__Heap____Time____Monad__OHeap_It__Product____Type__Ounit_J,type,
    heap_T5738788834812785303t_unit: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
    fun_set_set_nat_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_M_Eo_J,type,
    fun_set_set_int_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Set__Oset_I_Eo_J_J_Mt__Rat__Orat_J,type,
    fun_set_set_o_rat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Set__Oset_I_Eo_J_J_Mt__Nat__Onat_J,type,
    fun_set_set_o_nat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Code____Numeral__Ointeger_J_M_Eo_J,type,
    fun_se7289222521248229150eger_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_I_Eo_J_Mt__Code____Numeral__Ointeger_J,type,
    fun_se937664112047466216nteger: $tType ).

tff(ty_n_t__fun_It__Assertions__Oassn_Mt__fun_It__Rat__Orat_M_Eo_J_J,type,
    fun_assn_fun_rat_o: $tType ).

tff(ty_n_t__fun_It__Assertions__Oassn_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    fun_assn_fun_nat_o: $tType ).

tff(ty_n_t__fun_It__Assertions__Oassn_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    fun_assn_fun_int_o: $tType ).

tff(ty_n_t__fun_I_Eo_Mt__Set__Oset_It__Code____Numeral__Ointeger_J_J,type,
    fun_o_5240169576699714110nteger: $tType ).

tff(ty_n_t__Heap____Time____Monad__OHeap_It__Heap__Oarray_Itf__a_J_J,type,
    heap_T6362127782908069795rray_a: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Num__Onum_J_Mt__Num__Onum_J,type,
    fun_option_num_num: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Num__Onum_J_Mt__Nat__Onat_J,type,
    fun_option_num_nat: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Num__Onum_J_Mt__Int__Oint_J,type,
    fun_option_num_int: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Nat__Onat_J_Mt__Nat__Onat_J,type,
    fun_option_nat_nat: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Int__Oint_J_Mt__Int__Oint_J,type,
    fun_option_int_int: $tType ).

tff(ty_n_t__fun_It__Num__Onum_Mt__Option__Ooption_It__Num__Onum_J_J,type,
    fun_num_option_num: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Option__Ooption_It__Num__Onum_J_J,type,
    fun_nat_option_num: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Option__Ooption_It__Nat__Onat_J_J,type,
    fun_nat_option_nat: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__Option__Ooption_It__Num__Onum_J_J,type,
    fun_int_option_num: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__Option__Ooption_It__Int__Oint_J_J,type,
    fun_int_option_int: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_Mt__Rat__Orat_J_Mt__fun_I_Eo_M_Eo_J_J,type,
    fun_fu6337961365400742745un_o_o: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_Mt__Nat__Onat_J_Mt__fun_I_Eo_M_Eo_J_J,type,
    fun_fu6781074197733401937un_o_o: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_M_Eo_J_Mt__fun_I_Eo_Mt__Rat__Orat_J_J,type,
    fun_fu830079035465870425_o_rat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__Assertions__Oassn_J,type,
    fun_Pr6626665806141890376t_assn: $tType ).

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

tff(ty_n_t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
    heap_e7401611519738050253t_unit: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__fun_I_Eo_M_Eo_J_J,type,
    fun_Pr616739963666181091un_o_o: $tType ).

tff(ty_n_t__fun_I_Eo_Mt__fun_It__Product____Type__Ounit_M_Eo_J_J,type,
    fun_o_6763651944650080953unit_o: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
    product_prod_num_num: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J,type,
    product_prod_nat_num: $tType ).

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

tff(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
    product_prod_nat_int: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Int__Oint_Mt__Num__Onum_J,type,
    product_prod_int_num: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J,type,
    product_prod_int_nat: $tType ).

tff(ty_n_t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    product_prod_int_int: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__List__Olist_It__Nat__Onat_J_J,type,
    fun_nat_list_nat: $tType ).

tff(ty_n_t__fun_It__List__Olist_It__Nat__Onat_J_Mt__Nat__Onat_J,type,
    fun_list_nat_nat: $tType ).

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

tff(ty_n_t__fun_It__Set__Oset_It__Num__Onum_J_Mt__Num__Onum_J,type,
    fun_set_num_num: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Nat__Onat_J_Mt__Nat__Onat_J,type,
    fun_set_nat_nat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Int__Oint_J_Mt__Rat__Orat_J,type,
    fun_set_int_rat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Int__Oint_J_Mt__Int__Oint_J,type,
    fun_set_int_int: $tType ).

tff(ty_n_t__fun_It__Product____Type__Oprod_I_Eo_M_Eo_J_M_Eo_J,type,
    fun_Pr6984036127010467572_o_o_o: $tType ).

tff(ty_n_t__fun_It__Num__Onum_Mt__Code____Numeral__Onatural_J,type,
    fun_num_Code_natural: $tType ).

tff(ty_n_t__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J,type,
    fun_num_Code_integer: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    fun_nat_set_nat: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Set__Oset_It__Int__Oint_J_J,type,
    fun_nat_set_int: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Code____Numeral__Onatural_J,type,
    fun_nat_Code_natural: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J,type,
    fun_nat_Code_integer: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    fun_int_set_nat: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__Set__Oset_It__Int__Oint_J_J,type,
    fun_int_set_int: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__Code____Numeral__Onatural_J,type,
    fun_int_Code_natural: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__Code____Numeral__Ointeger_J,type,
    fun_int_Code_integer: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Onatural_Mt__Nat__Onat_J,type,
    fun_Code_natural_nat: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__Rat__Orat_J,type,
    fun_Code_integer_rat: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__Num__Onum_J,type,
    fun_Code_integer_num: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J,type,
    fun_Code_integer_nat: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_Mt__Int__Oint_J,type,
    fun_Code_integer_int: $tType ).

tff(ty_n_t__fun_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
    fun_assn_assn: $tType ).

tff(ty_n_t__fun_I_Eo_Mt__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    fun_o_4732642864545671890od_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Rat__Orat_Mt__Rat__Orat_J_M_Eo_J,type,
    fun_fun_rat_rat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Num__Onum_Mt__Int__Oint_J_M_Eo_J,type,
    fun_fun_num_int_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Num__Onum_J_M_Eo_J,type,
    fun_fun_nat_num_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
    fun_fun_nat_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Rat__Orat_J_M_Eo_J,type,
    fun_fun_int_rat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Num__Onum_J_M_Eo_J,type,
    fun_fun_int_num_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Nat__Onat_J_M_Eo_J,type,
    fun_fun_int_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
    fun_fun_int_int_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_I_Eo_J_Mt__Assertions__Oassn_J,type,
    fun_set_o_assn: $tType ).

tff(ty_n_t__fun_It__Rat__Orat_Mt__fun_It__Rat__Orat_M_Eo_J_J,type,
    fun_rat_fun_rat_o: $tType ).

tff(ty_n_t__fun_It__Rat__Orat_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    fun_rat_fun_nat_o: $tType ).

tff(ty_n_t__fun_It__Rat__Orat_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    fun_rat_fun_int_o: $tType ).

tff(ty_n_t__fun_It__Rat__Orat_Mt__fun_I_Eo_Mt__Rat__Orat_J_J,type,
    fun_rat_fun_o_rat: $tType ).

tff(ty_n_t__fun_It__Num__Onum_Mt__fun_It__Num__Onum_M_Eo_J_J,type,
    fun_num_fun_num_o: $tType ).

tff(ty_n_t__fun_It__Num__Onum_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    fun_num_fun_int_o: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Rat__Orat_M_Eo_J_J,type,
    fun_nat_fun_rat_o: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    fun_nat_fun_nat_o: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    fun_nat_fun_int_o: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__fun_It__Rat__Orat_M_Eo_J_J,type,
    fun_int_fun_rat_o: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__fun_It__Num__Onum_M_Eo_J_J,type,
    fun_int_fun_num_o: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    fun_int_fun_nat_o: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    fun_int_fun_int_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_I_Eo_J_Mt__Set__Oset_I_Eo_J_J,type,
    fun_set_o_set_o: $tType ).

tff(ty_n_t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J,type,
    sum_sum_nat_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Option__Ooption_It__Num__Onum_J_J,type,
    set_option_num: $tType ).

tff(ty_n_t__Set__Oset_It__Option__Ooption_It__Nat__Onat_J_J,type,
    set_option_nat: $tType ).

tff(ty_n_t__Set__Oset_It__Option__Ooption_It__Int__Oint_J_J,type,
    set_option_int: $tType ).

tff(ty_n_t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
    option_set_nat: $tType ).

tff(ty_n_t__Option__Ooption_It__Set__Oset_It__Int__Oint_J_J,type,
    option_set_int: $tType ).

tff(ty_n_t__Option__Ooption_It__Code____Numeral__Ointeger_J,type,
    option_Code_integer: $tType ).

tff(ty_n_t__fun_It__Set__Oset_I_Eo_J_Mt__fun_I_Eo_M_Eo_J_J,type,
    fun_set_o_fun_o_o: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__Rat__Orat_J,type,
    fun_Product_unit_rat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__Nat__Onat_J,type,
    fun_Product_unit_nat: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_Mt__Int__Oint_J,type,
    fun_Product_unit_int: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_It__Num__Onum_J_M_Eo_J,type,
    fun_option_num_o: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Product____Type__Ounit_J,type,
    fun_nat_Product_unit: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__Product____Type__Ounit_J,type,
    fun_int_Product_unit: $tType ).

tff(ty_n_t__fun_I_Eo_Mt__Option__Ooption_It__Num__Onum_J_J,type,
    fun_o_option_num: $tType ).

tff(ty_n_t__Option__Ooption_It__fun_It__Nat__Onat_M_Eo_J_J,type,
    option_fun_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_I_Eo_M_Eo_J_Mt__fun_I_Eo_M_Eo_J_J,type,
    fun_fun_o_o_fun_o_o: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Heap__Oarray_Itf__a_J_J,type,
    fun_nat_array_a: $tType ).

tff(ty_n_t__Option__Ooption_It__Product____Type__Ounit_J,type,
    option_Product_unit: $tType ).

tff(ty_n_t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
    set_list_nat: $tType ).

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

tff(ty_n_t__Product____Type__Oprod_It__Int__Oint_M_Eo_J,type,
    product_prod_int_o: $tType ).

tff(ty_n_t__Product____Type__Oprod_I_Eo_Mt__Num__Onum_J,type,
    product_prod_o_num: $tType ).

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

tff(ty_n_t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
    product_prod_o_int: $tType ).

tff(ty_n_t__fun_It__List__Olist_It__Nat__Onat_J_M_Eo_J,type,
    fun_list_nat_o: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Assertions__Oassn_J,type,
    fun_nat_assn: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__Assertions__Oassn_J,type,
    fun_int_assn: $tType ).

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

tff(ty_n_t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
    set_set_int: $tType ).

tff(ty_n_t__Set__Oset_It__Code____Numeral__Onatural_J,type,
    set_Code_natural: $tType ).

tff(ty_n_t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
    set_Code_integer: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Nat__Onat_J_M_Eo_J,type,
    fun_set_nat_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_It__Int__Oint_J_M_Eo_J,type,
    fun_set_int_o: $tType ).

tff(ty_n_t__fun_It__Set__Oset_I_Eo_J_Mt__Rat__Orat_J,type,
    fun_set_o_rat: $tType ).

tff(ty_n_t__fun_It__Set__Oset_I_Eo_J_Mt__Nat__Onat_J,type,
    fun_set_o_nat: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Set__Oset_I_Eo_J_J,type,
    fun_nat_set_o: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__Set__Oset_I_Eo_J_J,type,
    fun_int_set_o: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Onatural_M_Eo_J,type,
    fun_Code_natural_o: $tType ).

tff(ty_n_t__fun_It__Code____Numeral__Ointeger_M_Eo_J,type,
    fun_Code_integer_o: $tType ).

tff(ty_n_t__fun_I_Eo_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    fun_o_set_nat: $tType ).

tff(ty_n_t__fun_I_Eo_Mt__Set__Oset_It__Int__Oint_J_J,type,
    fun_o_set_int: $tType ).

tff(ty_n_t__fun_I_Eo_Mt__Code____Numeral__Ointeger_J,type,
    fun_o_Code_integer: $tType ).

tff(ty_n_t__Set__Oset_It__fun_It__Nat__Onat_M_Eo_J_J,type,
    set_fun_nat_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Nat__Onat_M_Eo_J_M_Eo_J,type,
    fun_fun_nat_o_o: $tType ).

tff(ty_n_t__fun_It__fun_It__Int__Oint_M_Eo_J_M_Eo_J,type,
    fun_fun_int_o_o: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__fun_I_Eo_M_Eo_J_J,type,
    fun_nat_fun_o_o: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__fun_I_Eo_M_Eo_J_J,type,
    fun_int_fun_o_o: $tType ).

tff(ty_n_t__fun_I_Eo_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    fun_o_fun_nat_o: $tType ).

tff(ty_n_t__Option__Ooption_It__Assertions__Oassn_J,type,
    option_assn: $tType ).

tff(ty_n_t__Heap__Oref_It__Product____Type__Ounit_J,type,
    ref_Product_unit: $tType ).

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

tff(ty_n_t__Set__Oset_It__Option__Ooption_I_Eo_J_J,type,
    set_option_o: $tType ).

tff(ty_n_t__Option__Ooption_It__Set__Oset_I_Eo_J_J,type,
    option_set_o: $tType ).

tff(ty_n_t__Heap__Oref_It__Heap__Oarray_Itf__a_J_J,type,
    ref_array_a: $tType ).

tff(ty_n_t__fun_It__Product____Type__Ounit_M_Eo_J,type,
    fun_Product_unit_o: $tType ).

tff(ty_n_t__fun_It__Option__Ooption_I_Eo_J_M_Eo_J,type,
    fun_option_o_o: $tType ).

tff(ty_n_t__fun_I_Eo_Mt__Product____Type__Ounit_J,type,
    fun_o_Product_unit: $tType ).

tff(ty_n_t__fun_I_Eo_Mt__Option__Ooption_I_Eo_J_J,type,
    fun_o_option_o: $tType ).

tff(ty_n_t__fun_It__Heap__Oarray_Itf__a_J_M_Eo_J,type,
    fun_array_a_o: $tType ).

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

tff(ty_n_t__fun_It__Rat__Orat_Mt__Rat__Orat_J,type,
    fun_rat_rat: $tType ).

tff(ty_n_t__fun_It__Rat__Orat_Mt__Nat__Onat_J,type,
    fun_rat_nat: $tType ).

tff(ty_n_t__fun_It__Num__Onum_Mt__Rat__Orat_J,type,
    fun_num_rat: $tType ).

tff(ty_n_t__fun_It__Num__Onum_Mt__Num__Onum_J,type,
    fun_num_num: $tType ).

tff(ty_n_t__fun_It__Num__Onum_Mt__Nat__Onat_J,type,
    fun_num_nat: $tType ).

tff(ty_n_t__fun_It__Num__Onum_Mt__Int__Oint_J,type,
    fun_num_int: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Rat__Orat_J,type,
    fun_nat_rat: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Num__Onum_J,type,
    fun_nat_num: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Nat__Onat_J,type,
    fun_nat_nat: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mt__Int__Oint_J,type,
    fun_nat_int: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__Rat__Orat_J,type,
    fun_int_rat: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__Num__Onum_J,type,
    fun_int_num: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__Nat__Onat_J,type,
    fun_int_nat: $tType ).

tff(ty_n_t__fun_It__Int__Oint_Mt__Int__Oint_J,type,
    fun_int_int: $tType ).

tff(ty_n_t__Set__Oset_It__Assertions__Oassn_J,type,
    set_assn: $tType ).

tff(ty_n_t__fun_It__Assertions__Oassn_M_Eo_J,type,
    fun_assn_o: $tType ).

tff(ty_n_t__fun_I_Eo_Mt__Assertions__Oassn_J,type,
    fun_o_assn: $tType ).

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

tff(ty_n_t__fun_I_Eo_Mt__Set__Oset_I_Eo_J_J,type,
    fun_o_set_o: $tType ).

tff(ty_n_t__Option__Ooption_It__Rat__Orat_J,type,
    option_rat: $tType ).

tff(ty_n_t__Option__Ooption_It__Num__Onum_J,type,
    option_num: $tType ).

tff(ty_n_t__Option__Ooption_It__Nat__Onat_J,type,
    option_nat: $tType ).

tff(ty_n_t__Option__Ooption_It__Int__Oint_J,type,
    option_int: $tType ).

tff(ty_n_t__List__Olist_It__String__Ochar_J,type,
    list_char: $tType ).

tff(ty_n_t__fun_I_Eo_Mt__fun_I_Eo_M_Eo_J_J,type,
    fun_o_fun_o_o: $tType ).

tff(ty_n_t__List__Olist_It__Nat__Onat_J,type,
    list_nat: $tType ).

tff(ty_n_t__List__Olist_It__Int__Oint_J,type,
    list_int: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_Mtf__a_J,type,
    fun_nat_a: $tType ).

tff(ty_n_t__Set__Oset_It__Rat__Orat_J,type,
    set_rat: $tType ).

tff(ty_n_t__Set__Oset_It__Num__Onum_J,type,
    set_num: $tType ).

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

tff(ty_n_t__Set__Oset_It__Int__Oint_J,type,
    set_int: $tType ).

tff(ty_n_t__Code____Numeral__Onatural,type,
    code_natural: $tType ).

tff(ty_n_t__Code____Numeral__Ointeger,type,
    code_integer: $tType ).

tff(ty_n_t__fun_It__Rat__Orat_M_Eo_J,type,
    fun_rat_o: $tType ).

tff(ty_n_t__fun_It__Num__Onum_M_Eo_J,type,
    fun_num_o: $tType ).

tff(ty_n_t__fun_It__Nat__Onat_M_Eo_J,type,
    fun_nat_o: $tType ).

tff(ty_n_t__fun_It__Int__Oint_M_Eo_J,type,
    fun_int_o: $tType ).

tff(ty_n_t__fun_I_Eo_Mt__Rat__Orat_J,type,
    fun_o_rat: $tType ).

tff(ty_n_t__fun_I_Eo_Mt__Nat__Onat_J,type,
    fun_o_nat: $tType ).

tff(ty_n_t__fun_I_Eo_Mt__Int__Oint_J,type,
    fun_o_int: $tType ).

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

tff(ty_n_t__Option__Ooption_I_Eo_J,type,
    option_o: $tType ).

tff(ty_n_t__Heap__Oarray_Itf__a_J,type,
    array_a: $tType ).

tff(ty_n_t__List__Olist_Itf__a_J,type,
    list_a: $tType ).

tff(ty_n_t__Typerep__Otyperep,type,
    typerep: $tType ).

tff(ty_n_t__Assertions__Oassn,type,
    assn: $tType ).

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

tff(ty_n_t__fun_I_Eo_M_Eo_J,type,
    fun_o_o: $tType ).

tff(ty_n_t__String__Ochar,type,
    char: $tType ).

tff(ty_n_t__Rat__Orat,type,
    rat: $tType ).

tff(ty_n_t__Num__Onum,type,
    num: $tType ).

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

tff(ty_n_t__Int__Oint,type,
    int: $tType ).

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

% Explicit typings (4299)
tff(sy_c_ATP_058Lamm__a____,type,
    aTP_Lamm_a: set_Pr4329608150637261639at_nat > fun_Pr3059359313727237556_nat_o ).

tff(sy_c_ATP_058Lamm__aa____,type,
    aTP_Lamm_aa: set_Pr1261947904930325089at_nat > fun_Pr4796943543331071514_nat_o ).

tff(sy_c_ATP_058Lamm__aaa____,type,
    aTP_Lamm_aaa: set_fu3629540756087427317e_term > fun_Pr9081111800474865985e_term ).

tff(sy_c_ATP_058Lamm__aab____,type,
    aTP_Lamm_aab: set_Pr958786334691620121nt_int > fun_fu3472058528428720115nt_int ).

tff(sy_c_ATP_058Lamm__aac____,type,
    aTP_Lamm_aac: fun_nat_Code_integer > fun_fu6201336427292363868nteger ).

tff(sy_c_ATP_058Lamm__aad____,type,
    aTP_Lamm_aad: fun_nat_Code_integer > fun_fu1723132215250845724er_nat ).

tff(sy_c_ATP_058Lamm__aae____,type,
    aTP_Lamm_aae: fun_nat_nat > fun_se8450096479846816355et_nat ).

tff(sy_c_ATP_058Lamm__aaf____,type,
    aTP_Lamm_aaf: fun_nat_Code_integer > fun_fu1491972344133157660er_int ).

tff(sy_c_ATP_058Lamm__aag____,type,
    aTP_Lamm_aag: fun_nat_int > fun_se3636548061058897599et_int ).

tff(sy_c_ATP_058Lamm__aah____,type,
    aTP_Lamm_aah: fun_nat_Code_integer > fun_fu1895414074638732388er_int ).

tff(sy_c_ATP_058Lamm__aai____,type,
    aTP_Lamm_aai: fun_int_int > fun_se2042144505192658715et_int ).

tff(sy_c_ATP_058Lamm__aaj____,type,
    aTP_Lamm_aaj: fun_nat_nat > fun_fu8284676920001830735nteger ).

tff(sy_c_ATP_058Lamm__aak____,type,
    aTP_Lamm_aak: fun_nat_Code_integer > fun_se2951167709562549603nteger ).

tff(sy_c_ATP_058Lamm__aal____,type,
    aTP_Lamm_aal: fun_nat_nat > fun_fu7012516915885544207at_nat ).

tff(sy_c_ATP_058Lamm__aam____,type,
    aTP_Lamm_aam: fun_nat_nat > fun_fu3125320701163054607at_int ).

tff(sy_c_ATP_058Lamm__aan____,type,
    aTP_Lamm_aan: fun_nat_int > fun_se7804972798165601458et_int ).

tff(sy_c_ATP_058Lamm__aao____,type,
    aTP_Lamm_aao: fun_nat_nat > fun_fu4152238915952267095at_int ).

tff(sy_c_ATP_058Lamm__aap____,type,
    aTP_Lamm_aap: fun_int_int > fun_se2974063760341720334et_int ).

tff(sy_c_ATP_058Lamm__aaq____,type,
    aTP_Lamm_aaq: fun_nat_int > fun_fu1188671613149117355nteger ).

tff(sy_c_ATP_058Lamm__aar____,type,
    aTP_Lamm_aar: fun_nat_Code_integer > fun_se8949688400205348287nteger ).

tff(sy_c_ATP_058Lamm__aas____,type,
    aTP_Lamm_aas: fun_nat_int > fun_fu2668056085831081835nt_nat ).

tff(sy_c_ATP_058Lamm__aat____,type,
    aTP_Lamm_aat: fun_nat_nat > fun_se180586794239543474et_nat ).

tff(sy_c_ATP_058Lamm__aau____,type,
    aTP_Lamm_aau: set_Code_integer > fun_fu5766609707292941056eger_o ).

tff(sy_c_ATP_058Lamm__aav____,type,
    aTP_Lamm_aav: set_o > fun_fu5370137289309429475un_o_o ).

tff(sy_c_ATP_058Lamm__aaw____,type,
    aTP_Lamm_aaw: set_int > fun_fu7671276271812522531_int_o ).

tff(sy_c_ATP_058Lamm__aax____,type,
    aTP_Lamm_aax: set_nat > fun_fu8708304106554588451_nat_o ).

tff(sy_c_ATP_058Lamm__aay____,type,
    aTP_Lamm_aay: set_o > fun_fu4049601875756261639un_o_o ).

tff(sy_c_ATP_058Lamm__aaz____,type,
    aTP_Lamm_aaz: set_int > fun_fu3900186759307340847_int_o ).

tff(sy_c_ATP_058Lamm__ab____,type,
    aTP_Lamm_ab: set_o > fun_o_o ).

tff(sy_c_ATP_058Lamm__aba____,type,
    aTP_Lamm_aba: set_nat > fun_fu4467818495196037351_nat_o ).

tff(sy_c_ATP_058Lamm__abb____,type,
    aTP_Lamm_abb: set_o > fun_fu8465396169103413603un_o_o ).

tff(sy_c_ATP_058Lamm__abc____,type,
    aTP_Lamm_abc: set_nat > fun_fu6344747128213397387_nat_o ).

tff(sy_c_ATP_058Lamm__abd____,type,
    aTP_Lamm_abd: set_int > fun_fu5777115392324700883_int_o ).

tff(sy_c_ATP_058Lamm__abe____,type,
    aTP_Lamm_abe: fun_Pr5098669352780829690e_term > fun_Pr894914116851403386nteger ).

tff(sy_c_ATP_058Lamm__abf____,type,
    aTP_Lamm_abf: fun_fu5971215405379524186nteger > fun_fu4173945377279696323nteger ).

tff(sy_c_ATP_058Lamm__abg____,type,
    aTP_Lamm_abg: fun_Pr6460944699146269935_nat_o > fun_Pr3017356861961520469et_nat ).

tff(sy_c_ATP_058Lamm__abh____,type,
    aTP_Lamm_abh: fun_fu2890809920214373946et_nat > fun_fu8357309440898100312et_nat ).

tff(sy_c_ATP_058Lamm__abi____,type,
    aTP_Lamm_abi: fun_Pr6460944699146269935_nat_o > fun_Pr4147293223664569617et_nat ).

tff(sy_c_ATP_058Lamm__abj____,type,
    aTP_Lamm_abj: fun_fu8357309440898100312et_nat > fun_fu5650763273978745334et_nat ).

tff(sy_c_ATP_058Lamm__abk____,type,
    aTP_Lamm_abk: fun_Pr7763680713840462443e_term > fun_Pr1547027809659849477nt_int ).

tff(sy_c_ATP_058Lamm__abl____,type,
    aTP_Lamm_abl: fun_fu4219362280553733319nt_int > fun_fu60724386564609697nt_int ).

tff(sy_c_ATP_058Lamm__abm____,type,
    aTP_Lamm_abm: fun_in5730379987311621695e_term > fun_Pr1951044811698827825nt_int ).

tff(sy_c_ATP_058Lamm__abn____,type,
    aTP_Lamm_abn: fun_fu3472058528428720115nt_int > fun_fu6029888860018473377nt_int ).

tff(sy_c_ATP_058Lamm__abo____,type,
    aTP_Lamm_abo: set_Pr1261947904930325089at_nat > fun_se1551789852802198377at_nat ).

tff(sy_c_ATP_058Lamm__abp____,type,
    aTP_Lamm_abp: fun_se953073389798102371at_nat > fun_se1551789852802198377at_nat ).

tff(sy_c_ATP_058Lamm__abq____,type,
    aTP_Lamm_abq: nat > fun_na7044673412300895210at_nat ).

tff(sy_c_ATP_058Lamm__abr____,type,
    aTP_Lamm_abr: fun_nat_set_nat > fun_na7044673412300895210at_nat ).

tff(sy_c_ATP_058Lamm__abs____,type,
    aTP_Lamm_abs: set_Pr4811707699266497531nteger > fun_Co744628173305925485nteger ).

tff(sy_c_ATP_058Lamm__abt____,type,
    aTP_Lamm_abt: set_Pr958786334691620121nt_int > fun_int_set_int ).

tff(sy_c_ATP_058Lamm__abu____,type,
    aTP_Lamm_abu: set_Pr2352657477744078772atural > fun_Co2944084857415636034atural ).

tff(sy_c_ATP_058Lamm__abv____,type,
    aTP_Lamm_abv: fun_na1476630412504255114at_nat ).

tff(sy_c_ATP_058Lamm__abw____,type,
    aTP_Lamm_abw: fun_Pr1308109350235310159nt_int ).

tff(sy_c_ATP_058Lamm__abx____,type,
    aTP_Lamm_abx: fun_Pr2478283820680522243nt_int ).

tff(sy_c_ATP_058Lamm__aby____,type,
    aTP_Lamm_aby: fun_se1551789852802198377at_nat ).

tff(sy_c_ATP_058Lamm__abz____,type,
    aTP_Lamm_abz: fun_na7044673412300895210at_nat ).

tff(sy_c_ATP_058Lamm__ac____,type,
    aTP_Lamm_ac: set_int > fun_int_o ).

tff(sy_c_ATP_058Lamm__aca____,type,
    aTP_Lamm_aca: fun_Pr1308109350235310159nt_int ).

tff(sy_c_ATP_058Lamm__acb____,type,
    aTP_Lamm_acb: fun_Pr2478283820680522243nt_int ).

tff(sy_c_ATP_058Lamm__acc____,type,
    aTP_Lamm_acc: $o > fun_se3315603611433934638_set_o ).

tff(sy_c_ATP_058Lamm__acd____,type,
    aTP_Lamm_acd: nat > fun_se5245582867311637764et_nat ).

tff(sy_c_ATP_058Lamm__ace____,type,
    aTP_Lamm_ace: int > fun_se241328533291454980et_int ).

tff(sy_c_ATP_058Lamm__acf____,type,
    aTP_Lamm_acf: $o > fun_se5315385049746747468_set_o ).

tff(sy_c_ATP_058Lamm__acg____,type,
    aTP_Lamm_acg: nat > fun_se3395149180098744406et_nat ).

tff(sy_c_ATP_058Lamm__ach____,type,
    aTP_Lamm_ach: int > fun_se2974063760341720334et_int ).

tff(sy_c_ATP_058Lamm__aci____,type,
    aTP_Lamm_aci: $o > fun_se7711175411341617392_set_o ).

tff(sy_c_ATP_058Lamm__acj____,type,
    aTP_Lamm_acj: nat > fun_se180586794239543474et_nat ).

tff(sy_c_ATP_058Lamm__ack____,type,
    aTP_Lamm_ack: int > fun_se8982873411337295210et_int ).

tff(sy_c_ATP_058Lamm__acl____,type,
    aTP_Lamm_acl: $o > fun_se7283963663803345157_set_o ).

tff(sy_c_ATP_058Lamm__acm____,type,
    aTP_Lamm_acm: fun_se953073389798102371at_nat > fun_fu7445151911848907075at_nat ).

tff(sy_c_ATP_058Lamm__acn____,type,
    aTP_Lamm_acn: set_nat > fun_se7316093745529328985et_nat ).

tff(sy_c_ATP_058Lamm__aco____,type,
    aTP_Lamm_aco: option_set_nat > fun_op386870758422531628et_nat ).

tff(sy_c_ATP_058Lamm__acp____,type,
    aTP_Lamm_acp: set_Pr4329608150637261639at_nat > fun_se7901873761543946185at_nat ).

tff(sy_c_ATP_058Lamm__acq____,type,
    aTP_Lamm_acq: option1583680563626158861at_nat > fun_op291006984297869545at_nat ).

tff(sy_c_ATP_058Lamm__acr____,type,
    aTP_Lamm_acr: product_unit > fun_Pr8303579546892975945t_unit ).

tff(sy_c_ATP_058Lamm__acs____,type,
    aTP_Lamm_acs: option_Product_unit > fun_op5903753652030861359t_unit ).

tff(sy_c_ATP_058Lamm__act____,type,
    aTP_Lamm_act: assn > fun_assn_option_assn ).

tff(sy_c_ATP_058Lamm__acu____,type,
    aTP_Lamm_acu: option_assn > fun_op4146996366486250514n_assn ).

tff(sy_c_ATP_058Lamm__acv____,type,
    aTP_Lamm_acv: nat > fun_na7928631014926962227_nat_o ).

tff(sy_c_ATP_058Lamm__acw____,type,
    aTP_Lamm_acw: fun_na5914473681949881652_nat_o ).

tff(sy_c_ATP_058Lamm__acx____,type,
    aTP_Lamm_acx: fun_Pr5098669352780829690e_term > fun_Pr471679772948460611nteger ).

tff(sy_c_ATP_058Lamm__acy____,type,
    aTP_Lamm_acy: fun_Pr6460944699146269935_nat_o > fun_Pr4459677240377800360et_nat ).

tff(sy_c_ATP_058Lamm__acz____,type,
    aTP_Lamm_acz: fun_Pr6460944699146269935_nat_o > fun_Pr386875378712213506et_nat ).

tff(sy_c_ATP_058Lamm__ad____,type,
    aTP_Lamm_ad: set_nat > fun_nat_o ).

tff(sy_c_ATP_058Lamm__ada____,type,
    aTP_Lamm_ada: fun_Pr7763680713840462443e_term > fun_Pr7963917038216275131nt_int ).

tff(sy_c_ATP_058Lamm__adb____,type,
    aTP_Lamm_adb: fun_in5730379987311621695e_term > fun_Pr5088371826558493971nt_int ).

tff(sy_c_ATP_058Lamm__adc____,type,
    aTP_Lamm_adc: set_Pr1261947904930325089at_nat > fun_se636550882185307767at_nat ).

tff(sy_c_ATP_058Lamm__add____,type,
    aTP_Lamm_add: nat > fun_na8167864584424996432at_nat ).

tff(sy_c_ATP_058Lamm__ade____,type,
    aTP_Lamm_ade: set_Pr1261947904930325089at_nat > fun_nat_set_nat ).

tff(sy_c_ATP_058Lamm__adf____,type,
    aTP_Lamm_adf: set_Product_prod_o_o > fun_o_set_o ).

tff(sy_c_ATP_058Lamm__adg____,type,
    aTP_Lamm_adg: fun_in1696471567231710611nt_int ).

tff(sy_c_ATP_058Lamm__adh____,type,
    aTP_Lamm_adh: nat > fun_he5234484606919320760it_nat ).

tff(sy_c_ATP_058Lamm__adi____,type,
    aTP_Lamm_adi: fun_rat_fun_int_o ).

tff(sy_c_ATP_058Lamm__adj____,type,
    aTP_Lamm_adj: fun_na819858167508000762st_nat ).

tff(sy_c_ATP_058Lamm__adk____,type,
    aTP_Lamm_adk: code_natural > fun_Co9168753396221475450atural ).

tff(sy_c_ATP_058Lamm__adl____,type,
    aTP_Lamm_adl: produc7822875418678951345atural > fun_Co1890133979025130057atural ).

tff(sy_c_ATP_058Lamm__adm____,type,
    aTP_Lamm_adm: code_natural > fun_Co1105491363547889651atural ).

tff(sy_c_ATP_058Lamm__adn____,type,
    aTP_Lamm_adn: fun_Co1105491363547889651atural ).

tff(sy_c_ATP_058Lamm__ado____,type,
    aTP_Lamm_ado: code_natural > fun_Co1105491363547889651atural ).

tff(sy_c_ATP_058Lamm__adp____,type,
    aTP_Lamm_adp: nat > fun_na7234455742697417626_nat_o ).

tff(sy_c_ATP_058Lamm__adq____,type,
    aTP_Lamm_adq: nat > fun_na7234455742697417626_nat_o ).

tff(sy_c_ATP_058Lamm__adr____,type,
    aTP_Lamm_adr: nat > fun_na7234455742697417626_nat_o ).

tff(sy_c_ATP_058Lamm__ae____,type,
    aTP_Lamm_ae: set_list_nat > fun_list_nat_o ).

tff(sy_c_ATP_058Lamm__af____,type,
    aTP_Lamm_af: array_a > fun_he281446669002384250it_nat ).

tff(sy_c_ATP_058Lamm__ag____,type,
    aTP_Lamm_ag: product_unit > fun_he4944555133437423336it_nat ).

tff(sy_c_ATP_058Lamm__ah____,type,
    aTP_Lamm_ah: fun_num_fun_num_o ).

tff(sy_c_ATP_058Lamm__ai____,type,
    aTP_Lamm_ai: produc8664842809031399944it_nat > fun_Pr8032424337255632745_nat_o ).

tff(sy_c_ATP_058Lamm__aj____,type,
    aTP_Lamm_aj: fun_Pr7068637894315934487_nat_o ).

tff(sy_c_ATP_058Lamm__ak____,type,
    aTP_Lamm_ak: fun_num_o ).

tff(sy_c_ATP_058Lamm__al____,type,
    aTP_Lamm_al: fun_Pr8032424337255632745_nat_o ).

tff(sy_c_ATP_058Lamm__am____,type,
    aTP_Lamm_am: fun_Co8499238673658658103nteger ).

tff(sy_c_ATP_058Lamm__an____,type,
    aTP_Lamm_an: fun_Pr7068637894315934487_nat_o ).

tff(sy_c_ATP_058Lamm__ao____,type,
    aTP_Lamm_ao: fun_num_o ).

tff(sy_c_ATP_058Lamm__ap____,type,
    aTP_Lamm_ap: fun_Pr8032424337255632745_nat_o ).

tff(sy_c_ATP_058Lamm__aq____,type,
    aTP_Lamm_aq: fun_int_int > fun_fu7117095973476296707um_int ).

tff(sy_c_ATP_058Lamm__ar____,type,
    aTP_Lamm_ar: fun_int_option_num > fun_fu7964671872712412353on_num ).

tff(sy_c_ATP_058Lamm__as____,type,
    aTP_Lamm_as: fun_int_num > fun_fu5322398707847370225um_num ).

tff(sy_c_ATP_058Lamm__at____,type,
    aTP_Lamm_at: fun_option_num_int > fun_fu1947565687807238081um_int ).

tff(sy_c_ATP_058Lamm__au____,type,
    aTP_Lamm_au: fun_op8989173174992673105on_num > fun_fu2987389051837124479on_num ).

tff(sy_c_ATP_058Lamm__av____,type,
    aTP_Lamm_av: fun_option_num_num > fun_fu152868422178311599um_num ).

tff(sy_c_ATP_058Lamm__aw____,type,
    aTP_Lamm_aw: fun_num_int > fun_fu726849872193282289um_int ).

tff(sy_c_ATP_058Lamm__ax____,type,
    aTP_Lamm_ax: fun_num_option_num > fun_fu4719417816141531311on_num ).

tff(sy_c_ATP_058Lamm__ay____,type,
    aTP_Lamm_ay: fun_num_num > fun_fu8155524643419131615um_num ).

tff(sy_c_ATP_058Lamm__az____,type,
    aTP_Lamm_az: fun_Pr1003294667014919570it_nat > fun_Pr3631287881653221602it_nat ).

tff(sy_c_ATP_058Lamm__ba____,type,
    aTP_Lamm_ba: fun_Pr1003294667014919570it_nat > fun_op4112804339236761266it_nat ).

tff(sy_c_ATP_058Lamm__bb____,type,
    aTP_Lamm_bb: fun_num_fun_num_num > fun_nu1049378303802735384on_num ).

tff(sy_c_ATP_058Lamm__bc____,type,
    aTP_Lamm_bc: fun_num_fun_num_num > fun_op3323321805596408808on_num ).

tff(sy_c_ATP_058Lamm__bd____,type,
    aTP_Lamm_bd: fun_Co2081214437782444048eger_o ).

tff(sy_c_ATP_058Lamm__be____,type,
    aTP_Lamm_be: option_Code_integer > fun_Code_integer_o ).

tff(sy_c_ATP_058Lamm__bf____,type,
    aTP_Lamm_bf: fun_rat_fun_rat_o ).

tff(sy_c_ATP_058Lamm__bg____,type,
    aTP_Lamm_bg: option_rat > fun_rat_o ).

tff(sy_c_ATP_058Lamm__bh____,type,
    aTP_Lamm_bh: fun_num_fun_num_o ).

tff(sy_c_ATP_058Lamm__bi____,type,
    aTP_Lamm_bi: option_num > fun_num_o ).

tff(sy_c_ATP_058Lamm__bj____,type,
    aTP_Lamm_bj: fun_nat_fun_nat_o ).

tff(sy_c_ATP_058Lamm__bk____,type,
    aTP_Lamm_bk: option_nat > fun_nat_o ).

tff(sy_c_ATP_058Lamm__bl____,type,
    aTP_Lamm_bl: fun_int_fun_int_o ).

tff(sy_c_ATP_058Lamm__bm____,type,
    aTP_Lamm_bm: option_int > fun_int_o ).

tff(sy_c_ATP_058Lamm__bn____,type,
    aTP_Lamm_bn: fun_he1504492240061592256it_nat ).

tff(sy_c_ATP_058Lamm__bo____,type,
    aTP_Lamm_bo: fun_he5234484606919320760it_nat ).

tff(sy_c_ATP_058Lamm__bp____,type,
    aTP_Lamm_bp: fun_he8413527710729349838unit_o > fun_fu4233702620870981175it_nat ).

tff(sy_c_ATP_058Lamm__bq____,type,
    aTP_Lamm_bq: fun_he8413527710729349838unit_o > fun_fu2492676192234506515it_nat ).

tff(sy_c_ATP_058Lamm__br____,type,
    aTP_Lamm_br: array_a > fun_he281446669002384250it_nat ).

tff(sy_c_ATP_058Lamm__bs____,type,
    aTP_Lamm_bs: product_unit > fun_he4944555133437423336it_nat ).

tff(sy_c_ATP_058Lamm__bt____,type,
    aTP_Lamm_bt: fun_he5123621388056232515t_unit > fun_he5234484606919320760it_nat ).

tff(sy_c_ATP_058Lamm__bu____,type,
    aTP_Lamm_bu: fun_se8406536441587994090_nat_o ).

tff(sy_c_ATP_058Lamm__bv____,type,
    aTP_Lamm_bv: fun_se4014881416909572940_nat_o ).

tff(sy_c_ATP_058Lamm__bw____,type,
    aTP_Lamm_bw: fun_se6163777255337707072eger_o ).

tff(sy_c_ATP_058Lamm__bx____,type,
    aTP_Lamm_bx: fun_se7509835969743050710_nat_o ).

tff(sy_c_ATP_058Lamm__by____,type,
    aTP_Lamm_by: fun_se4713689491525875926_nat_o ).

tff(sy_c_ATP_058Lamm__bz____,type,
    aTP_Lamm_bz: fun_se5710315616867461632_int_o ).

tff(sy_c_ATP_058Lamm__ca____,type,
    aTP_Lamm_ca: fun_se5644990602862975744_int_o ).

tff(sy_c_ATP_058Lamm__cb____,type,
    aTP_Lamm_cb: fun_Co1981900195452921617nteger ).

tff(sy_c_ATP_058Lamm__cc____,type,
    aTP_Lamm_cc: fun_Pr5876161306168176259nteger > fun_Co1561183069634336733nteger ).

tff(sy_c_ATP_058Lamm__cd____,type,
    aTP_Lamm_cd: fun_Pr5876161306168176259nteger > fun_fu4800041728187187127nteger ).

tff(sy_c_ATP_058Lamm__ce____,type,
    aTP_Lamm_ce: num > fun_nat_num ).

tff(sy_c_ATP_058Lamm__cf____,type,
    aTP_Lamm_cf: fun_num_num > fun_num_option_num ).

tff(sy_c_ATP_058Lamm__cg____,type,
    aTP_Lamm_cg: fun_num_num ).

tff(sy_c_ATP_058Lamm__ch____,type,
    aTP_Lamm_ch: option_set_nat > fun_set_nat_o ).

tff(sy_c_ATP_058Lamm__ci____,type,
    aTP_Lamm_ci: option_rat > fun_rat_o ).

tff(sy_c_ATP_058Lamm__cj____,type,
    aTP_Lamm_cj: option_num > fun_num_o ).

tff(sy_c_ATP_058Lamm__ck____,type,
    aTP_Lamm_ck: option_nat > fun_nat_o ).

tff(sy_c_ATP_058Lamm__cl____,type,
    aTP_Lamm_cl: option_int > fun_int_o ).

tff(sy_c_ATP_058Lamm__cm____,type,
    aTP_Lamm_cm: fun_assn_assn ).

tff(sy_c_ATP_058Lamm__cn____,type,
    aTP_Lamm_cn: fun_rat_rat ).

tff(sy_c_ATP_058Lamm__co____,type,
    aTP_Lamm_co: fun_nat_nat ).

tff(sy_c_ATP_058Lamm__cp____,type,
    aTP_Lamm_cp: fun_int_int ).

tff(sy_c_ATP_058Lamm__cq____,type,
    aTP_Lamm_cq: fun_na4138050610385705875at_nat ).

tff(sy_c_ATP_058Lamm__cr____,type,
    aTP_Lamm_cr: fun_nat_Code_integer > fun_nat_Code_integer ).

tff(sy_c_ATP_058Lamm__cs____,type,
    aTP_Lamm_cs: fun_nat_rat > fun_nat_rat ).

tff(sy_c_ATP_058Lamm__ct____,type,
    aTP_Lamm_ct: fun_nat_int > fun_nat_int ).

tff(sy_c_ATP_058Lamm__cu____,type,
    aTP_Lamm_cu: fun_na1668100129766719005at_nat > fun_Pr557098546508347797at_nat ).

tff(sy_c_ATP_058Lamm__cv____,type,
    aTP_Lamm_cv: fun_na5914473681949881652_nat_o > fun_Pr3455331679158536364_nat_o ).

tff(sy_c_ATP_058Lamm__cw____,type,
    aTP_Lamm_cw: fun_nat_nat > fun_fu1217771548038759377at_nat ).

tff(sy_c_ATP_058Lamm__cx____,type,
    aTP_Lamm_cx: fun_int_int > fun_fu6092417073193843705nt_int ).

tff(sy_c_ATP_058Lamm__cy____,type,
    aTP_Lamm_cy: fun_Pr982841511892225912nt_int > fun_fu717549361983437348nt_int ).

tff(sy_c_ATP_058Lamm__cz____,type,
    aTP_Lamm_cz: fun_in4211310926729683942nt_int > fun_fu918106826131887214nt_int ).

tff(sy_c_ATP_058Lamm__da____,type,
    aTP_Lamm_da: fun_na3970208099681795815_nat_o > fun_fu484727072080742171_nat_o ).

tff(sy_c_ATP_058Lamm__db____,type,
    aTP_Lamm_db: fun_fu1115759055147092071_o_nat > fun_fu4228150600790569371at_nat ).

tff(sy_c_ATP_058Lamm__dc____,type,
    aTP_Lamm_dc: fun_Pr2478283820680522243nt_int > fun_fu3898734532474705027nt_int ).

tff(sy_c_ATP_058Lamm__dd____,type,
    aTP_Lamm_dd: fun_na8713714802964096592at_nat > fun_fu1039311746440044420at_nat ).

tff(sy_c_ATP_058Lamm__de____,type,
    aTP_Lamm_de: fun_fu1413608398870722896at_nat > fun_fu7448223259553364356at_nat ).

tff(sy_c_ATP_058Lamm__df____,type,
    aTP_Lamm_df: fun_fu3275390434952296369_nat_o > fun_fu6384561554008368101_nat_o ).

tff(sy_c_ATP_058Lamm__dg____,type,
    aTP_Lamm_dg: fun_na4138050610385705875at_nat ).

tff(sy_c_ATP_058Lamm__dh____,type,
    aTP_Lamm_dh: fun_nat_nat > fun_nat_nat ).

tff(sy_c_ATP_058Lamm__di____,type,
    aTP_Lamm_di: fun_nat_nat > fun_nat_fun_nat_nat ).

tff(sy_c_ATP_058Lamm__dj____,type,
    aTP_Lamm_dj: fun_Pr2602117396471556196at_nat > fun_nat_fun_nat_nat ).

tff(sy_c_ATP_058Lamm__dk____,type,
    aTP_Lamm_dk: fun_Pr2477239776880934807at_nat > fun_na1668100129766719005at_nat ).

tff(sy_c_ATP_058Lamm__dl____,type,
    aTP_Lamm_dl: fun_Pr2028404973800837934_nat_o > fun_na5914473681949881652_nat_o ).

tff(sy_c_ATP_058Lamm__dm____,type,
    aTP_Lamm_dm: fun_Pr2478283820680522243nt_int > fun_in1696471567231710611nt_int ).

tff(sy_c_ATP_058Lamm__dn____,type,
    aTP_Lamm_dn: fun_Pr982841511892225912nt_int > fun_int_fun_int_int ).

tff(sy_c_ATP_058Lamm__do____,type,
    aTP_Lamm_do: fun_nat_nat > fun_na3244735409550470327at_nat ).

tff(sy_c_ATP_058Lamm__dp____,type,
    aTP_Lamm_dp: fun_na2338080690716861136at_nat > fun_na2338080690716861136at_nat ).

tff(sy_c_ATP_058Lamm__dq____,type,
    aTP_Lamm_dq: fun_nat_rat > fun_nat_rat ).

tff(sy_c_ATP_058Lamm__dr____,type,
    aTP_Lamm_dr: fun_nat_int > fun_nat_int ).

tff(sy_c_ATP_058Lamm__ds____,type,
    aTP_Lamm_ds: fun_nat_Code_integer > fun_nat_Code_integer ).

tff(sy_c_ATP_058Lamm__dt____,type,
    aTP_Lamm_dt: fun_nat_rat > fun_nat_rat ).

tff(sy_c_ATP_058Lamm__du____,type,
    aTP_Lamm_du: fun_nat_int > fun_nat_int ).

tff(sy_c_ATP_058Lamm__dv____,type,
    aTP_Lamm_dv: rat > fun_nat_fun_nat_rat ).

tff(sy_c_ATP_058Lamm__dw____,type,
    aTP_Lamm_dw: int > fun_nat_fun_nat_int ).

tff(sy_c_ATP_058Lamm__dx____,type,
    aTP_Lamm_dx: fun_nat_nat ).

tff(sy_c_ATP_058Lamm__dy____,type,
    aTP_Lamm_dy: fun_nat_Code_integer > fun_na7078387940644931716nteger ).

tff(sy_c_ATP_058Lamm__dz____,type,
    aTP_Lamm_dz: fun_na2338080690716861136at_nat > fun_na1945018436707187408at_nat ).

tff(sy_c_ATP_058Lamm__ea____,type,
    aTP_Lamm_ea: fun_nat_rat > fun_nat_fun_rat_rat ).

tff(sy_c_ATP_058Lamm__eb____,type,
    aTP_Lamm_eb: fun_nat_int > fun_nat_fun_int_int ).

tff(sy_c_ATP_058Lamm__ec____,type,
    aTP_Lamm_ec: fun_nat_nat > fun_nat_fun_nat_nat ).

tff(sy_c_ATP_058Lamm__ed____,type,
    aTP_Lamm_ed: fun_nat_Code_integer > fun_nat_Code_integer ).

tff(sy_c_ATP_058Lamm__ee____,type,
    aTP_Lamm_ee: fun_nat_rat > fun_nat_rat ).

tff(sy_c_ATP_058Lamm__ef____,type,
    aTP_Lamm_ef: fun_nat_int > fun_nat_int ).

tff(sy_c_ATP_058Lamm__eg____,type,
    aTP_Lamm_eg: fun_o_Code_integer > fun_fu2786480252100984515nteger ).

tff(sy_c_ATP_058Lamm__eh____,type,
    aTP_Lamm_eh: fun_nat_Code_integer > fun_fu2499394402704830801nteger ).

tff(sy_c_ATP_058Lamm__ei____,type,
    aTP_Lamm_ei: fun_int_Code_integer > fun_fu3628599891403802633nteger ).

tff(sy_c_ATP_058Lamm__ej____,type,
    aTP_Lamm_ej: fun_o_rat > fun_fu1989461620956114563_o_rat ).

tff(sy_c_ATP_058Lamm__ek____,type,
    aTP_Lamm_ek: fun_nat_rat > fun_fu8328862064278946247at_rat ).

tff(sy_c_ATP_058Lamm__el____,type,
    aTP_Lamm_el: fun_int_rat > fun_fu1008360527747082367nt_rat ).

tff(sy_c_ATP_058Lamm__em____,type,
    aTP_Lamm_em: fun_o_int > fun_fu6940589326549028739_o_int ).

tff(sy_c_ATP_058Lamm__en____,type,
    aTP_Lamm_en: fun_nat_int > fun_fu8464300013002972271at_int ).

tff(sy_c_ATP_058Lamm__eo____,type,
    aTP_Lamm_eo: fun_int_int > fun_fu1143798476471108391nt_int ).

tff(sy_c_ATP_058Lamm__ep____,type,
    aTP_Lamm_ep: fun_Pr6026251430685297nteger > fun_fu7390737412436561923nteger ).

tff(sy_c_ATP_058Lamm__eq____,type,
    aTP_Lamm_eq: nat > fun_nat_fun_nat_nat ).

tff(sy_c_ATP_058Lamm__er____,type,
    aTP_Lamm_er: fun_nat_nat > fun_fu7002938529518989751at_nat ).

tff(sy_c_ATP_058Lamm__es____,type,
    aTP_Lamm_es: fun_int_int > fun_fu1143798476471108391nt_int ).

tff(sy_c_ATP_058Lamm__et____,type,
    aTP_Lamm_et: set_Pr4329608150637261639at_nat > fun_se6980948925662697216_nat_o ).

tff(sy_c_ATP_058Lamm__eu____,type,
    aTP_Lamm_eu: set_Pr4329608150637261639at_nat > fun_se1700271160720914596_nat_o ).

tff(sy_c_ATP_058Lamm__ev____,type,
    aTP_Lamm_ev: set_Pr4329608150637261639at_nat > fun_se7382040709525900966_nat_o ).

tff(sy_c_ATP_058Lamm__ew____,type,
    aTP_Lamm_ew: set_Pr4329608150637261639at_nat > fun_se9209729713313069232_nat_o ).

tff(sy_c_ATP_058Lamm__ex____,type,
    aTP_Lamm_ex: set_Pr1261947904930325089at_nat > fun_se991814106188233920_nat_o ).

tff(sy_c_ATP_058Lamm__ey____,type,
    aTP_Lamm_ey: set_Pr1261947904930325089at_nat > fun_se3629081808164793780_nat_o ).

tff(sy_c_ATP_058Lamm__ez____,type,
    aTP_Lamm_ez: set_Pr1261947904930325089at_nat > fun_se3165749655728557022_nat_o ).

tff(sy_c_ATP_058Lamm__fa____,type,
    aTP_Lamm_fa: set_Pr1261947904930325089at_nat > fun_se218054151627931304_nat_o ).

tff(sy_c_ATP_058Lamm__fb____,type,
    aTP_Lamm_fb: fun_nat_o > fun_fu2677729659939697685_nat_o ).

tff(sy_c_ATP_058Lamm__fc____,type,
    aTP_Lamm_fc: fun_nat_o > fun_fu1617828088232643505_nat_o ).

tff(sy_c_ATP_058Lamm__fd____,type,
    aTP_Lamm_fd: nat > fun_na7928631014926962227_nat_o ).

tff(sy_c_ATP_058Lamm__fe____,type,
    aTP_Lamm_fe: fun_na5914473681949881652_nat_o ).

tff(sy_c_ATP_058Lamm__ff____,type,
    aTP_Lamm_ff: nat > fun_na7928631014926962227_nat_o ).

tff(sy_c_ATP_058Lamm__fg____,type,
    aTP_Lamm_fg: fun_na5914473681949881652_nat_o ).

tff(sy_c_ATP_058Lamm__fh____,type,
    aTP_Lamm_fh: fun_ar3891948820113774757rray_a > fun_ar4667500465507062749it_nat ).

tff(sy_c_ATP_058Lamm__fi____,type,
    aTP_Lamm_fi: fun_ar3891948820113774757rray_a > fun_ar7427004957847640857it_nat ).

tff(sy_c_ATP_058Lamm__fj____,type,
    aTP_Lamm_fj: fun_Pr5924905948197006361rray_a > fun_Pr2439654876356241257it_nat ).

tff(sy_c_ATP_058Lamm__fk____,type,
    aTP_Lamm_fk: fun_Pr5924905948197006361rray_a > fun_Pr2979129825601314957it_nat ).

tff(sy_c_ATP_058Lamm__fl____,type,
    aTP_Lamm_fl: fun_ar1074044450438384043t_unit > fun_ar5851962999413977351it_nat ).

tff(sy_c_ATP_058Lamm__fm____,type,
    aTP_Lamm_fm: fun_ar1074044450438384043t_unit > fun_ar4934926718671674165it_nat ).

tff(sy_c_ATP_058Lamm__fn____,type,
    aTP_Lamm_fn: fun_Pr292408699144966967t_unit > fun_Pr5739084258597601403it_nat ).

tff(sy_c_ATP_058Lamm__fo____,type,
    aTP_Lamm_fo: fun_Pr292408699144966967t_unit > fun_Pr925140355916870337it_nat ).

tff(sy_c_ATP_058Lamm__fp____,type,
    aTP_Lamm_fp: heap_T6362127782908069795rray_a > fun_fu7484024174323986552it_nat ).

tff(sy_c_ATP_058Lamm__fq____,type,
    aTP_Lamm_fq: heap_T5738788834812785303t_unit > fun_fu1080234963260751190it_nat ).

tff(sy_c_ATP_058Lamm__fr____,type,
    aTP_Lamm_fr: heap_T6362127782908069795rray_a > fun_fu5808343195260015654it_nat ).

tff(sy_c_ATP_058Lamm__fs____,type,
    aTP_Lamm_fs: heap_T5738788834812785303t_unit > fun_fu2217603491152269828it_nat ).

tff(sy_c_ATP_058Lamm__ft____,type,
    aTP_Lamm_ft: rat > fun_rat_fun_nat_rat ).

tff(sy_c_ATP_058Lamm__fu____,type,
    aTP_Lamm_fu: int > fun_int_fun_nat_int ).

tff(sy_c_ATP_058Lamm__fv____,type,
    aTP_Lamm_fv: code_integer > fun_Co6226381647958292740nteger ).

tff(sy_c_ATP_058Lamm__fw____,type,
    aTP_Lamm_fw: code_natural > fun_Co740390889742897050atural ).

tff(sy_c_ATP_058Lamm__fx____,type,
    aTP_Lamm_fx: nat > fun_nat_fun_nat_nat ).

tff(sy_c_ATP_058Lamm__fy____,type,
    aTP_Lamm_fy: nat > fun_na4143055713577223196at_nat ).

tff(sy_c_ATP_058Lamm__fz____,type,
    aTP_Lamm_fz: fun_na1668100129766719005at_nat ).

tff(sy_c_ATP_058Lamm__ga____,type,
    aTP_Lamm_ga: nat > fun_na4143055713577223196at_nat ).

tff(sy_c_ATP_058Lamm__gb____,type,
    aTP_Lamm_gb: fun_na1668100129766719005at_nat ).

tff(sy_c_ATP_058Lamm__gc____,type,
    aTP_Lamm_gc: nat > fun_na4143055713577223196at_nat ).

tff(sy_c_ATP_058Lamm__gd____,type,
    aTP_Lamm_gd: fun_na1668100129766719005at_nat ).

tff(sy_c_ATP_058Lamm__ge____,type,
    aTP_Lamm_ge: fun_na2338080690716861136at_nat > fun_na2338080690716861136at_nat ).

tff(sy_c_ATP_058Lamm__gf____,type,
    aTP_Lamm_gf: fun_nat_rat > fun_nat_rat ).

tff(sy_c_ATP_058Lamm__gg____,type,
    aTP_Lamm_gg: fun_nat_int > fun_nat_int ).

tff(sy_c_ATP_058Lamm__gh____,type,
    aTP_Lamm_gh: fun_nat_nat > fun_nat_nat ).

tff(sy_c_ATP_058Lamm__gi____,type,
    aTP_Lamm_gi: num > fun_na4138050610385705875at_nat ).

tff(sy_c_ATP_058Lamm__gj____,type,
    aTP_Lamm_gj: num > fun_in1696471567231710611nt_int ).

tff(sy_c_ATP_058Lamm__gk____,type,
    aTP_Lamm_gk: num > fun_Co2470855966376689427nteger ).

tff(sy_c_ATP_058Lamm__gl____,type,
    aTP_Lamm_gl: fun_se4097146774670233028at_nat > fun_se8406536441587994090_nat_o ).

tff(sy_c_ATP_058Lamm__gm____,type,
    aTP_Lamm_gm: fun_nat_nat > fun_se4014881416909572940_nat_o ).

tff(sy_c_ATP_058Lamm__gn____,type,
    aTP_Lamm_gn: fun_fu4810197545401214784nteger > fun_fu4530937843762191077eger_o ).

tff(sy_c_ATP_058Lamm__go____,type,
    aTP_Lamm_go: fun_fu2352890940381120596et_nat > fun_fu7582738562687708775_nat_o ).

tff(sy_c_ATP_058Lamm__gp____,type,
    aTP_Lamm_gp: fun_fu1905361174868762994et_nat > fun_fu4927615759029954091_nat_o ).

tff(sy_c_ATP_058Lamm__gq____,type,
    aTP_Lamm_gq: fun_fu4253467608928286509nt_int > fun_fu4695829907076200203_int_o ).

tff(sy_c_ATP_058Lamm__gr____,type,
    aTP_Lamm_gr: fun_fu5631754973857388633nt_int > fun_fu6286765928754279603_int_o ).

tff(sy_c_ATP_058Lamm__gs____,type,
    aTP_Lamm_gs: fun_Co2470855966376689427nteger ).

tff(sy_c_ATP_058Lamm__gt____,type,
    aTP_Lamm_gt: fun_in1696471567231710611nt_int ).

tff(sy_c_ATP_058Lamm__gu____,type,
    aTP_Lamm_gu: fun_na4138050610385705875at_nat ).

tff(sy_c_ATP_058Lamm__gv____,type,
    aTP_Lamm_gv: fun_Co2470855966376689427nteger ).

tff(sy_c_ATP_058Lamm__gw____,type,
    aTP_Lamm_gw: fun_in1696471567231710611nt_int ).

tff(sy_c_ATP_058Lamm__gx____,type,
    aTP_Lamm_gx: fun_na4138050610385705875at_nat ).

tff(sy_c_ATP_058Lamm__gy____,type,
    aTP_Lamm_gy: fun_rat_rat ).

tff(sy_c_ATP_058Lamm__gz____,type,
    aTP_Lamm_gz: fun_int_int ).

tff(sy_c_ATP_058Lamm__ha____,type,
    aTP_Lamm_ha: fun_nat_nat ).

tff(sy_c_ATP_058Lamm__hb____,type,
    aTP_Lamm_hb: fun_Co8499238673658658103nteger ).

tff(sy_c_ATP_058Lamm__hc____,type,
    aTP_Lamm_hc: fun_Co7398788559141407565atural ).

tff(sy_c_ATP_058Lamm__hd____,type,
    aTP_Lamm_hd: num > fun_num_int ).

tff(sy_c_ATP_058Lamm__he____,type,
    aTP_Lamm_he: fun_num_option_num ).

tff(sy_c_ATP_058Lamm__hf____,type,
    aTP_Lamm_hf: array_a > fun_he4035479571739904452rray_a ).

tff(sy_c_ATP_058Lamm__hg____,type,
    aTP_Lamm_hg: fun_ar6017029185804945652rray_a ).

tff(sy_c_ATP_058Lamm__hh____,type,
    aTP_Lamm_hh: product_unit > fun_he8708342781048922188t_unit ).

tff(sy_c_ATP_058Lamm__hi____,type,
    aTP_Lamm_hi: fun_Pr2049426570021530256t_unit ).

tff(sy_c_ATP_058Lamm__hj____,type,
    aTP_Lamm_hj: set_nat > fun_set_nat_o ).

tff(sy_c_ATP_058Lamm__hk____,type,
    aTP_Lamm_hk: fun_rat_fun_rat_o ).

tff(sy_c_ATP_058Lamm__hl____,type,
    aTP_Lamm_hl: fun_num_fun_num_o ).

tff(sy_c_ATP_058Lamm__hm____,type,
    aTP_Lamm_hm: fun_int_fun_int_o ).

tff(sy_c_ATP_058Lamm__hn____,type,
    aTP_Lamm_hn: fun_nat_fun_nat_o ).

tff(sy_c_ATP_058Lamm__ho____,type,
    aTP_Lamm_ho: fun_nat_Code_integer > fun_nat_Code_integer ).

tff(sy_c_ATP_058Lamm__hp____,type,
    aTP_Lamm_hp: fun_nat_rat > fun_nat_rat ).

tff(sy_c_ATP_058Lamm__hq____,type,
    aTP_Lamm_hq: fun_nat_int > fun_nat_int ).

tff(sy_c_ATP_058Lamm__hr____,type,
    aTP_Lamm_hr: fun_he6845747896722556172t_unit ).

tff(sy_c_ATP_058Lamm__hs____,type,
    aTP_Lamm_hs: fun_ar121531768175530460t_unit ).

tff(sy_c_ATP_058Lamm__ht____,type,
    aTP_Lamm_ht: fun_Pr7459525001844076368t_unit ).

tff(sy_c_ATP_058Lamm__hu____,type,
    aTP_Lamm_hu: fun_int_fun_int_int ).

tff(sy_c_ATP_058Lamm__hv____,type,
    aTP_Lamm_hv: nat > fun_nat_fun_nat_o ).

tff(sy_c_ATP_058Lamm__hw____,type,
    aTP_Lamm_hw: fun_nat_fun_nat_nat > fun_nat_fun_nat_nat ).

tff(sy_c_ATP_058Lamm__hx____,type,
    aTP_Lamm_hx: fun_nat_fun_nat_nat > fun_nat_nat ).

tff(sy_c_ATP_058Lamm__hy____,type,
    aTP_Lamm_hy: nat > fun_fu6327154928193479288nteger ).

tff(sy_c_ATP_058Lamm__hz____,type,
    aTP_Lamm_hz: nat > fun_fu6327154928193479288nteger ).

tff(sy_c_ATP_058Lamm__ia____,type,
    aTP_Lamm_ia: nat > fun_fu695563712076452518at_nat ).

tff(sy_c_ATP_058Lamm__ib____,type,
    aTP_Lamm_ib: nat > fun_fu695563712076452518at_nat ).

tff(sy_c_ATP_058Lamm__ic____,type,
    aTP_Lamm_ic: nat > fun_fu6579618355643354601at_rat ).

tff(sy_c_ATP_058Lamm__id____,type,
    aTP_Lamm_id: nat > fun_fu6579618355643354601at_rat ).

tff(sy_c_ATP_058Lamm__ie____,type,
    aTP_Lamm_ie: nat > fun_fu960360787657196261at_int ).

tff(sy_c_ATP_058Lamm__if____,type,
    aTP_Lamm_if: nat > fun_fu960360787657196261at_int ).

tff(sy_c_ATP_058Lamm__ig____,type,
    aTP_Lamm_ig: nat > fun_fu5935951186182374353at_nat ).

tff(sy_c_ATP_058Lamm__ih____,type,
    aTP_Lamm_ih: nat > fun_fu5935951186182374353at_nat ).

tff(sy_c_ATP_058Lamm__ii____,type,
    aTP_Lamm_ii: rat > fun_nat_rat ).

tff(sy_c_ATP_058Lamm__ij____,type,
    aTP_Lamm_ij: fun_num_option_num ).

tff(sy_c_ATP_058Lamm__ik____,type,
    aTP_Lamm_ik: rat > fun_nat_rat ).

tff(sy_c_ATP_058Lamm__il____,type,
    aTP_Lamm_il: rat > fun_nat_rat ).

tff(sy_c_ATP_058Lamm__im____,type,
    aTP_Lamm_im: nat > fun_nat_rat ).

tff(sy_c_ATP_058Lamm__in____,type,
    aTP_Lamm_in: nat > fun_ra8505079968215247908at_rat ).

tff(sy_c_ATP_058Lamm__io____,type,
    aTP_Lamm_io: nat > fun_ra8505079968215247908at_rat ).

tff(sy_c_ATP_058Lamm__ip____,type,
    aTP_Lamm_ip: nat > fun_ra8505079968215247908at_rat ).

tff(sy_c_ATP_058Lamm__iq____,type,
    aTP_Lamm_iq: nat > fun_nat_rat ).

tff(sy_c_ATP_058Lamm__ir____,type,
    aTP_Lamm_ir: rat > fun_nat_fun_rat_rat ).

tff(sy_c_ATP_058Lamm__is____,type,
    aTP_Lamm_is: nat > fun_nat_rat ).

tff(sy_c_ATP_058Lamm__it____,type,
    aTP_Lamm_it: fun_nat_fun_nat_int ).

tff(sy_c_ATP_058Lamm__iu____,type,
    aTP_Lamm_iu: nat > fun_nat_Code_integer ).

tff(sy_c_ATP_058Lamm__iv____,type,
    aTP_Lamm_iv: fun_nat_fun_nat_nat ).

tff(sy_c_ATP_058Lamm__iw____,type,
    aTP_Lamm_iw: nat > fun_nat_fun_nat_o ).

tff(sy_c_ATP_058Lamm__ix____,type,
    aTP_Lamm_ix: fun_nat_nat > fun_nat_fun_nat_nat ).

tff(sy_c_ATP_058Lamm__iy____,type,
    aTP_Lamm_iy: fun_nat_nat > fun_fu7002938529518989751at_nat ).

tff(sy_c_ATP_058Lamm__iz____,type,
    aTP_Lamm_iz: fun_nat_fun_nat_nat > fun_nat_nat ).

tff(sy_c_ATP_058Lamm__ja____,type,
    aTP_Lamm_ja: fun_nat_fun_nat_nat > fun_nat_fun_nat_nat ).

tff(sy_c_ATP_058Lamm__jb____,type,
    aTP_Lamm_jb: fun_nat_fun_nat_nat > fun_nat_fun_nat_nat ).

tff(sy_c_ATP_058Lamm__jc____,type,
    aTP_Lamm_jc: fun_nat_fun_nat_nat ).

tff(sy_c_ATP_058Lamm__jd____,type,
    aTP_Lamm_jd: fun_nat_fun_nat_nat ).

tff(sy_c_ATP_058Lamm__je____,type,
    aTP_Lamm_je: nat > fun_na3244735409550470327at_nat ).

tff(sy_c_ATP_058Lamm__jf____,type,
    aTP_Lamm_jf: code_integer > fun_na8856381646659805649nteger ).

tff(sy_c_ATP_058Lamm__jg____,type,
    aTP_Lamm_jg: rat > fun_na1148497095348402375at_rat ).

tff(sy_c_ATP_058Lamm__jh____,type,
    aTP_Lamm_jh: int > fun_na2382631619178260847at_int ).

tff(sy_c_ATP_058Lamm__ji____,type,
    aTP_Lamm_ji: code_integer > fun_na8856381646659805649nteger ).

tff(sy_c_ATP_058Lamm__jj____,type,
    aTP_Lamm_jj: rat > fun_na1148497095348402375at_rat ).

tff(sy_c_ATP_058Lamm__jk____,type,
    aTP_Lamm_jk: int > fun_na2382631619178260847at_int ).

tff(sy_c_ATP_058Lamm__jl____,type,
    aTP_Lamm_jl: nat > fun_na3244735409550470327at_nat ).

tff(sy_c_ATP_058Lamm__jm____,type,
    aTP_Lamm_jm: code_integer > fun_na8135612474337863287nteger ).

tff(sy_c_ATP_058Lamm__jn____,type,
    aTP_Lamm_jn: rat > fun_nat_fun_nat_rat ).

tff(sy_c_ATP_058Lamm__jo____,type,
    aTP_Lamm_jo: int > fun_nat_fun_nat_int ).

tff(sy_c_ATP_058Lamm__jp____,type,
    aTP_Lamm_jp: rat > fun_ra5513060666784058567at_rat ).

tff(sy_c_ATP_058Lamm__jq____,type,
    aTP_Lamm_jq: int > fun_in6793278964266839919at_int ).

tff(sy_c_ATP_058Lamm__jr____,type,
    aTP_Lamm_jr: code_integer > fun_Co5080488584548667985nteger ).

tff(sy_c_ATP_058Lamm__js____,type,
    aTP_Lamm_js: code_natural > fun_Co200561849269645671atural ).

tff(sy_c_ATP_058Lamm__jt____,type,
    aTP_Lamm_jt: nat > fun_nat_rat ).

tff(sy_c_ATP_058Lamm__ju____,type,
    aTP_Lamm_ju: fun_nat_fun_nat_int ).

tff(sy_c_ATP_058Lamm__jv____,type,
    aTP_Lamm_jv: nat > fun_nat_Code_integer ).

tff(sy_c_ATP_058Lamm__jw____,type,
    aTP_Lamm_jw: rat > fun_nat_fun_rat_rat ).

tff(sy_c_ATP_058Lamm__jx____,type,
    aTP_Lamm_jx: int > fun_nat_fun_int_int ).

tff(sy_c_ATP_058Lamm__jy____,type,
    aTP_Lamm_jy: code_integer > fun_na7078387940644931716nteger ).

tff(sy_c_ATP_058Lamm__jz____,type,
    aTP_Lamm_jz: code_natural > fun_na607345901702507418atural ).

tff(sy_c_ATP_058Lamm__ka____,type,
    aTP_Lamm_ka: nat > fun_nat_fun_nat_nat ).

tff(sy_c_ATP_058Lamm__kb____,type,
    aTP_Lamm_kb: fun_Co8521658056209057742er_num ).

tff(sy_c_ATP_058Lamm__kc____,type,
    aTP_Lamm_kc: fun_nat_nat > fun_na3244735409550470327at_nat ).

tff(sy_c_ATP_058Lamm__kd____,type,
    aTP_Lamm_kd: fun_nat_fun_nat_nat > fun_nat_nat ).

tff(sy_c_ATP_058Lamm__ke____,type,
    aTP_Lamm_ke: fun_nat_nat > fun_nat_fun_nat_nat ).

tff(sy_c_ATP_058Lamm__kf____,type,
    aTP_Lamm_kf: rat > fun_ra5513060666784058567at_rat ).

tff(sy_c_ATP_058Lamm__kg____,type,
    aTP_Lamm_kg: int > fun_in6793278964266839919at_int ).

tff(sy_c_ATP_058Lamm__kh____,type,
    aTP_Lamm_kh: code_integer > fun_Co5080488584548667985nteger ).

tff(sy_c_ATP_058Lamm__ki____,type,
    aTP_Lamm_ki: fun_Co3583066429914935172er_nat ).

tff(sy_c_ATP_058Lamm__kj____,type,
    aTP_Lamm_kj: rat > fun_nat_rat ).

tff(sy_c_ATP_058Lamm__kk____,type,
    aTP_Lamm_kk: fun_Co1092983284983208416er_int ).

tff(sy_c_ATP_058Lamm__kl____,type,
    aTP_Lamm_kl: code_integer > fun_Co2470855966376689427nteger ).

tff(sy_c_ATP_058Lamm__km____,type,
    aTP_Lamm_km: fun_he5369522480449343229at_nat ).

tff(sy_c_ATP_058Lamm__kn____,type,
    aTP_Lamm_kn: fun_ar8857663332695973421at_nat ).

tff(sy_c_ATP_058Lamm__ko____,type,
    aTP_Lamm_ko: fun_Pr3587966566883452857at_nat ).

tff(sy_c_ATP_058Lamm__kp____,type,
    aTP_Lamm_kp: fun_nat_nat ).

tff(sy_c_ATP_058Lamm__kq____,type,
    aTP_Lamm_kq: fun_nat_int ).

tff(sy_c_ATP_058Lamm__kr____,type,
    aTP_Lamm_kr: fun_int_int ).

tff(sy_c_ATP_058Lamm__ks____,type,
    aTP_Lamm_ks: fun_nat_int > fun_nat_fun_nat_int ).

tff(sy_c_ATP_058Lamm__kt____,type,
    aTP_Lamm_kt: fun_nat_int > fun_na7654559027617327379at_int ).

tff(sy_c_ATP_058Lamm__ku____,type,
    aTP_Lamm_ku: fun_nat_int > fun_nat_fun_nat_int ).

tff(sy_c_ATP_058Lamm__kv____,type,
    aTP_Lamm_kv: fun_nat_assn > fun_nat_assn ).

tff(sy_c_ATP_058Lamm__kw____,type,
    aTP_Lamm_kw: fun_nat_int > fun_na7654559027617327379at_int ).

tff(sy_c_ATP_058Lamm__kx____,type,
    aTP_Lamm_kx: fun_nat_fun_nat_nat > fun_nat_nat ).

tff(sy_c_ATP_058Lamm__ky____,type,
    aTP_Lamm_ky: fun_nat_fun_nat_nat > fun_nat_fun_nat_nat ).

tff(sy_c_ATP_058Lamm__kz____,type,
    aTP_Lamm_kz: fun_nat_fun_nat_int > fun_nat_int ).

tff(sy_c_ATP_058Lamm__la____,type,
    aTP_Lamm_la: fun_nat_fun_nat_int > fun_nat_fun_nat_int ).

tff(sy_c_ATP_058Lamm__lb____,type,
    aTP_Lamm_lb: fun_nat_fun_nat_int > fun_nat_fun_nat_int ).

tff(sy_c_ATP_058Lamm__lc____,type,
    aTP_Lamm_lc: fun_nat_nat > fun_nat_fun_nat_nat ).

tff(sy_c_ATP_058Lamm__ld____,type,
    aTP_Lamm_ld: fun_nat_int > fun_nat_fun_nat_int ).

tff(sy_c_ATP_058Lamm__le____,type,
    aTP_Lamm_le: fun_nat_fun_nat_nat > fun_nat_nat ).

tff(sy_c_ATP_058Lamm__lf____,type,
    aTP_Lamm_lf: fun_nat_fun_nat_int > fun_nat_int ).

tff(sy_c_ATP_058Lamm__lg____,type,
    aTP_Lamm_lg: fun_nat_Code_integer > fun_na7078387940644931716nteger ).

tff(sy_c_ATP_058Lamm__lh____,type,
    aTP_Lamm_lh: fun_nat_assn > fun_na2454419004871237530n_assn ).

tff(sy_c_ATP_058Lamm__li____,type,
    aTP_Lamm_li: fun_nat_rat > fun_nat_fun_rat_rat ).

tff(sy_c_ATP_058Lamm__lj____,type,
    aTP_Lamm_lj: fun_nat_nat > fun_nat_fun_nat_nat ).

tff(sy_c_ATP_058Lamm__lk____,type,
    aTP_Lamm_lk: fun_nat_int > fun_nat_fun_int_int ).

tff(sy_c_ATP_058Lamm__ll____,type,
    aTP_Lamm_ll: rat > fun_nat_rat ).

tff(sy_c_ATP_058Lamm__lm____,type,
    aTP_Lamm_lm: code_integer > fun_nat_Code_integer ).

tff(sy_c_ATP_058Lamm__ln____,type,
    aTP_Lamm_ln: code_natural > fun_nat_Code_natural ).

tff(sy_c_ATP_058Lamm__lo____,type,
    aTP_Lamm_lo: fun_nat_fun_nat_nat ).

tff(sy_c_ATP_058Lamm__lp____,type,
    aTP_Lamm_lp: int > fun_nat_int ).

tff(sy_c_ATP_058Lamm__lq____,type,
    aTP_Lamm_lq: rat > fun_nat_fun_nat_rat ).

tff(sy_c_ATP_058Lamm__lr____,type,
    aTP_Lamm_lr: code_integer > fun_na8135612474337863287nteger ).

tff(sy_c_ATP_058Lamm__ls____,type,
    aTP_Lamm_ls: code_natural > fun_na3365689438791330114atural ).

tff(sy_c_ATP_058Lamm__lt____,type,
    aTP_Lamm_lt: nat > fun_nat_fun_nat_nat ).

tff(sy_c_ATP_058Lamm__lu____,type,
    aTP_Lamm_lu: int > fun_nat_fun_nat_int ).

tff(sy_c_ATP_058Lamm__lv____,type,
    aTP_Lamm_lv: fun_nat_assn > fun_nat_assn ).

tff(sy_c_ATP_058Lamm__lw____,type,
    aTP_Lamm_lw: fun_nat_rat > fun_nat_rat ).

tff(sy_c_ATP_058Lamm__lx____,type,
    aTP_Lamm_lx: fun_nat_nat > fun_nat_nat ).

tff(sy_c_ATP_058Lamm__ly____,type,
    aTP_Lamm_ly: fun_nat_int > fun_nat_int ).

tff(sy_c_ATP_058Lamm__lz____,type,
    aTP_Lamm_lz: code_integer > fun_Co2470855966376689427nteger ).

tff(sy_c_ATP_058Lamm__ma____,type,
    aTP_Lamm_ma: code_integer > fun_Co2470855966376689427nteger ).

tff(sy_c_ATP_058Lamm__mb____,type,
    aTP_Lamm_mb: code_integer > fun_Co3544761417380347684eger_o ).

tff(sy_c_ATP_058Lamm__mc____,type,
    aTP_Lamm_mc: nat > fun_fu6327154928193479288nteger ).

tff(sy_c_ATP_058Lamm__md____,type,
    aTP_Lamm_md: nat > fun_fu3959123160307459545t_assn ).

tff(sy_c_ATP_058Lamm__me____,type,
    aTP_Lamm_me: nat > fun_fu3959123160307459545t_assn ).

tff(sy_c_ATP_058Lamm__mf____,type,
    aTP_Lamm_mf: nat > fun_fu6579618355643354601at_rat ).

tff(sy_c_ATP_058Lamm__mg____,type,
    aTP_Lamm_mg: nat > fun_fu5935951186182374353at_nat ).

tff(sy_c_ATP_058Lamm__mh____,type,
    aTP_Lamm_mh: nat > fun_fu960360787657196261at_int ).

tff(sy_c_ATP_058Lamm__mi____,type,
    aTP_Lamm_mi: nat > fun_num_option_num ).

tff(sy_c_ATP_058Lamm__mj____,type,
    aTP_Lamm_mj: nat > fun_num_option_num ).

tff(sy_c_ATP_058Lamm__mk____,type,
    aTP_Lamm_mk: num > fun_nat_option_num ).

tff(sy_c_ATP_058Lamm__ml____,type,
    aTP_Lamm_ml: fun_na7595719129879163854on_num ).

tff(sy_c_ATP_058Lamm__mm____,type,
    aTP_Lamm_mm: fun_nat_fun_nat_nat > fun_nat_nat ).

tff(sy_c_ATP_058Lamm__mn____,type,
    aTP_Lamm_mn: fun_nat_fun_nat_int > fun_nat_fun_nat_int ).

tff(sy_c_ATP_058Lamm__mo____,type,
    aTP_Lamm_mo: fun_nat_fun_nat_int > fun_nat_int ).

tff(sy_c_ATP_058Lamm__mp____,type,
    aTP_Lamm_mp: rat > fun_rat_rat ).

tff(sy_c_ATP_058Lamm__mq____,type,
    aTP_Lamm_mq: fun_int_fun_int_int ).

tff(sy_c_ATP_058Lamm__mr____,type,
    aTP_Lamm_mr: fun_nat_fun_nat_nat ).

tff(sy_c_ATP_058Lamm__ms____,type,
    aTP_Lamm_ms: fun_Co1981900195452921617nteger ).

tff(sy_c_ATP_058Lamm__mt____,type,
    aTP_Lamm_mt: rat > fun_rat_rat ).

tff(sy_c_ATP_058Lamm__mu____,type,
    aTP_Lamm_mu: fun_int_fun_int_int ).

tff(sy_c_ATP_058Lamm__mv____,type,
    aTP_Lamm_mv: fun_Co1981900195452921617nteger ).

tff(sy_c_ATP_058Lamm__mw____,type,
    aTP_Lamm_mw: rat > fun_rat_rat ).

tff(sy_c_ATP_058Lamm__mx____,type,
    aTP_Lamm_mx: int > fun_in2204242111582549184nt_int ).

tff(sy_c_ATP_058Lamm__my____,type,
    aTP_Lamm_my: rat > fun_in1696471567231710611nt_int ).

tff(sy_c_ATP_058Lamm__mz____,type,
    aTP_Lamm_mz: int > fun_in2204242111582549184nt_int ).

tff(sy_c_ATP_058Lamm__na____,type,
    aTP_Lamm_na: rat > fun_in1696471567231710611nt_int ).

tff(sy_c_ATP_058Lamm__nb____,type,
    aTP_Lamm_nb: fun_in1696471567231710611nt_int ).

tff(sy_c_ATP_058Lamm__nc____,type,
    aTP_Lamm_nc: fun_in1696471567231710611nt_int ).

tff(sy_c_ATP_058Lamm__nd____,type,
    aTP_Lamm_nd: int > fun_in2204242111582549184nt_int ).

tff(sy_c_ATP_058Lamm__ne____,type,
    aTP_Lamm_ne: rat > fun_in1696471567231710611nt_int ).

tff(sy_c_ATP_058Lamm__nf____,type,
    aTP_Lamm_nf: int > fun_in2204242111582549184nt_int ).

tff(sy_c_ATP_058Lamm__ng____,type,
    aTP_Lamm_ng: rat > fun_in1696471567231710611nt_int ).

tff(sy_c_ATP_058Lamm__nh____,type,
    aTP_Lamm_nh: fun_in1696471567231710611nt_int ).

tff(sy_c_ATP_058Lamm__ni____,type,
    aTP_Lamm_ni: fun_int_int ).

tff(sy_c_ATP_058Lamm__nj____,type,
    aTP_Lamm_nj: rat > fun_rat_fun_rat_rat ).

tff(sy_c_ATP_058Lamm__nk____,type,
    aTP_Lamm_nk: rat > fun_rat_fun_rat_rat ).

tff(sy_c_ATP_058Lamm__nl____,type,
    aTP_Lamm_nl: rat > fun_rat_fun_rat_rat ).

tff(sy_c_ATP_058Lamm__nm____,type,
    aTP_Lamm_nm: fun_se5244420045238757833at_nat ).

tff(sy_c_ATP_058Lamm__nn____,type,
    aTP_Lamm_nn: fun_nat_option_nat ).

tff(sy_c_ATP_058Lamm__no____,type,
    aTP_Lamm_no: rat > fun_rat_rat ).

tff(sy_c_ATP_058Lamm__np____,type,
    aTP_Lamm_np: rat > fun_rat_fun_rat_rat ).

tff(sy_c_ATP_058Lamm__nq____,type,
    aTP_Lamm_nq: fun_o_o ).

tff(sy_c_ATP_058Lamm__nr____,type,
    aTP_Lamm_nr: fun_num_fun_num_int ).

tff(sy_c_ATP_058Lamm__ns____,type,
    aTP_Lamm_ns: fun_nat_fun_nat_nat ).

tff(sy_c_ATP_058Lamm__nt____,type,
    aTP_Lamm_nt: fun_nat_fun_nat_nat ).

tff(sy_c_ATP_058Lamm__nu____,type,
    aTP_Lamm_nu: set_op3940070208846178154it_nat > fun_op4751157287140997969_nat_o ).

tff(sy_c_ATP_058Lamm__nv____,type,
    aTP_Lamm_nv: set_option_num > fun_option_num_o ).

tff(sy_c_ATP_058Lamm__nw____,type,
    aTP_Lamm_nw: set_op239864471688321678it_nat > fun_op479301348043730329_nat_o ).

tff(sy_c_ATP_058Lamm__nx____,type,
    aTP_Lamm_nx: $o > fun_fu2786480252100984515nteger ).

tff(sy_c_ATP_058Lamm__ny____,type,
    aTP_Lamm_ny: nat > fun_fu2499394402704830801nteger ).

tff(sy_c_ATP_058Lamm__nz____,type,
    aTP_Lamm_nz: int > fun_fu3628599891403802633nteger ).

tff(sy_c_ATP_058Lamm__oa____,type,
    aTP_Lamm_oa: code_integer > fun_fu1763652423599918571nteger ).

tff(sy_c_ATP_058Lamm__ob____,type,
    aTP_Lamm_ob: $o > fun_fu704708528062463619o_assn ).

tff(sy_c_ATP_058Lamm__oc____,type,
    aTP_Lamm_oc: nat > fun_fu2995346897264222311t_assn ).

tff(sy_c_ATP_058Lamm__od____,type,
    aTP_Lamm_od: int > fun_fu6568868615275847455t_assn ).

tff(sy_c_ATP_058Lamm__oe____,type,
    aTP_Lamm_oe: code_integer > fun_fu5082522747898945281r_assn ).

tff(sy_c_ATP_058Lamm__of____,type,
    aTP_Lamm_of: $o > fun_fu1989461620956114563_o_rat ).

tff(sy_c_ATP_058Lamm__og____,type,
    aTP_Lamm_og: nat > fun_fu8328862064278946247at_rat ).

tff(sy_c_ATP_058Lamm__oh____,type,
    aTP_Lamm_oh: $o > fun_fu2786480252100984515nteger ).

tff(sy_c_ATP_058Lamm__oi____,type,
    aTP_Lamm_oi: nat > fun_fu2499394402704830801nteger ).

tff(sy_c_ATP_058Lamm__oj____,type,
    aTP_Lamm_oj: int > fun_fu3628599891403802633nteger ).

tff(sy_c_ATP_058Lamm__ok____,type,
    aTP_Lamm_ok: code_integer > fun_fu1763652423599918571nteger ).

tff(sy_c_ATP_058Lamm__ol____,type,
    aTP_Lamm_ol: $o > fun_fu704708528062463619o_assn ).

tff(sy_c_ATP_058Lamm__om____,type,
    aTP_Lamm_om: nat > fun_fu2995346897264222311t_assn ).

tff(sy_c_ATP_058Lamm__on____,type,
    aTP_Lamm_on: int > fun_fu6568868615275847455t_assn ).

tff(sy_c_ATP_058Lamm__oo____,type,
    aTP_Lamm_oo: code_integer > fun_fu5082522747898945281r_assn ).

tff(sy_c_ATP_058Lamm__op____,type,
    aTP_Lamm_op: $o > fun_fu1989461620956114563_o_rat ).

tff(sy_c_ATP_058Lamm__oq____,type,
    aTP_Lamm_oq: nat > fun_fu8328862064278946247at_rat ).

tff(sy_c_ATP_058Lamm__or____,type,
    aTP_Lamm_or: set_int > fun_se2051630309975736070_int_o ).

tff(sy_c_ATP_058Lamm__os____,type,
    aTP_Lamm_os: set_Code_integer > fun_se5529282185252607396eger_o ).

tff(sy_c_ATP_058Lamm__ot____,type,
    aTP_Lamm_ot: set_Pr1261947904930325089at_nat > fun_se5639961202347202350_nat_o ).

tff(sy_c_ATP_058Lamm__ou____,type,
    aTP_Lamm_ou: set_nat > fun_se2170385732985038782_nat_o ).

tff(sy_c_ATP_058Lamm__ov____,type,
    aTP_Lamm_ov: fun_nat_o > fun_nat_fun_nat_o ).

tff(sy_c_ATP_058Lamm__ow____,type,
    aTP_Lamm_ow: fun_nat_nat > fun_nat_fun_nat_o ).

tff(sy_c_ATP_058Lamm__ox____,type,
    aTP_Lamm_ox: set_o > fun_fu3819205551299168222un_o_o ).

tff(sy_c_ATP_058Lamm__oy____,type,
    aTP_Lamm_oy: set_o > fun_fu8716660765737269145un_o_o ).

tff(sy_c_ATP_058Lamm__oz____,type,
    aTP_Lamm_oz: set_nat > fun_fu5838931486547983824_nat_o ).

tff(sy_c_ATP_058Lamm__pa____,type,
    aTP_Lamm_pa: set_nat > fun_fu8532066432991188095_nat_o ).

tff(sy_c_ATP_058Lamm__pb____,type,
    aTP_Lamm_pb: set_int > fun_fu5271299750659287320_int_o ).

tff(sy_c_ATP_058Lamm__pc____,type,
    aTP_Lamm_pc: set_int > fun_fu63825462011493995_int_o ).

tff(sy_c_ATP_058Lamm__pd____,type,
    aTP_Lamm_pd: set_Code_integer > fun_fu855086506144988854eger_o ).

tff(sy_c_ATP_058Lamm__pe____,type,
    aTP_Lamm_pe: set_Code_integer > fun_fu4083202260958266008eger_o ).

tff(sy_c_ATP_058Lamm__pf____,type,
    aTP_Lamm_pf: set_o > fun_fu6337961365400742745un_o_o ).

tff(sy_c_ATP_058Lamm__pg____,type,
    aTP_Lamm_pg: set_o > fun_fu2641566564518291801un_o_o ).

tff(sy_c_ATP_058Lamm__ph____,type,
    aTP_Lamm_ph: set_nat > fun_fu7145897819039579925_nat_o ).

tff(sy_c_ATP_058Lamm__pi____,type,
    aTP_Lamm_pi: set_nat > fun_fu1806770557662746761_nat_o ).

tff(sy_c_ATP_058Lamm__pj____,type,
    aTP_Lamm_pj: set_int > fun_fu3473604023002724957_int_o ).

tff(sy_c_ATP_058Lamm__pk____,type,
    aTP_Lamm_pk: set_int > fun_fu7714913403879666293_int_o ).

tff(sy_c_ATP_058Lamm__pl____,type,
    aTP_Lamm_pl: set_Code_integer > fun_fu4523568072766896123eger_o ).

tff(sy_c_ATP_058Lamm__pm____,type,
    aTP_Lamm_pm: set_Code_integer > fun_fu7141499545569947298eger_o ).

tff(sy_c_ATP_058Lamm__pn____,type,
    aTP_Lamm_pn: set_o > fun_fu6781074197733401937un_o_o ).

tff(sy_c_ATP_058Lamm__po____,type,
    aTP_Lamm_po: set_o > fun_fu5915781709770235737un_o_o ).

tff(sy_c_ATP_058Lamm__pp____,type,
    aTP_Lamm_pp: set_nat > fun_fu5477517762487726877_nat_o ).

tff(sy_c_ATP_058Lamm__pq____,type,
    aTP_Lamm_pq: set_nat > fun_fu6075382464776002713_nat_o ).

tff(sy_c_ATP_058Lamm__pr____,type,
    aTP_Lamm_pr: set_o > fun_fu3819205551299168222un_o_o ).

tff(sy_c_ATP_058Lamm__ps____,type,
    aTP_Lamm_ps: set_o > fun_fu8716660765737269145un_o_o ).

tff(sy_c_ATP_058Lamm__pt____,type,
    aTP_Lamm_pt: set_nat > fun_fu5838931486547983824_nat_o ).

tff(sy_c_ATP_058Lamm__pu____,type,
    aTP_Lamm_pu: set_nat > fun_fu8532066432991188095_nat_o ).

tff(sy_c_ATP_058Lamm__pv____,type,
    aTP_Lamm_pv: set_int > fun_fu5271299750659287320_int_o ).

tff(sy_c_ATP_058Lamm__pw____,type,
    aTP_Lamm_pw: set_int > fun_fu63825462011493995_int_o ).

tff(sy_c_ATP_058Lamm__px____,type,
    aTP_Lamm_px: set_Code_integer > fun_fu855086506144988854eger_o ).

tff(sy_c_ATP_058Lamm__py____,type,
    aTP_Lamm_py: set_Code_integer > fun_fu4083202260958266008eger_o ).

tff(sy_c_ATP_058Lamm__pz____,type,
    aTP_Lamm_pz: set_o > fun_fu3143923321121214633un_o_o ).

tff(sy_c_ATP_058Lamm__qa____,type,
    aTP_Lamm_qa: set_o > fun_fu5861359551626625881un_o_o ).

tff(sy_c_ATP_058Lamm__qb____,type,
    aTP_Lamm_qb: set_nat > fun_fu1116345184836134341_nat_o ).

tff(sy_c_ATP_058Lamm__qc____,type,
    aTP_Lamm_qc: set_nat > fun_fu3109912920687205353_nat_o ).

tff(sy_c_ATP_058Lamm__qd____,type,
    aTP_Lamm_qd: set_int > fun_fu2934462529731303693_int_o ).

tff(sy_c_ATP_058Lamm__qe____,type,
    aTP_Lamm_qe: set_int > fun_fu607692679349591509_int_o ).

tff(sy_c_ATP_058Lamm__qf____,type,
    aTP_Lamm_qf: set_Code_integer > fun_fu4844139638962010283eger_o ).

tff(sy_c_ATP_058Lamm__qg____,type,
    aTP_Lamm_qg: set_Code_integer > fun_fu4735791719682850818eger_o ).

tff(sy_c_ATP_058Lamm__qh____,type,
    aTP_Lamm_qh: set_o > fun_fu6337961365400742745un_o_o ).

tff(sy_c_ATP_058Lamm__qi____,type,
    aTP_Lamm_qi: set_o > fun_fu2641566564518291801un_o_o ).

tff(sy_c_ATP_058Lamm__qj____,type,
    aTP_Lamm_qj: set_nat > fun_fu7145897819039579925_nat_o ).

tff(sy_c_ATP_058Lamm__qk____,type,
    aTP_Lamm_qk: set_nat > fun_fu1806770557662746761_nat_o ).

tff(sy_c_ATP_058Lamm__ql____,type,
    aTP_Lamm_ql: fun_int_nat ).

tff(sy_c_ATP_058Lamm__qm____,type,
    aTP_Lamm_qm: fun_Product_unit_nat ).

tff(sy_c_ATP_058Lamm__qn____,type,
    aTP_Lamm_qn: fun_list_nat_nat ).

tff(sy_c_ATP_058Lamm__qo____,type,
    aTP_Lamm_qo: set_o > fun_fun_o_o_fun_o_o ).

tff(sy_c_ATP_058Lamm__qp____,type,
    aTP_Lamm_qp: fun_o_Code_integer > fun_fu7181763470137098718nteger ).

tff(sy_c_ATP_058Lamm__qq____,type,
    aTP_Lamm_qq: set_nat > fun_fu4001317426178549763_nat_o ).

tff(sy_c_ATP_058Lamm__qr____,type,
    aTP_Lamm_qr: fun_nat_Code_integer > fun_fu7898940055406642654nteger ).

tff(sy_c_ATP_058Lamm__qs____,type,
    aTP_Lamm_qs: set_int > fun_fu3883539188510166275_int_o ).

tff(sy_c_ATP_058Lamm__qt____,type,
    aTP_Lamm_qt: fun_int_Code_integer > fun_fu6361890901329191134nteger ).

tff(sy_c_ATP_058Lamm__qu____,type,
    aTP_Lamm_qu: set_Code_integer > fun_fu8094397175230428611eger_o ).

tff(sy_c_ATP_058Lamm__qv____,type,
    aTP_Lamm_qv: fun_Co8499238673658658103nteger > fun_fu2729256655946442782nteger ).

tff(sy_c_ATP_058Lamm__qw____,type,
    aTP_Lamm_qw: fun_o_assn > fun_fu7714003655882793385o_assn ).

tff(sy_c_ATP_058Lamm__qx____,type,
    aTP_Lamm_qx: fun_nat_assn > fun_fu2792963925203051945t_assn ).

tff(sy_c_ATP_058Lamm__qy____,type,
    aTP_Lamm_qy: fun_int_assn > fun_fu2048648494261043369t_assn ).

tff(sy_c_ATP_058Lamm__qz____,type,
    aTP_Lamm_qz: fun_Co4490034186337852034r_assn > fun_fu1898041513128675305r_assn ).

tff(sy_c_ATP_058Lamm__ra____,type,
    aTP_Lamm_ra: fun_o_rat > fun_fu830079035465870425_o_rat ).

tff(sy_c_ATP_058Lamm__rb____,type,
    aTP_Lamm_rb: fun_nat_rat > fun_fu3162257917499486297at_rat ).

tff(sy_c_ATP_058Lamm__rc____,type,
    aTP_Lamm_rc: $o > fun_fu1324339541976909620o_assn ).

tff(sy_c_ATP_058Lamm__rd____,type,
    aTP_Lamm_rd: product_unit > fun_fu7405491065986884212t_assn ).

tff(sy_c_ATP_058Lamm__re____,type,
    aTP_Lamm_re: nat > fun_fu1995072252941043084t_assn ).

tff(sy_c_ATP_058Lamm__rf____,type,
    aTP_Lamm_rf: int > fun_fu4482299812767249988t_assn ).

tff(sy_c_ATP_058Lamm__rg____,type,
    aTP_Lamm_rg: code_integer > fun_fu717556231145110950r_assn ).

tff(sy_c_ATP_058Lamm__rh____,type,
    aTP_Lamm_rh: $o > fun_fu8716238685137547908_o_rat ).

tff(sy_c_ATP_058Lamm__ri____,type,
    aTP_Lamm_ri: product_unit > fun_fu1171974497074579908it_rat ).

tff(sy_c_ATP_058Lamm__rj____,type,
    aTP_Lamm_rj: nat > fun_fu4710970720072501148at_rat ).

tff(sy_c_ATP_058Lamm__rk____,type,
    aTP_Lamm_rk: int > fun_fu114989186063767636nt_rat ).

tff(sy_c_ATP_058Lamm__rl____,type,
    aTP_Lamm_rl: code_integer > fun_fu3744699754670041014er_rat ).

tff(sy_c_ATP_058Lamm__rm____,type,
    aTP_Lamm_rm: fun_int_nat > fun_int_nat ).

tff(sy_c_ATP_058Lamm__rn____,type,
    aTP_Lamm_rn: fun_Product_unit_nat > fun_Product_unit_nat ).

tff(sy_c_ATP_058Lamm__ro____,type,
    aTP_Lamm_ro: fun_list_nat_nat > fun_list_nat_nat ).

tff(sy_c_ATP_058Lamm__rp____,type,
    aTP_Lamm_rp: fun_nat_nat > fun_nat_nat ).

tff(sy_c_ATP_058Lamm__rq____,type,
    aTP_Lamm_rq: fun_int_Code_integer > fun_int_o ).

tff(sy_c_ATP_058Lamm__rr____,type,
    aTP_Lamm_rr: fun_Co8499238673658658103nteger > fun_Code_integer_o ).

tff(sy_c_ATP_058Lamm__rs____,type,
    aTP_Lamm_rs: fun_int_assn > fun_int_o ).

tff(sy_c_ATP_058Lamm__rt____,type,
    aTP_Lamm_rt: fun_Co4490034186337852034r_assn > fun_Code_integer_o ).

tff(sy_c_ATP_058Lamm__ru____,type,
    aTP_Lamm_ru: fun_int_rat > fun_int_o ).

tff(sy_c_ATP_058Lamm__rv____,type,
    aTP_Lamm_rv: fun_Code_integer_rat > fun_Code_integer_o ).

tff(sy_c_ATP_058Lamm__rw____,type,
    aTP_Lamm_rw: fun_int_nat > fun_int_o ).

tff(sy_c_ATP_058Lamm__rx____,type,
    aTP_Lamm_rx: fun_Code_integer_nat > fun_Code_integer_o ).

tff(sy_c_ATP_058Lamm__ry____,type,
    aTP_Lamm_ry: fun_Code_integer_int > fun_Code_integer_o ).

tff(sy_c_ATP_058Lamm__rz____,type,
    aTP_Lamm_rz: fun_nat_Code_integer > fun_nat_o ).

tff(sy_c_ATP_058Lamm__sa____,type,
    aTP_Lamm_sa: code_integer > fun_fu8767785434844327952er_rat ).

tff(sy_c_ATP_058Lamm__sb____,type,
    aTP_Lamm_sb: code_integer > fun_fu2498091903632033272er_nat ).

tff(sy_c_ATP_058Lamm__sc____,type,
    aTP_Lamm_sc: code_integer > fun_fu1007793439646807308er_int ).

tff(sy_c_ATP_058Lamm__sd____,type,
    aTP_Lamm_sd: $o > fun_fu9039538216874201369_o_rat ).

tff(sy_c_ATP_058Lamm__se____,type,
    aTP_Lamm_se: $o > fun_fu3581538110357139729_o_nat ).

tff(sy_c_ATP_058Lamm__sf____,type,
    aTP_Lamm_sf: $o > fun_fu9026017786105829997_o_int ).

tff(sy_c_ATP_058Lamm__sg____,type,
    aTP_Lamm_sg: int > fun_fu1617438229336688381nt_rat ).

tff(sy_c_ATP_058Lamm__sh____,type,
    aTP_Lamm_sh: int > fun_fu973771059875708133nt_nat ).

tff(sy_c_ATP_058Lamm__si____,type,
    aTP_Lamm_si: nat > fun_fu6579618355643354601at_rat ).

tff(sy_c_ATP_058Lamm__sj____,type,
    aTP_Lamm_sj: nat > fun_fu960360787657196261at_int ).

tff(sy_c_ATP_058Lamm__sk____,type,
    aTP_Lamm_sk: $o > fun_se5639961202347202350_nat_o ).

tff(sy_c_ATP_058Lamm__sl____,type,
    aTP_Lamm_sl: $o > fun_nat_fun_nat_o ).

tff(sy_c_ATP_058Lamm__sm____,type,
    aTP_Lamm_sm: set_nat > fun_nat_fun_nat_o ).

tff(sy_c_ATP_058Lamm__sn____,type,
    aTP_Lamm_sn: set_nat > fun_nat_fun_nat_o ).

tff(sy_c_ATP_058Lamm__so____,type,
    aTP_Lamm_so: fun_o_Code_integer > fun_set_o_fun_o_o ).

tff(sy_c_ATP_058Lamm__sp____,type,
    aTP_Lamm_sp: fun_int_Code_integer > fun_se867122708194164540_int_o ).

tff(sy_c_ATP_058Lamm__sq____,type,
    aTP_Lamm_sq: fun_nat_Code_integer > fun_se382663106265794036_nat_o ).

tff(sy_c_ATP_058Lamm__sr____,type,
    aTP_Lamm_sr: fun_o_assn > fun_set_o_fun_o_o ).

tff(sy_c_ATP_058Lamm__ss____,type,
    aTP_Lamm_ss: fun_int_assn > fun_se867122708194164540_int_o ).

tff(sy_c_ATP_058Lamm__st____,type,
    aTP_Lamm_st: fun_nat_assn > fun_se382663106265794036_nat_o ).

tff(sy_c_ATP_058Lamm__su____,type,
    aTP_Lamm_su: fun_o_rat > fun_set_o_fun_o_o ).

tff(sy_c_ATP_058Lamm__sv____,type,
    aTP_Lamm_sv: fun_int_rat > fun_se867122708194164540_int_o ).

tff(sy_c_ATP_058Lamm__sw____,type,
    aTP_Lamm_sw: fun_nat_rat > fun_se382663106265794036_nat_o ).

tff(sy_c_ATP_058Lamm__sx____,type,
    aTP_Lamm_sx: fun_o_nat > fun_set_o_fun_o_o ).

tff(sy_c_ATP_058Lamm__sy____,type,
    aTP_Lamm_sy: fun_o_Code_integer > fun_fu2786480252100984515nteger ).

tff(sy_c_ATP_058Lamm__sz____,type,
    aTP_Lamm_sz: fun_nat_Code_integer > fun_fu2499394402704830801nteger ).

tff(sy_c_ATP_058Lamm__ta____,type,
    aTP_Lamm_ta: fun_int_Code_integer > fun_fu3628599891403802633nteger ).

tff(sy_c_ATP_058Lamm__tb____,type,
    aTP_Lamm_tb: fun_Co8499238673658658103nteger > fun_fu1763652423599918571nteger ).

tff(sy_c_ATP_058Lamm__tc____,type,
    aTP_Lamm_tc: fun_o_assn > fun_fu704708528062463619o_assn ).

tff(sy_c_ATP_058Lamm__td____,type,
    aTP_Lamm_td: fun_nat_assn > fun_fu2995346897264222311t_assn ).

tff(sy_c_ATP_058Lamm__te____,type,
    aTP_Lamm_te: fun_int_assn > fun_fu6568868615275847455t_assn ).

tff(sy_c_ATP_058Lamm__tf____,type,
    aTP_Lamm_tf: fun_Co4490034186337852034r_assn > fun_fu5082522747898945281r_assn ).

tff(sy_c_ATP_058Lamm__tg____,type,
    aTP_Lamm_tg: fun_o_rat > fun_fu1989461620956114563_o_rat ).

tff(sy_c_ATP_058Lamm__th____,type,
    aTP_Lamm_th: fun_nat_rat > fun_fu8328862064278946247at_rat ).

tff(sy_c_ATP_058Lamm__ti____,type,
    aTP_Lamm_ti: fun_Co8499238673658658103nteger > fun_se4239619783102168410eger_o ).

tff(sy_c_ATP_058Lamm__tj____,type,
    aTP_Lamm_tj: fun_Co4490034186337852034r_assn > fun_se4239619783102168410eger_o ).

tff(sy_c_ATP_058Lamm__tk____,type,
    aTP_Lamm_tk: fun_nat_rat > fun_fu8328862064278946247at_rat ).

tff(sy_c_ATP_058Lamm__tl____,type,
    aTP_Lamm_tl: fun_int_rat > fun_fu1008360527747082367nt_rat ).

tff(sy_c_ATP_058Lamm__tm____,type,
    aTP_Lamm_tm: fun_Code_integer_rat > fun_fu722387130092441185er_rat ).

tff(sy_c_ATP_058Lamm__tn____,type,
    aTP_Lamm_tn: fun_int_nat > fun_fu8905809029841901679nt_nat ).

tff(sy_c_ATP_058Lamm__to____,type,
    aTP_Lamm_to: fun_Code_integer_nat > fun_fu7724909810345500241er_nat ).

tff(sy_c_ATP_058Lamm__tp____,type,
    aTP_Lamm_tp: fun_nat_int > fun_fu8464300013002972271at_int ).

tff(sy_c_ATP_058Lamm__tq____,type,
    aTP_Lamm_tq: fun_Code_integer_int > fun_fu403917627589892361er_int ).

tff(sy_c_ATP_058Lamm__tr____,type,
    aTP_Lamm_tr: fun_Pr8317260874932935276at_rat > fun_fu3997796857297124035at_rat ).

tff(sy_c_ATP_058Lamm__ts____,type,
    aTP_Lamm_ts: fun_o_Code_integer > fun_fu2786480252100984515nteger ).

tff(sy_c_ATP_058Lamm__tt____,type,
    aTP_Lamm_tt: fun_nat_Code_integer > fun_fu2499394402704830801nteger ).

tff(sy_c_ATP_058Lamm__tu____,type,
    aTP_Lamm_tu: fun_int_Code_integer > fun_fu3628599891403802633nteger ).

tff(sy_c_ATP_058Lamm__tv____,type,
    aTP_Lamm_tv: fun_Co8499238673658658103nteger > fun_fu1763652423599918571nteger ).

tff(sy_c_ATP_058Lamm__tw____,type,
    aTP_Lamm_tw: fun_o_rat > fun_fu1989461620956114563_o_rat ).

tff(sy_c_ATP_058Lamm__tx____,type,
    aTP_Lamm_tx: fun_o_nat > fun_fu6701067901881939075_o_nat ).

tff(sy_c_ATP_058Lamm__ty____,type,
    aTP_Lamm_ty: fun_nat_fun_nat_nat ).

tff(sy_c_ATP_058Lamm__tz____,type,
    aTP_Lamm_tz: set_Pr8693737435421807431at_nat > fun_Pr2028404973800837934_nat_o ).

tff(sy_c_ATP_058Lamm__ua____,type,
    aTP_Lamm_ua: fun_se1823139391991869964it_int ).

tff(sy_c_ATP_058Lamm__ub____,type,
    aTP_Lamm_ub: set_set_Product_unit > fun_se2288280263375636942unit_o ).

tff(sy_c_ATP_058Lamm__uc____,type,
    aTP_Lamm_uc: fun_se1018900654481025269at_int ).

tff(sy_c_ATP_058Lamm__ud____,type,
    aTP_Lamm_ud: set_set_list_nat > fun_se5048694460222551717_nat_o ).

tff(sy_c_ATP_058Lamm__ue____,type,
    aTP_Lamm_ue: fun_set_set_int_int ).

tff(sy_c_ATP_058Lamm__uf____,type,
    aTP_Lamm_uf: set_set_int > fun_set_set_int_o ).

tff(sy_c_ATP_058Lamm__ug____,type,
    aTP_Lamm_ug: fun_se504249187503832818er_int ).

tff(sy_c_ATP_058Lamm__uh____,type,
    aTP_Lamm_uh: set_set_Code_integer > fun_se1103039064484435816eger_o ).

tff(sy_c_ATP_058Lamm__ui____,type,
    aTP_Lamm_ui: fun_se8575562297434572672at_int ).

tff(sy_c_ATP_058Lamm__uj____,type,
    aTP_Lamm_uj: set_se7855581050983116737at_nat > fun_se7504237348027150170_nat_o ).

tff(sy_c_ATP_058Lamm__uk____,type,
    aTP_Lamm_uk: fun_set_set_nat_int ).

tff(sy_c_ATP_058Lamm__ul____,type,
    aTP_Lamm_ul: set_set_nat > fun_set_set_nat_o ).

tff(sy_c_ATP_058Lamm__um____,type,
    aTP_Lamm_um: fun_Pr8371818785129130299nteger ).

tff(sy_c_ATP_058Lamm__un____,type,
    aTP_Lamm_un: fun_Pr5259258551928531321et_nat ).

tff(sy_c_ATP_058Lamm__uo____,type,
    aTP_Lamm_uo: fun_Pr8737872353715570297et_nat ).

tff(sy_c_ATP_058Lamm__up____,type,
    aTP_Lamm_up: fun_Pr8826142978676617911nt_int ).

tff(sy_c_ATP_058Lamm__uq____,type,
    aTP_Lamm_uq: fun_Pr4353654455642104759nt_int ).

tff(sy_c_ATP_058Lamm__ur____,type,
    aTP_Lamm_ur: fun_Co2470855966376689427nteger ).

tff(sy_c_ATP_058Lamm__us____,type,
    aTP_Lamm_us: fun_Co3643010573817537149atural ).

tff(sy_c_ATP_058Lamm__ut____,type,
    aTP_Lamm_ut: fun_in1696471567231710611nt_int ).

tff(sy_c_ATP_058Lamm__uu____,type,
    aTP_Lamm_uu: fun_Pr3688637647703109351atural ).

tff(sy_c_ATP_058Lamm__uv____,type,
    aTP_Lamm_uv: fun_nat_nat > fun_Pr2602117396471556196at_nat ).

tff(sy_c_ATP_058Lamm__uw____,type,
    aTP_Lamm_uw: fun_nat_nat > fun_nat_fun_nat_nat ).

tff(sy_c_ATP_058Lamm__ux____,type,
    aTP_Lamm_ux: fun_na8713714802964096592at_nat > fun_Pr2477239776880934807at_nat ).

tff(sy_c_ATP_058Lamm__uy____,type,
    aTP_Lamm_uy: fun_na8713714802964096592at_nat > fun_na1668100129766719005at_nat ).

tff(sy_c_ATP_058Lamm__uz____,type,
    aTP_Lamm_uz: fun_na3970208099681795815_nat_o > fun_Pr2028404973800837934_nat_o ).

tff(sy_c_ATP_058Lamm__va____,type,
    aTP_Lamm_va: fun_na3970208099681795815_nat_o > fun_na5914473681949881652_nat_o ).

tff(sy_c_ATP_058Lamm__vb____,type,
    aTP_Lamm_vb: fun_in4211310926729683942nt_int > fun_Pr2478283820680522243nt_int ).

tff(sy_c_ATP_058Lamm__vc____,type,
    aTP_Lamm_vc: fun_in4211310926729683942nt_int > fun_in1696471567231710611nt_int ).

tff(sy_c_ATP_058Lamm__vd____,type,
    aTP_Lamm_vd: fun_int_int > fun_Pr982841511892225912nt_int ).

tff(sy_c_ATP_058Lamm__ve____,type,
    aTP_Lamm_ve: fun_int_int > fun_int_fun_int_int ).

tff(sy_c_ATP_058Lamm__vf____,type,
    aTP_Lamm_vf: fun_Co1981900195452921617nteger ).

tff(sy_c_ATP_058Lamm__vg____,type,
    aTP_Lamm_vg: fun_Co1851440197950133416atural ).

tff(sy_c_ATP_058Lamm__vh____,type,
    aTP_Lamm_vh: fun_nat_fun_nat_nat ).

tff(sy_c_ATP_058Lamm__vi____,type,
    aTP_Lamm_vi: fun_int_fun_int_int ).

tff(sy_c_ATP_058Lamm__vj____,type,
    aTP_Lamm_vj: fun_nat_nat > fun_Pr2602117396471556196at_nat ).

tff(sy_c_ATP_058Lamm__vk____,type,
    aTP_Lamm_vk: fun_nat_nat > fun_nat_fun_nat_nat ).

tff(sy_c_ATP_058Lamm__vl____,type,
    aTP_Lamm_vl: fun_na8713714802964096592at_nat > fun_Pr2477239776880934807at_nat ).

tff(sy_c_ATP_058Lamm__vm____,type,
    aTP_Lamm_vm: fun_na8713714802964096592at_nat > fun_na1668100129766719005at_nat ).

tff(sy_c_ATP_058Lamm__vn____,type,
    aTP_Lamm_vn: fun_na3970208099681795815_nat_o > fun_Pr2028404973800837934_nat_o ).

tff(sy_c_ATP_058Lamm__vo____,type,
    aTP_Lamm_vo: fun_na3970208099681795815_nat_o > fun_na5914473681949881652_nat_o ).

tff(sy_c_ATP_058Lamm__vp____,type,
    aTP_Lamm_vp: fun_in4211310926729683942nt_int > fun_Pr2478283820680522243nt_int ).

tff(sy_c_ATP_058Lamm__vq____,type,
    aTP_Lamm_vq: fun_in4211310926729683942nt_int > fun_in1696471567231710611nt_int ).

tff(sy_c_ATP_058Lamm__vr____,type,
    aTP_Lamm_vr: fun_int_int > fun_Pr982841511892225912nt_int ).

tff(sy_c_ATP_058Lamm__vs____,type,
    aTP_Lamm_vs: fun_int_int > fun_int_fun_int_int ).

tff(sy_c_ATP_058Lamm__vt____,type,
    aTP_Lamm_vt: fun_nat_fun_nat_nat ).

tff(sy_c_ATP_058Lamm__vu____,type,
    aTP_Lamm_vu: fun_int_fun_int_int ).

tff(sy_c_ATP_058Lamm__vv____,type,
    aTP_Lamm_vv: fun_nat_set_nat > fun_na896109329399166627et_nat ).

tff(sy_c_ATP_058Lamm__vw____,type,
    aTP_Lamm_vw: fun_Pr6764980218223570944et_nat > fun_Pr6721000092112975824et_nat ).

tff(sy_c_ATP_058Lamm__vx____,type,
    aTP_Lamm_vx: fun_Pr9038118721296872730et_nat > fun_Pr2088208266900590058et_nat ).

tff(sy_c_ATP_058Lamm__vy____,type,
    aTP_Lamm_vy: fun_o_set_nat > fun_o_option_set_nat ).

tff(sy_c_ATP_058Lamm__vz____,type,
    aTP_Lamm_vz: fun_int_set_nat > fun_in2104226462327546623et_nat ).

tff(sy_c_ATP_058Lamm__wa____,type,
    aTP_Lamm_wa: fun_Pr8319229360018371625t_unit > fun_Pr5508761798988831599t_unit ).

tff(sy_c_ATP_058Lamm__wb____,type,
    aTP_Lamm_wb: fun_Pr2481279687482350479t_unit > fun_Pr648072847990616533t_unit ).

tff(sy_c_ATP_058Lamm__wc____,type,
    aTP_Lamm_wc: fun_o_Product_unit > fun_o_6261137236491177342t_unit ).

tff(sy_c_ATP_058Lamm__wd____,type,
    aTP_Lamm_wd: fun_nat_Product_unit > fun_na5635918068280204892t_unit ).

tff(sy_c_ATP_058Lamm__we____,type,
    aTP_Lamm_we: fun_int_Product_unit > fun_in5873495209930779904t_unit ).

tff(sy_c_ATP_058Lamm__wf____,type,
    aTP_Lamm_wf: fun_nat_set_nat > fun_nat_set_nat ).

tff(sy_c_ATP_058Lamm__wg____,type,
    aTP_Lamm_wg: fun_nat_set_nat > fun_na6128946301132549280et_nat ).

tff(sy_c_ATP_058Lamm__wh____,type,
    aTP_Lamm_wh: fun_o_4732642864545671890od_o_o ).

tff(sy_c_ATP_058Lamm__wi____,type,
    aTP_Lamm_wi: fun_na1476630412504255114at_nat ).

tff(sy_c_ATP_058Lamm__wj____,type,
    aTP_Lamm_wj: fun_fu5650529485467354185_nat_o ).

tff(sy_c_ATP_058Lamm__wk____,type,
    aTP_Lamm_wk: fun_nu5148503272595741012um_num ).

tff(sy_c_ATP_058Lamm__wl____,type,
    aTP_Lamm_wl: fun_Co6597186368970283863nteger ).

tff(sy_c_ATP_058Lamm__wm____,type,
    aTP_Lamm_wm: fun_in4211310926729683942nt_int ).

tff(sy_c_ATP_058Lamm__wn____,type,
    aTP_Lamm_wn: fun_Pr3133360822718887225atural ).

tff(sy_c_ATP_058Lamm__wo____,type,
    aTP_Lamm_wo: fun_na8176081009732395159er_nat > fun_Co8307959106670069728et_nat ).

tff(sy_c_ATP_058Lamm__wp____,type,
    aTP_Lamm_wp: fun_na5685997864800668403er_int > fun_Co5817875961738342972et_int ).

tff(sy_c_ATP_058Lamm__wq____,type,
    aTP_Lamm_wq: fun_na1596024190920976919nteger > fun_na9118744110877893344nteger ).

tff(sy_c_ATP_058Lamm__wr____,type,
    aTP_Lamm_wr: fun_na1476630412504255114at_nat > fun_nat_set_nat ).

tff(sy_c_ATP_058Lamm__ws____,type,
    aTP_Lamm_ws: fun_na8209919304427304166at_int > fun_nat_set_int ).

tff(sy_c_ATP_058Lamm__wt____,type,
    aTP_Lamm_wt: fun_na7604833841916551795nteger > fun_in6808926178784942396nteger ).

tff(sy_c_ATP_058Lamm__wu____,type,
    aTP_Lamm_wu: fun_na3663551987197276902nt_nat > fun_int_set_nat ).

tff(sy_c_ATP_058Lamm__wv____,type,
    aTP_Lamm_wv: fun_na3822476419092417572nteger > fun_Co744628173305925485nteger ).

tff(sy_c_ATP_058Lamm__ww____,type,
    aTP_Lamm_ww: fun_na1173468842265550146nt_int > fun_int_set_int ).

tff(sy_c_ATP_058Lamm__wx____,type,
    aTP_Lamm_wx: fun_Pr864343514034809617nteger > fun_Co744628173305925485nteger ).

tff(sy_c_ATP_058Lamm__wy____,type,
    aTP_Lamm_wy: fun_Co2081214437782444048eger_o > fun_fu5503004773767123511eger_o ).

tff(sy_c_ATP_058Lamm__wz____,type,
    aTP_Lamm_wz: fun_int_fun_int_o > fun_fu6598048713889201561_int_o ).

tff(sy_c_ATP_058Lamm__xa____,type,
    aTP_Lamm_xa: fun_Co2081214437782444048eger_o > fun_fu4285281161728579104eger_o ).

tff(sy_c_ATP_058Lamm__xb____,type,
    aTP_Lamm_xb: fun_int_fun_int_o > fun_fu4509100218321815938_int_o ).

tff(sy_c_ATP_058Lamm__xc____,type,
    aTP_Lamm_xc: fun_Co2081214437782444048eger_o > fun_fu7325869825756301971eger_o ).

tff(sy_c_ATP_058Lamm__xd____,type,
    aTP_Lamm_xd: fun_int_fun_int_o > fun_fu8565479202776651253_int_o ).

tff(sy_c_ATP_058Lamm__xe____,type,
    aTP_Lamm_xe: fun_Co9066792663755620495ural_o > fun_fu9211935013670480870ural_o ).

tff(sy_c_ATP_058Lamm__xf____,type,
    aTP_Lamm_xf: fun_Co9066792663755620495ural_o > fun_fu257250443624047805ural_o ).

tff(sy_c_ATP_058Lamm__xg____,type,
    aTP_Lamm_xg: fun_Co9066792663755620495ural_o > fun_fu660488089777143946ural_o ).

tff(sy_c_ATP_058Lamm__xh____,type,
    aTP_Lamm_xh: fun_fu7564235448449272366at_o_o > fun_fu6749285349733798471at_o_o ).

tff(sy_c_ATP_058Lamm__xi____,type,
    aTP_Lamm_xi: fun_nat_o > fun_fu2106003848923686156_nat_o ).

tff(sy_c_ATP_058Lamm__xj____,type,
    aTP_Lamm_xj: fun_nat_o > fun_nat_set_nat ).

tff(sy_c_ATP_058Lamm__xk____,type,
    aTP_Lamm_xk: fun_nat_o > fun_fu2721382957917623308_nat_o ).

tff(sy_c_ATP_058Lamm__xl____,type,
    aTP_Lamm_xl: fun_list_nat_o > fun_nat_set_list_nat ).

tff(sy_c_ATP_058Lamm__xm____,type,
    aTP_Lamm_xm: fun_list_nat_o > fun_fu2312272580554962172_nat_o ).

tff(sy_c_ATP_058Lamm__xn____,type,
    aTP_Lamm_xn: fun_nat_o > fun_list_nat_set_nat ).

tff(sy_c_ATP_058Lamm__xo____,type,
    aTP_Lamm_xo: fun_list_nat_o > fun_fu9062970525541950460_nat_o ).

tff(sy_c_ATP_058Lamm__xp____,type,
    aTP_Lamm_xp: fun_list_nat_o > fun_li1191372448985611379st_nat ).

tff(sy_c_ATP_058Lamm__xq____,type,
    aTP_Lamm_xq: fun_se953073389798102371at_nat ).

tff(sy_c_ATP_058Lamm__xr____,type,
    aTP_Lamm_xr: fun_nat_set_nat ).

tff(sy_c_ATP_058Lamm__xs____,type,
    aTP_Lamm_xs: set_o > fun_o_set_o ).

tff(sy_c_ATP_058Lamm__xt____,type,
    aTP_Lamm_xt: set_nat > fun_o_set_nat ).

tff(sy_c_ATP_058Lamm__xu____,type,
    aTP_Lamm_xu: set_int > fun_o_set_int ).

tff(sy_c_ATP_058Lamm__xv____,type,
    aTP_Lamm_xv: set_o > fun_nat_set_o ).

tff(sy_c_ATP_058Lamm__xw____,type,
    aTP_Lamm_xw: set_int > fun_nat_set_int ).

tff(sy_c_ATP_058Lamm__xx____,type,
    aTP_Lamm_xx: set_o > fun_int_set_o ).

tff(sy_c_ATP_058Lamm__xy____,type,
    aTP_Lamm_xy: set_nat > fun_int_set_nat ).

tff(sy_c_ATP_058Lamm__xz____,type,
    aTP_Lamm_xz: set_int > fun_int_set_int ).

tff(sy_c_ATP_058Lamm__ya____,type,
    aTP_Lamm_ya: set_nat > fun_nat_set_nat ).

tff(sy_c_ATP_058Lamm__yb____,type,
    aTP_Lamm_yb: set_o > fun_Pr8467005832278515962_set_o ).

tff(sy_c_ATP_058Lamm__yc____,type,
    aTP_Lamm_yc: set_se7855581050983116737at_nat > fun_se953073389798102371at_nat ).

tff(sy_c_ATP_058Lamm__yd____,type,
    aTP_Lamm_yd: fun_se953073389798102371at_nat ).

tff(sy_c_ATP_058Lamm__ye____,type,
    aTP_Lamm_ye: fun_nat_set_nat ).

tff(sy_c_ATP_058Lamm__yf____,type,
    aTP_Lamm_yf: fun_na896991816813928310t_unit ).

tff(sy_c_ATP_058Lamm__yg____,type,
    aTP_Lamm_yg: fun_nat_set_int ).

tff(sy_c_ATP_058Lamm__yh____,type,
    aTP_Lamm_yh: fun_Pr1628945989756059814et_nat ).

tff(sy_c_ATP_058Lamm__yi____,type,
    aTP_Lamm_yi: fun_Pr3013102738158121955t_unit ).

tff(sy_c_ATP_058Lamm__yj____,type,
    aTP_Lamm_yj: fun_Pr8362234881679108866et_int ).

tff(sy_c_ATP_058Lamm__yk____,type,
    aTP_Lamm_yk: fun_int_set_nat ).

tff(sy_c_ATP_058Lamm__yl____,type,
    aTP_Lamm_yl: fun_in4731230917697954842t_unit ).

tff(sy_c_ATP_058Lamm__ym____,type,
    aTP_Lamm_ym: fun_int_set_int ).

tff(sy_c_ATP_058Lamm__yn____,type,
    aTP_Lamm_yn: fun_nat_Code_integer > fun_se3841591170510310256nteger ).

tff(sy_c_ATP_058Lamm__yo____,type,
    aTP_Lamm_yo: fun_nat_set_nat > fun_se8125625266612218818et_nat ).

tff(sy_c_ATP_058Lamm__yp____,type,
    aTP_Lamm_yp: fun_nat_nat > fun_se3395149180098744406et_nat ).

tff(sy_c_ATP_058Lamm__yq____,type,
    aTP_Lamm_yq: fun_nat_int > fun_se4590410412306400526et_int ).

tff(sy_c_ATP_058Lamm__yr____,type,
    aTP_Lamm_yr: fun_int_int > fun_se8982873411337295210et_int ).

tff(sy_c_ATP_058Lamm__ys____,type,
    aTP_Lamm_ys: set_Code_integer > fun_Co744628173305925485nteger ).

tff(sy_c_ATP_058Lamm__yt____,type,
    aTP_Lamm_yt: fun_fu7564235448449272366at_o_o > fun_fu4957514873648614724at_o_o ).

tff(sy_c_ATP_058Lamm__yu____,type,
    aTP_Lamm_yu: fun_fu6699046866436802030_int_o > fun_fu560856344546067396_int_o ).

tff(sy_c_ATP_058Lamm__yv____,type,
    aTP_Lamm_yv: fun_fu7677565902479959693_rat_o > fun_fu3447610970239163469_rat_o ).

tff(sy_c_ATP_058Lamm__yw____,type,
    aTP_Lamm_yw: fun_fu6971708032831053102nt_o_o > fun_fu7129310890971069252nt_o_o ).

tff(sy_c_ATP_058Lamm__yx____,type,
    aTP_Lamm_yx: fun_fu4208408993564413984_int_o > fun_fu1677024581061081874_int_o ).

tff(sy_c_ATP_058Lamm__yy____,type,
    aTP_Lamm_yy: fun_fu7564235448449272366at_o_o > fun_fu4957514873648614724at_o_o ).

tff(sy_c_ATP_058Lamm__yz____,type,
    aTP_Lamm_yz: fun_fu6699046866436802030_int_o > fun_fu560856344546067396_int_o ).

tff(sy_c_ATP_058Lamm__za____,type,
    aTP_Lamm_za: fun_fu6699046866436802030_int_o > fun_fu8216932157852985630_rat_o ).

tff(sy_c_ATP_058Lamm__zb____,type,
    aTP_Lamm_zb: fun_fu7677565902479959693_rat_o > fun_fu61188948249169719_int_o ).

tff(sy_c_ATP_058Lamm__zc____,type,
    aTP_Lamm_zc: fun_fu7677565902479959693_rat_o > fun_fu2427765959047162121_rat_o ).

tff(sy_c_ATP_058Lamm__zd____,type,
    aTP_Lamm_zd: fun_fu6971708032831053102nt_o_o > fun_fu7129310890971069252nt_o_o ).

tff(sy_c_ATP_058Lamm__ze____,type,
    aTP_Lamm_ze: fun_fu4208408993564413984_int_o > fun_fu1677024581061081874_int_o ).

tff(sy_c_ATP_058Lamm__zf____,type,
    aTP_Lamm_zf: fun_nat_o > fun_fu6436183194761443139_nat_o ).

tff(sy_c_ATP_058Lamm__zg____,type,
    aTP_Lamm_zg: fun_nat_fun_nat_o > fun_nat_set_nat ).

tff(sy_c_ATP_058Lamm__zh____,type,
    aTP_Lamm_zh: fun_nat_o > fun_fu6714502955005156803_nat_o ).

tff(sy_c_ATP_058Lamm__zi____,type,
    aTP_Lamm_zi: fun_na7234455742697417626_nat_o > fun_nat_set_list_nat ).

tff(sy_c_ATP_058Lamm__zj____,type,
    aTP_Lamm_zj: fun_list_nat_o > fun_fu4568065243339218371_nat_o ).

tff(sy_c_ATP_058Lamm__zk____,type,
    aTP_Lamm_zk: fun_li2421049240157457050_nat_o > fun_list_nat_set_nat ).

tff(sy_c_ATP_058Lamm__zl____,type,
    aTP_Lamm_zl: fun_list_nat_o > fun_fu4946532526548972611_nat_o ).

tff(sy_c_ATP_058Lamm__zm____,type,
    aTP_Lamm_zm: fun_li1025265955262268170_nat_o > fun_li1191372448985611379st_nat ).

tff(sy_c_ATP_058Lamm__zn____,type,
    aTP_Lamm_zn: set_Pr4329608150637261639at_nat > fun_na5670658592214072528at_nat ).

tff(sy_c_ATP_058Lamm__zo____,type,
    aTP_Lamm_zo: set_Pr1261947904930325089at_nat > fun_na7044673412300895210at_nat ).

tff(sy_c_ATP_058Lamm__zp____,type,
    aTP_Lamm_zp: fun_nat_set_nat > fun_na6128946301132549280et_nat ).

tff(sy_c_ATP_058Lamm__zq____,type,
    aTP_Lamm_zq: fun_nat_set_nat > fun_fu7530206860547196985at_nat ).

tff(sy_c_ATP_058Lamm__zr____,type,
    aTP_Lamm_zr: fun_nat_set_nat > fun_se3395149180098744406et_nat ).

tff(sy_c_ATP_058Lamm__zs____,type,
    aTP_Lamm_zs: set_fu8280898353253485872e_term > fun_Pr5305228341155023582e_term ).

tff(sy_c_ATP_058Lamm__zt____,type,
    aTP_Lamm_zt: set_Pr4811707699266497531nteger > fun_fu5971215405379524186nteger ).

tff(sy_c_ATP_058Lamm__zu____,type,
    aTP_Lamm_zu: set_fu3555266933746557007_nat_o > fun_Pr8383423175210966566_nat_o ).

tff(sy_c_ATP_058Lamm__zv____,type,
    aTP_Lamm_zv: set_Pr3948176798113811640et_nat > fun_fu2890809920214373946et_nat ).

tff(sy_c_ATP_058Lamm__zw____,type,
    aTP_Lamm_zw: set_fu3555266933746557007_nat_o > fun_Pr7968690803259750408_nat_o ).

tff(sy_c_ATP_058Lamm__zx____,type,
    aTP_Lamm_zx: set_Pr1312406793078187350et_nat > fun_fu8357309440898100312et_nat ).

tff(sy_c_ATP_058Lamm__zy____,type,
    aTP_Lamm_zy: set_fu5653557704672872225e_term > fun_Pr4426623609552329069e_term ).

tff(sy_c_ATP_058Lamm__zz____,type,
    aTP_Lamm_zz: set_Pr958786334691620121nt_int > fun_fu4219362280553733319nt_int ).

tff(sy_c_Archimedean__Field_Oceiling_001t__Rat__Orat,type,
    archim2889992004027027881ng_rat: rat > int ).

tff(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Rat__Orat,type,
    archim3151403230148437115or_rat: rat > int ).

tff(sy_c_Archimedean__Field_Ofrac_001t__Rat__Orat,type,
    archimedean_frac_rat: fun_rat_rat ).

tff(sy_c_Archimedean__Field_Oround_001t__Rat__Orat,type,
    archim7778729529865785530nd_rat: rat > int ).

tff(sy_c_Array__Time_Omake_001tf__a,type,
    array_make_a: ( nat * fun_nat_a ) > heap_T6362127782908069795rray_a ).

tff(sy_c_Array__Time_Onew_001tf__a,type,
    array_new_a: ( nat * a ) > heap_T6362127782908069795rray_a ).

tff(sy_c_Array__Time_Oof__list_001tf__a,type,
    array_of_list_a: list_a > heap_T6362127782908069795rray_a ).

tff(sy_c_Assertions_Oassn_ORep__assn,type,
    rep_assn: assn > fun_Pr6460944699146269935_nat_o ).

tff(sy_c_Assertions_Oin__range,type,
    in_range: fun_Pr6460944699146269935_nat_o ).

tff(sy_c_Assertions_Oin__range__rel,type,
    in_range_rel: fun_Pr7920380315054183110_nat_o ).

tff(sy_c_Assertions_Oone__assn__raw,type,
    one_assn_raw: fun_Pr6460944699146269935_nat_o ).

tff(sy_c_Assertions_Oone__assn__raw__rel,type,
    one_assn_raw_rel: fun_Pr7920380315054183110_nat_o ).

tff(sy_c_Assertions_Oproper,type,
    proper: fun_fu5135969500543783852at_o_o ).

tff(sy_c_Assertions_Opure__assn,type,
    pure_assn: fun_o_assn ).

tff(sy_c_Assertions_OrelH,type,
    relH: ( set_nat * heap_e7401611519738050253t_unit ) > fun_he8413527710729349838unit_o ).

tff(sy_c_Assertions_Otimes__assn__raw,type,
    times_assn_raw: fun_Pr6460944699146269935_nat_o > fun_fu8419763957888848259_nat_o ).

tff(sy_c_Assertions_Otimes__assn__raw__rel,type,
    times_assn_raw_rel: fun_Pr3358449090565925198_nat_o ).

tff(sy_c_Assertions_Owand__assn,type,
    wand_assn: ( assn * assn ) > assn ).

tff(sy_c_Assertions_Owand__raw,type,
    wand_raw: fun_Pr6460944699146269935_nat_o > fun_fu8419763957888848259_nat_o ).

tff(sy_c_Assertions_Owand__raw__rel,type,
    wand_raw_rel: fun_Pr3358449090565925198_nat_o ).

tff(sy_c_BNF__Cardinal__Arithmetic_Octwo,type,
    bNF_Cardinal_ctwo: set_Product_prod_o_o ).

tff(sy_c_BNF__Cardinal__Arithmetic_Oczero_001_Eo,type,
    bNF_Cardinal_czero_o: set_Product_prod_o_o ).

tff(sy_c_BNF__Cardinal__Order__Relation_Ocard__of_001t__Nat__Onat,type,
    bNF_Ca3793111618940312692of_nat: set_nat > set_Pr1261947904930325089at_nat ).

tff(sy_c_BNF__Cardinal__Order__Relation_Ocard__order__on_001_Eo,type,
    bNF_Ca8331644756375544342r_on_o: ( set_o * set_Product_prod_o_o ) > $o ).

tff(sy_c_BNF__Cardinal__Order__Relation_OnatLeq,type,
    bNF_Ca8665028551170535155natLeq: set_Pr1261947904930325089at_nat ).

tff(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Int__Oint_001t__Nat__Onat,type,
    bNF_re1551779926989065179nt_nat: ( fun_o_fun_o_o * fun_int_fun_nat_o * fun_o_int * fun_o_nat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Int__Oint_001t__Rat__Orat,type,
    bNF_re916649866902569443nt_rat: ( fun_o_fun_o_o * fun_int_fun_rat_o * fun_o_int * fun_o_rat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
    bNF_re4863541036035986956nteger: ( fun_o_fun_o_o * fun_na6318815019539281885eger_o * fun_o_nat * fun_o_Code_integer ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Nat__Onat_001t__Int__Oint,type,
    bNF_re549935744578960347at_int: ( fun_o_fun_o_o * fun_nat_fun_int_o * fun_o_nat * fun_o_int ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_re552426215088010623at_nat: ( fun_o_fun_o_o * fun_nat_fun_nat_o * fun_o_nat * fun_o_nat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Nat__Onat_001t__Rat__Orat,type,
    bNF_re9140668191856290695at_rat: ( fun_o_fun_o_o * fun_nat_fun_rat_o * fun_o_nat * fun_o_rat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Rat__Orat_001t__Code____Numeral__Ointeger,type,
    bNF_re5635613845597506580nteger: ( fun_o_fun_o_o * fun_ra1401953663915778005eger_o * fun_o_rat * fun_o_Code_integer ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Rat__Orat_001t__Int__Oint,type,
    bNF_re233381100644094435at_int: ( fun_o_fun_o_o * fun_rat_fun_int_o * fun_o_rat * fun_o_int ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Rat__Orat_001t__Nat__Onat,type,
    bNF_re235871571153144711at_nat: ( fun_o_fun_o_o * fun_rat_fun_nat_o * fun_o_rat * fun_o_nat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Rat__Orat_001t__Rat__Orat,type,
    bNF_re8824113547921424783at_rat: ( fun_o_fun_o_o * fun_rat_fun_rat_o * fun_o_rat * fun_o_rat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Assertions__Oassn_001t__Assertions__Oassn_001t__Assertions__Oassn,type,
    bNF_re1143782165119297793n_assn: ( fun_assn_fun_assn_o * fun_assn_fun_assn_o ) > fun_fu829217510089154608assn_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Assertions__Oassn_001t__fun_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001t__fun_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
    bNF_re2386586829629292363n_assn: ( fun_assn_fun_assn_o * fun_fu829217510089154608assn_o * fun_as3983628580203722482n_assn * fun_as3983628580203722482n_assn ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Assertions__Oassn_001t__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_001t__fun_It__Nat__Onat_Mt__Assertions__Oassn_J,type,
    bNF_re8039158443969940635t_assn: ( fun_assn_fun_assn_o * fun_fu6461175078876253408assn_o * fun_as8240436605320707994t_assn * fun_as8240436605320707994t_assn ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Code____Numeral__Ointeger_001t__Assertions__Oassn_001t__Code____Numeral__Ointeger,type,
    bNF_re4134162077946812779nteger: ( fun_as7521517929205406341eger_o * fun_as7521517929205406341eger_o ) > fun_fu2770652263662631110eger_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Code____Numeral__Ointeger_001t__fun_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    bNF_re8333148941225519722nteger: ( fun_as7521517929205406341eger_o * fun_fu2770652263662631110eger_o * fun_as3983628580203722482n_assn * fun_Co1981900195452921617nteger ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Code____Numeral__Ointeger_001t__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_001t__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J,type,
    bNF_re5238271293363935365nteger: ( fun_as7521517929205406341eger_o * fun_fu5719784276005855083eger_o * fun_as8240436605320707994t_assn * fun_Co6226381647958292740nteger ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Int__Oint_001t__Assertions__Oassn_001t__Int__Oint,type,
    bNF_re2927800259774540553sn_int: ( fun_assn_fun_int_o * fun_assn_fun_int_o ) > fun_fu8462857099809827880_int_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Int__Oint_001t__fun_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001t__fun_It__Int__Oint_Mt__Int__Oint_J,type,
    bNF_re9179032068089188439nt_int: ( fun_assn_fun_int_o * fun_fu8462857099809827880_int_o * fun_as3983628580203722482n_assn * fun_int_fun_int_int ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Int__Oint_001t__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_001t__fun_It__Nat__Onat_Mt__Int__Oint_J,type,
    bNF_re8253829423823436451at_int: ( fun_assn_fun_int_o * fun_fu1909670345266947804_int_o * fun_as8240436605320707994t_assn * fun_int_fun_nat_int ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Nat__Onat_001t__Assertions__Oassn_001t__Nat__Onat,type,
    bNF_re6742580585434904145sn_nat: ( fun_assn_fun_nat_o * fun_assn_fun_nat_o ) > fun_fu5995116245991996640_nat_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Nat__Onat_001t__fun_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J,type,
    bNF_re4476954147854580547at_nat: ( fun_assn_fun_nat_o * fun_fu5995116245991996640_nat_o * fun_as3983628580203722482n_assn * fun_nat_fun_nat_nat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J,type,
    bNF_re8087912568774460395at_nat: ( fun_assn_fun_nat_o * fun_fu1837719853043986488_nat_o * fun_as8240436605320707994t_assn * fun_nat_fun_nat_nat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Rat__Orat_001t__Assertions__Oassn_001t__Rat__Orat,type,
    bNF_re9003240792272343649sn_rat: ( fun_assn_fun_rat_o * fun_assn_fun_rat_o ) > fun_fu2448905236868045008_rat_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Rat__Orat_001t__fun_It__Assertions__Oassn_Mt__Assertions__Oassn_J_001t__fun_It__Rat__Orat_Mt__Rat__Orat_J,type,
    bNF_re2823698778247379291at_rat: ( fun_assn_fun_rat_o * fun_fu2448905236868045008_rat_o * fun_as3983628580203722482n_assn * fun_rat_fun_rat_rat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Assertions__Oassn_001t__Rat__Orat_001t__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_001t__fun_It__Nat__Onat_Mt__Rat__Orat_J,type,
    bNF_re3141659225902627835at_rat: ( fun_assn_fun_rat_o * fun_fu3204908904631799856_rat_o * fun_as8240436605320707994t_assn * fun_rat_fun_nat_rat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Assertions__Oassn_001t__Code____Numeral__Ointeger_001t__Assertions__Oassn,type,
    bNF_re1475883931861434731r_assn: ( fun_Co4819230592921789445assn_o * fun_Co4819230592921789445assn_o ) > fun_fu8741070064424208326assn_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Assertions__Oassn_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
    bNF_re1352478543071193706n_assn: ( fun_Co4819230592921789445assn_o * fun_fu8741070064424208326assn_o * fun_Co1981900195452921617nteger * fun_as3983628580203722482n_assn ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Assertions__Oassn_001t__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Nat__Onat_Mt__Assertions__Oassn_J,type,
    bNF_re6260911108158577797t_assn: ( fun_Co4819230592921789445assn_o * fun_fu4239617643652599019assn_o * fun_Co6226381647958292740nteger * fun_as8240436605320707994t_assn ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    bNF_re1062419521925302741nteger: ( fun_Co2081214437782444048eger_o * fun_Co2081214437782444048eger_o ) > fun_fu4788845708739168348eger_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    bNF_re3535719783769048059nteger: ( fun_Co2081214437782444048eger_o * fun_Co2466309612238040426eger_o ) > fun_fu1909630106382427190eger_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    bNF_re9064814426586422153nteger: ( fun_Co2081214437782444048eger_o * fun_fu4788845708739168348eger_o * fun_Co1981900195452921617nteger * fun_Co1981900195452921617nteger ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J,type,
    bNF_re380175692409962607nteger: ( fun_Co2081214437782444048eger_o * fun_fu6536794386266229110eger_o * fun_Co6226381647958292740nteger * fun_Co6226381647958292740nteger ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
    bNF_re8292407664666371323nteger: ( fun_Co2081214437782444048eger_o * fun_fu8559083954280392170eger_o ) > fun_fu865538946246809014eger_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
    bNF_re2888858428391045491er_int: ( fun_Co8353275306710069249_int_o * fun_Co8353275306710069249_int_o ) > fun_fu7391974349310290878_int_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
    bNF_re2891348898900095767er_nat: ( fun_Co8353275306710069249_int_o * fun_Co1375048237525739357_nat_o ) > fun_fu7320023857087329562_nat_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Int__Oint_Mt__Int__Oint_J,type,
    bNF_re2755378959209877878nt_int: ( fun_Co8353275306710069249_int_o * fun_fu7391974349310290878_int_o * fun_Co1981900195452921617nteger * fun_int_fun_int_int ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Nat__Onat_Mt__Int__Oint_J,type,
    bNF_re5458596770363244685at_int: ( fun_Co8353275306710069249_int_o * fun_fu3760962777756892391_int_o * fun_Co6226381647958292740nteger * fun_int_fun_nat_int ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Num__Onum,type,
    bNF_re8228350525668042759er_num: ( fun_Co8353275306710069249_int_o * fun_fu7485687605903516013_num_o ) > fun_fu7909047026757000106_num_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
    bNF_re5201166830993046715er_nat: ( fun_Co1375048237525739357_nat_o * fun_Co1375048237525739357_nat_o ) > fun_fu4924233495492459638_nat_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
    bNF_re1758498617148825349er_num: ( fun_Co1375048237525739357_nat_o * fun_Co2133228800495250323_num_o ) > fun_fu5250823318952805804_num_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J,type,
    bNF_re2633667331928566882at_nat: ( fun_Co1375048237525739357_nat_o * fun_fu4924233495492459638_nat_o * fun_Co1981900195452921617nteger * fun_nat_fun_nat_nat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J,type,
    bNF_re1755872562029691349at_nat: ( fun_Co1375048237525739357_nat_o * fun_fu3689012285533931075_nat_o * fun_Co6226381647958292740nteger * fun_nat_fun_nat_nat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Num__Onum,type,
    bNF_re6729214450274395051er_num: ( fun_Co1375048237525739357_nat_o * fun_fu7485687605903516013_num_o ) > fun_fu5513256665162130182_num_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Num__Onum_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    bNF_re7350422212947406738nteger: ( fun_Co2133228800495250323_num_o * fun_Co2081214437782444048eger_o ) > fun_fu6011537917091710943eger_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Num__Onum_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
    bNF_re1115778939589153080nteger: ( fun_Co2133228800495250323_num_o * fun_fu8559083954280392170eger_o ) > fun_fu5480185501004512569eger_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Rat__Orat_001t__Code____Numeral__Ointeger_001t__Rat__Orat,type,
    bNF_re4698098036185532619er_rat: ( fun_Co625613742390903637_rat_o * fun_Co625613742390903637_rat_o ) > fun_fu1378022486368508006_rat_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Rat__Orat_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Rat__Orat_Mt__Rat__Orat_J,type,
    bNF_re7829844138342828666at_rat: ( fun_Co625613742390903637_rat_o * fun_fu1378022486368508006_rat_o * fun_Co1981900195452921617nteger * fun_rat_fun_rat_rat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Code____Numeral__Ointeger_001t__Rat__Orat_001t__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Nat__Onat_Mt__Rat__Orat_J,type,
    bNF_re419171836357356005at_rat: ( fun_Co625613742390903637_rat_o * fun_fu5056201337121744443_rat_o * fun_Co6226381647958292740nteger * fun_rat_fun_nat_rat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001_Eo_001_Eo,type,
    bNF_re6574881592172037608er_o_o: ( fun_in4891666191172872833eger_o * fun_o_fun_o_o ) > fun_fu4168831735773172575er_o_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
    bNF_re3379532845092657523nteger: ( fun_in4891666191172872833eger_o * fun_in4891666191172872833eger_o ) > fun_fu726873822431485118eger_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Int__Oint,type,
    bNF_re3804157879324367682nt_int: ( fun_in4891666191172872833eger_o * fun_int_fun_int_o * fun_int_int * fun_Code_integer_int ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
    bNF_re1831474436612530402atural: ( fun_in4891666191172872833eger_o * fun_na2240068485812228818ural_o * fun_int_nat * fun_Co3734316457315071362atural ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_re2807294637932363402at_nat: ( fun_in4891666191172872833eger_o * fun_nat_fun_nat_o * fun_int_nat * fun_Code_integer_nat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Num__Onum_001t__Num__Onum,type,
    bNF_re6718328864250387230um_num: ( fun_in4891666191172872833eger_o * fun_num_fun_num_o * fun_int_num * fun_Code_integer_num ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__fun_It__Int__Oint_M_Eo_J_001t__fun_It__Code____Numeral__Ointeger_M_Eo_J,type,
    bNF_re5122946609719563319eger_o: ( fun_in4891666191172872833eger_o * fun_fu4168831735773172575er_o_o * fun_int_fun_int_o * fun_Co2081214437782444048eger_o ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    bNF_re9130850084932126070nteger: ( fun_in4891666191172872833eger_o * fun_fu726873822431485118eger_o * fun_int_fun_int_int * fun_Co1981900195452921617nteger ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Nat__Onat_M_Eo_J,type,
    bNF_re6821560923358799272_nat_o: ( fun_in4891666191172872833eger_o * fun_fu7564235448449272366at_o_o * fun_int_fun_nat_o * fun_Co1375048237525739357_nat_o ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Onatural_001t__Int__Oint_001t__Code____Numeral__Onatural,type,
    bNF_re5484556299188842761atural: ( fun_in812919657445819766ural_o * fun_in812919657445819766ural_o ) > fun_fu2512357375982829608ural_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Onatural_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    bNF_re4876244239765966167atural: ( fun_in812919657445819766ural_o * fun_fu2512357375982829608ural_o * fun_int_fun_int_int * fun_Co6813818151677833714atural ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_Eo_001_Eo,type,
    bNF_re5089333283451836215nt_o_o: ( fun_int_fun_int_o * fun_o_fun_o_o ) > fun_fu6971708032831053102nt_o_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    bNF_re1784066744496875891nteger: ( fun_int_fun_int_o * fun_Co2081214437782444048eger_o * fun_int_Code_integer * fun_int_Code_integer ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
    bNF_re343602593470180162er_int: ( fun_int_fun_int_o * fun_Co8353275306710069249_int_o * fun_int_Code_integer * fun_int_int ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Rat__Orat,type,
    bNF_re8934335040747510510er_rat: ( fun_int_fun_int_o * fun_Co625613742390903637_rat_o * fun_int_Code_integer * fun_int_rat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    bNF_re6290619412732081552atural: ( fun_int_fun_int_o * fun_Co9066792663755620495ural_o * fun_int_Code_natural * fun_in7496697025202066910atural ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
    bNF_re982302072995117890nteger: ( fun_int_fun_int_o * fun_in4891666191172872833eger_o * fun_int_int * fun_int_Code_integer ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
    bNF_re4712519889275205905nt_int: ( fun_int_fun_int_o * fun_int_fun_int_o ) > fun_fu4208408993564413984_int_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Rat__Orat,type,
    bNF_re4079880299697760445nt_rat: ( fun_int_fun_int_o * fun_int_fun_rat_o * fun_int_int * fun_int_rat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_re3715656647883201625at_nat: ( fun_int_fun_int_o * fun_nat_fun_nat_o ) > fun_fu6391371659531026648_nat_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Num__Onum_001t__Num__Onum,type,
    bNF_re7626690874201225453um_num: ( fun_int_fun_int_o * fun_num_fun_num_o ) > fun_fu6636849678353221188_num_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    bNF_re6250860962936578807nt_int: ( fun_int_fun_int_o * fun_Pr9018117161326028078_int_o ) > fun_fu6699046866436802030_int_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
    bNF_re2214769303045360666nt_rat: ( fun_int_fun_int_o * fun_Pr7537129237977221859_rat_o ) > fun_fu7677565902479959693_rat_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Rat__Orat_001t__Code____Numeral__Ointeger,type,
    bNF_re1382721322319792878nteger: ( fun_int_fun_int_o * fun_ra1401953663915778005eger_o * fun_int_rat * fun_int_Code_integer ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Rat__Orat_001t__Int__Oint,type,
    bNF_re3396611533439285437at_int: ( fun_int_fun_int_o * fun_rat_fun_int_o * fun_int_rat * fun_int_int ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Rat__Orat_001t__Rat__Orat,type,
    bNF_re2763971943861839977at_rat: ( fun_int_fun_int_o * fun_rat_fun_rat_o * fun_int_rat * fun_int_rat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__fun_It__Int__Oint_M_Eo_J_001t__fun_It__Int__Oint_M_Eo_J,type,
    bNF_re8654322613993568759_int_o: ( fun_int_fun_int_o * fun_fu6971708032831053102nt_o_o ) > fun_fu3604077110225719534nt_o_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Int__Oint_Mt__Int__Oint_J,type,
    bNF_re5717476210804479843nt_int: ( fun_int_fun_int_o * fun_fu4208408993564413984_int_o ) > fun_fu6471771360118961870_int_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    bNF_re4808202430149235895nt_int: ( fun_int_fun_int_o * fun_fu6699046866436802030_int_o * fun_in1696471567231710611nt_int * fun_in1696471567231710611nt_int ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Int__Oint_Mt__Rat__Orat_J,type,
    bNF_re2486238095283335024nt_rat: ( fun_int_fun_int_o * fun_fu7677565902479959693_rat_o ) > fun_fu1057420046263839031_rat_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Nat__Onat_M_Eo_J,type,
    bNF_re8347998229424194295_nat_o: ( fun_int_fun_int_o * fun_fu7564235448449272366at_o_o ) > fun_fu1853282479105234414at_o_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat,type,
    bNF_re4343356799547411545nt_nat: ( fun_int_fun_nat_o * fun_int_fun_nat_o ) > fun_fu1740668139746582744_nat_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Nat__Onat_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J,type,
    bNF_re7487286609730949711at_nat: ( fun_int_fun_nat_o * fun_fu1740668139746582744_nat_o * fun_int_fun_int_int * fun_nat_fun_nat_nat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Num__Onum_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
    bNF_re151304249936775380nteger: ( fun_int_fun_num_o * fun_na6318815019539281885eger_o ) > fun_fu5133016914843556765eger_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Num__Onum_001t__Num__Onum_001t__Code____Numeral__Ointeger,type,
    bNF_re7315484114762210078nteger: ( fun_int_fun_num_o * fun_nu5413996832991386387eger_o ) > fun_fu914036251014348755eger_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Rat__Orat_001t__Int__Oint_001t__Rat__Orat,type,
    bNF_re4480299549022435433nt_rat: ( fun_int_fun_rat_o * fun_int_fun_rat_o ) > fun_fu7417829167477406920_rat_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Rat__Orat_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Rat__Orat_Mt__Rat__Orat_J,type,
    bNF_re3619483633275351143at_rat: ( fun_int_fun_rat_o * fun_fu7417829167477406920_rat_o * fun_int_fun_int_int * fun_rat_fun_rat_rat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
    bNF_re1599192376174140603nteger: ( fun_na6318815019539281885eger_o * fun_na6318815019539281885eger_o ) > fun_fu248784781839935862eger_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Num__Onum_001t__Code____Numeral__Ointeger,type,
    bNF_re8763372240999575301nteger: ( fun_na6318815019539281885eger_o * fun_nu5413996832991386387eger_o ) > fun_fu5877413357861189036eger_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    bNF_re5654810952157900898nteger: ( fun_na6318815019539281885eger_o * fun_fu248784781839935862eger_o * fun_nat_fun_nat_nat * fun_Co1981900195452921617nteger ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Onatural_001_Eo_001_Eo,type,
    bNF_re2785088596696291543al_o_o: ( fun_na2240068485812228818ural_o * fun_o_fun_o_o ) > fun_fu1622112948621879430al_o_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Onatural_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
    bNF_re5252274238750452962nteger: ( fun_na2240068485812228818ural_o * fun_in4891666191172872833eger_o * fun_nat_int * fun_Co2940338738630218498nteger ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Onatural_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
    bNF_re3704215830270325841atural: ( fun_na2240068485812228818ural_o * fun_na2240068485812228818ural_o ) > fun_fu2034268335391280352ural_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Onatural_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_re7333046803109187065at_nat: ( fun_na2240068485812228818ural_o * fun_nat_fun_nat_o * fun_nat_nat * fun_Code_natural_nat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Onatural_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Code____Numeral__Onatural_M_Eo_J,type,
    bNF_re701982943866114111ural_o: ( fun_na2240068485812228818ural_o * fun_fu1622112948621879430al_o_o * fun_nat_fun_nat_o * fun_Co7302518231560758906ural_o ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Onatural_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Nat__Onat_M_Eo_J,type,
    bNF_re2187160483004581015_nat_o: ( fun_na2240068485812228818ural_o * fun_fu7564235448449272366at_o_o * fun_nat_fun_nat_o * fun_Co196715998180962002_nat_o ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Code____Numeral__Onatural_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    bNF_re1400205106991740995atural: ( fun_na2240068485812228818ural_o * fun_fu2034268335391280352ural_o * fun_nat_fun_nat_nat * fun_Co6813818151677833714atural ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
    bNF_re6022984109467102297at_int: ( fun_nat_fun_int_o * fun_nat_fun_int_o ) > fun_fu2446185911988100312_int_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Int__Oint_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Int__Oint_Mt__Int__Oint_J,type,
    bNF_re3392879465770906191nt_int: ( fun_nat_fun_int_o * fun_fu2446185911988100312_int_o * fun_nat_fun_nat_nat * fun_int_fun_int_int ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001_Eo,type,
    bNF_re4705727531993890431at_o_o: ( fun_nat_fun_nat_o * fun_o_fun_o_o ) > fun_fu7564235448449272366at_o_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Assertions__Oassn_001t__Assertions__Oassn,type,
    bNF_re4051817429369991249n_assn: ( fun_nat_fun_nat_o * fun_assn_fun_assn_o ) > fun_fu6461175078876253408assn_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Assertions__Oassn_001t__Code____Numeral__Ointeger,type,
    bNF_re1831131418152741254nteger: ( fun_nat_fun_nat_o * fun_as7521517929205406341eger_o ) > fun_fu5719784276005855083eger_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Assertions__Oassn_001t__Int__Oint,type,
    bNF_re4792267480158271317sn_int: ( fun_nat_fun_nat_o * fun_assn_fun_int_o ) > fun_fu1909670345266947804_int_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Assertions__Oassn_001t__Nat__Onat,type,
    bNF_re4794757950667321593sn_nat: ( fun_nat_fun_nat_o * fun_assn_fun_nat_o ) > fun_fu1837719853043986488_nat_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Assertions__Oassn_001t__Rat__Orat,type,
    bNF_re4159627890580825857sn_rat: ( fun_nat_fun_nat_o * fun_assn_fun_rat_o ) > fun_fu3204908904631799856_rat_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Assertions__Oassn,type,
    bNF_re2692373401909853574r_assn: ( fun_nat_fun_nat_o * fun_Co4819230592921789445assn_o ) > fun_fu4239617643652599019assn_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    bNF_re1236659899165691067nteger: ( fun_nat_fun_nat_o * fun_Co2081214437782444048eger_o ) > fun_fu6536794386266229110eger_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
    bNF_re3514700588913618570er_int: ( fun_nat_fun_nat_o * fun_Co8353275306710069249_int_o ) > fun_fu3760962777756892391_int_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
    bNF_re3517191059422668846er_nat: ( fun_nat_fun_nat_o * fun_Co1375048237525739357_nat_o ) > fun_fu3689012285533931075_nat_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Rat__Orat,type,
    bNF_re2882060999336173110er_rat: ( fun_nat_fun_nat_o * fun_Co625613742390903637_rat_o ) > fun_fu5056201337121744443_rat_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    bNF_re6101645755646507080atural: ( fun_nat_fun_nat_o * fun_Co9066792663755620495ural_o * fun_nat_Code_natural * fun_na6574806417004769082atural ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
    bNF_re4153400068438556298nteger: ( fun_nat_fun_nat_o * fun_in4891666191172872833eger_o * fun_nat_int * fun_nat_Code_integer ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Code____Numeral__Onatural,type,
    bNF_re2976995220195273813atural: ( fun_nat_fun_nat_o * fun_in812919657445819766ural_o * fun_nat_int * fun_nat_Code_natural ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Int__Oint,type,
    bNF_re6650684261131312217nt_int: ( fun_nat_fun_nat_o * fun_int_fun_int_o * fun_nat_int * fun_nat_int ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat,type,
    bNF_re6653174731640362493nt_nat: ( fun_nat_fun_nat_o * fun_int_fun_nat_o * fun_nat_int * fun_nat_nat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Rat__Orat,type,
    bNF_re6018044671553866757nt_rat: ( fun_nat_fun_nat_o * fun_int_fun_rat_o * fun_nat_int * fun_nat_rat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
    bNF_re2605341659958429177atural: ( fun_nat_fun_nat_o * fun_na2240068485812228818ural_o * fun_nat_nat * fun_nat_Code_natural ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_re5653821019739307937at_nat: ( fun_nat_fun_nat_o * fun_nat_fun_nat_o ) > fun_fu9201817095025044880_nat_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Num__Onum_001t__Num__Onum,type,
    bNF_re341483209202555957um_num: ( fun_nat_fun_nat_o * fun_num_fun_num_o ) > fun_fu223923076992463612_num_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
    bNF_re6830278522597306478at_int: ( fun_nat_fun_nat_o * fun_Pr4738963024209204295_int_o * fun_na1476630412504255114at_nat * fun_nat_int ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat_001t__Code____Numeral__Ointeger,type,
    bNF_re4553819317763231286nteger: ( fun_nat_fun_nat_o * fun_ra1401953663915778005eger_o * fun_nat_rat * fun_nat_Code_integer ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat_001t__Code____Numeral__Onatural,type,
    bNF_re3377414469519948801atural: ( fun_nat_fun_nat_o * fun_ra6546579167043500746ural_o * fun_nat_rat * fun_nat_Code_natural ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat_001t__Int__Oint,type,
    bNF_re5334775905295391749at_int: ( fun_nat_fun_nat_o * fun_rat_fun_int_o * fun_nat_rat * fun_nat_int ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat_001t__Nat__Onat,type,
    bNF_re5337266375804442025at_nat: ( fun_nat_fun_nat_o * fun_rat_fun_nat_o * fun_nat_rat * fun_nat_nat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat_001t__Rat__Orat,type,
    bNF_re4702136315717946289at_rat: ( fun_nat_fun_nat_o * fun_rat_fun_rat_o * fun_nat_rat * fun_nat_rat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    bNF_re4578097776928471693nteger: ( fun_nat_fun_nat_o * fun_fu726873822431485118eger_o * fun_nat_fun_int_int * fun_na7078387940644931716nteger ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Int__Oint_Mt__Int__Oint_J,type,
    bNF_re5651586111134833323nt_int: ( fun_nat_fun_nat_o * fun_fu4208408993564413984_int_o * fun_nat_fun_int_int * fun_nat_fun_int_int ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Nat__Onat_M_Eo_J,type,
    bNF_re1448341924010609215_nat_o: ( fun_nat_fun_nat_o * fun_fu7564235448449272366at_o_o * fun_nat_fun_nat_o * fun_nat_fun_nat_o ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    bNF_re728283343719287275atural: ( fun_nat_fun_nat_o * fun_fu2034268335391280352ural_o * fun_nat_fun_nat_nat * fun_na607345901702507418atural ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J,type,
    bNF_re5162689864697376059at_nat: ( fun_nat_fun_nat_o * fun_fu9201817095025044880_nat_o * fun_nat_fun_nat_nat * fun_nat_fun_nat_nat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Rat__Orat_001t__Nat__Onat_001t__Rat__Orat,type,
    bNF_re5790763769214331825at_rat: ( fun_nat_fun_rat_o * fun_nat_fun_rat_o ) > fun_fu5655606085901093248_rat_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Rat__Orat_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Rat__Orat_Mt__Rat__Orat_J,type,
    bNF_re1294886888241777491at_rat: ( fun_nat_fun_rat_o * fun_fu5655606085901093248_rat_o * fun_nat_fun_nat_nat * fun_rat_fun_rat_rat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    bNF_re5202476307641864082nteger: ( fun_nu5413996832991386387eger_o * fun_Co2081214437782444048eger_o ) > fun_fu1832432239164473695eger_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    bNF_re8002177354109194296nteger: ( fun_nu5413996832991386387eger_o * fun_Co2466309612238040426eger_o ) > fun_fu7605985262670345913eger_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
    bNF_re6324211044263125204er_nat: ( fun_num_fun_int_o * fun_Co1375048237525739357_nat_o ) > fun_fu8841175022949123613_nat_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
    bNF_re2881542830418903838er_num: ( fun_num_fun_int_o * fun_Co2133228800495250323_num_o ) > fun_fu9167764846409469779_num_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    bNF_re6741283560065411407nteger: ( fun_num_fun_num_o * fun_Co2081214437782444048eger_o ) > fun_fu3131294797999541474eger_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
    bNF_re6501075790457514782nteger: ( fun_num_fun_num_o * fun_in4891666191172872833eger_o ) > fun_fu6196024946523381971eger_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Code____Numeral__Onatural,type,
    bNF_re5324670942214232297atural: ( fun_num_fun_num_o * fun_in812919657445819766ural_o * fun_num_int * fun_num_Code_natural ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Int__Oint,type,
    bNF_re1822329894187522285nt_int: ( fun_num_fun_num_o * fun_int_fun_int_o ) > fun_fu5908277796454533188_int_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Nat__Onat,type,
    bNF_re1824820364696572561nt_nat: ( fun_num_fun_num_o * fun_int_fun_nat_o * fun_num_int * fun_num_nat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Rat__Orat,type,
    bNF_re1189690304610076825nt_rat: ( fun_num_fun_num_o * fun_int_fun_rat_o * fun_num_int * fun_num_rat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
    bNF_re6129422230220670146nteger: ( fun_num_fun_num_o * fun_na6318815019539281885eger_o * fun_num_nat * fun_num_Code_integer ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
    bNF_re4953017381977387661atural: ( fun_num_fun_num_o * fun_na2240068485812228818ural_o * fun_num_nat * fun_num_Code_natural ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Nat__Onat_001t__Int__Oint,type,
    bNF_re822976182286467729at_int: ( fun_num_fun_num_o * fun_nat_fun_int_o * fun_num_nat * fun_num_int ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_re825466652795518005at_nat: ( fun_num_fun_num_o * fun_nat_fun_nat_o * fun_num_nat * fun_num_nat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Nat__Onat_001t__Rat__Orat,type,
    bNF_re190336592709022269at_rat: ( fun_num_fun_num_o * fun_nat_fun_rat_o * fun_num_nat * fun_num_rat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__fun_It__Num__Onum_Mt__Int__Oint_J_001t__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J,type,
    bNF_re4520166952630509772nteger: ( fun_num_fun_num_o * fun_fu6196024946523381971eger_o * fun_num_fun_num_int * fun_nu2537414170016844299nteger ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__fun_It__Num__Onum_Mt__Int__Oint_J_001t__fun_It__Num__Onum_Mt__Int__Oint_J,type,
    bNF_re6378542964492772123um_int: ( fun_num_fun_num_o * fun_fu5908277796454533188_int_o * fun_num_fun_num_int * fun_num_fun_num_int ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    bNF_re7145576690424134365nt_int: ( fun_Pr9018117161326028078_int_o * fun_Pr9018117161326028078_int_o ) > fun_fu5323616038969315652_int_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    bNF_re4734134812813710757nt_int: ( fun_Pr9018117161326028078_int_o * fun_fu5323616038969315652_int_o * fun_Pr1308109350235310159nt_int * fun_Pr1308109350235310159nt_int ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
    bNF_re8279943556446156061nt_rat: ( fun_Pr7537129237977221859_rat_o * fun_Pr7537129237977221859_rat_o ) > fun_fu4306744791715064858_rat_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Rat__Orat_Mt__Rat__Orat_J,type,
    bNF_re6323452265856231590at_rat: ( fun_Pr7537129237977221859_rat_o * fun_fu4306744791715064858_rat_o * fun_Pr1308109350235310159nt_int * fun_rat_fun_rat_rat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_Eo_001_Eo,type,
    bNF_re6644619430987730960nt_o_o: ( fun_Pr4738963024209204295_int_o * fun_o_fun_o_o ) > fun_fu9090758901314268781nt_o_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
    bNF_re7400052026677387805at_int: ( fun_Pr4738963024209204295_int_o * fun_Pr4738963024209204295_int_o ) > fun_fu4638078822479986034_int_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001t__fun_It__Int__Oint_M_Eo_J,type,
    bNF_re4195927319312321177_int_o: ( fun_Pr4738963024209204295_int_o * fun_fu9090758901314268781nt_o_o * fun_Pr2028404973800837934_nat_o * fun_int_fun_int_o ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Int__Oint_Mt__Int__Oint_J,type,
    bNF_re8869769828555196650nt_int: ( fun_Pr4738963024209204295_int_o * fun_fu4638078822479986034_int_o * fun_Pr2477239776880934807at_nat * fun_int_fun_int_int ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
    bNF_re3666534408544137501at_o_o: ( fun_Pr2028404973800837934_nat_o * fun_o_fun_o_o ) > fun_fu9045186299510176150at_o_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    bNF_re2241393799969408733at_nat: ( fun_Pr2028404973800837934_nat_o * fun_Pr2028404973800837934_nat_o ) > fun_fu3373238862511017284_nat_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
    bNF_re4103222659376994899_nat_o: ( fun_Pr2028404973800837934_nat_o * fun_fu9045186299510176150at_o_o * fun_Pr2028404973800837934_nat_o * fun_Pr2028404973800837934_nat_o ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    bNF_re6214786843070381989at_nat: ( fun_Pr2028404973800837934_nat_o * fun_fu3373238862511017284_nat_o * fun_Pr2477239776880934807at_nat * fun_Pr2477239776880934807at_nat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    bNF_re8417623677625516633nteger: ( fun_Pr1520749766685617582unit_o * fun_Co2081214437782444048eger_o * fun_Pr1820225556744648189nteger * fun_Pr1820225556744648189nteger ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    bNF_re5641277236161133866atural: ( fun_Pr1520749766685617582unit_o * fun_Co9066792663755620495ural_o * fun_Pr6278675377255837256atural * fun_Pr3616673511947161127atural ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Int__Oint_001t__Int__Oint,type,
    bNF_re8422471777688076791nt_int: ( fun_Pr1520749766685617582unit_o * fun_int_fun_int_o * fun_Product_unit_int * fun_Product_unit_int ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Code____Numeral__Ointeger_001t__Rat__Orat_001t__Code____Numeral__Ointeger,type,
    bNF_re2328245411608324299nteger: ( fun_ra1401953663915778005eger_o * fun_ra1401953663915778005eger_o ) > fun_fu841611025618976102eger_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Code____Numeral__Ointeger_001t__fun_It__Rat__Orat_Mt__Rat__Orat_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    bNF_re10698882459692666nteger: ( fun_ra1401953663915778005eger_o * fun_fu841611025618976102eger_o * fun_rat_fun_rat_rat * fun_Co1981900195452921617nteger ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Code____Numeral__Onatural_001t__Rat__Orat_001t__Code____Numeral__Onatural,type,
    bNF_re4433268865704509537atural: ( fun_ra6546579167043500746ural_o * fun_ra6546579167043500746ural_o ) > fun_fu2627094579170320592ural_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Code____Numeral__Onatural_001t__fun_It__Rat__Orat_Mt__Rat__Orat_J_001t__fun_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    bNF_re4979465074148308571atural: ( fun_ra6546579167043500746ural_o * fun_fu2627094579170320592ural_o * fun_rat_fun_rat_rat * fun_Co6813818151677833714atural ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Int__Oint_001t__Rat__Orat_001t__Int__Oint,type,
    bNF_re5838490730811218025at_int: ( fun_rat_fun_int_o * fun_rat_fun_int_o ) > fun_fu991806985645568200_int_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Int__Oint_001t__fun_It__Rat__Orat_Mt__Rat__Orat_J_001t__fun_It__Int__Oint_Mt__Int__Oint_J,type,
    bNF_re8256098235694157927nt_int: ( fun_rat_fun_int_o * fun_fu991806985645568200_int_o * fun_rat_fun_rat_rat * fun_int_fun_int_int ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Nat__Onat_001t__Rat__Orat_001t__Nat__Onat,type,
    bNF_re5469327641083423665at_nat: ( fun_rat_fun_nat_o * fun_rat_fun_nat_o ) > fun_fu7747438168682512768_nat_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Nat__Onat_001t__fun_It__Rat__Orat_Mt__Rat__Orat_J_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J,type,
    bNF_re802536597765851987at_nat: ( fun_rat_fun_nat_o * fun_fu7747438168682512768_nat_o * fun_rat_fun_rat_rat * fun_nat_fun_nat_nat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Rat__Orat_001t__Rat__Orat_001t__Rat__Orat,type,
    bNF_re5606270390558447553at_rat: ( fun_rat_fun_rat_o * fun_rat_fun_rat_o ) > fun_fu4201227159558561136_rat_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__Rat__Orat_001t__Rat__Orat_001t__fun_It__Rat__Orat_Mt__Rat__Orat_J_001t__fun_It__Rat__Orat_Mt__Rat__Orat_J,type,
    bNF_re6158105658165029227at_rat: ( fun_rat_fun_rat_o * fun_fu4201227159558561136_rat_o * fun_rat_fun_rat_rat * fun_rat_fun_rat_rat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J_001t__fun_It__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J,type,
    bNF_re6079157782214477977nteger: ( fun_fu4788845708739168348eger_o * fun_fu9208662316977796352eger_o * fun_fu5844746416483971737nteger * fun_fu5844746416483971737nteger ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_001t__fun_It__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J_001t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_J,type,
    bNF_re1917959877943869547nteger: ( fun_fu1909630106382427190eger_o * fun_fu7865199641817216212eger_o * fun_fu5844746416483971737nteger * fun_fu7234567020521114219nteger ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Int__Oint_Mt__Nat__Onat_J_001t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_001t__fun_It__Int__Oint_Mt__Num__Onum_J,type,
    bNF_re4971494712987572401nt_num: ( fun_fu7320023857087329562_nat_o * fun_fu7909047026757000106_num_o ) > fun_fu6437682067762269056_num_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Nat__Onat_Mt__Num__Onum_J_001t__fun_It__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J_001t__fun_It__fun_It__Int__Oint_Mt__Nat__Onat_J_Mt__fun_It__Int__Oint_Mt__Num__Onum_J_J,type,
    bNF_re2315437451418592029nt_num: ( fun_fu5250823318952805804_num_o * fun_fu7828939442023433772_num_o * fun_fu5844746416483971737nteger * fun_fu3670889464739865373nt_num ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_001t__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J,type,
    bNF_re4862162959298630877nteger: ( fun_fu6011537917091710943eger_o * fun_fu5480185501004512569eger_o ) > fun_fu8324349134136105556eger_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_J_001t__fun_It__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J,type,
    bNF_re1125984453589466475nteger: ( fun_fu865538946246809014eger_o * fun_fu8324349134136105556eger_o * fun_fu7234567020521114219nteger * fun_fu5844746416483971737nteger ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_001t__fun_It__Nat__Onat_Mt__Num__Onum_J_001t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_J_001t__fun_It__fun_It__Int__Oint_Mt__Nat__Onat_J_Mt__fun_It__Int__Oint_Mt__Num__Onum_J_J,type,
    bNF_re2788112638341148655nt_num: ( fun_fu5513256665162130182_num_o * fun_fu6437682067762269056_num_o * fun_fu7234567020521114219nteger * fun_fu3670889464739865373nt_num ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Int__Oint_M_Eo_J_001t__fun_It__Int__Oint_M_Eo_J_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Nat__Onat_M_Eo_J,type,
    bNF_re3413259116532488669_nat_o: ( fun_fu6971708032831053102nt_o_o * fun_fu7564235448449272366at_o_o ) > fun_fu5378497120668327052at_o_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    bNF_re347998642166628361_int_o: ( fun_fu4208408993564413984_int_o * fun_fu3604077110225719534nt_o_o ) > fun_fu6738731901453605870nt_o_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J,type,
    bNF_re6139702209426042631nt_int: ( fun_fu4208408993564413984_int_o * fun_fu6471771360118961870_int_o ) > fun_fu2657526370245387306_int_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Rat__Orat_J_J,type,
    bNF_re8704142042620765940nt_rat: ( fun_fu4208408993564413984_int_o * fun_fu1057420046263839031_rat_o ) > fun_fu2931456868620722337_rat_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    bNF_re3454423673187561737_nat_o: ( fun_fu4208408993564413984_int_o * fun_fu1853282479105234414at_o_o ) > fun_fu3188400912490975470at_o_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Int__Oint_Mt__Nat__Onat_J_001t__fun_It__Int__Oint_Mt__Nat__Onat_J_001t__fun_It__Int__Oint_Mt__Num__Onum_J_001t__fun_It__Int__Oint_Mt__Num__Onum_J,type,
    bNF_re7119215340858952409nt_num: ( fun_fu6391371659531026648_nat_o * fun_fu6636849678353221188_num_o ) > fun_fu2275682760404419928_num_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Int__Oint_Mt__Nat__Onat_J_001t__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Int__Oint_Mt__Num__Onum_J_001t__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J,type,
    bNF_re6745137351003365765nteger: ( fun_fu5133016914843556765eger_o * fun_fu914036251014348755eger_o ) > fun_fu867726335913497644eger_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    bNF_re8316297141629263453_int_o: ( fun_fu3604077110225719534nt_o_o * fun_fu3604077110225719534nt_o_o ) > fun_fu7309969077280154820nt_o_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J,type,
    bNF_re1265104817942401883nt_int: ( fun_fu3604077110225719534nt_o_o * fun_fu6471771360118961870_int_o ) > fun_fu4429252470074529710_int_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    bNF_re2199350135795421021_nat_o: ( fun_fu3604077110225719534nt_o_o * fun_fu1853282479105234414at_o_o ) > fun_fu3364590669033493516at_o_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_J_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_J,type,
    bNF_re1178300526625999197_int_o: ( fun_fu3604077110225719534nt_o_o * fun_fu6738731901453605870nt_o_o * fun_fu14259429304446855_int_o * fun_fu14259429304446855_int_o ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    bNF_re4000469476744628827_int_o: ( fun_fu6471771360118961870_int_o * fun_fu3604077110225719534nt_o_o ) > fun_fu783388071822146350nt_o_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    bNF_re7106894507765562203_nat_o: ( fun_fu6471771360118961870_int_o * fun_fu1853282479105234414at_o_o ) > fun_fu6282320651122755630at_o_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_J_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    bNF_re7874820051692727037nt_int: ( fun_fu6471771360118961870_int_o * fun_fu2657526370245387306_int_o * fun_fu3518228427392506443nt_int * fun_fu3518228427392506443nt_int ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Rat__Orat_J_J_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Rat__Orat_J_J_J,type,
    bNF_re424392766803272243nt_rat: ( fun_fu1057420046263839031_rat_o * fun_fu2931456868620722337_rat_o * fun_fu3528811849556752711nt_int * fun_fu4582018930532246947nt_rat ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    bNF_re3339008293687758685_int_o: ( fun_fu1853282479105234414at_o_o * fun_fu3604077110225719534nt_o_o ) > fun_fu2720337172504440700nt_o_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J,type,
    bNF_re2152976507081458779nt_int: ( fun_fu1853282479105234414at_o_o * fun_fu6471771360118961870_int_o ) > fun_fu6544435175084778670_int_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    bNF_re6445433324708692061_nat_o: ( fun_fu1853282479105234414at_o_o * fun_fu1853282479105234414at_o_o ) > fun_fu7998330801112555204at_o_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_J_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    bNF_re3759051196448504669_nat_o: ( fun_fu1853282479105234414at_o_o * fun_fu3188400912490975470at_o_o * fun_fu6802859072977114247_nat_o * fun_fu6802859072977114247_nat_o ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Int__Oint_M_Eo_J_001t__fun_It__Int__Oint_M_Eo_J,type,
    bNF_re7446626527360113117_int_o: ( fun_fu7564235448449272366at_o_o * fun_fu6971708032831053102nt_o_o ) > fun_fu6215369687776649212nt_o_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Int__Oint_Mt__Int__Oint_J,type,
    bNF_re8576606815926651977nt_int: ( fun_fu7564235448449272366at_o_o * fun_fu4208408993564413984_int_o ) > fun_fu7344996400627858478_int_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Nat__Onat_M_Eo_J,type,
    bNF_re7140302142790738653_nat_o: ( fun_fu7564235448449272366at_o_o * fun_fu7564235448449272366at_o_o ) > fun_fu7456240966027273028at_o_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Nat__Onat_Mt__Num__Onum_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__fun_It__Int__Oint_Mt__Nat__Onat_J_Mt__fun_It__Int__Oint_Mt__Num__Onum_J_J_001t__fun_It__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J,type,
    bNF_re8577298986372545309nteger: ( fun_fu5877413357861189036eger_o * fun_fu867726335913497644eger_o * fun_fu3670889464739865373nt_num * fun_fu5844746416483971737nteger ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Nat__Onat_Mt__Num__Onum_J_001t__fun_It__Nat__Onat_Mt__Num__Onum_J_001t__fun_It__fun_It__Int__Oint_Mt__Nat__Onat_J_Mt__fun_It__Int__Oint_Mt__Num__Onum_J_J_001t__fun_It__fun_It__Int__Oint_Mt__Nat__Onat_J_Mt__fun_It__Int__Oint_Mt__Num__Onum_J_J,type,
    bNF_re62826171660744097nt_num: ( fun_fu223923076992463612_num_o * fun_fu2275682760404419928_num_o * fun_fu3670889464739865373nt_num * fun_fu3670889464739865373nt_num ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    bNF_re6610812174003455837nteger: ( fun_fu1832432239164473695eger_o * fun_fu7605985262670345913eger_o ) > fun_fu7865199641817216212eger_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Int__Oint_Mt__Nat__Onat_J_001t__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Int__Oint_Mt__Num__Onum_J,type,
    bNF_re7101714357556715909nt_num: ( fun_fu8841175022949123613_nat_o * fun_fu9167764846409469779_num_o ) > fun_fu7828939442023433772_num_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J,type,
    bNF_re2651952162905501745nteger: ( fun_fu3131294797999541474eger_o * fun_fu3131294797999541474eger_o ) > fun_fu9208662316977796352eger_o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J_001t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J_001t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_J_001t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_J,type,
    bNF_re6875969029148314861_int_o: ( fun_fu4137625842417703236nt_o_o * fun_fu7309969077280154820nt_o_o * fun_fu4169772131120368835_int_o * fun_fu4169772131120368835_int_o ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_J_001t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    bNF_re9021905627891609437nt_int: ( fun_fu8074799898941972270_int_o * fun_fu4429252470074529710_int_o * fun_fu4482892469221626457nt_int * fun_fu4482892469221626457nt_int ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_J_001t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    bNF_re4285988172461392477_nat_o: ( fun_fu5378497120668327052at_o_o * fun_fu3364590669033493516at_o_o * fun_fu7618250142905304443_nat_o * fun_fu7618250142905304443_nat_o ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_M_Eo_J_J_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_M_Eo_J_J_001t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_J_001t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_J,type,
    bNF_re7201718523177301469_int_o: ( fun_fu7590976836756945966nt_o_o * fun_fu783388071822146350nt_o_o * fun_fu8897902691871853255_int_o * fun_fu8897902691871853255_int_o ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_J_001t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    bNF_re2173054563122083805_nat_o: ( fun_fu4899062771603708206at_o_o * fun_fu6282320651122755630at_o_o * fun_fu2354122332637403079_nat_o * fun_fu2354122332637403079_nat_o ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J_001t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J_001t__fun_It__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_J_001t__fun_It__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_J,type,
    bNF_re716005714690020221_int_o: ( fun_fu6215369687776649212nt_o_o * fun_fu2720337172504440700nt_o_o * fun_fu8028891822603792907_int_o * fun_fu8028891822603792907_int_o ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_J_001t__fun_It__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    bNF_re7734436216040599901nt_int: ( fun_fu7344996400627858478_int_o * fun_fu6544435175084778670_int_o * fun_fu353361380671289177nt_int * fun_fu353361380671289177nt_int ) > $o ).

tff(sy_c_BNF__Def_Orel__fun_001t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_J_001t__fun_It__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    bNF_re7349396894857873645_nat_o: ( fun_fu7456240966027273028at_o_o * fun_fu7998330801112555204at_o_o * fun_fu2253997797533952707_nat_o * fun_fu2253997797533952707_nat_o ) > $o ).

tff(sy_c_BNF__Wellorder__Constructions_OordIso_001_Eo_001_Eo,type,
    bNF_We2654380646378065620so_o_o: set_Pr1932065953672099015od_o_o ).

tff(sy_c_BNF__Wellorder__Constructions_OordIso_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_We5258908940166488438at_nat: set_Pr4329608150637261639at_nat ).

tff(sy_c_BNF__Wellorder__Constructions_OordLess_001_Eo_001t__Nat__Onat,type,
    bNF_We8182288985678559134_o_nat: set_Pr457366540195662369at_nat ).

tff(sy_c_Basic__BNF__LFPs_Oprod_Osize__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    basic_7565498685090299632nteger: ( fun_Code_integer_nat * fun_Code_integer_nat * produc8923325533196201883nteger ) > nat ).

tff(sy_c_Basic__BNF__LFPs_Oprod_Osize__prod_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    basic_8185638495112405971atural: ( fun_Code_natural_nat * fun_Pr2804840792690441492al_nat * produc5835291356934675326atural ) > nat ).

tff(sy_c_Basic__BNF__LFPs_Oprod_Osize__prod_001t__Int__Oint_001t__Int__Oint,type,
    basic_1872990034501187214nt_int: ( fun_int_nat * fun_int_nat * product_prod_int_int ) > nat ).

tff(sy_c_Binomial_Obinomial,type,
    binomial: fun_nat_fun_nat_nat ).

tff(sy_c_Binomial_Ogbinomial_001t__Code____Numeral__Ointeger,type,
    gbinom8545251970709558553nteger: code_integer > fun_nat_Code_integer ).

tff(sy_c_Binomial_Ogbinomial_001t__Int__Oint,type,
    gbinomial_int: int > fun_nat_int ).

tff(sy_c_Binomial_Ogbinomial_001t__Nat__Onat,type,
    gbinomial_nat: fun_nat_fun_nat_nat ).

tff(sy_c_Binomial_Ogbinomial_001t__Rat__Orat,type,
    gbinomial_rat: rat > fun_nat_rat ).

tff(sy_c_Bit__Operations_Oand__int__rel,type,
    bit_and_int_rel: fun_Pr9018117161326028078_int_o ).

tff(sy_c_Bit__Operations_Oand__not__num,type,
    bit_and_not_num: num > fun_num_option_num ).

tff(sy_c_Bit__Operations_Oand__not__num__rel,type,
    bit_and_not_num_rel: fun_Pr4799464687642144302_num_o ).

tff(sy_c_Bit__Operations_Oconcat__bit,type,
    bit_concat_bit: nat > fun_int_fun_int_int ).

tff(sy_c_Bit__Operations_Oor__not__num__neg,type,
    bit_or_not_num_neg: fun_num_fun_num_num ).

tff(sy_c_Bit__Operations_Oor__not__num__neg__rel,type,
    bit_or3848514188828904588eg_rel: fun_Pr4799464687642144302_num_o ).

tff(sy_c_Bit__Operations_Oring__bit__operations__class_Onot_001t__Code____Numeral__Ointeger,type,
    bit_ri7632146776885996613nteger: fun_Co8499238673658658103nteger ).

tff(sy_c_Bit__Operations_Oring__bit__operations__class_Onot_001t__Int__Oint,type,
    bit_ri7919022796975470100ot_int: fun_int_int ).

tff(sy_c_Bit__Operations_Oring__bit__operations__class_Osigned__take__bit_001t__Code____Numeral__Ointeger,type,
    bit_ri6519982836138164636nteger: nat > fun_Co8499238673658658103nteger ).

tff(sy_c_Bit__Operations_Oring__bit__operations__class_Osigned__take__bit_001t__Int__Oint,type,
    bit_ri631733984087533419it_int: nat > fun_int_int ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Code____Numeral__Ointeger,type,
    bit_se3949692690581998587nteger: fun_Co1981900195452921617nteger ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Code____Numeral__Onatural,type,
    bit_se2773287842338716102atural: fun_Co6813818151677833714atural ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Int__Oint,type,
    bit_se725231765392027082nd_int: fun_int_fun_int_int ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Nat__Onat,type,
    bit_se727722235901077358nd_nat: fun_nat_fun_nat_nat ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Code____Numeral__Ointeger,type,
    bit_se3928097537394005634nteger: fun_na7078387940644931716nteger ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Code____Numeral__Onatural,type,
    bit_se2751692689150723149atural: fun_na607345901702507418atural ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Int__Oint,type,
    bit_se8568078237143864401it_int: fun_nat_fun_int_int ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Nat__Onat,type,
    bit_se8570568707652914677it_nat: fun_nat_fun_nat_nat ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Code____Numeral__Ointeger,type,
    bit_se1345352211410354436nteger: fun_na7078387940644931716nteger ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Code____Numeral__Onatural,type,
    bit_se168947363167071951atural: fun_na607345901702507418atural ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Int__Oint,type,
    bit_se2159334234014336723it_int: fun_nat_fun_int_int ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Nat__Onat,type,
    bit_se2161824704523386999it_nat: fun_nat_fun_nat_nat ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Code____Numeral__Ointeger,type,
    bit_se2119862282449309892nteger: fun_nat_Code_integer ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Code____Numeral__Onatural,type,
    bit_se943457434206027407atural: fun_nat_Code_natural ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Int__Oint,type,
    bit_se2000444600071755411sk_int: fun_nat_int ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Nat__Onat,type,
    bit_se2002935070580805687sk_nat: fun_nat_nat ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Code____Numeral__Ointeger,type,
    bit_se1080825931792720795nteger: fun_Co1981900195452921617nteger ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Code____Numeral__Onatural,type,
    bit_se9127793120404214118atural: fun_Co6813818151677833714atural ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Int__Oint,type,
    bit_se1409905431419307370or_int: fun_int_fun_int_int ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Nat__Onat,type,
    bit_se1412395901928357646or_nat: fun_nat_fun_nat_nat ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Opush__bit_001t__Code____Numeral__Ointeger,type,
    bit_se7788150548672797655nteger: fun_na7078387940644931716nteger ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Opush__bit_001t__Code____Numeral__Onatural,type,
    bit_se6611745700429515170atural: fun_na607345901702507418atural ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Opush__bit_001t__Int__Oint,type,
    bit_se545348938243370406it_int: fun_nat_fun_int_int ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Opush__bit_001t__Nat__Onat,type,
    bit_se547839408752420682it_nat: fun_nat_fun_nat_nat ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Code____Numeral__Ointeger,type,
    bit_se2793503036327961859nteger: fun_na7078387940644931716nteger ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Code____Numeral__Onatural,type,
    bit_se1617098188084679374atural: fun_na607345901702507418atural ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Int__Oint,type,
    bit_se7879613467334960850it_int: fun_nat_fun_int_int ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Nat__Onat,type,
    bit_se7882103937844011126it_nat: fun_nat_fun_nat_nat ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Otake__bit_001t__Code____Numeral__Ointeger,type,
    bit_se1745604003318907178nteger: fun_na7078387940644931716nteger ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Otake__bit_001t__Code____Numeral__Onatural,type,
    bit_se569199155075624693atural: fun_na607345901702507418atural ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Otake__bit_001t__Int__Oint,type,
    bit_se2923211474154528505it_int: fun_nat_fun_int_int ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Otake__bit_001t__Nat__Onat,type,
    bit_se2925701944663578781it_nat: fun_nat_fun_nat_nat ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Ounset__bit_001t__Code____Numeral__Ointeger,type,
    bit_se8260200283734997820nteger: fun_na7078387940644931716nteger ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Ounset__bit_001t__Code____Numeral__Onatural,type,
    bit_se7083795435491715335atural: fun_na607345901702507418atural ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Ounset__bit_001t__Int__Oint,type,
    bit_se4203085406695923979it_int: fun_nat_fun_int_int ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Ounset__bit_001t__Nat__Onat,type,
    bit_se4205575877204974255it_nat: fun_nat_fun_nat_nat ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oxor_001t__Code____Numeral__Ointeger,type,
    bit_se3222712562003087583nteger: fun_Co1981900195452921617nteger ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oxor_001t__Code____Numeral__Onatural,type,
    bit_se2046307713759805098atural: fun_Co6813818151677833714atural ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oxor_001t__Int__Oint,type,
    bit_se6526347334894502574or_int: fun_int_fun_int_int ).

tff(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oxor_001t__Nat__Onat,type,
    bit_se6528837805403552850or_nat: fun_nat_fun_nat_nat ).

tff(sy_c_Bit__Operations_Osemiring__bits__class_Obit_001t__Code____Numeral__Ointeger,type,
    bit_se9216721137139052372nteger: fun_Co1375048237525739357_nat_o ).

tff(sy_c_Bit__Operations_Osemiring__bits__class_Obit_001t__Code____Numeral__Onatural,type,
    bit_se8040316288895769887atural: fun_Co196715998180962002_nat_o ).

tff(sy_c_Bit__Operations_Osemiring__bits__class_Obit_001t__Int__Oint,type,
    bit_se1146084159140164899it_int: fun_int_fun_nat_o ).

tff(sy_c_Bit__Operations_Osemiring__bits__class_Obit_001t__Nat__Onat,type,
    bit_se1148574629649215175it_nat: fun_nat_fun_nat_o ).

tff(sy_c_Bit__Operations_Otake__bit__num,type,
    bit_take_bit_num: nat > fun_num_option_num ).

tff(sy_c_Bit__Operations_Ounique__euclidean__semiring__with__bit__operations__class_Oand__num,type,
    bit_un7362597486090784418nd_num: num > fun_num_option_num ).

tff(sy_c_Bit__Operations_Ounique__euclidean__semiring__with__bit__operations__class_Oand__num__rel,type,
    bit_un4731106466462545111um_rel: fun_Pr4799464687642144302_num_o ).

tff(sy_c_Bit__Operations_Ounique__euclidean__semiring__with__bit__operations__class_Oor__num,type,
    bit_un6697907153464112080or_num: fun_num_fun_num_num ).

tff(sy_c_Bit__Operations_Ounique__euclidean__semiring__with__bit__operations__class_Oor__num__rel,type,
    bit_un4773296044027857193um_rel: fun_Pr4799464687642144302_num_o ).

tff(sy_c_Bit__Operations_Ounique__euclidean__semiring__with__bit__operations__class_Oxor__num,type,
    bit_un2480387367778600638or_num: num > fun_num_option_num ).

tff(sy_c_Bit__Operations_Ounique__euclidean__semiring__with__bit__operations__class_Oxor__num__rel,type,
    bit_un2901131394128224187um_rel: fun_Pr4799464687642144302_num_o ).

tff(sy_c_Boolean__Algebras_Oabstract__boolean__algebra_001t__Code____Numeral__Ointeger,type,
    boolea5643492148547655015nteger: ( fun_Co1981900195452921617nteger * fun_Co1981900195452921617nteger * fun_Co8499238673658658103nteger ) > fun_Co2081214437782444048eger_o ).

tff(sy_c_Boolean__Algebras_Oabstract__boolean__algebra_001t__Int__Oint,type,
    boolea5469654029284665142ra_int: ( fun_int_fun_int_int * fun_int_fun_int_int * fun_int_int ) > fun_int_fun_int_o ).

tff(sy_c_Boolean__Algebras_Oabstract__boolean__algebra__sym__diff_001t__Code____Numeral__Ointeger,type,
    boolea2445317508997433345nteger: ( fun_Co1981900195452921617nteger * fun_Co1981900195452921617nteger * fun_Co8499238673658658103nteger * code_integer * code_integer * fun_Co1981900195452921617nteger ) > $o ).

tff(sy_c_Boolean__Algebras_Oabstract__boolean__algebra__sym__diff_001t__Int__Oint,type,
    boolea8527374999097803216ff_int: ( fun_int_fun_int_int * fun_int_fun_int_int * fun_int_int * int * int * fun_int_fun_int_int ) > $o ).

tff(sy_c_Code__Numeral_ONat,type,
    code_Nat: fun_Co3734316457315071362atural ).

tff(sy_c_Code__Numeral_ONeg,type,
    code_Neg: fun_num_Code_integer ).

tff(sy_c_Code__Numeral_OPos,type,
    code_Pos: fun_num_Code_integer ).

tff(sy_c_Code__Numeral_OSuc,type,
    code_Suc: fun_Co7398788559141407565atural ).

tff(sy_c_Code__Numeral_Obit__cut__integer,type,
    code_bit_cut_integer: code_integer > produc6271795597528267376eger_o ).

tff(sy_c_Code__Numeral_Ocr__integer,type,
    code_cr_integer: fun_in4891666191172872833eger_o ).

tff(sy_c_Code__Numeral_Ocr__natural,type,
    code_cr_natural: fun_na2240068485812228818ural_o ).

tff(sy_c_Code__Numeral_Odivmod__abs,type,
    code_divmod_abs: code_integer > fun_Co6597186368970283863nteger ).

tff(sy_c_Code__Numeral_Odivmod__integer,type,
    code_divmod_integer: code_integer > fun_Co6597186368970283863nteger ).

tff(sy_c_Code__Numeral_Odup,type,
    code_dup: fun_Co8499238673658658103nteger ).

tff(sy_c_Code__Numeral_Ointeger_Oint__of__integer,type,
    code_int_of_integer: fun_Code_integer_int ).

tff(sy_c_Code__Numeral_Ointeger_Ointeger__of__int,type,
    code_integer_of_int: fun_int_Code_integer ).

tff(sy_c_Code__Numeral_Ointeger__of__nat,type,
    code_integer_of_nat: fun_nat_Code_integer ).

tff(sy_c_Code__Numeral_Ointeger__of__natural,type,
    code_i5400310926305786745atural: fun_Co2940338738630218498nteger ).

tff(sy_c_Code__Numeral_Ointeger__of__num,type,
    code_integer_of_num: fun_num_Code_integer ).

tff(sy_c_Code__Numeral_Onat__of__integer,type,
    code_nat_of_integer: fun_Code_integer_nat ).

tff(sy_c_Code__Numeral_Onatural_Onat__of__natural,type,
    code_nat_of_natural: fun_Code_natural_nat ).

tff(sy_c_Code__Numeral_Onatural_Onatural__of__nat,type,
    code_natural_of_nat: fun_nat_Code_natural ).

tff(sy_c_Code__Numeral_Onatural__of__integer,type,
    code_n4118661773612635043nteger: fun_Co3734316457315071362atural ).

tff(sy_c_Code__Numeral_Onegative,type,
    code_negative: fun_num_Code_integer ).

tff(sy_c_Code__Numeral_Onum__of__integer,type,
    code_num_of_integer: fun_Code_integer_num ).

tff(sy_c_Code__Numeral_Opcr__integer,type,
    code_pcr_integer: fun_in4891666191172872833eger_o ).

tff(sy_c_Code__Numeral_Opcr__natural,type,
    code_pcr_natural: fun_na2240068485812228818ural_o ).

tff(sy_c_Code__Numeral_Opositive,type,
    code_positive: fun_num_Code_integer ).

tff(sy_c_Code__Numeral_Osize__nat,type,
    code_size_nat: fun_Code_natural_nat ).

tff(sy_c_Code__Numeral_Osub,type,
    code_sub: fun_nu2537414170016844299nteger ).

tff(sy_c_Complete__Lattices_OInf__class_OInf_001t__Int__Oint,type,
    complete_Inf_Inf_int: fun_set_int_int ).

tff(sy_c_Complete__Lattices_OInf__class_OInf_001t__Nat__Onat,type,
    complete_Inf_Inf_nat: fun_set_nat_nat ).

tff(sy_c_Complete__Lattices_OInf__class_OInf_001t__Option__Ooption_It__Product____Type__Ounit_J,type,
    comple5564859526659248602t_unit: set_op3165557761946182707t_unit > option_Product_unit ).

tff(sy_c_Complete__Lattices_OInf__class_OInf_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
    comple3446467376476514063et_nat: set_option_set_nat > option_set_nat ).

tff(sy_c_Complete__Lattices_OInf__class_OInf_001t__Product____Type__Ounit,type,
    comple2584293577114468500t_unit: set_Product_unit > product_unit ).

tff(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_I_Eo_J,type,
    comple3063163877087187839_set_o: set_set_o > set_o ).

tff(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
    comple1256288197631046732nteger: set_set_Code_integer > set_Code_integer ).

tff(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_It__Int__Oint_J,type,
    comple3628384868704368283et_int: set_set_int > set_int ).

tff(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
    comple184543376406953807st_nat: set_set_list_nat > set_list_nat ).

tff(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_It__Nat__Onat_J,type,
    comple7806235888213564991et_nat: set_set_nat > set_nat ).

tff(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    comple1930127330929219688at_nat: set_se7855581050983116737at_nat > set_Pr1261947904930325089at_nat ).

tff(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    comple6751905152567503566at_nat: set_se5479201105039950375at_nat > set_Pr4329608150637261639at_nat ).

tff(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    comple8541757751631690782nt_int: set_se4391686895574802075nt_int > set_Pr4166680992137330533nt_int ).

tff(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    comple323433061773777925nteger: set_se7873143835621700354nteger > set_Pr3486312109254157132nteger ).

tff(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    comple3350261554931844495et_nat: set_se3290278062343509644et_nat > set_Pr1312406793078187350et_nat ).

tff(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    comple1792010244656199981et_nat: set_se6059149423757001258et_nat > set_Pr4040394263813967220et_nat ).

tff(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    comple4690283724815187698nt_int: set_se2743246391971219311nt_int > set_Pr6700895561065273913nt_int ).

tff(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    comple7216939928495492468t_unit: set_set_Product_unit > set_Product_unit ).

tff(sy_c_Complete__Lattices_OInf__class_OInf_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    comple6875853405106058289_nat_o: set_fu7727944524835118346_nat_o > fun_nat_fun_nat_o ).

tff(sy_c_Complete__Lattices_OInf__class_OInf_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J,type,
    comple531699222623097269_nat_o: set_fu5472951507345886094_nat_o > fun_se5639961202347202350_nat_o ).

tff(sy_c_Complete__Lattices_OInf__class_OInf_001t__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    comple6965962001593347671_int_o: set_fu804515216739278420_int_o > fun_fu2978539155105838238_int_o ).

tff(sy_c_Complete__Lattices_OInf__class_OInf_001t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
    comple4186225371594386736eger_o: set_fu7224585531122448557eger_o > fun_fu7695273699059480439eger_o ).

tff(sy_c_Complete__Lattices_OInf__class_OInf_001t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
    comple6813979064832585404_nat_o: set_fu3659417381080568633_nat_o > fun_fu8419763957888848259_nat_o ).

tff(sy_c_Complete__Lattices_OInf__class_OInf_001t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_J,type,
    comple4212820851778485918_nat_o: set_fu5576194784986904859_nat_o > fun_fu2611741329380808165_nat_o ).

tff(sy_c_Complete__Lattices_OInf__class_OInf_001t__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    comple6728638684779775107_int_o: set_fu1179388718870097536_int_o > fun_fu6865642474282033866_int_o ).

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

tff(sy_c_Complete__Lattices_OSup__class_OSup_001t__Int__Oint,type,
    complete_Sup_Sup_int: fun_set_int_int ).

tff(sy_c_Complete__Lattices_OSup__class_OSup_001t__Nat__Onat,type,
    complete_Sup_Sup_nat: fun_set_nat_nat ).

tff(sy_c_Complete__Lattices_OSup__class_OSup_001t__Option__Ooption_I_Eo_J,type,
    comple4490649148004324043tion_o: set_option_o > option_o ).

tff(sy_c_Complete__Lattices_OSup__class_OSup_001t__Option__Ooption_It__Product____Type__Ounit_J,type,
    comple7481738165189995200t_unit: set_op3165557761946182707t_unit > option_Product_unit ).

tff(sy_c_Complete__Lattices_OSup__class_OSup_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
    comple8455683388168444585et_nat: set_option_set_nat > option_set_nat ).

tff(sy_c_Complete__Lattices_OSup__class_OSup_001t__Product____Type__Ounit,type,
    comple4687483117567863418t_unit: set_Product_unit > product_unit ).

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

tff(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
    comple739944243200306918nteger: set_set_Code_integer > set_Code_integer ).

tff(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_It__Int__Oint_J,type,
    comple3221217463730067765et_int: set_set_int > set_int ).

tff(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
    comple8404747032580312297st_nat: set_set_list_nat > set_list_nat ).

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

tff(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    comple4956303571586142718atural: set_se3372686590935047281atural > set_Pr7564037697178849041atural ).

tff(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    comple5685304695842803022at_nat: set_se7855581050983116737at_nat > set_Pr1261947904930325089at_nat ).

tff(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    comple4364388969068068532at_nat: set_se5479201105039950375at_nat > set_Pr4329608150637261639at_nat ).

tff(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    comple7505710199608789688nt_int: set_se4391686895574802075nt_int > set_Pr4166680992137330533nt_int ).

tff(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    comple7749403179893457567nteger: set_se7873143835621700354nteger > set_Pr3486312109254157132nteger ).

tff(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    comple946752071900596009et_nat: set_se3290278062343509644et_nat > set_Pr1312406793078187350et_nat ).

tff(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    comple828966628661558727et_nat: set_se6059149423757001258et_nat > set_Pr4040394263813967220et_nat ).

tff(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    comple3054605461907987852nt_int: set_se2743246391971219311nt_int > set_Pr6700895561065273913nt_int ).

tff(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    comple3349607820504768346t_unit: set_set_Product_unit > set_Product_unit ).

tff(sy_c_Complete__Lattices_OSup__class_OSup_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    comple5361447358958659351_nat_o: set_fu7727944524835118346_nat_o > fun_nat_fun_nat_o ).

tff(sy_c_Complete__Lattices_OSup__class_OSup_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J,type,
    comple5471869746640610203_nat_o: set_fu5472951507345886094_nat_o > fun_se5639961202347202350_nat_o ).

tff(sy_c_Complete__Lattices_OSup__class_OSup_001t__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    comple9222649745891163889_int_o: set_fu804515216739278420_int_o > fun_fu2978539155105838238_int_o ).

tff(sy_c_Complete__Lattices_OSup__class_OSup_001t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
    comple5202257901570954698eger_o: set_fu7224585531122448557eger_o > fun_fu7695273699059480439eger_o ).

tff(sy_c_Complete__Lattices_OSup__class_OSup_001t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
    comple8308589925492879958_nat_o: set_fu3659417381080568633_nat_o > fun_fu8419763957888848259_nat_o ).

tff(sy_c_Complete__Lattices_OSup__class_OSup_001t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_J,type,
    comple4660109291472045368_nat_o: set_fu5576194784986904859_nat_o > fun_fu2611741329380808165_nat_o ).

tff(sy_c_Complete__Lattices_OSup__class_OSup_001t__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    comple8771317328093439261_int_o: set_fu1179388718870097536_int_o > fun_fu6865642474282033866_int_o ).

tff(sy_c_Countable_Onth__item__rel,type,
    nth_item_rel: fun_nat_fun_nat_o ).

tff(sy_c_Divides_Oadjust__div,type,
    adjust_div: fun_Pr982841511892225912nt_int ).

tff(sy_c_Divides_Odivmod__nat,type,
    divmod_nat: fun_na4138050610385705875at_nat ).

tff(sy_c_Divides_Oeucl__rel__int,type,
    eucl_rel_int: ( int * int ) > fun_Pr3238374608701176162_int_o ).

tff(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Code____Numeral__Ointeger,type,
    unique5706413561485394159nteger: fun_Pr7211993375558241536eger_o ).

tff(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Int__Oint,type,
    unique6319869463603278526ux_int: fun_Pr3238374608701176162_int_o ).

tff(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Nat__Onat,type,
    unique6322359934112328802ux_nat: fun_Pr4796943543331071514_nat_o ).

tff(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Code____Numeral__Ointeger,type,
    unique3479559517661332726nteger: ( num * num ) > produc8923325533196201883nteger ).

tff(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Int__Oint,type,
    unique5052692396658037445od_int: ( num * num ) > product_prod_int_int ).

tff(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Nat__Onat,type,
    unique5055182867167087721od_nat: ( num * num ) > product_prod_nat_nat ).

tff(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Code____Numeral__Ointeger,type,
    unique4921790084139445826nteger: num > fun_Pr5876161306168176259nteger ).

tff(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Int__Oint,type,
    unique5024387138958732305ep_int: num > fun_Pr2478283820680522243nt_int ).

tff(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Nat__Onat,type,
    unique5026877609467782581ep_nat: num > fun_Pr2118491707810114563at_nat ).

tff(sy_c_Euclidean__Division_Oeuclidean__semiring__class_Oeuclidean__size_001t__Code____Numeral__Ointeger,type,
    euclid6377331345833325938nteger: fun_Code_integer_nat ).

tff(sy_c_Euclidean__Division_Oeuclidean__semiring__class_Oeuclidean__size_001t__Code____Numeral__Onatural,type,
    euclid5200926497590043453atural: fun_Code_natural_nat ).

tff(sy_c_Euclidean__Division_Oeuclidean__semiring__class_Oeuclidean__size_001t__Int__Oint,type,
    euclid4774559944035922753ze_int: fun_int_nat ).

tff(sy_c_Euclidean__Division_Oeuclidean__semiring__class_Oeuclidean__size_001t__Nat__Onat,type,
    euclid4777050414544973029ze_nat: fun_nat_nat ).

tff(sy_c_Euclidean__Division_Ounique__euclidean__semiring__class_Odivision__segment_001t__Code____Numeral__Ointeger,type,
    euclid6289375185220004616nteger: fun_Co8499238673658658103nteger ).

tff(sy_c_Euclidean__Division_Ounique__euclidean__semiring__class_Odivision__segment_001t__Code____Numeral__Onatural,type,
    euclid5112970336976722131atural: fun_Co7398788559141407565atural ).

tff(sy_c_Euclidean__Division_Ounique__euclidean__semiring__class_Odivision__segment_001t__Int__Oint,type,
    euclid3395696857347342551nt_int: fun_int_int ).

tff(sy_c_Euclidean__Division_Ounique__euclidean__semiring__class_Odivision__segment_001t__Nat__Onat,type,
    euclid3398187327856392827nt_nat: fun_nat_nat ).

tff(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Code____Numeral__Ointeger,type,
    comm_s8582702949713902594nteger: code_integer > fun_nat_Code_integer ).

tff(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Code____Numeral__Onatural,type,
    comm_s7406298101470620109atural: code_natural > fun_nat_Code_natural ).

tff(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Int__Oint,type,
    comm_s4660882817536571857er_int: int > fun_nat_int ).

tff(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Nat__Onat,type,
    comm_s4663373288045622133er_nat: fun_nat_fun_nat_nat ).

tff(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Rat__Orat,type,
    comm_s4028243227959126397er_rat: rat > fun_nat_rat ).

tff(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Code____Numeral__Ointeger,type,
    semiri3624122377584611663nteger: fun_nat_Code_integer ).

tff(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Code____Numeral__Onatural,type,
    semiri2447717529341329178atural: fun_nat_Code_natural ).

tff(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Int__Oint,type,
    semiri1406184849735516958ct_int: fun_nat_int ).

tff(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Nat__Onat,type,
    semiri1408675320244567234ct_nat: fun_nat_nat ).

tff(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Rat__Orat,type,
    semiri773545260158071498ct_rat: fun_nat_rat ).

tff(sy_c_Fields_Oinverse__class_Oinverse_001t__Rat__Orat,type,
    inverse_inverse_rat: fun_rat_rat ).

tff(sy_c_Finite__Set_Ocard_001_Eo,type,
    finite_card_o: set_o > nat ).

tff(sy_c_Finite__Set_Ocard_001t__Code____Numeral__Ointeger,type,
    finite4902975817058060853nteger: set_Code_integer > nat ).

tff(sy_c_Finite__Set_Ocard_001t__Int__Oint,type,
    finite_card_int: set_int > nat ).

tff(sy_c_Finite__Set_Ocard_001t__List__Olist_It__Nat__Onat_J,type,
    finite_card_list_nat: set_list_nat > nat ).

tff(sy_c_Finite__Set_Ocard_001t__Nat__Onat,type,
    finite_card_nat: fun_set_nat_nat ).

tff(sy_c_Finite__Set_Ocard_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    finite711546835091564841at_nat: fun_se4097146774670233028at_nat ).

tff(sy_c_Finite__Set_Ocard_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    finite3771342082235030671at_nat: set_Pr4329608150637261639at_nat > nat ).

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

tff(sy_c_Finite__Set_Ocard_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
    finite1340570857867686763nteger: set_set_Code_integer > nat ).

tff(sy_c_Finite__Set_Ocard_001t__Set__Oset_It__Int__Oint_J,type,
    finite_card_set_int: set_set_int > nat ).

tff(sy_c_Finite__Set_Ocard_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
    finite2364142230527598318st_nat: set_set_list_nat > nat ).

tff(sy_c_Finite__Set_Ocard_001t__Set__Oset_It__Nat__Onat_J,type,
    finite_card_set_nat: set_set_nat > nat ).

tff(sy_c_Finite__Set_Ocard_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    finite4356350796350151305at_nat: set_se7855581050983116737at_nat > nat ).

tff(sy_c_Finite__Set_Ocard_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    finite22775419188893461t_unit: set_set_Product_unit > nat ).

tff(sy_c_Finite__Set_Ofinite_001_Eo,type,
    finite_finite_o: set_o > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Code____Numeral__Ointeger,type,
    finite6017078050557962740nteger: set_Code_integer > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Int__Oint,type,
    finite_finite_int: set_int > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Nat__Onat_J,type,
    finite8100373058378681591st_nat: set_list_nat > $o ).

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

tff(sy_c_Finite__Set_Ofinite_001t__Num__Onum,type,
    finite_finite_num: set_num > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_It__Code____Numeral__Ointeger_J,type,
    finite6785661671136154180nteger: set_op687863988967635939nteger > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_It__Int__Oint_J,type,
    finite1345302120164226195on_int: set_option_int > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_It__Nat__Onat_J,type,
    finite5523153139673422903on_nat: set_option_nat > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_It__Num__Onum_J,type,
    finite6231397076622260609on_num: set_option_num > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    finite6732403688824079472at_nat: set_op4508134149509766951at_nat > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    finite6292238467249657455it_nat: set_op239864471688321678it_nat > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_It__Product____Type__Ounit_J,type,
    finite1445617369574913404t_unit: set_op3165557761946182707t_unit > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
    finite6120865539452801872od_o_o: set_Product_prod_o_o > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    finite2154694888287295812nteger: set_Pr4811707699266497531nteger > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J,type,
    finite818523575018126227er_int: set_Pr6496905503482889930er_int > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J,type,
    finite4996374594527322935er_nat: set_Pr8986988648414616686er_nat > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    finite2970523954037356441et_nat: set_Pr3948176798113811640et_nat > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Int__Oint_Mt__Code____Numeral__Ointeger_J,type,
    finite1525696360262406931nteger: set_Pr8415741480598773322nteger > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    finite2998713641127702882nt_int: set_Pr958786334691620121nt_int > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J,type,
    finite7176564660636899590nt_nat: set_Pr3448869479623346877nt_nat > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J,type,
    finite1154042800025562295nteger: set_Pr2406931829603198446nteger > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
    finite1999359929226648326at_int: set_Pr7995236796853374141at_int > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    finite6177210948735845034at_nat: set_Pr1261947904930325089at_nat > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    finite4392333629123659920at_nat: set_Pr8693737435421807431at_nat > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    finite6446286893012251551it_nat: set_Pr1354866905816374718it_nat > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    finite4343798906461161616at_nat: set_Pr4329608150637261639at_nat > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    finite2753043699534600503et_nat: set_Pr1312406793078187350et_nat > $o ).

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

tff(sy_c_Finite__Set_Ofinite_001t__Rat__Orat,type,
    finite_finite_rat: set_rat > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
    finite6931041176100689706nteger: set_set_Code_integer > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Int__Oint_J,type,
    finite6197958912794628473et_int: set_set_int > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
    finite7047420756378620717st_nat: set_set_list_nat > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Nat__Onat_J,type,
    finite1152437895449049373et_nat: set_set_nat > $o ).

tff(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    finite9047747110432174090at_nat: set_se7855581050983116737at_nat > $o ).

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

tff(sy_c_Finite__Set_Ofold_001t__Int__Oint_001t__Int__Oint,type,
    finite_fold_int_int: ( fun_int_fun_int_int * int ) > fun_set_int_int ).

tff(sy_c_Finite__Set_Ofold_001t__Nat__Onat_001t__Int__Oint,type,
    finite_fold_nat_int: ( fun_nat_fun_int_int * int * set_nat ) > int ).

tff(sy_c_Finite__Set_Ofold_001t__Nat__Onat_001t__Nat__Onat,type,
    finite_fold_nat_nat: ( fun_nat_fun_nat_nat * nat ) > fun_set_nat_nat ).

tff(sy_c_Finite__Set_Ofold_001t__Nat__Onat_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    finite3745491028973389255at_nat: ( fun_na8167864584424996432at_nat * set_Pr1261947904930325089at_nat * set_nat ) > set_Pr1261947904930325089at_nat ).

tff(sy_c_Finite__Set_Ofold_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    finite5714315773265140383nteger: ( fun_Pr471679772948460611nteger * set_Pr3486312109254157132nteger * set_Pr4811707699266497531nteger ) > set_Pr3486312109254157132nteger ).

tff(sy_c_Finite__Set_Ofold_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    finite2242536663760659874et_nat: ( fun_Pr4459677240377800360et_nat * set_Pr1312406793078187350et_nat * set_Pr3948176798113811640et_nat ) > set_Pr1312406793078187350et_nat ).

tff(sy_c_Finite__Set_Ofold_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    finite5328971291029987030nt_int: ( fun_Pr5088371826558493971nt_int * set_Pr4166680992137330533nt_int * set_Pr958786334691620121nt_int ) > set_Pr4166680992137330533nt_int ).

tff(sy_c_Finite__Set_Ofold_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    finite5989910380944892330nt_int: ( fun_Pr7963917038216275131nt_int * set_Pr6700895561065273913nt_int * set_Pr958786334691620121nt_int ) > set_Pr6700895561065273913nt_int ).

tff(sy_c_Finite__Set_Ofold_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    finite7678581116841817694et_nat: ( fun_Pr386875378712213506et_nat * set_Pr4040394263813967220et_nat * set_Pr1312406793078187350et_nat ) > set_Pr4040394263813967220et_nat ).

tff(sy_c_Finite__Set_Ofold_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    finite3179781904389220718at_nat: ( fun_se636550882185307767at_nat * set_Pr4329608150637261639at_nat * set_se7855581050983116737at_nat ) > set_Pr4329608150637261639at_nat ).

tff(sy_c_Fun_Ocomp_001_Eo_001_Eo_001_Eo,type,
    comp_o_o_o: ( fun_o_o * fun_o_o ) > fun_o_o ).

tff(sy_c_Fun_Ocomp_001_Eo_001_Eo_001t__Nat__Onat,type,
    comp_o_o_nat: fun_o_o > fun_fu4001317426178549763_nat_o ).

tff(sy_c_Fun_Ocomp_001_Eo_001_Eo_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    comp_o8022916681612831582at_nat: fun_o_o > fun_fu3275390434952296369_nat_o ).

tff(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Assertions__Oassn_001t__Nat__Onat,type,
    comp_C8462447471145125178sn_nat: ( fun_Co4490034186337852034r_assn * fun_nat_Code_integer ) > fun_nat_assn ).

tff(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    comp_C7449957260575251196nteger: fun_Co8499238673658658103nteger > fun_fu1763652423599918571nteger ).

tff(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
    comp_C6974050283906349679er_nat: ( fun_Co8499238673658658103nteger * fun_nat_Code_integer ) > fun_nat_Code_integer ).

tff(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
    comp_C3531382070062128313er_num: fun_fu5844746416483971737nteger ).

tff(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    comp_C1043215000170864188nteger: ( fun_Co8499238673658658103nteger * fun_Pr6596356882939945227nteger ) > fun_Pr6596356882939945227nteger ).

tff(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Int__Oint,type,
    comp_C5046419837055054490nt_int: ( fun_Code_integer_int * fun_int_Code_integer ) > fun_int_int ).

tff(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Nat__Onat,type,
    comp_C5048910307564104766nt_nat: ( fun_Code_integer_int * fun_nat_Code_integer ) > fun_nat_int ).

tff(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Nat__Onat,type,
    comp_C4049556595663050210at_nat: ( fun_Code_integer_nat * fun_nat_Code_integer ) > fun_nat_nat ).

tff(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    comp_C2277306503614464128nteger: ( fun_Co6597186368970283863nteger * fun_Pr6596356882939945227nteger ) > fun_Pr5876161306168176259nteger ).

tff(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Product____Type__Ounit_001t__Nat__Onat,type,
    comp_C8086623346886033437it_nat: ( fun_Co1365676809456677961t_unit * fun_nat_Code_integer ) > fun_nat_Product_unit ).

tff(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Rat__Orat_001t__Nat__Onat,type,
    comp_C3733001951728184298at_nat: ( fun_Code_integer_rat * fun_nat_Code_integer ) > fun_nat_rat ).

tff(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger,type,
    comp_C7233611567195229654nteger: ( fun_Co1981900195452921617nteger * fun_Co8499238673658658103nteger ) > fun_Co1981900195452921617nteger ).

tff(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Num__Onum,type,
    comp_C6573007665814501267er_num: ( fun_Co1981900195452921617nteger * fun_num_Code_integer ) > fun_nu1287335591331657422nteger ).

tff(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
    comp_C7848664941760151970nteger: fun_fu7234567020521114219nteger ).

tff(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Num__Onum,type,
    comp_C2151251282054683487er_num: ( fun_Co1561183069634336733nteger * fun_num_Code_integer ) > fun_nu1379135015814352922nteger ).

tff(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    comp_C7827331287018003580nteger: ( fun_Co1561183069634336733nteger * fun_fu5689865433563736081nteger ) > fun_fu4800041728187187127nteger ).

tff(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Assertions__Oassn_001t__Int__Oint,type,
    comp_int_assn_int: ( fun_int_assn * fun_int_int ) > fun_int_assn ).

tff(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Assertions__Oassn_001t__Nat__Onat,type,
    comp_int_assn_nat: ( fun_int_assn * fun_nat_int ) > fun_nat_assn ).

tff(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
    comp_i1585864551200866970er_int: ( fun_int_Code_integer * fun_int_int ) > fun_int_Code_integer ).

tff(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
    comp_i1588355021709917246er_nat: ( fun_int_Code_integer * fun_nat_int ) > fun_nat_Code_integer ).

tff(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
    comp_int_int_int: fun_int_int > fun_fu1143798476471108391nt_int ).

tff(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat,type,
    comp_int_int_nat: ( fun_int_int * fun_nat_int ) > fun_nat_int ).

tff(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    comp_i4330622015127193916nt_int: ( fun_int_int * fun_Pr982841511892225912nt_int ) > fun_Pr982841511892225912nt_int ).

tff(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
    comp_int_nat_int: ( fun_int_nat * fun_int_int ) > fun_int_nat ).

tff(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
    comp_int_nat_nat: ( fun_int_nat * fun_nat_int ) > fun_nat_nat ).

tff(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Num__Onum_001t__Int__Oint,type,
    comp_int_num_int: ( fun_int_num * fun_int_int ) > fun_int_num ).

tff(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    comp_i5941103828406351439nt_int: ( fun_in4211310926729683942nt_int * fun_Pr982841511892225912nt_int ) > fun_Pr2478283820680522243nt_int ).

tff(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
    comp_i1108739374719436894at_int: ( fun_in4514472496968388910at_nat * fun_int_int ) > fun_in4514472496968388910at_nat ).

tff(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Rat__Orat_001t__Int__Oint,type,
    comp_int_rat_int: ( fun_int_rat * fun_int_int ) > fun_int_rat ).

tff(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Rat__Orat_001t__Nat__Onat,type,
    comp_int_rat_nat: ( fun_int_rat * fun_nat_int ) > fun_nat_rat ).

tff(sy_c_Fun_Ocomp_001t__Int__Oint_001t__fun_It__Int__Oint_M_Eo_J_001t__Int__Oint,type,
    comp_i4691081854165332386_o_int: fun_fu14259429304446855_int_o ).

tff(sy_c_Fun_Ocomp_001t__Int__Oint_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint,type,
    comp_i133330754224947090nt_int: fun_fu3518228427392506443nt_int ).

tff(sy_c_Fun_Ocomp_001t__Int__Oint_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__Nat__Onat,type,
    comp_i135821224733997366nt_nat: ( fun_int_fun_int_int * fun_nat_int ) > fun_nat_fun_int_int ).

tff(sy_c_Fun_Ocomp_001t__Int__Oint_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Int__Oint,type,
    comp_i5061236333258893123nt_int: fun_fu3528811849556752711nt_int ).

tff(sy_c_Fun_Ocomp_001t__Int__Oint_001t__fun_It__Int__Oint_Mt__Rat__Orat_J_001t__Int__Oint,type,
    comp_i2769097025877698878at_int: fun_fu4582018930532246947nt_rat ).

tff(sy_c_Fun_Ocomp_001t__Int__Oint_001t__fun_It__Nat__Onat_M_Eo_J_001t__Int__Oint,type,
    comp_i4004505821124781822_o_int: fun_fu6802859072977114247_nat_o ).

tff(sy_c_Fun_Ocomp_001t__Nat__Onat_001_Eo_001t__Nat__Onat,type,
    comp_nat_o_nat: ( fun_nat_o * fun_nat_nat ) > fun_nat_o ).

tff(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Assertions__Oassn_001t__Nat__Onat,type,
    comp_nat_assn_nat: ( fun_nat_assn * fun_nat_nat ) > fun_nat_assn ).

tff(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
    comp_n3898172953802868194er_nat: ( fun_nat_Code_integer * fun_nat_nat ) > fun_nat_Code_integer ).

tff(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Int__Oint_001t__Int__Oint,type,
    comp_nat_int_int: ( fun_nat_int * fun_int_nat ) > fun_int_int ).

tff(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat,type,
    comp_nat_int_nat: ( fun_nat_int * fun_nat_nat ) > fun_nat_int ).

tff(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Nat__Onat,type,
    comp_n8698576032424989604at_nat: ( fun_na2338080690716861136at_nat * fun_nat_nat ) > fun_na2338080690716861136at_nat ).

tff(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint,type,
    comp_nat_nat_int: ( fun_nat_nat * fun_int_nat ) > fun_int_nat ).

tff(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
    comp_nat_nat_nat: ( fun_nat_nat * fun_nat_nat ) > fun_nat_nat ).

tff(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Num__Onum_001t__Int__Oint,type,
    comp_nat_num_int: fun_fu3670889464739865373nt_num ).

tff(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Num__Onum_001t__Nat__Onat,type,
    comp_nat_num_nat: ( fun_nat_num * fun_nat_nat ) > fun_nat_num ).

tff(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Product____Type__Ounit_001t__Nat__Onat,type,
    comp_n9025697279074352746it_nat: ( fun_nat_Product_unit * fun_nat_nat ) > fun_nat_Product_unit ).

tff(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Rat__Orat_001t__Nat__Onat,type,
    comp_nat_rat_nat: ( fun_nat_rat * fun_nat_nat ) > fun_nat_rat ).

tff(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
    comp_n7084669201029016610at_nat: ( fun_nat_fun_nat_nat * fun_nat_nat ) > fun_nat_fun_nat_nat ).

tff(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
    comp_n6909714581898973814er_num: ( fun_num_Code_integer * fun_num_num ) > fun_num_Code_integer ).

tff(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Int__Oint_001t__Num__Onum,type,
    comp_num_int_num: ( fun_num_int * fun_num_num ) > fun_num_int ).

tff(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Nat__Onat_001t__Num__Onum,type,
    comp_num_nat_num: ( fun_num_nat * fun_num_num ) > fun_num_nat ).

tff(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint,type,
    comp_num_num_int: ( fun_num_num * fun_int_num ) > fun_int_num ).

tff(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Num__Onum_001t__Nat__Onat,type,
    comp_num_num_nat: ( fun_num_num * fun_nat_num ) > fun_nat_num ).

tff(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Num__Onum_001t__Num__Onum,type,
    comp_num_num_num: ( fun_num_num * fun_num_num ) > fun_num_num ).

tff(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Option__Ooption_It__Num__Onum_J_001t__Num__Onum,type,
    comp_n6731957995704128387um_num: ( fun_num_option_num * fun_num_num ) > fun_num_option_num ).

tff(sy_c_Fun_Ocomp_001t__Option__Ooption_I_Eo_J_001_Eo_001_Eo,type,
    comp_option_o_o_o: ( fun_option_o_o * fun_o_option_o ) > fun_o_o ).

tff(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Code____Numeral__Ointeger_J_001t__Option__Ooption_It__Code____Numeral__Ointeger_J_001t__Option__Ooption_It__Num__Onum_J,type,
    comp_o5321900959263616553on_num: ( fun_op1637087682669155543nteger * fun_op4521932154746760340nteger ) > fun_op4521932154746760340nteger ).

tff(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Code____Numeral__Ointeger_J_001t__Option__Ooption_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_001t__Option__Ooption_It__Code____Numeral__Ointeger_J,type,
    comp_o1169693055247830034nteger: ( fun_op3037383146056310525nteger * fun_op1637087682669155543nteger ) > fun_op3037383146056310525nteger ).

tff(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Int__Oint_J_001t__Int__Oint_001t__Int__Oint,type,
    comp_o2446264010603541305nt_int: ( fun_option_int_int * fun_int_option_int ) > fun_int_int ).

tff(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
    comp_o4663963155070737957at_nat: ( fun_option_nat_nat * fun_nat_option_nat ) > fun_nat_nat ).

tff(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Nat__Onat_J_001t__Option__Ooption_It__Num__Onum_J_001t__Option__Ooption_It__Int__Oint_J,type,
    comp_o3128663659858294251on_int: ( fun_op6210678640266353415on_num * fun_op6683169195675693337on_nat ) > fun_op2398388785115040099on_num ).

tff(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Num__Onum_J_001t__Nat__Onat_001t__Option__Ooption_It__Num__Onum_J,type,
    comp_o6878144249584144265on_num: ( fun_option_num_nat * fun_op8989173174992673105on_num ) > fun_option_num_nat ).

tff(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Num__Onum_J_001t__Num__Onum_001t__Num__Onum,type,
    comp_o6342398210560591875um_num: ( fun_option_num_num * fun_num_option_num ) > fun_num_num ).

tff(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Num__Onum_J_001t__Option__Ooption_It__Num__Onum_J_001t__Option__Ooption_It__Num__Onum_J,type,
    comp_o8931257242830428707on_num: ( fun_op8989173174992673105on_num * fun_op8989173174992673105on_num ) > fun_op8989173174992673105on_num ).

tff(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    comp_o279924169626513613it_nat: ( fun_op7765417307512062173it_nat * fun_Pr7644814098969791837it_nat ) > fun_Pr1033138224055104269it_nat ).

tff(sy_c_Fun_Ocomp_001t__Option__Ooption_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Option__Ooption_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_001t__Option__Ooption_It__Code____Numeral__Ointeger_J,type,
    comp_o7605500609165425388nteger: ( fun_op7507520395135695063nteger * fun_op8756596739451609009nteger ) > fun_op3037383146056310525nteger ).

tff(sy_c_Fun_Ocomp_001t__Option__Ooption_It__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Nat__Onat_M_Eo_J,type,
    comp_o311737599745908996_nat_o: ( fun_op9036024853803066045_nat_o * fun_fu5368785673109833417_nat_o ) > fun_fu4001317426178549763_nat_o ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001_Eo_001_Eo,type,
    comp_P2137996956111167876_o_o_o: ( fun_Pr6984036127010467572_o_o_o * fun_o_4732642864545671890od_o_o ) > fun_o_o ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    comp_P7111796090210262324nteger: ( fun_Pr6596356882939945227nteger * fun_Co6597186368970283863nteger ) > fun_Co8499238673658658103nteger ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
    comp_P3107242062624629507er_int: ( fun_Pr6596356882939945227nteger * fun_in4744367027289715400nteger ) > fun_int_Code_integer ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
    comp_P3109732533133679783er_nat: ( fun_Pr6596356882939945227nteger * fun_na3822476419092417572nteger ) > fun_nat_Code_integer ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    comp_P3428181540658402820nteger: ( fun_Pr6596356882939945227nteger * fun_Pr5876161306168176259nteger ) > fun_Pr6596356882939945227nteger ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger_001t__Product____Type__Ounit,type,
    comp_P659088277599099894t_unit: ( fun_Pr6596356882939945227nteger * fun_Pr864343514034809617nteger ) > fun_Pr1820225556744648189nteger ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
    comp_P2475326853202991862er_nat: ( fun_Pr2725840997377004378nteger * fun_na5685997864800668403er_int ) > fun_nat_Code_integer ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_001t__Int__Oint_001t__Nat__Onat,type,
    comp_P8345930540558018757nt_nat: ( fun_Pr9023817884608220585nt_int * fun_na5685997864800668403er_int ) > fun_nat_int ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
    comp_P5700178199414968986er_nat: ( fun_Pr5940403383236205310nteger * fun_na8176081009732395159er_nat ) > fun_nat_Code_integer ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
    comp_P1337767177661389325at_nat: ( fun_Pr1791375292569619697at_nat * fun_na8176081009732395159er_nat ) > fun_nat_nat ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    comp_P3067963646784605345atural: ( fun_Pr74676805955934211atural * fun_Pr2136124334875798924atural ) > fun_Pr2136124334875798924atural ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    comp_P4943825737035310295atural: ( fun_Pr3133360822718887225atural * fun_Pr2136124334875798924atural ) > fun_Pr8741579136290173250atural ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__Code____Numeral__Onatural_001t__Int__Oint,type,
    comp_P5589825499870570807al_int: ( fun_Pr5131589689703537955atural * fun_in4857920871562217639atural ) > fun_int_Code_natural ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__Code____Numeral__Onatural_001t__Nat__Onat,type,
    comp_P5592315970379621083al_nat: ( fun_Pr5131589689703537955atural * fun_na2094359461478415435atural ) > fun_nat_Code_natural ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__Code____Numeral__Onatural_001t__Product____Type__Ounit,type,
    comp_P210409258367696578t_unit: ( fun_Pr5131589689703537955atural * fun_Pr2548841491397842206atural ) > fun_Pr6278675377255837256atural ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Int__Oint,type,
    comp_P8475394669922486716al_int: ( fun_Pr2136124334875798924atural * fun_in4857920871562217639atural ) > fun_in7496697025202066910atural ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Nat__Onat,type,
    comp_P8477885140431536992al_nat: ( fun_Pr2136124334875798924atural * fun_na2094359461478415435atural ) > fun_na6574806417004769082atural ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    comp_P7610810914149544718atural: ( fun_Pr2136124334875798924atural * fun_Pr6891710885006071673atural ) > fun_Pr2136124334875798924atural ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Code____Numeral__Onatural_J,type,
    comp_P5756991293874479000atural: ( fun_Pr2136124334875798924atural * fun_Pr3377396784085331203atural * produc3981471736659609608atural ) > produc7822875418678951345atural ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Ounit,type,
    comp_P1945487127105810045t_unit: ( fun_Pr2136124334875798924atural * fun_Pr2548841491397842206atural ) > fun_Pr3616673511947161127atural ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
    comp_P2097125496263478628t_unit: ( fun_Pr8118912048244921225it_nat * fun_he281446669002384250it_nat ) > fun_he1504492240061592256it_nat ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
    comp_P6870028373966156406er_nat: ( fun_Pr3662307866719382234nteger * fun_na7604833841916551795nteger ) > fun_nat_Code_integer ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_001t__Int__Oint_001t__Nat__Onat,type,
    comp_P59025373045620805nt_nat: ( fun_Pr907818707165963561er_int * fun_na7604833841916551795nteger ) > fun_nat_int ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint_001t__Int__Oint,type,
    comp_P6651465171681656048nt_int: ( fun_Pr982841511892225912nt_int * fun_in4211310926729683942nt_int ) > fun_int_int ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint_001t__Nat__Onat,type,
    comp_P6653955642190706324nt_nat: ( fun_Pr982841511892225912nt_int * fun_na1173468842265550146nt_int ) > fun_nat_int ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    comp_P5356232565778667509nt_int: ( fun_Pr982841511892225912nt_int * fun_Pr2478283820680522243nt_int ) > fun_Pr982841511892225912nt_int ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint_001t__Product____Type__Ounit,type,
    comp_P6796073005956588617t_unit: ( fun_Pr982841511892225912nt_int * fun_Pr6733608168372577327nt_int ) > fun_Product_unit_int ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001t__Int__Oint,type,
    comp_P5335556815845735580at_int: fun_Pr1652463973008025892nt_rat > fun_fu7460908759652350970nt_rat ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    comp_P5648219952011055433nt_int: ( fun_Pr1652463973008025892nt_rat * fun_Pr2478283820680522243nt_int ) > fun_Pr1652463973008025892nt_rat ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J_001t__Int__Oint_001t__Nat__Onat,type,
    comp_P645145991195131448nt_nat: ( fun_Pr8019291974053979932at_int * fun_na3663551987197276902nt_nat ) > fun_nat_int ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
    comp_P8869164316148852700at_nat: ( fun_Pr2973770956708400832at_nat * fun_na3663551987197276902nt_nat ) > fun_nat_nat ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
    comp_P5461341465284484122er_nat: ( fun_Pr4523587930069869694nteger * fun_na1596024190920976919nteger ) > fun_nat_Code_integer ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001t__Nat__Onat_001t__Nat__Onat,type,
    comp_P9144323761349829517at_nat: ( fun_Pr7395487658768111217er_nat * fun_na1596024190920976919nteger ) > fun_nat_nat ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_001t__Int__Oint_001t__Nat__Onat,type,
    comp_P8963773574283657272nt_nat: ( fun_Pr611187951655381276nt_int * fun_na8209919304427304166at_int ) > fun_nat_int ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_001t__Nat__Onat_001t__Nat__Onat,type,
    comp_P7964419862382602716at_nat: ( fun_Pr4789038971164577984nt_nat * fun_na8209919304427304166at_int ) > fun_nat_nat ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001t__Int__Oint,type,
    comp_P1289042343629989734_o_int: ( fun_Pr4796943543331071514_nat_o * fun_in4514472496968388910at_nat ) > fun_int_o ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
    comp_P1955610211387027840at_nat: ( fun_Pr2602117396471556196at_nat * fun_na1476630412504255114at_nat ) > fun_nat_nat ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Product____Type__Ounit,type,
    comp_P2980510830910040157t_unit: ( fun_Pr2602117396471556196at_nat * fun_Pr7036769738611282295at_nat ) > fun_Product_unit_nat ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
    comp_P7428279379633703887at_int: ( fun_Pr2118491707810114563at_nat * fun_in4514472496968388910at_nat ) > fun_in4514472496968388910at_nat ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Int__Oint_M_Eo_J_001t__Int__Oint,type,
    comp_P2528745837942451219_o_int: ( fun_Pr4738963024209204295_int_o * fun_in4514472496968388910at_nat ) > fun_int_fun_int_o ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint,type,
    comp_P1001692864575718241nt_int: ( fun_Pr7267779425873451369nt_int * fun_in4514472496968388910at_nat ) > fun_int_fun_int_int ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J_001t__Num__Onum_001t__Num__Onum,type,
    comp_P864883071962432936um_num: ( fun_Pr3269564255357226306um_num * fun_nu5148503272595741012um_num ) > fun_num_num ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    comp_P3887058762840424708atural: ( fun_Pr7406272072912987266atural * fun_Pr4028877673837371139atural * produc5835291356934675326atural ) > produc7822875418678951345atural ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    comp_P230220204662055659atural: ( fun_Pr6967485491430695501atural * fun_Pr8741579136290173250atural ) > fun_Pr2136124334875798924atural ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
    comp_P3118722334806803912t_unit: ( fun_Pr7644814098969791837it_nat * fun_he4944555133437423336it_nat ) > fun_he5234484606919320760it_nat ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    comp_P3263061180182656590e_term: ( fun_Pr1552678306225191715nt_int * fun_Pr3284083897292419283nt_int * produc5464280974217902119e_term ) > product_prod_int_int ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    comp_P7738237167614049274e_term: ( fun_Pr7653582204007996523e_term * fun_Pr3284083897292419283nt_int * produc5464280974217902119e_term ) > fun_in5730379987311621695e_term ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__Nat__Onat_M_Eo_J_001t__Int__Oint,type,
    comp_P7610408208252206601_o_int: ( fun_Pr8136591464420530493_nat_o * fun_in7664021439913478804_nat_o ) > fun_int_fun_nat_o ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Nat__Onat_M_Eo_J,type,
    comp_P5634878600794835076_nat_o: ( fun_Pr8136591464420530493_nat_o * fun_fu5650529485467354185_nat_o ) > fun_fu4001317426178549763_nat_o ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    comp_P2694320290640119590e_term: ( fun_Pr6160931176198666718nteger * fun_Pr6966570558394395095nteger * produc592931078481472324e_term ) > produc8923325533196201883nteger ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    comp_P9209726524401416377e_term: ( fun_Pr4557384415951816845e_term * fun_Pr6966570558394395095nteger * produc592931078481472324e_term ) > fun_Pr5098669352780829690e_term ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
    comp_P172845262850278761_nat_o: ( fun_Pr2813956079162534559et_nat * fun_Pr5416369060549219583et_nat * produc2739566037923759970_nat_o ) > produc3658429121746597890et_nat ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
    comp_P2439397525924500238_nat_o: ( fun_Pr3233114924583728296_nat_o * fun_Pr5416369060549219583et_nat * produc2739566037923759970_nat_o ) > fun_Pr6460944699146269935_nat_o ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
    comp_P2867375532623115527_nat_o: ( fun_Pr2953255705995765467et_nat * fun_Pr8630787502178681855et_nat * produc6858501863712832324_nat_o ) > produc8799533983703829792et_nat ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
    comp_P8320187926549339218_nat_o: ( fun_Pr7618159474455865098_nat_o * fun_Pr8630787502178681855et_nat * produc6858501863712832324_nat_o ) > fun_Pr6460944699146269935_nat_o ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    comp_P8873622951661117094e_term: ( fun_Pr1987159835869338959nt_int * fun_Pr5010838083610845651nt_int * produc4155239895104388691e_term ) > product_prod_int_int ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    comp_P4791264009094562086e_term: ( fun_Pr5872836680101629291e_term * fun_Pr5010838083610845651nt_int * produc4155239895104388691e_term ) > fun_Pr7763680713840462443e_term ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Ounit_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
    comp_P756492639069434009er_nat: ( fun_Pr1820225556744648189nteger * fun_nat_Product_unit ) > fun_nat_Code_integer ).

tff(sy_c_Fun_Ocomp_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
    comp_P7645380973975430442t_unit: ( fun_Pr2191293291710260995t_unit * fun_Pr2191293291710260995t_unit ) > fun_Pr2191293291710260995t_unit ).

tff(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Nat__Onat_001t__Nat__Onat,type,
    comp_rat_nat_nat: ( fun_rat_nat * fun_nat_rat ) > fun_nat_nat ).

tff(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    comp_r4727614531642239972nt_int: ( fun_rat_rat * fun_Pr1652463973008025892nt_rat ) > fun_Pr1652463973008025892nt_rat ).

tff(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Rat__Orat_001t__Rat__Orat,type,
    comp_rat_rat_rat: ( fun_rat_rat * fun_rat_rat ) > fun_rat_rat ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    comp_f2642788907534428630nteger: ( fun_fu5689865433563736081nteger * fun_Co1981900195452921617nteger ) > fun_Co8499238673658658103nteger ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger,type,
    comp_f228016600672082096nteger: ( fun_fu1763652423599918571nteger * fun_Co1981900195452921617nteger ) > fun_Co1981900195452921617nteger ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_Mt__Num__Onum_J,type,
    comp_f1360117556308984045er_num: ( fun_fu1763652423599918571nteger * fun_fu9089537617116752462nteger ) > fun_fu9089537617116752462nteger ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Num__Onum_J,type,
    comp_f6909282360848428676er_num: ( fun_fu2219603532186391848nteger * fun_fu1714096010366225192nteger ) > fun_fu9168018664657815141nteger ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Num__Onum_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    comp_f4895884909053068781nteger: ( fun_fu5629128276443140046nteger * fun_fu1763652423599918571nteger ) > fun_fu5629128276443140046nteger ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
    comp_f6739083541385432444nteger: ( fun_fu4800041728187187127nteger * fun_Co1981900195452921617nteger ) > fun_Co1561183069634336733nteger ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Num__Onum,type,
    comp_f6099540932654157625er_num: ( fun_fu4800041728187187127nteger * fun_nu1287335591331657422nteger ) > fun_nu1379135015814352922nteger ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    comp_f3848972703483044950nteger: ( fun_fu4800041728187187127nteger * fun_fu1763652423599918571nteger ) > fun_fu4800041728187187127nteger ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_001t__fun_It__Num__Onum_Mt__Num__Onum_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Int__Oint_J,type,
    comp_f2587153255520370886er_int: ( fun_fu5315010139097431512um_num * fun_fu2894000772521619117er_nat ) > fun_fu43082730658364980um_num ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Int__Oint_M_Eo_J_001t__fun_It__Int__Oint_M_Eo_J_001t__Int__Oint,type,
    comp_f2592220016263698127_o_int: fun_fu4169772131120368835_int_o ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Int__Oint_M_Eo_J_001t__fun_It__Int__Oint_M_Eo_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
    comp_f4873873558822606653_nat_o: ( fun_fu3883539188510166275_int_o * fun_fu7075445697382584196_int_o ) > fun_fu7075445697382584196_int_o ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Int__Oint_M_Eo_J_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint,type,
    comp_f4365919156373684133nt_int: fun_fu4482892469221626457nt_int ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Int__Oint_M_Eo_J_001t__fun_It__Nat__Onat_M_Eo_J_001t__Int__Oint,type,
    comp_f1905643983223147563_o_int: fun_fu7618250142905304443_nat_o ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Int__Oint_M_Eo_J_001t__Int__Oint,type,
    comp_f4901222473752183353_o_int: fun_fu8897902691871853255_int_o ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint,type,
    comp_f8169149803026727611nt_int: ( fun_fu1143798476471108391nt_int * fun_int_fun_int_int ) > fun_int_fun_int_int ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Nat__Onat_M_Eo_J_001t__Int__Oint,type,
    comp_f4214646440711632789_o_int: fun_fu2354122332637403079_nat_o ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Int__Oint,type,
    comp_f4771325068212425615nt_int: ( fun_fu3661779633992098115nt_int * fun_in1696471567231710611nt_int ) > fun_in1696471567231710611nt_int ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Int__Oint_Mt__Rat__Orat_J_001t__Int__Oint,type,
    comp_f5638830786481540082at_int: ( fun_fu7460908759652350970nt_rat * fun_in1696471567231710611nt_int ) > fun_int_fun_int_rat ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Int__Oint_Mt__Rat__Orat_J_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    comp_f3282907328706250400nt_int: ( fun_fu7460908759652350970nt_rat * fun_fu3661779633992098115nt_int ) > fun_fu7460908759652350970nt_rat ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Int__Oint_Mt__Rat__Orat_J_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Int__Oint,type,
    comp_f647079087388013614nt_int: ( fun_fu4522195968571808382nt_int * fun_int_fun_int_rat ) > fun_in1696471567231710611nt_int ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Int__Oint_Mt__Rat__Orat_J_001t__fun_It__Int__Oint_Mt__Rat__Orat_J_001t__Int__Oint,type,
    comp_f5789916732873203219at_int: ( fun_fu1008360527747082367nt_rat * fun_int_fun_int_rat ) > fun_int_fun_int_rat ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Int__Oint_Mt__Rat__Orat_J_001t__fun_It__Int__Oint_Mt__Rat__Orat_J_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    comp_f8575242358056807743nt_int: ( fun_fu1008360527747082367nt_rat * fun_fu7460908759652350970nt_rat ) > fun_fu7460908759652350970nt_rat ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Int__Oint_M_Eo_J_001t__Int__Oint,type,
    comp_f1384102883335318131_o_int: fun_fu8028891822603792907_int_o ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint,type,
    comp_f2688405924591934721nt_int: fun_fu353361380671289177nt_int ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Nat__Onat_M_Eo_J_001t__Int__Oint,type,
    comp_f697526850294767567_o_int: fun_fu2253997797533952707_nat_o ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Nat__Onat_M_Eo_J,type,
    comp_f9002688672733719870_nat_o: ( fun_fu4001317426178549763_nat_o * fun_fu4001317426178549763_nat_o ) > fun_fu4001317426178549763_nat_o ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Num__Onum_Mt__Num__Onum_J,type,
    comp_f6195931460900804550um_num: ( fun_fu8508204053700405677nteger * fun_fu2252611666013297880nteger ) > fun_fu8261421317008872756nteger ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Int__Oint_Mt__Num__Onum_J_001t__fun_It__Num__Onum_Mt__Int__Oint_J,type,
    comp_f6389250438540085768um_int: ( fun_fu4905079693651358301nt_num * fun_fu7588784024441849949at_nat ) > fun_fu5490925188574218499nt_num ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
    comp_f6855635597449841736nteger: ( fun_fu4688806437979560835nteger * fun_Co1561183069634336733nteger ) > fun_Co1561183069634336733nteger ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001t__fun_It__Int__Oint_M_Eo_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    comp_f803626508496913273at_nat: ( fun_fu7075445697382584196_int_o * fun_Pr2028404973800837934_nat_o ) > fun_Pr4738963024209204295_int_o ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001t__fun_It__Int__Oint_M_Eo_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
    comp_f3219779300056495522_nat_o: ( fun_fu7075445697382584196_int_o * fun_fu3275390434952296369_nat_o ) > fun_fu7075445697382584196_int_o ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    comp_f6758108398856490500at_nat: ( fun_fu3064074204415222357nt_int * fun_Pr2477239776880934807at_nat ) > fun_Pr7267779425873451369nt_int ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Set__Oset_I_Eo_J_Mt__Assertions__Oassn_J_001t__fun_It__Set__Oset_It__Set__Oset_I_Eo_J_J_Mt__Assertions__Oassn_J_001t__fun_I_Eo_Mt__Assertions__Oassn_J,type,
    comp_f4038625060515458192o_assn: ( fun_fu3743863873453506915o_assn * fun_fu5561970054461773155o_assn * fun_o_assn ) > fun_set_set_o_assn ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Set__Oset_I_Eo_J_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Set__Oset_It__Set__Oset_I_Eo_J_J_Mt__Code____Numeral__Ointeger_J_001t__fun_I_Eo_Mt__Code____Numeral__Ointeger_J,type,
    comp_f1748852684562694277nteger: ( fun_fu1045876692016343459nteger * fun_fu6303754889700780451nteger * fun_o_Code_integer ) > fun_se5062308858318814664nteger ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Set__Oset_I_Eo_J_Mt__Nat__Onat_J_001t__fun_It__Set__Oset_It__Set__Oset_I_Eo_J_J_Mt__Nat__Onat_J_001t__fun_I_Eo_Mt__Nat__Onat_J,type,
    comp_f724240716414175032_o_nat: ( fun_fu1060865441899640675_o_nat * fun_fu8843157277860572003_o_nat * fun_o_nat ) > fun_set_set_o_nat ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Set__Oset_I_Eo_J_Mt__Rat__Orat_J_001t__fun_It__Set__Oset_It__Set__Oset_I_Eo_J_J_Mt__Rat__Orat_J_001t__fun_I_Eo_Mt__Rat__Orat_J,type,
    comp_f1055920047293692736_o_rat: ( fun_fu6849062756650152291_o_rat * fun_fu4803769369665013091_o_rat * fun_o_rat ) > fun_set_set_o_rat ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__Assertions__Oassn_J_001t__fun_It__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J_Mt__Assertions__Oassn_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Assertions__Oassn_J,type,
    comp_f96878100917031437r_assn: ( fun_fu4821026654811345315r_assn * fun_fu727159081937814839r_assn * fun_Co4490034186337852034r_assn ) > fun_se704019859950278126r_assn ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    comp_f3271019896647404588nteger: ( fun_fu2392828822626117773nteger * fun_fu4961913266064405537nteger * fun_Co8499238673658658103nteger ) > fun_se1218973151702474915nteger ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__Rat__Orat_J_001t__fun_It__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J_Mt__Rat__Orat_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Rat__Orat_J,type,
    comp_f227581914562382365er_rat: ( fun_fu6017686703198564611er_rat * fun_fu8198789307943805079er_rat * fun_Code_integer_rat ) > fun_se1173871648619632798er_rat ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Set__Oset_It__Int__Oint_J_Mt__Assertions__Oassn_J_001t__fun_It__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_Mt__Assertions__Oassn_J_001t__fun_It__Int__Oint_Mt__Assertions__Oassn_J,type,
    comp_f3572868634108735226t_assn: ( fun_fu7925354201654153025t_assn * fun_fu6757290529232567765t_assn * fun_int_assn ) > fun_set_set_int_assn ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Set__Oset_It__Int__Oint_J_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Int__Oint_Mt__Code____Numeral__Ointeger_J,type,
    comp_f8044896008013558041nteger: ( fun_fu2310701194077331499nteger * fun_fu7510501037550790335nteger * fun_int_Code_integer ) > fun_se8304080770522320754nteger ).

tff(sy_c_Fun_Ocomp_001t__fun_It__Set__Oset_It__Int__Oint_J_Mt__Rat__Orat_J_001t__fun_It__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_Mt__Rat__Orat_J_001t__fun_It__Int__Oint_Mt__Rat__Orat_J,type,
    comp_f7120815212173581066nt_rat: ( fun_fu8704076394632857761nt_rat * fun_fu3579422585476231989nt_rat * fun_int_rat ) > fun_set_set_int_rat ).

tff(sy_c_Fun_Ofun__upd_001_Eo_001_Eo,type,
    fun_upd_o_o: ( fun_o_o * $o ) > fun_o_fun_o_o ).

tff(sy_c_Fun_Ofun__upd_001_Eo_001t__Int__Oint,type,
    fun_upd_o_int: ( fun_o_int * $o * int ) > fun_o_int ).

tff(sy_c_Fun_Ofun__upd_001_Eo_001t__Nat__Onat,type,
    fun_upd_o_nat: ( fun_o_nat * $o * nat ) > fun_o_nat ).

tff(sy_c_Fun_Ofun__upd_001_Eo_001t__Option__Ooption_It__Num__Onum_J,type,
    fun_upd_o_option_num: ( fun_o_option_num * $o * option_num ) > fun_o_option_num ).

tff(sy_c_Fun_Ofun__upd_001_Eo_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    fun_up1288979561775348147it_nat: ( fun_o_7229649064035662211it_nat * $o * option8956607266484857688it_nat ) > fun_o_7229649064035662211it_nat ).

tff(sy_c_Fun_Ofun__upd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    fun_up8355007323143964473nteger: ( fun_Co8499238673658658103nteger * code_integer ) > fun_Co1981900195452921617nteger ).

tff(sy_c_Fun_Ofun__upd_001t__Code____Numeral__Ointeger_001t__Option__Ooption_It__Code____Numeral__Ointeger_J,type,
    fun_up6566892301432185865nteger: ( fun_Co8029881127924365703nteger * code_integer * option_Code_integer ) > fun_Co8029881127924365703nteger ).

tff(sy_c_Fun_Ofun__upd_001t__Code____Numeral__Ointeger_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    fun_up7364656672652868627nteger: ( fun_Co1981900195452921617nteger * code_integer * fun_Co8499238673658658103nteger ) > fun_Co1981900195452921617nteger ).

tff(sy_c_Fun_Ofun__upd_001t__Code____Numeral__Ointeger_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    fun_up1280136195588363103nteger: ( fun_Co1561183069634336733nteger * code_integer * fun_Pr5876161306168176259nteger ) > fun_Co1561183069634336733nteger ).

tff(sy_c_Fun_Ofun__upd_001t__Code____Numeral__Onatural_001t__Option__Ooption_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    fun_up2923169431403285008atural: ( fun_Co7921331830460615208atural * code_natural * option5403585828896915703atural ) > fun_Co7921331830460615208atural ).

tff(sy_c_Fun_Ofun__upd_001t__Int__Oint_001_Eo,type,
    fun_upd_int_o: ( fun_int_o * int * $o ) > fun_int_o ).

tff(sy_c_Fun_Ofun__upd_001t__Int__Oint_001t__Int__Oint,type,
    fun_upd_int_int: ( fun_int_int * int ) > fun_int_fun_int_int ).

tff(sy_c_Fun_Ofun__upd_001t__Int__Oint_001t__Nat__Onat,type,
    fun_upd_int_nat: ( fun_int_nat * int * nat ) > fun_int_nat ).

tff(sy_c_Fun_Ofun__upd_001t__Int__Oint_001t__Num__Onum,type,
    fun_upd_int_num: ( fun_int_num * int * num ) > fun_int_num ).

tff(sy_c_Fun_Ofun__upd_001t__Int__Oint_001t__Option__Ooption_It__Int__Oint_J,type,
    fun_up8666045135305973159on_int: ( fun_int_option_int * int * option_int ) > fun_int_option_int ).

tff(sy_c_Fun_Ofun__upd_001t__Int__Oint_001t__Option__Ooption_It__Num__Onum_J,type,
    fun_up4328768054909231765on_num: ( fun_int_option_num * int * option_num ) > fun_int_option_num ).

tff(sy_c_Fun_Ofun__upd_001t__Int__Oint_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    fun_up6992348036167380867it_nat: ( fun_in8543325783774419841it_nat * int * option8956607266484857688it_nat ) > fun_in8543325783774419841it_nat ).

tff(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001_Eo,type,
    fun_upd_nat_o: ( fun_nat_o * nat ) > fun_o_fun_nat_o ).

tff(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
    fun_up3904115110581602988nteger: ( fun_nat_Code_integer * nat * code_integer ) > fun_nat_Code_integer ).

tff(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__Int__Oint,type,
    fun_upd_nat_int: ( fun_nat_int * nat * int ) > fun_nat_int ).

tff(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__Nat__Onat,type,
    fun_upd_nat_nat: ( fun_nat_nat * nat ) > fun_nat_fun_nat_nat ).

tff(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__Option__Ooption_It__Nat__Onat_J,type,
    fun_up1493157387958331631on_nat: ( fun_nat_option_nat * nat * option_nat ) > fun_nat_option_nat ).

tff(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__Option__Ooption_It__Num__Onum_J,type,
    fun_up2201401324907169337on_num: ( fun_nat_option_num * nat * option_num ) > fun_nat_option_num ).

tff(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    fun_up4116053422210368295it_nat: ( fun_na5667031169817407269it_nat * nat * option8956607266484857688it_nat ) > fun_na5667031169817407269it_nat ).

tff(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
    fun_upd_nat_set_nat: ( fun_nat_set_nat * nat * set_nat ) > fun_nat_set_nat ).

tff(sy_c_Fun_Ofun__upd_001t__Num__Onum_001t__Code____Numeral__Ointeger,type,
    fun_up1844922938552261878nteger: ( fun_num_Code_integer * num * code_integer ) > fun_num_Code_integer ).

tff(sy_c_Fun_Ofun__upd_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Option__Ooption_It__Num__Onum_J,type,
    fun_up8025039454679724718on_num: ( fun_Pr7397166214287566974on_num * product_prod_nat_nat * option_num ) > fun_Pr7397166214287566974on_num ).

tff(sy_c_Fun_Ofun__upd_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    fun_up3996838528606387100it_nat: ( fun_Pr6624299372562097772it_nat * product_prod_nat_nat * option8956607266484857688it_nat ) > fun_Pr6624299372562097772it_nat ).

tff(sy_c_Fun_Ofun__upd_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Option__Ooption_It__Num__Onum_J,type,
    fun_up3286109336741039636on_num: ( fun_Pr6553355248451873380on_num * produc3843707927480180839at_nat * option_num ) > fun_Pr6553355248451873380on_num ).

tff(sy_c_Fun_Ofun__upd_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    fun_up5549328659429834498it_nat: ( fun_Pr6865292569827446866it_nat * produc3843707927480180839at_nat * option8956607266484857688it_nat ) > fun_Pr6865292569827446866it_nat ).

tff(sy_c_Fun_Ofun__upd_001t__Product____Type__Ounit_001t__Option__Ooption_It__Num__Onum_J,type,
    fun_up4695802795598371002on_num: ( fun_Pr792663941044724234on_num * product_unit * option_num ) > fun_Pr792663941044724234on_num ).

tff(sy_c_Fun_Ofun__upd_001t__Product____Type__Ounit_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    fun_up1973317344121680296it_nat: ( fun_Pr6171258863536582648it_nat * product_unit * option8956607266484857688it_nat ) > fun_Pr6171258863536582648it_nat ).

tff(sy_c_Fun_Oid_001_Eo,type,
    id_o: fun_o_o ).

tff(sy_c_Fun_Oid_001t__Code____Numeral__Ointeger,type,
    id_Code_integer: fun_Co8499238673658658103nteger ).

tff(sy_c_Fun_Oid_001t__Int__Oint,type,
    id_int: fun_int_int ).

tff(sy_c_Fun_Oid_001t__Nat__Onat,type,
    id_nat: fun_nat_nat ).

tff(sy_c_Fun_Oid_001t__Num__Onum,type,
    id_num: fun_num_num ).

tff(sy_c_Fun_Oid_001t__Option__Ooption_I_Eo_J,type,
    id_option_o: fun_op5853259939270031811tion_o ).

tff(sy_c_Fun_Oid_001t__Option__Ooption_It__Int__Oint_J,type,
    id_option_int: fun_op4193086050743966581on_int ).

tff(sy_c_Fun_Oid_001t__Option__Ooption_It__Nat__Onat_J,type,
    id_option_nat: fun_op1272087013972230845on_nat ).

tff(sy_c_Fun_Oid_001t__Option__Ooption_It__Num__Onum_J,type,
    id_option_num: fun_op8989173174992673105on_num ).

tff(sy_c_Fun_Oid_001t__Option__Ooption_It__fun_It__Nat__Onat_M_Eo_J_J,type,
    id_option_fun_nat_o: fun_op3284592519439835779_nat_o ).

tff(sy_c_Fun_Oid_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    id_Pro2309048762231606924nteger: fun_Pr5876161306168176259nteger ).

tff(sy_c_Fun_Oid_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    id_Pro4381231610383771306nt_int: fun_Pr2478283820680522243nt_int ).

tff(sy_c_Fun_Oid_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    id_Pro1159712480615372887it_nat: fun_Pr1033138224055104269it_nat ).

tff(sy_c_Fun_Oid_001t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    id_Pro8454827939775161726nt_int: fun_Pr5152393401594413531nt_int ).

tff(sy_c_Fun_Oid_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    id_Pro1988134236931701989nteger: fun_Pr3905736301278533417nteger ).

tff(sy_c_Fun_Oid_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    id_Pro1868950919225201135et_nat: fun_Pr836988951548913597et_nat ).

tff(sy_c_Fun_Oid_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    id_Pro6241762429208028941et_nat: fun_Pr6662792608368940153et_nat ).

tff(sy_c_Fun_Oid_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    id_Pro8963167613625125458nt_int: fun_Pr5846521507401124227nt_int ).

tff(sy_c_Fun_Oid_001t__Product____Type__Ounit,type,
    id_Product_unit: fun_Pr2191293291710260995t_unit ).

tff(sy_c_Fun_Oid_001t__Rat__Orat,type,
    id_rat: fun_rat_rat ).

tff(sy_c_Fun_Oid_001t__Set__Oset_I_Eo_J,type,
    id_set_o: fun_set_o_set_o ).

tff(sy_c_Fun_Oid_001t__Set__Oset_It__Int__Oint_J,type,
    id_set_int: fun_set_int_set_int ).

tff(sy_c_Fun_Oid_001t__Set__Oset_It__Nat__Onat_J,type,
    id_set_nat: fun_set_nat_set_nat ).

tff(sy_c_Fun_Oid_001t__Set__Oset_It__Num__Onum_J,type,
    id_set_num: fun_set_num_set_num ).

tff(sy_c_Fun_Oid_001t__Set__Oset_It__fun_It__Nat__Onat_M_Eo_J_J,type,
    id_set_fun_nat_o: fun_se2106923200977956867_nat_o ).

tff(sy_c_Fun_Oid_001t__fun_It__Nat__Onat_M_Eo_J,type,
    id_fun_nat_o: fun_fu4001317426178549763_nat_o ).

tff(sy_c_Fun_Oid_001t__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J,type,
    id_fun2933211968975237955nteger: fun_fu552866168194876645nteger ).

tff(sy_c_Fun_Oid_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    id_fun8244602250740870226nteger: fun_fu4688806437979560835nteger ).

tff(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    map_fu5082455417554595470nteger: ( fun_Co8499238673658658103nteger * fun_Co8499238673658658103nteger ) > fun_fu1763652423599918571nteger ).

tff(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    map_fu5403962169733074228nteger: ( fun_Co8499238673658658103nteger * fun_Co1561183069634336733nteger * fun_Co8499238673658658103nteger ) > fun_Co1561183069634336733nteger ).

tff(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Nat__Onat,type,
    map_fu5423760287386111952nt_nat: ( fun_Co8499238673658658103nteger * fun_int_nat ) > fun_fu2894000772521619117er_nat ).

tff(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum_001t__Code____Numeral__Ointeger,type,
    map_fu603974984455542859nteger: ( fun_Co8499238673658658103nteger * fun_num_Code_integer ) > fun_fu1714096010366225192nteger ).

tff(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    map_fu4199360331771201806nteger: ( fun_Co8499238673658658103nteger * fun_fu4800041728187187127nteger * fun_Co1981900195452921617nteger ) > fun_Co1561183069634336733nteger ).

tff(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_Eo_001_Eo,type,
    map_fu6957801986076833569nt_o_o: ( fun_Code_integer_int * fun_o_o ) > fun_fu8256284588060503314eger_o ).

tff(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
    map_fu2599414010547811884nteger: ( fun_Code_integer_int * fun_int_Code_integer ) > fun_fu6921880696561781257nteger ).

tff(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
    map_fu1051355602067684763atural: ( fun_Code_integer_int * fun_nat_Code_natural * fun_int_nat ) > fun_Co3734316457315071362atural ).

tff(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
    map_fu6539832666145259331at_nat: ( fun_Code_integer_int * fun_nat_nat * fun_int_nat ) > fun_Code_integer_nat ).

tff(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Num__Onum_001t__Num__Onum,type,
    map_fu1227494855608507351um_num: ( fun_Code_integer_int * fun_num_num * fun_int_num ) > fun_Code_integer_num ).

tff(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__fun_It__Int__Oint_M_Eo_J_001t__fun_It__Code____Numeral__Ointeger_M_Eo_J,type,
    map_fu4249723513525335408eger_o: ( fun_Code_integer_int * fun_fu8256284588060503314eger_o * fun_int_fun_int_o ) > fun_Co2081214437782444048eger_o ).

tff(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    map_fu1034890151506530863nteger: ( fun_Code_integer_int * fun_fu6921880696561781257nteger * fun_int_fun_int_int ) > fun_Co1981900195452921617nteger ).

tff(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Nat__Onat_M_Eo_J,type,
    map_fu2913747595474184929_nat_o: ( fun_Code_integer_int * fun_fu4001317426178549763_nat_o * fun_int_fun_nat_o ) > fun_Co1375048237525739357_nat_o ).

tff(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Num__Onum_001t__Code____Numeral__Ointeger,type,
    map_fu2459088713202864369nteger: ( fun_Co1561183069634336733nteger * fun_num_Code_integer ) > fun_fu9089537617116752462nteger ).

tff(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001_Eo_001_Eo,type,
    map_fu4892316939951275536at_o_o: ( fun_Code_natural_nat * fun_o_o ) > fun_fu2969420921405070251ural_o ).

tff(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
    map_fu2787874002554666395nteger: ( fun_Code_natural_nat * fun_int_Code_integer * fun_nat_int ) > fun_Co2940338738630218498nteger ).

tff(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
    map_fu1239815594074539274atural: ( fun_Code_natural_nat * fun_nat_Code_natural ) > fun_fu6924846375782198887atural ).

tff(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
    map_fu226235371393106610at_nat: ( fun_Code_natural_nat * fun_nat_nat * fun_nat_nat ) > fun_Code_natural_nat ).

tff(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Code____Numeral__Onatural_M_Eo_J,type,
    map_fu2458051687388636536ural_o: ( fun_Code_natural_nat * fun_fu2969420921405070251ural_o * fun_nat_fun_nat_o ) > fun_Co7302518231560758906ural_o ).

tff(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Nat__Onat_M_Eo_J,type,
    map_fu820683741283188176_nat_o: ( fun_Code_natural_nat * fun_fu4001317426178549763_nat_o * fun_nat_fun_nat_o ) > fun_Co196715998180962002_nat_o ).

tff(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    map_fu7613509917203888380atural: ( fun_Code_natural_nat * fun_fu6924846375782198887atural * fun_nat_fun_nat_nat ) > fun_Co6813818151677833714atural ).

tff(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Int__Oint_001_Eo_001_Eo,type,
    map_fun_int_int_o_o: ( fun_int_int * fun_o_o ) > fun_fu3883539188510166275_int_o ).

tff(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    map_fu2180209013632630320nt_int: ( fun_int_int * fun_Pr2478283820680522243nt_int ) > fun_fu3661779633992098115nt_int ).

tff(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
    map_fu3424225382358772769nt_rat: ( fun_int_int * fun_Pr1652463973008025892nt_rat ) > fun_fu7460908759652350970nt_rat ).

tff(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Int__Oint_001t__Rat__Orat_001t__Rat__Orat,type,
    map_fu6531859369801489698at_rat: ( fun_int_int * fun_rat_rat ) > fun_fu1008360527747082367nt_rat ).

tff(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Int__Oint_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Int__Oint_Mt__Rat__Orat_J,type,
    map_fu7945985449245211511nt_rat: ( fun_int_int * fun_fu7460908759652350970nt_rat * fun_in1696471567231710611nt_int ) > fun_int_fun_int_rat ).

tff(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    map_fu1717202910479192016nteger: ( fun_int_nat * fun_Co8499238673658658103nteger ) > fun_fu8508204053700405677nteger ).

tff(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat_001t__Num__Onum,type,
    map_fu3669222299741785344at_num: ( fun_int_nat * fun_nat_num ) > fun_fu4905079693651358301nt_num ).

tff(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Num__Onum_001t__Int__Oint_001t__Num__Onum,type,
    map_fu2609383839613498790nt_num: ( fun_int_num * fun_int_num ) > fun_fu5490925188574218499nt_num ).

tff(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Num__Onum_001t__Num__Onum_001t__Code____Numeral__Ointeger,type,
    map_fu229184005524548567nteger: ( fun_int_num * fun_num_Code_integer ) > fun_fu8261421317008872756nteger ).

tff(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
    map_fu4826362097070443709at_o_o: ( fun_in4514472496968388910at_nat * fun_o_o ) > fun_fu7075445697382584196_int_o ).

tff(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
    map_fu3667384564859982768at_int: ( fun_in4514472496968388910at_nat * fun_Pr7647638413817135296at_int ) > fun_fu3064074204415222357nt_int ).

tff(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001t__fun_It__Int__Oint_M_Eo_J,type,
    map_fu3191548434056052140_int_o: ( fun_in4514472496968388910at_nat * fun_fu7075445697382584196_int_o * fun_Pr2028404973800837934_nat_o ) > fun_int_fun_int_o ).

tff(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Int__Oint_Mt__Int__Oint_J,type,
    map_fu8294830438409148311nt_int: ( fun_in4514472496968388910at_nat * fun_fu3064074204415222357nt_int * fun_Pr2477239776880934807at_nat ) > fun_int_fun_int_int ).

tff(sy_c_Fun_Omap__fun_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001_Eo,type,
    map_fun_nat_nat_o_o: ( fun_nat_nat * fun_o_o ) > fun_fu4001317426178549763_nat_o ).

tff(sy_c_Fun_Omap__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
    map_fu6290471996055670595nteger: ( fun_nat_nat * fun_int_Code_integer * fun_nat_int ) > fun_nat_Code_integer ).

tff(sy_c_Fun_Omap__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
    map_fu4742413587575543474atural: ( fun_nat_nat * fun_nat_Code_natural * fun_nat_nat ) > fun_nat_Code_natural ).

tff(sy_c_Fun_Omap__fun_001t__Nat__Onat_001t__Nat__Onat_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    map_fu214667362969451334nteger: ( fun_nat_nat * fun_fu6921880696561781257nteger * fun_nat_fun_int_int ) > fun_na7078387940644931716nteger ).

tff(sy_c_Fun_Omap__fun_001t__Nat__Onat_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    map_fu5588224966615042724atural: ( fun_nat_nat * fun_fu6924846375782198887atural * fun_nat_fun_nat_nat ) > fun_na607345901702507418atural ).

tff(sy_c_Fun_Omap__fun_001t__Nat__Onat_001t__Num__Onum_001t__Int__Oint_001t__Nat__Onat,type,
    map_fu8361869985550671104nt_nat: ( fun_nat_num * fun_int_nat ) > fun_fu7588784024441849949at_nat ).

tff(sy_c_Fun_Omap__fun_001t__Nat__Onat_001t__Num__Onum_001t__Num__Onum_001t__Code____Numeral__Ointeger,type,
    map_fu1090464068875036027nteger: ( fun_nat_num * fun_num_Code_integer ) > fun_fu2252611666013297880nteger ).

tff(sy_c_Fun_Omap__fun_001t__Num__Onum_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    map_fu5269526691104299083nteger: ( fun_num_Code_integer * fun_Co8499238673658658103nteger ) > fun_fu2219603532186391848nteger ).

tff(sy_c_Fun_Omap__fun_001t__Num__Onum_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    map_fu1595501404987506033nteger: ( fun_num_Code_integer * fun_Co1561183069634336733nteger ) > fun_fu5629128276443140046nteger ).

tff(sy_c_Fun_Omap__fun_001t__Num__Onum_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Num__Onum,type,
    map_fu8479170043890205655nt_num: ( fun_num_Code_integer * fun_int_num ) > fun_fu43082730658364980um_num ).

tff(sy_c_Fun_Omap__fun_001t__Num__Onum_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Num__Onum,type,
    map_fu7479816331989151099at_num: ( fun_num_Code_integer * fun_nat_num ) > fun_fu5315010139097431512um_num ).

tff(sy_c_Fun_Omap__fun_001t__Num__Onum_001t__Code____Numeral__Ointeger_001t__Num__Onum_001t__Code____Numeral__Ointeger,type,
    map_fu8223014087597717000nteger: ( fun_num_Code_integer * fun_num_Code_integer ) > fun_fu9168018664657815141nteger ).

tff(sy_c_Fun_Omap__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
    map_fu8638147718074629079nteger: ( fun_num_num * fun_int_Code_integer ) > fun_fu3380082687118895412nteger ).

tff(sy_c_Fun_Omap__fun_001t__Num__Onum_001t__Num__Onum_001t__fun_It__Num__Onum_Mt__Int__Oint_J_001t__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J,type,
    map_fu8540202848259802501nteger: ( fun_num_num * fun_fu3380082687118895412nteger * fun_num_fun_num_int ) > fun_nu2537414170016844299nteger ).

tff(sy_c_Fun_Omap__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
    map_fu1707080289169145046at_o_o: ( fun_Pr2118491707810114563at_nat * fun_o_o ) > fun_fu3275390434952296369_nat_o ).

tff(sy_c_Fun_Omap__fun_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
    map_fu5673905371560938248nt_rat: ( fun_ra4503298312962071866nt_int * fun_Pr1652463973008025892nt_rat ) > fun_fu1098312133097393581at_rat ).

tff(sy_c_Fun_Omap__fun_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Rat__Orat_Mt__Rat__Orat_J,type,
    map_fu5968964422797239547at_rat: ( fun_ra4503298312962071866nt_int * fun_fu1098312133097393581at_rat * fun_Pr1308109350235310159nt_int ) > fun_rat_fun_rat_rat ).

tff(sy_c_Fun__Def_Omax__strict,type,
    fun_max_strict: set_Pr4329608150637261639at_nat ).

tff(sy_c_Fun__Def_Omax__weak,type,
    fun_max_weak: set_Pr4329608150637261639at_nat ).

tff(sy_c_Fun__Def_Omin__strict,type,
    fun_min_strict: set_Pr4329608150637261639at_nat ).

tff(sy_c_Fun__Def_Omin__weak,type,
    fun_min_weak: set_Pr4329608150637261639at_nat ).

tff(sy_c_Fun__Def_Opair__leq,type,
    fun_pair_leq: set_Pr8693737435421807431at_nat ).

tff(sy_c_Fun__Def_Opair__less,type,
    fun_pair_less: set_Pr8693737435421807431at_nat ).

tff(sy_c_Fun__Def_Oreduction__pair_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    fun_re7357418987779152907at_nat: produc4193628355235574503at_nat > $o ).

tff(sy_c_Fun__Def_Oreduction__pair_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    fun_re2478310338295953701at_nat: produc1319942482725812455at_nat > $o ).

tff(sy_c_GCD_OGcd__class_OGcd_001t__Nat__Onat,type,
    gcd_Gcd_nat: fun_set_nat_nat ).

tff(sy_c_GCD_OGcd__class_OLcm_001t__Nat__Onat,type,
    gcd_Lcm_nat: fun_set_nat_nat ).

tff(sy_c_GCD_Obezw,type,
    bezw: nat > fun_na1173468842265550146nt_int ).

tff(sy_c_GCD_Obezw__rel,type,
    bezw_rel: fun_Pr2028404973800837934_nat_o ).

tff(sy_c_GCD_Ogcd__class_Ogcd_001t__Int__Oint,type,
    gcd_gcd_int: fun_int_fun_int_int ).

tff(sy_c_GCD_Ogcd__class_Ogcd_001t__Nat__Onat,type,
    gcd_gcd_nat: fun_nat_fun_nat_nat ).

tff(sy_c_GCD_Ogcd__class_Olcm_001t__Nat__Onat,type,
    gcd_lcm_nat: fun_nat_fun_nat_nat ).

tff(sy_c_GCD_Ogcd__nat__rel,type,
    gcd_nat_rel: fun_Pr2028404973800837934_nat_o ).

tff(sy_c_Groups_Oabs__class_Oabs_001t__Code____Numeral__Ointeger,type,
    abs_abs_Code_integer: fun_Co8499238673658658103nteger ).

tff(sy_c_Groups_Oabs__class_Oabs_001t__Int__Oint,type,
    abs_abs_int: fun_int_int ).

tff(sy_c_Groups_Oabs__class_Oabs_001t__Rat__Orat,type,
    abs_abs_rat: fun_rat_rat ).

tff(sy_c_Groups_Ogroup_001t__Code____Numeral__Ointeger,type,
    group_Code_integer: ( fun_Co1981900195452921617nteger * code_integer * fun_Co8499238673658658103nteger ) > $o ).

tff(sy_c_Groups_Ogroup_001t__Int__Oint,type,
    group_int: ( fun_int_fun_int_int * int * fun_int_int ) > $o ).

tff(sy_c_Groups_Ogroup_001t__Rat__Orat,type,
    group_rat: ( fun_rat_fun_rat_rat * rat * fun_rat_rat ) > $o ).

tff(sy_c_Groups_Ominus__class_Ominus_001t__Code____Numeral__Ointeger,type,
    minus_8373710615458151222nteger: fun_Co1981900195452921617nteger ).

tff(sy_c_Groups_Ominus__class_Ominus_001t__Code____Numeral__Onatural,type,
    minus_7197305767214868737atural: fun_Co6813818151677833714atural ).

tff(sy_c_Groups_Ominus__class_Ominus_001t__Int__Oint,type,
    minus_minus_int: fun_int_fun_int_int ).

tff(sy_c_Groups_Ominus__class_Ominus_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    minus_4286766774447292334at_nat: ( multis2468970476368604999at_nat * multis2468970476368604999at_nat ) > multis2468970476368604999at_nat ).

tff(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
    minus_minus_nat: fun_nat_fun_nat_nat ).

tff(sy_c_Groups_Ominus__class_Ominus_001t__Rat__Orat,type,
    minus_minus_rat: rat > fun_rat_rat ).

tff(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_I_Eo_J,type,
    minus_minus_set_o: ( set_o * set_o ) > set_o ).

tff(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
    minus_2355218937544613996nteger: ( set_Code_integer * set_Code_integer ) > set_Code_integer ).

tff(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Int__Oint_J,type,
    minus_minus_set_int: ( set_int * set_int ) > set_int ).

tff(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
    minus_7954133019191499631st_nat: ( set_list_nat * set_list_nat ) > set_list_nat ).

tff(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Nat__Onat_J,type,
    minus_minus_set_nat: ( set_nat * set_nat ) > set_nat ).

tff(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Num__Onum_J,type,
    minus_minus_set_num: ( set_num * set_num ) > set_num ).

tff(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    minus_1356011639430497352at_nat: set_Pr1261947904930325089at_nat > fun_se320340636488258563at_nat ).

tff(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    minus_3314409938677909166at_nat: ( set_Pr4329608150637261639at_nat * set_Pr4329608150637261639at_nat ) > set_Pr4329608150637261639at_nat ).

tff(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 ).

tff(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Rat__Orat_J,type,
    minus_minus_set_rat: ( set_rat * set_rat ) > set_rat ).

tff(sy_c_Groups_Oone__class_Oone_001t__Assertions__Oassn,type,
    one_one_assn: assn ).

tff(sy_c_Groups_Oone__class_Oone_001t__Code____Numeral__Ointeger,type,
    one_one_Code_integer: code_integer ).

tff(sy_c_Groups_Oone__class_Oone_001t__Code____Numeral__Onatural,type,
    one_one_Code_natural: code_natural ).

tff(sy_c_Groups_Oone__class_Oone_001t__Int__Oint,type,
    one_one_int: int ).

tff(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
    one_one_nat: nat ).

tff(sy_c_Groups_Oone__class_Oone_001t__Rat__Orat,type,
    one_one_rat: rat ).

tff(sy_c_Groups_Oplus__class_Oplus_001t__Code____Numeral__Ointeger,type,
    plus_p5714425477246183910nteger: fun_Co1981900195452921617nteger ).

tff(sy_c_Groups_Oplus__class_Oplus_001t__Code____Numeral__Onatural,type,
    plus_p4538020629002901425atural: fun_Co6813818151677833714atural ).

tff(sy_c_Groups_Oplus__class_Oplus_001t__Int__Oint,type,
    plus_plus_int: fun_int_fun_int_int ).

tff(sy_c_Groups_Oplus__class_Oplus_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    plus_p7104986032573967614at_nat: multis2468970476368604999at_nat > fun_mu2328110650637990531at_nat ).

tff(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
    plus_plus_nat: fun_nat_fun_nat_nat ).

tff(sy_c_Groups_Oplus__class_Oplus_001t__Num__Onum,type,
    plus_plus_num: fun_num_fun_num_num ).

tff(sy_c_Groups_Oplus__class_Oplus_001t__Rat__Orat,type,
    plus_plus_rat: fun_rat_fun_rat_rat ).

tff(sy_c_Groups_Osgn__class_Osgn_001t__Code____Numeral__Ointeger,type,
    sgn_sgn_Code_integer: fun_Co8499238673658658103nteger ).

tff(sy_c_Groups_Osgn__class_Osgn_001t__Int__Oint,type,
    sgn_sgn_int: fun_int_int ).

tff(sy_c_Groups_Osgn__class_Osgn_001t__Rat__Orat,type,
    sgn_sgn_rat: fun_rat_rat ).

tff(sy_c_Groups_Otimes__class_Otimes_001t__Assertions__Oassn,type,
    times_times_assn: fun_as3983628580203722482n_assn ).

tff(sy_c_Groups_Otimes__class_Otimes_001t__Code____Numeral__Ointeger,type,
    times_3573771949741848930nteger: fun_Co1981900195452921617nteger ).

tff(sy_c_Groups_Otimes__class_Otimes_001t__Code____Numeral__Onatural,type,
    times_2397367101498566445atural: fun_Co6813818151677833714atural ).

tff(sy_c_Groups_Otimes__class_Otimes_001t__Int__Oint,type,
    times_times_int: fun_int_fun_int_int ).

tff(sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat,type,
    times_times_nat: fun_nat_fun_nat_nat ).

tff(sy_c_Groups_Otimes__class_Otimes_001t__Num__Onum,type,
    times_times_num: fun_num_fun_num_num ).

tff(sy_c_Groups_Otimes__class_Otimes_001t__Rat__Orat,type,
    times_times_rat: fun_rat_fun_rat_rat ).

tff(sy_c_Groups_Ouminus__class_Ouminus_001_Eo,type,
    uminus_uminus_o: fun_o_o ).

tff(sy_c_Groups_Ouminus__class_Ouminus_001t__Code____Numeral__Ointeger,type,
    uminus1351360451143612070nteger: fun_Co8499238673658658103nteger ).

tff(sy_c_Groups_Ouminus__class_Ouminus_001t__Int__Oint,type,
    uminus_uminus_int: fun_int_int ).

tff(sy_c_Groups_Ouminus__class_Ouminus_001t__Product____Type__Ounit,type,
    uminus2952777764628376836t_unit: fun_Pr2191293291710260995t_unit ).

tff(sy_c_Groups_Ouminus__class_Ouminus_001t__Rat__Orat,type,
    uminus_uminus_rat: fun_rat_rat ).

tff(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
    uminus804700908173204444nteger: set_Code_integer > set_Code_integer ).

tff(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Int__Oint_J,type,
    uminus1532241313380277803et_int: set_int > set_int ).

tff(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Nat__Onat_J,type,
    uminus5710092332889474511et_nat: set_nat > set_nat ).

tff(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    uminus5944136376168626660t_unit: set_Product_unit > set_Product_unit ).

tff(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Rat__Orat_J,type,
    uminus2201863774496077783et_rat: set_rat > set_rat ).

tff(sy_c_Groups_Ouminus__class_Ouminus_001t__fun_It__Nat__Onat_M_Eo_J,type,
    uminus6183504819137795864_nat_o: fun_fu4001317426178549763_nat_o ).

tff(sy_c_Groups_Ozero__class_Ozero_001t__Code____Numeral__Ointeger,type,
    zero_z3403309356797280102nteger: code_integer ).

tff(sy_c_Groups_Ozero__class_Ozero_001t__Code____Numeral__Onatural,type,
    zero_z2226904508553997617atural: code_natural ).

tff(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint,type,
    zero_zero_int: int ).

tff(sy_c_Groups_Ozero__class_Ozero_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    zero_z1048942125864253310at_nat: multis2468970476368604999at_nat ).

tff(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
    zero_zero_nat: nat ).

tff(sy_c_Groups_Ozero__class_Ozero_001t__Rat__Orat,type,
    zero_zero_rat: rat ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001_Eo_001t__Code____Numeral__Ointeger,type,
    groups4406642042086082107nteger: ( fun_o_Code_integer * set_o ) > code_integer ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001_Eo_001t__Int__Oint,type,
    groups8505340233167759370_o_int: ( fun_o_int * set_o ) > int ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001_Eo_001t__Nat__Onat,type,
    groups8507830703676809646_o_nat: ( fun_o_nat * set_o ) > nat ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001_Eo_001t__Rat__Orat,type,
    groups7872700643590313910_o_rat: ( fun_o_rat * set_o ) > rat ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    groups879477027807139574nteger: fun_Co8499238673658658103nteger > fun_se3773019727686582893nteger ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
    groups7234854612051535045er_int: ( fun_Code_integer_int * set_Code_integer ) > int ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
    groups7237345082560585321er_nat: ( fun_Code_integer_nat * set_Code_integer ) > nat ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Code____Numeral__Ointeger_001t__Rat__Orat,type,
    groups6602215022474089585er_rat: ( fun_Code_integer_rat * set_Code_integer ) > rat ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
    groups7873554091576472773nteger: ( fun_int_Code_integer * set_int ) > code_integer ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Int__Oint_001t__Int__Oint,type,
    groups4538972089207619220nt_int: fun_int_int > fun_set_int_int ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Int__Oint_001t__Nat__Onat,type,
    groups4541462559716669496nt_nat: ( fun_int_nat * set_int ) > nat ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Int__Oint_001t__Rat__Orat,type,
    groups3906332499630173760nt_rat: ( fun_int_rat * set_int ) > rat ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__List__Olist_It__Nat__Onat_J_001t__Nat__Onat,type,
    groups4396056296759096172at_nat: ( fun_list_nat_nat * set_list_nat ) > nat ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
    groups7501900531339628137nteger: ( fun_nat_Code_integer * set_nat ) > code_integer ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
    groups6325495683096345652atural: ( fun_nat_Code_natural * set_nat ) > code_natural ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Int__Oint,type,
    groups3539618377306564664at_int: ( fun_nat_int * set_nat ) > int ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    groups6857163185585827899at_nat: ( fun_na2338080690716861136at_nat * set_nat ) > multis2468970476368604999at_nat ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Nat__Onat,type,
    groups3542108847815614940at_nat: fun_nat_nat > fun_set_nat_nat ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Nat__Onat_001t__Rat__Orat,type,
    groups2906978787729119204at_rat: ( fun_nat_rat * set_nat ) > rat ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Num__Onum_001t__Code____Numeral__Ointeger,type,
    groups5442708359310287027nteger: ( fun_num_Code_integer * set_num ) > code_integer ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Code____Numeral__Ointeger,type,
    groups196832835297161892nteger: ( fun_Pr6026251430685297nteger * set_Pr1261947904930325089at_nat ) > code_integer ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
    groups977919841031483927at_nat: fun_Pr2602117396471556196at_nat > fun_se4097146774670233028at_nat ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Rat__Orat,type,
    groups342789780944988191at_rat: ( fun_Pr8317260874932935276at_rat * set_Pr1261947904930325089at_nat ) > rat ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Product____Type__Ounit_001t__Nat__Onat,type,
    groups8766797177574957219it_nat: ( fun_Product_unit_nat * set_Product_unit ) > nat ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J_001t__Int__Oint,type,
    groups2416162284031854641er_int: ( fun_se504249187503832818er_int * set_se8531188866349061887nteger ) > int ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_001t__Int__Oint,type,
    groups1080061135233207040nt_int: ( fun_set_set_int_int * set_set_set_int ) > int ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Set__Oset_It__Set__Oset_It__List__Olist_It__Nat__Onat_J_J_J_001t__Int__Oint,type,
    groups7004213669654646580at_int: ( fun_se1018900654481025269at_int * set_set_set_list_nat ) > int ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J_001t__Int__Oint,type,
    groups7084729577923612836at_int: ( fun_set_set_nat_int * set_set_set_nat ) > int ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Int__Oint,type,
    groups1759609815103008563at_int: ( fun_se8575562297434572672at_int * set_se5158245632345848097at_nat ) > int ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Set__Oset_It__Set__Oset_It__Product____Type__Ounit_J_J_001t__Int__Oint,type,
    groups9212676010950626495it_int: ( fun_se1823139391991869964it_int * set_se7118615804146677933t_unit ) > int ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_H_001_Eo_001t__Code____Numeral__Ointeger,type,
    groups1402912129352969042nteger: ( fun_o_Code_integer * set_o ) > code_integer ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_H_001_Eo_001t__Nat__Onat,type,
    groups4556407284786078405_o_nat: ( fun_o_nat * set_o ) > nat ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_H_001_Eo_001t__Rat__Orat,type,
    groups3921277224699582669_o_rat: ( fun_o_rat * set_o ) > rat ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_H_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    groups910942671188738463nteger: fun_Co8499238673658658103nteger > fun_se3773019727686582893nteger ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_H_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
    groups288081504127972206er_int: ( fun_Code_integer_int * set_Code_integer ) > int ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_H_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
    groups290571974637022482er_nat: ( fun_Code_integer_nat * set_Code_integer ) > nat ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_H_001t__Code____Numeral__Ointeger_001t__Rat__Orat,type,
    groups8878813951405302554er_rat: ( fun_Code_integer_rat * set_Code_integer ) > rat ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_H_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
    groups926780983652909934nteger: ( fun_int_Code_integer * set_int ) > code_integer ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_H_001t__Int__Oint_001t__Int__Oint,type,
    groups2983280209131991357nt_int: fun_int_int > fun_set_int_int ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_H_001t__Int__Oint_001t__Nat__Onat,type,
    groups2985770679641041633nt_nat: ( fun_int_nat * set_int ) > nat ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_H_001t__Int__Oint_001t__Rat__Orat,type,
    groups2350640619554545897nt_rat: ( fun_int_rat * set_int ) > rat ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_H_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
    groups555127423416065298nteger: ( fun_nat_Code_integer * set_nat ) > code_integer ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_H_001t__Nat__Onat_001t__Int__Oint,type,
    groups1983926497230936801at_int: ( fun_nat_int * set_nat ) > int ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_H_001t__Nat__Onat_001t__Nat__Onat,type,
    groups1986416967739987077at_nat: fun_nat_nat > fun_set_nat_nat ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_H_001t__Nat__Onat_001t__Rat__Orat,type,
    groups1351286907653491341at_rat: ( fun_nat_rat * set_nat ) > rat ).

tff(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_H_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Rat__Orat,type,
    groups3328076802468863542at_rat: ( fun_Pr8317260874932935276at_rat * set_Pr1261947904930325089at_nat ) > rat ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001_Eo_001t__Assertions__Oassn,type,
    groups5301882518646026715o_assn: fun_fu5561970054461773155o_assn ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001_Eo_001t__Code____Numeral__Ointeger,type,
    groups7694694392188491536nteger: fun_fu6303754889700780451nteger ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001_Eo_001t__Int__Oint,type,
    groups3502327434004483295_o_int: ( fun_o_int * set_o ) > int ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001_Eo_001t__Nat__Onat,type,
    groups3504817904513533571_o_nat: fun_fu8843157277860572003_o_nat ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001_Eo_001t__Rat__Orat,type,
    groups2869687844427037835_o_rat: fun_fu4803769369665013091_o_rat ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Code____Numeral__Ointeger_001t__Assertions__Oassn,type,
    groups1304777262505850412r_assn: fun_fu727159081937814839r_assn ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    groups3674199335183972705nteger: fun_fu4961913266064405537nteger ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
    groups3188404863801439024er_int: ( fun_Code_integer_int * set_Code_integer ) > int ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
    groups3190895334310489300er_nat: ( fun_Code_integer_nat * set_Code_integer ) > nat ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Code____Numeral__Ointeger_001t__Rat__Orat,type,
    groups2555765274223993564er_rat: fun_fu8198789307943805079er_rat ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Int__Oint_001t__Assertions__Oassn,type,
    groups7882442080178216443t_assn: fun_fu6757290529232567765t_assn ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
    groups3827104343326376752nteger: fun_fu7510501037550790335nteger ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Int__Oint_001t__Int__Oint,type,
    groups1705073143266064639nt_int: fun_int_int > fun_set_int_int ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Int__Oint_001t__Nat__Onat,type,
    groups1707563613775114915nt_nat: ( fun_int_nat * set_int ) > nat ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Int__Oint_001t__Rat__Orat,type,
    groups1072433553688619179nt_rat: fun_fu3579422585476231989nt_rat ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Nat__Onat_001t__Assertions__Oassn,type,
    groups6906906614972039071t_assn: ( fun_nat_assn * set_nat ) > assn ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
    groups3455450783089532116nteger: ( fun_nat_Code_integer * set_nat ) > code_integer ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
    groups2279045934846249631atural: ( fun_nat_Code_natural * set_nat ) > code_natural ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Nat__Onat_001t__Int__Oint,type,
    groups705719431365010083at_int: ( fun_nat_int * set_nat ) > int ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Nat__Onat_001t__Nat__Onat,type,
    groups708209901874060359at_nat: fun_nat_nat > fun_set_nat_nat ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Nat__Onat_001t__Rat__Orat,type,
    groups73079841787564623at_rat: ( fun_nat_rat * set_nat ) > rat ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Num__Onum_001t__Code____Numeral__Ointeger,type,
    groups1396258611060191006nteger: ( fun_num_Code_integer * set_num ) > code_integer ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
    groups4075276357253098568at_int: ( fun_Pr7647638413817135296at_int * set_Pr1261947904930325089at_nat ) > int ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
    groups4077766827762148844at_nat: fun_Pr2602117396471556196at_nat > fun_se4097146774670233028at_nat ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Product____Type__Ounit_001t__Assertions__Oassn,type,
    groups5360233303959380816t_assn: ( fun_Pr6626665806141890376t_assn * set_Product_unit ) > assn ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Product____Type__Ounit_001t__Code____Numeral__Ointeger,type,
    groups8185359811944078981nteger: ( fun_Pr1820225556744648189nteger * set_Product_unit ) > code_integer ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Product____Type__Ounit_001t__Rat__Orat,type,
    groups8984663225794451456it_rat: ( fun_Product_unit_rat * set_Product_unit ) > rat ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Set__Oset_I_Eo_J_001t__Assertions__Oassn,type,
    groups6963733262650904763o_assn: fun_fu3743863873453506915o_assn ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Set__Oset_I_Eo_J_001t__Code____Numeral__Ointeger,type,
    groups8987389756002350576nteger: fun_fu1045876692016343459nteger ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Set__Oset_I_Eo_J_001t__Nat__Onat,type,
    groups4868773677410035043_o_nat: fun_fu1060865441899640675_o_nat ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Set__Oset_I_Eo_J_001t__Rat__Orat,type,
    groups4233643617323539307_o_rat: fun_fu6849062756650152291_o_rat ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Set__Oset_It__Code____Numeral__Ointeger_J_001t__Assertions__Oassn,type,
    groups4245288774754739042r_assn: fun_fu4821026654811345315r_assn ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Set__Oset_It__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger,type,
    groups1474571732273379991nteger: fun_fu2392828822626117773nteger ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Set__Oset_It__Code____Numeral__Ointeger_J_001t__Rat__Orat,type,
    groups5409254039008640018er_rat: fun_fu6017686703198564611er_rat ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Set__Oset_It__Int__Oint_J_001t__Assertions__Oassn,type,
    groups5950967880310095793t_assn: fun_fu7925354201654153025t_assn ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Set__Oset_It__Int__Oint_J_001t__Code____Numeral__Ointeger,type,
    groups8770619586034088166nteger: fun_fu2310701194077331499nteger ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_001t__Set__Oset_It__Int__Oint_J_001t__Rat__Orat,type,
    groups5800339274786551393nt_rat: fun_fu8704076394632857761nt_rat ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_H_001_Eo_001t__Assertions__Oassn,type,
    groups12625163056032370o_assn: ( fun_o_assn * set_o ) > assn ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_H_001_Eo_001t__Code____Numeral__Ointeger,type,
    groups2836416601086271911nteger: ( fun_o_Code_integer * set_o ) > code_integer ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_H_001_Eo_001t__Int__Oint,type,
    groups5320751605702587254_o_int: ( fun_o_int * set_o ) > int ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_H_001_Eo_001t__Nat__Onat,type,
    groups5323242076211637530_o_nat: ( fun_o_nat * set_o ) > nat ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_H_001_Eo_001t__Rat__Orat,type,
    groups4688112016125141794_o_rat: ( fun_o_rat * set_o ) > rat ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_H_001t__Code____Numeral__Ointeger_001t__Assertions__Oassn,type,
    groups980104329299799381r_assn: ( fun_Co4490034186337852034r_assn * set_Code_integer ) > assn ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_H_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    groups7219916603568234122nteger: fun_Co8499238673658658103nteger > fun_se3773019727686582893nteger ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_H_001t__Int__Oint_001t__Assertions__Oassn,type,
    groups4891613008741529892t_assn: ( fun_int_assn * set_int ) > assn ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_H_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
    groups8661743855124024409nteger: ( fun_int_Code_integer * set_int ) > code_integer ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_H_001t__Int__Oint_001t__Int__Oint,type,
    groups5744458235038148136nt_int: fun_int_int > fun_set_int_int ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_H_001t__Int__Oint_001t__Nat__Onat,type,
    groups5746948705547198412nt_nat: ( fun_int_nat * set_int ) > nat ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_H_001t__Int__Oint_001t__Rat__Orat,type,
    groups5111818645460702676nt_rat: ( fun_int_rat * set_int ) > rat ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_H_001t__Nat__Onat_001t__Assertions__Oassn,type,
    groups3916077543535352520t_assn: ( fun_nat_assn * set_nat ) > assn ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_H_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
    groups8290090294887179773nteger: ( fun_nat_Code_integer * set_nat ) > code_integer ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_H_001t__Nat__Onat_001t__Int__Oint,type,
    groups4745104523137093580at_int: ( fun_nat_int * set_nat ) > int ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_H_001t__Nat__Onat_001t__Nat__Onat,type,
    groups4747594993646143856at_nat: fun_nat_nat > fun_set_nat_nat ).

tff(sy_c_Groups__Big_Ocomm__monoid__mult__class_Oprod_H_001t__Nat__Onat_001t__Rat__Orat,type,
    groups4112464933559648120at_rat: ( fun_nat_rat * set_nat ) > rat ).

tff(sy_c_Groups__List_Omonoid__add__class_Osum__list_001t__Nat__Onat,type,
    groups4561878855575611511st_nat: fun_list_nat_nat ).

tff(sy_c_HOL_ONO__MATCH_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    nO_MAT8252062027627875367nteger: fun_Co2081214437782444048eger_o ).

tff(sy_c_HOL_ONO__MATCH_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
    nO_MAT8427913294028938742er_int: fun_Co8353275306710069249_int_o ).

tff(sy_c_HOL_ONO__MATCH_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
    nO_MAT8430403764537989018er_nat: fun_Co1375048237525739357_nat_o ).

tff(sy_c_HOL_ONO__MATCH_001t__Code____Numeral__Ointeger_001t__Rat__Orat,type,
    nO_MAT7795273704451493282er_rat: fun_Co625613742390903637_rat_o ).

tff(sy_c_HOL_ONO__MATCH_001t__Int__Oint_001t__Int__Oint,type,
    nO_MATCH_int_int: fun_int_fun_int_o ).

tff(sy_c_HOL_ONO__MATCH_001t__Int__Oint_001t__Nat__Onat,type,
    nO_MATCH_int_nat: fun_int_fun_nat_o ).

tff(sy_c_HOL_ONO__MATCH_001t__Int__Oint_001t__Rat__Orat,type,
    nO_MATCH_int_rat: fun_int_fun_rat_o ).

tff(sy_c_HOL_ONO__MATCH_001t__Nat__Onat_001t__Int__Oint,type,
    nO_MATCH_nat_int: fun_nat_fun_int_o ).

tff(sy_c_HOL_ONO__MATCH_001t__Nat__Onat_001t__Nat__Onat,type,
    nO_MATCH_nat_nat: fun_nat_fun_nat_o ).

tff(sy_c_HOL_ONO__MATCH_001t__Nat__Onat_001t__Rat__Orat,type,
    nO_MATCH_nat_rat: fun_nat_fun_rat_o ).

tff(sy_c_HOL_ONO__MATCH_001t__Rat__Orat_001t__Rat__Orat,type,
    nO_MATCH_rat_rat: fun_rat_fun_rat_o ).

tff(sy_c_HOL_OThe_001t__Int__Oint,type,
    the_int: fun_int_o > int ).

tff(sy_c_HOL_Odefault__class_Odefault_001t__Product____Type__Ounit,type,
    defaul566961228789861419t_unit: product_unit ).

tff(sy_c_HOL_Oundefined_001t__Heap__Oarray_Itf__a_J,type,
    undefined_array_a: array_a ).

tff(sy_c_HOL_Oundefined_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
    undefi8805113437130903861t_unit: heap_e7401611519738050253t_unit ).

tff(sy_c_HOL_Oundefined_001t__Num__Onum,type,
    undefined_num: num ).

tff(sy_c_HOL_Oundefined_001t__Product____Type__Ounit,type,
    undefi2974082611360736373t_unit: product_unit ).

tff(sy_c_Heap_Oheap_Oarrays_001t__Product____Type__Ounit,type,
    arrays_Product_unit: ( heap_e7401611519738050253t_unit * typerep * nat ) > list_nat ).

tff(sy_c_Heap_Oheap_Olim_001t__Product____Type__Ounit,type,
    lim_Product_unit: heap_e7401611519738050253t_unit > nat ).

tff(sy_c_Heap_Oheap_Orefs_001t__Product____Type__Ounit,type,
    refs_Product_unit: ( heap_e7401611519738050253t_unit * typerep ) > fun_nat_nat ).

tff(sy_c_Heap__Time__Monad_OHeap_OHeap_001t__Heap__Oarray_Itf__a_J,type,
    heap_T1488828001306802186rray_a: fun_he1504492240061592256it_nat > heap_T6362127782908069795rray_a ).

tff(sy_c_Heap__Time__Monad_OHeap_OHeap_001t__Product____Type__Ounit,type,
    heap_T6183433275982383450t_unit: fun_he5234484606919320760it_nat > heap_T5738788834812785303t_unit ).

tff(sy_c_Heap__Time__Monad_OHeap_Osize__Heap_001t__Product____Type__Ounit,type,
    heap_T4142866422068808505t_unit: ( fun_Product_unit_nat * heap_T5738788834812785303t_unit ) > nat ).

tff(sy_c_Heap__Time__Monad_OHeap__ord_001t__Heap__Oarray_Itf__a_J,type,
    heap_T3039585018531920163rray_a: ( heap_T6362127782908069795rray_a * heap_T6362127782908069795rray_a ) > $o ).

tff(sy_c_Heap__Time__Monad_OHeap__ord_001t__Product____Type__Ounit,type,
    heap_T499439718319394433t_unit: ( heap_T5738788834812785303t_unit * heap_T5738788834812785303t_unit ) > $o ).

tff(sy_c_Heap__Time__Monad_Oassert_001t__Heap__Oarray_Itf__a_J,type,
    heap_T7971689983404357896rray_a: fun_array_a_o > fun_ar3891948820113774757rray_a ).

tff(sy_c_Heap__Time__Monad_Oassert_001t__Product____Type__Ounit,type,
    heap_T4208721593536448476t_unit: fun_Product_unit_o > fun_Pr292408699144966967t_unit ).

tff(sy_c_Heap__Time__Monad_Obind_001t__Heap__Oarray_Itf__a_J_001t__Heap__Oarray_Itf__a_J,type,
    heap_T2407400398799471159rray_a: ( heap_T6362127782908069795rray_a * fun_ar3891948820113774757rray_a ) > heap_T6362127782908069795rray_a ).

tff(sy_c_Heap__Time__Monad_Obind_001t__Heap__Oarray_Itf__a_J_001t__Product____Type__Ounit,type,
    heap_T7324619625323989613t_unit: ( heap_T6362127782908069795rray_a * fun_ar1074044450438384043t_unit ) > heap_T5738788834812785303t_unit ).

tff(sy_c_Heap__Time__Monad_Obind_001t__Product____Type__Ounit_001t__Heap__Oarray_Itf__a_J,type,
    heap_T7158140910958840029rray_a: ( heap_T5738788834812785303t_unit * fun_Pr5924905948197006361rray_a ) > heap_T6362127782908069795rray_a ).

tff(sy_c_Heap__Time__Monad_Obind_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
    heap_T2633723481742716231t_unit: ( heap_T5738788834812785303t_unit * fun_Pr292408699144966967t_unit ) > heap_T5738788834812785303t_unit ).

tff(sy_c_Heap__Time__Monad_Oeffect_001t__Heap__Oarray_Itf__a_J,type,
    heap_T5830633491639066771rray_a: ( heap_T6362127782908069795rray_a * heap_e7401611519738050253t_unit * heap_e7401611519738050253t_unit * array_a ) > fun_nat_o ).

tff(sy_c_Heap__Time__Monad_Oeffect_001t__Product____Type__Ounit,type,
    heap_T6553295506729943825t_unit: ( heap_T5738788834812785303t_unit * heap_e7401611519738050253t_unit * heap_e7401611519738050253t_unit * product_unit ) > fun_nat_o ).

tff(sy_c_Heap__Time__Monad_Oexecute_001t__Heap__Oarray_Itf__a_J,type,
    heap_T5591663578999710211rray_a: heap_T6362127782908069795rray_a > fun_he1504492240061592256it_nat ).

tff(sy_c_Heap__Time__Monad_Oexecute_001t__Product____Type__Ounit,type,
    heap_T875086893843062177t_unit: heap_T5738788834812785303t_unit > fun_he5234484606919320760it_nat ).

tff(sy_c_Heap__Time__Monad_Oguard_001t__Heap__Oarray_Itf__a_J,type,
    heap_T7685628758766326643rray_a: ( fun_he8413527710729349838unit_o * fun_he281446669002384250it_nat ) > heap_T6362127782908069795rray_a ).

tff(sy_c_Heap__Time__Monad_Oguard_001t__Product____Type__Ounit,type,
    heap_T8440541562793052209t_unit: ( fun_he8413527710729349838unit_o * fun_he4944555133437423336it_nat ) > heap_T5738788834812785303t_unit ).

tff(sy_c_Heap__Time__Monad_Oheap_001t__Heap__Oarray_Itf__a_J,type,
    heap_T7473999186002612558rray_a: fun_he281446669002384250it_nat > heap_T6362127782908069795rray_a ).

tff(sy_c_Heap__Time__Monad_Oheap_001t__Product____Type__Ounit,type,
    heap_T6927113302350381334t_unit: fun_he4944555133437423336it_nat > heap_T5738788834812785303t_unit ).

tff(sy_c_Heap__Time__Monad_Oraise_001t__Heap__Oarray_Itf__a_J,type,
    heap_T1552190017797416154rray_a: list_char > heap_T6362127782908069795rray_a ).

tff(sy_c_Heap__Time__Monad_Oraise_001t__Product____Type__Ounit,type,
    heap_T2927564422264180874t_unit: list_char > heap_T5738788834812785303t_unit ).

tff(sy_c_Heap__Time__Monad_Oreturn_001t__Heap__Oarray_Itf__a_J,type,
    heap_T4896204969850773234rray_a: fun_ar3891948820113774757rray_a ).

tff(sy_c_Heap__Time__Monad_Oreturn_001t__Product____Type__Ounit,type,
    heap_T7507251653302230130t_unit: fun_Pr292408699144966967t_unit ).

tff(sy_c_Heap__Time__Monad_Osuccess_001t__Heap__Oarray_Itf__a_J,type,
    heap_T6932021131025641745rray_a: heap_T6362127782908069795rray_a > fun_he8413527710729349838unit_o ).

tff(sy_c_Heap__Time__Monad_Osuccess_001t__Product____Type__Ounit,type,
    heap_T584514906347983379t_unit: heap_T5738788834812785303t_unit > fun_he8413527710729349838unit_o ).

tff(sy_c_Heap__Time__Monad_Otap_001t__Heap__Oarray_Itf__a_J,type,
    heap_T2055650868554030641rray_a: fun_he7369252872201260279rray_a > heap_T6362127782908069795rray_a ).

tff(sy_c_Heap__Time__Monad_Otap_001t__Product____Type__Ounit,type,
    heap_T560649228465745139t_unit: fun_he5123621388056232515t_unit > heap_T5738788834812785303t_unit ).

tff(sy_c_Heap__Time__Monad_OtimeFrame_001t__Heap__Oarray_Itf__a_J,type,
    heap_T531568236820715630rray_a: ( nat * option3216581401566546698it_nat ) > option3216581401566546698it_nat ).

tff(sy_c_Heap__Time__Monad_OtimeFrame_001t__Product____Type__Ounit,type,
    heap_T3616969660504097270t_unit: ( nat * option8956607266484857688it_nat ) > option8956607266484857688it_nat ).

tff(sy_c_Heap__Time__Monad_OtimeFrame__rel_001t__Heap__Oarray_Itf__a_J,type,
    heap_T6578553156929092987rray_a: fun_Pr5911813565203289452_nat_o ).

tff(sy_c_Heap__Time__Monad_OtimeFrame__rel_001t__Product____Type__Ounit,type,
    heap_T996182799752388649t_unit: fun_Pr6341106346053136302_nat_o ).

tff(sy_c_Heap__Time__Monad_Oureturn_001t__Heap__Oarray_Itf__a_J,type,
    heap_T4328122439115681491rray_a: fun_ar3891948820113774757rray_a ).

tff(sy_c_Heap__Time__Monad_Oureturn_001t__Product____Type__Ounit,type,
    heap_T4284346855313245393t_unit: fun_Pr292408699144966967t_unit ).

tff(sy_c_Heap__Time__Monad_Owait,type,
    heap_Time_wait: nat > heap_T5738788834812785303t_unit ).

tff(sy_c_Int_OAbs__Integ,type,
    abs_Integ: fun_Pr7647638413817135296at_int ).

tff(sy_c_Int_ONeg,type,
    neg: fun_num_int ).

tff(sy_c_Int_OPos,type,
    pos: fun_num_int ).

tff(sy_c_Int_ORep__Integ,type,
    rep_Integ: fun_in4514472496968388910at_nat ).

tff(sy_c_Int_Odup,type,
    dup: fun_int_int ).

tff(sy_c_Int_Ointrel,type,
    intrel: fun_Pr2028404973800837934_nat_o ).

tff(sy_c_Int_Onat,type,
    nat2: fun_int_nat ).

tff(sy_c_Int_Opcr__int,type,
    pcr_int: fun_Pr4738963024209204295_int_o ).

tff(sy_c_Int_Oring__1__class_OInts_001t__Code____Numeral__Ointeger,type,
    ring_11222124179247155820nteger: set_Code_integer ).

tff(sy_c_Int_Oring__1__class_OInts_001t__Int__Oint,type,
    ring_1_Ints_int: set_int ).

tff(sy_c_Int_Oring__1__class_OInts_001t__Rat__Orat,type,
    ring_1_Ints_rat: set_rat ).

tff(sy_c_Int_Oring__1__class_Oof__int_001t__Code____Numeral__Ointeger,type,
    ring_18347121197199848620nteger: fun_int_Code_integer ).

tff(sy_c_Int_Oring__1__class_Oof__int_001t__Int__Oint,type,
    ring_1_of_int_int: fun_int_int ).

tff(sy_c_Int_Oring__1__class_Oof__int_001t__Rat__Orat,type,
    ring_1_of_int_rat: fun_int_rat ).

tff(sy_c_Int_Osub,type,
    sub: num > fun_num_int ).

tff(sy_c_Lattices_Oinf__class_Oinf_001t__Assertions__Oassn,type,
    inf_inf_assn: ( assn * assn ) > assn ).

tff(sy_c_Lattices_Oinf__class_Oinf_001t__Product____Type__Ounit,type,
    inf_inf_Product_unit: product_unit > fun_Pr2191293291710260995t_unit ).

tff(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Nat__Onat_J,type,
    inf_inf_set_nat: ( set_nat * set_nat ) > set_nat ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Assertions__Oassn,type,
    sup_sup_assn: ( assn * assn ) > assn ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Option__Ooption_It__Assertions__Oassn_J,type,
    sup_sup_option_assn: ( option_assn * option_assn ) > option_assn ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Option__Ooption_It__Product____Type__Ounit_J,type,
    sup_su7717485023253700007t_unit: ( option_Product_unit * option_Product_unit ) > option_Product_unit ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
    sup_su3598758113090618626et_nat: ( option_set_nat * option_set_nat ) > option_set_nat ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    sup_su2273273666271716065at_nat: ( option1583680563626158861at_nat * option1583680563626158861at_nat ) > option1583680563626158861at_nat ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Product____Type__Ounit,type,
    sup_sup_Product_unit: product_unit > fun_Pr2191293291710260995t_unit ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_I_Eo_J,type,
    sup_sup_set_o: ( set_o * set_o ) > set_o ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
    sup_su848401254843788991nteger: ( set_Code_integer * set_Code_integer ) > set_Code_integer ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Int__Oint_J,type,
    sup_sup_set_int: ( set_int * set_int ) > set_int ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
    sup_sup_set_list_nat: ( set_list_nat * set_list_nat ) > set_list_nat ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
    sup_sup_set_nat: ( set_nat * set_nat ) > set_nat ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Num__Onum_J,type,
    sup_sup_set_num: ( set_num * set_num ) > set_num ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    sup_su5769328420594410459od_o_o: ( set_Product_prod_o_o * set_Product_prod_o_o ) > set_Product_prod_o_o ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_J,type,
    sup_su6189057272928884437_o_int: ( set_Pr8834758594704517033_o_int * set_Pr8834758594704517033_o_int ) > set_Pr8834758594704517033_o_int ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
    sup_su8679140417860611193_o_nat: ( set_Pr2101469702781467981_o_nat * set_Pr2101469702781467981_o_nat ) > set_Pr2101469702781467981_o_nat ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_M_Eo_J_J,type,
    sup_su7481598572368468931_int_o: ( set_Pr903927857289325719_int_o * set_Pr903927857289325719_int_o ) > set_Pr903927857289325719_int_o ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    sup_su6024340866399070445nt_int: ( set_Pr958786334691620121nt_int * set_Pr958786334691620121nt_int ) > set_Pr958786334691620121nt_int ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J_J,type,
    sup_su8514424011330797201nt_nat: ( set_Pr3448869479623346877nt_nat * set_Pr3448869479623346877nt_nat ) > set_Pr3448869479623346877nt_nat ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J,type,
    sup_su503371503184139039_nat_o: ( set_Pr3149072824959771635_nat_o * set_Pr3149072824959771635_nat_o ) > set_Pr3149072824959771635_nat_o ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_J,type,
    sup_su3837419291706048657at_int: ( set_Pr7995236796853374141at_int * set_Pr7995236796853374141at_int ) > set_Pr7995236796853374141at_int ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    sup_su6327502436637775413at_nat: set_Pr1261947904930325089at_nat > fun_se320340636488258563at_nat ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J,type,
    sup_su5921324857680904370_nat_o: ( set_Pr6558897299634722526_nat_o * set_Pr6558897299634722526_nat_o ) > set_Pr6558897299634722526_nat_o ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    sup_su5525570899277871387at_nat: ( set_Pr4329608150637261639at_nat * set_Pr4329608150637261639at_nat ) > set_Pr4329608150637261639at_nat ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    sup_su7513280395484302481nt_int: ( set_Pr4166680992137330533nt_int * set_Pr4166680992137330533nt_int ) > set_Pr4166680992137330533nt_int ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    sup_su4503389074446631032nteger: ( set_Pr3486312109254157132nteger * set_Pr3486312109254157132nteger ) > set_Pr3486312109254157132nteger ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    sup_su2387659076810923138et_nat: ( set_Pr1312406793078187350et_nat * set_Pr1312406793078187350et_nat ) > set_Pr1312406793078187350et_nat ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    sup_su5858552540197408416et_nat: ( set_Pr4040394263813967220et_nat * set_Pr4040394263813967220et_nat ) > set_Pr4040394263813967220et_nat ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    sup_su2017857570560100197nt_int: ( set_Pr6700895561065273913nt_int * set_Pr6700895561065273913nt_int ) > set_Pr6700895561065273913nt_int ).

tff(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 ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Rat__Orat_J,type,
    sup_sup_set_rat: ( set_rat * set_rat ) > set_rat ).

tff(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    sup_su3642409539654194069at_nat: ( set_se7855581050983116737at_nat * set_se7855581050983116737at_nat ) > set_se7855581050983116737at_nat ).

tff(sy_c_Lattices_Osup__class_Osup_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    sup_su8083968640029086462_nat_o: ( fun_nat_fun_nat_o * fun_nat_fun_nat_o ) > fun_nat_fun_nat_o ).

tff(sy_c_Lattices_Osup__class_Osup_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J,type,
    sup_su5424986631308460290_nat_o: ( fun_se5639961202347202350_nat_o * fun_se5639961202347202350_nat_o ) > fun_se5639961202347202350_nat_o ).

tff(sy_c_Lattices_Osup__class_Osup_001t__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    sup_su7230269426179251658_int_o: ( fun_fu2978539155105838238_int_o * fun_fu2978539155105838238_int_o ) > fun_fu2978539155105838238_int_o ).

tff(sy_c_Lattices_Osup__class_Osup_001t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
    sup_su8446958762992054435eger_o: ( fun_fu7695273699059480439eger_o * fun_fu7695273699059480439eger_o ) > fun_fu7695273699059480439eger_o ).

tff(sy_c_Lattices_Osup__class_Osup_001t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
    sup_su4970993554803434671_nat_o: ( fun_fu8419763957888848259_nat_o * fun_fu8419763957888848259_nat_o ) > fun_fu8419763957888848259_nat_o ).

tff(sy_c_Lattices_Osup__class_Osup_001t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_J,type,
    sup_su6780828561269846801_nat_o: ( fun_fu2611741329380808165_nat_o * fun_fu2611741329380808165_nat_o ) > fun_fu2611741329380808165_nat_o ).

tff(sy_c_Lattices_Osup__class_Osup_001t__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    sup_su2175524065394371574_int_o: ( fun_fu6865642474282033866_int_o * fun_fu6865642474282033866_int_o ) > fun_fu6865642474282033866_int_o ).

tff(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
    lattic8265883725875713057ax_nat: fun_set_nat_nat ).

tff(sy_c_Lattices__Big_Osemilattice__neutr__set_OF_001t__Nat__Onat,type,
    lattic7826324295020591184_F_nat: ( fun_nat_fun_nat_nat * nat ) > fun_set_nat_nat ).

tff(sy_c_Lifting_OQuotient_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
    quotie2291698863146621601nteger: ( fun_int_fun_int_o * fun_int_Code_integer * fun_Code_integer_int * fun_in4891666191172872833eger_o ) > $o ).

tff(sy_c_Lifting_OQuotient_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
    quotie743640454666494480atural: ( fun_nat_fun_nat_o * fun_nat_Code_natural * fun_Code_natural_nat * fun_na2240068485812228818ural_o ) > $o ).

tff(sy_c_List_Oappend_001t__Int__Oint,type,
    append_int: ( list_int * list_int ) > list_int ).

tff(sy_c_List_Oappend_001t__Nat__Onat,type,
    append_nat: ( list_nat * list_nat ) > list_nat ).

tff(sy_c_List_Obutlast_001t__Nat__Onat,type,
    butlast_nat: list_nat > list_nat ).

tff(sy_c_List_Odrop_001t__Nat__Onat,type,
    drop_nat: ( nat * list_nat ) > list_nat ).

tff(sy_c_List_Ofilter_001t__Nat__Onat,type,
    filter_nat: ( fun_nat_o * list_nat ) > list_nat ).

tff(sy_c_List_Ofold_001t__Nat__Onat_001t__Nat__Onat,type,
    fold_nat_nat: ( fun_nat_fun_nat_nat * list_nat ) > fun_nat_nat ).

tff(sy_c_List_Olast_001t__Nat__Onat,type,
    last_nat: fun_list_nat_nat ).

tff(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
    linord2614967742042102400et_nat: set_nat > list_nat ).

tff(sy_c_List_Olist_OCons_001t__Int__Oint,type,
    cons_int: ( int * list_int ) > list_int ).

tff(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
    cons_nat: ( nat * list_nat ) > list_nat ).

tff(sy_c_List_Olist_ONil_001t__Int__Oint,type,
    nil_int: list_int ).

tff(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
    nil_nat: list_nat ).

tff(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
    map_nat_nat: ( fun_nat_nat * list_nat ) > list_nat ).

tff(sy_c_List_Olist_Oset_001t__Int__Oint,type,
    set_int2: list_int > set_int ).

tff(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
    set_nat2: list_nat > set_nat ).

tff(sy_c_List_Onth_001t__Int__Oint,type,
    nth_int: list_int > fun_nat_int ).

tff(sy_c_List_Onth_001t__Nat__Onat,type,
    nth_nat: list_nat > fun_nat_nat ).

tff(sy_c_List_Otake_001t__Nat__Onat,type,
    take_nat: ( nat * list_nat ) > list_nat ).

tff(sy_c_List_Oupt,type,
    upt: ( nat * nat ) > list_nat ).

tff(sy_c_List_Oupto,type,
    upto: ( int * int ) > list_int ).

tff(sy_c_List_Oupto__rel,type,
    upto_rel: fun_Pr9018117161326028078_int_o ).

tff(sy_c_Misc_OEps__Opt_001t__Nat__Onat,type,
    eps_Opt_nat: fun_nat_o > option_nat ).

tff(sy_c_Misc_OEps__Opt_001t__Num__Onum,type,
    eps_Opt_num: fun_num_o > option_num ).

tff(sy_c_Misc_OEps__Opt_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    eps_Op9034888937550303799nteger: fun_Pr7211993375558241536eger_o > option2651255830984564193nteger ).

tff(sy_c_Misc_OEps__Opt_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    eps_Op1141264490366522080it_nat: fun_Pr7068637894315934487_nat_o > option3216581401566546698it_nat ).

tff(sy_c_Misc_OEps__Opt_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    eps_Op2013419657081471078et_nat: fun_fu2352890940381120596et_nat ).

tff(sy_c_Misc_OEps__Opt_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    eps_Op2446201859369042517nt_int: fun_Pr3238374608701176162_int_o > option4624381673175914239nt_int ).

tff(sy_c_Misc_OEps__Opt_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    eps_Op3393321821070424684it_nat: fun_Pr8032424337255632745_nat_o > option8956607266484857688it_nat ).

tff(sy_c_Misc_OEps__Opt_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    eps_Op5936278548196508548et_nat: fun_Pr2620521676128474833_nat_o > option4955102875562834416et_nat ).

tff(sy_c_Misc_OEps__Opt_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    eps_Op994234036888646909at_nat: fun_se4782206882984618170_nat_o > option8963830502488799655at_nat ).

tff(sy_c_Misc_Obijective_001t__Nat__Onat_001t__Nat__Onat,type,
    bijective_nat_nat: set_Pr1261947904930325089at_nat > $o ).

tff(sy_c_Misc_Obijective_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    biject3388518990857851981at_nat: set_Pr4329608150637261639at_nat > $o ).

tff(sy_c_Misc_Obijective_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    biject9165800892491502059nt_int: set_Pr4166680992137330533nt_int > $o ).

tff(sy_c_Misc_Obijective_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    biject6040901034283248210nteger: set_Pr3486312109254157132nteger > $o ).

tff(sy_c_Misc_Obijective_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    biject6574446902887564708et_nat: set_Pr1312406793078187350et_nat > $o ).

tff(sy_c_Misc_Obijective_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    biject4066639966817638850et_nat: set_Pr4040394263813967220et_nat > $o ).

tff(sy_c_Misc_Obijective_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    biject1579208791189821119nt_int: set_Pr6700895561065273913nt_int > $o ).

tff(sy_c_Misc_Odflt__None__set_001_Eo,type,
    dflt_None_set_o: set_o > option_set_o ).

tff(sy_c_Misc_Odflt__None__set_001t__Int__Oint,type,
    dflt_None_set_int: set_int > option_set_int ).

tff(sy_c_Misc_Odflt__None__set_001t__Nat__Onat,type,
    dflt_None_set_nat: set_nat > option_set_nat ).

tff(sy_c_Misc_Odflt__None__set_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    dflt_N6592383573632408824at_nat: set_Pr1261947904930325089at_nat > option8963830502488799655at_nat ).

tff(sy_c_Misc_Odflt__None__set_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    dflt_N3208751546879591902at_nat: set_Pr4329608150637261639at_nat > option1583680563626158861at_nat ).

tff(sy_c_Misc_Omap__mmupd_001_Eo_001t__Num__Onum,type,
    map_mmupd_o_num: ( fun_o_option_num * set_o * num ) > fun_o_option_num ).

tff(sy_c_Misc_Omap__mmupd_001_Eo_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    map_mm4340940675810032635it_nat: ( fun_o_7229649064035662211it_nat * set_o * produc8664842809031399944it_nat ) > fun_o_7229649064035662211it_nat ).

tff(sy_c_Misc_Omap__mmupd_001t__Int__Oint_001t__Num__Onum,type,
    map_mmupd_int_num: ( fun_int_option_num * set_int * num ) > fun_int_option_num ).

tff(sy_c_Misc_Omap__mmupd_001t__Int__Oint_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    map_mm5942422175790858651it_nat: ( fun_in8543325783774419841it_nat * set_int * produc8664842809031399944it_nat ) > fun_in8543325783774419841it_nat ).

tff(sy_c_Misc_Omap__mmupd_001t__Nat__Onat_001t__Num__Onum,type,
    map_mmupd_nat_num: ( fun_nat_option_num * set_nat * num ) > fun_nat_option_num ).

tff(sy_c_Misc_Omap__mmupd_001t__Nat__Onat_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    map_mm4316137065318800191it_nat: ( fun_na5667031169817407269it_nat * set_nat * produc8664842809031399944it_nat ) > fun_na5667031169817407269it_nat ).

tff(sy_c_Misc_Omap__mmupd_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Num__Onum,type,
    map_mm6272435474268545910at_num: ( fun_Pr7397166214287566974on_num * set_Pr1261947904930325089at_nat * num ) > fun_Pr7397166214287566974on_num ).

tff(sy_c_Misc_Omap__mmupd_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    map_mm8925508573636269924it_nat: ( fun_Pr6624299372562097772it_nat * set_Pr1261947904930325089at_nat * produc8664842809031399944it_nat ) > fun_Pr6624299372562097772it_nat ).

tff(sy_c_Misc_Omap__mmupd_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Num__Onum,type,
    map_mm2124855372588256220at_num: ( fun_Pr6553355248451873380on_num * set_Pr4329608150637261639at_nat * num ) > fun_Pr6553355248451873380on_num ).

tff(sy_c_Misc_Omap__mmupd_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    map_mm6227321356191524810it_nat: ( fun_Pr6865292569827446866it_nat * set_Pr4329608150637261639at_nat * produc8664842809031399944it_nat ) > fun_Pr6865292569827446866it_nat ).

tff(sy_c_Misc_Opairself_001t__Int__Oint_001t__Int__Oint,type,
    pairself_int_int: fun_int_int > fun_Pr2478283820680522243nt_int ).

tff(sy_c_Misc_Opairself_001t__Int__Oint_001t__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J,type,
    pairse3534876335208825186e_term: ( fun_in5730379987311621695e_term * product_prod_int_int ) > produc6576344331059438605e_term ).

tff(sy_c_Misc_Opairself_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
    pairse4825235148789309005nteger: fun_nat_Code_integer > fun_Pr5056853159479207325nteger ).

tff(sy_c_Misc_Opairself_001t__Nat__Onat_001t__Int__Oint,type,
    pairself_nat_int: fun_nat_int > fun_Pr1815330137571409595nt_int ).

tff(sy_c_Misc_Opairself_001t__Nat__Onat_001t__Nat__Onat,type,
    pairself_nat_nat: fun_nat_nat > fun_Pr2118491707810114563at_nat ).

tff(sy_c_Misc_Opairself_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
    pairself_nat_set_nat: fun_nat_set_nat > fun_Pr5733170697710890607et_nat ).

tff(sy_c_Misc_Opairself__rel_001t__Int__Oint_001t__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J,type,
    pairse6848479906795794847e_term: fun_Pr886604116968709228_int_o ).

tff(sy_c_Misc_Orel__of_001t__Nat__Onat_001t__Nat__Onat,type,
    rel_of_nat_nat: ( fun_nat_option_nat * fun_Pr4796943543331071514_nat_o ) > set_Pr1261947904930325089at_nat ).

tff(sy_c_Misc_Orel__of_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    rel_of6563097375766832824at_nat: ( fun_se5244420045238757833at_nat * fun_Pr3059359313727237556_nat_o ) > set_Pr4329608150637261639at_nat ).

tff(sy_c_Misc_Orel__of_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    rel_of6825086619541906112nt_int: ( fun_fu5631754973857388633nt_int * fun_Pr1196100989263358594_int_o ) > set_Pr4166680992137330533nt_int ).

tff(sy_c_Misc_Orel__of_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    rel_of3240586176920340263nteger: ( fun_fu4810197545401214784nteger * fun_Pr7015759342434529115eger_o ) > set_Pr3486312109254157132nteger ).

tff(sy_c_Misc_Orel__of_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    rel_of7233497478102412281et_nat: ( fun_fu2352890940381120596et_nat * fun_Pr2620521676128474833_nat_o ) > set_Pr1312406793078187350et_nat ).

tff(sy_c_Misc_Orel__of_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    rel_of4573248530116435351et_nat: ( fun_fu1905361174868762994et_nat * fun_Pr1227177680593602867_nat_o ) > set_Pr4040394263813967220et_nat ).

tff(sy_c_Misc_Orel__of_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    rel_of9206080981073604500nt_int: ( fun_fu4253467608928286509nt_int * fun_Pr3540825087398332590_int_o ) > set_Pr6700895561065273913nt_int ).

tff(sy_c_Misc_Oset__to__map_001_Eo_001t__Num__Onum,type,
    set_to_map_o_num: set_Pr7040061329075590551_o_num > fun_o_option_num ).

tff(sy_c_Misc_Oset__to__map_001_Eo_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    set_to3023635543527487849it_nat: set_Pr6777250647868329861it_nat > fun_o_7229649064035662211it_nat ).

tff(sy_c_Misc_Oset__to__map_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    set_to6264436334439079987nteger: set_Pr4811707699266497531nteger > fun_Co8029881127924365703nteger ).

tff(sy_c_Misc_Oset__to__map_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    set_to6039658477269176016atural: set_Pr2352657477744078772atural > fun_Co7921331830460615208atural ).

tff(sy_c_Misc_Oset__to__map_001t__Int__Oint_001t__Int__Oint,type,
    set_to_map_int_int: set_Pr958786334691620121nt_int > fun_int_option_int ).

tff(sy_c_Misc_Oset__to__map_001t__Int__Oint_001t__Num__Onum,type,
    set_to_map_int_num: set_Pr8387461105917469447nt_num > fun_int_option_num ).

tff(sy_c_Misc_Oset__to__map_001t__Nat__Onat_001t__Nat__Onat,type,
    set_to_map_nat_nat: set_Pr1261947904930325089at_nat > fun_nat_option_nat ).

tff(sy_c_Misc_Oset__to__map_001t__Nat__Onat_001t__Num__Onum,type,
    set_to_map_nat_num: set_Pr6200539531224447659at_num > fun_nat_option_num ).

tff(sy_c_Misc_Oset__to__map_001t__Nat__Onat_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    set_to785951348762482001it_nat: set_Pr633603713510679705it_nat > fun_na5667031169817407269it_nat ).

tff(sy_c_Misc_Oset__to__map_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Num__Onum,type,
    set_to5081529003106763492at_num: set_Pr7477759153910077568at_num > fun_Pr7397166214287566974on_num ).

tff(sy_c_Misc_Oset__to__map_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    set_to4447731662395764663at_nat: set_Pr4329608150637261639at_nat > fun_se5244420045238757833at_nat ).

tff(sy_c_Misc_Oset__to__map_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    set_to2016340311434469377nt_int: set_Pr4166680992137330533nt_int > fun_fu5631754973857388633nt_int ).

tff(sy_c_Misc_Oset__to__map_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    set_to765696221487571048nteger: set_Pr3486312109254157132nteger > fun_fu4810197545401214784nteger ).

tff(sy_c_Misc_Oset__to__map_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    set_to2037224588991580346et_nat: set_Pr1312406793078187350et_nat > fun_fu2352890940381120596et_nat ).

tff(sy_c_Misc_Oset__to__map_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    set_to3162555076294590936et_nat: set_Pr4040394263813967220et_nat > fun_fu1905361174868762994et_nat ).

tff(sy_c_Misc_Oset__to__map_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    set_to8251664086025573589nt_int: set_Pr6700895561065273913nt_int > fun_fu4253467608928286509nt_int ).

tff(sy_c_Misc_Othe__default_001t__Num__Onum,type,
    the_default_num: num > fun_option_num_num ).

tff(sy_c_Misc_Othe__default_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    the_de8559148246674365659it_nat: ( produc6714399278180371524it_nat * option3216581401566546698it_nat ) > produc6714399278180371524it_nat ).

tff(sy_c_Misc_Othe__default_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    the_de2487931475039285041it_nat: ( produc8664842809031399944it_nat * option8956607266484857688it_nat ) > produc8664842809031399944it_nat ).

tff(sy_c_Misc_Othe__default_001t__Set__Oset_I_Eo_J,type,
    the_default_set_o: ( set_o * option_set_o ) > set_o ).

tff(sy_c_Misc_Othe__default_001t__Set__Oset_It__Int__Oint_J,type,
    the_default_set_int: ( set_int * option_set_int ) > set_int ).

tff(sy_c_Misc_Othe__default_001t__Set__Oset_It__Nat__Onat_J,type,
    the_default_set_nat: ( set_nat * option_set_nat ) > set_nat ).

tff(sy_c_Misc_Othe__default_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    the_de3668382347305825784at_nat: ( set_Pr1261947904930325089at_nat * option8963830502488799655at_nat ) > set_Pr1261947904930325089at_nat ).

tff(sy_c_Misc_Othe__default_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    the_de6830073021511528542at_nat: ( set_Pr4329608150637261639at_nat * option1583680563626158861at_nat ) > set_Pr4329608150637261639at_nat ).

tff(sy_c_Misc_Ouncurry_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
    uncurry_int_int_int: fun_int_fun_int_int > fun_Pr982841511892225912nt_int ).

tff(sy_c_Misc_Ouncurry_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    uncurr7650761721940715016nt_int: fun_in1696471567231710611nt_int > fun_Pr2478283820680522243nt_int ).

tff(sy_c_Misc_Ouncurry_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
    uncurry_nat_nat_nat: fun_nat_fun_nat_nat > fun_Pr2602117396471556196at_nat ).

tff(sy_c_Misc_Ouncurry_001t__Nat__Onat_001t__Nat__Onat_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
    uncurr8479020417594943315_nat_o: fun_na5914473681949881652_nat_o > fun_Pr2028404973800837934_nat_o ).

tff(sy_c_Misc_Ouncurry_001t__Nat__Onat_001t__Nat__Onat_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    uncurr9212869592684144700at_nat: fun_na1668100129766719005at_nat > fun_Pr2477239776880934807at_nat ).

tff(sy_c_Multiset_Oadd__mset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    add_ms2612439473150266591at_nat: ( product_prod_nat_nat * multis2468970476368604999at_nat ) > multis2468970476368604999at_nat ).

tff(sy_c_Multiset_Oms__strict,type,
    ms_strict: set_Pr8551490117392284871at_nat ).

tff(sy_c_Multiset_Oms__weak,type,
    ms_weak: set_Pr8551490117392284871at_nat ).

tff(sy_c_Multiset_Opw__leq,type,
    pw_leq: ( multis2468970476368604999at_nat * multis2468970476368604999at_nat ) > $o ).

tff(sy_c_Multiset_Oset__mset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    set_ms8126754132646256062at_nat: multis2468970476368604999at_nat > set_Pr1261947904930325089at_nat ).

tff(sy_c_Nat_OSuc,type,
    suc: fun_nat_nat ).

tff(sy_c_Nat_Ocompow_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J,type,
    compow_fun_nat_nat: ( nat * fun_nat_nat ) > fun_nat_nat ).

tff(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
    case_nat_option_num: ( option_num * fun_nat_option_num ) > fun_nat_option_num ).

tff(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
    semiri4939895301339042750nteger: fun_nat_Code_integer ).

tff(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Onatural,type,
    semiri3763490453095760265atural: fun_nat_Code_natural ).

tff(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
    semiri1314217659103216013at_int: fun_nat_int ).

tff(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
    semiri1316708129612266289at_nat: fun_nat_nat ).

tff(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
    semiri681578069525770553at_rat: fun_nat_rat ).

tff(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Code____Numeral__Ointeger,type,
    semiri4055485073559036834nteger: ( fun_Co8499238673658658103nteger * nat ) > fun_Co8499238673658658103nteger ).

tff(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Code____Numeral__Onatural,type,
    semiri2879080225315754349atural: ( fun_Co7398788559141407565atural * nat ) > fun_Co7398788559141407565atural ).

tff(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Int__Oint,type,
    semiri8420488043553186161ux_int: ( fun_int_int * nat ) > fun_int_int ).

tff(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Nat__Onat,type,
    semiri8422978514062236437ux_nat: fun_nat_nat > fun_nat_fun_nat_nat ).

tff(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Rat__Orat,type,
    semiri7787848453975740701ux_rat: ( fun_rat_rat * nat ) > fun_rat_rat ).

tff(sy_c_Nat_Osize__class_Osize_001t__Heap____Time____Monad__OHeap_It__Product____Type__Ounit_J,type,
    size_s1564113455978345259t_unit: heap_T5738788834812785303t_unit > nat ).

tff(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
    size_size_list_int: list_int > nat ).

tff(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
    size_size_list_nat: fun_list_nat_nat ).

tff(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
    size_size_num: fun_num_nat ).

tff(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Num__Onum_J,type,
    size_size_option_num: option_num > nat ).

tff(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    size_s6797157356856800118it_nat: option3216581401566546698it_nat > nat ).

tff(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    size_s8766407808098229740it_nat: option8956607266484857688it_nat > nat ).

tff(sy_c_Nat__Bijection_Olist__decode,type,
    nat_list_decode: nat > list_nat ).

tff(sy_c_Nat__Bijection_Olist__decode__rel,type,
    nat_list_decode_rel: fun_nat_fun_nat_o ).

tff(sy_c_Nat__Bijection_Olist__encode,type,
    nat_list_encode: fun_list_nat_nat ).

tff(sy_c_Nat__Bijection_Olist__encode__rel,type,
    nat_list_encode_rel: fun_li1025265955262268170_nat_o ).

tff(sy_c_Nat__Bijection_Oprod__decode,type,
    nat_prod_decode: fun_na1476630412504255114at_nat ).

tff(sy_c_Nat__Bijection_Oprod__decode__aux,type,
    nat_prod_decode_aux: fun_na4138050610385705875at_nat ).

tff(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
    nat_pr5047031295181774490ux_rel: fun_Pr2028404973800837934_nat_o ).

tff(sy_c_Nat__Bijection_Oprod__encode,type,
    nat_prod_encode: fun_Pr2602117396471556196at_nat ).

tff(sy_c_Nat__Bijection_Oset__decode,type,
    nat_set_decode: fun_nat_set_nat ).

tff(sy_c_Nat__Bijection_Oset__encode,type,
    nat_set_encode: fun_set_nat_nat ).

tff(sy_c_Nat__Bijection_Osum__decode,type,
    nat_sum_decode: nat > sum_sum_nat_nat ).

tff(sy_c_Nat__Bijection_Otriangle,type,
    nat_triangle: fun_nat_nat ).

tff(sy_c_Num_OBitM,type,
    bitM: fun_num_num ).

tff(sy_c_Num_Oinc,type,
    inc: fun_num_num ).

tff(sy_c_Num_Onat__of__num,type,
    nat_of_num: fun_num_nat ).

tff(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
    neg_nu8804712462038260780nteger: fun_Co8499238673658658103nteger ).

tff(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
    neg_numeral_dbl_int: fun_int_int ).

tff(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
    neg_numeral_dbl_rat: fun_rat_rat ).

tff(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Code____Numeral__Ointeger,type,
    neg_nu7757733837767384882nteger: fun_Co8499238673658658103nteger ).

tff(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
    neg_nu3811975205180677377ec_int: fun_int_int ).

tff(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
    neg_nu3179335615603231917ec_rat: fun_rat_rat ).

tff(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Code____Numeral__Ointeger,type,
    neg_nu5831290666863070958nteger: fun_Co8499238673658658103nteger ).

tff(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
    neg_nu5851722552734809277nc_int: fun_int_int ).

tff(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
    neg_nu5219082963157363817nc_rat: fun_rat_rat ).

tff(sy_c_Num_Oneg__numeral__class_Ois__num_001t__Code____Numeral__Ointeger,type,
    neg_nu2435721316971906650nteger: fun_Code_integer_o ).

tff(sy_c_Num_Oneg__numeral__class_Ois__num_001t__Int__Oint,type,
    neg_nu7441568979088483369um_int: fun_int_o ).

tff(sy_c_Num_Oneg__numeral__class_Ois__num_001t__Rat__Orat,type,
    neg_nu6808929389511037909um_rat: fun_rat_o ).

tff(sy_c_Num_Oneg__numeral__class_Osub_001t__Code____Numeral__Ointeger,type,
    neg_nu5755505904847501662nteger: num > fun_num_Code_integer ).

tff(sy_c_Num_Oneg__numeral__class_Osub_001t__Int__Oint,type,
    neg_numeral_sub_int: num > fun_num_int ).

tff(sy_c_Num_Oneg__numeral__class_Osub_001t__Rat__Orat,type,
    neg_numeral_sub_rat: ( num * num ) > rat ).

tff(sy_c_Num_Onum_OBit0,type,
    bit0: fun_num_num ).

tff(sy_c_Num_Onum_OBit1,type,
    bit1: fun_num_num ).

tff(sy_c_Num_Onum_OOne,type,
    one: num ).

tff(sy_c_Num_Onum_Ocase__num_001t__Option__Ooption_It__Num__Onum_J,type,
    case_num_option_num: ( option_num * fun_num_option_num * fun_num_option_num ) > fun_num_option_num ).

tff(sy_c_Num_Onum_Osize__num,type,
    size_num: fun_num_nat ).

tff(sy_c_Num_Onum__of__nat,type,
    num_of_nat: fun_nat_num ).

tff(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Ointeger,type,
    numera6620942414471956472nteger: fun_num_Code_integer ).

tff(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Onatural,type,
    numera5444537566228673987atural: fun_num_Code_natural ).

tff(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint,type,
    numeral_numeral_int: fun_num_int ).

tff(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
    numeral_numeral_nat: fun_num_nat ).

tff(sy_c_Num_Onumeral__class_Onumeral_001t__Rat__Orat,type,
    numeral_numeral_rat: fun_num_rat ).

tff(sy_c_Num_Opred__numeral,type,
    pred_numeral: fun_num_nat ).

tff(sy_c_Num_Oring__1__class_Oiszero_001t__Code____Numeral__Ointeger,type,
    ring_16219924574208605041nteger: fun_Code_integer_o ).

tff(sy_c_Num_Oring__1__class_Oiszero_001t__Int__Oint,type,
    ring_1_iszero_int: fun_int_o ).

tff(sy_c_Num_Oring__1__class_Oiszero_001t__Rat__Orat,type,
    ring_1_iszero_rat: fun_rat_o ).

tff(sy_c_Num_Osqr,type,
    sqr: fun_num_num ).

tff(sy_c_Option_Obind_001t__Num__Onum_001t__Num__Onum,type,
    bind_num_num: ( option_num * fun_num_option_num ) > option_num ).

tff(sy_c_Option_Obind_001t__Num__Onum_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    bind_n6186876254402743274it_nat: ( option_num * fun_nu5903705430729240393it_nat ) > option3216581401566546698it_nat ).

tff(sy_c_Option_Obind_001t__Num__Onum_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    bind_n550516262659884002it_nat: ( option_num * fun_nu8356290101743979119it_nat ) > option8956607266484857688it_nat ).

tff(sy_c_Option_Obind_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Num__Onum,type,
    bind_P7816469540982926368at_num: ( option3216581401566546698it_nat * fun_Pr2994431579521131585on_num ) > option_num ).

tff(sy_c_Option_Obind_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    bind_P1787608729393679550it_nat: ( option3216581401566546698it_nat * fun_Pr8118912048244921225it_nat ) > option3216581401566546698it_nat ).

tff(sy_c_Option_Obind_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    bind_P3087804342168909838it_nat: ( option3216581401566546698it_nat * fun_Pr245379829043246639it_nat ) > option8956607266484857688it_nat ).

tff(sy_c_Option_Obind_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Num__Onum,type,
    bind_P4387644102537648098at_num: ( option8956607266484857688it_nat * fun_Pr1661544312997278575on_num ) > option_num ).

tff(sy_c_Option_Obind_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    bind_P1106314856888375420it_nat: ( option8956607266484857688it_nat * fun_Pr7518090501403545819it_nat ) > option3216581401566546698it_nat ).

tff(sy_c_Option_Obind_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    bind_P7351952464966851536it_nat: ( option8956607266484857688it_nat * fun_Pr7644814098969791837it_nat ) > option8956607266484857688it_nat ).

tff(sy_c_Option_Ocombine__options_001t__Num__Onum,type,
    combine_options_num: ( fun_num_fun_num_num * option_num ) > fun_op8989173174992673105on_num ).

tff(sy_c_Option_Ocombine__options_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    combin3867838909898076099it_nat: ( fun_Pr6442729728054246170it_nat * option3216581401566546698it_nat * option3216581401566546698it_nat ) > option3216581401566546698it_nat ).

tff(sy_c_Option_Ocombine__options_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    combin4318129983670048329it_nat: ( fun_Pr1003294667014919570it_nat * option8956607266484857688it_nat * option8956607266484857688it_nat ) > option8956607266484857688it_nat ).

tff(sy_c_Option_Ooption_ONone_001_Eo,type,
    none_o: option_o ).

tff(sy_c_Option_Ooption_ONone_001t__Int__Oint,type,
    none_int: option_int ).

tff(sy_c_Option_Ooption_ONone_001t__Nat__Onat,type,
    none_nat: option_nat ).

tff(sy_c_Option_Ooption_ONone_001t__Num__Onum,type,
    none_num: option_num ).

tff(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    none_P2587165478634041381it_nat: option3216581401566546698it_nat ).

tff(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    none_P5556105721700978146at_nat: option4927543243414619207at_nat ).

tff(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    none_P9117596204409417319it_nat: option8956607266484857688it_nat ).

tff(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    none_P5811896708078067656at_nat: option8699557107911914541at_nat ).

tff(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    none_P1716269551890668430nt_int: option6186025235080601855nt_int ).

tff(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    none_P612323165605163765nteger: option983905398058327270nteger ).

tff(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    none_P7891021755743879167et_nat: option4955102875562834416et_nat ).

tff(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    none_P2758821087663475997et_nat: option5899113203645146382et_nat ).

tff(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    none_P3112835510759997538nt_int: option1544258867535432659nt_int ).

tff(sy_c_Option_Ooption_ONone_001t__Product____Type__Ounit,type,
    none_Product_unit: option_Product_unit ).

tff(sy_c_Option_Ooption_ONone_001t__Set__Oset_I_Eo_J,type,
    none_set_o: option_set_o ).

tff(sy_c_Option_Ooption_ONone_001t__Set__Oset_It__Int__Oint_J,type,
    none_set_int: option_set_int ).

tff(sy_c_Option_Ooption_ONone_001t__Set__Oset_It__Nat__Onat_J,type,
    none_set_nat: option_set_nat ).

tff(sy_c_Option_Ooption_ONone_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    none_s625347054029921090at_nat: option8963830502488799655at_nat ).

tff(sy_c_Option_Ooption_ONone_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    none_s6518873173954064040at_nat: option1583680563626158861at_nat ).

tff(sy_c_Option_Ooption_OSome_001_Eo,type,
    some_o: fun_o_option_o ).

tff(sy_c_Option_Ooption_OSome_001t__Assertions__Oassn,type,
    some_assn: assn > option_assn ).

tff(sy_c_Option_Ooption_OSome_001t__Code____Numeral__Ointeger,type,
    some_Code_integer: fun_Co8029881127924365703nteger ).

tff(sy_c_Option_Ooption_OSome_001t__Int__Oint,type,
    some_int: fun_int_option_int ).

tff(sy_c_Option_Ooption_OSome_001t__Nat__Onat,type,
    some_nat: fun_nat_option_nat ).

tff(sy_c_Option_Ooption_OSome_001t__Num__Onum,type,
    some_num: fun_num_option_num ).

tff(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    some_P6772290148444788224nteger: produc8923325533196201883nteger > option2651255830984564193nteger ).

tff(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    some_P5671840033927537686atural: produc7822875418678951345atural > option5403585828896915703atural ).

tff(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    some_P6105628898608307625it_nat: fun_Pr8118912048244921225it_nat ).

tff(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    some_P624177172695371229et_nat: produc3658429121746597890et_nat > option936205604648967762et_nat ).

tff(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    some_P4184893108420464158nt_int: product_prod_int_int > option4624381673175914239nt_int ).

tff(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    some_P7363390416028606310at_nat: fun_Pr7804344347641417161at_nat ).

tff(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    some_P1914260805536162275it_nat: fun_Pr7644814098969791837it_nat ).

tff(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    some_P131194445498448716at_nat: produc3843707927480180839at_nat > option8699557107911914541at_nat ).

tff(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    some_P8798507657793832714nt_int: produc4788131091073775919nt_int > option6186025235080601855nt_int ).

tff(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    some_P7453818414240362097nteger: produc2453742332425399446nteger > option983905398058327270nteger ).

tff(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    some_P994283844982041979et_nat: produc8799533983703829792et_nat > option4955102875562834416et_nat ).

tff(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    some_P3006888012174695577et_nat: produc3112576180687729086et_nat > option5899113203645146382et_nat ).

tff(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    some_P9145269820779039710nt_int: produc3043004577601930755nt_int > option1544258867535432659nt_int ).

tff(sy_c_Option_Ooption_OSome_001t__Product____Type__Ounit,type,
    some_Product_unit: fun_Pr8303579546892975945t_unit ).

tff(sy_c_Option_Ooption_OSome_001t__Rat__Orat,type,
    some_rat: rat > option_rat ).

tff(sy_c_Option_Ooption_OSome_001t__Set__Oset_I_Eo_J,type,
    some_set_o: set_o > option_set_o ).

tff(sy_c_Option_Ooption_OSome_001t__Set__Oset_It__Int__Oint_J,type,
    some_set_int: set_int > option_set_int ).

tff(sy_c_Option_Ooption_OSome_001t__Set__Oset_It__Nat__Onat_J,type,
    some_set_nat: fun_se7316093745529328985et_nat ).

tff(sy_c_Option_Ooption_OSome_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    some_s147305329494351046at_nat: set_Pr1261947904930325089at_nat > option8963830502488799655at_nat ).

tff(sy_c_Option_Ooption_OSome_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    some_s5890477192898017836at_nat: set_Pr4329608150637261639at_nat > option1583680563626158861at_nat ).

tff(sy_c_Option_Ooption_OSome_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    some_s8043159101241848530t_unit: set_Product_unit > option8137458692691377843t_unit ).

tff(sy_c_Option_Ooption_OSome_001t__fun_It__Nat__Onat_M_Eo_J,type,
    some_fun_nat_o: fun_fu5368785673109833417_nat_o ).

tff(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Code____Numeral__Ointeger,type,
    case_o43118980978444458nteger: ( $o * fun_Code_integer_o * option_Code_integer ) > $o ).

tff(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Int__Oint,type,
    case_option_o_int: ( $o * fun_int_o * option_int ) > $o ).

tff(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Nat__Onat,type,
    case_option_o_nat: ( $o * fun_nat_o * option_nat ) > $o ).

tff(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Num__Onum,type,
    case_option_o_num: ( $o * fun_num_o ) > fun_option_num_o ).

tff(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    case_o2169478532838437047it_nat: ( $o * fun_Pr7068637894315934487_nat_o ) > fun_op4751157287140997969_nat_o ).

tff(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    case_o2686588417244861013it_nat: ( $o * fun_Pr8032424337255632745_nat_o ) > fun_op479301348043730329_nat_o ).

tff(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Rat__Orat,type,
    case_option_o_rat: ( $o * fun_rat_o * option_rat ) > $o ).

tff(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Set__Oset_It__Nat__Onat_J,type,
    case_o4401850862724306899et_nat: ( $o * fun_set_nat_o * option_set_nat ) > $o ).

tff(sy_c_Option_Ooption_Ocase__option_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    case_o9049918639272118855nteger: ( code_integer * fun_Co8499238673658658103nteger * option_Code_integer ) > code_integer ).

tff(sy_c_Option_Ooption_Ocase__option_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
    case_o356765784539232260er_num: ( code_integer * fun_num_Code_integer * option_num ) > code_integer ).

tff(sy_c_Option_Ooption_Ocase__option_001t__Code____Numeral__Onatural_001t__Num__Onum,type,
    case_o5621594795226839503al_num: ( code_natural * fun_num_Code_natural * option_num ) > code_natural ).

tff(sy_c_Option_Ooption_Ocase__option_001t__Heap__Oarray_Itf__a_J_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    case_o8314599424437789472it_nat: ( array_a * fun_Pr8833188457053967342rray_a * option3216581401566546698it_nat ) > array_a ).

tff(sy_c_Option_Ooption_Ocase__option_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    case_o8180226181140434498it_nat: ( heap_e7401611519738050253t_unit * fun_Pr3456093102767711692t_unit * option3216581401566546698it_nat ) > heap_e7401611519738050253t_unit ).

tff(sy_c_Option_Ooption_Ocase__option_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    case_o2566993838309857162it_nat: ( heap_e7401611519738050253t_unit * fun_Pr1970694993525554974t_unit * option8956607266484857688it_nat ) > heap_e7401611519738050253t_unit ).

tff(sy_c_Option_Ooption_Ocase__option_001t__Int__Oint_001t__Num__Onum,type,
    case_option_int_num: ( int * fun_num_int ) > fun_option_num_int ).

tff(sy_c_Option_Ooption_Ocase__option_001t__Nat__Onat_001t__Num__Onum,type,
    case_option_nat_num: ( nat * fun_num_nat * option_num ) > nat ).

tff(sy_c_Option_Ooption_Ocase__option_001t__Nat__Onat_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    case_o1134687144775446439it_nat: ( nat * fun_Pr515337093925520551at_nat * option3216581401566546698it_nat ) > nat ).

tff(sy_c_Option_Ooption_Ocase__option_001t__Nat__Onat_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    case_o5424514124273913701it_nat: ( nat * fun_Pr367382672041210069at_nat * option8956607266484857688it_nat ) > nat ).

tff(sy_c_Option_Ooption_Ocase__option_001t__Num__Onum_001t__Int__Oint,type,
    case_option_num_int: ( num * fun_int_num * option_int ) > num ).

tff(sy_c_Option_Ooption_Ocase__option_001t__Num__Onum_001t__Nat__Onat,type,
    case_option_num_nat: ( num * fun_nat_num * option_nat ) > num ).

tff(sy_c_Option_Ooption_Ocase__option_001t__Num__Onum_001t__Num__Onum,type,
    case_option_num_num: ( num * fun_num_num ) > fun_option_num_num ).

tff(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Assertions__Oassn_J_001t__Assertions__Oassn,type,
    case_o4484465799723439917n_assn: ( option_assn * fun_assn_option_assn * option_assn ) > option_assn ).

tff(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Num__Onum_J_001t__Num__Onum,type,
    case_o6005452278849405969um_num: ( option_num * fun_num_option_num ) > fun_op8989173174992673105on_num ).

tff(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    case_o8555119740594961093it_nat: ( option3216581401566546698it_nat * fun_Pr8118912048244921225it_nat * option3216581401566546698it_nat ) > option3216581401566546698it_nat ).

tff(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    case_o5699750240967658439it_nat: ( option3216581401566546698it_nat * fun_Pr7518090501403545819it_nat * option8956607266484857688it_nat ) > option3216581401566546698it_nat ).

tff(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    case_o3886096569520666655it_nat: ( option8956607266484857688it_nat * fun_Pr245379829043246639it_nat * option3216581401566546698it_nat ) > option8956607266484857688it_nat ).

tff(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    case_o2963978774867076333it_nat: ( option8956607266484857688it_nat * fun_Pr7644814098969791837it_nat * option8956607266484857688it_nat ) > option8956607266484857688it_nat ).

tff(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Product____Type__Ounit_J_001t__Product____Type__Ounit,type,
    case_o2985186191577459077t_unit: ( option_Product_unit * fun_Pr8303579546892975945t_unit * option_Product_unit ) > option_Product_unit ).

tff(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_001t__Set__Oset_It__Nat__Onat_J,type,
    case_o4054078431260844265et_nat: ( option_set_nat * fun_se7316093745529328985et_nat * option_set_nat ) > option_set_nat ).

tff(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    case_o9080059180780454917at_nat: ( option1583680563626158861at_nat * fun_se7901873761543946185at_nat * option1583680563626158861at_nat ) > option1583680563626158861at_nat ).

tff(sy_c_Option_Ooption_Ocase__option_001t__Product____Type__Ounit_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    case_o9196786658626276042it_nat: ( product_unit * fun_Pr7475791014719349342t_unit * option8956607266484857688it_nat ) > product_unit ).

tff(sy_c_Option_Ooption_Ocase__option_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
    case_o6517734911099809389nteger: ( fun_Pr5876161306168176259nteger * fun_Co1561183069634336733nteger * option_Code_integer ) > fun_Pr5876161306168176259nteger ).

tff(sy_c_Option_Ooption_Ocase__option_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    case_o4513113946662230855nteger: ( fun_Pr5876161306168176259nteger * fun_fu4800041728187187127nteger * option8886115935005447431nteger ) > fun_Pr5876161306168176259nteger ).

tff(sy_c_Option_Ooption_Omap__option_001_Eo_001_Eo,type,
    map_option_o_o: fun_o_o > fun_op5853259939270031811tion_o ).

tff(sy_c_Option_Ooption_Omap__option_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    map_op3669829223712506439nteger: fun_Co8499238673658658103nteger > fun_op1637087682669155543nteger ).

tff(sy_c_Option_Ooption_Omap__option_001t__Code____Numeral__Ointeger_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    map_op3919597019539041057nteger: fun_Co1981900195452921617nteger > fun_op8756596739451609009nteger ).

tff(sy_c_Option_Ooption_Omap__option_001t__Code____Numeral__Ointeger_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    map_op3703932585503671661nteger: fun_Co1561183069634336733nteger > fun_op3037383146056310525nteger ).

tff(sy_c_Option_Ooption_Omap__option_001t__Int__Oint_001t__Int__Oint,type,
    map_option_int_int: fun_int_int > fun_op4193086050743966581on_int ).

tff(sy_c_Option_Ooption_Omap__option_001t__Int__Oint_001t__Nat__Onat,type,
    map_option_int_nat: fun_int_nat > fun_op6683169195675693337on_nat ).

tff(sy_c_Option_Ooption_Omap__option_001t__Int__Oint_001t__Num__Onum,type,
    map_option_int_num: fun_int_num > fun_op2398388785115040099on_num ).

tff(sy_c_Option_Ooption_Omap__option_001t__Nat__Onat_001t__Nat__Onat,type,
    map_option_nat_nat: fun_nat_nat > fun_op1272087013972230845on_nat ).

tff(sy_c_Option_Ooption_Omap__option_001t__Nat__Onat_001t__Num__Onum,type,
    map_option_nat_num: fun_nat_num > fun_op6210678640266353415on_num ).

tff(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__Code____Numeral__Ointeger,type,
    map_op2849635639313731588nteger: fun_num_Code_integer > fun_op4521932154746760340nteger ).

tff(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__Num__Onum,type,
    map_option_num_num: fun_num_num > fun_op8989173174992673105on_num ).

tff(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    map_op6598675229099881181it_nat: ( fun_nu2241728722996109699it_nat * option_num ) > option3216581401566546698it_nat ).

tff(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    map_op8118133509425879471it_nat: ( fun_nu5234077238548837151it_nat * option_num ) > option8956607266484857688it_nat ).

tff(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Num__Onum,type,
    map_op8228268515680064275at_num: ( fun_Pr1223581030874358257at_num * option3216581401566546698it_nat ) > option_num ).

tff(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    map_op6002829699023054091it_nat: ( fun_Pr3819237756034508227it_nat * option3216581401566546698it_nat ) > option3216581401566546698it_nat ).

tff(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    map_op674526153330701057it_nat: ( fun_Pr2014882013869309663it_nat * option3216581401566546698it_nat ) > option8956607266484857688it_nat ).

tff(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Num__Onum,type,
    map_op2731889312448867759at_num: ( fun_Pr1075626608990047775at_num * option8956607266484857688it_nat ) > option_num ).

tff(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    map_op7916408704904942447it_nat: ( fun_Pr3908927074708932117it_nat * option8956607266484857688it_nat ) > option3216581401566546698it_nat ).

tff(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    map_op8673683442680995229it_nat: ( fun_Pr1033138224055104269it_nat * option8956607266484857688it_nat ) > option8956607266484857688it_nat ).

tff(sy_c_Option_Ooption_Omap__option_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    map_op7435587552923436871nteger: fun_fu4800041728187187127nteger > fun_op7507520395135695063nteger ).

tff(sy_c_Option_Ooption_Omap__option_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Nat__Onat_M_Eo_J,type,
    map_op4725796707522037195_nat_o: fun_fu4001317426178549763_nat_o > fun_op3284592519439835779_nat_o ).

tff(sy_c_Option_Ooption_Osize__option_001t__Num__Onum,type,
    size_option_num: fun_num_nat > fun_option_num_nat ).

tff(sy_c_Option_Ooption_Osize__option_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    size_o5312321843473198183it_nat: ( fun_Pr515337093925520551at_nat * option3216581401566546698it_nat ) > nat ).

tff(sy_c_Option_Ooption_Osize__option_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    size_o29782932136985253it_nat: ( fun_Pr367382672041210069at_nat * option8956607266484857688it_nat ) > nat ).

tff(sy_c_Option_Ooption_Othe_001_Eo,type,
    the_o: fun_option_o_o ).

tff(sy_c_Option_Ooption_Othe_001t__Int__Oint,type,
    the_int2: fun_option_int_int ).

tff(sy_c_Option_Ooption_Othe_001t__Nat__Onat,type,
    the_nat: fun_option_nat_nat ).

tff(sy_c_Option_Ooption_Othe_001t__Num__Onum,type,
    the_num: fun_option_num_num ).

tff(sy_c_Option_Ooption_Othe_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    the_Pr5856008525237892824it_nat: fun_op8917697677373047293it_nat ).

tff(sy_c_Option_Ooption_Othe_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    the_Pr7776125533777466484it_nat: fun_op7765417307512062173it_nat ).

tff(sy_c_Option_Ooption_Othe_001t__fun_It__Nat__Onat_M_Eo_J,type,
    the_fun_nat_o: fun_op9036024853803066045_nat_o ).

tff(sy_c_Option_Othese_001_Eo,type,
    these_o: set_option_o > set_o ).

tff(sy_c_Option_Othese_001t__Int__Oint,type,
    these_int: set_option_int > set_int ).

tff(sy_c_Option_Othese_001t__Nat__Onat,type,
    these_nat: set_option_nat > set_nat ).

tff(sy_c_Option_Othese_001t__Num__Onum,type,
    these_num: set_option_num > set_num ).

tff(sy_c_Option_Othese_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    these_6645423997822192641it_nat: set_op3940070208846178154it_nat > set_Pr5142436192348053284it_nat ).

tff(sy_c_Option_Othese_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    these_8061402112538453438at_nat: set_op4508134149509766951at_nat > set_Pr1261947904930325089at_nat ).

tff(sy_c_Option_Othese_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    these_3407724651694999947it_nat: set_op239864471688321678it_nat > set_Pr1354866905816374718it_nat ).

tff(sy_c_Option_Othese_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    these_1872268174106123684at_nat: set_op989438649584373901at_nat > set_Pr4329608150637261639at_nat ).

tff(sy_c_Option_Othese_001t__Product____Type__Ounit,type,
    these_Product_unit: set_op3165557761946182707t_unit > set_Product_unit ).

tff(sy_c_Option_Othese_001t__Set__Oset_It__Nat__Onat_J,type,
    these_set_nat: set_option_set_nat > set_set_nat ).

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

tff(sy_c_Orderings_Obot__class_Obot_001t__Assertions__Oassn,type,
    bot_bot_assn: assn ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Nat__Onat,type,
    bot_bot_nat: nat ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Option__Ooption_It__Num__Onum_J,type,
    bot_bot_option_num: option_num ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Product____Type__Ounit,type,
    bot_bot_Product_unit: product_unit ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_I_Eo_J,type,
    bot_bot_set_o: set_o ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
    bot_bo3990330152332043303nteger: set_Code_integer ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Int__Oint_J,type,
    bot_bot_set_int: set_int ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
    bot_bot_set_list_nat: set_list_nat ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
    bot_bot_set_nat: set_nat ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Num__Onum_J,type,
    bot_bot_set_num: set_num ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_I_Eo_J_J,type,
    bot_bot_set_option_o: set_option_o ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_It__Int__Oint_J_J,type,
    bot_bo2519760366563279686on_int: set_option_int ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_It__Nat__Onat_J_J,type,
    bot_bo5009843511495006442on_nat: set_option_nat ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_It__Num__Onum_J_J,type,
    bot_bo725063100934353204on_num: set_option_num ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    bot_bo8185009268211221974it_nat: set_op3940070208846178154it_nat ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    bot_bo3414888551220300179at_nat: set_op4508134149509766951at_nat ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    bot_bo1172055076661450530it_nat: set_op239864471688321678it_nat ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    bot_bo1471150103859235065at_nat: set_op989438649584373901at_nat ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_It__Product____Type__Ounit_J_J,type,
    bot_bo2792743115866486943t_unit: set_op3165557761946182707t_unit ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_J,type,
    bot_bo5650944848895983264et_nat: set_option_set_nat ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    bot_bo7073875226086086771od_o_o: set_Product_prod_o_o ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_J,type,
    bot_bo6799815435448350781_o_int: set_Pr8834758594704517033_o_int ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
    bot_bo66526543525301729_o_nat: set_Pr2101469702781467981_o_nat ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    bot_bo6361524548789211024it_nat: set_Pr5142436192348053284it_nat ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_M_Eo_J_J,type,
    bot_bo8092356734887935275_int_o: set_Pr903927857289325719_int_o ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    bot_bo1796632182523588997nt_int: set_Pr958786334691620121nt_int ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J_J,type,
    bot_bo4286715327455315753nt_nat: set_Pr3448869479623346877nt_nat ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J,type,
    bot_bo1114129665703605383_nat_o: set_Pr3149072824959771635_nat_o ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_J,type,
    bot_bo8833082644685343017at_int: set_Pr7995236796853374141at_int ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    bot_bo2099793752762293965at_nat: set_Pr1261947904930325089at_nat ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J,type,
    bot_bo5454027612061941066_nat_o: set_Pr6558897299634722526_nat_o ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    bot_bo5327735625951526323at_nat: set_Pr8693737435421807431at_nat ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    bot_bo7193250159860175667at_nat: set_Pr5564308138774400199at_nat ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    bot_bo5696401558416705618it_nat: set_Pr1354866905816374718it_nat ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    bot_bo228742789529271731at_nat: set_Pr4329608150637261639at_nat ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    bot_bo5189594446080201209nt_int: set_Pr4166680992137330533nt_int ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    bot_bo9050247954524366304nteger: set_Pr3486312109254157132nteger ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    bot_bo1493351289776401898et_nat: set_Pr1312406793078187350et_nat ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    bot_bo6121529163330120712et_nat: set_Pr4040394263813967220et_nat ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    bot_bo2501116328598523085nt_int: set_Pr6700895561065273913nt_int ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    bot_bo3957492148770167129t_unit: set_Product_unit ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Rat__Orat_J,type,
    bot_bot_set_rat: set_rat ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J,type,
    bot_bo9204850693367297629nteger: set_set_Code_integer ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
    bot_bot_set_set_int: set_set_int ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Set__Oset_It__List__Olist_It__Nat__Onat_J_J_J,type,
    bot_bo3886227569956363488st_nat: set_set_list_nat ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
    bot_bot_set_set_nat: set_set_nat ).

tff(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    bot_bo3083307316010499117at_nat: set_se7855581050983116737at_nat ).

tff(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 ).

tff(sy_c_Orderings_Obot__class_Obot_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    bot_bo1118997454112379798_nat_o: fun_nat_fun_nat_o ).

tff(sy_c_Orderings_Obot__class_Obot_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J,type,
    bot_bo1070391751820557722_nat_o: fun_se5639961202347202350_nat_o ).

tff(sy_c_Orderings_Obot__class_Obot_001t__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    bot_bo6524246659364023090_int_o: fun_fu2978539155105838238_int_o ).

tff(sy_c_Orderings_Obot__class_Obot_001t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
    bot_bo4567088895781559819eger_o: fun_fu7695273699059480439eger_o ).

tff(sy_c_Orderings_Obot__class_Obot_001t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
    bot_bo3509460380234399255_nat_o: fun_fu8419763957888848259_nat_o ).

tff(sy_c_Orderings_Obot__class_Obot_001t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_J,type,
    bot_bo5031374944739956857_nat_o: fun_fu2611741329380808165_nat_o ).

tff(sy_c_Orderings_Obot__class_Obot_001t__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    bot_bo1117279750869432670_int_o: fun_fu6865642474282033866_int_o ).

tff(sy_c_Orderings_Oord__class_Oless_001_Eo,type,
    ord_less_o: fun_o_fun_o_o ).

tff(sy_c_Orderings_Oord__class_Oless_001t__Code____Numeral__Ointeger,type,
    ord_le6747313008572928689nteger: fun_Co2081214437782444048eger_o ).

tff(sy_c_Orderings_Oord__class_Oless_001t__Code____Numeral__Onatural,type,
    ord_le5570908160329646204atural: fun_Co7302518231560758906ural_o ).

tff(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
    ord_less_int: fun_int_fun_int_o ).

tff(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
    ord_less_nat: fun_nat_fun_nat_o ).

tff(sy_c_Orderings_Oord__class_Oless_001t__Num__Onum,type,
    ord_less_num: fun_num_fun_num_o ).

tff(sy_c_Orderings_Oord__class_Oless_001t__Option__Ooption_It__Code____Numeral__Ointeger_J,type,
    ord_le7113747843092208513nteger: ( option_Code_integer * option_Code_integer ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless_001t__Option__Ooption_It__Int__Oint_J,type,
    ord_less_option_int: ( option_int * option_int ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless_001t__Option__Ooption_It__Nat__Onat_J,type,
    ord_less_option_nat: ( option_nat * option_nat ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless_001t__Option__Ooption_It__Num__Onum_J,type,
    ord_less_option_num: fun_op493924057549976310_num_o ).

tff(sy_c_Orderings_Oord__class_Oless_001t__Option__Ooption_It__Rat__Orat_J,type,
    ord_less_option_rat: ( option_rat * option_rat ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless_001t__Product____Type__Ounit,type,
    ord_le361264281704409273t_unit: fun_Pr1520749766685617582unit_o ).

tff(sy_c_Orderings_Oord__class_Oless_001t__Rat__Orat,type,
    ord_less_rat: fun_rat_fun_rat_o ).

tff(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_I_Eo_J,type,
    ord_less_set_o: ( set_o * set_o ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
    ord_le1307284697595431911nteger: ( set_Code_integer * set_Code_integer ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Int__Oint_J,type,
    ord_less_set_int: ( set_int * set_int ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Nat__Onat_J,type,
    ord_less_set_nat: ( set_nat * set_nat ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Num__Onum_J,type,
    ord_less_set_num: ( set_num * set_num ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    ord_le7866589430770878221at_nat: fun_se5639961202347202350_nat_o ).

tff(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    ord_le2604355607129572851at_nat: ( set_Pr4329608150637261639at_nat * set_Pr4329608150637261639at_nat ) > $o ).

tff(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 ).

tff(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Rat__Orat_J,type,
    ord_less_set_rat: ( set_rat * set_rat ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
    ord_less_set_set_nat: ( set_set_nat * set_set_nat ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001_Eo,type,
    ord_less_eq_o: fun_o_fun_o_o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Code____Numeral__Ointeger,type,
    ord_le3102999989581377725nteger: fun_Co2081214437782444048eger_o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Code____Numeral__Onatural,type,
    ord_le1926595141338095240atural: fun_Co7302518231560758906ural_o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Int__Oint,type,
    ord_less_eq_int: fun_int_fun_int_o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
    ord_less_eq_nat: fun_nat_fun_nat_o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Num__Onum,type,
    ord_less_eq_num: fun_num_fun_num_o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Option__Ooption_It__Int__Oint_J,type,
    ord_le1736525451366464988on_int: ( option_int * option_int ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Option__Ooption_It__Nat__Onat_J,type,
    ord_le5914376470875661696on_nat: ( option_nat * option_nat ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Option__Ooption_It__Num__Onum_J,type,
    ord_le6622620407824499402on_num: fun_op493924057549976310_num_o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Option__Ooption_It__Rat__Orat_J,type,
    ord_le2406147912482264968on_rat: ( option_rat * option_rat ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
    ord_le2843612097646854710et_nat: ( option_set_nat * option_set_nat ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Product____Type__Ounit,type,
    ord_le3221252021190050221t_unit: fun_Pr1520749766685617582unit_o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Rat__Orat,type,
    ord_less_eq_rat: fun_rat_fun_rat_o ).

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

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
    ord_le7084787975880047091nteger: ( set_Code_integer * set_Code_integer ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Int__Oint_J,type,
    ord_less_eq_set_int: ( set_int * set_int ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
    ord_le6045566169113846134st_nat: ( set_list_nat * set_list_nat ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
    ord_less_eq_set_nat: set_nat > fun_set_nat_o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Num__Onum_J,type,
    ord_less_eq_set_num: ( set_num * set_num ) > $o ).

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

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_J,type,
    ord_le3982295392052344841_o_int: ( set_Pr8834758594704517033_o_int * set_Pr8834758594704517033_o_int ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
    ord_le6472378536984071597_o_nat: ( set_Pr2101469702781467981_o_nat * set_Pr2101469702781467981_o_nat ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    ord_le3725938330318615451nteger: ( set_Pr4811707699266497531nteger * set_Pr4811707699266497531nteger ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_J,type,
    ord_le719211969347571306er_int: ( set_Pr6496905503482889930er_int * set_Pr6496905503482889930er_int ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_J,type,
    ord_le3209295114279298062er_nat: ( set_Pr8986988648414616686er_nat * set_Pr8986988648414616686er_nat ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    ord_le6478268328230966961atural: ( set_Pr7564037697178849041atural * set_Pr7564037697178849041atural ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J,type,
    ord_le2202040463148982292atural: ( set_Pr2352657477744078772atural * set_Pr2352657477744078772atural ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    ord_le8090042543978450200et_nat: ( set_Pr3948176798113811640et_nat * set_Pr3948176798113811640et_nat ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_M_Eo_J_J,type,
    ord_le5274836691491929335_int_o: ( set_Pr903927857289325719_int_o * set_Pr903927857289325719_int_o ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_J,type,
    ord_le2638047946463454698nteger: ( set_Pr8415741480598773322nteger * set_Pr8415741480598773322nteger ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    ord_le2843351958646193337nt_int: ( set_Pr958786334691620121nt_int * set_Pr958786334691620121nt_int ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J_J,type,
    ord_le5333435103577920093nt_nat: ( set_Pr3448869479623346877nt_nat * set_Pr3448869479623346877nt_nat ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J,type,
    ord_le7519981659162375251_nat_o: ( set_Pr3149072824959771635_nat_o * set_Pr3149072824959771635_nat_o ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_J,type,
    ord_le5852610332322655630nteger: ( set_Pr2406931829603198446nteger * set_Pr2406931829603198446nteger ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_J,type,
    ord_le656430383953171549at_int: ( set_Pr7995236796853374141at_int * set_Pr7995236796853374141at_int ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    ord_le3146513528884898305at_nat: fun_se5639961202347202350_nat_o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    ord_le3050193496395145148at_nat: ( set_Pr7717912310451564380at_nat * set_Pr7717912310451564380at_nat ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    ord_le3218026494883419554at_nat: ( set_Pr1625285437083415874at_nat * set_Pr1625285437083415874at_nat ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J,type,
    ord_le5919393503700438654_nat_o: ( set_Pr6558897299634722526_nat_o * set_Pr6558897299634722526_nat_o ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J_J,type,
    ord_le7094820750414311574at_nat: ( set_Pr2539167527615954998at_nat * set_Pr2539167527615954998at_nat ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Nat__Onat_J_J,type,
    ord_le2145644191787020796at_nat: ( set_Pr552903133987017116at_nat * set_Pr552903133987017116at_nat ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    ord_le1268244103169919719at_nat: ( set_Pr4329608150637261639at_nat * set_Pr4329608150637261639at_nat ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    ord_le3197784583289274309nt_int: ( set_Pr4166680992137330533nt_int * set_Pr4166680992137330533nt_int ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    ord_le9038753718846915815_nat_o: ( set_Pr2929610433303031111_nat_o * set_Pr2929610433303031111_nat_o ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    ord_le2932375828722672556nteger: ( set_Pr3486312109254157132nteger * set_Pr3486312109254157132nteger ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    ord_le3919382008627836342et_nat: ( set_Pr1312406793078187350et_nat * set_Pr1312406793078187350et_nat ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    ord_le5189643068899110356et_nat: ( set_Pr4040394263813967220et_nat * set_Pr4040394263813967220et_nat ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    ord_le3990897393281686169nt_int: ( set_Pr6700895561065273913nt_int * set_Pr6700895561065273913nt_int ) > $o ).

tff(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 ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Rat__Orat_J,type,
    ord_less_eq_set_rat: ( set_rat * set_rat ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J,type,
    ord_le1914454125413604393nteger: ( set_set_Code_integer * set_set_Code_integer ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
    ord_le4403425263959731960et_int: ( set_set_int * set_set_int ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__List__Olist_It__Nat__Onat_J_J_J,type,
    ord_le1068707526560357548st_nat: ( set_set_list_nat * set_set_list_nat ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
    ord_le6893508408891458716et_nat: ( set_set_nat * set_set_nat ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    ord_le2077887516847798113at_nat: ( set_se7855581050983116737at_nat * set_se7855581050983116737at_nat ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Product____Type__Ounit_J_J,type,
    ord_le3674001228145610605t_unit: ( set_set_Product_unit * set_set_Product_unit ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    ord_le2047893094613950805e_term: ( set_fu3629540756087427317e_term * set_fu3629540756087427317e_term ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    ord_le8538105397850660240e_term: ( set_fu8280898353253485872e_term * set_fu8280898353253485872e_term ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
    ord_le5394272759557949423_nat_o: ( set_fu3555266933746557007_nat_o * set_fu3555266933746557007_nat_o ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    ord_le792320400390739841e_term: ( set_fu5653557704672872225e_term * set_fu5653557704672872225e_term ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__fun_It__List__Olist_It__Nat__Onat_J_M_Eo_J,type,
    ord_le4972187363741583025_nat_o: ( fun_list_nat_o * fun_list_nat_o ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__fun_It__List__Olist_It__Nat__Onat_J_Mt__fun_It__List__Olist_It__Nat__Onat_J_M_Eo_J_J,type,
    ord_le4470944457981725354_nat_o: ( fun_li1025265955262268170_nat_o * fun_li1025265955262268170_nat_o ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__fun_It__Nat__Onat_M_Eo_J,type,
    ord_le7240017405068453697_nat_o: fun_fu7564235448449272366at_o_o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    ord_le768339454706049738_nat_o: ( fun_nat_fun_nat_o * fun_nat_fun_nat_o ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
    ord_le14110778710936002_int_o: ( fun_Pr3238374608701176162_int_o * fun_Pr3238374608701176162_int_o ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    ord_le1416746762259324110_int_o: ( fun_Pr9018117161326028078_int_o * fun_Pr9018117161326028078_int_o ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
    ord_le1572679713340831354_nat_o: fun_Pr4796943543331071514_nat_o > fun_fu6891447142836604759at_o_o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J,type,
    ord_le3650406611588909774_nat_o: ( fun_Pr2028404973800837934_nat_o * fun_Pr2028404973800837934_nat_o ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_M_Eo_J,type,
    ord_le3896530374514135251_nat_o: ( fun_Pr1227177680593602867_nat_o * fun_Pr1227177680593602867_nat_o ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_M_Eo_J_J,type,
    ord_le6446978100474826990_nat_o: ( fun_Pr3358449090565925198_nat_o * fun_Pr3358449090565925198_nat_o ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J,type,
    ord_le5606610691101069006_nat_o: ( fun_se5639961202347202350_nat_o * fun_se5639961202347202350_nat_o ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    ord_le2876595303158420734_int_o: ( fun_fu2978539155105838238_int_o * fun_fu2978539155105838238_int_o ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
    ord_le4825817444062779351eger_o: ( fun_fu7695273699059480439eger_o * fun_fu7695273699059480439eger_o ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
    ord_le3580378406483493347_nat_o: ( fun_fu8419763957888848259_nat_o * fun_fu8419763957888848259_nat_o ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_J,type,
    ord_le2834457679758710341_nat_o: ( fun_fu2611741329380808165_nat_o * fun_fu2611741329380808165_nat_o ) > $o ).

tff(sy_c_Orderings_Oord__class_Oless__eq_001t__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    ord_le4806730579060245290_int_o: ( fun_fu6865642474282033866_int_o * fun_fu6865642474282033866_int_o ) > $o ).

tff(sy_c_Orderings_Oord__class_Omax_001t__Code____Numeral__Ointeger,type,
    ord_max_Code_integer: fun_Co1981900195452921617nteger ).

tff(sy_c_Orderings_Oord__class_Omax_001t__Code____Numeral__Onatural,type,
    ord_max_Code_natural: code_natural > fun_Co7398788559141407565atural ).

tff(sy_c_Orderings_Oord__class_Omax_001t__Int__Oint,type,
    ord_max_int: fun_int_fun_int_int ).

tff(sy_c_Orderings_Oord__class_Omax_001t__Nat__Onat,type,
    ord_max_nat: fun_nat_fun_nat_nat ).

tff(sy_c_Orderings_Oord__class_Omax_001t__Rat__Orat,type,
    ord_max_rat: rat > fun_rat_rat ).

tff(sy_c_Orderings_Oord__class_Omin_001t__Code____Numeral__Ointeger,type,
    ord_min_Code_integer: fun_Co1981900195452921617nteger ).

tff(sy_c_Orderings_Oord__class_Omin_001t__Code____Numeral__Onatural,type,
    ord_min_Code_natural: code_natural > fun_Co7398788559141407565atural ).

tff(sy_c_Orderings_Oord__class_Omin_001t__Int__Oint,type,
    ord_min_int: fun_int_fun_int_int ).

tff(sy_c_Orderings_Oord__class_Omin_001t__Nat__Onat,type,
    ord_min_nat: fun_nat_fun_nat_nat ).

tff(sy_c_Orderings_Oord__class_Omin_001t__Num__Onum,type,
    ord_min_num: fun_num_fun_num_num ).

tff(sy_c_Orderings_Oord__class_Omin_001t__Rat__Orat,type,
    ord_min_rat: rat > fun_rat_rat ).

tff(sy_c_Orderings_Oord__class_Omin_001t__Set__Oset_It__Nat__Onat_J,type,
    ord_min_set_nat: ( set_nat * set_nat ) > set_nat ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Assertions__Oassn,type,
    top_top_assn: assn ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Option__Ooption_It__Assertions__Oassn_J,type,
    top_top_option_assn: option_assn ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Option__Ooption_It__Product____Type__Ounit_J,type,
    top_to4322782652514146083t_unit: option_Product_unit ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Option__Ooption_It__Set__Oset_It__Int__Oint_J_J,type,
    top_to2336371874512884450et_int: option_set_int ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
    top_to4826455019444611206et_nat: option_set_nat ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Ounit_J_J,type,
    top_to7662761140297458691t_unit: option8137458692691377843t_unit ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Product____Type__Ounit,type,
    top_top_Product_unit: product_unit ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_Eo_J,type,
    top_top_set_o: set_o ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Assertions__Oassn_J,type,
    top_top_set_assn: set_assn ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
    top_to4645266643341252675nteger: set_Code_integer ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Int__Oint_J,type,
    top_top_set_int: set_int ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
    top_top_set_nat: set_nat ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Num__Onum_J,type,
    top_top_set_num: set_num ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__Code____Numeral__Ointeger_J_J,type,
    top_to5929521628599800467nteger: set_op687863988967635939nteger ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__Int__Oint_J_J,type,
    top_to6430115241214627170on_int: set_option_int ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__Nat__Onat_J_J,type,
    top_to8920198386146353926on_nat: set_option_nat ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__Num__Onum_J_J,type,
    top_to4635417975585700688on_num: set_option_num ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    top_to7137183367772546234it_nat: set_op3940070208846178154it_nat ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    top_to3251141154256563319at_nat: set_op4508134149509766951at_nat ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    top_to6632602878615679294it_nat: set_op239864471688321678it_nat ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__Product____Type__Ounit_J_J,type,
    top_to2690860209552263555t_unit: set_op3165557761946182707t_unit ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    top_to3995162779041354868it_nat: set_Pr5142436192348053284it_nat ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    top_to4366644338036079209nt_int: set_Pr958786334691620121nt_int ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J_J,type,
    top_to6856727482967805965nt_nat: set_Pr3448869479623346877nt_nat ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Product____Type__Ounit_J_J,type,
    top_to876157113852465980t_unit: set_Pr5889264611543340172t_unit ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_J,type,
    top_to2179722763343057421at_int: set_Pr7995236796853374141at_int ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    top_to4669805908274784177at_nat: set_Pr1261947904930325089at_nat ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Ounit_J_J,type,
    top_to8544742955230171288t_unit: set_Pr4334478416066269672t_unit ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Int__Oint_J_J,type,
    top_to3484027333181043534it_int: set_Pr8497134830871917726it_int ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Nat__Onat_J_J,type,
    top_to5974110478112770290it_nat: set_Pr1763845938948868674it_nat ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    top_to4082048134677576814it_nat: set_Pr1354866905816374718it_nat ).

tff(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 ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    top_to6833984726390702231at_nat: set_Pr4329608150637261639at_nat ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    top_to1212741241995312661nt_int: set_Pr4166680992137330533nt_int ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    top_to7525899545246753276nteger: set_Pr3486312109254157132nteger ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    top_to2987642378616949766et_nat: set_Pr1312406793078187350et_nat ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    top_to2648389616742571044et_nat: set_Pr4040394263813967220et_nat ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    top_to6107225058432391401nt_int: set_Pr6700895561065273913nt_int ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    top_to1996260823553986621t_unit: set_Product_unit ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Rat__Orat_J,type,
    top_top_set_rat: set_rat ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_I_Eo_J_J,type,
    top_top_set_set_o: set_set_o ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
    top_top_set_set_int: set_set_int ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
    top_top_set_set_nat: set_set_nat ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    top_to7629004291339433233at_nat: set_se7855581050983116737at_nat ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    top_to1754375979021635447at_nat: set_se5479201105039950375at_nat ).

tff(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 ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    top_to805621317456759325nteger: set_fu5818728815147633517nteger ).

tff(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__fun_It__Nat__Onat_M_Eo_J_J,type,
    top_to8708385046839970129_nat_o: set_fun_nat_o ).

tff(sy_c_Orderings_Otop__class_Otop_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    top_to5288702739685986426_nat_o: fun_nat_fun_nat_o ).

tff(sy_c_Orderings_Otop__class_Otop_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J,type,
    top_to7888465585648448638_nat_o: fun_se5639961202347202350_nat_o ).

tff(sy_c_Orderings_Otop__class_Otop_001t__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    top_to1089409542825796430_int_o: fun_fu2978539155105838238_int_o ).

tff(sy_c_Orderings_Otop__class_Otop_001t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
    top_to2784585791485011495eger_o: fun_fu7695273699059480439eger_o ).

tff(sy_c_Orderings_Otop__class_Otop_001t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
    top_to2712223222597888051_nat_o: fun_fu8419763957888848259_nat_o ).

tff(sy_c_Orderings_Otop__class_Otop_001t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_J,type,
    top_to3067105749023872149_nat_o: fun_fu2611741329380808165_nat_o ).

tff(sy_c_Orderings_Otop__class_Otop_001t__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    top_to1218662295448195450_int_o: fun_fu6865642474282033866_int_o ).

tff(sy_c_Power_Opower__class_Opower_001t__Assertions__Oassn,type,
    power_power_assn: fun_as8240436605320707994t_assn ).

tff(sy_c_Power_Opower__class_Opower_001t__Code____Numeral__Ointeger,type,
    power_8256067586552552935nteger: fun_Co6226381647958292740nteger ).

tff(sy_c_Power_Opower__class_Opower_001t__Code____Numeral__Onatural,type,
    power_7079662738309270450atural: code_natural > fun_nat_Code_natural ).

tff(sy_c_Power_Opower__class_Opower_001t__Int__Oint,type,
    power_power_int: fun_int_fun_nat_int ).

tff(sy_c_Power_Opower__class_Opower_001t__Nat__Onat,type,
    power_power_nat: fun_nat_fun_nat_nat ).

tff(sy_c_Power_Opower__class_Opower_001t__Rat__Orat,type,
    power_power_rat: fun_rat_fun_nat_rat ).

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

tff(sy_c_Product__Type_OPair_001_Eo_001t__Int__Oint,type,
    product_Pair_o_int: ( $o * int ) > product_prod_o_int ).

tff(sy_c_Product__Type_OPair_001_Eo_001t__Nat__Onat,type,
    product_Pair_o_nat: ( $o * nat ) > product_prod_o_nat ).

tff(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001_Eo,type,
    produc6677183202524767010eger_o: ( code_integer * $o ) > produc6271795597528267376eger_o ).

tff(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    produc1086072967326762835nteger: code_integer > fun_Co6597186368970283863nteger ).

tff(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
    produc8805100893531834658er_int: ( code_integer * int ) > produc2256096406371053034er_int ).

tff(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
    produc8807591364040884934er_nat: code_integer > fun_na8176081009732395159er_nat ).

tff(sy_c_Product__Type_OPair_001t__Code____Numeral__Onatural_001t__Code____Numeral__Onatural,type,
    produc3574140220909816553atural: ( code_natural * code_natural ) > produc7822875418678951345atural ).

tff(sy_c_Product__Type_OPair_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    produc6639722614265839536atural: code_natural > fun_Pr7769407664385210434atural ).

tff(sy_c_Product__Type_OPair_001t__Heap__Oarray_Itf__a_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
    produc1733996804261680252it_nat: ( array_a * produc6653097349344004940it_nat ) > produc6714399278180371524it_nat ).

tff(sy_c_Product__Type_OPair_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Nat__Onat,type,
    produc584006145561248582it_nat: ( heap_e7401611519738050253t_unit * nat ) > produc6653097349344004940it_nat ).

tff(sy_c_Product__Type_OPair_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Set__Oset_It__Nat__Onat_J,type,
    produc7507926704131184380et_nat: ( heap_e7401611519738050253t_unit * set_nat ) > produc3658429121746597890et_nat ).

tff(sy_c_Product__Type_OPair_001t__Int__Oint_001_Eo,type,
    product_Pair_int_o: ( int * $o ) > product_prod_int_o ).

tff(sy_c_Product__Type_OPair_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
    produc220428336201996578nteger: ( int * code_integer ) > produc2963269191615333738nteger ).

tff(sy_c_Product__Type_OPair_001t__Int__Oint_001t__Int__Oint,type,
    product_Pair_int_int: fun_in1696471567231710611nt_int ).

tff(sy_c_Product__Type_OPair_001t__Int__Oint_001t__Nat__Onat,type,
    product_Pair_int_nat: int > fun_na3663551987197276902nt_nat ).

tff(sy_c_Product__Type_OPair_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    produc4348348721325984599at_nat: ( multis2468970476368604999at_nat * multis2468970476368604999at_nat ) > produc4166570645942440679at_nat ).

tff(sy_c_Product__Type_OPair_001t__Nat__Onat_001_Eo,type,
    product_Pair_nat_o: ( nat * $o ) > product_prod_nat_o ).

tff(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
    produc9072146812819927750nteger: ( nat * code_integer ) > produc2591615631378489102nteger ).

tff(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Int__Oint,type,
    product_Pair_nat_int: ( nat * int ) > product_prod_nat_int ).

tff(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
    product_Pair_nat_nat: fun_na4138050610385705875at_nat ).

tff(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Num__Onum,type,
    product_Pair_nat_num: ( nat * num ) > product_prod_nat_num ).

tff(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    produc3378006678175723489it_nat: ( nat * option3216581401566546698it_nat ) > produc2867611627572283311it_nat ).

tff(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    produc638857205735767105it_nat: ( nat * option8956607266484857688it_nat ) > produc3911288613690379145it_nat ).

tff(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    produc487386426758144856at_nat: ( nat * product_prod_nat_nat ) > produc7248412053542808358at_nat ).

tff(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    produc5463602008962177208at_nat: ( nat * set_Pr1261947904930325089at_nat ) > produc3313772616054891654at_nat ).

tff(sy_c_Product__Type_OPair_001t__Num__Onum_001t__Num__Onum,type,
    product_Pair_num_num: ( num * num ) > product_prod_num_num ).

tff(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_001t__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J,type,
    produc5950683997804057413e_term: ( option6357759511663192854e_term * option6357759511663192854e_term ) > produc6576344331059438605e_term ).

tff(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    produc4911887526399440471nteger: ( produc8923325533196201883nteger * produc8923325533196201883nteger ) > produc3334582477557816039nteger ).

tff(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Code____Numeral__Onatural,type,
    produc1272419604612767874atural: ( produc7822875418678951345atural * code_natural ) > produc3981471736659609608atural ).

tff(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    produc4480994950612372183atural: ( produc7822875418678951345atural * produc7822875418678951345atural ) > produc6756470014200349799atural ).

tff(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    produc8199053930788261021et_nat: ( produc3658429121746597890et_nat * produc3658429121746597890et_nat ) > produc8111630337999740517et_nat ).

tff(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    produc3646306378393792727nt_int: ( product_prod_int_int * product_prod_int_int ) > produc1219242969750017639nt_int ).

tff(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo,type,
    produc855456346497908590_nat_o: ( product_prod_nat_nat * $o ) > produc652263959640188542_nat_o ).

tff(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    produc6161850002892822231at_nat: ( product_prod_nat_nat * product_prod_nat_nat ) > produc859450856879609959at_nat ).

tff(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc8824474337961625893at_nat: ( produc3313772616054891654at_nat * produc3313772616054891654at_nat ) > produc2714363965264676845at_nat ).

tff(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J,type,
    produc3585720979125124569at_nat: ( produc366245978424229472at_nat * produc366245978424229472at_nat ) > produc2087150632810049441at_nat ).

tff(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc2335810615602371415at_nat: ( produc3843707927480180839at_nat * produc3843707927480180839at_nat ) > produc1906917888121415911at_nat ).

tff(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    produc4613263410003446007nt_int: ( produc4788131091073775919nt_int * produc4788131091073775919nt_int ) > produc3192696172498486335nt_int ).

tff(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    produc2269347123789068741nteger: ( produc2453742332425399446nteger * produc2453742332425399446nteger ) > produc7379341420752632205nteger ).

tff(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    produc8050396023069295193et_nat: ( produc8799533983703829792et_nat * produc8799533983703829792et_nat ) > produc8893060842726229537et_nat ).

tff(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    produc7768440062179809557et_nat: ( produc3112576180687729086et_nat * produc3112576180687729086et_nat ) > produc505541996239113949et_nat ).

tff(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    produc5411871556384885407nt_int: ( produc3043004577601930755nt_int * produc3043004577601930755nt_int ) > produc881187336974765031nt_int ).

tff(sy_c_Product__Type_OPair_001t__Product____Type__Ounit_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
    produc7133225469290080770it_nat: ( product_unit * produc6653097349344004940it_nat ) > produc8664842809031399944it_nat ).

tff(sy_c_Product__Type_OPair_001t__Set__Oset_I_Eo_J_001t__Set__Oset_I_Eo_J,type,
    produc5838405689764958487_set_o: ( set_o * set_o ) > produc7369051934464679207_set_o ).

tff(sy_c_Product__Type_OPair_001t__Set__Oset_It__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
    produc7443773368509356479nteger: ( set_Code_integer * set_Code_integer ) > produc6491284506569428743nteger ).

tff(sy_c_Product__Type_OPair_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J,type,
    produc6363374080413544029et_int: ( set_int * set_int ) > produc2115011035271226405et_int ).

tff(sy_c_Product__Type_OPair_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
    produc4532415448927165861et_nat: ( set_nat * set_nat ) > produc7819656566062154093et_nat ).

tff(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
    produc763777882069021527od_o_o: ( set_Product_prod_o_o * set_Product_prod_o_o ) > produc2934264451710624999od_o_o ).

tff(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    produc8517790099723286449at_nat: ( set_Product_prod_o_o * set_Pr1261947904930325089at_nat ) > produc732395585841259969at_nat ).

tff(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    produc5245064249948416855at_nat: ( set_Pr8551490117392284871at_nat * set_Pr8551490117392284871at_nat ) > produc4193628355235574503at_nat ).

tff(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Nat__Onat,type,
    produc3149970401713881818at_nat: ( set_Pr1261947904930325089at_nat * nat ) > produc366245978424229472at_nat ).

tff(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    produc2922128104949294807at_nat: ( set_Pr1261947904930325089at_nat * set_Pr1261947904930325089at_nat ) > produc3843707927480180839at_nat ).

tff(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    produc9060074326276436823at_nat: ( set_Pr4329608150637261639at_nat * set_Pr4329608150637261639at_nat ) > produc1319942482725812455at_nat ).

tff(sy_c_Product__Type_OPair_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc7462898802507495127at_nat: ( set_se7855581050983116737at_nat * set_se7855581050983116737at_nat ) > produc7299876168958306407at_nat ).

tff(sy_c_Product__Type_OPair_001t__fun_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    produc7264323995540650962nteger: ( fun_Co3460408610320954864e_term * produc8923325533196201883nteger ) > produc7509114972854644512nteger ).

tff(sy_c_Product__Type_OPair_001t__fun_It__Code____Numeral__Onatural_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    produc3379161622255323613atural: ( fun_Co6386927884524458043e_term * produc7822875418678951345atural ) > produc7476732711998919211atural ).

tff(sy_c_Product__Type_OPair_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    produc4729913460834754785nt_int: fun_fu465145433024125141nt_int ).

tff(sy_c_Product__Type_OPair_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    produc5508588179030252311e_term: ( fun_in5730379987311621695e_term * fun_in5730379987311621695e_term ) > produc7249898413471085407e_term ).

tff(sy_c_Product__Type_OPair_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Nat__Onat_M_Eo_J,type,
    produc3725555944217366743_nat_o: ( fun_nat_o * fun_nat_o ) > produc7704145150520151143_nat_o ).

tff(sy_c_Product__Type_OPair_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    produc2818902965508115497at_nat: ( fun_nat_fun_nat_nat * produc7248412053542808358at_nat ) > produc9217583074051984497at_nat ).

tff(sy_c_Product__Type_OPair_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    produc565448451787809096nteger: fun_fu8946524575271555235nteger ).

tff(sy_c_Product__Type_OPair_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    produc2518349463292777741e_term: ( fun_Pr5098669352780829690e_term * fun_Pr5098669352780829690e_term ) > produc8529534078076073941e_term ).

tff(sy_c_Product__Type_OPair_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    produc3399137497101226409atural: ( fun_Pr285225112257423215e_term * produc7822875418678951345atural ) > produc9140211490168418807atural ).

tff(sy_c_Product__Type_OPair_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    produc6017135503889078682et_nat: fun_fu2265384587115734689et_nat ).

tff(sy_c_Product__Type_OPair_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    produc7291855603632349880et_nat: fun_fu3932451362284101085et_nat ).

tff(sy_c_Product__Type_OPair_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
    produc4714251849521319255_nat_o: ( fun_Pr6460944699146269935_nat_o * fun_Pr6460944699146269935_nat_o ) > produc6671579610312156647_nat_o ).

tff(sy_c_Product__Type_OPair_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    produc7320969046608631221nt_int: fun_fu9160953773549289085nt_int ).

tff(sy_c_Product__Type_OPair_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    produc6823973692863303023e_term: ( fun_Pr7763680713840462443e_term * fun_Pr7763680713840462443e_term ) > produc9065761207657906103e_term ).

tff(sy_c_Product__Type_OSigma_001_Eo_001_Eo,type,
    product_Sigma_o_o: ( set_o * fun_o_set_o ) > set_Product_prod_o_o ).

tff(sy_c_Product__Type_OSigma_001_Eo_001t__Int__Oint,type,
    product_Sigma_o_int: ( set_o * fun_o_set_int ) > set_Pr8834758594704517033_o_int ).

tff(sy_c_Product__Type_OSigma_001_Eo_001t__Nat__Onat,type,
    product_Sigma_o_nat: ( set_o * fun_o_set_nat ) > set_Pr2101469702781467981_o_nat ).

tff(sy_c_Product__Type_OSigma_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    produc5882431272649516420nteger: ( set_Code_integer * fun_Co744628173305925485nteger ) > set_Pr4811707699266497531nteger ).

tff(sy_c_Product__Type_OSigma_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
    produc4258167722180586323er_int: ( set_Code_integer * fun_Co5817875961738342972et_int ) > set_Pr6496905503482889930er_int ).

tff(sy_c_Product__Type_OSigma_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
    produc4260658192689636599er_nat: ( set_Code_integer * fun_Co8307959106670069728et_nat ) > set_Pr8986988648414616686er_nat ).

tff(sy_c_Product__Type_OSigma_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    produc6231535905537262655atural: ( set_Code_natural * fun_Co2944084857415636034atural ) > set_Pr2352657477744078772atural ).

tff(sy_c_Product__Type_OSigma_001t__Int__Oint_001_Eo,type,
    product_Sigma_int_o: ( set_int * fun_int_set_o ) > set_Pr903927857289325719_int_o ).

tff(sy_c_Product__Type_OSigma_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
    produc4896867201705524051nteger: ( set_int * fun_in6808926178784942396nteger ) > set_Pr8415741480598773322nteger ).

tff(sy_c_Product__Type_OSigma_001t__Int__Oint_001t__Int__Oint,type,
    produc1453890548195736866nt_int: ( set_int * fun_int_set_int ) > set_Pr958786334691620121nt_int ).

tff(sy_c_Product__Type_OSigma_001t__Int__Oint_001t__Nat__Onat,type,
    produc1456381018704787142nt_nat: ( set_int * fun_int_set_nat ) > set_Pr3448869479623346877nt_nat ).

tff(sy_c_Product__Type_OSigma_001t__Int__Oint_001t__Product____Type__Ounit,type,
    produc2622961094310184599t_unit: ( set_int * fun_in4731230917697954842t_unit ) > set_Pr5889264611543340172t_unit ).

tff(sy_c_Product__Type_OSigma_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_It__Nat__Onat_J,type,
    produc6850429418872557834st_nat: ( set_list_nat * fun_li1191372448985611379st_nat ) > set_Pr3451248702717554689st_nat ).

tff(sy_c_Product__Type_OSigma_001t__List__Olist_It__Nat__Onat_J_001t__Nat__Onat,type,
    produc7466890150575444730at_nat: ( set_list_nat * fun_list_nat_set_nat ) > set_Pr7549493975000385137at_nat ).

tff(sy_c_Product__Type_OSigma_001t__Nat__Onat_001_Eo,type,
    product_Sigma_nat_o: ( set_nat * fun_nat_set_o ) > set_Pr3149072824959771635_nat_o ).

tff(sy_c_Product__Type_OSigma_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
    produc4525213641468679415nteger: ( set_nat * fun_na9118744110877893344nteger ) > set_Pr2406931829603198446nteger ).

tff(sy_c_Product__Type_OSigma_001t__Nat__Onat_001t__Int__Oint,type,
    produc454536836294682310at_int: ( set_nat * fun_nat_set_int ) > set_Pr7995236796853374141at_int ).

tff(sy_c_Product__Type_OSigma_001t__Nat__Onat_001t__List__Olist_It__Nat__Onat_J,type,
    produc5227933103413159546st_nat: ( set_nat * fun_nat_set_list_nat ) > set_Pr698032948827214833st_nat ).

tff(sy_c_Product__Type_OSigma_001t__Nat__Onat_001t__Nat__Onat,type,
    produc457027306803732586at_nat: ( set_nat * fun_nat_set_nat ) > set_Pr1261947904930325089at_nat ).

tff(sy_c_Product__Type_OSigma_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    produc1809337555817847783at_nat: ( set_nat * fun_na7044673412300895210at_nat ) > set_Pr7717912310451564380at_nat ).

tff(sy_c_Product__Type_OSigma_001t__Nat__Onat_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    produc396409126344608333at_nat: ( set_nat * fun_na5670658592214072528at_nat ) > set_Pr1625285437083415874at_nat ).

tff(sy_c_Product__Type_OSigma_001t__Nat__Onat_001t__Product____Type__Ounit,type,
    produc5506539147108004339t_unit: ( set_nat * fun_na896991816813928310t_unit ) > set_Pr4334478416066269672t_unit ).

tff(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    produc6630550384232064845e_term: ( set_Pr4811707699266497531nteger * fun_Pr5305228341155023582e_term ) > set_Pr3944325338781952762e_term ).

tff(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
    produc7293743972641680163_nat_o: ( set_Pr3948176798113811640et_nat * fun_Pr8383423175210966566_nat_o ) > set_Pr3013394129895136920_nat_o ).

tff(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    produc4575053565521557168e_term: ( set_Pr958786334691620121nt_int * fun_Pr9081111800474865985e_term ) > set_Pr4417106977106297437e_term ).

tff(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    produc276578409427628764e_term: ( set_Pr958786334691620121nt_int * fun_Pr4426623609552329069e_term ) > set_Pr3640028372902554249e_term ).

tff(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo,type,
    produc203973861852599583_nat_o: ( set_Pr1261947904930325089at_nat * fun_Pr8467005832278515962_set_o ) > set_Pr6558897299634722526_nat_o ).

tff(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
    produc7672662199629908489at_nat: ( set_Pr1261947904930325089at_nat * fun_Pr9038118721296872730et_nat ) > set_Pr2539167527615954998at_nat ).

tff(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Nat__Onat,type,
    produc1095920968030776047at_nat: ( set_Pr4329608150637261639at_nat * fun_Pr6764980218223570944et_nat ) > set_Pr552903133987017116at_nat ).

tff(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
    produc4533482196970043141_nat_o: ( set_Pr1312406793078187350et_nat * fun_Pr7968690803259750408_nat_o ) > set_Pr7905283282039288826_nat_o ).

tff(sy_c_Product__Type_OSigma_001t__Product____Type__Ounit_001t__Int__Oint,type,
    produc6872886531786962417it_int: ( set_Product_unit * fun_Pr8362234881679108866et_int ) > set_Pr8497134830871917726it_int ).

tff(sy_c_Product__Type_OSigma_001t__Product____Type__Ounit_001t__Nat__Onat,type,
    produc6875377002296012693it_nat: ( set_Product_unit * fun_Pr1628945989756059814et_nat ) > set_Pr1763845938948868674it_nat ).

tff(sy_c_Product__Type_OSigma_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
    produc6121607364029222536t_unit: ( set_Product_unit * fun_Pr3013102738158121955t_unit ) > set_Pr5094982260447487303t_unit ).

tff(sy_c_Product__Type_OSigma_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
    produc105401717395143638et_nat: ( set_set_nat * fun_se3362872515591026879et_nat ) > set_Pr5488025237498180813et_nat ).

tff(sy_c_Product__Type_OSigma_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    produc7726050920695093128at_nat: ( set_se7855581050983116737at_nat * fun_se953073389798102371at_nat ) > set_Pr4329608150637261639at_nat ).

tff(sy_c_Product__Type_OSigma_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    produc1533099051242823152nt_int: ( set_fu3629540756087427317e_term * fun_fu3472058528428720115nt_int ) > set_Pr4166680992137330533nt_int ).

tff(sy_c_Product__Type_OSigma_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    produc5453309460576862807nteger: ( set_fu8280898353253485872e_term * fun_fu5971215405379524186nteger ) > set_Pr3486312109254157132nteger ).

tff(sy_c_Product__Type_OSigma_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    produc6971759541029228329et_nat: ( set_fu3555266933746557007_nat_o * fun_fu2890809920214373946et_nat ) > set_Pr1312406793078187350et_nat ).

tff(sy_c_Product__Type_OSigma_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    produc5673588578087545031et_nat: ( set_fu3555266933746557007_nat_o * fun_fu8357309440898100312et_nat ) > set_Pr4040394263813967220et_nat ).

tff(sy_c_Product__Type_OSigma_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    produc3974764367135812292nt_int: ( set_fu5653557704672872225e_term * fun_fu4219362280553733319nt_int ) > set_Pr6700895561065273913nt_int ).

tff(sy_c_Product__Type_OUnity,type,
    product_Unity: product_unit ).

tff(sy_c_Product__Type_Oapfst_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    produc3195571438000033749nteger: fun_fu4800041728187187127nteger ).

tff(sy_c_Product__Type_Oapfst_001t__Code____Numeral__Ointeger_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Code____Numeral__Ointeger,type,
    produc1373560857238714551nteger: ( fun_Co1966082167426949785e_term * produc8923325533196201883nteger ) > produc2752406535750279421nteger ).

tff(sy_c_Product__Type_Oapfst_001t__Code____Numeral__Ointeger_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    produc4855684316150773471nt_int: ( fun_Co1966082167426949785e_term * produc382792921321436433nt_int ) > produc4788131091073775919nt_int ).

tff(sy_c_Product__Type_Oapfst_001t__Code____Numeral__Ointeger_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Code____Numeral__Ointeger,type,
    produc7864119354571335282nteger: ( fun_Co3668495603736800980e_term * produc8923325533196201883nteger ) > produc2402493665305094840nteger ).

tff(sy_c_Product__Type_Oapfst_001t__Code____Numeral__Ointeger_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    produc8945651981546028870nteger: ( fun_Co3668495603736800980e_term * produc3346328345660746739nteger ) > produc2453742332425399446nteger ).

tff(sy_c_Product__Type_Oapfst_001t__Code____Numeral__Ointeger_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Code____Numeral__Ointeger,type,
    produc8160162946510343411nteger: ( fun_Co9016714620104711083_nat_o * produc8923325533196201883nteger ) > produc3954786194548828667nteger ).

tff(sy_c_Product__Type_Oapfst_001t__Code____Numeral__Ointeger_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    produc4116213131564642456et_nat: ( fun_Co9016714620104711083_nat_o * produc8299537390109905600et_nat ) > produc8799533983703829792et_nat ).

tff(sy_c_Product__Type_Oapfst_001t__Code____Numeral__Ointeger_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Code____Numeral__Ointeger,type,
    produc444321889415134435nteger: ( fun_Co4988957157240174789e_term * produc8923325533196201883nteger ) > produc1284174907132067113nteger ).

tff(sy_c_Product__Type_Oapfst_001t__Code____Numeral__Ointeger_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    produc8228542470718774195nt_int: ( fun_Co4988957157240174789e_term * produc382792921321436433nt_int ) > produc3043004577601930755nt_int ).

tff(sy_c_Product__Type_Oapfst_001t__Code____Numeral__Onatural_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    produc4623092060929046819atural: fun_Co7398788559141407565atural > fun_Pr6891710885006071673atural ).

tff(sy_c_Product__Type_Oapfst_001t__Code____Numeral__Onatural_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    produc8013365792570017484atural: ( fun_Co298994598804093668e_term * produc5835291356934675326atural ) > produc714035400761762599atural ).

tff(sy_c_Product__Type_Oapfst_001t__Code____Numeral__Onatural_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    produc5719200830196637908nt_int: ( fun_Co298994598804093668e_term * produc5665947927044467078nt_int ) > produc4788131091073775919nt_int ).

tff(sy_c_Product__Type_Oapfst_001t__Code____Numeral__Onatural_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    produc7959249324659417101et_nat: ( fun_Co2051191115980488992_nat_o * produc5111566536631596683et_nat ) > produc8799533983703829792et_nat ).

tff(sy_c_Product__Type_Oapfst_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
    produc2355237562570658114nt_int: fun_int_int > fun_Pr2478283820680522243nt_int ).

tff(sy_c_Product__Type_Oapfst_001t__Int__Oint_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Int__Oint,type,
    produc6429934853825515733rm_int: ( fun_in94812177438132456e_term * product_prod_int_int ) > produc1164942017926883148rm_int ).

tff(sy_c_Product__Type_Oapfst_001t__Int__Oint_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    produc1852316473262731728nt_int: ( fun_in94812177438132456e_term * produc759720530913461378nt_int ) > produc4788131091073775919nt_int ).

tff(sy_c_Product__Type_Oapfst_001t__Int__Oint_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Int__Oint,type,
    produc3213193131064493712rm_int: ( fun_in7158797356850311459e_term * product_prod_int_int ) > produc8574895079301897479rm_int ).

tff(sy_c_Product__Type_Oapfst_001t__Int__Oint_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    produc8552504676914255415nteger: ( fun_in7158797356850311459e_term * produc6162884466328367972nteger ) > produc2453742332425399446nteger ).

tff(sy_c_Product__Type_Oapfst_001t__Int__Oint_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Int__Oint,type,
    produc2698142598960073523_o_int: ( fun_in1927439276604979228_nat_o * product_prod_int_int ) > produc217860453747927114_o_int ).

tff(sy_c_Product__Type_Oapfst_001t__Int__Oint_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    produc2858799776146633481et_nat: ( fun_in1927439276604979228_nat_o * produc8065447618272157327et_nat ) > produc8799533983703829792et_nat ).

tff(sy_c_Product__Type_Oapfst_001t__Int__Oint_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Int__Oint,type,
    produc1502976015219776769rm_int: ( fun_in237891044757944084e_term * product_prod_int_int ) > produc6693577919049233272rm_int ).

tff(sy_c_Product__Type_Oapfst_001t__Int__Oint_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    produc7648640027116863140nt_int: ( fun_in237891044757944084e_term * produc759720530913461378nt_int ) > produc3043004577601930755nt_int ).

tff(sy_c_Product__Type_Oapfst_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    produc5901819666759714173nt_int: ( fun_fu4810317505167811835e_term * produc4788131091073775919nt_int ) > produc4788131091073775919nt_int ).

tff(sy_c_Product__Type_Oapfst_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    produc479425830829021777nt_int: ( fun_fu1176768540439120679e_term * produc4788131091073775919nt_int ) > produc3043004577601930755nt_int ).

tff(sy_c_Product__Type_Oapfst_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    produc183566614307960809nteger: ( fun_fu2505754153367914865e_term * produc2453742332425399446nteger ) > produc2453742332425399446nteger ).

tff(sy_c_Product__Type_Oapfst_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    produc1926458052860118910et_nat: fun_fu8419763957888848259_nat_o > fun_Pr836988951548913597et_nat ).

tff(sy_c_Product__Type_Oapfst_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    produc7064264152226348700et_nat: ( fun_fu8419763957888848259_nat_o * produc3112576180687729086et_nat ) > produc3112576180687729086et_nat ).

tff(sy_c_Product__Type_Oapfst_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    produc7965835600623382609nt_int: ( fun_fu4835546211937200935e_term * produc3043004577601930755nt_int ) > produc4788131091073775919nt_int ).

tff(sy_c_Product__Type_Oapfst_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    produc7857123342865048869nt_int: ( fun_fu836511555612062035e_term * produc3043004577601930755nt_int ) > produc3043004577601930755nt_int ).

tff(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    produc6499014454317279255nteger: fun_fu4800041728187187127nteger ).

tff(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger,type,
    produc7166930624044334813nteger: ( fun_Co6597186368970283863nteger * produc8923325533196201883nteger ) > produc3346328345660746739nteger ).

tff(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    produc2089341081295086202e_term: ( fun_Co6597186368970283863nteger * produc2402493665305094840nteger ) > produc2453742332425399446nteger ).

tff(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Code____Numeral__Ointeger,type,
    produc7246245855585345468nteger: ( fun_Co4803750647967840348et_nat * produc8923325533196201883nteger ) > produc8299537390109905600et_nat ).

tff(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
    produc3435428346196091856_nat_o: ( fun_Co4803750647967840348et_nat * produc3954786194548828667nteger ) > produc8799533983703829792et_nat ).

tff(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Code____Numeral__Ointeger,type,
    produc3535056655957556987nteger: ( fun_Co4113693717567439989nt_int * produc8923325533196201883nteger ) > produc382792921321436433nt_int ).

tff(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    produc6970591705382700509e_term: ( fun_Co4113693717567439989nt_int * produc2752406535750279421nteger ) > produc4788131091073775919nt_int ).

tff(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    produc2185162023461554697e_term: ( fun_Co4113693717567439989nt_int * produc1284174907132067113nteger ) > produc3043004577601930755nt_int ).

tff(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
    produc5043883716779652157nteger: ( fun_Co1561183069634336733nteger * produc8923325533196201883nteger ) > produc8903623710181579841nteger ).

tff(sy_c_Product__Type_Oapsnd_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
    produc4463282112584876420nt_int: fun_int_int > fun_Pr2478283820680522243nt_int ).

tff(sy_c_Product__Type_Oapsnd_001t__Int__Oint_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Int__Oint,type,
    produc2935421404040714269er_int: ( fun_in4744367027289715400nteger * product_prod_int_int ) > produc6162884466328367972nteger ).

tff(sy_c_Product__Type_Oapsnd_001t__Int__Oint_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    produc5655117854151192939e_term: ( fun_in4744367027289715400nteger * produc8574895079301897479rm_int ) > produc2453742332425399446nteger ).

tff(sy_c_Product__Type_Oapsnd_001t__Int__Oint_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Int__Oint,type,
    produc9121118195053341018at_int: ( fun_in4666789911842550827et_nat * product_prod_int_int ) > produc8065447618272157327et_nat ).

tff(sy_c_Product__Type_Oapsnd_001t__Int__Oint_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
    produc1318474093340237377_nat_o: ( fun_in4666789911842550827et_nat * produc217860453747927114_o_int ) > produc8799533983703829792et_nat ).

tff(sy_c_Product__Type_Oapsnd_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint,type,
    produc6100211334659168315nt_int: ( fun_in4211310926729683942nt_int * product_prod_int_int ) > produc759720530913461378nt_int ).

tff(sy_c_Product__Type_Oapsnd_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    produc4251495004083222734e_term: ( fun_in4211310926729683942nt_int * produc1164942017926883148rm_int ) > produc4788131091073775919nt_int ).

tff(sy_c_Product__Type_Oapsnd_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    produc5266752770087298298e_term: ( fun_in4211310926729683942nt_int * produc6693577919049233272rm_int ) > produc3043004577601930755nt_int ).

tff(sy_c_Product__Type_Oapsnd_001t__Num__Onum_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    produc7418200839687411156nteger: ( fun_num_Code_integer * produc7142191362829087448er_num ) > produc8923325533196201883nteger ).

tff(sy_c_Product__Type_Oapsnd_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    produc2265439103302406840e_term: ( fun_Pr5876161306168176259nteger * produc2453742332425399446nteger ) > produc2453742332425399446nteger ).

tff(sy_c_Product__Type_Oapsnd_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Code____Numeral__Onatural,type,
    produc4464772112783624294atural: fun_Pr74676805955934211atural > fun_Pr6891710885006071673atural ).

tff(sy_c_Product__Type_Oapsnd_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Code____Numeral__Onatural,type,
    produc1304257963789341151atural: ( fun_Pr7425815736541306438et_nat * produc5835291356934675326atural ) > produc5111566536631596683et_nat ).

tff(sy_c_Product__Type_Oapsnd_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Code____Numeral__Onatural,type,
    produc5167862320620071534atural: ( fun_Pr5596209257725365771nt_int * produc5835291356934675326atural ) > produc5665947927044467078nt_int ).

tff(sy_c_Product__Type_Oapsnd_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    produc5989561616416747397e_term: ( fun_Pr5596209257725365771nt_int * produc714035400761762599atural ) > produc4788131091073775919nt_int ).

tff(sy_c_Product__Type_Oapsnd_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
    produc1991759244683392747_nat_o: fun_Pr7091840695141096449et_nat > fun_Pr836988951548913597et_nat ).

tff(sy_c_Product__Type_Oapsnd_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
    produc4622684310891945677_nat_o: ( fun_Pr4885567672785483807et_nat * produc8799533983703829792et_nat ) > produc3112576180687729086et_nat ).

tff(sy_c_Product__Type_Oapsnd_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    produc2254893824690362237e_term: ( fun_Pr2478283820680522243nt_int * produc4788131091073775919nt_int ) > produc4788131091073775919nt_int ).

tff(sy_c_Product__Type_Oapsnd_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    produc8061333830752525225e_term: ( fun_Pr2478283820680522243nt_int * produc3043004577601930755nt_int ) > produc3043004577601930755nt_int ).

tff(sy_c_Product__Type_Oapsnd_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
    produc174852792182663501_nat_o: ( fun_Pr2813956079162534559et_nat * produc3112576180687729086et_nat ) > produc8799533983703829792et_nat ).

tff(sy_c_Product__Type_Oapsnd_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
    produc2056317742435807279_nat_o: ( fun_Pr836988951548913597et_nat * produc3112576180687729086et_nat ) > produc3112576180687729086et_nat ).

tff(sy_c_Product__Type_Ocurry_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
    produc1016772743285680337nt_int: fun_Pr982841511892225912nt_int > fun_int_fun_int_int ).

tff(sy_c_Product__Type_Ocurry_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    produc8249235968001453780nt_int: fun_Pr2478283820680522243nt_int > fun_in1696471567231710611nt_int ).

tff(sy_c_Product__Type_Ocurry_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
    produc8871627978511607229at_nat: fun_Pr2602117396471556196at_nat > fun_nat_fun_nat_nat ).

tff(sy_c_Product__Type_Ocurry_001t__Nat__Onat_001t__Nat__Onat_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
    produc2062876521443793799_nat_o: fun_Pr2028404973800837934_nat_o > fun_na5914473681949881652_nat_o ).

tff(sy_c_Product__Type_Ocurry_001t__Nat__Onat_001t__Nat__Onat_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    produc4701859392678344816at_nat: fun_Pr2477239776880934807at_nat > fun_na1668100129766719005at_nat ).

tff(sy_c_Product__Type_Ocurry_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo,type,
    produc2168430993391648169_int_o: fun_Pr1196100989263358594_int_o > fun_fu2978539155105838238_int_o ).

tff(sy_c_Product__Type_Ocurry_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_Eo,type,
    produc177509963858859394eger_o: fun_Pr7015759342434529115eger_o > fun_fu7695273699059480439eger_o ).

tff(sy_c_Product__Type_Ocurry_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001_Eo,type,
    produc4701769847872139056_nat_o: fun_Pr2620521676128474833_nat_o > fun_fu8419763957888848259_nat_o ).

tff(sy_c_Product__Type_Ocurry_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001_Eo,type,
    produc3333590387107866898_nat_o: fun_Pr1227177680593602867_nat_o > fun_fu2611741329380808165_nat_o ).

tff(sy_c_Product__Type_Ocurry_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo,type,
    produc443495763101479893_int_o: fun_Pr3540825087398332590_int_o > fun_fu6865642474282033866_int_o ).

tff(sy_c_Product__Type_Ointernal__case__prod_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
    produc7926200574084438792nt_int: fun_fu5207212825597307859nt_int ).

tff(sy_c_Product__Type_Ointernal__case__prod_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    produc297006045350968285nt_int: fun_fu6741006549690681129nt_int ).

tff(sy_c_Product__Type_Ointernal__case__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
    produc6557683772455589876at_nat: fun_fu5660447535128473811at_nat ).

tff(sy_c_Product__Type_Ointernal__case__prod_001t__Nat__Onat_001t__Nat__Onat_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
    produc9189008374811844670_nat_o: fun_fu2847332191311216467_nat_o ).

tff(sy_c_Product__Type_Ointernal__case__prod_001t__Nat__Onat_001t__Nat__Onat_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    produc8104577556401574439at_nat: fun_fu2716251949043459987at_nat ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001_Eo,type,
    produc2066375834425727024eger_o: fun_Co2081214437782444048eger_o > fun_Pr7211993375558241536eger_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    produc7469247390737344965nteger: ( fun_Co1981900195452921617nteger * produc8923325533196201883nteger ) > code_integer ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
    produc1553301316500091796er_int: ( fun_Co1092983284983208416er_int * produc8923325533196201883nteger ) > int ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
    produc1555791787009142072er_nat: ( fun_Co3583066429914935172er_nat * produc8923325533196201883nteger ) > nat ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
    produc7336495610019696514er_num: ( fun_Co8521658056209057742er_num * produc8923325533196201883nteger ) > num ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
    produc9125791028180074456eger_o: ( fun_Co3544761417380347684eger_o * produc8923325533196201883nteger ) > produc6271795597528267376eger_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    produc6916734918728496179nteger: fun_Co2470855966376689427nteger > fun_Pr5876161306168176259nteger ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    produc4281629032016041417nteger: ( fun_Co1561183069634336733nteger * produc3346328345660746739nteger ) > produc8923325533196201883nteger ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Onatural_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    produc8282080750456430313atural: ( fun_Co1890133979025130057atural * produc7822875418678951345atural ) > produc6756470014200349799atural ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001_Eo,type,
    produc7358226366420480123ural_o: fun_Co9066792663755620495ural_o > fun_Pr513970351136536563ural_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    produc6302656368764539796atural: ( fun_Co1851440197950133416atural * produc5835291356934675326atural ) > produc7822875418678951345atural ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Code____Numeral__Onatural_J,type,
    produc6785097126449100389atural: fun_Co3643010573817537149atural > fun_Pr4028877673837371139atural ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Heap__Oarray_Itf__a_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_001t__Heap__Oarray_Itf__a_J,type,
    produc8767961711439910440rray_a: fun_ar6017029185804945652rray_a > fun_Pr8833188457053967342rray_a ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Heap__Oarray_Itf__a_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
    produc7016084256669755260t_unit: fun_ar121531768175530460t_unit > fun_Pr3456093102767711692t_unit ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Heap__Oarray_Itf__a_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_001t__Nat__Onat,type,
    produc6028340861379781217at_nat: fun_ar8857663332695973421at_nat > fun_Pr515337093925520551at_nat ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Heap__Oarray_Itf__a_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    produc8915672860170107321it_nat: fun_ar7427004957847640857it_nat > fun_Pr8118912048244921225it_nat ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Heap__Oarray_Itf__a_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    produc3495058329975564393it_nat: fun_ar4934926718671674165it_nat > fun_Pr245379829043246639it_nat ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Nat__Onat_001t__Heap__Oarray_Itf__a_J,type,
    produc2025300630104146186rray_a: fun_he4035479571739904452rray_a > fun_Pr8777304358194983264rray_a ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Nat__Onat_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
    produc9092781844693468442t_unit: fun_he6845747896722556172t_unit > fun_Pr2419607445322970330t_unit ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Nat__Onat_001t__Nat__Onat,type,
    produc4278983685114131267at_nat: fun_he5369522480449343229at_nat > fun_Pr4343998633453697049at_nat ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Nat__Onat_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    produc921929042997482327it_nat: fun_he2390400765173608009it_nat > fun_Pr192538292188806807it_nat ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Nat__Onat_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    produc7488178964372371019it_nat: fun_he8369595706569872389it_nat > fun_Pr5651933991979716257it_nat ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Nat__Onat_001t__Product____Type__Ounit,type,
    produc1863717115126956122t_unit: fun_he8708342781048922188t_unit > fun_Pr9045474026565384218t_unit ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
    produc4947309494688390418_int_o: fun_int_fun_int_o > fun_Pr3238374608701176162_int_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
    produc8211389475949308722nt_int: fun_fu5207212825597307859nt_int ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    produc4245557441103728435nt_int: fun_fu6741006549690681129nt_int ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_It__Nat__Onat_J_001_Eo,type,
    produc6382697403170970154_nat_o: fun_li1025265955262268170_nat_o > fun_Pr5375745717004158586_nat_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__List__Olist_It__Nat__Onat_J_001t__Nat__Onat_001_Eo,type,
    produc7308574044827705018_nat_o: fun_li2421049240157457050_nat_o > fun_Pr7575312783043447050_nat_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Int__Oint_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J,type,
    produc1728318271963197120er_int: fun_na937208397672391712er_int > fun_Pr3118124138693225744er_int ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
    produc1486167065449562675at_int: fun_na7450791247808564371at_int > fun_Pr7754697619089165059at_int ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__List__Olist_It__Nat__Onat_J_001_Eo,type,
    produc5265810065896090426_nat_o: fun_na7234455742697417626_nat_o > fun_Pr961374740995693450_nat_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
    produc6081775807080527818_nat_o: fun_fu6778223257468740055_nat_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint,type,
    produc6840382203811409530at_int: fun_nat_fun_nat_int > fun_Pr7647638413817135296at_int ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__List__Olist_It__Nat__Onat_J,type,
    produc2761476792215241774st_nat: ( fun_na819858167508000762st_nat * product_prod_nat_nat ) > list_nat ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
    produc6842872674320459806at_nat: fun_fu5660447535128473811at_nat ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    produc39701218431283661nteger: fun_na5644505769342238765nteger > fun_Pr5056853159479207325nteger ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J,type,
    produc9191653645064861724er_int: fun_na7153028460132482940er_int > fun_Pr110572164298541164er_int ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J,type,
    produc4146132627719282624er_nat: fun_na2743204842065625888er_nat > fun_Pr2600655309230267920er_nat ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Code____Numeral__Ointeger_J,type,
    produc675454393454366620nteger: fun_na5353050896416397052nteger > fun_Pr2029408141414424556nteger ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J,type,
    produc3625529712395680143nt_nat: fun_na7356754204550075887nt_nat > fun_Pr4305413282503136351nt_nat ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J,type,
    produc303800833217521984nteger: fun_na3504973565017656480nteger > fun_Pr5243970527273625488nteger ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
    produc7671697017840204687at_int: fun_na8547874228452562927at_int > fun_Pr8851780599733163615at_int ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    produc2626176000494625587at_nat: fun_na4138050610385705875at_nat > fun_Pr2118491707810114563at_nat ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    produc8197505143624133779at_nat: fun_na1790740735814032627at_nat > fun_Pr1469247711798767971at_nat ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
    produc6395135316500328296_nat_o: fun_fu2847332191311216467_nat_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    produc4528391901023682385at_nat: fun_fu2716251949043459987at_nat ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Option__Ooption_It__Num__Onum_J,type,
    produc478579273971653890on_num: ( fun_na7595719129879163854on_num * product_prod_nat_num ) > option_num ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_Eo,type,
    produc7997411485876045171_nat_o: fun_na4518284863240432007_nat_o > fun_Pr8338385031646565611_nat_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J,type,
    produc5481773914224270406_nat_o: fun_na7109657165716327514_nat_o > fun_Pr4146420783962613950_nat_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    produc1137639668546780417nteger: fun_Pr8371818785129130299nteger > fun_Pr6966570558394395095nteger ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    produc1198152457851389869atural: fun_Pr3688637647703109351atural > fun_Pr3377396784085331203atural ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    produc1257024432443326049et_nat: fun_Pr5259258551928531321et_nat > fun_Pr5416369060549219583et_nat ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    produc8624921108698535677nt_int: fun_Pr4353654455642104759nt_int > fun_Pr3284083897292419283nt_int ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    produc4605791130040086525nt_int: fun_Pr8826142978676617911nt_int > fun_Pr5010838083610845651nt_int ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo,type,
    produc6590410687421337004_nat_o: fun_Pr2028404973800837934_nat_o > fun_Pr363642936170290612_nat_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001_Eo,type,
    produc7830147906768200158_nat_o: fun_Pr4146420783962613950_nat_o > fun_Pr6861956506527726894_nat_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J_001_Eo,type,
    produc8701595406162815018_nat_o: fun_Pr5440946310329839626_nat_o > fun_Pr2493370495569891450_nat_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001_Eo,type,
    produc1561160019221259564_nat_o: fun_Pr5947183769845927726_nat_o > fun_Pr5502292500389099060_nat_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    produc5430029401411191265et_nat: fun_Pr8737872353715570297et_nat > fun_Pr8630787502178681855et_nat ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Ounit_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
    produc6568152436032731486t_unit: fun_Pr7459525001844076368t_unit > fun_Pr1970694993525554974t_unit ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Ounit_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_001t__Nat__Onat,type,
    produc5629734405777326591at_nat: fun_Pr3587966566883452857at_nat > fun_Pr367382672041210069at_nat ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Ounit_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    produc875294279294635931it_nat: fun_Pr2979129825601314957it_nat > fun_Pr7518090501403545819it_nat ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Ounit_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    produc1230459020282432263it_nat: fun_Pr925140355916870337it_nat > fun_Pr7644814098969791837it_nat ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Product____Type__Ounit_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_001t__Product____Type__Ounit,type,
    produc5075907435489727646t_unit: fun_Pr2049426570021530256t_unit > fun_Pr7475791014719349342t_unit ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J_001_Eo,type,
    produc6247414631856714078_nat_o: fun_se2170385732985038782_nat_o > fun_Pr3947133745332865710_nat_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Nat__Onat_001_Eo,type,
    produc3595121349294487249_nat_o: fun_se7755072775241076291_nat_o > fun_Pr1057819736042215569_nat_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Nat__Onat_001t__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J_M_Eo_J,type,
    produc6627902574045077578_nat_o: fun_se7979130632333208764_nat_o > fun_Pr5440946310329839626_nat_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_Eo,type,
    produc410239310623530412_nat_o: fun_fu3198693465525813493_nat_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Int__Oint,type,
    produc3999165221712921880at_int: fun_se5286484986886725186at_int > fun_Pr6298746545499001766at_int ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Nat__Onat,type,
    produc4001655692221972156at_nat: fun_se7776568131818451942at_nat > fun_Pr1253225528153422666at_nat ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J,type,
    produc7150000874791569568_nat_o: fun_se5316394792625908170_nat_o > fun_Pr5947183769845927726_nat_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001_Eo,type,
    produc1491100424724016556_nat_o: fun_se7001366092147120942_nat_o > fun_Pr7663348063272484276_nat_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo,type,
    produc7271678899836001034_int_o: fun_fu5894409982295737917_int_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    produc7102243260366339645nt_int: fun_fu465145433024125141nt_int > fun_Pr5152393401594413531nt_int ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_I_Eo_J,type,
    produc8509172437693241834_set_o: ( fun_fu4618385802829667198_set_o * produc4788131091073775919nt_int ) > set_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J,type,
    produc833192924009095408et_int: ( fun_fu4266222366127506568et_int * produc4788131091073775919nt_int ) > set_int ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__Nat__Onat_J,type,
    produc5011043943518292116et_nat: ( fun_fu9079770784915425324et_nat * produc4788131091073775919nt_int ) > set_nat ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    produc8603558621761785811at_nat: ( fun_fu6029601804184707687at_nat * produc4788131091073775919nt_int ) > set_Pr1261947904930325089at_nat ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Nat__Onat_M_Eo_J_001_Eo,type,
    produc8121780756122614700at_o_o: fun_fu7564235448449272366at_o_o > fun_Pr6629464623532871604at_o_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_Eo,type,
    produc7373287791920631523eger_o: fun_fu7060041198443644797eger_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    produc697581972998607883nteger: fun_fu8946524575271555235nteger > fun_Pr3905736301278533417nteger ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_I_Eo_J,type,
    produc8770320508000790979_set_o: ( fun_fu6788480576040630871_set_o * produc2453742332425399446nteger ) > set_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Int__Oint_J,type,
    produc1986806150084229463et_int: ( fun_fu6941240126142778863et_int * produc2453742332425399446nteger ) > set_int ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Nat__Onat_J,type,
    produc6164657169593426171et_nat: ( fun_fu2531416508075921811et_nat * produc2453742332425399446nteger ) > set_nat ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001_Eo,type,
    produc2915205735004773393_nat_o: fun_fu3464598166661278695_nat_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    produc1949718844479134567et_nat: fun_fu2265384587115734689et_nat > fun_Pr836988951548913597et_nat ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Set__Oset_I_Eo_J,type,
    produc330442800291577585_set_o: ( fun_fu4934440599869564003_set_o * produc8799533983703829792et_nat ) > set_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Set__Oset_It__Int__Oint_J,type,
    produc2069798332927708073et_int: ( fun_fu4495862163342753507et_int * produc8799533983703829792et_nat ) > set_int ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Set__Oset_It__Nat__Onat_J,type,
    produc6247649352436904781et_nat: ( fun_fu86038545275896455et_nat * produc8799533983703829792et_nat ) > set_nat ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001_Eo,type,
    produc4465912260561112435_nat_o: fun_fu5983609555712719719_nat_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    produc2255458887868536227et_nat: fun_fu3932451362284101085et_nat > fun_Pr6662792608368940153et_nat ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo,type,
    produc2207054017359051062_int_o: fun_fu2458202332514215229_int_o ).

tff(sy_c_Product__Type_Oprod_Ocase__prod_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    produc6823905543215200229nt_int: fun_fu9160953773549289085nt_int > fun_Pr5846521507401124227nt_int ).

tff(sy_c_Product__Type_Oprod_Ofst_001_Eo_001_Eo,type,
    product_fst_o_o: fun_Pr6984036127010467572_o_o_o ).

tff(sy_c_Product__Type_Oprod_Ofst_001_Eo_001t__Int__Oint,type,
    product_fst_o_int: fun_Pr1358870568642713662_int_o ).

tff(sy_c_Product__Type_Oprod_Ofst_001_Eo_001t__Nat__Onat,type,
    product_fst_o_nat: fun_Pr3604015536313159578_nat_o ).

tff(sy_c_Product__Type_Oprod_Ofst_001_Eo_001t__Num__Onum,type,
    product_fst_o_num: fun_Pr4362196099282670544_num_o ).

tff(sy_c_Product__Type_Oprod_Ofst_001_Eo_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    produc1440270732834495325it_nat: fun_Pr914940982395022178_nat_o ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    produc8508995932063986495nteger: fun_Pr6596356882939945227nteger ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
    produc8630172574501217550er_int: fun_Pr2725840997377004378nteger ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
    produc8632663045010267826er_nat: fun_Pr5940403383236205310nteger ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    produc1861665112190112313nteger: produc3346328345660746739nteger > code_integer ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    produc497848011034438852atural: fun_Pr5131589689703537955atural ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Heap__Oarray_Itf__a_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
    produc491454361838572648it_nat: produc6714399278180371524it_nat > array_a ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Nat__Onat,type,
    produc2838810277069100634it_nat: produc6653097349344004940it_nat > heap_e7401611519738050253t_unit ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001_Eo,type,
    product_fst_int_o: fun_Pr5835976712988771210_o_int ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
    produc45500017171379470nteger: fun_Pr907818707165963561er_int ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Int__Oint,type,
    product_fst_int_int: fun_Pr982841511892225912nt_int ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Nat__Onat,type,
    product_fst_int_nat: fun_Pr8019291974053979932at_int ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Num__Onum,type,
    product_fst_int_num: fun_Pr814315031165377638um_int ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001_Eo,type,
    product_fst_nat_o: fun_Pr103879662602641546_o_nat ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
    produc8897218493789310642nteger: fun_Pr7395487658768111217er_nat ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Int__Oint,type,
    product_fst_nat_int: fun_Pr4789038971164577984nt_nat ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Nat__Onat,type,
    product_fst_nat_nat: fun_Pr2602117396471556196at_nat ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Num__Onum,type,
    product_fst_nat_num: fun_Pr4620512490437729710um_nat ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    produc5854401122675660893it_nat: fun_Pr8519750050727906972at_nat ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Num__Onum_001t__Num__Onum,type,
    product_fst_num_num: fun_Pr3269564255357226306um_num ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    produc3658391496133417298e_term: produc592931078481472324e_term > produc8923325533196201883nteger ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Code____Numeral__Onatural,type,
    produc4353917038236142998atural: fun_Pr7406272072912987266atural ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    produc1537665297809786051atural: fun_Pr6967485491430695501atural ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
    produc5647884604762787496_nat_o: produc2739566037923759970_nat_o > produc3658429121746597890et_nat ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    produc7504962776628944053e_term: produc5464280974217902119e_term > product_prod_int_int ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    produc8655982770948792545e_term: produc4155239895104388691e_term > product_prod_int_int ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Num__Onum,type,
    produc1179527155093393624at_num: fun_Pr8866567302531502864at_nat ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
    produc2938390969378414602_nat_o: produc6858501863712832324_nat_o > produc8799533983703829792et_nat ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Product____Type__Ounit_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
    produc4530234641508181270it_nat: produc8664842809031399944it_nat > product_unit ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    produc6011863565407846595at_nat: fun_Pr6212429452034653949at_nat ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    produc4463008262350210037nt_int: fun_Pr7653582204007996523e_term ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Nat__Onat_M_Eo_J,type,
    produc4111623175521333955_nat_o: fun_Pr8136591464420530493_nat_o ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    produc2481150572478215260nteger: fun_Pr4557384415951816845e_term ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    produc5325900173150335662et_nat: fun_Pr3233114924583728296_nat_o ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    produc4078497350495916492et_nat: fun_Pr7618159474455865098_nat_o ).

tff(sy_c_Product__Type_Oprod_Ofst_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    produc3130796691802200265nt_int: fun_Pr5872836680101629291e_term ).

tff(sy_c_Product__Type_Oprod_Osnd_001_Eo_001_Eo,type,
    product_snd_o_o: fun_Pr6984036127010467572_o_o_o ).

tff(sy_c_Product__Type_Oprod_Osnd_001_Eo_001t__Int__Oint,type,
    product_snd_o_int: fun_Pr3595050827490992028nt_int ).

tff(sy_c_Product__Type_Oprod_Osnd_001_Eo_001t__Nat__Onat,type,
    product_snd_o_nat: fun_Pr5585980272307166948at_nat ).

tff(sy_c_Product__Type_Oprod_Osnd_001_Eo_001t__Num__Onum,type,
    product_snd_o_num: product_prod_o_num > num ).

tff(sy_c_Product__Type_Oprod_Osnd_001_Eo_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    produc5978051280710547099it_nat: produc2900562427881843919it_nat > produc8664842809031399944it_nat ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    produc6174133586879617921nteger: fun_Pr6596356882939945227nteger ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
    produc1514845087660660048er_int: fun_Pr9023817884608220585nt_int ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
    produc1517335558169710324er_nat: fun_Pr1791375292569619697at_nat ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    produc7955729907432593271nteger: produc3346328345660746739nteger > produc8923325533196201883nteger ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    produc6591912806276919810atural: fun_Pr2136124334875798924atural ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__Heap__Oarray_Itf__a_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
    produc6991280839920081578it_nat: produc6714399278180371524it_nat > produc6653097349344004940it_nat ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Nat__Onat,type,
    produc2594868675584459928it_nat: produc6653097349344004940it_nat > nat ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001_Eo,type,
    product_snd_int_o: fun_Pr1059884994059025616nt_o_o ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
    produc2153544567185597776nteger: fun_Pr3662307866719382234nteger ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
    product_snd_int_int: fun_Pr982841511892225912nt_int ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Nat__Onat,type,
    product_snd_int_nat: fun_Pr2973770956708400832at_nat ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Num__Onum,type,
    product_snd_int_num: product_prod_int_num > num ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001_Eo,type,
    product_snd_nat_o: fun_Pr2976697613021001844at_o_o ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
    produc1781891006948753140nteger: fun_Pr4523587930069869694nteger ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Int__Oint,type,
    product_snd_nat_int: fun_Pr611187951655381276nt_int ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Nat__Onat,type,
    product_snd_nat_nat: fun_Pr2602117396471556196at_nat ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Num__Onum,type,
    product_snd_nat_num: product_prod_nat_num > num ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    produc8417671938598930591it_nat: produc3839731585411834681it_nat > produc8664842809031399944it_nat ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__Num__Onum_001t__Num__Onum,type,
    product_snd_num_num: fun_Pr3269564255357226306um_num ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    produc7766732615400916880e_term: produc592931078481472324e_term > fun_Pr5098669352780829690e_term ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    produc7455300194457530885atural: fun_Pr6967485491430695501atural ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
    produc5282040756795020774_nat_o: produc2739566037923759970_nat_o > fun_Pr6460944699146269935_nat_o ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    produc1448379345012327155e_term: produc5464280974217902119e_term > fun_in5730379987311621695e_term ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    produc7082206506123769631e_term: produc4155239895104388691e_term > fun_Pr7763680713840462443e_term ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Num__Onum,type,
    produc8847702614181477910at_num: produc9082142974458947146at_num > num ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
    produc7941837674541168712_nat_o: produc6858501863712832324_nat_o > fun_Pr6460944699146269935_nat_o ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__Product____Type__Ounit_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
    produc8604850587836428116it_nat: produc8664842809031399944it_nat > produc6653097349344004940it_nat ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    produc2937545259423399429at_nat: fun_Pr6212429452034653949at_nat ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    produc7629796867588368947nt_int: fun_Pr1552678306225191715nt_int ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Nat__Onat_M_Eo_J,type,
    produc3666050907618188293_nat_o: fun_Pr8136591464420530493_nat_o ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    produc6589491691745714842nteger: fun_Pr6160931176198666718nteger ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    produc4960056325182568940et_nat: fun_Pr2813956079162534559et_nat ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    produc9081944055658670602et_nat: fun_Pr2953255705995765467et_nat ).

tff(sy_c_Product__Type_Oprod_Osnd_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    produc1557020426977177351nt_int: fun_Pr1987159835869338959nt_int ).

tff(sy_c_Product__Type_Oscomp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    produc5538323210962509403atural: ( fun_Pr7769407664385210434atural * fun_Co1105491363547889651atural ) > fun_Pr7769407664385210434atural ).

tff(sy_c_Product__Type_Ounit_OAbs__unit,type,
    product_Abs_unit: fun_o_Product_unit ).

tff(sy_c_Product__Type_Ounit_ORep__unit,type,
    product_Rep_unit: fun_Product_unit_o ).

tff(sy_c_Random_Oinc__shift,type,
    inc_shift: code_natural > fun_Co7398788559141407565atural ).

tff(sy_c_Random_Oiterate_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    iterat8892046348760725948atural: ( code_natural * fun_Co1105491363547889651atural * code_natural ) > fun_Pr7769407664385210434atural ).

tff(sy_c_Random_Olog,type,
    log: code_natural > fun_Co7398788559141407565atural ).

tff(sy_c_Random_Olog__rel,type,
    log_rel: fun_Pr3592279944642289454ural_o ).

tff(sy_c_Random_Ominus__shift,type,
    minus_shift: ( code_natural * code_natural ) > fun_Co7398788559141407565atural ).

tff(sy_c_Random_Onext,type,
    next: fun_Pr7769407664385210434atural ).

tff(sy_c_Random_Orange,type,
    range: code_natural > fun_Pr7769407664385210434atural ).

tff(sy_c_Random_Osplit__seed,type,
    split_seed: produc7822875418678951345atural > produc6756470014200349799atural ).

tff(sy_c_Rat_OAbs__Rat,type,
    abs_Rat: fun_Pr1652463973008025892nt_rat ).

tff(sy_c_Rat_OFract,type,
    fract: fun_int_fun_int_rat ).

tff(sy_c_Rat_OFrct,type,
    frct: fun_Pr1652463973008025892nt_rat ).

tff(sy_c_Rat_ORep__Rat,type,
    rep_Rat: fun_ra4503298312962071866nt_int ).

tff(sy_c_Rat_Onormalize,type,
    normalize: fun_Pr2478283820680522243nt_int ).

tff(sy_c_Rat_Oof__int,type,
    of_int: fun_int_rat ).

tff(sy_c_Rat_Opcr__rat,type,
    pcr_rat: fun_Pr7537129237977221859_rat_o ).

tff(sy_c_Rat_Opositive,type,
    positive: fun_rat_o ).

tff(sy_c_Rat_Oquotient__of,type,
    quotient_of: rat > product_prod_int_int ).

tff(sy_c_Rat_Oratrel,type,
    ratrel: fun_Pr9018117161326028078_int_o ).

tff(sy_c_Ref__Time_Ochange_001t__Heap__Oarray_Itf__a_J,type,
    ref_change_array_a: ( fun_array_a_array_a * ref_array_a ) > heap_T6362127782908069795rray_a ).

tff(sy_c_Ref__Time_Ochange_001t__Product____Type__Ounit,type,
    ref_ch7259622376331601608t_unit: ( fun_Pr2191293291710260995t_unit * ref_Product_unit ) > heap_T5738788834812785303t_unit ).

tff(sy_c_Ref__Time_Oget_001t__Heap__Oarray_Itf__a_J,type,
    ref_get_array_a: ( heap_e7401611519738050253t_unit * ref_array_a ) > array_a ).

tff(sy_c_Ref__Time_Oget_001t__Product____Type__Ounit,type,
    ref_get_Product_unit: ( heap_e7401611519738050253t_unit * ref_Product_unit ) > product_unit ).

tff(sy_c_Ref__Time_Olookup_001t__Heap__Oarray_Itf__a_J,type,
    ref_lookup_array_a: ref_array_a > heap_T6362127782908069795rray_a ).

tff(sy_c_Ref__Time_Olookup_001t__Product____Type__Ounit,type,
    ref_lo7930775386976318366t_unit: ref_Product_unit > heap_T5738788834812785303t_unit ).

tff(sy_c_Ref__Time_Oset_001t__Heap__Oarray_Itf__a_J,type,
    ref_set_array_a: ( ref_array_a * array_a * heap_e7401611519738050253t_unit ) > heap_e7401611519738050253t_unit ).

tff(sy_c_Ref__Time_Oset_001t__Product____Type__Ounit,type,
    ref_set_Product_unit: ( ref_Product_unit * product_unit * heap_e7401611519738050253t_unit ) > heap_e7401611519738050253t_unit ).

tff(sy_c_Refine__Imp__Hol_Oassert_H,type,
    refine_Imp_assert: $o > heap_T5738788834812785303t_unit ).

tff(sy_c_Relation_ODomainp_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
    domain452967906960104687nteger: fun_in4891666191172872833eger_o > fun_int_o ).

tff(sy_c_Relation_ODomainp_001t__Int__Oint_001t__Int__Oint,type,
    domainp_int_int: fun_int_fun_int_o > fun_int_o ).

tff(sy_c_Relation_ODomainp_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
    domain8128281535334753374atural: fun_na2240068485812228818ural_o > fun_nat_o ).

tff(sy_c_Relation_ODomainp_001t__Nat__Onat_001t__Nat__Onat,type,
    domainp_nat_nat: fun_nat_fun_nat_o > fun_nat_o ).

tff(sy_c_Relation_OField_001_Eo,type,
    field_o: set_Product_prod_o_o > set_o ).

tff(sy_c_Relation_OField_001t__Code____Numeral__Ointeger,type,
    field_Code_integer: set_Pr4811707699266497531nteger > set_Code_integer ).

tff(sy_c_Relation_OField_001t__Int__Oint,type,
    field_int: set_Pr958786334691620121nt_int > set_int ).

tff(sy_c_Relation_OField_001t__Nat__Onat,type,
    field_nat: set_Pr1261947904930325089at_nat > set_nat ).

tff(sy_c_Relation_OField_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    field_4706345496283612622at_nat: set_Pr8693737435421807431at_nat > set_Pr1261947904930325089at_nat ).

tff(sy_c_Relation_OField_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    field_2862844103579723188at_nat: set_Pr5564308138774400199at_nat > set_Pr4329608150637261639at_nat ).

tff(sy_c_Relation_OField_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    field_3145993188331922222at_nat: set_Pr4329608150637261639at_nat > set_se7855581050983116737at_nat ).

tff(sy_c_Relation_OId__on_001_Eo,type,
    id_on_o: set_o > set_Product_prod_o_o ).

tff(sy_c_Relation_OId__on_001t__Int__Oint,type,
    id_on_int: set_int > set_Pr958786334691620121nt_int ).

tff(sy_c_Relation_OId__on_001t__Nat__Onat,type,
    id_on_nat: set_nat > set_Pr1261947904930325089at_nat ).

tff(sy_c_Relation_OId__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    id_on_2554058798563519774at_nat: set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat ).

tff(sy_c_Relation_OId__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    id_on_7869290023980668164at_nat: set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat ).

tff(sy_c_Relation_OId__on_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    id_on_6713504163309144702at_nat: set_se7855581050983116737at_nat > set_Pr4329608150637261639at_nat ).

tff(sy_c_Relation_Oinv__image_001t__Nat__Onat_001t__Nat__Onat,type,
    inv_image_nat_nat: ( set_Pr1261947904930325089at_nat * fun_nat_nat ) > set_Pr1261947904930325089at_nat ).

tff(sy_c_Relation_Oinv__image_001t__Nat__Onat_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    inv_im6750873321330482877at_nat: ( set_Pr1261947904930325089at_nat * fun_se4097146774670233028at_nat ) > set_Pr4329608150637261639at_nat ).

tff(sy_c_Relation_Oinv__image_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Nat__Onat,type,
    inv_im4437241714082187487at_nat: ( set_Pr4329608150637261639at_nat * fun_na7044673412300895210at_nat ) > set_Pr1261947904930325089at_nat ).

tff(sy_c_Relation_Oinv__image_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    inv_im7023619800666061458at_nat: ( set_Pr4329608150637261639at_nat * fun_se320340636488258563at_nat ) > set_Pr4329608150637261639at_nat ).

tff(sy_c_Relation_Orelcompp_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
    relcom967497705283160040nteger: ( fun_int_fun_int_o * fun_in4891666191172872833eger_o ) > fun_in4891666191172872833eger_o ).

tff(sy_c_Relation_Orelcompp_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
    relcom1729257228895983867atural: ( fun_nat_fun_nat_o * fun_na2240068485812228818ural_o ) > fun_na2240068485812228818ural_o ).

tff(sy_c_Relation_Ototal__on_001_Eo,type,
    total_on_o: ( set_o * set_Product_prod_o_o ) > $o ).

tff(sy_c_Relation_Ototal__on_001t__Int__Oint,type,
    total_on_int: ( set_int * set_Pr958786334691620121nt_int ) > $o ).

tff(sy_c_Relation_Ototal__on_001t__Nat__Onat,type,
    total_on_nat: ( set_nat * set_Pr1261947904930325089at_nat ) > $o ).

tff(sy_c_Relation_Ototal__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    total_3592101749530773125at_nat: ( set_Pr1261947904930325089at_nat * set_Pr8693737435421807431at_nat ) > $o ).

tff(sy_c_Relation_Ototal__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    total_1513685709984341995at_nat: ( set_Pr4329608150637261639at_nat * set_Pr5564308138774400199at_nat ) > $o ).

tff(sy_c_Relation_Ototal__on_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    total_7212417256332265445at_nat: ( set_se7855581050983116737at_nat * set_Pr4329608150637261639at_nat ) > $o ).

tff(sy_c_Rings_Oalgebraic__semidom__class_Ocoprime_001t__Int__Oint,type,
    algebr932160517623751201me_int: fun_int_fun_int_o ).

tff(sy_c_Rings_Oalgebraic__semidom__class_Ocoprime_001t__Nat__Onat,type,
    algebr934650988132801477me_nat: fun_nat_fun_nat_o ).

tff(sy_c_Rings_Odivide__class_Odivide_001t__Code____Numeral__Ointeger,type,
    divide6298287555418463151nteger: fun_Co1981900195452921617nteger ).

tff(sy_c_Rings_Odivide__class_Odivide_001t__Code____Numeral__Onatural,type,
    divide5121882707175180666atural: fun_Co6813818151677833714atural ).

tff(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint,type,
    divide_divide_int: fun_int_fun_int_int ).

tff(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
    divide_divide_nat: fun_nat_fun_nat_nat ).

tff(sy_c_Rings_Odivide__class_Odivide_001t__Rat__Orat,type,
    divide_divide_rat: rat > fun_rat_rat ).

tff(sy_c_Rings_Odvd__class_Odvd_001t__Assertions__Oassn,type,
    dvd_dvd_assn: fun_assn_fun_assn_o ).

tff(sy_c_Rings_Odvd__class_Odvd_001t__Code____Numeral__Ointeger,type,
    dvd_dvd_Code_integer: fun_Co2081214437782444048eger_o ).

tff(sy_c_Rings_Odvd__class_Odvd_001t__Code____Numeral__Onatural,type,
    dvd_dvd_Code_natural: code_natural > fun_Code_natural_o ).

tff(sy_c_Rings_Odvd__class_Odvd_001t__Int__Oint,type,
    dvd_dvd_int: fun_int_fun_int_o ).

tff(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat,type,
    dvd_dvd_nat: fun_nat_fun_nat_o ).

tff(sy_c_Rings_Odvd__class_Odvd_001t__Rat__Orat,type,
    dvd_dvd_rat: fun_rat_fun_rat_o ).

tff(sy_c_Rings_Omodulo__class_Omodulo_001t__Code____Numeral__Ointeger,type,
    modulo364778990260209775nteger: fun_Co1981900195452921617nteger ).

tff(sy_c_Rings_Omodulo__class_Omodulo_001t__Code____Numeral__Onatural,type,
    modulo8411746178871703098atural: fun_Co6813818151677833714atural ).

tff(sy_c_Rings_Omodulo__class_Omodulo_001t__Int__Oint,type,
    modulo_modulo_int: fun_int_fun_int_int ).

tff(sy_c_Rings_Omodulo__class_Omodulo_001t__Nat__Onat,type,
    modulo_modulo_nat: fun_nat_fun_nat_nat ).

tff(sy_c_Rings_Ounit__factor__class_Ounit__factor_001t__Nat__Onat,type,
    unit_f2748546683901255202or_nat: fun_nat_nat ).

tff(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Code____Numeral__Ointeger,type,
    zero_n356916108424825756nteger: fun_o_Code_integer ).

tff(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Code____Numeral__Onatural,type,
    zero_n8403883297036319079atural: $o > code_natural ).

tff(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Int__Oint,type,
    zero_n2684676970156552555ol_int: fun_o_int ).

tff(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Nat__Onat,type,
    zero_n2687167440665602831ol_nat: fun_o_nat ).

tff(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Rat__Orat,type,
    zero_n2052037380579107095ol_rat: fun_o_rat ).

tff(sy_c_Set_OCollect_001_Eo,type,
    collect_o: fun_o_o > set_o ).

tff(sy_c_Set_OCollect_001t__Code____Numeral__Ointeger,type,
    collect_Code_integer: fun_Code_integer_o > set_Code_integer ).

tff(sy_c_Set_OCollect_001t__Int__Oint,type,
    collect_int: fun_int_o > set_int ).

tff(sy_c_Set_OCollect_001t__List__Olist_It__Nat__Onat_J,type,
    collect_list_nat: fun_list_nat_o > set_list_nat ).

tff(sy_c_Set_OCollect_001t__Nat__Onat,type,
    collect_nat: fun_nat_o > set_nat ).

tff(sy_c_Set_OCollect_001t__Num__Onum,type,
    collect_num: fun_num_o > set_num ).

tff(sy_c_Set_OCollect_001t__Option__Ooption_It__Num__Onum_J,type,
    collect_option_num: fun_option_num_o > set_option_num ).

tff(sy_c_Set_OCollect_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    collec8141831914148684149it_nat: fun_op4751157287140997969_nat_o > set_op3940070208846178154it_nat ).

tff(sy_c_Set_OCollect_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    collec5742531119322951597it_nat: fun_op479301348043730329_nat_o > set_op239864471688321678it_nat ).

tff(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    collec7766031446232907142nteger: fun_Pr7211993375558241536eger_o > set_Pr4811707699266497531nteger ).

tff(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    collec1991479681304692691atural: fun_Pr513970351136536563ural_o > set_Pr2352657477744078772atural ).

tff(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    collec213857154873943460nt_int: fun_Pr3238374608701176162_int_o > set_Pr958786334691620121nt_int ).

tff(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Nat__Onat_J_J,type,
    collec1570431334306492044st_nat: fun_Pr5375745717004158586_nat_o > set_Pr3451248702717554689st_nat ).

tff(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__Nat__Onat_J,type,
    collec8096645339561496572at_nat: fun_Pr7575312783043447050_nat_o > set_Pr7549493975000385137at_nat ).

tff(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__List__Olist_It__Nat__Onat_J_J,type,
    collec1907656820224499068st_nat: fun_Pr961374740995693450_nat_o > set_Pr698032948827214833st_nat ).

tff(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    collec3392354462482085612at_nat: fun_fu381918921314004384at_nat ).

tff(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    collec7088162979684241874at_nat: fun_Pr363642936170290612_nat_o > set_Pr8693737435421807431at_nat ).

tff(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    collec2088441199205367000at_nat: fun_Pr6861956506527726894_nat_o > set_Pr2072254264782222413at_nat ).

tff(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J_J,type,
    collec1461227866750739596at_nat: fun_Pr2493370495569891450_nat_o > set_Pr5070339090747523585at_nat ).

tff(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    collec223960383693904210at_nat: fun_Pr5502292500389099060_nat_o > set_Pr5564308138774400199at_nat ).

tff(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    collec6662362479098859352et_nat: fun_Pr3947133745332865710_nat_o > set_Pr5488025237498180813et_nat ).

tff(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    collec6321179662152712658at_nat: fun_fu5127092707984472044at_nat ).

tff(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    collec2601550354786890194at_nat: fun_Pr7663348063272484276_nat_o > set_Pr1604112560894399303at_nat ).

tff(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    collec8113046454796679940nt_int: fun_fu9132409297049680378nt_int ).

tff(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    collec8329916443099062226_nat_o: fun_Pr6629464623532871604at_o_o > set_Pr2929610433303031111_nat_o ).

tff(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    collec2950617477150063211nteger: fun_fu5535353563232763194nteger ).

tff(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    collec6193113176214168693et_nat: fun_fu2239858650119588794et_nat ).

tff(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    collec5916191906451531411et_nat: fun_fu3515393148397969210et_nat ).

tff(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    collec2586211367037964248nt_int: fun_fu4502062894868904186nt_int ).

tff(sy_c_Set_OCollect_001t__Rat__Orat,type,
    collect_rat: fun_rat_o > set_rat ).

tff(sy_c_Set_OCollect_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
    collec574505750873337192nteger: fun_se7289222521248229150eger_o > set_set_Code_integer ).

tff(sy_c_Set_OCollect_001t__Set__Oset_It__Int__Oint_J,type,
    collect_set_int: fun_set_int_o > set_set_int ).

tff(sy_c_Set_OCollect_001t__Set__Oset_It__Nat__Onat_J,type,
    collect_set_nat: fun_set_nat_o > set_set_nat ).

tff(sy_c_Set_OCollect_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    collec5514110066124741708at_nat: fun_se4782206882984618170_nat_o > set_se7855581050983116737at_nat ).

tff(sy_c_Set_OCollect_001t__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J,type,
    collec9208119312383884190nteger: fun_se1103039064484435816eger_o > set_se8531188866349061887nteger ).

tff(sy_c_Set_OCollect_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
    collect_set_set_int: fun_set_set_int_o > set_set_set_int ).

tff(sy_c_Set_OCollect_001t__Set__Oset_It__Set__Oset_It__List__Olist_It__Nat__Onat_J_J_J,type,
    collec4691811733418234273st_nat: fun_se5048694460222551717_nat_o > set_set_set_list_nat ).

tff(sy_c_Set_OCollect_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
    collect_set_set_nat: fun_set_set_nat_o > set_set_set_nat ).

tff(sy_c_Set_OCollect_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    collec6698286964019821996at_nat: fun_se7504237348027150170_nat_o > set_se5158245632345848097at_nat ).

tff(sy_c_Set_OCollect_001t__Set__Oset_It__Set__Oset_It__Product____Type__Ounit_J_J,type,
    collec4600646233855244344t_unit: fun_se2288280263375636942unit_o > set_se7118615804146677933t_unit ).

tff(sy_c_Set_OCollect_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    collec730690896700161715nteger: fun_fu7325869825756301971eger_o > set_fu2873095257816804008nteger ).

tff(sy_c_Set_OCollect_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J,type,
    collec2331594442325604092atural: fun_fu660488089777143946ural_o > set_fu2445755650934904413atural ).

tff(sy_c_Set_OCollect_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    collec3508451719371212753nt_int: fun_fu8565479202776651253_int_o > set_fu8487152106118010054nt_int ).

tff(sy_c_Set_OCollect_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    collec3185346009407167487_nat_o: fun_fu6749285349733798471at_o_o > set_fu1437006448190940916_nat_o ).

tff(sy_c_Set_OCollect_001t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    collec9032172325357639695nteger: fun_fu5503004773767123511eger_o > set_fu4273546686648440324nteger ).

tff(sy_c_Set_OCollect_001t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J,type,
    collec8791405069096577696atural: fun_fu9211935013670480870ural_o > set_fu3555100300013713409atural ).

tff(sy_c_Set_OCollect_001t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    collec470609634907078957nt_int: fun_fu6598048713889201561_int_o > set_fu360863049907232802nt_int ).

tff(sy_c_Set_OCollect_001t__fun_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    collec7092214437839010534nteger: fun_fu4285281161728579104eger_o > set_fu2374436075715859015nteger ).

tff(sy_c_Set_OCollect_001t__fun_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J,type,
    collec5409277387225504521atural: fun_fu257250443624047805ural_o > set_fu2713250876831336446atural ).

tff(sy_c_Set_OCollect_001t__fun_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    collec2114256676250786820nt_int: fun_fu4509100218321815938_int_o > set_fu6863465268813640805nt_int ).

tff(sy_c_Set_Oimage_001_Eo_001_Eo,type,
    image_o_o: fun_o_o > fun_set_o_set_o ).

tff(sy_c_Set_Oimage_001_Eo_001t__Int__Oint,type,
    image_o_int: ( fun_o_int * set_o ) > set_int ).

tff(sy_c_Set_Oimage_001_Eo_001t__Nat__Onat,type,
    image_o_nat: ( fun_o_nat * set_o ) > set_nat ).

tff(sy_c_Set_Oimage_001_Eo_001t__Option__Ooption_I_Eo_J,type,
    image_o_option_o: ( fun_o_option_o * set_o ) > set_option_o ).

tff(sy_c_Set_Oimage_001_Eo_001t__Option__Ooption_It__Num__Onum_J,type,
    image_o_option_num: ( fun_o_option_num * set_o ) > set_option_num ).

tff(sy_c_Set_Oimage_001_Eo_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    image_5849929686412825643it_nat: ( fun_o_7229649064035662211it_nat * set_o ) > set_op239864471688321678it_nat ).

tff(sy_c_Set_Oimage_001_Eo_001t__Option__Ooption_It__Product____Type__Ounit_J,type,
    image_4415570909310888640t_unit: ( fun_o_6261137236491177342t_unit * set_o ) > set_op3165557761946182707t_unit ).

tff(sy_c_Set_Oimage_001_Eo_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
    image_966425688229763753et_nat: ( fun_o_option_set_nat * set_o ) > set_option_set_nat ).

tff(sy_c_Set_Oimage_001_Eo_001t__Product____Type__Ounit,type,
    image_o_Product_unit: ( fun_o_Product_unit * set_o ) > set_Product_unit ).

tff(sy_c_Set_Oimage_001_Eo_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
    image_6491638074533506790nteger: ( fun_o_5240169576699714110nteger * set_o ) > set_set_Code_integer ).

tff(sy_c_Set_Oimage_001_Eo_001t__Set__Oset_It__Int__Oint_J,type,
    image_o_set_int: ( fun_o_set_int * set_o ) > set_set_int ).

tff(sy_c_Set_Oimage_001_Eo_001t__Set__Oset_It__Nat__Onat_J,type,
    image_o_set_nat: ( fun_o_set_nat * set_o ) > set_set_nat ).

tff(sy_c_Set_Oimage_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    image_4470545334726330049nteger: ( fun_Co8499238673658658103nteger * set_Code_integer ) > set_Code_integer ).

tff(sy_c_Set_Oimage_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
    image_948535463418740880er_int: ( fun_Code_integer_int * set_Code_integer ) > set_int ).

tff(sy_c_Set_Oimage_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
    image_951025933927791156er_nat: ( fun_Code_integer_nat * set_Code_integer ) > set_nat ).

tff(sy_c_Set_Oimage_001t__Code____Numeral__Ointeger_001t__Option__Ooption_It__Code____Numeral__Ointeger_J,type,
    image_8960079959263999889nteger: ( fun_Co8029881127924365703nteger * set_Code_integer ) > set_op687863988967635939nteger ).

tff(sy_c_Set_Oimage_001t__Code____Numeral__Ointeger_001t__Product____Type__Ounit,type,
    image_7182656606676592809t_unit: ( fun_Co1365676809456677961t_unit * set_Code_integer ) > set_Product_unit ).

tff(sy_c_Set_Oimage_001t__Code____Numeral__Ointeger_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
    image_2291390168754192375nteger: ( fun_Co744628173305925485nteger * set_Code_integer ) > set_set_Code_integer ).

tff(sy_c_Set_Oimage_001t__Code____Numeral__Ointeger_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    image_2716445779319712667nteger: ( fun_Co1981900195452921617nteger * set_Code_integer ) > set_fu5818728815147633517nteger ).

tff(sy_c_Set_Oimage_001t__Code____Numeral__Onatural_001t__Set__Oset_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    image_3530315724569248802atural: ( fun_Co2944084857415636034atural * set_Code_natural ) > set_se3372686590935047281atural ).

tff(sy_c_Set_Oimage_001t__Int__Oint_001_Eo,type,
    image_int_o: ( fun_int_o * set_int ) > set_o ).

tff(sy_c_Set_Oimage_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
    image_1587234942943678608nteger: ( fun_int_Code_integer * set_int ) > set_Code_integer ).

tff(sy_c_Set_Oimage_001t__Int__Oint_001t__Int__Oint,type,
    image_int_int: fun_int_int > fun_set_int_set_int ).

tff(sy_c_Set_Oimage_001t__Int__Oint_001t__Nat__Onat,type,
    image_int_nat: ( fun_int_nat * set_int ) > set_nat ).

tff(sy_c_Set_Oimage_001t__Int__Oint_001t__Num__Onum,type,
    image_int_num: ( fun_int_num * set_int ) > set_num ).

tff(sy_c_Set_Oimage_001t__Int__Oint_001t__Option__Ooption_It__Int__Oint_J,type,
    image_int_option_int: ( fun_int_option_int * set_int ) > set_option_int ).

tff(sy_c_Set_Oimage_001t__Int__Oint_001t__Option__Ooption_It__Num__Onum_J,type,
    image_int_option_num: ( fun_int_option_num * set_int ) > set_option_num ).

tff(sy_c_Set_Oimage_001t__Int__Oint_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    image_7905038228067148555it_nat: ( fun_in8543325783774419841it_nat * set_int ) > set_op239864471688321678it_nat ).

tff(sy_c_Set_Oimage_001t__Int__Oint_001t__Option__Ooption_It__Product____Type__Ounit_J,type,
    image_1735198859854722016t_unit: ( fun_in5873495209930779904t_unit * set_int ) > set_op3165557761946182707t_unit ).

tff(sy_c_Set_Oimage_001t__Int__Oint_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
    image_2293489338514188681et_nat: ( fun_in2104226462327546623et_nat * set_int ) > set_option_set_nat ).

tff(sy_c_Set_Oimage_001t__Int__Oint_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    image_5194296484788039592nteger: ( fun_in4744367027289715400nteger * set_int ) > set_Pr4811707699266497531nteger ).

tff(sy_c_Set_Oimage_001t__Int__Oint_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    image_6835604608220425009atural: ( fun_in4857920871562217639atural * set_int ) > set_Pr2352657477744078772atural ).

tff(sy_c_Set_Oimage_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    image_5705468584675977158nt_int: ( fun_in4211310926729683942nt_int * set_int ) > set_Pr958786334691620121nt_int ).

tff(sy_c_Set_Oimage_001t__Int__Oint_001t__Product____Type__Oprod_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    image_7736141092170400500_nat_o: ( fun_in7664021439913478804_nat_o * set_int ) > set_Pr2929610433303031111_nat_o ).

tff(sy_c_Set_Oimage_001t__Int__Oint_001t__Product____Type__Ounit,type,
    image_5846526143423701914t_unit: ( fun_int_Product_unit * set_int ) > set_Product_unit ).

tff(sy_c_Set_Oimage_001t__Int__Oint_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
    image_75573793354812870nteger: ( fun_in6808926178784942396nteger * set_int ) > set_set_Code_integer ).

tff(sy_c_Set_Oimage_001t__Int__Oint_001t__Set__Oset_It__Int__Oint_J,type,
    image_int_set_int: ( fun_int_set_int * set_int ) > set_set_int ).

tff(sy_c_Set_Oimage_001t__Int__Oint_001t__Set__Oset_It__Nat__Onat_J,type,
    image_int_set_nat: ( fun_int_set_nat * set_int ) > set_set_nat ).

tff(sy_c_Set_Oimage_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    image_2516384619306764229at_nat: ( fun_mu2328110650637990531at_nat * set_mu2057375006010111271at_nat ) > set_mu2057375006010111271at_nat ).

tff(sy_c_Set_Oimage_001t__Nat__Onat_001_Eo,type,
    image_nat_o: ( fun_nat_o * set_nat ) > set_o ).

tff(sy_c_Set_Oimage_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
    image_1215581382706833972nteger: ( fun_nat_Code_integer * set_nat ) > set_Code_integer ).

tff(sy_c_Set_Oimage_001t__Nat__Onat_001t__Int__Oint,type,
    image_nat_int: ( fun_nat_int * set_nat ) > set_int ).

tff(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
    image_nat_nat: fun_nat_nat > fun_set_nat_set_nat ).

tff(sy_c_Set_Oimage_001t__Nat__Onat_001t__Num__Onum,type,
    image_nat_num: ( fun_nat_num * set_nat ) > set_num ).

tff(sy_c_Set_Oimage_001t__Nat__Onat_001t__Option__Ooption_It__Nat__Onat_J,type,
    image_nat_option_nat: ( fun_nat_option_nat * set_nat ) > set_option_nat ).

tff(sy_c_Set_Oimage_001t__Nat__Onat_001t__Option__Ooption_It__Num__Onum_J,type,
    image_nat_option_num: ( fun_nat_option_num * set_nat ) > set_option_num ).

tff(sy_c_Set_Oimage_001t__Nat__Onat_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    image_5028743614110135983it_nat: ( fun_na5667031169817407269it_nat * set_nat ) > set_op239864471688321678it_nat ).

tff(sy_c_Set_Oimage_001t__Nat__Onat_001t__Option__Ooption_It__Product____Type__Ounit_J,type,
    image_1497621718204147004t_unit: ( fun_na5635918068280204892t_unit * set_nat ) > set_op3165557761946182707t_unit ).

tff(sy_c_Set_Oimage_001t__Nat__Onat_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
    image_1085372205585808685et_nat: ( fun_na896109329399166627et_nat * set_nat ) > set_option_set_nat ).

tff(sy_c_Set_Oimage_001t__Nat__Onat_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    image_4272405876590741764nteger: ( fun_na3822476419092417572nteger * set_nat ) > set_Pr4811707699266497531nteger ).

tff(sy_c_Set_Oimage_001t__Nat__Onat_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J,type,
    image_8172478253469051731er_int: ( fun_na5685997864800668403er_int * set_nat ) > set_Pr6496905503482889930er_int ).

tff(sy_c_Set_Oimage_001t__Nat__Onat_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J,type,
    image_3126957236123472631er_nat: ( fun_na8176081009732395159er_nat * set_nat ) > set_Pr8986988648414616686er_nat ).

tff(sy_c_Set_Oimage_001t__Nat__Onat_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    image_4072043198136622805atural: ( fun_na2094359461478415435atural * set_nat ) > set_Pr2352657477744078772atural ).

tff(sy_c_Set_Oimage_001t__Nat__Onat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Code____Numeral__Ointeger_J,type,
    image_8879651038713332435nteger: ( fun_na7604833841916551795nteger * set_nat ) > set_Pr8415741480598773322nteger ).

tff(sy_c_Set_Oimage_001t__Nat__Onat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    image_2667626500211843362nt_int: ( fun_na1173468842265550146nt_int * set_nat ) > set_Pr958786334691620121nt_int ).

tff(sy_c_Set_Oimage_001t__Nat__Onat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J,type,
    image_6845477519721040070nt_nat: ( fun_na3663551987197276902nt_nat * set_nat ) > set_Pr3448869479623346877nt_nat ).

tff(sy_c_Set_Oimage_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J,type,
    image_8507997478476487799nteger: ( fun_na1596024190920976919nteger * set_nat ) > set_Pr2406931829603198446nteger ).

tff(sy_c_Set_Oimage_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
    image_1668272788310788806at_int: ( fun_na8209919304427304166at_int * set_nat ) > set_Pr7995236796853374141at_int ).

tff(sy_c_Set_Oimage_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    image_5846123807819985514at_nat: ( fun_na1476630412504255114at_nat * set_nat ) > set_Pr1261947904930325089at_nat ).

tff(sy_c_Set_Oimage_001t__Nat__Onat_001t__Product____Type__Ounit,type,
    image_8730104196221521654t_unit: ( fun_nat_Product_unit * set_nat ) > set_Product_unit ).

tff(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
    image_2385391725447763818nteger: ( fun_na9118744110877893344nteger * set_nat ) > set_set_Code_integer ).

tff(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_It__Int__Oint_J,type,
    image_nat_set_int: ( fun_nat_set_int * set_nat ) > set_set_int ).

tff(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
    image_nat_set_nat: ( fun_nat_set_nat * set_nat ) > set_set_nat ).

tff(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    image_7178329752028323786at_nat: ( fun_na7044673412300895210at_nat * set_nat ) > set_se7855581050983116737at_nat ).

tff(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    image_1087905878993176368at_nat: ( fun_na5670658592214072528at_nat * set_nat ) > set_se5479201105039950375at_nat ).

tff(sy_c_Set_Oimage_001t__Num__Onum_001t__Code____Numeral__Ointeger,type,
    image_8379761247532268670nteger: ( fun_num_Code_integer * set_num ) > set_Code_integer ).

tff(sy_c_Set_Oimage_001t__Num__Onum_001t__Num__Onum,type,
    image_num_num: fun_num_num > fun_set_num_set_num ).

tff(sy_c_Set_Oimage_001t__Num__Onum_001t__Option__Ooption_It__Num__Onum_J,type,
    image_num_option_num: ( fun_num_option_num * set_num ) > set_option_num ).

tff(sy_c_Set_Oimage_001t__Option__Ooption_It__Num__Onum_J_001t__Num__Onum,type,
    image_option_num_num: ( fun_option_num_num * set_option_num ) > set_num ).

tff(sy_c_Set_Oimage_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    image_5549452628634654015it_nat: ( fun_op8917697677373047293it_nat * set_op3940070208846178154it_nat ) > set_Pr5142436192348053284it_nat ).

tff(sy_c_Set_Oimage_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    image_1237920015125996135it_nat: ( fun_op7765417307512062173it_nat * set_op239864471688321678it_nat ) > set_Pr1354866905816374718it_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001_Eo,type,
    image_7896445794123959606_o_o_o: ( fun_Pr6984036127010467572_o_o_o * set_Product_prod_o_o ) > set_o ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_001_Eo,type,
    image_5860565421610830622_int_o: ( fun_Pr1358870568642713662_int_o * set_Pr8834758594704517033_o_int ) > set_o ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_001t__Int__Oint,type,
    image_7072963285496371238nt_int: ( fun_Pr3595050827490992028nt_int * set_Pr8834758594704517033_o_int ) > set_int ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001_Eo,type,
    image_8105710389281276538_nat_o: ( fun_Pr3604015536313159578_nat_o * set_Pr2101469702781467981_o_nat ) > set_o ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001t__Nat__Onat,type,
    image_4888532181312399726at_nat: ( fun_Pr5585980272307166948at_nat * set_Pr2101469702781467981_o_nat ) > set_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_Eo_Mt__Num__Onum_J_001_Eo,type,
    image_8863890952250787504_num_o: ( fun_Pr4362196099282670544_num_o * set_Pr7040061329075590551_o_num ) > set_o ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001_Eo,type,
    image_5849890305759347266_nat_o: ( fun_Pr914940982395022178_nat_o * set_Pr6777250647868329861it_nat ) > set_o ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger,type,
    image_6316824473203919795nteger: ( fun_Pr6596356882939945227nteger * set_Pr4811707699266497531nteger ) > set_Code_integer ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    image_1718222391602322082nteger: ( fun_Pr894914116851403386nteger * set_Pr4811707699266497531nteger ) > set_se7873143835621700354nteger ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__Code____Numeral__Onatural,type,
    image_8194678751871465133atural: ( fun_Pr5131589689703537955atural * set_Pr2352657477744078772atural ) > set_Code_natural ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    image_3837677093542026988atural: ( fun_Pr2136124334875798924atural * set_Pr2352657477744078772atural ) > set_Pr7564037697178849041atural ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    image_4799632500972785611it_nat: ( fun_Pr8118912048244921225it_nat * set_Pr5142436192348053284it_nat ) > set_op3940070208846178154it_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    image_7009121673873379551et_nat: ( fun_Pr3017356861961520469et_nat * set_Pr3948176798113811640et_nat ) > set_se3290278062343509644et_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Int__Oint_M_Eo_J_001_Eo,type,
    image_5561579847027142576nt_o_o: ( fun_Pr1059884994059025616nt_o_o * set_Pr903927857289325719_int_o ) > set_o ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Int__Oint_M_Eo_J_001t__Int__Oint,type,
    image_90517134139374612_o_int: ( fun_Pr5835976712988771210_o_int * set_Pr903927857289325719_int_o ) > set_int ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint,type,
    image_5042161079198086560nt_int: ( fun_Pr982841511892225912nt_int * set_Pr958786334691620121nt_int ) > set_int ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    image_2653370878348428101nt_int: ( fun_Pr2478283820680522243nt_int * set_Pr958786334691620121nt_int ) > set_Pr958786334691620121nt_int ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    image_2686860183053050585nt_int: ( fun_Pr1951044811698827825nt_int * set_Pr958786334691620121nt_int ) > set_se4391686895574802075nt_int ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    image_6157797188692319661nt_int: ( fun_Pr1547027809659849477nt_int * set_Pr958786334691620121nt_int ) > set_se2743246391971219311nt_int ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J_001t__Int__Oint,type,
    image_2855239504505064772at_int: ( fun_Pr8019291974053979932at_int * set_Pr3448869479623346877nt_nat ) > set_int ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J_001t__Nat__Onat,type,
    image_2857729975014115048at_nat: ( fun_Pr2973770956708400832at_nat * set_Pr3448869479623346877nt_nat ) > set_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Int__Oint_Mt__Num__Onum_J_001t__Int__Oint,type,
    image_4873634598471238286um_int: ( fun_Pr814315031165377638um_int * set_Pr8387461105917469447nt_num ) > set_int ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_001_Eo,type,
    image_7478392465989118804at_o_o: ( fun_Pr2976697613021001844at_o_o * set_Pr3149072824959771635_nat_o ) > set_o ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_001t__Nat__Onat,type,
    image_8629803608462650132_o_nat: ( fun_Pr103879662602641546_o_nat * set_Pr3149072824959771635_nat_o ) > set_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_001t__Int__Oint,type,
    image_4670507518961241924nt_int: ( fun_Pr611187951655381276nt_int * set_Pr7995236796853374141at_int ) > set_int ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_001t__Nat__Onat,type,
    image_4672997989470292200nt_nat: ( fun_Pr4789038971164577984nt_nat * set_Pr7995236796853374141at_int ) > set_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J,type,
    image_202211252889950930er_int: ( fun_Pr3118124138693225744er_int * set_Pr7995236796853374141at_int ) > set_Pr6496905503482889930er_int ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
    image_9117352539549038149at_int: ( fun_Pr7754697619089165059at_int * set_Pr7995236796853374141at_int ) > set_Pr7995236796853374141at_int ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo,type,
    image_3693632289388996572_nat_o: ( fun_Pr4796943543331071514_nat_o * set_Pr1261947904930325089at_nat ) > set_o ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
    image_2483585944268220136at_int: ( fun_Pr7647638413817135296at_int * set_Pr1261947904930325089at_nat ) > set_int ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
    image_2486076414777270412at_nat: ( fun_Pr2602117396471556196at_nat * set_Pr1261947904930325089at_nat ) > set_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Option__Ooption_It__Num__Onum_J,type,
    image_1023191801488348454on_num: ( fun_Pr7397166214287566974on_num * set_Pr1261947904930325089at_nat ) > set_option_num ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    image_4198897800814241419at_nat: ( fun_Pr7804344347641417161at_nat * set_Pr1261947904930325089at_nat ) > set_op4508134149509766951at_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    image_5755308894823448084it_nat: ( fun_Pr6624299372562097772it_nat * set_Pr1261947904930325089at_nat ) > set_op239864471688321678it_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Option__Ooption_It__Product____Type__Ounit_J,type,
    image_7548311901266006551t_unit: ( fun_Pr648072847990616533t_unit * set_Pr1261947904930325089at_nat ) > set_op3165557761946182707t_unit ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
    image_7383884694314771602et_nat: ( fun_Pr2088208266900590058et_nat * set_Pr1261947904930325089at_nat ) > set_option_set_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    image_5669961043262023647nteger: ( fun_Pr5056853159479207325nteger * set_Pr1261947904930325089at_nat ) > set_Pr4811707699266497531nteger ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J,type,
    image_6418031315350042158er_int: ( fun_Pr110572164298541164er_int * set_Pr1261947904930325089at_nat ) > set_Pr6496905503482889930er_int ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J,type,
    image_1372510298004463058er_nat: ( fun_Pr2600655309230267920er_nat * set_Pr1261947904930325089at_nat ) > set_Pr8986988648414616686er_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Code____Numeral__Ointeger_J,type,
    image_7125204100594322862nteger: ( fun_Pr2029408141414424556nteger * set_Pr1261947904930325089at_nat ) > set_Pr8415741480598773322nteger ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    image_1990417195239315453nt_int: ( fun_Pr1815330137571409595nt_int * set_Pr1261947904930325089at_nat ) > set_Pr958786334691620121nt_int ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J,type,
    image_6168268214748512161nt_nat: ( fun_Pr4305413282503136351nt_nat * set_Pr1261947904930325089at_nat ) > set_Pr3448869479623346877nt_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J,type,
    image_6753550540357478226nteger: ( fun_Pr5243970527273625488nteger * set_Pr1261947904930325089at_nat ) > set_Pr2406931829603198446nteger ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
    image_991063483338260897at_int: ( fun_Pr8851780599733163615at_int * set_Pr1261947904930325089at_nat ) > set_Pr7995236796853374141at_int ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    image_5168914502847457605at_nat: fun_Pr2118491707810114563at_nat > fun_se320340636488258563at_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    image_4566292076127975857et_nat: ( fun_Pr5733170697710890607et_nat * set_Pr1261947904930325089at_nat ) > set_Pr5488025237498180813et_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Ounit,type,
    image_6169909464789311569t_unit: ( fun_Pr2481279687482350479t_unit * set_Pr1261947904930325089at_nat ) > set_Product_unit ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Set__Oset_It__Int__Oint_J,type,
    image_5061345727057949854et_int: ( fun_Pr6548035576365145974et_int * set_Pr1261947904930325089at_nat ) > set_set_int ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
    image_15824709712370754et_nat: ( fun_Pr9038118721296872730et_nat * set_Pr1261947904930325089at_nat ) > set_set_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    image_5423882813909314213at_nat: fun_Pr1469247711798767971at_nat > fun_se953073389798102371at_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
    image_2420546460570504406_nat_o: ( fun_Pr2028404973800837934_nat_o * set_Pr1261947904930325089at_nat ) > set_fu8838435424971791696_nat_o ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J_001t__Nat__Onat,type,
    image_4504471508743443926um_nat: ( fun_Pr4620512490437729710um_nat * set_Pr6200539531224447659at_num ) > set_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Nat__Onat,type,
    image_5261730836495542980at_nat: ( fun_Pr8519750050727906972at_nat * set_Pr633603713510679705it_nat ) > set_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    image_3617234230432879585nteger: ( fun_Pr6966570558394395095nteger * set_Pr3944325338781952762e_term ) > set_Pr3486312109254157132nteger ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    image_2538532745900505353et_nat: ( fun_Pr5416369060549219583et_nat * set_Pr3013394129895136920_nat_o ) > set_Pr1312406793078187350et_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J_001t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    image_4281971784858038109nt_int: ( fun_Pr3284083897292419283nt_int * set_Pr4417106977106297437e_term ) > set_Pr4166680992137330533nt_int ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    image_3062550852079041117nt_int: ( fun_Pr5010838083610845651nt_int * set_Pr3640028372902554249e_term ) > set_Pr6700895561065273913nt_int ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Num__Onum_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    image_7418169580930627696at_nat: ( fun_Pr8866567302531502864at_nat * set_Pr7477759153910077568at_num ) > set_Pr1261947904930325089at_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    image_660286381542540297et_nat: ( fun_Pr8630787502178681855et_nat * set_Pr7905283282039288826_nat_o ) > set_Pr4040394263813967220et_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    image_3455408117458022631it_nat: ( fun_Pr7644814098969791837it_nat * set_Pr1354866905816374718it_nat ) > set_op239864471688321678it_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001_Eo,type,
    image_3500134854233901558_nat_o: ( fun_Pr3059359313727237556_nat_o * set_Pr4329608150637261639at_nat ) > set_o ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Int__Oint,type,
    image_3196035031069704014at_int: ( fun_Pr6298746545499001766at_int * set_Pr4329608150637261639at_nat ) > set_int ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Nat__Onat,type,
    image_3198525501578754290at_nat: ( fun_Pr1253225528153422666at_nat * set_Pr4329608150637261639at_nat ) > set_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Option__Ooption_It__Num__Onum_J,type,
    image_8464016542990802060on_num: ( fun_Pr6553355248451873380on_num * set_Pr4329608150637261639at_nat ) > set_option_num ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    image_140351626946063738it_nat: ( fun_Pr6865292569827446866it_nat * set_Pr4329608150637261639at_nat ) > set_op239864471688321678it_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Option__Ooption_It__Product____Type__Ounit_J,type,
    image_8585598761158579761t_unit: ( fun_Pr5508761798988831599t_unit * set_Pr4329608150637261639at_nat ) > set_op3165557761946182707t_unit ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
    image_934083234596377592et_nat: ( fun_Pr6721000092112975824et_nat * set_Pr4329608150637261639at_nat ) > set_option_set_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Ounit,type,
    image_7082456443403096939t_unit: ( fun_Pr8319229360018371625t_unit * set_Pr4329608150637261639at_nat ) > set_Product_unit ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Set__Oset_It__Nat__Onat_J,type,
    image_3160451284896210088et_nat: ( fun_Pr6764980218223570944et_nat * set_Pr4329608150637261639at_nat ) > set_set_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    image_7979982168039674559at_nat: ( fun_Pr6212429452034653949at_nat * set_Pr4329608150637261639at_nat ) > set_se7855581050983116737at_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    image_5733965904763621635nt_int: ( fun_Pr1552678306225191715nt_int * set_Pr4166680992137330533nt_int ) > set_Pr958786334691620121nt_int ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    image_7516633138899002997e_term: ( fun_Pr7653582204007996523e_term * set_Pr4166680992137330533nt_int ) > set_fu3629540756087427317e_term ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    image_2271979006234848446nteger: ( fun_Pr6160931176198666718nteger * set_Pr3486312109254157132nteger ) > set_Pr4811707699266497531nteger ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    image_5882744770105888791e_term: ( fun_Pr4557384415951816845e_term * set_Pr3486312109254157132nteger ) > set_fu8280898353253485872e_term ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    image_5643293374885392937et_nat: ( fun_Pr2813956079162534559et_nat * set_Pr1312406793078187350et_nat ) > set_Pr3948176798113811640et_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    image_3818865380660343963et_nat: ( fun_Pr4147293223664569617et_nat * set_Pr1312406793078187350et_nat ) > set_se6059149423757001258et_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
    image_4444162529858428168_nat_o: ( fun_Pr3233114924583728296_nat_o * set_Pr1312406793078187350et_nat ) > set_fu3555266933746557007_nat_o ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    image_1425188809386248805et_nat: ( fun_Pr2953255705995765467et_nat * set_Pr4040394263813967220et_nat ) > set_Pr1312406793078187350et_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
    image_8400968272122294250_nat_o: ( fun_Pr7618159474455865098_nat_o * set_Pr4040394263813967220et_nat ) > set_fu3555266933746557007_nat_o ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    image_5003770246312495919nt_int: ( fun_Pr1987159835869338959nt_int * set_Pr6700895561065273913nt_int ) > set_Pr958786334691620121nt_int ).

tff(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    image_143812984558558581e_term: ( fun_Pr5872836680101629291e_term * set_Pr6700895561065273913nt_int ) > set_fu5653557704672872225e_term ).

tff(sy_c_Set_Oimage_001t__Product____Type__Ounit_001t__Code____Numeral__Ointeger,type,
    image_3815118110082124069nteger: ( fun_Pr1820225556744648189nteger * set_Product_unit ) > set_Code_integer ).

tff(sy_c_Set_Oimage_001t__Product____Type__Ounit_001t__Int__Oint,type,
    image_873079544045703924it_int: ( fun_Product_unit_int * set_Product_unit ) > set_int ).

tff(sy_c_Set_Oimage_001t__Product____Type__Ounit_001t__Nat__Onat,type,
    image_875570014554754200it_nat: ( fun_Product_unit_nat * set_Product_unit ) > set_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Ounit_001t__Option__Ooption_It__Num__Onum_J,type,
    image_5965367930834091826on_num: ( fun_Pr792663941044724234on_num * set_Product_unit ) > set_option_num ).

tff(sy_c_Set_Oimage_001t__Product____Type__Ounit_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    image_5022536681399171104it_nat: ( fun_Pr6171258863536582648it_nat * set_Product_unit ) > set_op239864471688321678it_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Ounit_001t__Option__Ooption_It__Product____Type__Ounit_J,type,
    image_7094380055901048587t_unit: ( fun_Pr8303579546892975945t_unit * set_Product_unit ) > set_op3165557761946182707t_unit ).

tff(sy_c_Set_Oimage_001t__Product____Type__Ounit_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    image_8089323762101378259nteger: ( fun_Pr864343514034809617nteger * set_Product_unit ) > set_Pr4811707699266497531nteger ).

tff(sy_c_Set_Oimage_001t__Product____Type__Ounit_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    image_220848230107539526atural: ( fun_Pr2548841491397842206atural * set_Product_unit ) > set_Pr2352657477744078772atural ).

tff(sy_c_Set_Oimage_001t__Product____Type__Ounit_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    image_4103462098156874993nt_int: ( fun_Pr6733608168372577327nt_int * set_Product_unit ) > set_Pr958786334691620121nt_int ).

tff(sy_c_Set_Oimage_001t__Product____Type__Ounit_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    image_7281959405765017145at_nat: ( fun_Pr7036769738611282295at_nat * set_Product_unit ) > set_Pr1261947904930325089at_nat ).

tff(sy_c_Set_Oimage_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
    image_405062704495631173t_unit: ( fun_Pr2191293291710260995t_unit * set_Product_unit ) > set_Product_unit ).

tff(sy_c_Set_Oimage_001t__Rat__Orat_001t__Rat__Orat,type,
    image_rat_rat: ( fun_rat_rat * set_rat ) > set_rat ).

tff(sy_c_Set_Oimage_001t__Set__Oset_It__Nat__Onat_J_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
    image_838307146230912995et_nat: ( fun_se7316093745529328985et_nat * set_set_nat ) > set_option_set_nat ).

tff(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    image_6898982319499645995at_nat: ( fun_se1551789852802198377at_nat * set_se7855581050983116737at_nat ) > set_se5479201105039950375at_nat ).

tff(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    image_8883634599237391886_nat_o: ( fun_se4014881416909572940_nat_o * set_se7855581050983116737at_nat ) > set_fu7727944524835118346_nat_o ).

tff(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J,type,
    image_8577875265703384492_nat_o: ( fun_se8406536441587994090_nat_o * set_se5479201105039950375at_nat ) > set_fu5472951507345886094_nat_o ).

tff(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_001t__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    image_3387664822671061514_int_o: ( fun_se5644990602862975744_int_o * set_se4391686895574802075nt_int ) > set_fu804515216739278420_int_o ).

tff(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_001t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
    image_5178492454380347850eger_o: ( fun_se6163777255337707072eger_o * set_se7873143835621700354nteger ) > set_fu7224585531122448557eger_o ).

tff(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_001t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
    image_4714915674727665248_nat_o: ( fun_se7509835969743050710_nat_o * set_se3290278062343509644et_nat ) > set_fu3659417381080568633_nat_o ).

tff(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J_001t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_J,type,
    image_4566770532344737120_nat_o: ( fun_se4713689491525875926_nat_o * set_se6059149423757001258et_nat ) > set_fu5576194784986904859_nat_o ).

tff(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_001t__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    image_5621923772749203210_int_o: ( fun_se5710315616867461632_int_o * set_se2743246391971219311nt_int ) > set_fu1179388718870097536_int_o ).

tff(sy_c_Set_Oimage_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    image_3787029643364842667nt_int: ( fun_fu6029888860018473377nt_int * set_fu3629540756087427317e_term ) > set_se4391686895574802075nt_int ).

tff(sy_c_Set_Oimage_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Nat__Onat_M_Eo_J,type,
    image_2153120922742433605_nat_o: fun_fu4001317426178549763_nat_o > fun_se2106923200977956867_nat_o ).

tff(sy_c_Set_Oimage_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
    image_8786112330847644287_nat_o: ( fun_fu6778223257468740055_nat_o * set_fu7727944524835118346_nat_o ) > set_fu8838435424971791696_nat_o ).

tff(sy_c_Set_Oimage_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    image_5753923617458574413nteger: ( fun_fu4173945377279696323nteger * set_fu8280898353253485872e_term ) > set_se7873143835621700354nteger ).

tff(sy_c_Set_Oimage_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    image_1549266068120649472et_nat: ( fun_fu8357309440898100312et_nat * set_fu3555266933746557007_nat_o ) > set_se3290278062343509644et_nat ).

tff(sy_c_Set_Oimage_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    image_67816568901280286et_nat: ( fun_fu5650763273978745334et_nat * set_fu3555266933746557007_nat_o ) > set_se6059149423757001258et_nat ).

tff(sy_c_Set_Oimage_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    image_7441934579048575915nt_int: ( fun_fu60724386564609697nt_int * set_fu5653557704672872225e_term ) > set_se2743246391971219311nt_int ).

tff(sy_c_Set_Oimage_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    image_19007421832380416at_nat: ( fun_fu381918921314004384at_nat * set_fu8838435424971791696_nat_o ) > set_se7855581050983116737at_nat ).

tff(sy_c_Set_Oimage_001t__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    image_2888349181732859468at_nat: ( fun_fu5127092707984472044at_nat * set_fu1867049230074397546_nat_o ) > set_se5479201105039950375at_nat ).

tff(sy_c_Set_Oimage_001t__fun_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    image_2644176692661446050nt_int: ( fun_fu9132409297049680378nt_int * set_fu5828550712561173602_int_o ) > set_se4391686895574802075nt_int ).

tff(sy_c_Set_Oimage_001t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_M_Eo_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    image_6599205263586403426nteger: ( fun_fu5535353563232763194nteger * set_fu6463009222652410043eger_o ) > set_se7873143835621700354nteger ).

tff(sy_c_Set_Oimage_001t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    image_7089400406489661154et_nat: ( fun_fu2239858650119588794et_nat * set_fu6830718107662835377_nat_o ) > set_se3290278062343509644et_nat ).

tff(sy_c_Set_Oimage_001t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_M_Eo_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    image_1768751647092834et_nat: ( fun_fu3515393148397969210et_nat * set_fu4385504767878589843_nat_o ) > set_se6059149423757001258et_nat ).

tff(sy_c_Set_Oimage_001t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    image_2420199643309514402nt_int: ( fun_fu4502062894868904186nt_int * set_fu5926610517471843470_int_o ) > set_se2743246391971219311nt_int ).

tff(sy_c_Set_Oimage_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J_001t__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J,type,
    image_3264509002305780637_nat_o: ( fun_fu3198693465525813493_nat_o * set_fu5472951507345886094_nat_o ) > set_fu1867049230074397546_nat_o ).

tff(sy_c_Set_Oimage_001t__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J_001t__fun_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J,type,
    image_39754620896724637_int_o: ( fun_fu5894409982295737917_int_o * set_fu804515216739278420_int_o ) > set_fu5828550712561173602_int_o ).

tff(sy_c_Set_Oimage_001t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J_001t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_M_Eo_J,type,
    image_6084557897575152733eger_o: ( fun_fu7060041198443644797eger_o * set_fu7224585531122448557eger_o ) > set_fu6463009222652410043eger_o ).

tff(sy_c_Set_Oimage_001t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J_001t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J,type,
    image_6813257014334645959_nat_o: ( fun_fu3464598166661278695_nat_o * set_fu3659417381080568633_nat_o ) > set_fu6830718107662835377_nat_o ).

tff(sy_c_Set_Oimage_001t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_J_001t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_M_Eo_J,type,
    image_8687135387450530375_nat_o: ( fun_fu5983609555712719719_nat_o * set_fu5576194784986904859_nat_o ) > set_fu4385504767878589843_nat_o ).

tff(sy_c_Set_Oimage_001t__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J_001t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J,type,
    image_8230742269165341597_int_o: ( fun_fu2458202332514215229_int_o * set_fu1179388718870097536_int_o ) > set_fu5926610517471843470_int_o ).

tff(sy_c_Set_Oinsert_001_Eo,type,
    insert_o: ( $o * set_o ) > set_o ).

tff(sy_c_Set_Oinsert_001t__Code____Numeral__Ointeger,type,
    insert_Code_integer: ( code_integer * set_Code_integer ) > set_Code_integer ).

tff(sy_c_Set_Oinsert_001t__Int__Oint,type,
    insert_int: ( int * set_int ) > set_int ).

tff(sy_c_Set_Oinsert_001t__List__Olist_It__Nat__Onat_J,type,
    insert_list_nat: ( list_nat * set_list_nat ) > set_list_nat ).

tff(sy_c_Set_Oinsert_001t__Nat__Onat,type,
    insert_nat: ( nat * set_nat ) > set_nat ).

tff(sy_c_Set_Oinsert_001t__Num__Onum,type,
    insert_num: ( num * set_num ) > set_num ).

tff(sy_c_Set_Oinsert_001t__Option__Ooption_I_Eo_J,type,
    insert_option_o: ( option_o * set_option_o ) > set_option_o ).

tff(sy_c_Set_Oinsert_001t__Option__Ooption_It__Int__Oint_J,type,
    insert_option_int: ( option_int * set_option_int ) > set_option_int ).

tff(sy_c_Set_Oinsert_001t__Option__Ooption_It__Nat__Onat_J,type,
    insert_option_nat: ( option_nat * set_option_nat ) > set_option_nat ).

tff(sy_c_Set_Oinsert_001t__Option__Ooption_It__Num__Onum_J,type,
    insert_option_num: ( option_num * set_option_num ) > set_option_num ).

tff(sy_c_Set_Oinsert_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    insert7468008629046257882it_nat: ( option3216581401566546698it_nat * set_op3940070208846178154it_nat ) > set_op3940070208846178154it_nat ).

tff(sy_c_Set_Oinsert_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    insert6842972033726296599at_nat: ( option4927543243414619207at_nat * set_op4508134149509766951at_nat ) > set_op4508134149509766951at_nat ).

tff(sy_c_Set_Oinsert_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    insert2007652293347934600it_nat: ( option8956607266484857688it_nat * set_op239864471688321678it_nat ) > set_op239864471688321678it_nat ).

tff(sy_c_Set_Oinsert_001t__Option__Ooption_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    insert6833468608972679677at_nat: ( option8699557107911914541at_nat * set_op989438649584373901at_nat ) > set_op989438649584373901at_nat ).

tff(sy_c_Set_Oinsert_001t__Option__Ooption_It__Product____Type__Ounit_J,type,
    insert2866144167138965411t_unit: ( option_Product_unit * set_op3165557761946182707t_unit ) > set_op3165557761946182707t_unit ).

tff(sy_c_Set_Oinsert_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
    insert6281397740311767046et_nat: ( option_set_nat * set_option_set_nat ) > set_option_set_nat ).

tff(sy_c_Set_Oinsert_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
    insert6201435330877294327od_o_o: ( product_prod_o_o * set_Product_prod_o_o ) > set_Product_prod_o_o ).

tff(sy_c_Set_Oinsert_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
    insert3770363720049103139_o_int: ( product_prod_o_int * set_Pr8834758594704517033_o_int ) > set_Pr8834758594704517033_o_int ).

tff(sy_c_Set_Oinsert_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
    insert7948214739558299847_o_nat: ( product_prod_o_nat * set_Pr2101469702781467981_o_nat ) > set_Pr2101469702781467981_o_nat ).

tff(sy_c_Set_Oinsert_001t__Product____Type__Oprod_I_Eo_Mt__Num__Onum_J,type,
    insert8656458676507137553_o_num: ( product_prod_o_num * set_Pr7040061329075590551_o_num ) > set_Pr7040061329075590551_o_num ).

tff(sy_c_Set_Oinsert_001t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    insert6915099157023601407it_nat: ( produc2900562427881843919it_nat * set_Pr6777250647868329861it_nat ) > set_Pr6777250647868329861it_nat ).

tff(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    insert4913895101485356395nteger: ( produc8923325533196201883nteger * set_Pr4811707699266497531nteger ) > set_Pr4811707699266497531nteger ).

tff(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    insert6505218763252461998atural: ( produc5835291356934675326atural * set_Pr2352657477744078772atural ) > set_Pr2352657477744078772atural ).

tff(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Int__Oint_M_Eo_J,type,
    insert412334881326329105_int_o: ( product_prod_int_o * set_Pr903927857289325719_int_o ) > set_Pr903927857289325719_int_o ).

tff(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    insert5033312907999012233nt_int: ( product_prod_int_int * set_Pr958786334691620121nt_int ) > set_Pr958786334691620121nt_int ).

tff(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J,type,
    insert9211163927508208941nt_nat: ( product_prod_int_nat * set_Pr3448869479623346877nt_nat ) > set_Pr3448869479623346877nt_nat ).

tff(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Int__Oint_Mt__Num__Onum_J,type,
    insert696035827602270839nt_num: ( product_prod_int_num * set_Pr8387461105917469447nt_num ) > set_Pr8387461105917469447nt_num ).

tff(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
    insert2233377226759017069_nat_o: ( product_prod_nat_o * set_Pr3149072824959771635_nat_o ) > set_Pr3149072824959771635_nat_o ).

tff(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
    insert4033959196097957677at_int: ( product_prod_nat_int * set_Pr7995236796853374141at_int ) > set_Pr7995236796853374141at_int ).

tff(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    insert8211810215607154385at_nat: product_prod_nat_nat > fun_se320340636488258563at_nat ).

tff(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J,type,
    insert8920054152555992091at_num: ( product_prod_nat_num * set_Pr6200539531224447659at_num ) > set_Pr6200539531224447659at_num ).

tff(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    insert2528233410557839625it_nat: ( produc3839731585411834681it_nat * set_Pr633603713510679705it_nat ) > set_Pr633603713510679705it_nat ).

tff(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
    insert2126339615020983374_nat_o: ( produc652263959640188542_nat_o * set_Pr6558897299634722526_nat_o ) > set_Pr6558897299634722526_nat_o ).

tff(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Num__Onum_J,type,
    insert2790150385885543546at_num: ( produc9082142974458947146at_num * set_Pr7477759153910077568at_num ) > set_Pr7477759153910077568at_num ).

tff(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    insert5050368324300391991at_nat: ( produc859450856879609959at_nat * set_Pr8693737435421807431at_nat ) > set_Pr8693737435421807431at_nat ).

tff(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    insert398606708087465655at_nat: ( produc1906917888121415911at_nat * set_Pr5564308138774400199at_nat ) > set_Pr5564308138774400199at_nat ).

tff(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    insert5940566491043231800it_nat: ( produc8664842809031399944it_nat * set_Pr1354866905816374718it_nat ) > set_Pr1354866905816374718it_nat ).

tff(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    insert9069300056098147895at_nat: produc3843707927480180839at_nat > fun_se6846035212209387651at_nat ).

tff(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    insert845627424500119391nt_int: produc4788131091073775919nt_int > fun_se2900878183379320647nt_int ).

tff(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    insert4459515811902188230nteger: produc2453742332425399446nteger > fun_se2190013347424485781nteger ).

tff(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    insert663245765287195472et_nat: produc8799533983703829792et_nat > fun_se9157011578508667433et_nat ).

tff(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    insert727258735945777134et_nat: produc3112576180687729086et_nat > fun_se2331804103973993189et_nat ).

tff(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    insert4130518925788644403nt_int: produc3043004577601930755nt_int > fun_se1594822257893229295nt_int ).

tff(sy_c_Set_Oinsert_001t__Product____Type__Ounit,type,
    insert_Product_unit: ( product_unit * set_Product_unit ) > set_Product_unit ).

tff(sy_c_Set_Oinsert_001t__Rat__Orat,type,
    insert_rat: ( rat * set_rat ) > set_rat ).

tff(sy_c_Set_Oinsert_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    insert9200635055090092081at_nat: ( set_Pr1261947904930325089at_nat * set_se7855581050983116737at_nat ) > set_se7855581050983116737at_nat ).

tff(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Assertions__Oassn,type,
    set_fo1959793692361082170t_assn: ( fun_na2454419004871237530n_assn * nat * nat * assn ) > assn ).

tff(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Code____Numeral__Ointeger,type,
    set_fo1084959871951514735nteger: ( fun_na7078387940644931716nteger * nat * nat ) > fun_Co8499238673658658103nteger ).

tff(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Code____Numeral__Onatural,type,
    set_fo9131927060563008058atural: ( fun_na607345901702507418atural * nat * nat ) > fun_Co7398788559141407565atural ).

tff(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Int__Oint,type,
    set_fo2581907887559384638at_int: ( fun_nat_fun_int_int * nat * nat ) > fun_int_int ).

tff(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    set_fo4497565046347964853at_nat: ( fun_na1945018436707187408at_nat * nat * nat * multis2468970476368604999at_nat ) > multis2468970476368604999at_nat ).

tff(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Nat__Onat,type,
    set_fo2584398358068434914at_nat: ( fun_nat_fun_nat_nat * nat ) > fun_nat_fun_nat_nat ).

tff(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Rat__Orat,type,
    set_fo1949268297981939178at_rat: ( fun_nat_fun_rat_rat * nat * nat ) > fun_rat_rat ).

tff(sy_c_Set__Interval_Ofold__atLeastAtMost__nat__rel_001t__Nat__Onat,type,
    set_fo3699595496184130361el_nat: fun_Pr8463018485500633518_nat_o ).

tff(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001_Eo,type,
    set_or8904488021354931149Most_o: $o > fun_o_set_o ).

tff(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Assertions__Oassn,type,
    set_or7959216805967363635t_assn: ( assn * assn ) > set_assn ).

tff(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Code____Numeral__Ointeger,type,
    set_or189985376899183464nteger: code_integer > fun_Co744628173305925485nteger ).

tff(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Int__Oint,type,
    set_or1266510415728281911st_int: int > fun_int_set_int ).

tff(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Nat__Onat,type,
    set_or1269000886237332187st_nat: nat > fun_nat_set_nat ).

tff(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Num__Onum,type,
    set_or7049704709247886629st_num: ( num * num ) > set_num ).

tff(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Product____Type__Ounit,type,
    set_or5692540242118139586t_unit: ( product_unit * product_unit ) > set_Product_unit ).

tff(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Rat__Orat,type,
    set_or633870826150836451st_rat: ( rat * rat ) > set_rat ).

tff(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_I_Eo_J,type,
    set_or266616469461849773_set_o: ( set_o * set_o ) > set_set_o ).

tff(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Int__Oint_J,type,
    set_or370866239135849197et_int: ( set_int * set_int ) > set_set_int ).

tff(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Nat__Onat_J,type,
    set_or4548717258645045905et_nat: ( set_nat * set_nat ) > set_set_nat ).

tff(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    set_or2784603332384507286at_nat: set_Pr1261947904930325089at_nat > fun_se953073389798102371at_nat ).

tff(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    set_or4049648398082403068at_nat: ( set_Pr4329608150637261639at_nat * set_Pr4329608150637261639at_nat ) > set_se5479201105039950375at_nat ).

tff(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    set_or269330187037242274t_unit: ( set_Product_unit * set_Product_unit ) > set_set_Product_unit ).

tff(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001_Eo,type,
    set_or7139685690850216873Than_o: $o > fun_o_set_o ).

tff(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Code____Numeral__Ointeger,type,
    set_or8404916559141939852nteger: code_integer > fun_Co744628173305925485nteger ).

tff(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Int__Oint,type,
    set_or4662586982721622107an_int: int > fun_int_set_int ).

tff(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Nat__Onat,type,
    set_or4665077453230672383an_nat: nat > fun_nat_set_nat ).

tff(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Num__Onum,type,
    set_or1222409239386451017an_num: ( num * num ) > set_num ).

tff(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Product____Type__Ounit,type,
    set_or4663484573592751262t_unit: ( product_unit * product_unit ) > set_Product_unit ).

tff(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Rat__Orat,type,
    set_or4029947393144176647an_rat: ( rat * rat ) > set_rat ).

tff(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Set__Oset_It__Nat__Onat_J,type,
    set_or3540276404033026485et_nat: ( set_nat * set_nat ) > set_set_nat ).

tff(sy_c_Set__Interval_Oord__class_OatLeast_001t__Nat__Onat,type,
    set_ord_atLeast_nat: fun_nat_set_nat ).

tff(sy_c_Set__Interval_Oord__class_OatMost_001_Eo,type,
    set_ord_atMost_o: fun_o_set_o ).

tff(sy_c_Set__Interval_Oord__class_OatMost_001t__Assertions__Oassn,type,
    set_ord_atMost_assn: assn > set_assn ).

tff(sy_c_Set__Interval_Oord__class_OatMost_001t__Code____Numeral__Ointeger,type,
    set_or9101266186257409494nteger: fun_Co744628173305925485nteger ).

tff(sy_c_Set__Interval_Oord__class_OatMost_001t__Int__Oint,type,
    set_ord_atMost_int: fun_int_set_int ).

tff(sy_c_Set__Interval_Oord__class_OatMost_001t__Nat__Onat,type,
    set_ord_atMost_nat: fun_nat_set_nat ).

tff(sy_c_Set__Interval_Oord__class_OatMost_001t__Num__Onum,type,
    set_ord_atMost_num: num > set_num ).

tff(sy_c_Set__Interval_Oord__class_OatMost_001t__Product____Type__Ounit,type,
    set_or8621721900777396692t_unit: product_unit > set_Product_unit ).

tff(sy_c_Set__Interval_Oord__class_OatMost_001t__Rat__Orat,type,
    set_ord_atMost_rat: rat > set_rat ).

tff(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_I_Eo_J,type,
    set_ord_atMost_set_o: set_o > set_set_o ).

tff(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_It__Int__Oint_J,type,
    set_or58775011639299419et_int: set_int > set_set_int ).

tff(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_It__Nat__Onat_J,type,
    set_or4236626031148496127et_nat: set_nat > set_set_nat ).

tff(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    set_or2762583123196137896at_nat: fun_se953073389798102371at_nat ).

tff(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    set_or4071486571221009422at_nat: set_Pr4329608150637261639at_nat > set_se5479201105039950375at_nat ).

tff(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    set_or2827140217781692084t_unit: set_Product_unit > set_set_Product_unit ).

tff(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Code____Numeral__Ointeger,type,
    set_or2715278749043346189nteger: code_integer > fun_Co744628173305925485nteger ).

tff(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Int__Oint,type,
    set_or6656581121297822940st_int: int > fun_int_set_int ).

tff(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Nat__Onat,type,
    set_or6659071591806873216st_nat: nat > fun_nat_set_nat ).

tff(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001_Eo,type,
    set_or1716231572884733764Than_o: $o > fun_o_set_o ).

tff(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Code____Numeral__Ointeger,type,
    set_or4266950643985792945nteger: code_integer > fun_Co744628173305925485nteger ).

tff(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Int__Oint,type,
    set_or5832277885323065728an_int: int > fun_int_set_int ).

tff(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Nat__Onat,type,
    set_or5834768355832116004an_nat: nat > fun_nat_set_nat ).

tff(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Num__Onum,type,
    set_or2392100141987894638an_num: ( num * num ) > set_num ).

tff(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Rat__Orat,type,
    set_or5199638295745620268an_rat: ( rat * rat ) > set_rat ).

tff(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Set__Oset_It__Nat__Onat_J,type,
    set_or8625682525731655386et_nat: ( set_nat * set_nat ) > set_set_nat ).

tff(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Nat__Onat,type,
    set_or1210151606488870762an_nat: fun_nat_set_nat ).

tff(sy_c_Set__Interval_Oord__class_OlessThan_001_Eo,type,
    set_ord_lessThan_o: fun_o_set_o ).

tff(sy_c_Set__Interval_Oord__class_OlessThan_001t__Code____Numeral__Ointeger,type,
    set_or5754767410780653050nteger: fun_Co744628173305925485nteger ).

tff(sy_c_Set__Interval_Oord__class_OlessThan_001t__Int__Oint,type,
    set_ord_lessThan_int: fun_int_set_int ).

tff(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
    set_ord_lessThan_nat: fun_nat_set_nat ).

tff(sy_c_Set__Interval_Oord__class_OlessThan_001t__Num__Onum,type,
    set_ord_lessThan_num: num > set_num ).

tff(sy_c_Set__Interval_Oord__class_OlessThan_001t__Product____Type__Ounit,type,
    set_or8708608758551125680t_unit: product_unit > set_Product_unit ).

tff(sy_c_Set__Interval_Oord__class_OlessThan_001t__Rat__Orat,type,
    set_ord_lessThan_rat: rat > set_rat ).

tff(sy_c_Set__Interval_Oord__class_OlessThan_001t__Set__Oset_I_Eo_J,type,
    set_or3489638696441961371_set_o: set_o > set_set_o ).

tff(sy_c_Set__Interval_Oord__class_OlessThan_001t__Set__Oset_It__Int__Oint_J,type,
    set_or5935648273017318783et_int: set_int > set_set_int ).

tff(sy_c_Set__Interval_Oord__class_OlessThan_001t__Set__Oset_It__Nat__Onat_J,type,
    set_or890127255671739683et_nat: set_nat > set_set_nat ).

tff(sy_c_Set__Interval_Oord__class_OlessThan_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    set_or5243998310507771012at_nat: fun_se953073389798102371at_nat ).

tff(sy_c_Set__Interval_Oord__class_OlessThan_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    set_or2137699863726836970at_nat: set_Pr4329608150637261639at_nat > set_se5479201105039950375at_nat ).

tff(sy_c_Set__Interval_Oord__class_OlessThan_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    set_or3324826255835560848t_unit: set_Product_unit > set_set_Product_unit ).

tff(sy_c_String_Ochar_OChar,type,
    char2: ( $o * $o * $o * $o * $o * $o * $o * $o ) > char ).

tff(sy_c_String_Ointeger__of__char,type,
    integer_of_char: char > code_integer ).

tff(sy_c_Sum__Type_OInl_001t__Nat__Onat_001t__Nat__Onat,type,
    sum_Inl_nat_nat: nat > sum_sum_nat_nat ).

tff(sy_c_Sum__Type_OInr_001t__Nat__Onat_001t__Nat__Onat,type,
    sum_Inr_nat_nat: nat > sum_sum_nat_nat ).

tff(sy_c_Syntax__Match_Osyntax__fo__nomatch_001t__Int__Oint_001t__Int__Oint,type,
    syntax5678989248478167196nt_int: fun_int_fun_int_o ).

tff(sy_c_Syntax__Match_Osyntax__fo__nomatch_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    syntax5084084251851430274at_nat: ( multis2468970476368604999at_nat * multis2468970476368604999at_nat ) > $o ).

tff(sy_c_Syntax__Match_Osyntax__fo__nomatch_001t__Nat__Onat_001t__Nat__Onat,type,
    syntax4682126007086162916at_nat: fun_nat_fun_nat_o ).

tff(sy_c_Syntax__Match_Osyntax__fo__nomatch_001t__Rat__Orat_001t__Rat__Orat,type,
    syntax3730441303064801268at_rat: fun_rat_fun_rat_o ).

tff(sy_c_Time__Reasoning_Ofails_001t__Heap__Oarray_Itf__a_J,type,
    time_fails_array_a: heap_T6362127782908069795rray_a > fun_he8413527710729349838unit_o ).

tff(sy_c_Time__Reasoning_Ofails_001t__Product____Type__Ounit,type,
    time_f8834461667527620124t_unit: heap_T5738788834812785303t_unit > fun_he8413527710729349838unit_o ).

tff(sy_c_Time__Reasoning_Othe__heap_001t__Heap__Oarray_Itf__a_J,type,
    time_t490086488869527696rray_a: ( heap_T6362127782908069795rray_a * heap_e7401611519738050253t_unit ) > heap_e7401611519738050253t_unit ).

tff(sy_c_Time__Reasoning_Othe__heap_001t__Product____Type__Ounit,type,
    time_t3350536682685678164t_unit: ( heap_T5738788834812785303t_unit * heap_e7401611519738050253t_unit ) > heap_e7401611519738050253t_unit ).

tff(sy_c_Time__Reasoning_Othe__res_001t__Heap__Oarray_Itf__a_J,type,
    time_the_res_array_a: heap_T6362127782908069795rray_a > fun_he7369252872201260279rray_a ).

tff(sy_c_Time__Reasoning_Othe__res_001t__Product____Type__Ounit,type,
    time_t2745601220510131320t_unit: heap_T5738788834812785303t_unit > fun_he5123621388056232515t_unit ).

tff(sy_c_Time__Reasoning_Otime_001t__Heap__Oarray_Itf__a_J,type,
    time_time_array_a: ( heap_T6362127782908069795rray_a * heap_e7401611519738050253t_unit ) > nat ).

tff(sy_c_Time__Reasoning_Otime_001t__Product____Type__Ounit,type,
    time_t4224138285095624986t_unit: ( heap_T5738788834812785303t_unit * heap_e7401611519738050253t_unit ) > nat ).

tff(sy_c_Transitive__Closure_Ortrancl_001t__Nat__Onat,type,
    transi2905341329935302413cl_nat: fun_se320340636488258563at_nat ).

tff(sy_c_Transitive__Closure_Otrancl_001t__Nat__Onat,type,
    transi6264000038957366511cl_nat: fun_se320340636488258563at_nat ).

tff(sy_c_Typedef_Otype__definition_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
    type_d8366093980585677751er_int: ( fun_Code_integer_int * fun_int_Code_integer * set_int ) > $o ).

tff(sy_c_Typedef_Otype__definition_001t__Code____Numeral__Onatural_001t__Nat__Onat,type,
    type_d4410041424927559462al_nat: ( fun_Code_natural_nat * fun_nat_Code_natural * set_nat ) > $o ).

tff(sy_c_Typedef_Otype__definition_001t__Product____Type__Ounit_001_Eo,type,
    type_d6188575255521822967unit_o: ( fun_Product_unit_o * fun_o_Product_unit * set_o ) > $o ).

tff(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
    accp_list_nat: fun_li1025265955262268170_nat_o > fun_list_nat_o ).

tff(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
    accp_nat: fun_nat_fun_nat_o > fun_nat_o ).

tff(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    accp_P8126237942716283194atural: fun_Pr3592279944642289454ural_o > fun_Pr8359263388657976682ural_o ).

tff(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    accp_P5801069581201407417et_nat: fun_Pr7920380315054183110_nat_o > fun_Pr6460944699146269935_nat_o ).

tff(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    accp_P1096762738010456898nt_int: fun_Pr9018117161326028078_int_o > fun_Pr3238374608701176162_int_o ).

tff(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    accp_P4275260045618599050at_nat: fun_Pr2028404973800837934_nat_o > fun_Pr4796943543331071514_nat_o ).

tff(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    accp_P8948468358075348838it_nat: ( fun_Pr5911813565203289452_nat_o * produc2867611627572283311it_nat ) > $o ).

tff(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    accp_P414730952086964626it_nat: ( fun_Pr6341106346053136302_nat_o * produc3911288613690379145it_nat ) > $o ).

tff(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
    accp_P3113834385874906142um_num: ( fun_Pr4799464687642144302_num_o * product_prod_num_num ) > $o ).

tff(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    accp_P3253464921323968230nt_int: fun_Pr886604116968709228_int_o > fun_Pr1196100989263358594_int_o ).

tff(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    accp_P4694664897847628410at_nat: ( fun_Pr8463018485500633518_nat_o * produc9217583074051984497at_nat ) > $o ).

tff(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    accp_P1394777952347926645et_nat: fun_Pr3358449090565925198_nat_o > fun_Pr1227177680593602867_nat_o ).

tff(sy_c_Wellfounded_Ofinite__psubset_001t__Code____Numeral__Ointeger,type,
    finite2416775604798480986nteger: set_Pr7577011563204128103nteger ).

tff(sy_c_Wellfounded_Ofinite__psubset_001t__Int__Oint,type,
    finite_psubset_int: set_Pr2522554150109002629et_int ).

tff(sy_c_Wellfounded_Ofinite__psubset_001t__Nat__Onat,type,
    finite_psubset_nat: set_Pr5488025237498180813et_nat ).

tff(sy_c_Wellfounded_Ofinite__psubset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    finite469560695537375940at_nat: set_Pr4329608150637261639at_nat ).

tff(sy_c_Wellfounded_Oless__than,type,
    less_than: set_Pr1261947904930325089at_nat ).

tff(sy_c_Wellfounded_Olex__prod_001t__Nat__Onat_001t__Nat__Onat,type,
    lex_prod_nat_nat: ( set_Pr1261947904930325089at_nat * set_Pr1261947904930325089at_nat ) > set_Pr8693737435421807431at_nat ).

tff(sy_c_Wellfounded_Olex__prod_001t__Nat__Onat_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    lex_pr4265550801952275104at_nat: ( set_Pr1261947904930325089at_nat * set_Pr4329608150637261639at_nat ) > set_Pr2072254264782222413at_nat ).

tff(sy_c_Wellfounded_Olex__prod_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Nat__Onat,type,
    lex_pr1951919194703979714at_nat: ( set_Pr4329608150637261639at_nat * set_Pr1261947904930325089at_nat ) > set_Pr5070339090747523585at_nat ).

tff(sy_c_Wellfounded_Olex__prod_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    lex_pr8000699672184251119at_nat: ( set_Pr4329608150637261639at_nat * set_Pr4329608150637261639at_nat ) > set_Pr5564308138774400199at_nat ).

tff(sy_c_Wellfounded_Olex__prod_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    lex_pr421891345023438537nt_int: ( set_Pr7847555563209246911e_term * set_Pr2560585780119916871nt_int ) > set_Pr3703873761940759199nt_int ).

tff(sy_c_Wellfounded_Olex__prod_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    lex_pr1401158619140779824nteger: ( set_Pr2514328457256655413e_term * set_Pr5052581263052047815nteger ) > set_Pr6949033248718891245nteger ).

tff(sy_c_Wellfounded_Olex__prod_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    lex_pr6479962325641483138et_nat: ( set_Pr2890355626087285447_nat_o * set_Pr719794911490849221et_nat ) > set_Pr9066344408807579265et_nat ).

tff(sy_c_Wellfounded_Olex__prod_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    lex_pr1264321499788159136et_nat: ( set_Pr2890355626087285447_nat_o * set_Pr9066344408807579265et_nat ) > set_Pr7057080801110549565et_nat ).

tff(sy_c_Wellfounded_Olex__prod_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    lex_pr7544126028092883869nt_int: ( set_Pr257197284073945367e_term * set_Pr2560585780119916871nt_int ) > set_Pr3767905878465553991nt_int ).

tff(sy_c_Wellfounded_Omax__ext_001_Eo,type,
    max_ext_o: set_Product_prod_o_o > set_Pr4577759397028426247_set_o ).

tff(sy_c_Wellfounded_Omax__ext_001t__Code____Numeral__Ointeger,type,
    max_ext_Code_integer: set_Pr4811707699266497531nteger > set_Pr7577011563204128103nteger ).

tff(sy_c_Wellfounded_Omax__ext_001t__Int__Oint,type,
    max_ext_int: set_Pr958786334691620121nt_int > set_Pr2522554150109002629et_int ).

tff(sy_c_Wellfounded_Omax__ext_001t__Nat__Onat,type,
    max_ext_nat: set_Pr1261947904930325089at_nat > set_Pr5488025237498180813et_nat ).

tff(sy_c_Wellfounded_Omax__ext_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    max_ex8135407076693332796at_nat: set_Pr8693737435421807431at_nat > set_Pr4329608150637261639at_nat ).

tff(sy_c_Wellfounded_Omax__ext_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    max_ex8833738776070432290at_nat: set_Pr5564308138774400199at_nat > set_Pr7459493094073627847at_nat ).

tff(sy_c_Wellfounded_Omax__ext_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    max_ex4535816423174879388at_nat: set_Pr4329608150637261639at_nat > set_Pr1604112560894399303at_nat ).

tff(sy_c_Wellfounded_Omax__extp_001t__Nat__Onat,type,
    max_extp_nat: fun_nat_fun_nat_o > fun_se2170385732985038782_nat_o ).

tff(sy_c_Wellfounded_Omax__extp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    max_ex4864111882549613972at_nat: fun_Pr2028404973800837934_nat_o > fun_se5639961202347202350_nat_o ).

tff(sy_c_Wellfounded_Omax__extp_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    max_ex4845989503969680116at_nat: fun_se5639961202347202350_nat_o > fun_se7001366092147120942_nat_o ).

tff(sy_c_Wellfounded_Omeasure_001t__Nat__Onat,type,
    measure_nat: fun_nat_nat > set_Pr1261947904930325089at_nat ).

tff(sy_c_Wellfounded_Omeasure_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    measur1827424007717751593at_nat: fun_se4097146774670233028at_nat > set_Pr4329608150637261639at_nat ).

tff(sy_c_Wellfounded_Omin__ext_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    min_ex6901939911449802026at_nat: set_Pr8693737435421807431at_nat > set_Pr4329608150637261639at_nat ).

tff(sy_c_Wellfounded_Omlex__prod_001t__Nat__Onat,type,
    mlex_prod_nat: fun_nat_nat > fun_se320340636488258563at_nat ).

tff(sy_c_Wellfounded_Omlex__prod_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    mlex_p3502713205431853936at_nat: ( fun_se4097146774670233028at_nat * set_Pr4329608150637261639at_nat ) > set_Pr4329608150637261639at_nat ).

tff(sy_c_Wellfounded_Opred__nat,type,
    pred_nat: set_Pr1261947904930325089at_nat ).

tff(sy_c_Wfrec_Osame__fst_001t__Nat__Onat_001t__Nat__Onat,type,
    same_fst_nat_nat: ( fun_nat_o * fun_na7044673412300895210at_nat ) > set_Pr8693737435421807431at_nat ).

tff(sy_c_Wfrec_Osame__fst_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    same_f1121446225334236108nt_int: ( fun_fu3265955482920998386term_o * fun_fu786557078278636193nt_int ) > set_Pr3703873761940759199nt_int ).

tff(sy_c_Wfrec_Osame__fst_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    same_f8215626710265358387nteger: ( fun_fu4736795817735658359term_o * fun_fu8543582513329703974nteger ) > set_Pr6949033248718891245nteger ).

tff(sy_c_Wfrec_Osame__fst_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    same_f842378046369478405et_nat: ( fun_fu5135969500543783852at_o_o * fun_fu5004560472337415769et_nat ) > set_Pr9066344408807579265et_nat ).

tff(sy_c_Wfrec_Osame__fst_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    same_f7796809703074202275et_nat: ( fun_fu5135969500543783852at_o_o * fun_fu951349246861503509et_nat ) > set_Pr7057080801110549565et_nat ).

tff(sy_c_Wfrec_Osame__fst_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    same_f9192169231508103328nt_int: ( fun_fu6378075912484669126term_o * fun_fu4812223801888690549nt_int ) > set_Pr3767905878465553991nt_int ).

tff(sy_c_aa_001_Eo_001_Eo,type,
    aa_o_o: ( fun_o_o * $o ) > $o ).

tff(sy_c_aa_001_Eo_001t__Assertions__Oassn,type,
    aa_o_assn: ( fun_o_assn * $o ) > assn ).

tff(sy_c_aa_001_Eo_001t__Code____Numeral__Ointeger,type,
    aa_o_Code_integer: ( fun_o_Code_integer * $o ) > code_integer ).

tff(sy_c_aa_001_Eo_001t__Int__Oint,type,
    aa_o_int: ( fun_o_int * $o ) > int ).

tff(sy_c_aa_001_Eo_001t__Nat__Onat,type,
    aa_o_nat: ( fun_o_nat * $o ) > nat ).

tff(sy_c_aa_001_Eo_001t__Option__Ooption_I_Eo_J,type,
    aa_o_option_o: ( fun_o_option_o * $o ) > option_o ).

tff(sy_c_aa_001_Eo_001t__Option__Ooption_It__Num__Onum_J,type,
    aa_o_option_num: ( fun_o_option_num * $o ) > option_num ).

tff(sy_c_aa_001_Eo_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    aa_o_o5708127299350256820it_nat: ( fun_o_7229649064035662211it_nat * $o ) > option8956607266484857688it_nat ).

tff(sy_c_aa_001_Eo_001t__Option__Ooption_It__Product____Type__Ounit_J,type,
    aa_o_o3081425935505226615t_unit: ( fun_o_6261137236491177342t_unit * $o ) > option_Product_unit ).

tff(sy_c_aa_001_Eo_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
    aa_o_option_set_nat: ( fun_o_option_set_nat * $o ) > option_set_nat ).

tff(sy_c_aa_001_Eo_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
    aa_o_P8186867570850176203od_o_o: ( fun_o_4732642864545671890od_o_o * $o ) > product_prod_o_o ).

tff(sy_c_aa_001_Eo_001t__Product____Type__Ounit,type,
    aa_o_Product_unit: ( fun_o_Product_unit * $o ) > product_unit ).

tff(sy_c_aa_001_Eo_001t__Rat__Orat,type,
    aa_o_rat: ( fun_o_rat * $o ) > rat ).

tff(sy_c_aa_001_Eo_001t__Set__Oset_I_Eo_J,type,
    aa_o_set_o: ( fun_o_set_o * $o ) > set_o ).

tff(sy_c_aa_001_Eo_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
    aa_o_s5402425747378369775nteger: ( fun_o_5240169576699714110nteger * $o ) > set_Code_integer ).

tff(sy_c_aa_001_Eo_001t__Set__Oset_It__Int__Oint_J,type,
    aa_o_set_int: ( fun_o_set_int * $o ) > set_int ).

tff(sy_c_aa_001_Eo_001t__Set__Oset_It__Nat__Onat_J,type,
    aa_o_set_nat: ( fun_o_set_nat * $o ) > set_nat ).

tff(sy_c_aa_001_Eo_001t__fun_I_Eo_M_Eo_J,type,
    aa_o_fun_o_o: ( fun_o_fun_o_o * $o ) > fun_o_o ).

tff(sy_c_aa_001_Eo_001t__fun_It__Nat__Onat_M_Eo_J,type,
    aa_o_fun_nat_o: ( fun_o_fun_nat_o * $o ) > fun_nat_o ).

tff(sy_c_aa_001_Eo_001t__fun_It__Product____Type__Ounit_M_Eo_J,type,
    aa_o_f4945551202706114282unit_o: ( fun_o_6763651944650080953unit_o * $o ) > fun_Product_unit_o ).

tff(sy_c_aa_001t__Assertions__Oassn_001_Eo,type,
    aa_assn_o: ( fun_assn_o * assn ) > $o ).

tff(sy_c_aa_001t__Assertions__Oassn_001t__Assertions__Oassn,type,
    aa_assn_assn: ( fun_assn_assn * assn ) > assn ).

tff(sy_c_aa_001t__Assertions__Oassn_001t__Option__Ooption_It__Assertions__Oassn_J,type,
    aa_assn_option_assn: ( fun_assn_option_assn * assn ) > option_assn ).

tff(sy_c_aa_001t__Assertions__Oassn_001t__fun_I_Eo_Mt__Assertions__Oassn_J,type,
    aa_assn_fun_o_assn: ( fun_assn_fun_o_assn * assn ) > fun_o_assn ).

tff(sy_c_aa_001t__Assertions__Oassn_001t__fun_It__Assertions__Oassn_M_Eo_J,type,
    aa_assn_fun_assn_o: ( fun_assn_fun_assn_o * assn ) > fun_assn_o ).

tff(sy_c_aa_001t__Assertions__Oassn_001t__fun_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
    aa_ass954072293579886259n_assn: ( fun_as3983628580203722482n_assn * assn ) > fun_assn_assn ).

tff(sy_c_aa_001t__Assertions__Oassn_001t__fun_It__Code____Numeral__Ointeger_M_Eo_J,type,
    aa_ass2896223873163428078eger_o: ( fun_as7521517929205406341eger_o * assn ) > fun_Code_integer_o ).

tff(sy_c_aa_001t__Assertions__Oassn_001t__fun_It__Code____Numeral__Ointeger_Mt__Assertions__Oassn_J,type,
    aa_ass6027779773078136296r_assn: ( fun_as4904527345752988583r_assn * assn ) > fun_Co4490034186337852034r_assn ).

tff(sy_c_aa_001t__Assertions__Oassn_001t__fun_It__Int__Oint_M_Eo_J,type,
    aa_assn_fun_int_o: ( fun_assn_fun_int_o * assn ) > fun_int_o ).

tff(sy_c_aa_001t__Assertions__Oassn_001t__fun_It__Int__Oint_Mt__Assertions__Oassn_J,type,
    aa_assn_fun_int_assn: ( fun_as3432858861813084150t_assn * assn ) > fun_int_assn ).

tff(sy_c_aa_001t__Assertions__Oassn_001t__fun_It__Nat__Onat_M_Eo_J,type,
    aa_assn_fun_nat_o: ( fun_assn_fun_nat_o * assn ) > fun_nat_o ).

tff(sy_c_aa_001t__Assertions__Oassn_001t__fun_It__Nat__Onat_Mt__Assertions__Oassn_J,type,
    aa_assn_fun_nat_assn: ( fun_as8240436605320707994t_assn * assn ) > fun_nat_assn ).

tff(sy_c_aa_001t__Assertions__Oassn_001t__fun_It__Product____Type__Ounit_Mt__Assertions__Oassn_J,type,
    aa_ass3177796706412234594t_assn: ( fun_as4019953064511417593t_assn * assn ) > fun_Pr6626665806141890376t_assn ).

tff(sy_c_aa_001t__Assertions__Oassn_001t__fun_It__Rat__Orat_M_Eo_J,type,
    aa_assn_fun_rat_o: ( fun_assn_fun_rat_o * assn ) > fun_rat_o ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001_Eo,type,
    aa_Code_integer_o: ( fun_Code_integer_o * code_integer ) > $o ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__Assertions__Oassn,type,
    aa_Code_integer_assn: ( fun_Co4490034186337852034r_assn * code_integer ) > assn ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
    aa_Cod1783974652533396728nteger: ( fun_Co8499238673658658103nteger * code_integer ) > code_integer ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Onatural,type,
    aa_Cod607569804290114243atural: ( fun_Co3734316457315071362atural * code_integer ) > code_natural ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
    aa_Code_integer_int: ( fun_Code_integer_int * code_integer ) > int ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
    aa_Code_integer_nat: ( fun_Code_integer_nat * code_integer ) > nat ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
    aa_Code_integer_num: ( fun_Code_integer_num * code_integer ) > num ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__Option__Ooption_It__Code____Numeral__Ointeger_J,type,
    aa_Cod5017737808611256136nteger: ( fun_Co8029881127924365703nteger * code_integer ) > option_Code_integer ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
    aa_Cod3168588076859124107eger_o: ( fun_Co1766037875893669450eger_o * code_integer ) > produc6271795597528267376eger_o ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    aa_Cod6977894654539884864nteger: ( fun_Co6597186368970283863nteger * code_integer ) > produc8923325533196201883nteger ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    aa_Cod7444061876693584541et_nat: ( fun_Co4803750647967840348et_nat * code_integer ) > produc3658429121746597890et_nat ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    aa_Cod6375820294346531166nt_int: ( fun_Co4113693717567439989nt_int * code_integer ) > product_prod_int_int ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__Rat__Orat,type,
    aa_Code_integer_rat: ( fun_Code_integer_rat * code_integer ) > rat ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
    aa_Cod2813182003028390446nteger: ( fun_Co744628173305925485nteger * code_integer ) > set_Code_integer ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__Set__Oset_It__Int__Oint_J,type,
    aa_Cod1964855514770062461et_int: ( fun_Co5817875961738342972et_int * code_integer ) > set_int ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__Set__Oset_It__Nat__Onat_J,type,
    aa_Cod6142706534279259169et_nat: ( fun_Co8307959106670069728et_nat * code_integer ) > set_nat ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__fun_It__Assertions__Oassn_M_Eo_J,type,
    aa_Cod8400811354895609070assn_o: ( fun_Co4819230592921789445assn_o * code_integer ) > fun_assn_o ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__fun_It__Code____Numeral__Ointeger_M_Eo_J,type,
    aa_Cod326357343816142457eger_o: ( fun_Co2081214437782444048eger_o * code_integer ) > fun_Code_integer_o ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    aa_Cod4161879620478718930nteger: ( fun_Co1981900195452921617nteger * code_integer ) > fun_Co8499238673658658103nteger ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__fun_It__Code____Numeral__Ointeger_Mt__Int__Oint_J,type,
    aa_Cod1242632294114111009er_int: ( fun_Co1092983284983208416er_int * code_integer ) > fun_Code_integer_int ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__fun_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J,type,
    aa_Cod5420483313623307717er_nat: ( fun_Co3583066429914935172er_nat * code_integer ) > fun_Code_integer_nat ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__fun_It__Code____Numeral__Ointeger_Mt__Num__Onum_J,type,
    aa_Cod6128727250572145423er_num: ( fun_Co8521658056209057742er_num * code_integer ) > fun_Code_integer_num ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__fun_It__Code____Numeral__Ointeger_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_J,type,
    aa_Cod1096751537565085541eger_o: ( fun_Co3544761417380347684eger_o * code_integer ) > fun_Co1766037875893669450eger_o ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__fun_It__Code____Numeral__Ointeger_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    aa_Cod8380929501330563836nteger: ( fun_Co2470855966376689427nteger * code_integer ) > fun_Co6597186368970283863nteger ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__fun_It__Int__Oint_M_Eo_J,type,
    aa_Cod8477617969808203498_int_o: ( fun_Co8353275306710069249_int_o * code_integer ) > fun_int_o ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    aa_Cod5541156447037011290e_term: ( fun_Co1966082167426949785e_term * code_integer ) > fun_in5730379987311621695e_term ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__fun_It__Nat__Onat_M_Eo_J,type,
    aa_Cod1075288278386115654_nat_o: ( fun_Co1375048237525739357_nat_o * code_integer ) > fun_nat_o ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J,type,
    aa_Cod1578151519121547077nteger: ( fun_Co6226381647958292740nteger * code_integer ) > fun_nat_Code_integer ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_J,type,
    aa_Cod3140087502949435154nteger: ( fun_Co5080488584548667985nteger * code_integer ) > fun_na8135612474337863287nteger ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    aa_Cod1978467581589928094nteger: ( fun_Co1561183069634336733nteger * code_integer ) > fun_Pr5876161306168176259nteger ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    aa_Cod8918851774953611029e_term: ( fun_Co3668495603736800980e_term * code_integer ) > fun_Pr5098669352780829690e_term ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
    aa_Cod5288490272431355796_nat_o: ( fun_Co9016714620104711083_nat_o * code_integer ) > fun_Pr6460944699146269935_nat_o ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    aa_Cod5337730273189675398e_term: ( fun_Co4988957157240174789e_term * code_integer ) > fun_Pr7763680713840462443e_term ).

tff(sy_c_aa_001t__Code____Numeral__Ointeger_001t__fun_It__Rat__Orat_M_Eo_J,type,
    aa_Cod6561327387924323390_rat_o: ( fun_Co625613742390903637_rat_o * code_integer ) > fun_rat_o ).

tff(sy_c_aa_001t__Code____Numeral__Onatural_001_Eo,type,
    aa_Code_natural_o: ( fun_Code_natural_o * code_natural ) > $o ).

tff(sy_c_aa_001t__Code____Numeral__Onatural_001t__Code____Numeral__Ointeger,type,
    aa_Cod5448446754359732931nteger: ( fun_Co2940338738630218498nteger * code_natural ) > code_integer ).

tff(sy_c_aa_001t__Code____Numeral__Onatural_001t__Code____Numeral__Onatural,type,
    aa_Cod4272041906116450446atural: ( fun_Co7398788559141407565atural * code_natural ) > code_natural ).

tff(sy_c_aa_001t__Code____Numeral__Onatural_001t__Nat__Onat,type,
    aa_Code_natural_nat: ( fun_Code_natural_nat * code_natural ) > nat ).

tff(sy_c_aa_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    aa_Cod6383727878942225636atural: ( fun_Co4337079049361313443atural * code_natural ) > produc5835291356934675326atural ).

tff(sy_c_aa_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    aa_Cod6808739660676082561atural: ( fun_Co5709460363461100952atural * code_natural ) > produc6756470014200349799atural ).

tff(sy_c_aa_001t__Code____Numeral__Onatural_001t__Set__Oset_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    aa_Cod7772718489437220139atural: ( fun_Co2944084857415636034atural * code_natural ) > set_Pr7564037697178849041atural ).

tff(sy_c_aa_001t__Code____Numeral__Onatural_001t__fun_It__Code____Numeral__Onatural_M_Eo_J,type,
    aa_Cod1485054954640246627ural_o: ( fun_Co7302518231560758906ural_o * code_natural ) > fun_Code_natural_o ).

tff(sy_c_aa_001t__Code____Numeral__Onatural_001t__fun_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    aa_Cod5141017464274028979atural: ( fun_Co6813818151677833714atural * code_natural ) > fun_Co7398788559141407565atural ).

tff(sy_c_aa_001t__Code____Numeral__Onatural_001t__fun_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J,type,
    aa_Cod4292056611156568242atural: ( fun_Co1890133979025130057atural * code_natural ) > fun_Co5709460363461100952atural ).

tff(sy_c_aa_001t__Code____Numeral__Onatural_001t__fun_It__Code____Numeral__Onatural_Mt__fun_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J_J,type,
    aa_Cod8811915439870959971atural: ( fun_Co9168753396221475450atural * code_natural ) > fun_Co1890133979025130057atural ).

tff(sy_c_aa_001t__Code____Numeral__Onatural_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    aa_Cod3874068878414155173e_term: ( fun_Co298994598804093668e_term * code_natural ) > fun_in5730379987311621695e_term ).

tff(sy_c_aa_001t__Code____Numeral__Onatural_001t__fun_It__Nat__Onat_M_Eo_J,type,
    aa_Cod9120328075896114107_nat_o: ( fun_Co196715998180962002_nat_o * code_natural ) > fun_nat_o ).

tff(sy_c_aa_001t__Code____Numeral__Onatural_001t__fun_It__Nat__Onat_Mt__Code____Numeral__Onatural_J,type,
    aa_Cod5320533616963873627atural: ( fun_Co740390889742897050atural * code_natural ) > fun_nat_Code_natural ).

tff(sy_c_aa_001t__Code____Numeral__Onatural_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Code____Numeral__Onatural_J_J,type,
    aa_Cod217761371205376936atural: ( fun_Co200561849269645671atural * code_natural ) > fun_na3365689438791330114atural ).

tff(sy_c_aa_001t__Code____Numeral__Onatural_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_M_Eo_J,type,
    aa_Cod1393124287678120144ural_o: ( fun_Co9066792663755620495ural_o * code_natural ) > fun_Pr8359263388657976682ural_o ).

tff(sy_c_aa_001t__Code____Numeral__Onatural_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    aa_Cod1269109650860651881atural: ( fun_Co1851440197950133416atural * code_natural ) > fun_Pr74676805955934211atural ).

tff(sy_c_aa_001t__Code____Numeral__Onatural_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J,type,
    aa_Cod6352003912080677724atural: ( fun_Co1105491363547889651atural * code_natural ) > fun_Pr7769407664385210434atural ).

tff(sy_c_aa_001t__Code____Numeral__Onatural_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Code____Numeral__Onatural_J_J,type,
    aa_Cod3489170700911977190atural: ( fun_Co3643010573817537149atural * code_natural ) > fun_Pr4906574453216509900atural ).

tff(sy_c_aa_001t__Code____Numeral__Onatural_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
    aa_Cod7546338805161909513_nat_o: ( fun_Co2051191115980488992_nat_o * code_natural ) > fun_Pr6460944699146269935_nat_o ).

tff(sy_c_aa_001t__Heap__Oarray_Itf__a_J_001_Eo,type,
    aa_array_a_o: ( fun_array_a_o * array_a ) > $o ).

tff(sy_c_aa_001t__Heap__Oarray_Itf__a_J_001t__Heap__Oarray_Itf__a_J,type,
    aa_array_a_array_a: ( fun_array_a_array_a * array_a ) > array_a ).

tff(sy_c_aa_001t__Heap__Oarray_Itf__a_J_001t__Heap____Time____Monad__OHeap_It__Heap__Oarray_Itf__a_J_J,type,
    aa_arr1142863274018860686rray_a: ( fun_ar3891948820113774757rray_a * array_a ) > heap_T6362127782908069795rray_a ).

tff(sy_c_aa_001t__Heap__Oarray_Itf__a_J_001t__Heap____Time____Monad__OHeap_It__Product____Type__Ounit_J,type,
    aa_arr7999650297717212780t_unit: ( fun_ar1074044450438384043t_unit * array_a ) > heap_T5738788834812785303t_unit ).

tff(sy_c_aa_001t__Heap__Oarray_Itf__a_J_001t__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__fun_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J_J,type,
    aa_arr9035823794894939038it_nat: ( fun_ar4667500465507062749it_nat * array_a ) > fun_he2390400765173608009it_nat ).

tff(sy_c_aa_001t__Heap__Oarray_Itf__a_J_001t__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__fun_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J_J,type,
    aa_arr8018972492040254448it_nat: ( fun_ar5851962999413977351it_nat * array_a ) > fun_he8369595706569872389it_nat ).

tff(sy_c_aa_001t__Heap__Oarray_Itf__a_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__Heap__Oarray_Itf__a_J_J,type,
    aa_arr5115324663822341685rray_a: ( fun_ar6017029185804945652rray_a * array_a ) > fun_Pr8777304358194983264rray_a ).

tff(sy_c_aa_001t__Heap__Oarray_Itf__a_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J,type,
    aa_arr3387439787600506181t_unit: ( fun_ar121531768175530460t_unit * array_a ) > fun_Pr2419607445322970330t_unit ).

tff(sy_c_aa_001t__Heap__Oarray_Itf__a_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__Nat__Onat_J,type,
    aa_arr7625186775369825262at_nat: ( fun_ar8857663332695973421at_nat * array_a ) > fun_Pr4343998633453697049at_nat ).

tff(sy_c_aa_001t__Heap__Oarray_Itf__a_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    aa_arr7695238004252175618it_nat: ( fun_ar7427004957847640857it_nat * array_a ) > fun_Pr192538292188806807it_nat ).

tff(sy_c_aa_001t__Heap__Oarray_Itf__a_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    aa_arr6895087029218458358it_nat: ( fun_ar4934926718671674165it_nat * array_a ) > fun_Pr5651933991979716257it_nat ).

tff(sy_c_aa_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001_Eo,type,
    aa_hea7994211679605476167unit_o: ( fun_he8413527710729349838unit_o * heap_e7401611519738050253t_unit ) > $o ).

tff(sy_c_aa_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Heap__Oarray_Itf__a_J,type,
    aa_hea3268681801748734376rray_a: ( fun_he7369252872201260279rray_a * heap_e7401611519738050253t_unit ) > array_a ).

tff(sy_c_aa_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    aa_hea5936688510613671481it_nat: ( fun_he1504492240061592256it_nat * heap_e7401611519738050253t_unit ) > option3216581401566546698it_nat ).

tff(sy_c_aa_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    aa_hea684056619475940329it_nat: ( fun_he5234484606919320760it_nat * heap_e7401611519738050253t_unit ) > option8956607266484857688it_nat ).

tff(sy_c_aa_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    aa_hea1118439097112461811it_nat: ( fun_he281446669002384250it_nat * heap_e7401611519738050253t_unit ) > produc6714399278180371524it_nat ).

tff(sy_c_aa_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    aa_hea256619718444519449it_nat: ( fun_he4944555133437423336it_nat * heap_e7401611519738050253t_unit ) > produc8664842809031399944it_nat ).

tff(sy_c_aa_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Product____Type__Ounit,type,
    aa_hea4146273921685161788t_unit: ( fun_he5123621388056232515t_unit * heap_e7401611519738050253t_unit ) > product_unit ).

tff(sy_c_aa_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__fun_It__Nat__Onat_Mt__Heap__Oarray_Itf__a_J_J,type,
    aa_hea2549104158996286709rray_a: ( fun_he4035479571739904452rray_a * heap_e7401611519738050253t_unit ) > fun_nat_array_a ).

tff(sy_c_aa_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__fun_It__Nat__Onat_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J,type,
    aa_hea3178159646823327365t_unit: ( fun_he6845747896722556172t_unit * heap_e7401611519738050253t_unit ) > fun_na8669532458821385046t_unit ).

tff(sy_c_aa_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J,type,
    aa_hea461265506217620142at_nat: ( fun_he5369522480449343229at_nat * heap_e7401611519738050253t_unit ) > fun_nat_nat ).

tff(sy_c_aa_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__fun_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    aa_hea7328941321439323714it_nat: ( fun_he2390400765173608009it_nat * heap_e7401611519738050253t_unit ) > fun_na4198017608689007891it_nat ).

tff(sy_c_aa_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__fun_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    aa_hea5083147195637387702it_nat: ( fun_he8369595706569872389it_nat * heap_e7401611519738050253t_unit ) > fun_na5667031169817407269it_nat ).

tff(sy_c_aa_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__fun_It__Nat__Onat_Mt__Product____Type__Ounit_J,type,
    aa_hea3828351310419263941t_unit: ( fun_he8708342781048922188t_unit * heap_e7401611519738050253t_unit ) > fun_nat_Product_unit ).

tff(sy_c_aa_001t__Int__Oint_001_Eo,type,
    aa_int_o: ( fun_int_o * int ) > $o ).

tff(sy_c_aa_001t__Int__Oint_001t__Assertions__Oassn,type,
    aa_int_assn: ( fun_int_assn * int ) > assn ).

tff(sy_c_aa_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
    aa_int_Code_integer: ( fun_int_Code_integer * int ) > code_integer ).

tff(sy_c_aa_001t__Int__Oint_001t__Int__Oint,type,
    aa_int_int: ( fun_int_int * int ) > int ).

tff(sy_c_aa_001t__Int__Oint_001t__Nat__Onat,type,
    aa_int_nat: ( fun_int_nat * int ) > nat ).

tff(sy_c_aa_001t__Int__Oint_001t__Num__Onum,type,
    aa_int_num: ( fun_int_num * int ) > num ).

tff(sy_c_aa_001t__Int__Oint_001t__Option__Ooption_It__Int__Oint_J,type,
    aa_int_option_int: ( fun_int_option_int * int ) > option_int ).

tff(sy_c_aa_001t__Int__Oint_001t__Option__Ooption_It__Num__Onum_J,type,
    aa_int_option_num: ( fun_int_option_num * int ) > option_num ).

tff(sy_c_aa_001t__Int__Oint_001t__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J,type,
    aa_int3262262799336221824e_term: ( fun_in5730379987311621695e_term * int ) > option6357759511663192854e_term ).

tff(sy_c_aa_001t__Int__Oint_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    aa_int6681284322438024898it_nat: ( fun_in8543325783774419841it_nat * int ) > option8956607266484857688it_nat ).

tff(sy_c_aa_001t__Int__Oint_001t__Option__Ooption_It__Product____Type__Ounit_J,type,
    aa_int400517244715908841t_unit: ( fun_in5873495209930779904t_unit * int ) > option_Product_unit ).

tff(sy_c_aa_001t__Int__Oint_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
    aa_int9046179520680703296et_nat: ( fun_in2104226462327546623et_nat * int ) > option_set_nat ).

tff(sy_c_aa_001t__Int__Oint_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    aa_int77912060771590321nteger: ( fun_in4744367027289715400nteger * int ) > produc8923325533196201883nteger ).

tff(sy_c_aa_001t__Int__Oint_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J,type,
    aa_int593519447396103936er_int: ( fun_in7446034528553779607er_int * int ) > produc2256096406371053034er_int ).

tff(sy_c_aa_001t__Int__Oint_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    aa_int9033694857635096172et_nat: ( fun_in4666789911842550827et_nat * int ) > produc3658429121746597890et_nat ).

tff(sy_c_aa_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    aa_int7462565939943104719nt_int: ( fun_in4211310926729683942nt_int * int ) > product_prod_int_int ).

tff(sy_c_aa_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
    aa_int6463212228042050163at_int: ( fun_in2024389352036662154at_int * int ) > product_prod_nat_int ).

tff(sy_c_aa_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    aa_int1417691210696471063at_nat: ( fun_in4514472496968388910at_nat * int ) > product_prod_nat_nat ).

tff(sy_c_aa_001t__Int__Oint_001t__Product____Type__Ounit,type,
    aa_int_Product_unit: ( fun_int_Product_unit * int ) > product_unit ).

tff(sy_c_aa_001t__Int__Oint_001t__Rat__Orat,type,
    aa_int_rat: ( fun_int_rat * int ) > rat ).

tff(sy_c_aa_001t__Int__Oint_001t__Set__Oset_I_Eo_J,type,
    aa_int_set_o: ( fun_int_set_o * int ) > set_o ).

tff(sy_c_aa_001t__Int__Oint_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
    aa_int6612375148016655357nteger: ( fun_in6808926178784942396nteger * int ) > set_Code_integer ).

tff(sy_c_aa_001t__Int__Oint_001t__Set__Oset_It__Int__Oint_J,type,
    aa_int_set_int: ( fun_int_set_int * int ) > set_int ).

tff(sy_c_aa_001t__Int__Oint_001t__Set__Oset_It__Nat__Onat_J,type,
    aa_int_set_nat: ( fun_int_set_nat * int ) > set_nat ).

tff(sy_c_aa_001t__Int__Oint_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    aa_int6548451963861500163t_unit: ( fun_in4731230917697954842t_unit * int ) > set_Product_unit ).

tff(sy_c_aa_001t__Int__Oint_001t__fun_I_Eo_M_Eo_J,type,
    aa_int_fun_o_o: ( fun_int_fun_o_o * int ) > fun_o_o ).

tff(sy_c_aa_001t__Int__Oint_001t__fun_It__Code____Numeral__Ointeger_M_Eo_J,type,
    aa_int5993532643906289898eger_o: ( fun_in4891666191172872833eger_o * int ) > fun_Code_integer_o ).

tff(sy_c_aa_001t__Int__Oint_001t__fun_It__Code____Numeral__Onatural_M_Eo_J,type,
    aa_int7075551964079801951ural_o: ( fun_in812919657445819766ural_o * int ) > fun_Code_natural_o ).

tff(sy_c_aa_001t__Int__Oint_001t__fun_It__Int__Oint_M_Eo_J,type,
    aa_int_fun_int_o: ( fun_int_fun_int_o * int ) > fun_int_o ).

tff(sy_c_aa_001t__Int__Oint_001t__fun_It__Int__Oint_Mt__Int__Oint_J,type,
    aa_int_fun_int_int: ( fun_int_fun_int_int * int ) > fun_int_int ).

tff(sy_c_aa_001t__Int__Oint_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    aa_int408404503994301353e_term: ( fun_in94812177438132456e_term * int ) > fun_in5730379987311621695e_term ).

tff(sy_c_aa_001t__Int__Oint_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    aa_int2565445551602696444nt_int: ( fun_in1696471567231710611nt_int * int ) > fun_in4211310926729683942nt_int ).

tff(sy_c_aa_001t__Int__Oint_001t__fun_It__Int__Oint_Mt__Rat__Orat_J,type,
    aa_int_fun_int_rat: ( fun_int_fun_int_rat * int ) > fun_int_rat ).

tff(sy_c_aa_001t__Int__Oint_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    aa_int1966403025003302569nt_int: ( fun_in2204242111582549184nt_int * int ) > fun_in1696471567231710611nt_int ).

tff(sy_c_aa_001t__Int__Oint_001t__fun_It__Nat__Onat_M_Eo_J,type,
    aa_int_fun_nat_o: ( fun_int_fun_nat_o * int ) > fun_nat_o ).

tff(sy_c_aa_001t__Int__Oint_001t__fun_It__Nat__Onat_Mt__Int__Oint_J,type,
    aa_int_fun_nat_int: ( fun_int_fun_nat_int * int ) > fun_nat_int ).

tff(sy_c_aa_001t__Int__Oint_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Int__Oint_J_J,type,
    aa_int431785320988601264at_int: ( fun_in6793278964266839919at_int * int ) > fun_nat_fun_nat_int ).

tff(sy_c_aa_001t__Int__Oint_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    aa_int1137397288593391972e_term: ( fun_in7158797356850311459e_term * int ) > fun_Pr5098669352780829690e_term ).

tff(sy_c_aa_001t__Int__Oint_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
    aa_int7568080844962427909_nat_o: ( fun_in1927439276604979228_nat_o * int ) > fun_Pr6460944699146269935_nat_o ).

tff(sy_c_aa_001t__Int__Oint_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    aa_int8219552307768696789e_term: ( fun_in237891044757944084e_term * int ) > fun_Pr7763680713840462443e_term ).

tff(sy_c_aa_001t__Int__Oint_001t__fun_It__Product____Type__Ounit_M_Eo_J,type,
    aa_int8968792772080532472unit_o: ( fun_in8984369272479023031unit_o * int ) > fun_Product_unit_o ).

tff(sy_c_aa_001t__Int__Oint_001t__fun_It__Rat__Orat_M_Eo_J,type,
    aa_int_fun_rat_o: ( fun_int_fun_rat_o * int ) > fun_rat_o ).

tff(sy_c_aa_001t__List__Olist_It__Nat__Onat_J_001_Eo,type,
    aa_list_nat_o: ( fun_list_nat_o * list_nat ) > $o ).

tff(sy_c_aa_001t__List__Olist_It__Nat__Onat_J_001t__Nat__Onat,type,
    aa_list_nat_nat: ( fun_list_nat_nat * list_nat ) > nat ).

tff(sy_c_aa_001t__List__Olist_It__Nat__Onat_J_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
    aa_lis5329267923302741684st_nat: ( fun_li1191372448985611379st_nat * list_nat ) > set_list_nat ).

tff(sy_c_aa_001t__List__Olist_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
    aa_list_nat_set_nat: ( fun_list_nat_set_nat * list_nat ) > set_nat ).

tff(sy_c_aa_001t__List__Olist_It__Nat__Onat_J_001t__fun_It__List__Olist_It__Nat__Onat_J_M_Eo_J,type,
    aa_lis557685189327716851_nat_o: ( fun_li1025265955262268170_nat_o * list_nat ) > fun_list_nat_o ).

tff(sy_c_aa_001t__List__Olist_It__Nat__Onat_J_001t__fun_It__Nat__Onat_M_Eo_J,type,
    aa_lis1686035672126679939_nat_o: ( fun_li2421049240157457050_nat_o * list_nat ) > fun_nat_o ).

tff(sy_c_aa_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    aa_mul5754855110707352700at_nat: ( fun_mu2328110650637990531at_nat * multis2468970476368604999at_nat ) > multis2468970476368604999at_nat ).

tff(sy_c_aa_001t__Nat__Onat_001_Eo,type,
    aa_nat_o: ( fun_nat_o * nat ) > $o ).

tff(sy_c_aa_001t__Nat__Onat_001t__Assertions__Oassn,type,
    aa_nat_assn: ( fun_nat_assn * nat ) > assn ).

tff(sy_c_aa_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
    aa_nat_Code_integer: ( fun_nat_Code_integer * nat ) > code_integer ).

tff(sy_c_aa_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
    aa_nat_Code_natural: ( fun_nat_Code_natural * nat ) > code_natural ).

tff(sy_c_aa_001t__Nat__Onat_001t__Heap__Oarray_Itf__a_J,type,
    aa_nat_array_a: ( fun_nat_array_a * nat ) > array_a ).

tff(sy_c_aa_001t__Nat__Onat_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
    aa_nat4191430056936421439t_unit: ( fun_na8669532458821385046t_unit * nat ) > heap_e7401611519738050253t_unit ).

tff(sy_c_aa_001t__Nat__Onat_001t__Int__Oint,type,
    aa_nat_int: ( fun_nat_int * nat ) > int ).

tff(sy_c_aa_001t__Nat__Onat_001t__List__Olist_It__Nat__Onat_J,type,
    aa_nat_list_nat: ( fun_nat_list_nat * nat ) > list_nat ).

tff(sy_c_aa_001t__Nat__Onat_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    aa_nat2240542744625857721at_nat: ( fun_na2338080690716861136at_nat * nat ) > multis2468970476368604999at_nat ).

tff(sy_c_aa_001t__Nat__Onat_001t__Nat__Onat,type,
    aa_nat_nat: ( fun_nat_nat * nat ) > nat ).

tff(sy_c_aa_001t__Nat__Onat_001t__Num__Onum,type,
    aa_nat_num: ( fun_nat_num * nat ) > num ).

tff(sy_c_aa_001t__Nat__Onat_001t__Option__Ooption_It__Nat__Onat_J,type,
    aa_nat_option_nat: ( fun_nat_option_nat * nat ) > option_nat ).

tff(sy_c_aa_001t__Nat__Onat_001t__Option__Ooption_It__Num__Onum_J,type,
    aa_nat_option_num: ( fun_nat_option_num * nat ) > option_num ).

tff(sy_c_aa_001t__Nat__Onat_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    aa_nat5919723204993609852it_nat: ( fun_na4198017608689007891it_nat * nat ) > option3216581401566546698it_nat ).

tff(sy_c_aa_001t__Nat__Onat_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    aa_nat3804989708481012326it_nat: ( fun_na5667031169817407269it_nat * nat ) > option8956607266484857688it_nat ).

tff(sy_c_aa_001t__Nat__Onat_001t__Option__Ooption_It__Product____Type__Ounit_J,type,
    aa_nat162940103065333829t_unit: ( fun_na5635918068280204892t_unit * nat ) > option_Product_unit ).

tff(sy_c_aa_001t__Nat__Onat_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
    aa_nat7838062387752323300et_nat: ( fun_na896109329399166627et_nat * nat ) > option_set_nat ).

tff(sy_c_aa_001t__Nat__Onat_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    aa_nat8379393489429068301nteger: ( fun_na3822476419092417572nteger * nat ) > produc8923325533196201883nteger ).

tff(sy_c_aa_001t__Nat__Onat_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J,type,
    aa_nat8056854820497768540er_int: ( fun_na5685997864800668403er_int * nat ) > produc2256096406371053034er_int ).

tff(sy_c_aa_001t__Nat__Onat_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J,type,
    aa_nat3011333803152189440er_nat: ( fun_na8176081009732395159er_nat * nat ) > produc6433947425880249742er_nat ).

tff(sy_c_aa_001t__Nat__Onat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Code____Numeral__Ointeger_J,type,
    aa_nat8764027605742049244nteger: ( fun_na7604833841916551795nteger * nat ) > produc2963269191615333738nteger ).

tff(sy_c_aa_001t__Nat__Onat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    aa_nat4424723855478970923nt_int: ( fun_na1173468842265550146nt_int * nat ) > product_prod_int_int ).

tff(sy_c_aa_001t__Nat__Onat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J,type,
    aa_nat8602574874988167631nt_nat: ( fun_na3663551987197276902nt_nat * nat ) > product_prod_int_nat ).

tff(sy_c_aa_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J,type,
    aa_nat8392374045505204608nteger: ( fun_na1596024190920976919nteger * nat ) > produc2591615631378489102nteger ).

tff(sy_c_aa_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
    aa_nat3425370143577916367at_int: ( fun_na8209919304427304166at_int * nat ) > product_prod_nat_int ).

tff(sy_c_aa_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    aa_nat7603221163087113075at_nat: ( fun_na1476630412504255114at_nat * nat ) > product_prod_nat_nat ).

tff(sy_c_aa_001t__Nat__Onat_001t__Product____Type__Ounit,type,
    aa_nat_Product_unit: ( fun_nat_Product_unit * nat ) > product_unit ).

tff(sy_c_aa_001t__Nat__Onat_001t__Rat__Orat,type,
    aa_nat_rat: ( fun_nat_rat * nat ) > rat ).

tff(sy_c_aa_001t__Nat__Onat_001t__Set__Oset_I_Eo_J,type,
    aa_nat_set_o: ( fun_nat_set_o * nat ) > set_o ).

tff(sy_c_aa_001t__Nat__Onat_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
    aa_nat8922193080109606305nteger: ( fun_na9118744110877893344nteger * nat ) > set_Code_integer ).

tff(sy_c_aa_001t__Nat__Onat_001t__Set__Oset_It__Int__Oint_J,type,
    aa_nat_set_int: ( fun_nat_set_int * nat ) > set_int ).

tff(sy_c_aa_001t__Nat__Onat_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
    aa_nat_set_list_nat: ( fun_nat_set_list_nat * nat ) > set_list_nat ).

tff(sy_c_aa_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
    aa_nat_set_nat: ( fun_nat_set_nat * nat ) > set_nat ).

tff(sy_c_aa_001t__Nat__Onat_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    aa_nat7062706319057040595at_nat: ( fun_na7044673412300895210at_nat * nat ) > set_Pr1261947904930325089at_nat ).

tff(sy_c_aa_001t__Nat__Onat_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    aa_nat8843416860741599929at_nat: ( fun_na5670658592214072528at_nat * nat ) > set_Pr4329608150637261639at_nat ).

tff(sy_c_aa_001t__Nat__Onat_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    aa_nat2714212862977473631t_unit: ( fun_na896991816813928310t_unit * nat ) > set_Product_unit ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_I_Eo_M_Eo_J,type,
    aa_nat_fun_o_o: ( fun_nat_fun_o_o * nat ) > fun_o_o ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Assertions__Oassn_Mt__Assertions__Oassn_J,type,
    aa_nat_fun_assn_assn: ( fun_na2454419004871237530n_assn * nat ) > fun_assn_assn ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Code____Numeral__Ointeger_M_Eo_J,type,
    aa_nat7420681472272698950eger_o: ( fun_na6318815019539281885eger_o * nat ) > fun_Code_integer_o ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    aa_nat6383147911832638789nteger: ( fun_na7078387940644931716nteger * nat ) > fun_Co8499238673658658103nteger ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_J,type,
    aa_nat2351529209232473362nteger: ( fun_na8856381646659805649nteger * nat ) > fun_Co6226381647958292740nteger ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Code____Numeral__Onatural_M_Eo_J,type,
    aa_nat8502700792446211003ural_o: ( fun_na2240068485812228818ural_o * nat ) > fun_Code_natural_o ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    aa_nat5282697797315388251atural: ( fun_na607345901702507418atural * nat ) > fun_Co7398788559141407565atural ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Int__Oint_M_Eo_J,type,
    aa_nat_fun_int_o: ( fun_nat_fun_int_o * nat ) > fun_int_o ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Int__Oint_Mt__Int__Oint_J,type,
    aa_nat_fun_int_int: ( fun_nat_fun_int_int * nat ) > fun_int_int ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_J,type,
    aa_nat7897264773445658633er_int: ( fun_na937208397672391712er_int * nat ) > fun_in7446034528553779607er_int ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_J,type,
    aa_nat128175214796122620at_int: ( fun_na7450791247808564371at_int * nat ) > fun_in2024389352036662154at_int ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_Mt__Int__Oint_J_J,type,
    aa_nat6704147566042551216at_int: ( fun_na2382631619178260847at_int * nat ) > fun_int_fun_nat_int ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__List__Olist_It__Nat__Onat_J_M_Eo_J,type,
    aa_nat5883842100386203267_nat_o: ( fun_na7234455742697417626_nat_o * nat ) > fun_list_nat_o ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    aa_nat1862996181841379217at_nat: ( fun_na1945018436707187408at_nat * nat ) > fun_mu2328110650637990531at_nat ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Nat__Onat_M_Eo_J,type,
    aa_nat_fun_nat_o: ( fun_nat_fun_nat_o * nat ) > fun_nat_o ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J,type,
    aa_nat2010205248571845816nteger: ( fun_na8135612474337863287nteger * nat ) > fun_nat_Code_integer ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__Code____Numeral__Onatural_J,type,
    aa_nat6468655069083034883atural: ( fun_na3365689438791330114atural * nat ) > fun_nat_Code_natural ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__Int__Oint_J,type,
    aa_nat_fun_nat_int: ( fun_nat_fun_nat_int * nat ) > fun_nat_int ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__List__Olist_It__Nat__Onat_J_J,type,
    aa_nat6157064778417537467st_nat: ( fun_na819858167508000762st_nat * nat ) > fun_nat_list_nat ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J,type,
    aa_nat_fun_nat_nat: ( fun_nat_fun_nat_nat * nat ) > fun_nat_nat ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    aa_nat4718444463496506006nteger: ( fun_na5644505769342238765nteger * nat ) > fun_na3822476419092417572nteger ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_J,type,
    aa_nat6137228109692547429er_int: ( fun_na7153028460132482940er_int * nat ) > fun_na5685997864800668403er_int ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_J,type,
    aa_nat8627311254624274185er_nat: ( fun_na2743204842065625888er_nat * nat ) > fun_na8176081009732395159er_nat ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_J,type,
    aa_nat8056064086808430821nteger: ( fun_na5353050896416397052nteger * nat ) > fun_na7604833841916551795nteger ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J_J,type,
    aa_nat1767337849956737368nt_nat: ( fun_na7356754204550075887nt_nat * nat ) > fun_na3663551987197276902nt_nat ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_J,type,
    aa_nat2047254435812855945nteger: ( fun_na3504973565017656480nteger * nat ) > fun_na1596024190920976919nteger ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_J,type,
    aa_nat6313705167186764632at_int: ( fun_na8547874228452562927at_int * nat ) > fun_na8209919304427304166at_int ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    aa_nat8803788312118491388at_nat: ( fun_na4138050610385705875at_nat * nat ) > fun_na1476630412504255114at_nat ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__Rat__Orat_J,type,
    aa_nat_fun_nat_rat: ( fun_nat_fun_nat_rat * nat ) > fun_nat_rat ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    aa_nat1818925681583257441et_nat: ( fun_na6128946301132549280et_nat * nat ) > fun_nat_set_nat ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    aa_nat7495903657192774236at_nat: ( fun_na1790740735814032627at_nat * nat ) > fun_na7044673412300895210at_nat ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    aa_nat8314798964848609180_nat_o: ( fun_na7928631014926962227_nat_o * nat ) > fun_nat_fun_nat_o ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Int__Oint_J_J,type,
    aa_nat1293065384339088724at_int: ( fun_na7654559027617327379at_int * nat ) > fun_nat_fun_nat_int ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    aa_nat3783148529270815480at_nat: ( fun_na3244735409550470327at_nat * nat ) > fun_nat_fun_nat_nat ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    aa_nat4158579785191972357at_nat: ( fun_na4143055713577223196at_nat * nat ) > fun_na4138050610385705875at_nat ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    aa_nat7293937527460703909_nat_o: ( fun_na927404270896789692_nat_o * nat ) > fun_na7928631014926962227_nat_o ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J,type,
    aa_nat4259715169212259317_nat_o: ( fun_na5914473681949881652_nat_o * nat ) > fun_na3970208099681795815_nat_o ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    aa_nat5682243440470347102at_nat: ( fun_na1668100129766719005at_nat * nat ) > fun_na8713714802964096592at_nat ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Num__Onum_Mt__Option__Ooption_It__Num__Onum_J_J,type,
    aa_nat3713591252005393295on_num: ( fun_na7595719129879163854on_num * nat ) > fun_num_option_num ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
    aa_nat7695548938202568488_nat_o: ( fun_na3970208099681795815_nat_o * nat ) > fun_Pr4796943543331071514_nat_o ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    aa_nat7997280740862404369at_nat: ( fun_na8713714802964096592at_nat * nat ) > fun_Pr2118491707810114563at_nat ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J_M_Eo_J,type,
    aa_nat6907252128894768643_nat_o: ( fun_na8508211072120413978_nat_o * nat ) > fun_Pr1057819736042215569_nat_o ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Product____Type__Ounit_M_Eo_J,type,
    aa_nat5955485856412068252unit_o: ( fun_na5971062356810558811unit_o * nat ) > fun_Product_unit_o ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Rat__Orat_M_Eo_J,type,
    aa_nat_fun_rat_o: ( fun_nat_fun_rat_o * nat ) > fun_rat_o ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Rat__Orat_Mt__Rat__Orat_J,type,
    aa_nat_fun_rat_rat: ( fun_nat_fun_rat_rat * nat ) > fun_rat_rat ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Rat__Orat_Mt__fun_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
    aa_nat298952458717073160at_rat: ( fun_na1148497095348402375at_rat * nat ) > fun_rat_fun_nat_rat ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J,type,
    aa_nat1727191234135941576_nat_o: ( fun_na4518284863240432007_nat_o * nat ) > fun_se4782206882984618170_nat_o ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    aa_nat5789291038776893201at_nat: ( fun_na8167864584424996432at_nat * nat ) > fun_se320340636488258563at_nat ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    aa_nat3868275710975325009_nat_o: ( fun_na3424944204176166544_nat_o * nat ) > fun_se7755072775241076291_nat_o ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J_J,type,
    aa_nat8542548088120273133_nat_o: ( fun_na7330042712434367748_nat_o * nat ) > fun_se5991283330978499451_nat_o ).

tff(sy_c_aa_001t__Nat__Onat_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J_J,type,
    aa_nat2460170648439927835_nat_o: ( fun_na7109657165716327514_nat_o * nat ) > fun_se8417120708266284045_nat_o ).

tff(sy_c_aa_001t__Num__Onum_001_Eo,type,
    aa_num_o: ( fun_num_o * num ) > $o ).

tff(sy_c_aa_001t__Num__Onum_001t__Code____Numeral__Ointeger,type,
    aa_num_Code_integer: ( fun_num_Code_integer * num ) > code_integer ).

tff(sy_c_aa_001t__Num__Onum_001t__Code____Numeral__Onatural,type,
    aa_num_Code_natural: ( fun_num_Code_natural * num ) > code_natural ).

tff(sy_c_aa_001t__Num__Onum_001t__Int__Oint,type,
    aa_num_int: ( fun_num_int * num ) > int ).

tff(sy_c_aa_001t__Num__Onum_001t__Nat__Onat,type,
    aa_num_nat: ( fun_num_nat * num ) > nat ).

tff(sy_c_aa_001t__Num__Onum_001t__Num__Onum,type,
    aa_num_num: ( fun_num_num * num ) > num ).

tff(sy_c_aa_001t__Num__Onum_001t__Option__Ooption_It__Num__Onum_J,type,
    aa_num_option_num: ( fun_num_option_num * num ) > option_num ).

tff(sy_c_aa_001t__Num__Onum_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    aa_num7625411027033842354it_nat: ( fun_nu5903705430729240393it_nat * num ) > option3216581401566546698it_nat ).

tff(sy_c_aa_001t__Num__Onum_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    aa_num6494248640407584176it_nat: ( fun_nu8356290101743979119it_nat * num ) > option8956607266484857688it_nat ).

tff(sy_c_aa_001t__Num__Onum_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
    aa_num3156681643174609981um_num: ( fun_nu5148503272595741012um_num * num ) > product_prod_num_num ).

tff(sy_c_aa_001t__Num__Onum_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    aa_num7171627272556384352it_nat: ( fun_nu5234077238548837151it_nat * num ) > produc8664842809031399944it_nat ).

tff(sy_c_aa_001t__Num__Onum_001t__Rat__Orat,type,
    aa_num_rat: ( fun_num_rat * num ) > rat ).

tff(sy_c_aa_001t__Num__Onum_001t__fun_It__Num__Onum_M_Eo_J,type,
    aa_num_fun_num_o: ( fun_num_fun_num_o * num ) > fun_num_o ).

tff(sy_c_aa_001t__Num__Onum_001t__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J,type,
    aa_num5808785979904431436nteger: ( fun_nu2537414170016844299nteger * num ) > fun_num_Code_integer ).

tff(sy_c_aa_001t__Num__Onum_001t__fun_It__Num__Onum_Mt__Int__Oint_J,type,
    aa_num_fun_num_int: ( fun_num_fun_num_int * num ) > fun_num_int ).

tff(sy_c_aa_001t__Num__Onum_001t__fun_It__Num__Onum_Mt__Num__Onum_J,type,
    aa_num_fun_num_num: ( fun_num_fun_num_num * num ) > fun_num_num ).

tff(sy_c_aa_001t__Num__Onum_001t__fun_It__Num__Onum_Mt__Option__Ooption_It__Num__Onum_J_J,type,
    aa_num6390622462783740633on_num: ( fun_nu1049378303802735384on_num * num ) > fun_num_option_num ).

tff(sy_c_aa_001t__Option__Ooption_I_Eo_J_001t__Option__Ooption_I_Eo_J,type,
    aa_option_o_option_o: ( fun_op5853259939270031811tion_o * option_o ) > option_o ).

tff(sy_c_aa_001t__Option__Ooption_It__Assertions__Oassn_J_001t__fun_It__Assertions__Oassn_Mt__Option__Ooption_It__Assertions__Oassn_J_J,type,
    aa_opt1471905160178427347n_assn: ( fun_op4146996366486250514n_assn * option_assn ) > fun_assn_option_assn ).

tff(sy_c_aa_001t__Option__Ooption_It__Code____Numeral__Ointeger_J_001t__Option__Ooption_It__Code____Numeral__Ointeger_J,type,
    aa_opt5394215800039610008nteger: ( fun_op1637087682669155543nteger * option_Code_integer ) > option_Code_integer ).

tff(sy_c_aa_001t__Option__Ooption_It__Code____Numeral__Ointeger_J_001t__Option__Ooption_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    aa_opt6635412093559109234nteger: ( fun_op8756596739451609009nteger * option_Code_integer ) > option8886115935005447431nteger ).

tff(sy_c_aa_001t__Option__Ooption_It__Code____Numeral__Ointeger_J_001t__Option__Ooption_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    aa_opt8008171047296870846nteger: ( fun_op3037383146056310525nteger * option_Code_integer ) > option5210736251575913683nteger ).

tff(sy_c_aa_001t__Option__Ooption_It__Int__Oint_J_001t__Option__Ooption_It__Int__Oint_J,type,
    aa_opt3115652020397860022on_int: ( fun_op4193086050743966581on_int * option_int ) > option_int ).

tff(sy_c_aa_001t__Option__Ooption_It__Int__Oint_J_001t__Option__Ooption_It__Nat__Onat_J,type,
    aa_opt7293503039907056730on_nat: ( fun_op6683169195675693337on_nat * option_int ) > option_nat ).

tff(sy_c_aa_001t__Option__Ooption_It__Int__Oint_J_001t__Option__Ooption_It__Num__Onum_J,type,
    aa_opt8001746976855894436on_num: ( fun_op2398388785115040099on_num * option_int ) > option_num ).

tff(sy_c_aa_001t__Option__Ooption_It__Nat__Onat_J_001t__Option__Ooption_It__Nat__Onat_J,type,
    aa_opt1882420858203594238on_nat: ( fun_op1272087013972230845on_nat * option_nat ) > option_nat ).

tff(sy_c_aa_001t__Option__Ooption_It__Nat__Onat_J_001t__Option__Ooption_It__Num__Onum_J,type,
    aa_opt2590664795152431944on_num: ( fun_op6210678640266353415on_num * option_nat ) > option_num ).

tff(sy_c_aa_001t__Option__Ooption_It__Num__Onum_J_001_Eo,type,
    aa_option_num_o: ( fun_option_num_o * option_num ) > $o ).

tff(sy_c_aa_001t__Option__Ooption_It__Num__Onum_J_001t__Int__Oint,type,
    aa_option_num_int: ( fun_option_num_int * option_num ) > int ).

tff(sy_c_aa_001t__Option__Ooption_It__Num__Onum_J_001t__Nat__Onat,type,
    aa_option_num_nat: ( fun_option_num_nat * option_num ) > nat ).

tff(sy_c_aa_001t__Option__Ooption_It__Num__Onum_J_001t__Num__Onum,type,
    aa_option_num_num: ( fun_option_num_num * option_num ) > num ).

tff(sy_c_aa_001t__Option__Ooption_It__Num__Onum_J_001t__Option__Ooption_It__Code____Numeral__Ointeger_J,type,
    aa_opt692344247527444053nteger: ( fun_op4521932154746760340nteger * option_num ) > option_Code_integer ).

tff(sy_c_aa_001t__Option__Ooption_It__Num__Onum_J_001t__Option__Ooption_It__Num__Onum_J,type,
    aa_opt5369159329878751634on_num: ( fun_op8989173174992673105on_num * option_num ) > option_num ).

tff(sy_c_aa_001t__Option__Ooption_It__Num__Onum_J_001t__fun_It__Num__Onum_Mt__Option__Ooption_It__Num__Onum_J_J,type,
    aa_opt8899475237019873193on_num: ( fun_op3323321805596408808on_num * option_num ) > fun_num_option_num ).

tff(sy_c_aa_001t__Option__Ooption_It__Num__Onum_J_001t__fun_It__Option__Ooption_It__Num__Onum_J_M_Eo_J,type,
    aa_opt8674010985164783839_num_o: ( fun_op493924057549976310_num_o * option_num ) > fun_option_num_o ).

tff(sy_c_aa_001t__Option__Ooption_It__Num__Onum_J_001t__fun_It__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_M_Eo_J,type,
    aa_opt1082509876067759737_nat_o: ( fun_op261120641589640376_nat_o * option_num ) > fun_op4751157287140997969_nat_o ).

tff(sy_c_aa_001t__Option__Ooption_It__Num__Onum_J_001t__fun_It__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_M_Eo_J,type,
    aa_opt6324340006354107505_nat_o: ( fun_op298641349230941576_nat_o * option_num ) > fun_op479301348043730329_nat_o ).

tff(sy_c_aa_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001_Eo,type,
    aa_opt4809530629565672394_nat_o: ( fun_op4751157287140997969_nat_o * option3216581401566546698it_nat ) > $o ).

tff(sy_c_aa_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    aa_opt2040853179424174198it_nat: ( fun_op8917697677373047293it_nat * option3216581401566546698it_nat ) > produc6714399278180371524it_nat ).

tff(sy_c_aa_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__fun_It__Option__Ooption_It__Num__Onum_J_M_Eo_J,type,
    aa_opt2228701783387358009_num_o: ( fun_op3129816456743790912_num_o * option3216581401566546698it_nat ) > fun_option_num_o ).

tff(sy_c_aa_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__fun_It__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_M_Eo_J,type,
    aa_opt6043028115961832863_nat_o: ( fun_op2352717853092002798_nat_o * option3216581401566546698it_nat ) > fun_op4751157287140997969_nat_o ).

tff(sy_c_aa_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__fun_It__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_M_Eo_J,type,
    aa_opt1571526544311817931_nat_o: ( fun_op101698441058542546_nat_o * option3216581401566546698it_nat ) > fun_op479301348043730329_nat_o ).

tff(sy_c_aa_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001_Eo,type,
    aa_opt8360315729766332930_nat_o: ( fun_op479301348043730329_nat_o * option8956607266484857688it_nat ) > $o ).

tff(sy_c_aa_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    aa_opt6779208767223616030it_nat: ( fun_op7765417307512062173it_nat * option8956607266484857688it_nat ) > produc8664842809031399944it_nat ).

tff(sy_c_aa_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__fun_It__Option__Ooption_It__Num__Onum_J_M_Eo_J,type,
    aa_opt3964967581558639985_num_o: ( fun_op6018817604785332104_num_o * option8956607266484857688it_nat ) > fun_option_num_o ).

tff(sy_c_aa_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__fun_It__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_M_Eo_J,type,
    aa_opt3816109826176937319_nat_o: ( fun_op8703326495438967718_nat_o * option8956607266484857688it_nat ) > fun_op4751157287140997969_nat_o ).

tff(sy_c_aa_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__fun_It__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_M_Eo_J,type,
    aa_opt6948326687743049987_nat_o: ( fun_op1633239139951409690_nat_o * option8956607266484857688it_nat ) > fun_op479301348043730329_nat_o ).

tff(sy_c_aa_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__fun_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    aa_opt7728438819757478003it_nat: ( fun_op4112804339236761266it_nat * option8956607266484857688it_nat ) > fun_Pr7644814098969791837it_nat ).

tff(sy_c_aa_001t__Option__Ooption_It__Product____Type__Ounit_J_001t__fun_It__Product____Type__Ounit_Mt__Option__Ooption_It__Product____Type__Ounit_J_J,type,
    aa_opt8900914514660672992t_unit: ( fun_op5903753652030861359t_unit * option_Product_unit ) > fun_Pr8303579546892975945t_unit ).

tff(sy_c_aa_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_001t__fun_It__Set__Oset_It__Nat__Onat_J_Mt__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_J,type,
    aa_opt5648106117674462701et_nat: ( fun_op386870758422531628et_nat * option_set_nat ) > fun_se7316093745529328985et_nat ).

tff(sy_c_aa_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_J,type,
    aa_opt1027706798495913626at_nat: ( fun_op291006984297869545at_nat * option1583680563626158861at_nat ) > fun_se7901873761543946185at_nat ).

tff(sy_c_aa_001t__Option__Ooption_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Option__Ooption_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    aa_opt235805188696355736nteger: ( fun_op7507520395135695063nteger * option8886115935005447431nteger ) > option5210736251575913683nteger ).

tff(sy_c_aa_001t__Option__Ooption_It__fun_It__Nat__Onat_M_Eo_J_J_001t__Option__Ooption_It__fun_It__Nat__Onat_M_Eo_J_J,type,
    aa_opt7724086761683053692_nat_o: ( fun_op3284592519439835779_nat_o * option_fun_nat_o ) > option_fun_nat_o ).

tff(sy_c_aa_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001_Eo,type,
    aa_Pro2802791181778974573_o_o_o: ( fun_Pr6984036127010467572_o_o_o * product_prod_o_o ) > $o ).

tff(sy_c_aa_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_001_Eo,type,
    aa_Pro2847156015387483303_int_o: ( fun_Pr1358870568642713662_int_o * product_prod_o_int ) > $o ).

tff(sy_c_aa_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_001t__Int__Oint,type,
    aa_Pro306596563698563805nt_int: ( fun_Pr3595050827490992028nt_int * product_prod_o_int ) > int ).

tff(sy_c_aa_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001_Eo,type,
    aa_Pro5092300983057929219_nat_o: ( fun_Pr3604015536313159578_nat_o * product_prod_o_nat ) > $o ).

tff(sy_c_aa_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_001t__Nat__Onat,type,
    aa_Pro7345537496369368101at_nat: ( fun_Pr5585980272307166948at_nat * product_prod_o_nat ) > nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_I_Eo_Mt__Num__Onum_J_001_Eo,type,
    aa_Pro5850481546027440185_num_o: ( fun_Pr4362196099282670544_num_o * product_prod_o_num ) > $o ).

tff(sy_c_aa_001t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001_Eo,type,
    aa_Pro2750588290097631179_nat_o: ( fun_Pr914940982395022178_nat_o * produc2900562427881843919it_nat ) > $o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_Eo,type,
    aa_Pro4926521453222654329eger_o: ( fun_Pr7211993375558241536eger_o * produc8923325533196201883nteger ) > $o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger,type,
    aa_Pro5245656335456409788nteger: ( fun_Pr6596356882939945227nteger * produc8923325533196201883nteger ) > code_integer ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    aa_Pro4693618923521437820nteger: ( fun_Pr5876161306168176259nteger * produc8923325533196201883nteger ) > produc8923325533196201883nteger ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    aa_Pro4291442876242880245nteger: ( fun_Pr2985126522952997572nteger * produc8923325533196201883nteger ) > produc2453742332425399446nteger ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_I_Eo_J,type,
    aa_Pro3874180734779831385_set_o: ( fun_Pr1817902730575146976_set_o * produc8923325533196201883nteger ) > set_o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Int__Oint_J,type,
    aa_Pro5426537197693075521et_int: ( fun_Pr3914994171019630096et_int * produc8923325533196201883nteger ) > set_int ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Nat__Onat_J,type,
    aa_Pro381016180347496421et_nat: ( fun_Pr6405077315951356852et_nat * produc8923325533196201883nteger ) > set_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    aa_Pro659252730400088491nteger: ( fun_Pr894914116851403386nteger * produc8923325533196201883nteger ) > set_Pr3486312109254157132nteger ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    aa_Pro3049322369718103567e_term: ( fun_Pr5305228341155023582e_term * produc8923325533196201883nteger ) > set_fu8280898353253485872e_term ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_J,type,
    aa_Pro5511408310453641204nteger: ( fun_Pr471679772948460611nteger * produc8923325533196201883nteger ) > fun_se2190013347424485781nteger ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_Eo_J,type,
    aa_Pro9035772811636298456term_o: ( fun_Pr4680327687137491167term_o * produc8923325533196201883nteger ) > fun_fu4736795817735658359term_o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    aa_Pro5774345223241026284nteger: ( fun_Pr8371818785129130299nteger * produc8923325533196201883nteger ) > fun_fu8902681562042749453nteger ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001_Eo,type,
    aa_Pro6073791466322389475ural_o: ( fun_Pr8359263388657976682ural_o * produc7822875418678951345atural ) > $o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Nat__Onat,type,
    aa_Pro1523461786693152325al_nat: ( fun_Pr2804840792690441492al_nat * produc7822875418678951345atural ) > nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    aa_Pro4262726347734369532atural: ( fun_Pr74676805955934211atural * produc7822875418678951345atural ) > produc7822875418678951345atural ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    aa_Pro7165575656943818355atural: ( fun_Pr7769407664385210434atural * produc7822875418678951345atural ) > produc5835291356934675326atural ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    aa_Pro4690339539107573879et_nat: ( fun_Pr7425815736541306438et_nat * produc7822875418678951345atural ) > produc3658429121746597890et_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    aa_Pro7164870388581637892nt_int: ( fun_Pr5596209257725365771nt_int * produc7822875418678951345atural ) > product_prod_int_int ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Code____Numeral__Onatural_J,type,
    aa_Pro5311756036668752637atural: ( fun_Pr4906574453216509900atural * produc7822875418678951345atural ) > produc3981471736659609608atural ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    aa_Pro1971126414814181170atural: ( fun_Pr3133360822718887225atural * produc7822875418678951345atural ) > produc6756470014200349799atural ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__fun_It__Code____Numeral__Onatural_M_Eo_J,type,
    aa_Pro3271585298577294228ural_o: ( fun_Pr3928691295121555099ural_o * produc7822875418678951345atural ) > fun_Code_natural_o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__fun_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J,type,
    aa_Pro4688176541098407832atural: ( fun_Pr3688637647703109351atural * produc7822875418678951345atural ) > fun_Co4337079049361313443atural ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__Code____Numeral__Onatural,type,
    aa_Pro5806155842103967332atural: ( fun_Pr5131589689703537955atural * produc5835291356934675326atural ) > code_natural ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    aa_Pro3673693039631929973atural: ( fun_Pr2136124334875798924atural * produc5835291356934675326atural ) > produc7822875418678951345atural ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    aa_Pro4026365172444991930atural: ( fun_Pr6891710885006071673atural * produc5835291356934675326atural ) > produc5835291356934675326atural ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001_Eo,type,
    aa_Pro7528120012624322448_nat_o: ( fun_Pr7068637894315934487_nat_o * produc6714399278180371524it_nat ) > $o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Option__Ooption_It__Num__Onum_J,type,
    aa_Pro976347780353151090on_num: ( fun_Pr2994431579521131585on_num * produc6714399278180371524it_nat ) > option_num ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    aa_Pro1291033051762305794it_nat: ( fun_Pr8118912048244921225it_nat * produc6714399278180371524it_nat ) > option3216581401566546698it_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    aa_Pro8990453184240486752it_nat: ( fun_Pr245379829043246639it_nat * produc6714399278180371524it_nat ) > option8956607266484857688it_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001_Eo,type,
    aa_Pro653082453696054616_nat_o: ( fun_Pr6460944699146269935_nat_o * produc3658429121746597890et_nat ) > $o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    aa_Pro3679490825741336130et_nat: ( fun_Pr7091840695141096449et_nat * produc3658429121746597890et_nat ) > produc3658429121746597890et_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    aa_Pro434340453207536480et_nat: ( fun_Pr4885567672785483807et_nat * produc3658429121746597890et_nat ) > produc8799533983703829792et_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Set__Oset_I_Eo_J,type,
    aa_Pro3581020192872483896_set_o: ( fun_Pr5633121574208248783_set_o * produc3658429121746597890et_nat ) > set_o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Set__Oset_It__Int__Oint_J,type,
    aa_Pro8461671945164021282et_int: ( fun_Pr847751653925389281et_int * produc3658429121746597890et_nat ) > set_int ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Set__Oset_It__Nat__Onat_J,type,
    aa_Pro3416150927818442182et_nat: ( fun_Pr3337834798857116037et_nat * produc3658429121746597890et_nat ) > set_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    aa_Pro3465147227354336150et_nat: ( fun_Pr3017356861961520469et_nat * produc3658429121746597890et_nat ) > set_Pr1312406793078187350et_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Set__Oset_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
    aa_Pro7009299959260105231_nat_o: ( fun_Pr8383423175210966566_nat_o * produc3658429121746597890et_nat ) > set_fu3555266933746557007_nat_o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    aa_Pro4237038916479365225et_nat: ( fun_Pr4459677240377800360et_nat * produc3658429121746597890et_nat ) > fun_se9157011578508667433et_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_Eo_J,type,
    aa_Pro3588693547670092268at_o_o: ( fun_Pr5843349257357397163at_o_o * produc3658429121746597890et_nat ) > fun_fu5135969500543783852at_o_o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    aa_Pro3220439978920015074et_nat: ( fun_Pr5259258551928531321et_nat * produc3658429121746597890et_nat ) > fun_fu8710561278413400866et_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_M_Eo_J_001_Eo,type,
    aa_Pro2548170440803795257nt_o_o: ( fun_Pr1059884994059025616nt_o_o * product_prod_int_o ) > $o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_M_Eo_J_001t__Int__Oint,type,
    aa_Pro2547522449196342987_o_int: ( fun_Pr5835976712988771210_o_int * product_prod_int_o ) > int ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo,type,
    aa_Pro4592068669816069595_int_o: ( fun_Pr3238374608701176162_int_o * product_prod_int_int ) > $o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint,type,
    aa_Pro6799258434465214121nt_int: ( fun_Pr982841511892225912nt_int * product_prod_int_int ) > int ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    aa_Pro6970504127699319548nt_int: ( fun_Pr2478283820680522243nt_int * product_prod_int_int ) > product_prod_int_int ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    aa_Pro8800328608558162860nt_int: ( fun_Pr8696298990344678139nt_int * product_prod_int_int ) > produc4788131091073775919nt_int ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    aa_Pro5748361610964203648nt_int: ( fun_Pr4781553364444837327nt_int * product_prod_int_int ) > produc3043004577601930755nt_int ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
    aa_Pro6166618844887768661nt_rat: ( fun_Pr1652463973008025892nt_rat * product_prod_int_int ) > rat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_I_Eo_J,type,
    aa_Pro2653658648327035067_set_o: ( fun_Pr5150627949553849410_set_o * product_prod_int_int ) > set_o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J,type,
    aa_Pro8644714012989290591et_int: ( fun_Pr1023655258412994094et_int * product_prod_int_int ) > set_int ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__Nat__Onat_J,type,
    aa_Pro3599192995643711491et_nat: ( fun_Pr3513738403344720850et_nat * product_prod_int_int ) > set_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    aa_Pro6675321895958450596at_nat: ( fun_Pr5398690294390750379at_nat * product_prod_int_int ) > set_Pr1261947904930325089at_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    aa_Pro3986193103337010658nt_int: ( fun_Pr1951044811698827825nt_int * product_prod_int_int ) > set_Pr4166680992137330533nt_int ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    aa_Pro1072212120072018102nt_int: ( fun_Pr1547027809659849477nt_int * product_prod_int_int ) > set_Pr6700895561065273913nt_int ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    aa_Pro1848062444984653554e_term: ( fun_Pr9081111800474865985e_term * product_prod_int_int ) > set_fu3629540756087427317e_term ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    aa_Pro5850374426668061982e_term: ( fun_Pr4426623609552329069e_term * product_prod_int_int ) > set_fu5653557704672872225e_term ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
    aa_Pro3952998155787061599_int_o: ( fun_Pr9018117161326028078_int_o * product_prod_int_int ) > fun_Pr3238374608701176162_int_o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    aa_Pro4124234152028750080nt_int: ( fun_Pr1308109350235310159nt_int * product_prod_int_int ) > fun_Pr2478283820680522243nt_int ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Rat__Orat_M_Eo_J,type,
    aa_Pro2298929076809959388_rat_o: ( fun_Pr7537129237977221859_rat_o * product_prod_int_int ) > fun_rat_o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
    aa_Pro6698456444936022468nt_int: ( fun_Pr5088371826558493971nt_int * product_prod_int_int ) > fun_se2900878183379320647nt_int ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
    aa_Pro1409070577063066988nt_int: ( fun_Pr7963917038216275131nt_int * product_prod_int_int ) > fun_se1594822257893229295nt_int ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_Eo_J,type,
    aa_Pro1235490124264145077term_o: ( fun_Pr7145817153658775868term_o * product_prod_int_int ) > fun_fu3265955482920998386term_o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    aa_Pro3263785050932909160nt_int: ( fun_Pr4353654455642104759nt_int * product_prod_int_int ) > fun_fu4545303443005895275nt_int ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_Eo_J,type,
    aa_Pro1023942307601852809term_o: ( fun_Pr5526332658708858896term_o * product_prod_int_int ) > fun_fu6378075912484669126term_o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    aa_Pro7187055436517876584nt_int: ( fun_Pr8826142978676617911nt_int * product_prod_int_int ) > fun_fu5813366174458671467nt_int ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J_001t__Int__Oint,type,
    aa_Pro4612336859772192333at_int: ( fun_Pr8019291974053979932at_int * product_prod_int_nat ) > int ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J_001t__Nat__Onat,type,
    aa_Pro4614827330281242609at_nat: ( fun_Pr2973770956708400832at_nat * product_prod_int_nat ) > nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Int__Oint_Mt__Num__Onum_J_001t__Int__Oint,type,
    aa_Pro6630731953738365847um_int: ( fun_Pr814315031165377638um_int * product_prod_int_num ) > int ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_001_Eo,type,
    aa_Pro4464983059765771485at_o_o: ( fun_Pr2976697613021001844at_o_o * product_prod_nat_o ) > $o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_001t__Nat__Onat,type,
    aa_Pro1863436886664842699_o_nat: ( fun_Pr103879662602641546_o_nat * product_prod_nat_o ) > nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_001t__Int__Oint,type,
    aa_Pro6427604874228369485nt_int: ( fun_Pr611187951655381276nt_int * product_prod_nat_int ) > int ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_001t__Nat__Onat,type,
    aa_Pro6430095344737419761nt_nat: ( fun_Pr4789038971164577984nt_nat * product_prod_nat_int ) > nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo,type,
    aa_Pro6150637604445964947_nat_o: ( fun_Pr4796943543331071514_nat_o * product_prod_nat_nat ) > $o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Code____Numeral__Ointeger,type,
    aa_Pro4764841431850000930nteger: ( fun_Pr6026251430685297nteger * product_prod_nat_nat ) > code_integer ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
    aa_Pro4240683299535347697at_int: ( fun_Pr7647638413817135296at_int * product_prod_nat_nat ) > int ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
    aa_Pro4243173770044397973at_nat: ( fun_Pr2602117396471556196at_nat * product_prod_nat_nat ) > nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Option__Ooption_It__Num__Onum_J,type,
    aa_Pro7308558959993556143on_num: ( fun_Pr7397166214287566974on_num * product_prod_nat_nat ) > option_num ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    aa_Pro4773402355715522498at_nat: ( fun_Pr7804344347641417161at_nat * product_prod_nat_nat ) > option4927543243414619207at_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    aa_Pro5591324840913351069it_nat: ( fun_Pr6624299372562097772it_nat * product_prod_nat_nat ) > option8956607266484857688it_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Option__Ooption_It__Product____Type__Ounit_J,type,
    aa_Pro4935752218105739214t_unit: ( fun_Pr648072847990616533t_unit * product_prod_nat_nat ) > option_Product_unit ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
    aa_Pro2437148896120846363et_nat: ( fun_Pr2088208266900590058et_nat * product_prod_nat_nat ) > option_set_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    aa_Pro262675715343573244at_nat: ( fun_Pr2118491707810114563at_nat * product_prod_nat_nat ) > product_prod_nat_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Ounit,type,
    aa_Pro676242055593665672t_unit: ( fun_Pr2481279687482350479t_unit * product_prod_nat_nat ) > product_unit ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Rat__Orat,type,
    aa_Pro3608043709957902237at_rat: ( fun_Pr8317260874932935276at_rat * product_prod_nat_nat ) > rat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Set__Oset_I_Eo_J,type,
    aa_Pro5970036531051701619_set_o: ( fun_Pr8467005832278515962_set_o * product_prod_nat_nat ) > set_o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Set__Oset_It__Int__Oint_J,type,
    aa_Pro4945722294086666663et_int: ( fun_Pr6548035576365145974et_int * product_prod_nat_nat ) > set_int ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
    aa_Pro9123573313595863371et_nat: ( fun_Pr9038118721296872730et_nat * product_prod_nat_nat ) > set_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Int__Oint_M_Eo_J,type,
    aa_Pro2912763917461432128_int_o: ( fun_Pr4738963024209204295_int_o * product_prod_nat_nat ) > fun_int_o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    aa_Pro1957341097241355813_nat_o: ( fun_Pr3455331679158536364_nat_o * product_prod_nat_nat ) > fun_nat_fun_nat_o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    aa_Pro6895555690143131534at_nat: ( fun_Pr557098546508347797at_nat * product_prod_nat_nat ) > fun_na4138050610385705875at_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
    aa_Pro989595756709598047_nat_o: ( fun_Pr2028404973800837934_nat_o * product_prod_nat_nat ) > fun_Pr4796943543331071514_nat_o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    aa_Pro8023792847356852296at_nat: ( fun_Pr2477239776880934807at_nat * product_prod_nat_nat ) > fun_Pr2118491707810114563at_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J_001t__Nat__Onat,type,
    aa_Pro6261568864010571487um_nat: ( fun_Pr4620512490437729710um_nat * product_prod_nat_num ) > nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Nat__Onat,type,
    aa_Pro8662700311855308749at_nat: ( fun_Pr8519750050727906972at_nat * produc3839731585411834681it_nat ) > nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    aa_Pro8943840777669118315atural: ( fun_Pr7406272072912987266atural * produc3981471736659609608atural ) > produc7822875418678951345atural ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Num__Onum_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
    aa_Pro8934633562067165177at_nat: ( fun_Pr8866567302531502864at_nat * produc9082142974458947146at_num ) > product_prod_nat_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001_Eo,type,
    aa_Pro4744234731172327378_nat_o: ( fun_Pr8032424337255632745_nat_o * produc8664842809031399944it_nat ) > $o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Nat__Onat,type,
    aa_Pro5228051289423594006at_nat: ( fun_Pr367382672041210069at_nat * produc8664842809031399944it_nat ) > nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Num__Onum,type,
    aa_Pro1785383075579372640at_num: ( fun_Pr1075626608990047775at_num * produc8664842809031399944it_nat ) > num ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Option__Ooption_It__Num__Onum_J,type,
    aa_Pro8341797174369656752on_num: ( fun_Pr1661544312997278575on_num * produc8664842809031399944it_nat ) > option_num ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    aa_Pro875131464217814084it_nat: ( fun_Pr7518090501403545819it_nat * produc8664842809031399944it_nat ) > option3216581401566546698it_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    aa_Pro8996696869555642526it_nat: ( fun_Pr7644814098969791837it_nat * produc8664842809031399944it_nat ) > option8956607266484857688it_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    aa_Pro550487673543749710it_nat: ( fun_Pr1033138224055104269it_nat * produc8664842809031399944it_nat ) > produc8664842809031399944it_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__fun_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    aa_Pro5635350972512700067it_nat: ( fun_Pr3631287881653221602it_nat * produc8664842809031399944it_nat ) > fun_Pr7644814098969791837it_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__fun_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    aa_Pro4096753284154920275it_nat: ( fun_Pr1003294667014919570it_nat * produc8664842809031399944it_nat ) > fun_Pr1033138224055104269it_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001_Eo,type,
    aa_Pro5947980084102686253_nat_o: ( fun_Pr3059359313727237556_nat_o * produc3843707927480180839at_nat ) > $o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Option__Ooption_It__Num__Onum_J,type,
    aa_Pro6040048559569557on_num: ( fun_Pr6553355248451873380on_num * produc3843707927480180839at_nat ) > option_num ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    aa_Pro6559690566658787203it_nat: ( fun_Pr6865292569827446866it_nat * produc3843707927480180839at_nat ) > option8956607266484857688it_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Option__Ooption_It__Product____Type__Ounit_J,type,
    aa_Pro436454883488707944t_unit: ( fun_Pr5508761798988831599t_unit * produc3843707927480180839at_nat ) > option_Product_unit ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
    aa_Pro708668050254188033et_nat: ( fun_Pr6721000092112975824et_nat * produc3843707927480180839at_nat ) > option_set_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Ounit,type,
    aa_Pro1279885795167260962t_unit: ( fun_Pr8319229360018371625t_unit * produc3843707927480180839at_nat ) > product_unit ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Set__Oset_It__Nat__Onat_J,type,
    aa_Pro1692590229789857841et_nat: ( fun_Pr6764980218223570944et_nat * produc3843707927480180839at_nat ) > set_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    aa_Pro441628658106787830at_nat: ( fun_Pr6212429452034653949at_nat * produc3843707927480180839at_nat ) > set_Pr1261947904930325089at_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_Eo,type,
    aa_Pro5451197003417746155_int_o: ( fun_Pr1196100989263358594_int_o * produc4788131091073775919nt_int ) > $o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    aa_Pro4437156595432605708nt_int: ( fun_Pr1552678306225191715nt_int * produc4788131091073775919nt_int ) > product_prod_int_int ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    aa_Pro356110846173809308nt_int: ( fun_Pr5152393401594413531nt_int * produc4788131091073775919nt_int ) > produc4788131091073775919nt_int ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    aa_Pro2551989255418117932e_term: ( fun_Pr7653582204007996523e_term * produc4788131091073775919nt_int ) > fun_in5730379987311621695e_term ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001_Eo,type,
    aa_Pro4148064003102580676eger_o: ( fun_Pr7015759342434529115eger_o * produc2453742332425399446nteger ) > $o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    aa_Pro4625778721341478855nteger: ( fun_Pr6160931176198666718nteger * produc2453742332425399446nteger ) > produc8923325533196201883nteger ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    aa_Pro5909916214238876522nteger: ( fun_Pr3905736301278533417nteger * produc2453742332425399446nteger ) > produc2453742332425399446nteger ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    aa_Pro4276937008533432526e_term: ( fun_Pr4557384415951816845e_term * produc2453742332425399446nteger ) > fun_Pr5098669352780829690e_term ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001_Eo,type,
    aa_Pro5643009357358181178_nat_o: ( fun_Pr2620521676128474833_nat_o * produc8799533983703829792et_nat ) > $o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    aa_Pro5541488491759012064et_nat: ( fun_Pr2813956079162534559et_nat * produc8799533983703829792et_nat ) > produc3658429121746597890et_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    aa_Pro5931322043027775230et_nat: ( fun_Pr836988951548913597et_nat * produc8799533983703829792et_nat ) > produc8799533983703829792et_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    aa_Pro1979504083478021276et_nat: ( fun_Pr3978243888342905947et_nat * produc8799533983703829792et_nat ) > produc3112576180687729086et_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    aa_Pro1476848909050865746et_nat: ( fun_Pr4147293223664569617et_nat * produc8799533983703829792et_nat ) > set_Pr4040394263813967220et_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__Set__Oset_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
    aa_Pro1505388192238479345_nat_o: ( fun_Pr7968690803259750408_nat_o * produc8799533983703829792et_nat ) > set_fu3555266933746557007_nat_o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
    aa_Pro8262445894397805713_nat_o: ( fun_Pr3233114924583728296_nat_o * produc8799533983703829792et_nat ) > fun_Pr6460944699146269935_nat_o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J_J,type,
    aa_Pro702454294891323331et_nat: ( fun_Pr386875378712213506et_nat * produc8799533983703829792et_nat ) > fun_se2331804103973993189et_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_Eo_J,type,
    aa_Pro1702148226396177290at_o_o: ( fun_Pr2647030239595059785at_o_o * produc8799533983703829792et_nat ) > fun_fu5135969500543783852at_o_o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    aa_Pro8681318422064110306et_nat: ( fun_Pr8737872353715570297et_nat * produc8799533983703829792et_nat ) > fun_fu6196531292930346304et_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_001_Eo,type,
    aa_Pro2671238023309943196_nat_o: ( fun_Pr1227177680593602867_nat_o * produc3112576180687729086et_nat ) > $o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    aa_Pro7798056222271281692et_nat: ( fun_Pr2953255705995765467et_nat * produc3112576180687729086et_nat ) > produc8799533983703829792et_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    aa_Pro5822770074865754298et_nat: ( fun_Pr6662792608368940153et_nat * produc3112576180687729086et_nat ) > produc3112576180687729086et_nat ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
    aa_Pro2837773213478468339_nat_o: ( fun_Pr7618159474455865098_nat_o * produc3112576180687729086et_nat ) > fun_Pr6460944699146269935_nat_o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_001t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_M_Eo_J,type,
    aa_Pro4671852207856306999_nat_o: ( fun_Pr3358449090565925198_nat_o * produc3112576180687729086et_nat ) > fun_Pr1227177680593602867_nat_o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_Eo,type,
    aa_Pro2601676399929874711_int_o: ( fun_Pr3540825087398332590_int_o * produc3043004577601930755nt_int ) > $o ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    aa_Pro2675344531184151096nt_int: ( fun_Pr1987159835869338959nt_int * produc3043004577601930755nt_int ) > product_prod_int_int ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    aa_Pro1064545558308985924nt_int: ( fun_Pr5846521507401124227nt_int * produc3043004577601930755nt_int ) > produc3043004577601930755nt_int ).

tff(sy_c_aa_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    aa_Pro4010435699744810540e_term: ( fun_Pr5872836680101629291e_term * produc3043004577601930755nt_int ) > fun_Pr7763680713840462443e_term ).

tff(sy_c_aa_001t__Product____Type__Ounit_001_Eo,type,
    aa_Product_unit_o: ( fun_Product_unit_o * product_unit ) > $o ).

tff(sy_c_aa_001t__Product____Type__Ounit_001t__Assertions__Oassn,type,
    aa_Product_unit_assn: ( fun_Pr6626665806141890376t_assn * product_unit ) > assn ).

tff(sy_c_aa_001t__Product____Type__Ounit_001t__Code____Numeral__Ointeger,type,
    aa_Pro1705297278780387758nteger: ( fun_Pr1820225556744648189nteger * product_unit ) > code_integer ).

tff(sy_c_aa_001t__Product____Type__Ounit_001t__Heap____Time____Monad__OHeap_It__Heap__Oarray_Itf__a_J_J,type,
    aa_Pro755961224256580114rray_a: ( fun_Pr5924905948197006361rray_a * product_unit ) > heap_T6362127782908069795rray_a ).

tff(sy_c_aa_001t__Product____Type__Ounit_001t__Heap____Time____Monad__OHeap_It__Product____Type__Ounit_J,type,
    aa_Pro1108561329362217960t_unit: ( fun_Pr292408699144966967t_unit * product_unit ) > heap_T5738788834812785303t_unit ).

tff(sy_c_aa_001t__Product____Type__Ounit_001t__Int__Oint,type,
    aa_Product_unit_int: ( fun_Product_unit_int * product_unit ) > int ).

tff(sy_c_aa_001t__Product____Type__Ounit_001t__Nat__Onat,type,
    aa_Product_unit_nat: ( fun_Product_unit_nat * product_unit ) > nat ).

tff(sy_c_aa_001t__Product____Type__Ounit_001t__Option__Ooption_It__Product____Type__Ounit_J,type,
    aa_Pro7616171890175246658t_unit: ( fun_Pr8303579546892975945t_unit * product_unit ) > option_Product_unit ).

tff(sy_c_aa_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
    aa_Pro8294289767544744956t_unit: ( fun_Pr2191293291710260995t_unit * product_unit ) > product_unit ).

tff(sy_c_aa_001t__Product____Type__Ounit_001t__Rat__Orat,type,
    aa_Product_unit_rat: ( fun_Product_unit_rat * product_unit ) > rat ).

tff(sy_c_aa_001t__Product____Type__Ounit_001t__Set__Oset_It__Int__Oint_J,type,
    aa_Pro1886178141017053491et_int: ( fun_Pr8362234881679108866et_int * product_unit ) > set_int ).

tff(sy_c_aa_001t__Product____Type__Ounit_001t__Set__Oset_It__Nat__Onat_J,type,
    aa_Pro6064029160526250199et_nat: ( fun_Pr1628945989756059814et_nat * product_unit ) > set_nat ).

tff(sy_c_aa_001t__Product____Type__Ounit_001t__Set__Oset_It__Product____Type__Ounit_J,type,
    aa_Pro234974305641502940t_unit: ( fun_Pr3013102738158121955t_unit * product_unit ) > set_Product_unit ).

tff(sy_c_aa_001t__Product____Type__Ounit_001t__fun_I_Eo_M_Eo_J,type,
    aa_Pro7286578113964105876un_o_o: ( fun_Pr616739963666181091un_o_o * product_unit ) > fun_o_o ).

tff(sy_c_aa_001t__Product____Type__Ounit_001t__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__fun_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J_J,type,
    aa_Pro9169072840722635546it_nat: ( fun_Pr2439654876356241257it_nat * product_unit ) > fun_he2390400765173608009it_nat ).

tff(sy_c_aa_001t__Product____Type__Ounit_001t__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__fun_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J_J,type,
    aa_Pro5266438804776016756it_nat: ( fun_Pr5739084258597601403it_nat * product_unit ) > fun_he8369595706569872389it_nat ).

tff(sy_c_aa_001t__Product____Type__Ounit_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_J,type,
    aa_Pro2296358444443531977t_unit: ( fun_Pr7459525001844076368t_unit * product_unit ) > fun_Pr2419607445322970330t_unit ).

tff(sy_c_aa_001t__Product____Type__Ounit_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__Nat__Onat_J,type,
    aa_Pro5533504860201378154at_nat: ( fun_Pr3587966566883452857at_nat * product_unit ) > fun_Pr4343998633453697049at_nat ).

tff(sy_c_aa_001t__Product____Type__Ounit_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    aa_Pro1936865637519295110it_nat: ( fun_Pr2979129825601314957it_nat * product_unit ) > fun_Pr192538292188806807it_nat ).

tff(sy_c_aa_001t__Product____Type__Ounit_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    aa_Pro6627971106333230706it_nat: ( fun_Pr925140355916870337it_nat * product_unit ) > fun_Pr5651933991979716257it_nat ).

tff(sy_c_aa_001t__Product____Type__Ounit_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_Mt__Product____Type__Ounit_J,type,
    aa_Pro371939380295300617t_unit: ( fun_Pr2049426570021530256t_unit * product_unit ) > fun_Pr9045474026565384218t_unit ).

tff(sy_c_aa_001t__Product____Type__Ounit_001t__fun_It__Product____Type__Ounit_M_Eo_J,type,
    aa_Pro4895447120693452255unit_o: ( fun_Pr1520749766685617582unit_o * product_unit ) > fun_Product_unit_o ).

tff(sy_c_aa_001t__Rat__Orat_001_Eo,type,
    aa_rat_o: ( fun_rat_o * rat ) > $o ).

tff(sy_c_aa_001t__Rat__Orat_001t__Nat__Onat,type,
    aa_rat_nat: ( fun_rat_nat * rat ) > nat ).

tff(sy_c_aa_001t__Rat__Orat_001t__Rat__Orat,type,
    aa_rat_rat: ( fun_rat_rat * rat ) > rat ).

tff(sy_c_aa_001t__Rat__Orat_001t__fun_I_Eo_Mt__Rat__Orat_J,type,
    aa_rat_fun_o_rat: ( fun_rat_fun_o_rat * rat ) > fun_o_rat ).

tff(sy_c_aa_001t__Rat__Orat_001t__fun_It__Code____Numeral__Ointeger_M_Eo_J,type,
    aa_rat2503820116649195070eger_o: ( fun_ra1401953663915778005eger_o * rat ) > fun_Code_integer_o ).

tff(sy_c_aa_001t__Rat__Orat_001t__fun_It__Code____Numeral__Ointeger_Mt__Rat__Orat_J,type,
    aa_rat6553461586499541832er_rat: ( fun_ra3321464020636160263er_rat * rat ) > fun_Code_integer_rat ).

tff(sy_c_aa_001t__Rat__Orat_001t__fun_It__Code____Numeral__Onatural_M_Eo_J,type,
    aa_rat3585839436822707123ural_o: ( fun_ra6546579167043500746ural_o * rat ) > fun_Code_natural_o ).

tff(sy_c_aa_001t__Rat__Orat_001t__fun_It__Int__Oint_M_Eo_J,type,
    aa_rat_fun_int_o: ( fun_rat_fun_int_o * rat ) > fun_int_o ).

tff(sy_c_aa_001t__Rat__Orat_001t__fun_It__Int__Oint_Mt__Rat__Orat_J,type,
    aa_rat_fun_int_rat: ( fun_rat_fun_int_rat * rat ) > fun_int_rat ).

tff(sy_c_aa_001t__Rat__Orat_001t__fun_It__Nat__Onat_M_Eo_J,type,
    aa_rat_fun_nat_o: ( fun_rat_fun_nat_o * rat ) > fun_nat_o ).

tff(sy_c_aa_001t__Rat__Orat_001t__fun_It__Nat__Onat_Mt__Rat__Orat_J,type,
    aa_rat_fun_nat_rat: ( fun_rat_fun_nat_rat * rat ) > fun_nat_rat ).

tff(sy_c_aa_001t__Rat__Orat_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
    aa_rat250263598611652360at_rat: ( fun_ra5513060666784058567at_rat * rat ) > fun_nat_fun_nat_rat ).

tff(sy_c_aa_001t__Rat__Orat_001t__fun_It__Product____Type__Ounit_Mt__Rat__Orat_J,type,
    aa_rat6507435564262174562it_rat: ( fun_ra5613769993463817465it_rat * rat ) > fun_Product_unit_rat ).

tff(sy_c_aa_001t__Rat__Orat_001t__fun_It__Rat__Orat_M_Eo_J,type,
    aa_rat_fun_rat_o: ( fun_rat_fun_rat_o * rat ) > fun_rat_o ).

tff(sy_c_aa_001t__Rat__Orat_001t__fun_It__Rat__Orat_Mt__Rat__Orat_J,type,
    aa_rat_fun_rat_rat: ( fun_rat_fun_rat_rat * rat ) > fun_rat_rat ).

tff(sy_c_aa_001t__Rat__Orat_001t__fun_It__Rat__Orat_Mt__fun_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
    aa_rat3146053865535587600at_rat: ( fun_ra3995598502166916815at_rat * rat ) > fun_rat_fun_nat_rat ).

tff(sy_c_aa_001t__Rat__Orat_001t__fun_It__Rat__Orat_Mt__fun_It__Rat__Orat_Mt__fun_It__Nat__Onat_Mt__Rat__Orat_J_J_J,type,
    aa_rat7467449789483521253at_rat: ( fun_ra8505079968215247908at_rat * rat ) > fun_ra3995598502166916815at_rat ).

tff(sy_c_aa_001t__Set__Oset_I_Eo_J_001t__Assertions__Oassn,type,
    aa_set_o_assn: ( fun_set_o_assn * set_o ) > assn ).

tff(sy_c_aa_001t__Set__Oset_I_Eo_J_001t__Code____Numeral__Ointeger,type,
    aa_set3804579329223923353nteger: ( fun_se937664112047466216nteger * set_o ) > code_integer ).

tff(sy_c_aa_001t__Set__Oset_I_Eo_J_001t__Nat__Onat,type,
    aa_set_o_nat: ( fun_set_o_nat * set_o ) > nat ).

tff(sy_c_aa_001t__Set__Oset_I_Eo_J_001t__Rat__Orat,type,
    aa_set_o_rat: ( fun_set_o_rat * set_o ) > rat ).

tff(sy_c_aa_001t__Set__Oset_I_Eo_J_001t__Set__Oset_I_Eo_J,type,
    aa_set_o_set_o: ( fun_set_o_set_o * set_o ) > set_o ).

tff(sy_c_aa_001t__Set__Oset_I_Eo_J_001t__fun_I_Eo_M_Eo_J,type,
    aa_set_o_fun_o_o: ( fun_set_o_fun_o_o * set_o ) > fun_o_o ).

tff(sy_c_aa_001t__Set__Oset_I_Eo_J_001t__fun_I_Eo_Mt__Set__Oset_I_Eo_J_J,type,
    aa_set_o_fun_o_set_o: ( fun_se3315603611433934638_set_o * set_o ) > fun_o_set_o ).

tff(sy_c_aa_001t__Set__Oset_I_Eo_J_001t__fun_It__Int__Oint_Mt__Set__Oset_I_Eo_J_J,type,
    aa_set1244563521713955817_set_o: ( fun_se7711175411341617392_set_o * set_o ) > fun_int_set_o ).

tff(sy_c_aa_001t__Set__Oset_I_Eo_J_001t__fun_It__Nat__Onat_Mt__Set__Oset_I_Eo_J_J,type,
    aa_set557987488673405253_set_o: ( fun_se5315385049746747468_set_o * set_o ) > fun_nat_set_o ).

tff(sy_c_aa_001t__Set__Oset_I_Eo_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Set__Oset_I_Eo_J_J,type,
    aa_set1227366709740544310_set_o: ( fun_se7283963663803345157_set_o * set_o ) > fun_Pr8467005832278515962_set_o ).

tff(sy_c_aa_001t__Set__Oset_It__Code____Numeral__Ointeger_J_001_Eo,type,
    aa_set5643387332196575111eger_o: ( fun_se7289222521248229150eger_o * set_Code_integer ) > $o ).

tff(sy_c_aa_001t__Set__Oset_It__Code____Numeral__Ointeger_J_001t__Assertions__Oassn,type,
    aa_set7873363181767135481r_assn: ( fun_se244736854054144952r_assn * set_Code_integer ) > assn ).

tff(sy_c_aa_001t__Set__Oset_It__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger,type,
    aa_set8546232603906849326nteger: ( fun_se3773019727686582893nteger * set_Code_integer ) > code_integer ).

tff(sy_c_aa_001t__Set__Oset_It__Code____Numeral__Ointeger_J_001t__Rat__Orat,type,
    aa_set3519029356358064041er_rat: ( fun_se2244710085602452072er_rat * set_Code_integer ) > rat ).

tff(sy_c_aa_001t__Set__Oset_It__Code____Numeral__Ointeger_J_001t__fun_It__Code____Numeral__Ointeger_M_Eo_J,type,
    aa_set8032437628614644675eger_o: ( fun_se4239619783102168410eger_o * set_Code_integer ) > fun_Code_integer_o ).

tff(sy_c_aa_001t__Set__Oset_It__Code____Numeral__Ointeger_J_001t__fun_It__Set__Oset_It__Code____Numeral__Ointeger_J_M_Eo_J,type,
    aa_set4044230130517860621eger_o: ( fun_se5529282185252607396eger_o * set_Code_integer ) > fun_se7289222521248229150eger_o ).

tff(sy_c_aa_001t__Set__Oset_It__Int__Oint_J_001_Eo,type,
    aa_set_int_o: ( fun_set_int_o * set_int ) > $o ).

tff(sy_c_aa_001t__Set__Oset_It__Int__Oint_J_001t__Assertions__Oassn,type,
    aa_set_int_assn: ( fun_set_int_assn * set_int ) > assn ).

tff(sy_c_aa_001t__Set__Oset_It__Int__Oint_J_001t__Code____Numeral__Ointeger,type,
    aa_set6880394903383512189nteger: ( fun_se4372286887653997756nteger * set_int ) > code_integer ).

tff(sy_c_aa_001t__Set__Oset_It__Int__Oint_J_001t__Int__Oint,type,
    aa_set_int_int: ( fun_set_int_int * set_int ) > int ).

tff(sy_c_aa_001t__Set__Oset_It__Int__Oint_J_001t__Rat__Orat,type,
    aa_set_int_rat: ( fun_set_int_rat * set_int ) > rat ).

tff(sy_c_aa_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J,type,
    aa_set_int_set_int: ( fun_set_int_set_int * set_int ) > set_int ).

tff(sy_c_aa_001t__Set__Oset_It__Int__Oint_J_001t__fun_I_Eo_Mt__Set__Oset_It__Int__Oint_J_J,type,
    aa_set8238700067146519789et_int: ( fun_se241328533291454980et_int * set_int ) > fun_o_set_int ).

tff(sy_c_aa_001t__Set__Oset_It__Int__Oint_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Set__Oset_It__Int__Oint_J_J,type,
    aa_set8360975810291373660et_int: ( fun_se2042144505192658715et_int * set_int ) > fun_Co5817875961738342972et_int ).

tff(sy_c_aa_001t__Set__Oset_It__Int__Oint_J_001t__fun_It__Int__Oint_M_Eo_J,type,
    aa_set_int_fun_int_o: ( fun_se867122708194164540_int_o * set_int ) > fun_int_o ).

tff(sy_c_aa_001t__Set__Oset_It__Int__Oint_J_001t__fun_It__Int__Oint_Mt__Set__Oset_It__Int__Oint_J_J,type,
    aa_set2836339071814736939et_int: ( fun_se8982873411337295210et_int * set_int ) > fun_int_set_int ).

tff(sy_c_aa_001t__Set__Oset_It__Int__Oint_J_001t__fun_It__Nat__Onat_Mt__Set__Oset_It__Int__Oint_J_J,type,
    aa_set2464685511577892303et_int: ( fun_se2974063760341720334et_int * set_int ) > fun_nat_set_int ).

tff(sy_c_aa_001t__Set__Oset_It__Int__Oint_J_001t__fun_It__Set__Oset_It__Int__Oint_J_M_Eo_J,type,
    aa_set5425576183772390127_int_o: ( fun_se2051630309975736070_int_o * set_int ) > fun_set_int_o ).

tff(sy_c_aa_001t__Set__Oset_It__Nat__Onat_J_001_Eo,type,
    aa_set_nat_o: ( fun_set_nat_o * set_nat ) > $o ).

tff(sy_c_aa_001t__Set__Oset_It__Nat__Onat_J_001t__Nat__Onat,type,
    aa_set_nat_nat: ( fun_set_nat_nat * set_nat ) > nat ).

tff(sy_c_aa_001t__Set__Oset_It__Nat__Onat_J_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
    aa_set6119337032432945050et_nat: ( fun_se7316093745529328985et_nat * set_nat ) > option_set_nat ).

tff(sy_c_aa_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
    aa_set_nat_set_nat: ( fun_set_nat_set_nat * set_nat ) > set_nat ).

tff(sy_c_aa_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
    aa_set7246812951530217472et_nat: ( fun_se3362872515591026879et_nat * set_nat ) > set_set_nat ).

tff(sy_c_aa_001t__Set__Oset_It__Nat__Onat_J_001t__fun_I_Eo_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    aa_set1696117090455734765et_nat: ( fun_se5245582867311637764et_nat * set_nat ) > fun_o_set_nat ).

tff(sy_c_aa_001t__Set__Oset_It__Nat__Onat_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Set__Oset_It__Code____Numeral__Ointeger_J_J,type,
    aa_set1342327774797759281nteger: ( fun_se3841591170510310256nteger * set_nat ) > fun_Co744628173305925485nteger ).

tff(sy_c_aa_001t__Set__Oset_It__Nat__Onat_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Set__Oset_It__Int__Oint_J_J,type,
    aa_set732007329302836736et_int: ( fun_se3636548061058897599et_int * set_nat ) > fun_Co5817875961738342972et_int ).

tff(sy_c_aa_001t__Set__Oset_It__Nat__Onat_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    aa_set3222090474234563492et_nat: ( fun_se8450096479846816355et_nat * set_nat ) > fun_Co8307959106670069728et_nat ).

tff(sy_c_aa_001t__Set__Oset_It__Nat__Onat_J_001t__fun_It__Int__Oint_Mt__Set__Oset_It__Code____Numeral__Ointeger_J_J,type,
    aa_set1723057546349436160nteger: ( fun_se8949688400205348287nteger * set_nat ) > fun_in6808926178784942396nteger ).

tff(sy_c_aa_001t__Set__Oset_It__Nat__Onat_J_001t__fun_It__Int__Oint_Mt__Set__Oset_It__Int__Oint_J_J,type,
    aa_set7667248109638618063et_int: ( fun_se4590410412306400526et_int * set_nat ) > fun_int_set_int ).

tff(sy_c_aa_001t__Set__Oset_It__Nat__Onat_J_001t__fun_It__Int__Oint_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    aa_set933959217715569011et_nat: ( fun_se180586794239543474et_nat * set_nat ) > fun_int_set_nat ).

tff(sy_c_aa_001t__Set__Oset_It__Nat__Onat_J_001t__fun_It__Nat__Onat_M_Eo_J,type,
    aa_set_nat_fun_nat_o: ( fun_se382663106265794036_nat_o * set_nat ) > fun_nat_o ).

tff(sy_c_aa_001t__Set__Oset_It__Nat__Onat_J_001t__fun_It__Nat__Onat_Mt__Set__Oset_It__Code____Numeral__Ointeger_J_J,type,
    aa_set4032875478442387108nteger: ( fun_se2951167709562549603nteger * set_nat ) > fun_na9118744110877893344nteger ).

tff(sy_c_aa_001t__Set__Oset_It__Nat__Onat_J_001t__fun_It__Nat__Onat_Mt__Set__Oset_It__Int__Oint_J_J,type,
    aa_set7295594549401773427et_int: ( fun_se7804972798165601458et_int * set_nat ) > fun_nat_set_int ).

tff(sy_c_aa_001t__Set__Oset_It__Nat__Onat_J_001t__fun_It__Nat__Onat_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    aa_set562305657478724375et_nat: ( fun_se3395149180098744406et_nat * set_nat ) > fun_nat_set_nat ).

tff(sy_c_aa_001t__Set__Oset_It__Nat__Onat_J_001t__fun_It__Set__Oset_It__Nat__Onat_J_M_Eo_J,type,
    aa_set7861427066675100071_nat_o: ( fun_se2170385732985038782_nat_o * set_nat ) > fun_set_nat_o ).

tff(sy_c_aa_001t__Set__Oset_It__Nat__Onat_J_001t__fun_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J_J,type,
    aa_set3960572117082860675et_nat: ( fun_se8125625266612218818et_nat * set_nat ) > fun_se3362872515591026879et_nat ).

tff(sy_c_aa_001t__Set__Oset_It__Num__Onum_J_001t__Num__Onum,type,
    aa_set_num_num: ( fun_set_num_num * set_num ) > num ).

tff(sy_c_aa_001t__Set__Oset_It__Num__Onum_J_001t__Set__Oset_It__Num__Onum_J,type,
    aa_set_num_set_num: ( fun_set_num_set_num * set_num ) > set_num ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_Eo,type,
    aa_set3702741264012733747_nat_o: ( fun_se4782206882984618170_nat_o * set_Pr1261947904930325089at_nat ) > $o ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Int__Oint,type,
    aa_set4746584241299694929at_int: ( fun_se9142667792015812128at_int * set_Pr1261947904930325089at_nat ) > int ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Nat__Onat,type,
    aa_set4749074711808745205at_nat: ( fun_se4097146774670233028at_nat * set_Pr1261947904930325089at_nat ) > nat ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    aa_set2934564513904597954at_nat: ( fun_se5244420045238757833at_nat * set_Pr1261947904930325089at_nat ) > option8963830502488799655at_nat ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    aa_set8868280134176360700at_nat: ( fun_se320340636488258563at_nat * set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    aa_set1427696295806717282at_nat: ( fun_se1551789852802198377at_nat * set_Pr1261947904930325089at_nat ) > set_Pr4329608150637261639at_nat ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    aa_set6242432332095302236at_nat: ( fun_se953073389798102371at_nat * set_Pr1261947904930325089at_nat ) > set_se7855581050983116737at_nat ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Nat__Onat_M_Eo_J,type,
    aa_set5175029118278479676_nat_o: ( fun_se7755072775241076291_nat_o * set_Pr1261947904930325089at_nat ) > fun_nat_o ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    aa_set2634951030311766213_nat_o: ( fun_se4014881416909572940_nat_o * set_Pr1261947904930325089at_nat ) > fun_nat_fun_nat_o ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J_J_J,type,
    aa_set1591873763996598871_nat_o: ( fun_se3165749655728557022_nat_o * set_Pr1261947904930325089at_nat ) > fun_na927404270896789692_nat_o ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J_J,type,
    aa_set1501693898512841689_nat_o: ( fun_se218054151627931304_nat_o * set_Pr1261947904930325089at_nat ) > fun_na5914473681949881652_nat_o ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J_M_Eo_J_J,type,
    aa_set7004941124559686709_nat_o: ( fun_se7979130632333208764_nat_o * set_Pr1261947904930325089at_nat ) > fun_na8508211072120413978_nat_o ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Nat__Onat_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J,type,
    aa_set4096294849986607660_nat_o: ( fun_se5991283330978499451_nat_o * set_Pr1261947904930325089at_nat ) > fun_na4518284863240432007_nat_o ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Nat__Onat_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    aa_set6059588303149383989_nat_o: ( fun_se2918291395271296516_nat_o * set_Pr1261947904930325089at_nat ) > fun_na3424944204176166544_nat_o ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J,type,
    aa_set4888932223548040198_nat_o: ( fun_se8417120708266284045_nat_o * set_Pr1261947904930325089at_nat ) > fun_Pr8338385031646565611_nat_o ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J,type,
    aa_set5283925091486981337_nat_o: ( fun_se1934056669979388328_nat_o * set_Pr1261947904930325089at_nat ) > fun_Pr3059359313727237556_nat_o ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J,type,
    aa_set7675215768510388063_nat_o: ( fun_se5639961202347202350_nat_o * set_Pr1261947904930325089at_nat ) > fun_se4782206882984618170_nat_o ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Int__Oint_J,type,
    aa_set2438460329721899707at_int: ( fun_se5286484986886725186at_int * set_Pr1261947904930325089at_nat ) > fun_se9142667792015812128at_int ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J,type,
    aa_set6616311349231096415at_nat: ( fun_se7776568131818451942at_nat * set_Pr1261947904930325089at_nat ) > fun_se4097146774670233028at_nat ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J_M_Eo_J_J_J,type,
    aa_set5873268817925218273_nat_o: ( fun_se9209729713313069232_nat_o * set_Pr1261947904930325089at_nat ) > fun_se7979130632333208764_nat_o ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_J_J,type,
    aa_set4461581360499344159_nat_o: ( fun_se7382040709525900966_nat_o * set_Pr1261947904930325089at_nat ) > fun_se2918291395271296516_nat_o ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J_J,type,
    aa_set3180801629657254467_nat_o: ( fun_se5316394792625908170_nat_o * set_Pr1261947904930325089at_nat ) > fun_se1934056669979388328_nat_o ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J,type,
    aa_set8959908230745118793_nat_o: ( fun_se6502775985981750992_nat_o * set_Pr1261947904930325089at_nat ) > fun_se5639961202347202350_nat_o ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J_J,type,
    aa_set5113931935655255541_nat_o: ( fun_se8716479205685501124_nat_o * set_Pr1261947904930325089at_nat ) > fun_se6502775985981750992_nat_o ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    aa_set7180998873066629928at_nat: ( fun_se636550882185307767at_nat * set_Pr1261947904930325089at_nat ) > fun_se6846035212209387651at_nat ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    aa_set7071694670514008770at_nat: ( fun_se7901873761543946185at_nat * set_Pr4329608150637261639at_nat ) > option1583680563626158861at_nat ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    aa_set4883462369968598652at_nat: ( fun_se6846035212209387651at_nat * set_Pr4329608150637261639at_nat ) > set_Pr4329608150637261639at_nat ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001t__fun_It__Nat__Onat_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Nat__Onat_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J_J_J,type,
    aa_set1734484532169114937_nat_o: ( fun_se991814106188233920_nat_o * set_Pr4329608150637261639at_nat ) > fun_na7330042712434367748_nat_o ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001t__fun_It__Nat__Onat_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J_J_J,type,
    aa_set2321460896359935973_nat_o: ( fun_se3629081808164793780_nat_o * set_Pr4329608150637261639at_nat ) > fun_na7109657165716327514_nat_o ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J,type,
    aa_set5605188905385065315_nat_o: ( fun_se8406536441587994090_nat_o * set_Pr4329608150637261639at_nat ) > fun_se5639961202347202350_nat_o ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J_J_J,type,
    aa_set2810100084588730581_nat_o: ( fun_se1700271160720914596_nat_o * set_Pr4329608150637261639at_nat ) > fun_se5316394792625908170_nat_o ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J_J_J,type,
    aa_set2536000832573987193_nat_o: ( fun_se6980948925662697216_nat_o * set_Pr4329608150637261639at_nat ) > fun_se8716479205685501124_nat_o ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    aa_set3385707584125383432nt_int: ( fun_se2900878183379320647nt_int * set_Pr4166680992137330533nt_int ) > set_Pr4166680992137330533nt_int ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_001t__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    aa_set6932945912113297217_int_o: ( fun_se5644990602862975744_int_o * set_Pr4166680992137330533nt_int ) > fun_fu2978539155105838238_int_o ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    aa_set4655596970315180246nteger: ( fun_se2190013347424485781nteger * set_Pr3486312109254157132nteger ) > set_Pr3486312109254157132nteger ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_001t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
    aa_set282680696547864321eger_o: ( fun_se6163777255337707072eger_o * set_Pr3486312109254157132nteger ) > fun_fu7695273699059480439eger_o ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    aa_set4110577973744520298et_nat: ( fun_se9157011578508667433et_nat * set_Pr1312406793078187350et_nat ) > set_Pr1312406793078187350et_nat ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_001t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
    aa_set6295625606485646487_nat_o: ( fun_se7509835969743050710_nat_o * set_Pr1312406793078187350et_nat ) > fun_fu8419763957888848259_nat_o ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    aa_set7201747738020000294et_nat: ( fun_se2331804103973993189et_nat * set_Pr4040394263813967220et_nat ) > set_Pr4040394263813967220et_nat ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J_001t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_J,type,
    aa_set2269662337286943895_nat_o: ( fun_se4713689491525875926_nat_o * set_Pr4040394263813967220et_nat ) > fun_fu2611741329380808165_nat_o ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    aa_set3423462778074857648nt_int: ( fun_se1594822257893229295nt_int * set_Pr6700895561065273913nt_int ) > set_Pr6700895561065273913nt_int ).

tff(sy_c_aa_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_001t__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    aa_set8857007276572228673_int_o: ( fun_se5710315616867461632_int_o * set_Pr6700895561065273913nt_int ) > fun_fu6865642474282033866_int_o ).

tff(sy_c_aa_001t__Set__Oset_It__Set__Oset_I_Eo_J_J_001t__Assertions__Oassn,type,
    aa_set_set_o_assn: ( fun_set_set_o_assn * set_set_o ) > assn ).

tff(sy_c_aa_001t__Set__Oset_It__Set__Oset_I_Eo_J_J_001t__Code____Numeral__Ointeger,type,
    aa_set5709627445990591865nteger: ( fun_se5062308858318814664nteger * set_set_o ) > code_integer ).

tff(sy_c_aa_001t__Set__Oset_It__Set__Oset_I_Eo_J_J_001t__Nat__Onat,type,
    aa_set_set_o_nat: ( fun_set_set_o_nat * set_set_o ) > nat ).

tff(sy_c_aa_001t__Set__Oset_It__Set__Oset_I_Eo_J_J_001t__Rat__Orat,type,
    aa_set_set_o_rat: ( fun_set_set_o_rat * set_set_o ) > rat ).

tff(sy_c_aa_001t__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J_001_Eo,type,
    aa_set6460979282782877649eger_o: ( fun_se1103039064484435816eger_o * set_set_Code_integer ) > $o ).

tff(sy_c_aa_001t__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J_001t__Assertions__Oassn,type,
    aa_set586451247737764655r_assn: ( fun_se704019859950278126r_assn * set_set_Code_integer ) > assn ).

tff(sy_c_aa_001t__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
    aa_set1330082717382260836nteger: ( fun_se1218973151702474915nteger * set_set_Code_integer ) > code_integer ).

tff(sy_c_aa_001t__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J_001t__Int__Oint,type,
    aa_set5345935369443442227er_int: ( fun_se504249187503832818er_int * set_set_Code_integer ) > int ).

tff(sy_c_aa_001t__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J_001t__Rat__Orat,type,
    aa_set4713295779865996767er_rat: ( fun_se1173871648619632798er_rat * set_set_Code_integer ) > rat ).

tff(sy_c_aa_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_001_Eo,type,
    aa_set_set_int_o: ( fun_set_set_int_o * set_set_int ) > $o ).

tff(sy_c_aa_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_001t__Assertions__Oassn,type,
    aa_set_set_int_assn: ( fun_set_set_int_assn * set_set_int ) > assn ).

tff(sy_c_aa_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_001t__Code____Numeral__Ointeger,type,
    aa_set3853921609887811379nteger: ( fun_se8304080770522320754nteger * set_set_int ) > code_integer ).

tff(sy_c_aa_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_001t__Int__Oint,type,
    aa_set_set_int_int: ( fun_set_set_int_int * set_set_int ) > int ).

tff(sy_c_aa_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_001t__Rat__Orat,type,
    aa_set_set_int_rat: ( fun_set_set_int_rat * set_set_int ) > rat ).

tff(sy_c_aa_001t__Set__Oset_It__Set__Oset_It__List__Olist_It__Nat__Onat_J_J_J_001_Eo,type,
    aa_set7045010141486209806_nat_o: ( fun_se5048694460222551717_nat_o * set_set_list_nat ) > $o ).

tff(sy_c_aa_001t__Set__Oset_It__Set__Oset_It__List__Olist_It__Nat__Onat_J_J_J_001t__Int__Oint,type,
    aa_set4520658747456594998at_int: ( fun_se1018900654481025269at_int * set_set_list_nat ) > int ).

tff(sy_c_aa_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J_001_Eo,type,
    aa_set_set_nat_o: ( fun_set_set_nat_o * set_set_nat ) > $o ).

tff(sy_c_aa_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J_001t__Int__Oint,type,
    aa_set_set_nat_int: ( fun_set_set_nat_int * set_set_nat ) > int ).

tff(sy_c_aa_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001_Eo,type,
    aa_set5218765425691562963_nat_o: ( fun_se7504237348027150170_nat_o * set_se7855581050983116737at_nat ) > $o ).

tff(sy_c_aa_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Int__Oint,type,
    aa_set2246171803582654129at_int: ( fun_se8575562297434572672at_int * set_se7855581050983116737at_nat ) > int ).

tff(sy_c_aa_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__fun_It__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J,type,
    aa_set8824140522937572191_nat_o: ( fun_se7001366092147120942_nat_o * set_se7855581050983116737at_nat ) > fun_se7504237348027150170_nat_o ).

tff(sy_c_aa_001t__Set__Oset_It__Set__Oset_It__Product____Type__Ounit_J_J_001_Eo,type,
    aa_set1868964232251763271unit_o: ( fun_se2288280263375636942unit_o * set_set_Product_unit ) > $o ).

tff(sy_c_aa_001t__Set__Oset_It__Set__Oset_It__Product____Type__Ounit_J_J_001t__Int__Oint,type,
    aa_set1590017630834857277it_int: ( fun_se1823139391991869964it_int * set_set_Product_unit ) > int ).

tff(sy_c_aa_001t__Set__Oset_It__fun_It__Nat__Onat_M_Eo_J_J_001t__Set__Oset_It__fun_It__Nat__Onat_M_Eo_J_J,type,
    aa_set8811106445076359420_nat_o: ( fun_se2106923200977956867_nat_o * set_fun_nat_o ) > set_fun_nat_o ).

tff(sy_c_aa_001t__fun_I_Eo_M_Eo_J_001t__fun_I_Eo_M_Eo_J,type,
    aa_fun_o_o_fun_o_o: ( fun_fun_o_o_fun_o_o * fun_o_o ) > fun_o_o ).

tff(sy_c_aa_001t__fun_I_Eo_M_Eo_J_001t__fun_I_Eo_Mt__Assertions__Oassn_J,type,
    aa_fun8560762093604944786o_assn: ( fun_fu7714003655882793385o_assn * fun_o_o ) > fun_o_assn ).

tff(sy_c_aa_001t__fun_I_Eo_M_Eo_J_001t__fun_I_Eo_Mt__Code____Numeral__Ointeger_J,type,
    aa_fun6542514109734600263nteger: ( fun_fu7181763470137098718nteger * fun_o_o ) > fun_o_Code_integer ).

tff(sy_c_aa_001t__fun_I_Eo_M_Eo_J_001t__fun_I_Eo_Mt__Rat__Orat_J,type,
    aa_fun_o_o_fun_o_rat: ( fun_fu830079035465870425_o_rat * fun_o_o ) > fun_o_rat ).

tff(sy_c_aa_001t__fun_I_Eo_Mt__Assertions__Oassn_J_001t__fun_I_Eo_M_Eo_J,type,
    aa_fun8382565201914911066un_o_o: ( fun_fu3143923321121214633un_o_o * fun_o_assn ) > fun_o_o ).

tff(sy_c_aa_001t__fun_I_Eo_Mt__Assertions__Oassn_J_001t__fun_I_Eo_Mt__Assertions__Oassn_J,type,
    aa_fun4536517337817438332o_assn: ( fun_fu704708528062463619o_assn * fun_o_assn ) > fun_o_assn ).

tff(sy_c_aa_001t__fun_I_Eo_Mt__Assertions__Oassn_J_001t__fun_It__Assertions__Oassn_Mt__fun_I_Eo_Mt__Assertions__Oassn_J_J,type,
    aa_fun7777267157241973165o_assn: ( fun_fu1324339541976909620o_assn * fun_o_assn ) > fun_assn_fun_o_assn ).

tff(sy_c_aa_001t__fun_I_Eo_Mt__Assertions__Oassn_J_001t__fun_It__Set__Oset_I_Eo_J_Mt__Assertions__Oassn_J,type,
    aa_fun1914167119812169564o_assn: ( fun_fu5561970054461773155o_assn * fun_o_assn ) > fun_set_o_assn ).

tff(sy_c_aa_001t__fun_I_Eo_Mt__Assertions__Oassn_J_001t__fun_It__fun_I_Eo_Mt__Assertions__Oassn_J_Mt__fun_I_Eo_M_Eo_J_J,type,
    aa_fun5794833117214906962un_o_o: ( fun_fu5861359551626625881un_o_o * fun_o_assn ) > fun_fu3143923321121214633un_o_o ).

tff(sy_c_aa_001t__fun_I_Eo_Mt__Code____Numeral__Ointeger_J_001t__fun_I_Eo_M_Eo_J,type,
    aa_fun8192762245619933327un_o_o: ( fun_fu3819205551299168222un_o_o * fun_o_Code_integer ) > fun_o_o ).

tff(sy_c_aa_001t__fun_I_Eo_Mt__Code____Numeral__Ointeger_J_001t__fun_I_Eo_Mt__Code____Numeral__Ointeger_J,type,
    aa_fun8520278569782659900nteger: ( fun_fu2786480252100984515nteger * fun_o_Code_integer ) > fun_o_Code_integer ).

tff(sy_c_aa_001t__fun_I_Eo_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Set__Oset_I_Eo_J_Mt__Code____Numeral__Ointeger_J,type,
    aa_fun2057504995935393308nteger: ( fun_fu6303754889700780451nteger * fun_o_Code_integer ) > fun_se937664112047466216nteger ).

tff(sy_c_aa_001t__fun_I_Eo_Mt__Code____Numeral__Ointeger_J_001t__fun_It__fun_I_Eo_Mt__Code____Numeral__Ointeger_J_Mt__fun_I_Eo_M_Eo_J_J,type,
    aa_fun1865401534164435218un_o_o: ( fun_fu8716660765737269145un_o_o * fun_o_Code_integer ) > fun_fu3819205551299168222un_o_o ).

tff(sy_c_aa_001t__fun_I_Eo_Mt__Int__Oint_J_001t__fun_I_Eo_Mt__Int__Oint_J,type,
    aa_fun4727766026823762812_o_int: ( fun_fu6940589326549028739_o_int * fun_o_int ) > fun_o_int ).

tff(sy_c_aa_001t__fun_I_Eo_Mt__Int__Oint_J_001t__fun_It__fun_I_Eo_Mt__Int__Oint_J_Mt__fun_I_Eo_Mt__Int__Oint_J_J,type,
    aa_fun5648456818326528798_o_int: ( fun_fu9026017786105829997_o_int * fun_o_int ) > fun_fu6940589326549028739_o_int ).

tff(sy_c_aa_001t__fun_I_Eo_Mt__Nat__Onat_J_001t__fun_I_Eo_M_Eo_J,type,
    aa_fun_o_nat_fun_o_o: ( fun_fu6781074197733401937un_o_o * fun_o_nat ) > fun_o_o ).

tff(sy_c_aa_001t__fun_I_Eo_Mt__Nat__Onat_J_001t__fun_I_Eo_Mt__Nat__Onat_J,type,
    aa_fun6176012476734143100_o_nat: ( fun_fu6701067901881939075_o_nat * fun_o_nat ) > fun_o_nat ).

tff(sy_c_aa_001t__fun_I_Eo_Mt__Nat__Onat_J_001t__fun_It__Set__Oset_I_Eo_J_Mt__Nat__Onat_J,type,
    aa_fun8470299178418016604_o_nat: ( fun_fu8843157277860572003_o_nat * fun_o_nat ) > fun_set_o_nat ).

tff(sy_c_aa_001t__fun_I_Eo_Mt__Nat__Onat_J_001t__fun_It__fun_I_Eo_Mt__Nat__Onat_J_Mt__fun_I_Eo_M_Eo_J_J,type,
    aa_fun5833554292436378194un_o_o: ( fun_fu5915781709770235737un_o_o * fun_o_nat ) > fun_fu6781074197733401937un_o_o ).

tff(sy_c_aa_001t__fun_I_Eo_Mt__Nat__Onat_J_001t__fun_It__fun_I_Eo_Mt__Nat__Onat_J_Mt__fun_I_Eo_Mt__Nat__Onat_J_J,type,
    aa_fun6251207968994965954_o_nat: ( fun_fu3581538110357139729_o_nat * fun_o_nat ) > fun_fu6701067901881939075_o_nat ).

tff(sy_c_aa_001t__fun_I_Eo_Mt__Rat__Orat_J_001t__fun_I_Eo_M_Eo_J,type,
    aa_fun_o_rat_fun_o_o: ( fun_fu6337961365400742745un_o_o * fun_o_rat ) > fun_o_o ).

tff(sy_c_aa_001t__fun_I_Eo_Mt__Rat__Orat_J_001t__fun_I_Eo_Mt__Rat__Orat_J,type,
    aa_fun4336163974892599420_o_rat: ( fun_fu1989461620956114563_o_rat * fun_o_rat ) > fun_o_rat ).

tff(sy_c_aa_001t__fun_I_Eo_Mt__Rat__Orat_J_001t__fun_It__Rat__Orat_Mt__fun_I_Eo_Mt__Rat__Orat_J_J,type,
    aa_fun5241534567979455741_o_rat: ( fun_fu8716238685137547908_o_rat * fun_o_rat ) > fun_rat_fun_o_rat ).

tff(sy_c_aa_001t__fun_I_Eo_Mt__Rat__Orat_J_001t__fun_It__Set__Oset_I_Eo_J_Mt__Rat__Orat_J,type,
    aa_fun7302669049306738524_o_rat: ( fun_fu4803769369665013091_o_rat * fun_o_rat ) > fun_set_o_rat ).

tff(sy_c_aa_001t__fun_I_Eo_Mt__Rat__Orat_J_001t__fun_It__fun_I_Eo_Mt__Rat__Orat_J_Mt__fun_I_Eo_M_Eo_J_J,type,
    aa_fun5510981055783399506un_o_o: ( fun_fu2641566564518291801un_o_o * fun_o_rat ) > fun_fu6337961365400742745un_o_o ).

tff(sy_c_aa_001t__fun_I_Eo_Mt__Rat__Orat_J_001t__fun_It__fun_I_Eo_Mt__Rat__Orat_J_Mt__fun_I_Eo_Mt__Rat__Orat_J_J,type,
    aa_fun2919298112881465802_o_rat: ( fun_fu9039538216874201369_o_rat * fun_o_rat ) > fun_fu1989461620956114563_o_rat ).

tff(sy_c_aa_001t__fun_I_Eo_Mt__Set__Oset_I_Eo_J_J_001t__fun_I_Eo_M_Eo_J,type,
    aa_fun4619127644298054564un_o_o: ( fun_fu5370137289309429475un_o_o * fun_o_set_o ) > fun_o_o ).

tff(sy_c_aa_001t__fun_I_Eo_Mt__Set__Oset_It__Int__Oint_J_J_001t__fun_I_Eo_M_Eo_J,type,
    aa_fun3615580826569402900un_o_o: ( fun_fu8465396169103413603un_o_o * fun_o_set_int ) > fun_o_o ).

tff(sy_c_aa_001t__fun_I_Eo_Mt__Set__Oset_It__Nat__Onat_J_J_001t__fun_I_Eo_M_Eo_J,type,
    aa_fun8423158570077026744un_o_o: ( fun_fu4049601875756261639un_o_o * fun_o_set_nat ) > fun_o_o ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_M_Eo_J_001t__fun_It__Code____Numeral__Ointeger_M_Eo_J,type,
    aa_fun8214818745163655228eger_o: ( fun_fu8094397175230428611eger_o * fun_Code_integer_o ) > fun_Code_integer_o ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_M_Eo_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Assertions__Oassn_J,type,
    aa_fun6392223008197429786r_assn: ( fun_fu1898041513128675305r_assn * fun_Code_integer_o ) > fun_Co4490034186337852034r_assn ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_M_Eo_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    aa_fun791458909507501263nteger: ( fun_fu2729256655946442782nteger * fun_Code_integer_o ) > fun_Co8499238673658658103nteger ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Assertions__Oassn_J_001t__fun_It__Assertions__Oassn_Mt__fun_It__Code____Numeral__Ointeger_Mt__Assertions__Oassn_J_J,type,
    aa_fun5785710901775686247r_assn: ( fun_fu717556231145110950r_assn * fun_Co4490034186337852034r_assn ) > fun_as4904527345752988583r_assn ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Assertions__Oassn_J_001t__fun_It__Code____Numeral__Ointeger_M_Eo_J,type,
    aa_fun6538703224075513620eger_o: ( fun_fu4844139638962010283eger_o * fun_Co4490034186337852034r_assn ) > fun_Code_integer_o ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Assertions__Oassn_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Assertions__Oassn_J,type,
    aa_fun4119713415300323650r_assn: ( fun_fu5082522747898945281r_assn * fun_Co4490034186337852034r_assn ) > fun_Co4490034186337852034r_assn ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Assertions__Oassn_J_001t__fun_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__Assertions__Oassn_J,type,
    aa_fun4520394192108194424r_assn: ( fun_fu727159081937814839r_assn * fun_Co4490034186337852034r_assn ) > fun_se244736854054144952r_assn ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Assertions__Oassn_J_001t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Assertions__Oassn_J_Mt__fun_It__Code____Numeral__Ointeger_M_Eo_J_J,type,
    aa_fun4422309413433313771eger_o: ( fun_fu4735791719682850818eger_o * fun_Co4490034186337852034r_assn ) > fun_fu4844139638962010283eger_o ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_Eo,type,
    aa_fun774133186966548707eger_o: ( fun_fu1769128043447206010eger_o * fun_Co8499238673658658103nteger ) > $o ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger,type,
    aa_fun2937960011630702546nteger: ( fun_fu5689865433563736081nteger * fun_Co8499238673658658103nteger ) > code_integer ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Code____Numeral__Ointeger_M_Eo_J,type,
    aa_fun7159535342743012639eger_o: ( fun_fu855086506144988854eger_o * fun_Co8499238673658658103nteger ) > fun_Code_integer_o ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    aa_fun4435975922079263404nteger: ( fun_fu1763652423599918571nteger * fun_Co8499238673658658103nteger ) > fun_Co8499238673658658103nteger ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    aa_fun4856328718102079442nteger: ( fun_fu2039158179202302481nteger * fun_Co8499238673658658103nteger ) > fun_Co1561183069634336733nteger ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J,type,
    aa_fun4882090679079481449nteger: ( fun_fu2219603532186391848nteger * fun_Co8499238673658658103nteger ) > fun_num_Code_integer ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Num__Onum_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    aa_fun4796990323277771791nteger: ( fun_fu5629128276443140046nteger * fun_Co8499238673658658103nteger ) > fun_nu1379135015814352922nteger ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    aa_fun2509385170507305080nteger: ( fun_fu4800041728187187127nteger * fun_Co8499238673658658103nteger ) > fun_Pr5876161306168176259nteger ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__Code____Numeral__Ointeger_J,type,
    aa_fun7145370688314743778nteger: ( fun_fu4961913266064405537nteger * fun_Co8499238673658658103nteger ) > fun_se3773019727686582893nteger ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J,type,
    aa_fun8448071180471187909eger_o: ( fun_fu4788845708739168348eger_o * fun_Co8499238673658658103nteger ) > fun_fu1769128043447206010eger_o ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Code____Numeral__Ointeger_M_Eo_J_J,type,
    aa_fun5296778454019918337eger_o: ( fun_fu4083202260958266008eger_o * fun_Co8499238673658658103nteger ) > fun_fu855086506144988854eger_o ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
    aa_fun4591545111762374183_int_o: ( fun_fu7391974349310290878_int_o * fun_Co8499238673658658103nteger ) > fun_fun_int_int_o ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_J,type,
    aa_fun2129879960000001626nteger: ( fun_fu5844746416483971737nteger * fun_Co8499238673658658103nteger ) > fun_fu552866168194876645nteger ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__fun_It__fun_It__Rat__Orat_Mt__Rat__Orat_J_M_Eo_J,type,
    aa_fun7658886767390183119_rat_o: ( fun_fu1378022486368508006_rat_o * fun_Co8499238673658658103nteger ) > fun_fun_rat_rat_o ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Int__Oint_J,type,
    aa_fun3291479149765983562er_int: ( fun_fu403917627589892361er_int * fun_Code_integer_int ) > fun_Code_integer_int ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J,type,
    aa_fun7469330169275180270er_nat: ( fun_fu2894000772521619117er_nat * fun_Code_integer_int ) > fun_Code_integer_nat ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_001t__fun_It__Num__Onum_Mt__Num__Onum_J,type,
    aa_fun4497822097518049269um_num: ( fun_fu43082730658364980um_num * fun_Code_integer_int ) > fun_num_num ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_001t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_J,type,
    aa_fun4411173778969602765er_int: ( fun_fu1007793439646807308er_int * fun_Code_integer_int ) > fun_fu403917627589892361er_int ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J,type,
    aa_fun3076867170244285586er_nat: ( fun_fu7724909810345500241er_nat * fun_Code_integer_nat ) > fun_Code_integer_nat ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_001t__fun_It__Num__Onum_Mt__Num__Onum_J,type,
    aa_fun546377469102339993um_num: ( fun_fu5315010139097431512um_num * fun_Code_integer_nat ) > fun_num_num ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_001t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_J,type,
    aa_fun7635586485349294009er_nat: ( fun_fu2498091903632033272er_nat * fun_Code_integer_nat ) > fun_fu7724909810345500241er_nat ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Num__Onum_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    aa_fun8156166258484938729nteger: ( fun_fu1714096010366225192nteger * fun_Code_integer_num ) > fun_Co8499238673658658103nteger ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Num__Onum_J_001t__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J,type,
    aa_fun7431108047665086886nteger: ( fun_fu9168018664657815141nteger * fun_Code_integer_num ) > fun_num_Code_integer ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Rat__Orat_J_001t__fun_It__Code____Numeral__Ointeger_M_Eo_J,type,
    aa_fun6395433285121891940eger_o: ( fun_fu4523568072766896123eger_o * fun_Code_integer_rat ) > fun_Code_integer_o ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Rat__Orat_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Rat__Orat_J,type,
    aa_fun8169474305930283170er_rat: ( fun_fu722387130092441185er_rat * fun_Code_integer_rat ) > fun_Code_integer_rat ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Rat__Orat_J_001t__fun_It__Rat__Orat_Mt__fun_It__Code____Numeral__Ointeger_Mt__Rat__Orat_J_J,type,
    aa_fun8320714231555830903er_rat: ( fun_fu3744699754670041014er_rat * fun_Code_integer_rat ) > fun_ra3321464020636160263er_rat ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Rat__Orat_J_001t__fun_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__Rat__Orat_J,type,
    aa_fun5443269377828775384er_rat: ( fun_fu8198789307943805079er_rat * fun_Code_integer_rat ) > fun_se2244710085602452072er_rat ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Rat__Orat_J_001t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Rat__Orat_J_Mt__fun_It__Code____Numeral__Ointeger_M_Eo_J_J,type,
    aa_fun4095556841599367307eger_o: ( fun_fu7141499545569947298eger_o * fun_Code_integer_rat ) > fun_fu4523568072766896123eger_o ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Rat__Orat_J_001t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Rat__Orat_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__Rat__Orat_J_J,type,
    aa_fun1894662059565830609er_rat: ( fun_fu8767785434844327952er_rat * fun_Code_integer_rat ) > fun_fu722387130092441185er_rat ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__Set__Oset_It__Code____Numeral__Ointeger_J_J_001t__fun_It__Code____Numeral__Ointeger_M_Eo_J,type,
    aa_fun7245632122240156009eger_o: ( fun_fu5766609707292941056eger_o * fun_Co744628173305925485nteger ) > fun_Code_integer_o ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_001t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_J,type,
    aa_fun1515160681128992300nteger: ( fun_fu7234567020521114219nteger * fun_Co1561183069634336733nteger ) > fun_fu2039158179202302481nteger ).

tff(sy_c_aa_001t__fun_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001_Eo,type,
    aa_fun1921403200066283853ural_o: ( fun_fu2916398056546941156ural_o * fun_Co7398788559141407565atural ) > $o ).

tff(sy_c_aa_001t__fun_It__Heap__Oarray_Itf__a_J_Mt__Heap____Time____Monad__OHeap_It__Heap__Oarray_Itf__a_J_J_J_001t__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    aa_fun8757595186270888873it_nat: ( fun_fu7484024174323986552it_nat * fun_ar3891948820113774757rray_a ) > fun_he1504492240061592256it_nat ).

tff(sy_c_aa_001t__fun_It__Heap__Oarray_Itf__a_J_Mt__Heap____Time____Monad__OHeap_It__Product____Type__Ounit_J_J_001t__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    aa_fun3741944862212262031it_nat: ( fun_fu5808343195260015654it_nat * fun_ar1074044450438384043t_unit ) > fun_he5234484606919320760it_nat ).

tff(sy_c_aa_001t__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    aa_fun3106883476453902712it_nat: ( fun_fu4233702620870981175it_nat * fun_he281446669002384250it_nat ) > fun_he1504492240061592256it_nat ).

tff(sy_c_aa_001t__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    aa_fun2986507860694160780it_nat: ( fun_fu2492676192234506515it_nat * fun_he4944555133437423336it_nat ) > fun_he5234484606919320760it_nat ).

tff(sy_c_aa_001t__fun_It__Int__Oint_M_Eo_J_001_Eo,type,
    aa_fun_int_o_o: ( fun_fun_int_o_o * fun_int_o ) > $o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_M_Eo_J_001t__fun_It__Int__Oint_M_Eo_J,type,
    aa_fun6243517787477317628_int_o: ( fun_fu3883539188510166275_int_o * fun_int_o ) > fun_int_o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_M_Eo_J_001t__fun_It__Int__Oint_Mt__Assertions__Oassn_J,type,
    aa_fun9028805181350005338t_assn: ( fun_fu2048648494261043369t_assn * fun_int_o ) > fun_int_assn ).

tff(sy_c_aa_001t__fun_It__Int__Oint_M_Eo_J_001t__fun_It__Int__Oint_Mt__Code____Numeral__Ointeger_J,type,
    aa_fun6019004165459918095nteger: ( fun_fu6361890901329191134nteger * fun_int_o ) > fun_int_Code_integer ).

tff(sy_c_aa_001t__fun_It__Int__Oint_M_Eo_J_001t__fun_It__fun_It__Int__Oint_M_Eo_J_M_Eo_J,type,
    aa_fun1331825017273370463nt_o_o: ( fun_fu6971708032831053102nt_o_o * fun_int_o ) > fun_fun_int_o_o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Assertions__Oassn_J_001t__fun_It__Assertions__Oassn_Mt__fun_It__Int__Oint_Mt__Assertions__Oassn_J_J,type,
    aa_fun3470678483766860421t_assn: ( fun_fu4482299812767249988t_assn * fun_int_assn ) > fun_as3432858861813084150t_assn ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Assertions__Oassn_J_001t__fun_It__Int__Oint_M_Eo_J,type,
    aa_fun202081646129719286_int_o: ( fun_fu2934462529731303693_int_o * fun_int_assn ) > fun_int_o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Assertions__Oassn_J_001t__fun_It__Int__Oint_Mt__Assertions__Oassn_J,type,
    aa_fun919007281442365664t_assn: ( fun_fu6568868615275847455t_assn * fun_int_assn ) > fun_int_assn ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Assertions__Oassn_J_001t__fun_It__Set__Oset_It__Int__Oint_J_Mt__Assertions__Oassn_J,type,
    aa_fun6757465843467192982t_assn: ( fun_fu6757290529232567765t_assn * fun_int_assn ) > fun_set_int_assn ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Assertions__Oassn_J_001t__fun_It__fun_It__Int__Oint_Mt__Assertions__Oassn_J_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    aa_fun871127997271750846_int_o: ( fun_fu607692679349591509_int_o * fun_int_assn ) > fun_fu2934462529731303693_int_o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Int__Oint_M_Eo_J,type,
    aa_fun3336537925265328129_int_o: ( fun_fu5271299750659287320_int_o * fun_int_Code_integer ) > fun_int_o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Int__Oint_Mt__Code____Numeral__Ointeger_J,type,
    aa_fun5304498221708291146nteger: ( fun_fu3628599891403802633nteger * fun_int_Code_integer ) > fun_int_Code_integer ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Set__Oset_It__Int__Oint_J_Mt__Code____Numeral__Ointeger_J,type,
    aa_fun5294558456829105664nteger: ( fun_fu7510501037550790335nteger * fun_int_Code_integer ) > fun_se4372286887653997756nteger ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_001t__fun_It__fun_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    aa_fun8818272713621706452_int_o: ( fun_fu63825462011493995_int_o * fun_int_Code_integer ) > fun_fu5271299750659287320_int_o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001_Eo,type,
    aa_fun_int_int_o: ( fun_fun_int_int_o * fun_int_int ) > $o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    aa_fun8964553180794676938nteger: ( fun_fu6921880696561781257nteger * fun_int_int ) > fun_Co8499238673658658103nteger ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Int__Oint_Mt__Int__Oint_J,type,
    aa_fun6280345759651049192nt_int: ( fun_fu1143798476471108391nt_int * fun_int_int ) > fun_int_int ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J,type,
    aa_fun5911324870756489105nt_int: ( fun_fu923337204662071120nt_int * fun_int_int ) > fun_int_fun_int_int ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Rat__Orat_J_J,type,
    aa_fun2021421678210538301nt_rat: ( fun_fu5158109473865063676nt_rat * fun_int_int ) > fun_int_fun_int_rat ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Nat__Onat_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_J_J,type,
    aa_fun3338573009006755021er_int: ( fun_fu1895414074638732388er_int * fun_int_int ) > fun_na937208397672391712er_int ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__Nat__Onat_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_J_J,type,
    aa_fun566144318431074624at_int: ( fun_fu4152238915952267095at_int * fun_int_int ) > fun_na7450791247808564371at_int ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J,type,
    aa_fun6864876441520360999eger_o: ( fun_fu726873822431485118eger_o * fun_int_int ) > fun_fu1769128043447206010eger_o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
    aa_fun2545150047610057353_int_o: ( fun_fu4208408993564413984_int_o * fun_int_int ) > fun_fun_int_int_o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Int__Oint_J_001t__fun_It__fun_It__Rat__Orat_Mt__Rat__Orat_J_M_Eo_J,type,
    aa_fun5612491703237866289_rat_o: ( fun_fu7417829167477406920_rat_o * fun_int_int ) > fun_fun_rat_rat_o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Nat__Onat_J_001_Eo,type,
    aa_fun_int_nat_o: ( fun_fun_int_nat_o * fun_int_nat ) > $o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Nat__Onat_J_001t__fun_It__Int__Oint_Mt__Nat__Onat_J,type,
    aa_fun6506752150744536624nt_nat: ( fun_fu8905809029841901679nt_nat * fun_int_nat ) > fun_int_nat ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Nat__Onat_J_001t__fun_It__Int__Oint_Mt__Num__Onum_J,type,
    aa_fun7214996087693374330nt_num: ( fun_fu4621028619281248441nt_num * fun_int_nat ) > fun_int_num ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Nat__Onat_J_001t__fun_It__fun_It__Int__Oint_Mt__Nat__Onat_J_M_Eo_J,type,
    aa_fun7045208173470077249_nat_o: ( fun_fu6391371659531026648_nat_o * fun_int_nat ) > fun_fun_int_nat_o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Nat__Onat_J_001t__fun_It__fun_It__Int__Oint_Mt__Nat__Onat_J_Mt__fun_It__Int__Oint_Mt__Nat__Onat_J_J,type,
    aa_fun5407591398502139302nt_nat: ( fun_fu973771059875708133nt_nat * fun_int_nat ) > fun_fu8905809029841901679nt_nat ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Num__Onum_J_001_Eo,type,
    aa_fun_int_num_o: ( fun_fun_int_num_o * fun_int_num ) > $o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Num__Onum_J_001t__fun_It__fun_It__Int__Oint_Mt__Num__Onum_J_M_Eo_J,type,
    aa_fun7722276931801436589_num_o: ( fun_fu6636849678353221188_num_o * fun_int_num ) > fun_fun_int_num_o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001_Eo,type,
    aa_fun3020711759848831579term_o: ( fun_fu3265955482920998386term_o * fun_in5730379987311621695e_term ) > $o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    aa_fun3970441718214872642nt_int: ( fun_fu5631754973857388633nt_int * fun_in5730379987311621695e_term ) > option4624381673175914239nt_int ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    aa_fun3520829229142255404nt_int: ( fun_fu4545303443005895275nt_int * fun_in5730379987311621695e_term ) > produc4788131091073775919nt_int ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    aa_fun2636263158522872028nt_int: ( fun_fu3472058528428720115nt_int * fun_in5730379987311621695e_term ) > set_Pr958786334691620121nt_int ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    aa_fun4587069911532227722nt_int: ( fun_fu786557078278636193nt_int * fun_in5730379987311621695e_term ) > set_Pr2560585780119916871nt_int ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    aa_fun5435896075006949730nt_int: ( fun_fu6029888860018473377nt_int * fun_in5730379987311621695e_term ) > set_Pr4166680992137330533nt_int ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    aa_fun5947755341433680828e_term: ( fun_fu4810317505167811835e_term * fun_in5730379987311621695e_term ) > fun_in5730379987311621695e_term ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
    aa_fun586359091965693151_int_o: ( fun_fu2978539155105838238_int_o * fun_in5730379987311621695e_term ) > fun_Pr3238374608701176162_int_o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    aa_fun260840925927807678nt_int: ( fun_fu465145433024125141nt_int * fun_in5730379987311621695e_term ) > fun_Pr8696298990344678139nt_int ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Set__Oset_I_Eo_J_J,type,
    aa_fun8934358842864497599_set_o: ( fun_fu4618385802829667198_set_o * fun_in5730379987311621695e_term ) > fun_Pr5150627949553849410_set_o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Set__Oset_It__Int__Oint_J_J,type,
    aa_fun5919120857301092337et_int: ( fun_fu4266222366127506568et_int * fun_in5730379987311621695e_term ) > fun_Pr1023655258412994094et_int ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    aa_fun8409204002232819093et_nat: ( fun_fu9079770784915425324et_nat * fun_in5730379987311621695e_term ) > fun_Pr3513738403344720850et_nat ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    aa_fun712031703178175272at_nat: ( fun_fu6029601804184707687at_nat * fun_in5730379987311621695e_term ) > fun_Pr5398690294390750379at_nat ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    aa_fun1932935823081541608e_term: ( fun_fu1176768540439120679e_term * fun_in5730379987311621695e_term ) > fun_Pr7763680713840462443e_term ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001_Eo,type,
    aa_fun6795050498662842124eger_o: ( fun_fu7325869825756301971eger_o * fun_in4744367027289715400nteger ) > $o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J_001_Eo,type,
    aa_fun3094526197865446643ural_o: ( fun_fu660488089777143946ural_o * fun_in4857920871562217639atural ) > $o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_Eo,type,
    aa_fun8476666123149806190_int_o: ( fun_fu8565479202776651253_int_o * fun_in4211310926729683942nt_int ) > $o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    aa_fun6626262031093723324nt_int: ( fun_fu3661779633992098115nt_int * fun_in4211310926729683942nt_int ) > fun_in4211310926729683942nt_int ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Int__Oint_Mt__Rat__Orat_J,type,
    aa_fun1809696235935464875nt_rat: ( fun_fu7460908759652350970nt_rat * fun_in4211310926729683942nt_int ) > fun_int_rat ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J,type,
    aa_fun1009039980557175711_int_o: ( fun_fu6699046866436802030_int_o * fun_in4211310926729683942nt_int ) > fun_fu8565479202776651253_int_o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__fun_It__Int__Oint_Mt__Rat__Orat_J_M_Eo_J,type,
    aa_fun5827461210593834758_rat_o: ( fun_fu7677565902479959693_rat_o * fun_in4211310926729683942nt_int ) > fun_fun_int_rat_o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_J_001_Eo,type,
    aa_fun5734334393156979392at_o_o: ( fun_fu6749285349733798471at_o_o * fun_in7664021439913478804_nat_o ) > $o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Rat__Orat_J_001_Eo,type,
    aa_fun_int_rat_o: ( fun_fun_int_rat_o * fun_int_rat ) > $o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Rat__Orat_J_001t__fun_It__Int__Oint_M_Eo_J,type,
    aa_fun7094158214180239686_int_o: ( fun_fu3473604023002724957_int_o * fun_int_rat ) > fun_int_o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Rat__Orat_J_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    aa_fun1163745293653399015nt_int: ( fun_fu4522195968571808382nt_int * fun_int_rat ) > fun_in4211310926729683942nt_int ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Rat__Orat_J_001t__fun_It__Int__Oint_Mt__Rat__Orat_J,type,
    aa_fun1481061427733998144nt_rat: ( fun_fu1008360527747082367nt_rat * fun_int_rat ) > fun_int_rat ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Rat__Orat_J_001t__fun_It__Rat__Orat_Mt__fun_It__Int__Oint_Mt__Rat__Orat_J_J,type,
    aa_fun9155288305517341845nt_rat: ( fun_fu114989186063767636nt_rat * fun_int_rat ) > fun_rat_fun_int_rat ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Rat__Orat_J_001t__fun_It__Set__Oset_It__Int__Oint_J_Mt__Rat__Orat_J,type,
    aa_fun991771802548846582nt_rat: ( fun_fu3579422585476231989nt_rat * fun_int_rat ) > fun_set_int_rat ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Rat__Orat_J_001t__fun_It__fun_It__Int__Oint_Mt__Rat__Orat_J_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    aa_fun1445893531507182942_int_o: ( fun_fu7714913403879666293_int_o * fun_int_rat ) > fun_fu3473604023002724957_int_o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Rat__Orat_J_001t__fun_It__fun_It__Int__Oint_Mt__Rat__Orat_J_Mt__fun_It__Int__Oint_Mt__Rat__Orat_J_J,type,
    aa_fun2191249852558612414nt_rat: ( fun_fu1617438229336688381nt_rat * fun_int_rat ) > fun_fu1008360527747082367nt_rat ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Set__Oset_I_Eo_J_J_001t__fun_It__Int__Oint_M_Eo_J,type,
    aa_fun4291261932532047132_int_o: ( fun_fu7671276271812522531_int_o * fun_int_set_o ) > fun_int_o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Set__Oset_It__Int__Oint_J_J_001t__fun_It__Int__Oint_M_Eo_J,type,
    aa_fun3842353566930741692_int_o: ( fun_fu5777115392324700883_int_o * fun_int_set_int ) > fun_int_o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__Set__Oset_It__Nat__Onat_J_J_001t__fun_It__Int__Oint_M_Eo_J,type,
    aa_fun1965424933913381656_int_o: ( fun_fu3900186759307340847_int_o * fun_int_set_nat ) > fun_int_o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_001_Eo,type,
    aa_fun227585529652676578nt_o_o: ( fun_fu5353592940419373929nt_o_o * fun_int_fun_int_o ) > $o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    aa_fun6133342665515662012_int_o: ( fun_fu138107234227827011_int_o * fun_int_fun_int_o ) > fun_int_fun_int_o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_001t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_M_Eo_J,type,
    aa_fun1090463484742261919nt_o_o: ( fun_fu3604077110225719534nt_o_o * fun_int_fun_int_o ) > fun_fu5353592940419373929nt_o_o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_001_Eo,type,
    aa_fun3498034192445020252_int_o: ( fun_fu7363466011001354227_int_o * fun_int_fun_int_int ) > $o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J,type,
    aa_fun6119123525526402106nt_int: ( fun_fu6092417073193843705nt_int * fun_int_fun_int_int ) > fun_int_fun_int_int ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    aa_fun1034830265760468567nt_int: ( fun_fu918106826131887214nt_int * fun_int_fun_int_int ) > fun_in1696471567231710611nt_int ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Int__Oint_J,type,
    aa_fun914008879417524284nt_int: ( fun_fu5207212825597307859nt_int * fun_int_fun_int_int ) > fun_Pr982841511892225912nt_int ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    aa_fun5609932731973438348nt_int: ( fun_fu3518228427392506443nt_int * fun_int_fun_int_int ) > fun_fu923337204662071120nt_int ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J,type,
    aa_fun3119206668089765047_int_o: ( fun_fu6471771360118961870_int_o * fun_int_fun_int_int ) > fun_fu7363466011001354227_int_o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J,type,
    aa_fun7461304428735181397nt_int: ( fun_fu717549361983437348nt_int * fun_in1696471567231710611nt_int ) > fun_int_fun_int_int ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    aa_fun4152872853588681340nt_int: ( fun_fu3898734532474705027nt_int * fun_in1696471567231710611nt_int ) > fun_in1696471567231710611nt_int ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    aa_fun8026974734089330650nt_int: ( fun_fu6741006549690681129nt_int * fun_in1696471567231710611nt_int ) > fun_Pr2478283820680522243nt_int ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_001t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Rat__Orat_J_J_M_Eo_J,type,
    aa_fun3867120139247291696_rat_o: ( fun_fu1057420046263839031_rat_o * fun_in1696471567231710611nt_int ) > fun_fu8658704570366206279_rat_o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Rat__Orat_J_J_001_Eo,type,
    aa_fun4793272751809872304_rat_o: ( fun_fu8658704570366206279_rat_o * fun_int_fun_int_rat ) > $o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Rat__Orat_J_J_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_Mt__Rat__Orat_J_J_J,type,
    aa_fun3093514174373113060nt_rat: ( fun_fu4582018930532246947nt_rat * fun_int_fun_int_rat ) > fun_fu5158109473865063676nt_rat ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_001_Eo,type,
    aa_fun8451603854606397830at_o_o: ( fun_fu4354239228518319373at_o_o * fun_int_fun_nat_o ) > $o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    aa_fun16395659681819580_nat_o: ( fun_fu927436805355353155_nat_o * fun_int_fun_nat_o ) > fun_int_fun_nat_o ).

tff(sy_c_aa_001t__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_M_Eo_J,type,
    aa_fun527236716413744031at_o_o: ( fun_fu1853282479105234414at_o_o * fun_int_fun_nat_o ) > fun_fu4354239228518319373at_o_o ).

tff(sy_c_aa_001t__fun_It__List__Olist_It__Nat__Onat_J_M_Eo_J_001t__fun_It__List__Olist_It__Nat__Onat_J_Mt__fun_It__List__Olist_It__Nat__Onat_J_M_Eo_J_J,type,
    aa_fun3567724338799755637_nat_o: ( fun_fu9062970525541950460_nat_o * fun_list_nat_o ) > fun_li1025265955262268170_nat_o ).

tff(sy_c_aa_001t__fun_It__List__Olist_It__Nat__Onat_J_M_Eo_J_001t__fun_It__Nat__Onat_Mt__fun_It__List__Olist_It__Nat__Onat_J_M_Eo_J_J,type,
    aa_fun6290253675283700613_nat_o: ( fun_fu2721382957917623308_nat_o * fun_list_nat_o ) > fun_na7234455742697417626_nat_o ).

tff(sy_c_aa_001t__fun_It__List__Olist_It__Nat__Onat_J_Mt__fun_It__List__Olist_It__Nat__Onat_J_M_Eo_J_J_001t__fun_It__List__Olist_It__Nat__Onat_J_Mt__fun_It__List__Olist_It__Nat__Onat_J_M_Eo_J_J,type,
    aa_fun6462763351938039228_nat_o: ( fun_fu4946532526548972611_nat_o * fun_li1025265955262268170_nat_o ) > fun_li1025265955262268170_nat_o ).

tff(sy_c_aa_001t__fun_It__List__Olist_It__Nat__Onat_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__List__Olist_It__Nat__Onat_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    aa_fun6275404141584987452_nat_o: ( fun_fu4568065243339218371_nat_o * fun_li2421049240157457050_nat_o ) > fun_li2421049240157457050_nat_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_M_Eo_J_001_Eo,type,
    aa_fun_nat_o_o: ( fun_fun_nat_o_o * fun_nat_o ) > $o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_M_Eo_J_001t__Product____Type__Oprod_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    aa_fun2081456873842488898_nat_o: ( fun_fu5650529485467354185_nat_o * fun_nat_o ) > produc7704145150520151143_nat_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__List__Olist_It__Nat__Onat_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    aa_fun823229757805912181_nat_o: ( fun_fu2312272580554962172_nat_o * fun_nat_o ) > fun_li2421049240157457050_nat_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Nat__Onat_M_Eo_J,type,
    aa_fun5937193402907943164_nat_o: ( fun_fu4001317426178549763_nat_o * fun_nat_o ) > fun_nat_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Nat__Onat_Mt__Assertions__Oassn_J,type,
    aa_fun3990007403578212698t_assn: ( fun_fu2792963925203051945t_assn * fun_nat_o ) > fun_nat_assn ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J,type,
    aa_fun3969837373441324047nteger: ( fun_fu7898940055406642654nteger * fun_nat_o ) > fun_nat_Code_integer ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Nat__Onat_Mt__Rat__Orat_J,type,
    aa_fun696632391729880074at_rat: ( fun_fu3162257917499486297at_rat * fun_nat_o ) > fun_nat_rat ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    aa_fun5001253801653566085_nat_o: ( fun_fu2106003848923686156_nat_o * fun_nat_o ) > fun_nat_fun_nat_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_M_Eo_J_001t__fun_It__fun_It__Nat__Onat_M_Eo_J_M_Eo_J,type,
    aa_fun4840518763754620511at_o_o: ( fun_fu7564235448449272366at_o_o * fun_nat_o ) > fun_fun_nat_o_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_001t__fun_It__Assertions__Oassn_Mt__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_J,type,
    aa_fun2404858873066863565t_assn: ( fun_fu1995072252941043084t_assn * fun_nat_assn ) > fun_as8240436605320707994t_assn ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_001t__fun_It__Nat__Onat_M_Eo_J,type,
    aa_fun7183233715851567790_nat_o: ( fun_fu1116345184836134341_nat_o * fun_nat_assn ) > fun_nat_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_001t__fun_It__Nat__Onat_Mt__Assertions__Oassn_J,type,
    aa_fun785744391571715112t_assn: ( fun_fu2995346897264222311t_assn * fun_nat_assn ) > fun_nat_assn ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_001t__fun_It__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    aa_fun8595640264602358482_nat_o: ( fun_fu3109912920687205353_nat_o * fun_nat_assn ) > fun_fu1116345184836134341_nat_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_001t__fun_It__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_Mt__fun_It__Nat__Onat_Mt__Assertions__Oassn_J_J,type,
    aa_fun6591345337174305434t_assn: ( fun_fu3959123160307459545t_assn * fun_nat_assn ) > fun_fu2995346897264222311t_assn ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001_Eo,type,
    aa_fun4755383761576212144eger_o: ( fun_fu2893655071357150791eger_o * fun_nat_Code_integer ) > $o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Int__Oint_Mt__Code____Numeral__Ointeger_J,type,
    aa_fun960730347150118382nteger: ( fun_fu8508204053700405677nteger * fun_nat_Code_integer ) > fun_int_Code_integer ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Nat__Onat_M_Eo_J,type,
    aa_fun3480067038916266681_nat_o: ( fun_fu5838931486547983824_nat_o * fun_nat_Code_integer ) > fun_nat_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J,type,
    aa_fun589076786913273746nteger: ( fun_fu2499394402704830801nteger * fun_nat_Code_integer ) > fun_nat_Code_integer ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    aa_fun7952091224041096005nteger: ( fun_fu6201336427292363868nteger * fun_nat_Code_integer ) > fun_na5644505769342238765nteger ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Code____Numeral__Ointeger_J_J_J,type,
    aa_fun947730671064037908nteger: ( fun_fu1188671613149117355nteger * fun_nat_Code_integer ) > fun_na5353050896416397052nteger ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_J_J,type,
    aa_fun8323025376520073144nteger: ( fun_fu8284676920001830735nteger * fun_nat_Code_integer ) > fun_na3504973565017656480nteger ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001t__fun_It__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_M_Eo_J,type,
    aa_fun1781415190607348063eger_o: ( fun_fu6536794386266229110eger_o * fun_nat_Code_integer ) > fun_fu2893655071357150791eger_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001t__fun_It__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    aa_fun2745573882733218024_nat_o: ( fun_fu8532066432991188095_nat_o * fun_nat_Code_integer ) > fun_fu5838931486547983824_nat_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001t__fun_It__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_Mt__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_J,type,
    aa_fun3918145391673965625nteger: ( fun_fu6327154928193479288nteger * fun_nat_Code_integer ) > fun_fu2499394402704830801nteger ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Int__Oint_J_001t__fun_It__Nat__Onat_Mt__Int__Oint_J,type,
    aa_fun5565043122120104496at_int: ( fun_fu8464300013002972271at_int * fun_nat_int ) > fun_nat_int ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Int__Oint_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Int__Oint_J_J_J,type,
    aa_fun8714824397388734853er_int: ( fun_fu1491972344133157660er_int * fun_nat_int ) > fun_na7153028460132482940er_int ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Int__Oint_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_J_J,type,
    aa_fun2313822316067610104at_int: ( fun_fu3125320701163054607at_int * fun_nat_int ) > fun_na8547874228452562927at_int ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Int__Oint_J_001t__fun_It__fun_It__Nat__Onat_Mt__Int__Oint_J_Mt__fun_It__Nat__Onat_Mt__Int__Oint_J_J,type,
    aa_fun5140708168904641446at_int: ( fun_fu960360787657196261at_int * fun_nat_int ) > fun_fu8464300013002972271at_int ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__fun_It__Nat__Onat_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    aa_fun4141531684813184444at_nat: ( fun_fu7433494735876822851at_nat * fun_na2338080690716861136at_nat ) > fun_na2338080690716861136at_nat ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__fun_It__fun_It__Nat__Onat_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__fun_It__Nat__Onat_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    aa_fun8230936523094545239at_nat: ( fun_fu695563712076452518at_nat * fun_na2338080690716861136at_nat ) > fun_fu7433494735876822851at_nat ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo,type,
    aa_fun_nat_nat_o: ( fun_fun_nat_nat_o * fun_nat_nat ) > $o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    aa_fun5114738747585492520atural: ( fun_fu6924846375782198887atural * fun_nat_nat ) > fun_Co7398788559141407565atural ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Int__Oint_Mt__Num__Onum_J,type,
    aa_fun7499047162063484190nt_num: ( fun_fu4905079693651358301nt_num * fun_nat_nat ) > fun_int_num ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Nat__Onat_M_Eo_J,type,
    aa_fun8673969331427483654_nat_o: ( fun_fu5477517762487726877_nat_o * fun_nat_nat ) > fun_nat_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J,type,
    aa_fun5791449513213591928at_nat: ( fun_fu7002938529518989751at_nat * fun_nat_nat ) > fun_nat_nat ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_J_J,type,
    aa_fun7093963954598080645er_nat: ( fun_fu1723132215250845724er_nat * fun_nat_nat ) > fun_na2743204842065625888er_nat ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J_J_J,type,
    aa_fun7567701811046127444nt_nat: ( fun_fu2668056085831081835nt_nat * fun_nat_nat ) > fun_na7356754204550075887nt_nat ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    aa_fun4348998216881757432at_nat: ( fun_fu7012516915885544207at_nat * fun_nat_nat ) > fun_na4138050610385705875at_nat ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__fun_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_M_Eo_J,type,
    aa_fun7534057414028546889ural_o: ( fun_fu2034268335391280352ural_o * fun_nat_nat ) > fun_fu2916398056546941156ural_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__fun_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
    aa_fun2341495900663639033_nat_o: ( fun_fu9201817095025044880_nat_o * fun_nat_nat ) > fun_fun_nat_nat_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__fun_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    aa_fun6348600740168882050_nat_o: ( fun_fu6075382464776002713_nat_o * fun_nat_nat ) > fun_fu5477517762487726877_nat_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J_001t__fun_It__fun_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    aa_fun6854695580826382482at_nat: ( fun_fu5935951186182374353at_nat * fun_nat_nat ) > fun_fu7002938529518989751at_nat ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Num__Onum_J_001_Eo,type,
    aa_fun_nat_num_o: ( fun_fun_nat_num_o * fun_nat_num ) > $o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Num__Onum_J_001t__fun_It__fun_It__Int__Oint_Mt__Nat__Onat_J_Mt__fun_It__Int__Oint_Mt__Num__Onum_J_J,type,
    aa_fun6849364718390456542nt_num: ( fun_fu3670889464739865373nt_num * fun_nat_num ) > fun_fu4621028619281248441nt_num ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Num__Onum_J_001t__fun_It__fun_It__Nat__Onat_Mt__Num__Onum_J_M_Eo_J,type,
    aa_fun3018564658994998373_num_o: ( fun_fu223923076992463612_num_o * fun_nat_num ) > fun_fun_nat_num_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001_Eo,type,
    aa_fun4972185446673663664eger_o: ( fun_fu5503004773767123511eger_o * fun_na3822476419092417572nteger ) > $o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J_001_Eo,type,
    aa_fun2422601084904007759ural_o: ( fun_fu9211935013670480870ural_o * fun_na2094359461478415435atural ) > $o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_Eo,type,
    aa_fun6509235634262356498_int_o: ( fun_fu6598048713889201561_int_o * fun_na1173468842265550146nt_int ) > $o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Rat__Orat_J_001t__fun_It__Nat__Onat_M_Eo_J,type,
    aa_fun1118977351124560894_nat_o: ( fun_fu7145897819039579925_nat_o * fun_nat_rat ) > fun_nat_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Rat__Orat_J_001t__fun_It__Nat__Onat_Mt__Rat__Orat_J,type,
    aa_fun765758790203053448at_rat: ( fun_fu8328862064278946247at_rat * fun_nat_rat ) > fun_nat_rat ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Rat__Orat_J_001t__fun_It__Rat__Orat_Mt__fun_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
    aa_fun5559679822142647773at_rat: ( fun_fu4710970720072501148at_rat * fun_nat_rat ) > fun_rat_fun_nat_rat ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Rat__Orat_J_001t__fun_It__fun_It__Nat__Onat_Mt__Rat__Orat_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    aa_fun8314661095172591474_nat_o: ( fun_fu1806770557662746761_nat_o * fun_nat_rat ) > fun_fu7145897819039579925_nat_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Rat__Orat_J_001t__fun_It__fun_It__Nat__Onat_Mt__Rat__Orat_J_Mt__fun_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
    aa_fun3638354034882855594at_rat: ( fun_fu6579618355643354601at_rat * fun_nat_rat ) > fun_fu8328862064278946247at_rat ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Set__Oset_I_Eo_J_J_001t__fun_It__Nat__Onat_M_Eo_J,type,
    aa_fun4904187145036355100_nat_o: ( fun_fu8708304106554588451_nat_o * fun_nat_set_o ) > fun_nat_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Set__Oset_It__Int__Oint_J_J_001t__fun_It__Nat__Onat_M_Eo_J,type,
    aa_fun3985882680581680244_nat_o: ( fun_fu6344747128213397387_nat_o * fun_nat_set_int ) > fun_nat_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Set__Oset_It__Nat__Onat_J_J_001t__fun_It__Nat__Onat_M_Eo_J,type,
    aa_fun2108954047564320208_nat_o: ( fun_fu4467818495196037351_nat_o * fun_nat_set_nat ) > fun_nat_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Set__Oset_It__Nat__Onat_J_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    aa_fun2373699841287868962at_nat: ( fun_fu7530206860547196985at_nat * fun_nat_set_nat ) > fun_na1790740735814032627at_nat ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J_J_J,type,
    aa_fun5017297687458839182_nat_o: ( fun_fu2677729659939697685_nat_o * fun_na7044673412300895210at_nat ) > fun_na927404270896789692_nat_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J_J,type,
    aa_fun1888629816020924642_nat_o: ( fun_fu1617828088232643505_nat_o * fun_na7044673412300895210at_nat ) > fun_na5914473681949881652_nat_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__fun_It__List__Olist_It__Nat__Onat_J_M_Eo_J_J_001t__fun_It__Nat__Onat_Mt__fun_It__List__Olist_It__Nat__Onat_J_M_Eo_J_J,type,
    aa_fun6745918892298368316_nat_o: ( fun_fu6714502955005156803_nat_o * fun_na7234455742697417626_nat_o ) > fun_na7234455742697417626_nat_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    aa_fun6699960423209655484_nat_o: ( fun_fu6436183194761443139_nat_o * fun_nat_fun_nat_o ) > fun_nat_fun_nat_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
    aa_fun7564604662015400456_nat_o: ( fun_fu6778223257468740055_nat_o * fun_nat_fun_nat_o ) > fun_Pr4796943543331071514_nat_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    aa_fun7716529229553496594at_nat: ( fun_fu1217771548038759377at_nat * fun_nat_fun_nat_nat ) > fun_nat_fun_nat_nat ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J_J,type,
    aa_fun2100511394839469148_nat_o: ( fun_fu484727072080742171_nat_o * fun_nat_fun_nat_nat ) > fun_na5914473681949881652_nat_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    aa_fun2484538639213223237at_nat: ( fun_fu1039311746440044420at_nat * fun_nat_fun_nat_nat ) > fun_na1668100129766719005at_nat ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J,type,
    aa_fun500577536901462844at_nat: ( fun_fu5660447535128473811at_nat * fun_nat_fun_nat_nat ) > fun_Pr2602117396471556196at_nat ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    aa_fun3680403850923830236at_nat: ( fun_fu4228150600790569371at_nat * fun_na5914473681949881652_nat_o ) > fun_nat_fun_nat_nat ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J_J,type,
    aa_fun824319262034445606_nat_o: ( fun_fu6384561554008368101_nat_o * fun_na5914473681949881652_nat_o ) > fun_na5914473681949881652_nat_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J,type,
    aa_fun5912894404062470332_nat_o: ( fun_fu2847332191311216467_nat_o * fun_na5914473681949881652_nat_o ) > fun_Pr2028404973800837934_nat_o ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    aa_fun8817627472026143685at_nat: ( fun_fu7448223259553364356at_nat * fun_na1668100129766719005at_nat ) > fun_nat_fun_nat_nat ).

tff(sy_c_aa_001t__fun_It__Nat__Onat_Mt__fun_It__Nat__Onat_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    aa_fun6875833325056119164at_nat: ( fun_fu2716251949043459987at_nat * fun_na1668100129766719005at_nat ) > fun_Pr2477239776880934807at_nat ).

tff(sy_c_aa_001t__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001_Eo,type,
    aa_fun5823441391821850086eger_o: ( fun_fu3961712701602788733eger_o * fun_num_Code_integer ) > $o ).

tff(sy_c_aa_001t__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J,type,
    aa_fun8039327588056924198nteger: ( fun_fu552866168194876645nteger * fun_num_Code_integer ) > fun_num_Code_integer ).

tff(sy_c_aa_001t__fun_It__Num__Onum_Mt__Int__Oint_J_001_Eo,type,
    aa_fun_num_int_o: ( fun_fun_num_int_o * fun_num_int ) > $o ).

tff(sy_c_aa_001t__fun_It__Num__Onum_Mt__Int__Oint_J_001t__fun_It__Int__Oint_Mt__Num__Onum_J,type,
    aa_fun8084892656986344388nt_num: ( fun_fu5490925188574218499nt_num * fun_num_int ) > fun_int_num ).

tff(sy_c_aa_001t__fun_It__Num__Onum_Mt__Int__Oint_J_001t__fun_It__Nat__Onat_Mt__Nat__Onat_J,type,
    aa_fun6377295008136452126at_nat: ( fun_fu7588784024441849949at_nat * fun_num_int ) > fun_nat_nat ).

tff(sy_c_aa_001t__fun_It__Num__Onum_Mt__Int__Oint_J_001t__fun_It__Num__Onum_Mt__Int__Oint_J,type,
    aa_fun329774391934724804um_int: ( fun_fu7117095973476296707um_int * fun_num_int ) > fun_num_int ).

tff(sy_c_aa_001t__fun_It__Num__Onum_Mt__Int__Oint_J_001t__fun_It__Num__Onum_Mt__Num__Onum_J,type,
    aa_fun5215869348392759218um_num: ( fun_fu5322398707847370225um_num * fun_num_int ) > fun_num_num ).

tff(sy_c_aa_001t__fun_It__Num__Onum_Mt__Int__Oint_J_001t__fun_It__Num__Onum_Mt__Option__Ooption_It__Num__Onum_J_J,type,
    aa_fun3858197967482829954on_num: ( fun_fu7964671872712412353on_num * fun_num_int ) > fun_num_option_num ).

tff(sy_c_aa_001t__fun_It__Num__Onum_Mt__Int__Oint_J_001t__fun_It__fun_It__Num__Onum_Mt__Code____Numeral__Ointeger_J_M_Eo_J,type,
    aa_fun7362828224538899388eger_o: ( fun_fu6196024946523381971eger_o * fun_num_int ) > fun_fu3961712701602788733eger_o ).

tff(sy_c_aa_001t__fun_It__Num__Onum_Mt__Int__Oint_J_001t__fun_It__fun_It__Num__Onum_Mt__Int__Oint_J_M_Eo_J,type,
    aa_fun5980320688621196205_int_o: ( fun_fu5908277796454533188_int_o * fun_num_int ) > fun_fun_num_int_o ).

tff(sy_c_aa_001t__fun_It__Num__Onum_Mt__Num__Onum_J_001t__fun_It__Int__Oint_Mt__Code____Numeral__Ointeger_J,type,
    aa_fun3714269538864306549nteger: ( fun_fu8261421317008872756nteger * fun_num_num ) > fun_int_Code_integer ).

tff(sy_c_aa_001t__fun_It__Num__Onum_Mt__Num__Onum_J_001t__fun_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J,type,
    aa_fun3342615978627461913nteger: ( fun_fu2252611666013297880nteger * fun_num_num ) > fun_nat_Code_integer ).

tff(sy_c_aa_001t__fun_It__Num__Onum_Mt__Num__Onum_J_001t__fun_It__Num__Onum_Mt__Int__Oint_J,type,
    aa_fun3162900327506486194um_int: ( fun_fu726849872193282289um_int * fun_num_num ) > fun_num_int ).

tff(sy_c_aa_001t__fun_It__Num__Onum_Mt__Num__Onum_J_001t__fun_It__Num__Onum_Mt__Num__Onum_J,type,
    aa_fun8048995283964520608um_num: ( fun_fu8155524643419131615um_num * fun_num_num ) > fun_num_num ).

tff(sy_c_aa_001t__fun_It__Num__Onum_Mt__Num__Onum_J_001t__fun_It__Num__Onum_Mt__Option__Ooption_It__Num__Onum_J_J,type,
    aa_fun612943910911948912on_num: ( fun_fu4719417816141531311on_num * fun_num_num ) > fun_num_option_num ).

tff(sy_c_aa_001t__fun_It__Num__Onum_Mt__Option__Ooption_It__Num__Onum_J_J_001t__fun_It__Num__Onum_Mt__Int__Oint_J,type,
    aa_fun2256179333612926594um_int: ( fun_fu1947565687807238081um_int * fun_num_option_num ) > fun_num_int ).

tff(sy_c_aa_001t__fun_It__Num__Onum_Mt__Option__Ooption_It__Num__Onum_J_J_001t__fun_It__Num__Onum_Mt__Num__Onum_J,type,
    aa_fun7142274290070961008um_num: ( fun_fu152868422178311599um_num * fun_num_option_num ) > fun_num_num ).

tff(sy_c_aa_001t__fun_It__Num__Onum_Mt__Option__Ooption_It__Num__Onum_J_J_001t__fun_It__Num__Onum_Mt__Option__Ooption_It__Num__Onum_J_J,type,
    aa_fun3636977833914307392on_num: ( fun_fu2987389051837124479on_num * fun_num_option_num ) > fun_num_option_num ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001_Eo,type,
    aa_fun7993445754732355552term_o: ( fun_fu4736795817735658359term_o * fun_Pr5098669352780829690e_term ) > $o ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    aa_fun1271726682903785001nteger: ( fun_fu4810197545401214784nteger * fun_Pr5098669352780829690e_term ) > option2651255830984564193nteger ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    aa_fun8425650785172306510nteger: ( fun_fu8902681562042749453nteger * fun_Pr5098669352780829690e_term ) > produc2453742332425399446nteger ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    aa_fun6394921419180517443nteger: ( fun_fu5971215405379524186nteger * fun_Pr5098669352780829690e_term ) > set_Pr4811707699266497531nteger ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    aa_fun435912938702255631nteger: ( fun_fu8543582513329703974nteger * fun_Pr5098669352780829690e_term ) > set_Pr5052581263052047815nteger ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    aa_fun207332883101880580nteger: ( fun_fu4173945377279696323nteger * fun_Pr5098669352780829690e_term ) > set_Pr3486312109254157132nteger ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J,type,
    aa_fun4505422719058378424eger_o: ( fun_fu7695273699059480439eger_o * fun_Pr5098669352780829690e_term ) > fun_Pr7211993375558241536eger_o ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    aa_fun8303988899834042124nteger: ( fun_fu8946524575271555235nteger * fun_Pr5098669352780829690e_term ) > fun_Pr2985126522952997572nteger ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Set__Oset_I_Eo_J_J,type,
    aa_fun6611983550656184728_set_o: ( fun_fu6788480576040630871_set_o * fun_Pr5098669352780829690e_term ) > fun_Pr1817902730575146976_set_o ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Set__Oset_It__Int__Oint_J_J,type,
    aa_fun1598286855320232536et_int: ( fun_fu6941240126142778863et_int * fun_Pr5098669352780829690e_term ) > fun_Pr3914994171019630096et_int ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    aa_fun4088370000251959292et_nat: ( fun_fu2531416508075921811et_nat * fun_Pr5098669352780829690e_term ) > fun_Pr6405077315951356852et_nat ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    aa_fun1248587000295462322e_term: ( fun_fu2505754153367914865e_term * fun_Pr5098669352780829690e_term ) > fun_Pr5098669352780829690e_term ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001_Eo,type,
    aa_fun1675921005893230629at_o_o: ( fun_fu5135969500543783852at_o_o * fun_Pr6460944699146269935_nat_o ) > $o ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    aa_fun5824947343344787589et_nat: ( fun_fu2352890940381120596et_nat * fun_Pr6460944699146269935_nat_o ) > option936205604648967762et_nat ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Option__Ooption_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    aa_fun1716447855799474851et_nat: ( fun_fu1905361174868762994et_nat * fun_Pr6460944699146269935_nat_o ) > option4955102875562834416et_nat ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    aa_fun179180238660531795et_nat: ( fun_fu8710561278413400866et_nat * fun_Pr6460944699146269935_nat_o ) > produc8799533983703829792et_nat ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    aa_fun8682008811809929585et_nat: ( fun_fu6196531292930346304et_nat * fun_Pr6460944699146269935_nat_o ) > produc3112576180687729086et_nat ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Set__Oset_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    aa_fun786139119071955819et_nat: ( fun_fu2890809920214373946et_nat * fun_Pr6460944699146269935_nat_o ) > set_Pr3948176798113811640et_nat ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    aa_fun8297425419345108306et_nat: ( fun_fu5004560472337415769et_nat * fun_Pr6460944699146269935_nat_o ) > set_Pr719794911490849221et_nat ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    aa_fun313470179692725518et_nat: ( fun_fu951349246861503509et_nat * fun_Pr6460944699146269935_nat_o ) > set_Pr9066344408807579265et_nat ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    aa_fun4924015400185905801et_nat: ( fun_fu8357309440898100312et_nat * fun_Pr6460944699146269935_nat_o ) > set_Pr1312406793078187350et_nat ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    aa_fun6480417777262397735et_nat: ( fun_fu5650763273978745334et_nat * fun_Pr6460944699146269935_nat_o ) > set_Pr4040394263813967220et_nat ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
    aa_fun2638059832795814268_nat_o: ( fun_fu8419763957888848259_nat_o * fun_Pr6460944699146269935_nat_o ) > fun_Pr6460944699146269935_nat_o ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    aa_fun3926903090414666066et_nat: ( fun_fu2265384587115734689et_nat * fun_Pr6460944699146269935_nat_o ) > fun_Pr4885567672785483807et_nat ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__Set__Oset_I_Eo_J_J,type,
    aa_fun1634346356166085724_set_o: ( fun_fu4934440599869564003_set_o * fun_Pr6460944699146269935_nat_o ) > fun_Pr5633121574208248783_set_o ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__Set__Oset_It__Int__Oint_J_J,type,
    aa_fun3987806617159061652et_int: ( fun_fu4495862163342753507et_int * fun_Pr6460944699146269935_nat_o ) > fun_Pr847751653925389281et_int ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    aa_fun6477889762090788408et_nat: ( fun_fu86038545275896455et_nat * fun_Pr6460944699146269935_nat_o ) > fun_Pr3337834798857116037et_nat ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J,type,
    aa_fun912680268133416158_nat_o: ( fun_fu2611741329380808165_nat_o * fun_Pr6460944699146269935_nat_o ) > fun_Pr2620521676128474833_nat_o ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    aa_fun615918787490101902et_nat: ( fun_fu3932451362284101085et_nat * fun_Pr6460944699146269935_nat_o ) > fun_Pr3978243888342905947et_nat ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_Eo,type,
    aa_fun2650603632653508759_int_o: ( fun_fu7503566767892366382_int_o * fun_Pr2478283820680522243nt_int ) > $o ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__Rat__Orat_Mt__Rat__Orat_J,type,
    aa_fun7041730090766645614at_rat: ( fun_fu1098312133097393581at_rat * fun_Pr2478283820680522243nt_int ) > fun_rat_rat ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J,type,
    aa_fun3734617511155415725_int_o: ( fun_fu5323616038969315652_int_o * fun_Pr2478283820680522243nt_int ) > fun_fu7503566767892366382_int_o ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__fun_It__Rat__Orat_Mt__Rat__Orat_J_M_Eo_J,type,
    aa_fun382765352565706371_rat_o: ( fun_fu4306744791715064858_rat_o * fun_Pr2478283820680522243nt_int ) > fun_fun_rat_rat_o ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001_Eo,type,
    aa_fun7650857933016935215term_o: ( fun_fu6378075912484669126term_o * fun_Pr7763680713840462443e_term ) > $o ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    aa_fun251074914522852630nt_int: ( fun_fu4253467608928286509nt_int * fun_Pr7763680713840462443e_term ) > option4624381673175914239nt_int ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    aa_fun9040010020517048364nt_int: ( fun_fu5813366174458671467nt_int * fun_Pr7763680713840462443e_term ) > produc3043004577601930755nt_int ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    aa_fun2513960992105274800nt_int: ( fun_fu4219362280553733319nt_int * fun_Pr7763680713840462443e_term ) > set_Pr958786334691620121nt_int ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    aa_fun5011775822604196702nt_int: ( fun_fu4812223801888690549nt_int * fun_Pr7763680713840462443e_term ) > set_Pr2560585780119916871nt_int ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    aa_fun8411382924985671778nt_int: ( fun_fu60724386564609697nt_int * fun_Pr7763680713840462443e_term ) > set_Pr6700895561065273913nt_int ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    aa_fun3544567364070095336e_term: ( fun_fu4835546211937200935e_term * fun_Pr7763680713840462443e_term ) > fun_in5730379987311621695e_term ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
    aa_fun3538162476766722827_int_o: ( fun_fu6865642474282033866_int_o * fun_Pr7763680713840462443e_term ) > fun_Pr3238374608701176162_int_o ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    aa_fun3265472288063244902nt_int: ( fun_fu9160953773549289085nt_int * fun_Pr7763680713840462443e_term ) > fun_Pr4781553364444837327nt_int ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    aa_fun49903357033182740e_term: ( fun_fu836511555612062035e_term * fun_Pr7763680713840462443e_term ) > fun_Pr7763680713840462443e_term ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_Eo,type,
    aa_fun8408151826566693824at_o_o: ( fun_fu6891447142836604759at_o_o * fun_Pr4796943543331071514_nat_o ) > $o ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001t__Nat__Onat,type,
    aa_fun1432809138467554728_o_nat: ( fun_fu1115759055147092071_o_nat * fun_Pr4796943543331071514_nat_o ) > nat ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    aa_fun7046812543386002057at_nat: ( fun_fu381918921314004384at_nat * fun_Pr4796943543331071514_nat_o ) > set_Pr1261947904930325089at_nat ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001t__fun_It__Int__Oint_M_Eo_J,type,
    aa_fun1490936263268389485_int_o: ( fun_fu7075445697382584196_int_o * fun_Pr4796943543331071514_nat_o ) > fun_int_o ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
    aa_fun359341089595923442_nat_o: ( fun_fu3275390434952296369_nat_o * fun_Pr4796943543331071514_nat_o ) > fun_Pr4796943543331071514_nat_o ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Code____Numeral__Ointeger_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Code____Numeral__Ointeger_J,type,
    aa_fun1555571767557915900nteger: ( fun_fu7390737412436561923nteger * fun_Pr6026251430685297nteger ) > fun_Pr6026251430685297nteger ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_Eo,type,
    aa_fun3538214411680374423_nat_o: ( fun_fu8391177546919232046_nat_o * fun_Pr2118491707810114563at_nat ) > $o ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Nat__Onat,type,
    aa_fun7582795104022253201at_nat: ( fun_fu1413608398870722896at_nat * fun_Pr2118491707810114563at_nat ) > nat ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__Int__Oint_Mt__Int__Oint_J,type,
    aa_fun8399641135911395862nt_int: ( fun_fu3064074204415222357nt_int * fun_Pr2118491707810114563at_nat ) > fun_int_int ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
    aa_fun856177901615811547_int_o: ( fun_fu4638078822479986034_int_o * fun_Pr2118491707810114563at_nat ) > fun_fun_int_int_o ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__fun_It__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J,type,
    aa_fun6920661532540581549_nat_o: ( fun_fu3373238862511017284_nat_o * fun_Pr2118491707810114563at_nat ) > fun_fu8391177546919232046_nat_o ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Rat__Orat_J_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Rat__Orat_J,type,
    aa_fun1488288443938188604at_rat: ( fun_fu3997796857297124035at_rat * fun_Pr8317260874932935276at_rat ) > fun_Pr8317260874932935276at_rat ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    aa_fun1965866159956205013at_nat: ( fun_fu5127092707984472044at_nat * fun_Pr3059359313727237556_nat_o ) > set_Pr4329608150637261639at_nat ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    aa_fun3799641615823574443nt_int: ( fun_fu9132409297049680378nt_int * fun_Pr1196100989263358594_int_o ) > set_Pr4166680992137330533nt_int ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J_001t__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    aa_fun8601777901039773924_int_o: ( fun_fu6286765928754279603_int_o * fun_Pr1196100989263358594_int_o ) > fun_fu2978539155105838238_int_o ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_M_Eo_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    aa_fun1565836460712643691nteger: ( fun_fu5535353563232763194nteger * fun_Pr7015759342434529115eger_o ) > set_Pr3486312109254157132nteger ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_M_Eo_J_001t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
    aa_fun5185621348090534806eger_o: ( fun_fu4530937843762191077eger_o * fun_Pr7015759342434529115eger_o ) > fun_fu7695273699059480439eger_o ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    aa_fun4278629577996002795et_nat: ( fun_fu2239858650119588794et_nat * fun_Pr2620521676128474833_nat_o ) > set_Pr1312406793078187350et_nat ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_001t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
    aa_fun1045796833200626456_nat_o: ( fun_fu7582738562687708775_nat_o * fun_Pr2620521676128474833_nat_o ) > fun_fu8419763957888848259_nat_o ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_M_Eo_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    aa_fun766325623412317803et_nat: ( fun_fu3515393148397969210et_nat * fun_Pr1227177680593602867_nat_o ) > set_Pr4040394263813967220et_nat ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_M_Eo_J_001t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_J,type,
    aa_fun4422562838209026524_nat_o: ( fun_fu4927615759029954091_nat_o * fun_Pr1227177680593602867_nat_o ) > fun_fu2611741329380808165_nat_o ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J_001t__Set__Oset_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    aa_fun4710078337987813035nt_int: ( fun_fu4502062894868904186nt_int * fun_Pr3540825087398332590_int_o ) > set_Pr6700895561065273913nt_int ).

tff(sy_c_aa_001t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J_001t__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    aa_fun1054583131507368252_int_o: ( fun_fu4695829907076200203_int_o * fun_Pr3540825087398332590_int_o ) > fun_fu6865642474282033866_int_o ).

tff(sy_c_aa_001t__fun_It__Product____Type__Ounit_Mt__Assertions__Oassn_J_001t__fun_It__Assertions__Oassn_Mt__fun_It__Product____Type__Ounit_Mt__Assertions__Oassn_J_J,type,
    aa_fun5779862164363648365t_assn: ( fun_fu7405491065986884212t_assn * fun_Pr6626665806141890376t_assn ) > fun_as4019953064511417593t_assn ).

tff(sy_c_aa_001t__fun_It__Product____Type__Ounit_Mt__Heap____Time____Monad__OHeap_It__Heap__Oarray_Itf__a_J_J_J_001t__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    aa_fun6304779250881220759it_nat: ( fun_fu1080234963260751190it_nat * fun_Pr5924905948197006361rray_a ) > fun_he1504492240061592256it_nat ).

tff(sy_c_aa_001t__fun_It__Product____Type__Ounit_Mt__Heap____Time____Monad__OHeap_It__Product____Type__Ounit_J_J_001t__fun_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_J,type,
    aa_fun3883837016763096701it_nat: ( fun_fu2217603491152269828it_nat * fun_Pr292408699144966967t_unit ) > fun_he5234484606919320760it_nat ).

tff(sy_c_aa_001t__fun_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001_Eo,type,
    aa_fun6524165814161438345eger_o: ( fun_fu4285281161728579104eger_o * fun_Pr864343514034809617nteger ) > $o ).

tff(sy_c_aa_001t__fun_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J_001_Eo,type,
    aa_fun3223653959534381366ural_o: ( fun_fu257250443624047805ural_o * fun_Pr2548841491397842206atural ) > $o ).

tff(sy_c_aa_001t__fun_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_Eo,type,
    aa_fun7140827668162456043_int_o: ( fun_fu4509100218321815938_int_o * fun_Pr6733608168372577327nt_int ) > $o ).

tff(sy_c_aa_001t__fun_It__Product____Type__Ounit_Mt__Rat__Orat_J_001t__fun_It__Rat__Orat_Mt__fun_It__Product____Type__Ounit_Mt__Rat__Orat_J_J,type,
    aa_fun5217320890768598205it_rat: ( fun_fu1171974497074579908it_rat * fun_Product_unit_rat ) > fun_ra5613769993463817465it_rat ).

tff(sy_c_aa_001t__fun_It__Rat__Orat_Mt__Rat__Orat_J_001_Eo,type,
    aa_fun_rat_rat_o: ( fun_fun_rat_rat_o * fun_rat_rat ) > $o ).

tff(sy_c_aa_001t__fun_It__Rat__Orat_Mt__Rat__Orat_J_001t__fun_It__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J,type,
    aa_fun6979613644707851983eger_o: ( fun_fu841611025618976102eger_o * fun_rat_rat ) > fun_fu1769128043447206010eger_o ).

tff(sy_c_aa_001t__fun_It__Rat__Orat_Mt__Rat__Orat_J_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
    aa_fun8551920076545987377_int_o: ( fun_fu991806985645568200_int_o * fun_rat_rat ) > fun_fun_int_int_o ).

tff(sy_c_aa_001t__fun_It__Rat__Orat_Mt__Rat__Orat_J_001t__fun_It__fun_It__Rat__Orat_Mt__Rat__Orat_J_M_Eo_J,type,
    aa_fun2395889695319020505_rat_o: ( fun_fu4201227159558561136_rat_o * fun_rat_rat ) > fun_fun_rat_rat_o ).

tff(sy_c_aa_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    aa_fun3786497492886271492at_nat: ( fun_fu7445151911848907075at_nat * fun_se953073389798102371at_nat ) > fun_se953073389798102371at_nat ).

tff(sy_c_aa_001t__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__fun_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J_001t__fun_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J,type,
    aa_fun762164075915671590_nat_o: ( fun_fu3198693465525813493_nat_o * fun_se5639961202347202350_nat_o ) > fun_Pr3059359313727237556_nat_o ).

tff(sy_c_aa_001t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J_001_Eo,type,
    aa_fun201744096300836759nt_o_o: ( fun_fu5016089569405303598nt_o_o * fun_fu3883539188510166275_int_o ) > $o ).

tff(sy_c_aa_001t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J_001t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__fun_It__Int__Oint_M_Eo_J_M_Eo_J_J,type,
    aa_fun7316249240758406317nt_o_o: ( fun_fu7129310890971069252nt_o_o * fun_fu3883539188510166275_int_o ) > fun_fu6971708032831053102nt_o_o ).

tff(sy_c_aa_001t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J_001t__fun_It__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Int__Oint_M_Eo_J_J_J,type,
    aa_fun508258970086480260_int_o: ( fun_fu4169772131120368835_int_o * fun_fu3883539188510166275_int_o ) > fun_fu138107234227827011_int_o ).

tff(sy_c_aa_001t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J_001t__fun_It__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J_M_Eo_J,type,
    aa_fun5360630777332656813nt_o_o: ( fun_fu4137625842417703236nt_o_o * fun_fu3883539188510166275_int_o ) > fun_fu5016089569405303598nt_o_o ).

tff(sy_c_aa_001t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_001_Eo,type,
    aa_fun5704287868122599399_int_o: ( fun_fu7060637683870700398_int_o * fun_fu7811933856372049837nt_int ) > $o ).

tff(sy_c_aa_001t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J,type,
    aa_fun9002780452483867999_int_o: ( fun_fu8074799898941972270_int_o * fun_fu7811933856372049837nt_int ) > fun_fu7060637683870700398_int_o ).

tff(sy_c_aa_001t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_001_Eo,type,
    aa_fun8425762421254558011at_o_o: ( fun_fu4016735857504249042at_o_o * fun_fu6128684156180612191_nat_o ) > $o ).

tff(sy_c_aa_001t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_M_Eo_J,type,
    aa_fun7789069918375247861at_o_o: ( fun_fu5378497120668327052at_o_o * fun_fu6128684156180612191_nat_o ) > fun_fu4016735857504249042at_o_o ).

tff(sy_c_aa_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_M_Eo_J_J_001_Eo,type,
    aa_fun9191990550722779531nt_o_o: ( fun_fu1324968329616104722nt_o_o * fun_fu4534828536049688329_int_o ) > $o ).

tff(sy_c_aa_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_M_Eo_J_J_001t__fun_It__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_M_Eo_J_J_M_Eo_J,type,
    aa_fun6205200682927395935nt_o_o: ( fun_fu7590976836756945966nt_o_o * fun_fu4534828536049688329_int_o ) > fun_fu1324968329616104722nt_o_o ).

tff(sy_c_aa_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    aa_fun6233912309721051003_int_o: ( fun_fu1677024581061081874_int_o * fun_fu1143798476471108391nt_int ) > fun_fu4208408993564413984_int_o ).

tff(sy_c_aa_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_001_Eo,type,
    aa_fun8192636838821724975at_o_o: ( fun_fu325614617715050166at_o_o * fun_fu6779973503720134245_nat_o ) > $o ).

tff(sy_c_aa_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_M_Eo_J,type,
    aa_fun4700854480566125407at_o_o: ( fun_fu4899062771603708206at_o_o * fun_fu6779973503720134245_nat_o ) > fun_fu325614617715050166at_o_o ).

tff(sy_c_aa_001t__fun_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J_001t__fun_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J,type,
    aa_fun1749673562058638246_int_o: ( fun_fu5894409982295737917_int_o * fun_fu2978539155105838238_int_o ) > fun_Pr1196100989263358594_int_o ).

tff(sy_c_aa_001t__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_001t__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J_J,type,
    aa_fun3789280421985926445_int_o: ( fun_fu560856344546067396_int_o * fun_fu3661779633992098115nt_int ) > fun_fu6699046866436802030_int_o ).

tff(sy_c_aa_001t__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_001t__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__Rat__Orat_J_M_Eo_J_J,type,
    aa_fun2399579938715134478_rat_o: ( fun_fu3447610970239163469_rat_o * fun_fu3661779633992098115nt_int ) > fun_fu7677565902479959693_rat_o ).

tff(sy_c_aa_001t__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__Int__Oint_Mt__Rat__Orat_J_J_001t__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J_J,type,
    aa_fun8496196461586942128_int_o: ( fun_fu61188948249169719_int_o * fun_fu7460908759652350970nt_rat ) > fun_fu6699046866436802030_int_o ).

tff(sy_c_aa_001t__fun_It__fun_It__Int__Oint_Mt__Rat__Orat_J_Mt__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_001t__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__Rat__Orat_J_M_Eo_J_J,type,
    aa_fun4351174416053881551_rat_o: ( fun_fu8216932157852985630_rat_o * fun_fu4522195968571808382nt_int ) > fun_fu7677565902479959693_rat_o ).

tff(sy_c_aa_001t__fun_It__fun_It__Int__Oint_Mt__Rat__Orat_J_Mt__fun_It__Int__Oint_Mt__Rat__Orat_J_J_001t__fun_It__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__fun_It__fun_It__Int__Oint_Mt__Rat__Orat_J_M_Eo_J_J,type,
    aa_fun8956737304536474314_rat_o: ( fun_fu2427765959047162121_rat_o * fun_fu1008360527747082367nt_rat ) > fun_fu7677565902479959693_rat_o ).

tff(sy_c_aa_001t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J_001_Eo,type,
    aa_fun5590877032271586035nt_o_o: ( fun_fu1181850468521277066nt_o_o * fun_fu1756172458508103847_int_o ) > $o ).

tff(sy_c_aa_001t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J_001t__fun_It__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J_M_Eo_J,type,
    aa_fun2176986693441167205nt_o_o: ( fun_fu6215369687776649212nt_o_o * fun_fu1756172458508103847_int_o ) > fun_fu1181850468521277066nt_o_o ).

tff(sy_c_aa_001t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_001_Eo,type,
    aa_fun4496170735194219403_int_o: ( fun_fu5852520550942320402_int_o * fun_fu15710647883683081nt_int ) > $o ).

tff(sy_c_aa_001t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_001t__fun_It__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J,type,
    aa_fun6780808746871264351_int_o: ( fun_fu7344996400627858478_int_o * fun_fu15710647883683081nt_int ) > fun_fu5852520550942320402_int_o ).

tff(sy_c_aa_001t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_001_Eo,type,
    aa_fun4591523320370531479at_o_o: ( fun_fu182496756620222510at_o_o * fun_fu4001317426178549763_nat_o ) > $o ).

tff(sy_c_aa_001t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_Mt__fun_It__Int__Oint_Mt__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    aa_fun483808154807695236_nat_o: ( fun_fu2253997797533952707_nat_o * fun_fu4001317426178549763_nat_o ) > fun_fu927436805355353155_nat_o ).

tff(sy_c_aa_001t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__fun_It__Nat__Onat_M_Eo_J_M_Eo_J_J,type,
    aa_fun2763792489458032301at_o_o: ( fun_fu4957514873648614724at_o_o * fun_fu4001317426178549763_nat_o ) > fun_fu7564235448449272366at_o_o ).

tff(sy_c_aa_001t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_001t__fun_It__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_M_Eo_J,type,
    aa_fun4605425834483758253at_o_o: ( fun_fu7456240966027273028at_o_o * fun_fu4001317426178549763_nat_o ) > fun_fu182496756620222510at_o_o ).

tff(sy_c_aa_001t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_Mt__Num__Onum_J_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    aa_fun4497772300331625231nteger: ( fun_fu9089537617116752462nteger * fun_fu8347129338434488602er_num ) > fun_Co8499238673658658103nteger ).

tff(sy_c_aa_001t__fun_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J_001t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_M_Eo_J,type,
    aa_fun7761728421758185830eger_o: ( fun_fu7060041198443644797eger_o * fun_fu7695273699059480439eger_o ) > fun_Pr7015759342434529115eger_o ).

tff(sy_c_aa_001t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J_001t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J,type,
    aa_fun6593097867094858448_nat_o: ( fun_fu3464598166661278695_nat_o * fun_fu8419763957888848259_nat_o ) > fun_Pr2620521676128474833_nat_o ).

tff(sy_c_aa_001t__fun_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_J_001t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_M_Eo_J,type,
    aa_fun4447940216497214800_nat_o: ( fun_fu5983609555712719719_nat_o * fun_fu2611741329380808165_nat_o ) > fun_Pr1227177680593602867_nat_o ).

tff(sy_c_aa_001t__fun_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J_001t__fun_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J,type,
    aa_fun6978165455603620006_int_o: ( fun_fu2458202332514215229_int_o * fun_fu6865642474282033866_int_o ) > fun_Pr3540825087398332590_int_o ).

tff(sy_c_fequal_001_Eo,type,
    fequal_o: fun_o_fun_o_o ).

tff(sy_c_fequal_001t__Code____Numeral__Ointeger,type,
    fequal_Code_integer: fun_Co2081214437782444048eger_o ).

tff(sy_c_fequal_001t__Int__Oint,type,
    fequal_int: fun_int_fun_int_o ).

tff(sy_c_fequal_001t__Nat__Onat,type,
    fequal_nat: fun_nat_fun_nat_o ).

tff(sy_c_fequal_001t__Num__Onum,type,
    fequal_num: fun_num_fun_num_o ).

tff(sy_c_fequal_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    fequal1407654770548522611it_nat: produc8664842809031399944it_nat > fun_Pr8032424337255632745_nat_o ).

tff(sy_c_fequal_001t__Product____Type__Ounit,type,
    fequal_Product_unit: fun_Pr1520749766685617582unit_o ).

tff(sy_c_fequal_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    fequal7260506811903038370nteger: fun_fu4788845708739168348eger_o ).

tff(sy_c_fequal_001t__fun_It__Int__Oint_M_Eo_J,type,
    fequal_fun_int_o: fun_fu6971708032831053102nt_o_o ).

tff(sy_c_fequal_001t__fun_It__Int__Oint_Mt__Int__Oint_J,type,
    fequal_fun_int_int: fun_fu4208408993564413984_int_o ).

tff(sy_c_fequal_001t__fun_It__Nat__Onat_M_Eo_J,type,
    fequal_fun_nat_o: fun_fu7564235448449272366at_o_o ).

tff(sy_c_fequal_001t__fun_It__Nat__Onat_Mt__Num__Onum_J,type,
    fequal_fun_nat_num: fun_fu223923076992463612_num_o ).

tff(sy_c_fequal_001t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    fequal2058191982396926190_int_o: fun_fu4137625842417703236nt_o_o ).

tff(sy_c_fequal_001t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J,type,
    fequal5394626278453804162nt_int: fun_fu8074799898941972270_int_o ).

tff(sy_c_fequal_001t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    fequal4303336950067372106_nat_o: fun_fu5378497120668327052at_o_o ).

tff(sy_c_fequal_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    fequal2117520958131442654_int_o: fun_fu7590976836756945966nt_o_o ).

tff(sy_c_fequal_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    fequal4362665925801888570_nat_o: fun_fu4899062771603708206at_o_o ).

tff(sy_c_fequal_001t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J,type,
    fequal9154197289249639570_int_o: fun_fu6215369687776649212nt_o_o ).

tff(sy_c_fequal_001t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J,type,
    fequal6821775106820213214nt_int: fun_fu7344996400627858478_int_o ).

tff(sy_c_fequal_001t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J,type,
    fequal2175970220065309678_nat_o: fun_fu7456240966027273028at_o_o ).

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

tff(sy_c_member_001t__Code____Numeral__Ointeger,type,
    member_Code_integer: ( code_integer * set_Code_integer ) > $o ).

tff(sy_c_member_001t__Code____Numeral__Onatural,type,
    member_Code_natural: ( code_natural * set_Code_natural ) > $o ).

tff(sy_c_member_001t__Int__Oint,type,
    member_int: ( int * set_int ) > $o ).

tff(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
    member_list_nat: ( list_nat * set_list_nat ) > $o ).

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

tff(sy_c_member_001t__Num__Onum,type,
    member_num: ( num * set_num ) > $o ).

tff(sy_c_member_001t__Option__Ooption_I_Eo_J,type,
    member_option_o: ( option_o * set_option_o ) > $o ).

tff(sy_c_member_001t__Option__Ooption_It__Int__Oint_J,type,
    member_option_int: ( option_int * set_option_int ) > $o ).

tff(sy_c_member_001t__Option__Ooption_It__Nat__Onat_J,type,
    member_option_nat: ( option_nat * set_option_nat ) > $o ).

tff(sy_c_member_001t__Option__Ooption_It__Num__Onum_J,type,
    member_option_num: ( option_num * set_option_num ) > $o ).

tff(sy_c_member_001t__Option__Ooption_It__Product____Type__Oprod_It__Heap__Oarray_Itf__a_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    member3517700364412436275it_nat: ( option3216581401566546698it_nat * set_op3940070208846178154it_nat ) > $o ).

tff(sy_c_member_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    member3954567711264315760at_nat: ( option4927543243414619207at_nat * set_op4508134149509766951at_nat ) > $o ).

tff(sy_c_member_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
    member5596548051065438575it_nat: ( option8956607266484857688it_nat * set_op239864471688321678it_nat ) > $o ).

tff(sy_c_member_001t__Option__Ooption_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    member4288423094740844502at_nat: ( option8699557107911914541at_nat * set_op989438649584373901at_nat ) > $o ).

tff(sy_c_member_001t__Option__Ooption_It__Product____Type__Ounit_J,type,
    member1378114217278917244t_unit: ( option_Product_unit * set_op3165557761946182707t_unit ) > $o ).

tff(sy_c_member_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
    member8989860449721436141et_nat: ( option_set_nat * set_option_set_nat ) > $o ).

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

tff(sy_c_member_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
    member7847949116333733898_o_int: ( product_prod_o_int * set_Pr8834758594704517033_o_int ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
    member2802428098988154798_o_nat: ( product_prod_o_nat * set_Pr2101469702781467981_o_nat ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    member157494554546826820nteger: ( produc8923325533196201883nteger * set_Pr4811707699266497531nteger ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
    member8280416476884352090atural: ( produc7822875418678951345atural * set_Pr7564037697178849041atural ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
    member2108296798382401941atural: ( produc5835291356934675326atural * set_Pr2352657477744078772atural ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    member6260224972018164377et_nat: ( produc3658429121746597890et_nat * set_Pr3948176798113811640et_nat ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Int__Oint_M_Eo_J,type,
    member4489920277610959864_int_o: ( product_prod_int_o * set_Pr903927857289325719_int_o ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
    member5262025264175285858nt_int: ( product_prod_int_int * set_Pr958786334691620121nt_int ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J,type,
    member216504246829706758nt_nat: ( product_prod_int_nat * set_Pr3448869479623346877nt_nat ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    member6689249552917799696at_nat: ( produc4166570645942440679at_nat * set_Pr8551490117392284871at_nat ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
    member6310962623043647828_nat_o: ( product_prod_nat_o * set_Pr3149072824959771635_nat_o ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
    member4262671552274231302at_int: ( product_prod_nat_int * set_Pr7995236796853374141at_int ) > $o ).

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

tff(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    member335077259223437328nteger: ( produc3334582477557816039nteger * set_Pr5052581263052047815nteger ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    member6099555550032318734et_nat: ( produc8111630337999740517et_nat * set_Pr719794911490849221et_nat ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    member8566619992076573584nt_int: ( produc1219242969750017639nt_int * set_Pr2560585780119916871nt_int ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
    member2200362271989506215_nat_o: ( produc652263959640188542_nat_o * set_Pr6558897299634722526_nat_o ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    member8206827879206165904at_nat: ( produc859450856879609959at_nat * set_Pr8693737435421807431at_nat ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    member4107301959146914710at_nat: ( produc2714363965264676845at_nat * set_Pr2072254264782222413at_nat ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J_J,type,
    member3480088626692287306at_nat: ( produc2087150632810049441at_nat * set_Pr5070339090747523585at_nat ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    member6009668390874684176at_nat: ( produc1906917888121415911at_nat * set_Pr5564308138774400199at_nat ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    member9155761383210387176nt_int: ( produc3192696172498486335nt_int * set_Pr3703873761940759199nt_int ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
    member5045372342328489014nteger: ( produc7379341420752632205nteger * set_Pr6949033248718891245nteger ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    member2216856746449346506et_nat: ( produc8893060842726229537et_nat * set_Pr9066344408807579265et_nat ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
    member2136425100634443654et_nat: ( produc505541996239113949et_nat * set_Pr7057080801110549565et_nat ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    member8789097660028509840nt_int: ( produc881187336974765031nt_int * set_Pr3767905878465553991nt_int ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
    member3421417852355157663it_nat: ( produc8664842809031399944it_nat * set_Pr1354866905816374718it_nat ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_I_Eo_J_Mt__Set__Oset_I_Eo_J_J,type,
    member9116954335612470352_set_o: ( produc7369051934464679207_set_o * set_Pr4577759397028426247_set_o ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__Set__Oset_It__Code____Numeral__Ointeger_J_J,type,
    member4307123515891402160nteger: ( produc6491284506569428743nteger * set_Pr7577011563204128103nteger ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Int__Oint_J_Mt__Set__Oset_It__Int__Oint_J_J,type,
    member2572552093476627150et_int: ( produc2115011035271226405et_int * set_Pr2522554150109002629et_int ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    member8277197624267554838et_nat: ( produc7819656566062154093et_nat * set_Pr5488025237498180813et_nat ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
    member444158400953824016od_o_o: ( produc2934264451710624999od_o_o * set_Pr1932065953672099015od_o_o ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    member4095101504841534314at_nat: ( produc732395585841259969at_nat * set_Pr457366540195662369at_nat ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
    member8757157785044589968at_nat: ( produc3843707927480180839at_nat * set_Pr4329608150637261639at_nat ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
    member1466754251312161552at_nat: ( produc1319942482725812455at_nat * set_Pr7459493094073627847at_nat ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
    member4300370950623927696at_nat: ( produc7299876168958306407at_nat * set_Pr1604112560894399303at_nat ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    member5890090881338784710nt_int: ( produc4788131091073775919nt_int * set_Pr4166680992137330533nt_int ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    member4035412867189635336e_term: ( produc7249898413471085407e_term * set_Pr7847555563209246911e_term ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    member8978266922497061677nteger: ( produc2453742332425399446nteger * set_Pr3486312109254157132nteger ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    member6921354900009420158e_term: ( produc8529534078076073941e_term * set_Pr2514328457256655413e_term ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
    member4513763875858039863et_nat: ( produc8799533983703829792et_nat * set_Pr1312406793078187350et_nat ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
    member9174161442226468181et_nat: ( produc3112576180687729086et_nat * set_Pr4040394263813967220et_nat ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
    member3012145478770660624_nat_o: ( produc6671579610312156647_nat_o * set_Pr2890355626087285447_nat_o ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    member753276645541486746nt_int: ( produc3043004577601930755nt_int * set_Pr6700895561065273913nt_int ) > $o ).

tff(sy_c_member_001t__Product____Type__Oprod_It__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_J,type,
    member8891660375229322592e_term: ( produc9065761207657906103e_term * set_Pr257197284073945367e_term ) > $o ).

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

tff(sy_c_member_001t__Rat__Orat,type,
    member_rat: ( rat * set_rat ) > $o ).

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

tff(sy_c_member_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
    member1834298987299537450nteger: ( set_Code_integer * set_set_Code_integer ) > $o ).

tff(sy_c_member_001t__Set__Oset_It__Int__Oint_J,type,
    member_set_int: ( set_int * set_set_int ) > $o ).

tff(sy_c_member_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
    member_set_list_nat: ( set_list_nat * set_set_list_nat ) > $o ).

tff(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
    member_set_nat: ( set_nat * set_set_nat ) > $o ).

tff(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
    member2643936169264416010at_nat: ( set_Pr1261947904930325089at_nat * set_se7855581050983116737at_nat ) > $o ).

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

tff(sy_c_member_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
    member8321684580148902862nteger: ( fun_Co8499238673658658103nteger * set_fu5818728815147633517nteger ) > $o ).

tff(sy_c_member_001t__fun_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    member4871225538671630166e_term: ( fun_in5730379987311621695e_term * set_fu3629540756087427317e_term ) > $o ).

tff(sy_c_member_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    member6122918666798267249nteger: ( fun_in4744367027289715400nteger * set_fu2873095257816804008nteger ) > $o ).

tff(sy_c_member_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J,type,
    member8246479418148113598atural: ( fun_in4857920871562217639atural * set_fu2445755650934904413atural ) > $o ).

tff(sy_c_member_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    member6164479600762057871nt_int: ( fun_in4211310926729683942nt_int * set_fu8487152106118010054nt_int ) > $o ).

tff(sy_c_member_001t__fun_It__Int__Oint_Mt__Product____Type__Oprod_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_J,type,
    member6435579483112855485_nat_o: ( fun_in7664021439913478804_nat_o * set_fu1437006448190940916_nat_o ) > $o ).

tff(sy_c_member_001t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    member5201028058600969421nteger: ( fun_na3822476419092417572nteger * set_fu4273546686648440324nteger ) > $o ).

tff(sy_c_member_001t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J,type,
    member5482918008064311394atural: ( fun_na2094359461478415435atural * set_fu3555100300013713409atural ) > $o ).

tff(sy_c_member_001t__fun_It__Nat__Onat_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    member3126637516297924075nt_int: ( fun_na1173468842265550146nt_int * set_fu360863049907232802nt_int ) > $o ).

tff(sy_c_member_001t__fun_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    member8464590939221061905e_term: ( fun_Pr5098669352780829690e_term * set_fu8280898353253485872e_term ) > $o ).

tff(sy_c_member_001t__fun_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
    member7544390268018397336_nat_o: ( fun_Pr6460944699146269935_nat_o * set_fu3555266933746557007_nat_o ) > $o ).

tff(sy_c_member_001t__fun_It__Product____Type__Oprod_It__Int__Oint_Mt__fun_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
    member1495369047980753794e_term: ( fun_Pr7763680713840462443e_term * set_fu5653557704672872225e_term ) > $o ).

tff(sy_c_member_001t__fun_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
    member485394258709547313_nat_o: ( fun_Pr4796943543331071514_nat_o * set_fu8838435424971791696_nat_o ) > $o ).

tff(sy_c_member_001t__fun_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
    member4432617224738826152nteger: ( fun_Pr864343514034809617nteger * set_fu2374436075715859015nteger ) > $o ).

tff(sy_c_member_001t__fun_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_J,type,
    member5905631239291665351atural: ( fun_Pr2548841491397842206atural * set_fu2713250876831336446atural ) > $o ).

tff(sy_c_member_001t__fun_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
    member7232304512501848262nt_int: ( fun_Pr6733608168372577327nt_int * set_fu6863465268813640805nt_int ) > $o ).

tff(sy_v_h,type,
    h: heap_e7401611519738050253t_unit ).

tff(sy_v_xs,type,
    xs: list_a ).

% Relevant facts (8724)
tff(fact_0_fails__def,axiom,
    ! [M: heap_T6362127782908069795rray_a,Ha: heap_e7401611519738050253t_unit] :
      ( aa_hea7994211679605476167unit_o(time_fails_array_a(M),Ha)
    <=> ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(M),Ha) = none_P2587165478634041381it_nat ) ) ).

% fails_def
tff(fact_1_fails__def,axiom,
    ! [M: heap_T5738788834812785303t_unit,Ha: heap_e7401611519738050253t_unit] :
      ( aa_hea7994211679605476167unit_o(time_f8834461667527620124t_unit(M),Ha)
    <=> ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(M),Ha) = none_P9117596204409417319it_nat ) ) ).

% fails_def
tff(fact_2_Heap__eqI,axiom,
    ! [F: heap_T6362127782908069795rray_a,G: heap_T6362127782908069795rray_a] :
      ( ! [H: heap_e7401611519738050253t_unit] : aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(F),H) = aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(G),H)
     => ( F = G ) ) ).

% Heap_eqI
tff(fact_3_Heap__eqI,axiom,
    ! [F: heap_T5738788834812785303t_unit,G: heap_T5738788834812785303t_unit] :
      ( ! [H: heap_e7401611519738050253t_unit] : aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(F),H) = aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(G),H)
     => ( F = G ) ) ).

% Heap_eqI
tff(fact_4_execute__raise,axiom,
    ! [S: list_char,X: heap_e7401611519738050253t_unit] : aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(heap_T1552190017797416154rray_a(S)),X) = none_P2587165478634041381it_nat ).

% execute_raise
tff(fact_5_execute__raise,axiom,
    ! [S: list_char,X: heap_e7401611519738050253t_unit] : aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(heap_T2927564422264180874t_unit(S)),X) = none_P9117596204409417319it_nat ).

% execute_raise
tff(fact_6_execute__guard_I1_J,axiom,
    ! [P: fun_he8413527710729349838unit_o,Ha: heap_e7401611519738050253t_unit,F: fun_he281446669002384250it_nat] :
      ( ~ aa_hea7994211679605476167unit_o(P,Ha)
     => ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(heap_T7685628758766326643rray_a(P,F)),Ha) = none_P2587165478634041381it_nat ) ) ).

% execute_guard(1)
tff(fact_7_execute__guard_I1_J,axiom,
    ! [P: fun_he8413527710729349838unit_o,Ha: heap_e7401611519738050253t_unit,F: fun_he4944555133437423336it_nat] :
      ( ~ aa_hea7994211679605476167unit_o(P,Ha)
     => ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(heap_T8440541562793052209t_unit(P,F)),Ha) = none_P9117596204409417319it_nat ) ) ).

% execute_guard(1)
tff(fact_8_execute__assert_I2_J,axiom,
    ! [P: fun_array_a_o,X2: array_a,Ha: heap_e7401611519738050253t_unit] :
      ( ~ aa_array_a_o(P,X2)
     => ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(aa_arr1142863274018860686rray_a(heap_T7971689983404357896rray_a(P),X2)),Ha) = none_P2587165478634041381it_nat ) ) ).

% execute_assert(2)
tff(fact_9_execute__assert_I2_J,axiom,
    ! [P: fun_Product_unit_o,X2: product_unit,Ha: heap_e7401611519738050253t_unit] :
      ( ~ aa_Product_unit_o(P,X2)
     => ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(aa_Pro1108561329362217960t_unit(heap_T4208721593536448476t_unit(P),X2)),Ha) = none_P9117596204409417319it_nat ) ) ).

% execute_assert(2)
tff(fact_10_successI,axiom,
    ! [F: heap_T6362127782908069795rray_a,Ha: heap_e7401611519738050253t_unit] :
      ( ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(F),Ha) != none_P2587165478634041381it_nat )
     => aa_hea7994211679605476167unit_o(heap_T6932021131025641745rray_a(F),Ha) ) ).

% successI
tff(fact_11_successI,axiom,
    ! [F: heap_T5738788834812785303t_unit,Ha: heap_e7401611519738050253t_unit] :
      ( ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(F),Ha) != none_P9117596204409417319it_nat )
     => aa_hea7994211679605476167unit_o(heap_T584514906347983379t_unit(F),Ha) ) ).

% successI
tff(fact_12_success__def,axiom,
    ! [F: heap_T6362127782908069795rray_a,Ha: heap_e7401611519738050253t_unit] :
      ( aa_hea7994211679605476167unit_o(heap_T6932021131025641745rray_a(F),Ha)
    <=> ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(F),Ha) != none_P2587165478634041381it_nat ) ) ).

% success_def
tff(fact_13_success__def,axiom,
    ! [F: heap_T5738788834812785303t_unit,Ha: heap_e7401611519738050253t_unit] :
      ( aa_hea7994211679605476167unit_o(heap_T584514906347983379t_unit(F),Ha)
    <=> ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(F),Ha) != none_P9117596204409417319it_nat ) ) ).

% success_def
tff(fact_14_Heap__ordE,axiom,
    ! [X2: heap_T6362127782908069795rray_a,Y: heap_T6362127782908069795rray_a,Ha: heap_e7401611519738050253t_unit] :
      ( heap_T3039585018531920163rray_a(X2,Y)
     => ( ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(X2),Ha) != none_P2587165478634041381it_nat )
       => ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(X2),Ha) = aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(Y),Ha) ) ) ) ).

% Heap_ordE
tff(fact_15_Heap__ordE,axiom,
    ! [X2: heap_T5738788834812785303t_unit,Y: heap_T5738788834812785303t_unit,Ha: heap_e7401611519738050253t_unit] :
      ( heap_T499439718319394433t_unit(X2,Y)
     => ( ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(X2),Ha) != none_P9117596204409417319it_nat )
       => ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(X2),Ha) = aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(Y),Ha) ) ) ) ).

% Heap_ordE
tff(fact_16_Heap__ordI,axiom,
    ! [X2: heap_T6362127782908069795rray_a,Y: heap_T6362127782908069795rray_a] :
      ( ! [H: heap_e7401611519738050253t_unit] :
          ( ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(X2),H) = none_P2587165478634041381it_nat )
          | ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(X2),H) = aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(Y),H) ) )
     => heap_T3039585018531920163rray_a(X2,Y) ) ).

% Heap_ordI
tff(fact_17_Heap__ordI,axiom,
    ! [X2: heap_T5738788834812785303t_unit,Y: heap_T5738788834812785303t_unit] :
      ( ! [H: heap_e7401611519738050253t_unit] :
          ( ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(X2),H) = none_P9117596204409417319it_nat )
          | ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(X2),H) = aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(Y),H) ) )
     => heap_T499439718319394433t_unit(X2,Y) ) ).

% Heap_ordI
tff(fact_18_execute__bind_I2_J,axiom,
    ! [F: heap_T6362127782908069795rray_a,Ha: heap_e7401611519738050253t_unit,G: fun_ar3891948820113774757rray_a] :
      ( ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(F),Ha) = none_P2587165478634041381it_nat )
     => ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(heap_T2407400398799471159rray_a(F,G)),Ha) = none_P2587165478634041381it_nat ) ) ).

% execute_bind(2)
tff(fact_19_execute__bind_I2_J,axiom,
    ! [F: heap_T6362127782908069795rray_a,Ha: heap_e7401611519738050253t_unit,G: fun_ar1074044450438384043t_unit] :
      ( ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(F),Ha) = none_P2587165478634041381it_nat )
     => ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(heap_T7324619625323989613t_unit(F,G)),Ha) = none_P9117596204409417319it_nat ) ) ).

% execute_bind(2)
tff(fact_20_execute__bind_I2_J,axiom,
    ! [F: heap_T5738788834812785303t_unit,Ha: heap_e7401611519738050253t_unit,G: fun_Pr5924905948197006361rray_a] :
      ( ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(F),Ha) = none_P9117596204409417319it_nat )
     => ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(heap_T7158140910958840029rray_a(F,G)),Ha) = none_P2587165478634041381it_nat ) ) ).

% execute_bind(2)
tff(fact_21_execute__bind_I2_J,axiom,
    ! [F: heap_T5738788834812785303t_unit,Ha: heap_e7401611519738050253t_unit,G: fun_Pr292408699144966967t_unit] :
      ( ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(F),Ha) = none_P9117596204409417319it_nat )
     => ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(heap_T2633723481742716231t_unit(F,G)),Ha) = none_P9117596204409417319it_nat ) ) ).

% execute_bind(2)
tff(fact_22_the__default_Osimps_I2_J,axiom,
    ! [X2: produc6714399278180371524it_nat] : the_de8559148246674365659it_nat(X2,none_P2587165478634041381it_nat) = X2 ).

% the_default.simps(2)
tff(fact_23_the__default_Osimps_I2_J,axiom,
    ! [X2: num] : aa_option_num_num(the_default_num(X2),none_num) = X2 ).

% the_default.simps(2)
tff(fact_24_the__default_Osimps_I2_J,axiom,
    ! [X2: produc8664842809031399944it_nat] : the_de2487931475039285041it_nat(X2,none_P9117596204409417319it_nat) = X2 ).

% the_default.simps(2)
tff(fact_25_raise__bind,axiom,
    ! [E: list_char,F: fun_Pr292408699144966967t_unit] : heap_T2633723481742716231t_unit(heap_T2927564422264180874t_unit(E),F) = heap_T2927564422264180874t_unit(E) ).

% raise_bind
tff(fact_26_raise__bind,axiom,
    ! [E: list_char,F: fun_Pr5924905948197006361rray_a] : heap_T7158140910958840029rray_a(heap_T2927564422264180874t_unit(E),F) = heap_T1552190017797416154rray_a(E) ).

% raise_bind
tff(fact_27_raise__bind,axiom,
    ! [E: list_char,F: fun_ar1074044450438384043t_unit] : heap_T7324619625323989613t_unit(heap_T1552190017797416154rray_a(E),F) = heap_T2927564422264180874t_unit(E) ).

% raise_bind
tff(fact_28_raise__bind,axiom,
    ! [E: list_char,F: fun_ar3891948820113774757rray_a] : heap_T2407400398799471159rray_a(heap_T1552190017797416154rray_a(E),F) = heap_T1552190017797416154rray_a(E) ).

% raise_bind
tff(fact_29_heap_Oleq__refl,axiom,
    ! [X2: heap_T5738788834812785303t_unit] : heap_T499439718319394433t_unit(X2,X2) ).

% heap.leq_refl
tff(fact_30_heap_Oleq__refl,axiom,
    ! [X2: heap_T6362127782908069795rray_a] : heap_T3039585018531920163rray_a(X2,X2) ).

% heap.leq_refl
tff(fact_31_heap_Oleq__trans,axiom,
    ! [X2: heap_T5738788834812785303t_unit,Y: heap_T5738788834812785303t_unit,Z: heap_T5738788834812785303t_unit] :
      ( heap_T499439718319394433t_unit(X2,Y)
     => ( heap_T499439718319394433t_unit(Y,Z)
       => heap_T499439718319394433t_unit(X2,Z) ) ) ).

% heap.leq_trans
tff(fact_32_heap_Oleq__trans,axiom,
    ! [X2: heap_T6362127782908069795rray_a,Y: heap_T6362127782908069795rray_a,Z: heap_T6362127782908069795rray_a] :
      ( heap_T3039585018531920163rray_a(X2,Y)
     => ( heap_T3039585018531920163rray_a(Y,Z)
       => heap_T3039585018531920163rray_a(X2,Z) ) ) ).

% heap.leq_trans
tff(fact_33_heap_Oleq__antisym,axiom,
    ! [X2: heap_T5738788834812785303t_unit,Y: heap_T5738788834812785303t_unit] :
      ( heap_T499439718319394433t_unit(X2,Y)
     => ( heap_T499439718319394433t_unit(Y,X2)
       => ( X2 = Y ) ) ) ).

% heap.leq_antisym
tff(fact_34_heap_Oleq__antisym,axiom,
    ! [X2: heap_T6362127782908069795rray_a,Y: heap_T6362127782908069795rray_a] :
      ( heap_T3039585018531920163rray_a(X2,Y)
     => ( heap_T3039585018531920163rray_a(Y,X2)
       => ( X2 = Y ) ) ) ).

% heap.leq_antisym
tff(fact_35_success__ifI,axiom,
    ! [C: $o,T: heap_T5738788834812785303t_unit,Ha: heap_e7401611519738050253t_unit,E: heap_T5738788834812785303t_unit] :
      ( ( (C)
       => aa_hea7994211679605476167unit_o(heap_T584514906347983379t_unit(T),Ha) )
     => ( ( ~ (C)
         => aa_hea7994211679605476167unit_o(heap_T584514906347983379t_unit(E),Ha) )
       => aa_hea7994211679605476167unit_o(heap_T584514906347983379t_unit($ite((C),T,E)),Ha) ) ) ).

% success_ifI
tff(fact_36_success__ifI,axiom,
    ! [C: $o,T: heap_T6362127782908069795rray_a,Ha: heap_e7401611519738050253t_unit,E: heap_T6362127782908069795rray_a] :
      ( ( (C)
       => aa_hea7994211679605476167unit_o(heap_T6932021131025641745rray_a(T),Ha) )
     => ( ( ~ (C)
         => aa_hea7994211679605476167unit_o(heap_T6932021131025641745rray_a(E),Ha) )
       => aa_hea7994211679605476167unit_o(heap_T6932021131025641745rray_a($ite((C),T,E)),Ha) ) ) ).

% success_ifI
tff(fact_37_success__guardI,axiom,
    ! [P: fun_he8413527710729349838unit_o,Ha: heap_e7401611519738050253t_unit,F: fun_he4944555133437423336it_nat] :
      ( aa_hea7994211679605476167unit_o(P,Ha)
     => aa_hea7994211679605476167unit_o(heap_T584514906347983379t_unit(heap_T8440541562793052209t_unit(P,F)),Ha) ) ).

% success_guardI
tff(fact_38_success__guardI,axiom,
    ! [P: fun_he8413527710729349838unit_o,Ha: heap_e7401611519738050253t_unit,F: fun_he281446669002384250it_nat] :
      ( aa_hea7994211679605476167unit_o(P,Ha)
     => aa_hea7994211679605476167unit_o(heap_T6932021131025641745rray_a(heap_T7685628758766326643rray_a(P,F)),Ha) ) ).

% success_guardI
tff(fact_39_success__assertI,axiom,
    ! [P: fun_Product_unit_o,X2: product_unit,Ha: heap_e7401611519738050253t_unit] :
      ( aa_Product_unit_o(P,X2)
     => aa_hea7994211679605476167unit_o(heap_T584514906347983379t_unit(aa_Pro1108561329362217960t_unit(heap_T4208721593536448476t_unit(P),X2)),Ha) ) ).

% success_assertI
tff(fact_40_success__assertI,axiom,
    ! [P: fun_array_a_o,X2: array_a,Ha: heap_e7401611519738050253t_unit] :
      ( aa_array_a_o(P,X2)
     => aa_hea7994211679605476167unit_o(heap_T6932021131025641745rray_a(aa_arr1142863274018860686rray_a(heap_T7971689983404357896rray_a(P),X2)),Ha) ) ).

% success_assertI
tff(fact_41_fails__bind,axiom,
    ! [M: heap_T5738788834812785303t_unit,F: fun_Pr292408699144966967t_unit,Ha: heap_e7401611519738050253t_unit] :
      ( aa_hea7994211679605476167unit_o(time_f8834461667527620124t_unit(heap_T2633723481742716231t_unit(M,F)),Ha)
    <=> ( ~ aa_hea7994211679605476167unit_o(time_f8834461667527620124t_unit(M),Ha)
       => aa_hea7994211679605476167unit_o(time_f8834461667527620124t_unit(aa_Pro1108561329362217960t_unit(F,aa_hea4146273921685161788t_unit(time_t2745601220510131320t_unit(M),Ha))),time_t3350536682685678164t_unit(M,Ha)) ) ) ).

% fails_bind
tff(fact_42_fails__bind,axiom,
    ! [M: heap_T6362127782908069795rray_a,F: fun_ar1074044450438384043t_unit,Ha: heap_e7401611519738050253t_unit] :
      ( aa_hea7994211679605476167unit_o(time_f8834461667527620124t_unit(heap_T7324619625323989613t_unit(M,F)),Ha)
    <=> ( ~ aa_hea7994211679605476167unit_o(time_fails_array_a(M),Ha)
       => aa_hea7994211679605476167unit_o(time_f8834461667527620124t_unit(aa_arr7999650297717212780t_unit(F,aa_hea3268681801748734376rray_a(time_the_res_array_a(M),Ha))),time_t490086488869527696rray_a(M,Ha)) ) ) ).

% fails_bind
tff(fact_43_fails__bind,axiom,
    ! [M: heap_T5738788834812785303t_unit,F: fun_Pr5924905948197006361rray_a,Ha: heap_e7401611519738050253t_unit] :
      ( aa_hea7994211679605476167unit_o(time_fails_array_a(heap_T7158140910958840029rray_a(M,F)),Ha)
    <=> ( ~ aa_hea7994211679605476167unit_o(time_f8834461667527620124t_unit(M),Ha)
       => aa_hea7994211679605476167unit_o(time_fails_array_a(aa_Pro755961224256580114rray_a(F,aa_hea4146273921685161788t_unit(time_t2745601220510131320t_unit(M),Ha))),time_t3350536682685678164t_unit(M,Ha)) ) ) ).

% fails_bind
tff(fact_44_fails__bind,axiom,
    ! [M: heap_T6362127782908069795rray_a,F: fun_ar3891948820113774757rray_a,Ha: heap_e7401611519738050253t_unit] :
      ( aa_hea7994211679605476167unit_o(time_fails_array_a(heap_T2407400398799471159rray_a(M,F)),Ha)
    <=> ( ~ aa_hea7994211679605476167unit_o(time_fails_array_a(M),Ha)
       => aa_hea7994211679605476167unit_o(time_fails_array_a(aa_arr1142863274018860686rray_a(F,aa_hea3268681801748734376rray_a(time_the_res_array_a(M),Ha))),time_t490086488869527696rray_a(M,Ha)) ) ) ).

% fails_bind
tff(fact_45_success__of__listI,axiom,
    ! [Xsa: list_a,Ha: heap_e7401611519738050253t_unit] : aa_hea7994211679605476167unit_o(heap_T6932021131025641745rray_a(array_of_list_a(Xsa)),Ha) ).

% success_of_listI
tff(fact_46_success__tapI,axiom,
    ! [F: fun_he5123621388056232515t_unit,Ha: heap_e7401611519738050253t_unit] : aa_hea7994211679605476167unit_o(heap_T584514906347983379t_unit(heap_T560649228465745139t_unit(F)),Ha) ).

% success_tapI
tff(fact_47_success__tapI,axiom,
    ! [F: fun_he7369252872201260279rray_a,Ha: heap_e7401611519738050253t_unit] : aa_hea7994211679605476167unit_o(heap_T6932021131025641745rray_a(heap_T2055650868554030641rray_a(F)),Ha) ).

% success_tapI
tff(fact_48_success__heapI,axiom,
    ! [F: fun_he4944555133437423336it_nat,Ha: heap_e7401611519738050253t_unit] : aa_hea7994211679605476167unit_o(heap_T584514906347983379t_unit(heap_T6927113302350381334t_unit(F)),Ha) ).

% success_heapI
tff(fact_49_success__heapI,axiom,
    ! [F: fun_he281446669002384250it_nat,Ha: heap_e7401611519738050253t_unit] : aa_hea7994211679605476167unit_o(heap_T6932021131025641745rray_a(heap_T7473999186002612558rray_a(F)),Ha) ).

% success_heapI
tff(fact_50_success__ureturnI,axiom,
    ! [X2: product_unit,Ha: heap_e7401611519738050253t_unit] : aa_hea7994211679605476167unit_o(heap_T584514906347983379t_unit(aa_Pro1108561329362217960t_unit(heap_T4284346855313245393t_unit,X2)),Ha) ).

% success_ureturnI
tff(fact_51_success__ureturnI,axiom,
    ! [X2: array_a,Ha: heap_e7401611519738050253t_unit] : aa_hea7994211679605476167unit_o(heap_T6932021131025641745rray_a(aa_arr1142863274018860686rray_a(heap_T4328122439115681491rray_a,X2)),Ha) ).

% success_ureturnI
tff(fact_52_execute__guard_I2_J,axiom,
    ! [P: fun_he8413527710729349838unit_o,Ha: heap_e7401611519738050253t_unit,F: fun_he281446669002384250it_nat] :
      ( aa_hea7994211679605476167unit_o(P,Ha)
     => ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(heap_T7685628758766326643rray_a(P,F)),Ha) = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,aa_hea1118439097112461811it_nat(F,Ha)) ) ) ).

% execute_guard(2)
tff(fact_53_execute__guard_I2_J,axiom,
    ! [P: fun_he8413527710729349838unit_o,Ha: heap_e7401611519738050253t_unit,F: fun_he4944555133437423336it_nat] :
      ( aa_hea7994211679605476167unit_o(P,Ha)
     => ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(heap_T8440541562793052209t_unit(P,F)),Ha) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,aa_hea256619718444519449it_nat(F,Ha)) ) ) ).

% execute_guard(2)
tff(fact_54_combine__options__simps_I1_J,axiom,
    ! [F: fun_Pr6442729728054246170it_nat,Y: option3216581401566546698it_nat] : combin3867838909898076099it_nat(F,none_P2587165478634041381it_nat,Y) = Y ).

% combine_options_simps(1)
tff(fact_55_combine__options__simps_I1_J,axiom,
    ! [F: fun_num_fun_num_num,Y: option_num] : aa_opt5369159329878751634on_num(combine_options_num(F,none_num),Y) = Y ).

% combine_options_simps(1)
tff(fact_56_combine__options__simps_I1_J,axiom,
    ! [F: fun_Pr1003294667014919570it_nat,Y: option8956607266484857688it_nat] : combin4318129983670048329it_nat(F,none_P9117596204409417319it_nat,Y) = Y ).

% combine_options_simps(1)
tff(fact_57_combine__options__simps_I2_J,axiom,
    ! [F: fun_Pr6442729728054246170it_nat,X2: option3216581401566546698it_nat] : combin3867838909898076099it_nat(F,X2,none_P2587165478634041381it_nat) = X2 ).

% combine_options_simps(2)
tff(fact_58_combine__options__simps_I2_J,axiom,
    ! [F: fun_num_fun_num_num,X2: option_num] : aa_opt5369159329878751634on_num(combine_options_num(F,X2),none_num) = X2 ).

% combine_options_simps(2)
tff(fact_59_combine__options__simps_I2_J,axiom,
    ! [F: fun_Pr1003294667014919570it_nat,X2: option8956607266484857688it_nat] : combin4318129983670048329it_nat(F,X2,none_P9117596204409417319it_nat) = X2 ).

% combine_options_simps(2)
tff(fact_60_option_Oinject,axiom,
    ! [X22: num,Y2: num] :
      ( ( aa_num_option_num(some_num,X22) = aa_num_option_num(some_num,Y2) )
    <=> ( X22 = Y2 ) ) ).

% option.inject
tff(fact_61_option_Oinject,axiom,
    ! [X22: produc8664842809031399944it_nat,Y2: produc8664842809031399944it_nat] :
      ( ( aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X22) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,Y2) )
    <=> ( X22 = Y2 ) ) ).

% option.inject
tff(fact_62_not__None__eq,axiom,
    ! [X2: option3216581401566546698it_nat] :
      ( ( X2 != none_P2587165478634041381it_nat )
    <=> ? [Y3: produc6714399278180371524it_nat] : X2 = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,Y3) ) ).

% not_None_eq
tff(fact_63_not__None__eq,axiom,
    ! [X2: option_num] :
      ( ( X2 != none_num )
    <=> ? [Y3: num] : X2 = aa_num_option_num(some_num,Y3) ) ).

% not_None_eq
tff(fact_64_not__None__eq,axiom,
    ! [X2: option8956607266484857688it_nat] :
      ( ( X2 != none_P9117596204409417319it_nat )
    <=> ? [Y3: produc8664842809031399944it_nat] : X2 = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,Y3) ) ).

% not_None_eq
tff(fact_65_not__Some__eq,axiom,
    ! [X2: option3216581401566546698it_nat] :
      ( ! [Y3: produc6714399278180371524it_nat] : X2 != aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,Y3)
    <=> ( X2 = none_P2587165478634041381it_nat ) ) ).

% not_Some_eq
tff(fact_66_not__Some__eq,axiom,
    ! [X2: option_num] :
      ( ! [Y3: num] : X2 != aa_num_option_num(some_num,Y3)
    <=> ( X2 = none_num ) ) ).

% not_Some_eq
tff(fact_67_not__Some__eq,axiom,
    ! [X2: option8956607266484857688it_nat] :
      ( ! [Y3: produc8664842809031399944it_nat] : X2 != aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,Y3)
    <=> ( X2 = none_P9117596204409417319it_nat ) ) ).

% not_Some_eq
tff(fact_68_combine__options__simps_I3_J,axiom,
    ! [F: fun_num_fun_num_num,A: num,B: num] : aa_opt5369159329878751634on_num(combine_options_num(F,aa_num_option_num(some_num,A)),aa_num_option_num(some_num,B)) = aa_num_option_num(some_num,aa_num_num(aa_num_fun_num_num(F,A),B)) ).

% combine_options_simps(3)
tff(fact_69_combine__options__simps_I3_J,axiom,
    ! [F: fun_Pr1003294667014919570it_nat,A: produc8664842809031399944it_nat,B: produc8664842809031399944it_nat] : combin4318129983670048329it_nat(F,aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,A),aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,B)) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,aa_Pro550487673543749710it_nat(aa_Pro4096753284154920275it_nat(F,A),B)) ).

% combine_options_simps(3)
tff(fact_70_mem__Collect__eq,axiom,
    ! [A: produc3843707927480180839at_nat,P: fun_Pr3059359313727237556_nat_o] :
      ( member8757157785044589968at_nat(A,aa_fun1965866159956205013at_nat(collec6321179662152712658at_nat,P))
    <=> aa_Pro5947980084102686253_nat_o(P,A) ) ).

% mem_Collect_eq
tff(fact_71_mem__Collect__eq,axiom,
    ! [A: product_prod_nat_nat,P: fun_Pr4796943543331071514_nat_o] :
      ( member8440522571783428010at_nat(A,aa_fun7046812543386002057at_nat(collec3392354462482085612at_nat,P))
    <=> aa_Pro6150637604445964947_nat_o(P,A) ) ).

% mem_Collect_eq
tff(fact_72_mem__Collect__eq,axiom,
    ! [A: $o,P: fun_o_o] :
      ( member_o((A),collect_o(P))
    <=> aa_o_o(P,(A)) ) ).

% mem_Collect_eq
tff(fact_73_mem__Collect__eq,axiom,
    ! [A: int,P: fun_int_o] :
      ( member_int(A,collect_int(P))
    <=> aa_int_o(P,A) ) ).

% mem_Collect_eq
tff(fact_74_mem__Collect__eq,axiom,
    ! [A: nat,P: fun_nat_o] :
      ( member_nat(A,collect_nat(P))
    <=> aa_nat_o(P,A) ) ).

% mem_Collect_eq
tff(fact_75_mem__Collect__eq,axiom,
    ! [A: list_nat,P: fun_list_nat_o] :
      ( member_list_nat(A,collect_list_nat(P))
    <=> aa_list_nat_o(P,A) ) ).

% mem_Collect_eq
tff(fact_76_Collect__mem__eq,axiom,
    ! [A2: set_Pr4329608150637261639at_nat] : aa_fun1965866159956205013at_nat(collec6321179662152712658at_nat,aTP_Lamm_a(A2)) = A2 ).

% Collect_mem_eq
tff(fact_77_Collect__mem__eq,axiom,
    ! [A2: set_Pr1261947904930325089at_nat] : aa_fun7046812543386002057at_nat(collec3392354462482085612at_nat,aTP_Lamm_aa(A2)) = A2 ).

% Collect_mem_eq
tff(fact_78_Collect__mem__eq,axiom,
    ! [A2: set_o] : collect_o(aTP_Lamm_ab(A2)) = A2 ).

% Collect_mem_eq
tff(fact_79_Collect__mem__eq,axiom,
    ! [A2: set_int] : collect_int(aTP_Lamm_ac(A2)) = A2 ).

% Collect_mem_eq
tff(fact_80_Collect__mem__eq,axiom,
    ! [A2: set_nat] : collect_nat(aTP_Lamm_ad(A2)) = A2 ).

% Collect_mem_eq
tff(fact_81_Collect__mem__eq,axiom,
    ! [A2: set_list_nat] : collect_list_nat(aTP_Lamm_ae(A2)) = A2 ).

% Collect_mem_eq
tff(fact_82_Collect__cong,axiom,
    ! [P: fun_nat_o,Q: fun_nat_o] :
      ( ! [X3: nat] :
          ( aa_nat_o(P,X3)
        <=> aa_nat_o(Q,X3) )
     => ( collect_nat(P) = collect_nat(Q) ) ) ).

% Collect_cong
tff(fact_83_Collect__cong,axiom,
    ! [P: fun_list_nat_o,Q: fun_list_nat_o] :
      ( ! [X3: list_nat] :
          ( aa_list_nat_o(P,X3)
        <=> aa_list_nat_o(Q,X3) )
     => ( collect_list_nat(P) = collect_list_nat(Q) ) ) ).

% Collect_cong
tff(fact_84_option_Odistinct_I1_J,axiom,
    ! [X22: produc6714399278180371524it_nat] : none_P2587165478634041381it_nat != aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,X22) ).

% option.distinct(1)
tff(fact_85_option_Odistinct_I1_J,axiom,
    ! [X22: num] : none_num != aa_num_option_num(some_num,X22) ).

% option.distinct(1)
tff(fact_86_option_Odistinct_I1_J,axiom,
    ! [X22: produc8664842809031399944it_nat] : none_P9117596204409417319it_nat != aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X22) ).

% option.distinct(1)
tff(fact_87_option_OdiscI,axiom,
    ! [Option: option3216581401566546698it_nat,X22: produc6714399278180371524it_nat] :
      ( ( Option = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,X22) )
     => ( Option != none_P2587165478634041381it_nat ) ) ).

% option.discI
tff(fact_88_option_OdiscI,axiom,
    ! [Option: option_num,X22: num] :
      ( ( Option = aa_num_option_num(some_num,X22) )
     => ( Option != none_num ) ) ).

% option.discI
tff(fact_89_option_OdiscI,axiom,
    ! [Option: option8956607266484857688it_nat,X22: produc8664842809031399944it_nat] :
      ( ( Option = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X22) )
     => ( Option != none_P9117596204409417319it_nat ) ) ).

% option.discI
tff(fact_90_option_Oexhaust,axiom,
    ! [Y: option3216581401566546698it_nat] :
      ( ( Y != none_P2587165478634041381it_nat )
     => ~ ! [X23: produc6714399278180371524it_nat] : Y != aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,X23) ) ).

% option.exhaust
tff(fact_91_option_Oexhaust,axiom,
    ! [Y: option_num] :
      ( ( Y != none_num )
     => ~ ! [X23: num] : Y != aa_num_option_num(some_num,X23) ) ).

% option.exhaust
tff(fact_92_option_Oexhaust,axiom,
    ! [Y: option8956607266484857688it_nat] :
      ( ( Y != none_P9117596204409417319it_nat )
     => ~ ! [X23: produc8664842809031399944it_nat] : Y != aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X23) ) ).

% option.exhaust
tff(fact_93_split__option__ex,axiom,
    ! [P: fun_op4751157287140997969_nat_o] :
      ( ? [X_1: option3216581401566546698it_nat] : aa_opt4809530629565672394_nat_o(P,X_1)
    <=> ( aa_opt4809530629565672394_nat_o(P,none_P2587165478634041381it_nat)
        | ? [X4: produc6714399278180371524it_nat] : aa_opt4809530629565672394_nat_o(P,aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,X4)) ) ) ).

% split_option_ex
tff(fact_94_split__option__ex,axiom,
    ! [P: fun_option_num_o] :
      ( ? [X_1: option_num] : aa_option_num_o(P,X_1)
    <=> ( aa_option_num_o(P,none_num)
        | ? [X4: num] : aa_option_num_o(P,aa_num_option_num(some_num,X4)) ) ) ).

% split_option_ex
tff(fact_95_split__option__ex,axiom,
    ! [P: fun_op479301348043730329_nat_o] :
      ( ? [X_1: option8956607266484857688it_nat] : aa_opt8360315729766332930_nat_o(P,X_1)
    <=> ( aa_opt8360315729766332930_nat_o(P,none_P9117596204409417319it_nat)
        | ? [X4: produc8664842809031399944it_nat] : aa_opt8360315729766332930_nat_o(P,aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X4)) ) ) ).

% split_option_ex
tff(fact_96_split__option__all,axiom,
    ! [P: fun_op4751157287140997969_nat_o] :
      ( ! [X_1: option3216581401566546698it_nat] : aa_opt4809530629565672394_nat_o(P,X_1)
    <=> ( aa_opt4809530629565672394_nat_o(P,none_P2587165478634041381it_nat)
        & ! [X4: produc6714399278180371524it_nat] : aa_opt4809530629565672394_nat_o(P,aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,X4)) ) ) ).

% split_option_all
tff(fact_97_split__option__all,axiom,
    ! [P: fun_option_num_o] :
      ( ! [X_1: option_num] : aa_option_num_o(P,X_1)
    <=> ( aa_option_num_o(P,none_num)
        & ! [X4: num] : aa_option_num_o(P,aa_num_option_num(some_num,X4)) ) ) ).

% split_option_all
tff(fact_98_split__option__all,axiom,
    ! [P: fun_op479301348043730329_nat_o] :
      ( ! [X_1: option8956607266484857688it_nat] : aa_opt8360315729766332930_nat_o(P,X_1)
    <=> ( aa_opt8360315729766332930_nat_o(P,none_P9117596204409417319it_nat)
        & ! [X4: produc8664842809031399944it_nat] : aa_opt8360315729766332930_nat_o(P,aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X4)) ) ) ).

% split_option_all
tff(fact_99_combine__options__cases,axiom,
    ! [X2: option3216581401566546698it_nat,P: fun_op2352717853092002798_nat_o,Y: option3216581401566546698it_nat] :
      ( ( ( X2 = none_P2587165478634041381it_nat )
       => aa_opt4809530629565672394_nat_o(aa_opt6043028115961832863_nat_o(P,X2),Y) )
     => ( ( ( Y = none_P2587165478634041381it_nat )
         => aa_opt4809530629565672394_nat_o(aa_opt6043028115961832863_nat_o(P,X2),Y) )
       => ( ! [A3: produc6714399278180371524it_nat,B2: produc6714399278180371524it_nat] :
              ( ( X2 = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,A3) )
             => ( ( Y = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,B2) )
               => aa_opt4809530629565672394_nat_o(aa_opt6043028115961832863_nat_o(P,X2),Y) ) )
         => aa_opt4809530629565672394_nat_o(aa_opt6043028115961832863_nat_o(P,X2),Y) ) ) ) ).

% combine_options_cases
tff(fact_100_combine__options__cases,axiom,
    ! [X2: option3216581401566546698it_nat,P: fun_op3129816456743790912_num_o,Y: option_num] :
      ( ( ( X2 = none_P2587165478634041381it_nat )
       => aa_option_num_o(aa_opt2228701783387358009_num_o(P,X2),Y) )
     => ( ( ( Y = none_num )
         => aa_option_num_o(aa_opt2228701783387358009_num_o(P,X2),Y) )
       => ( ! [A3: produc6714399278180371524it_nat,B2: num] :
              ( ( X2 = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,A3) )
             => ( ( Y = aa_num_option_num(some_num,B2) )
               => aa_option_num_o(aa_opt2228701783387358009_num_o(P,X2),Y) ) )
         => aa_option_num_o(aa_opt2228701783387358009_num_o(P,X2),Y) ) ) ) ).

% combine_options_cases
tff(fact_101_combine__options__cases,axiom,
    ! [X2: option3216581401566546698it_nat,P: fun_op101698441058542546_nat_o,Y: option8956607266484857688it_nat] :
      ( ( ( X2 = none_P2587165478634041381it_nat )
       => aa_opt8360315729766332930_nat_o(aa_opt1571526544311817931_nat_o(P,X2),Y) )
     => ( ( ( Y = none_P9117596204409417319it_nat )
         => aa_opt8360315729766332930_nat_o(aa_opt1571526544311817931_nat_o(P,X2),Y) )
       => ( ! [A3: produc6714399278180371524it_nat,B2: produc8664842809031399944it_nat] :
              ( ( X2 = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,A3) )
             => ( ( Y = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,B2) )
               => aa_opt8360315729766332930_nat_o(aa_opt1571526544311817931_nat_o(P,X2),Y) ) )
         => aa_opt8360315729766332930_nat_o(aa_opt1571526544311817931_nat_o(P,X2),Y) ) ) ) ).

% combine_options_cases
tff(fact_102_combine__options__cases,axiom,
    ! [X2: option_num,P: fun_op261120641589640376_nat_o,Y: option3216581401566546698it_nat] :
      ( ( ( X2 = none_num )
       => aa_opt4809530629565672394_nat_o(aa_opt1082509876067759737_nat_o(P,X2),Y) )
     => ( ( ( Y = none_P2587165478634041381it_nat )
         => aa_opt4809530629565672394_nat_o(aa_opt1082509876067759737_nat_o(P,X2),Y) )
       => ( ! [A3: num,B2: produc6714399278180371524it_nat] :
              ( ( X2 = aa_num_option_num(some_num,A3) )
             => ( ( Y = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,B2) )
               => aa_opt4809530629565672394_nat_o(aa_opt1082509876067759737_nat_o(P,X2),Y) ) )
         => aa_opt4809530629565672394_nat_o(aa_opt1082509876067759737_nat_o(P,X2),Y) ) ) ) ).

% combine_options_cases
tff(fact_103_combine__options__cases,axiom,
    ! [X2: option_num,P: fun_op493924057549976310_num_o,Y: option_num] :
      ( ( ( X2 = none_num )
       => aa_option_num_o(aa_opt8674010985164783839_num_o(P,X2),Y) )
     => ( ( ( Y = none_num )
         => aa_option_num_o(aa_opt8674010985164783839_num_o(P,X2),Y) )
       => ( ! [A3: num,B2: num] :
              ( ( X2 = aa_num_option_num(some_num,A3) )
             => ( ( Y = aa_num_option_num(some_num,B2) )
               => aa_option_num_o(aa_opt8674010985164783839_num_o(P,X2),Y) ) )
         => aa_option_num_o(aa_opt8674010985164783839_num_o(P,X2),Y) ) ) ) ).

% combine_options_cases
tff(fact_104_combine__options__cases,axiom,
    ! [X2: option_num,P: fun_op298641349230941576_nat_o,Y: option8956607266484857688it_nat] :
      ( ( ( X2 = none_num )
       => aa_opt8360315729766332930_nat_o(aa_opt6324340006354107505_nat_o(P,X2),Y) )
     => ( ( ( Y = none_P9117596204409417319it_nat )
         => aa_opt8360315729766332930_nat_o(aa_opt6324340006354107505_nat_o(P,X2),Y) )
       => ( ! [A3: num,B2: produc8664842809031399944it_nat] :
              ( ( X2 = aa_num_option_num(some_num,A3) )
             => ( ( Y = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,B2) )
               => aa_opt8360315729766332930_nat_o(aa_opt6324340006354107505_nat_o(P,X2),Y) ) )
         => aa_opt8360315729766332930_nat_o(aa_opt6324340006354107505_nat_o(P,X2),Y) ) ) ) ).

% combine_options_cases
tff(fact_105_combine__options__cases,axiom,
    ! [X2: option8956607266484857688it_nat,P: fun_op8703326495438967718_nat_o,Y: option3216581401566546698it_nat] :
      ( ( ( X2 = none_P9117596204409417319it_nat )
       => aa_opt4809530629565672394_nat_o(aa_opt3816109826176937319_nat_o(P,X2),Y) )
     => ( ( ( Y = none_P2587165478634041381it_nat )
         => aa_opt4809530629565672394_nat_o(aa_opt3816109826176937319_nat_o(P,X2),Y) )
       => ( ! [A3: produc8664842809031399944it_nat,B2: produc6714399278180371524it_nat] :
              ( ( X2 = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,A3) )
             => ( ( Y = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,B2) )
               => aa_opt4809530629565672394_nat_o(aa_opt3816109826176937319_nat_o(P,X2),Y) ) )
         => aa_opt4809530629565672394_nat_o(aa_opt3816109826176937319_nat_o(P,X2),Y) ) ) ) ).

% combine_options_cases
tff(fact_106_combine__options__cases,axiom,
    ! [X2: option8956607266484857688it_nat,P: fun_op6018817604785332104_num_o,Y: option_num] :
      ( ( ( X2 = none_P9117596204409417319it_nat )
       => aa_option_num_o(aa_opt3964967581558639985_num_o(P,X2),Y) )
     => ( ( ( Y = none_num )
         => aa_option_num_o(aa_opt3964967581558639985_num_o(P,X2),Y) )
       => ( ! [A3: produc8664842809031399944it_nat,B2: num] :
              ( ( X2 = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,A3) )
             => ( ( Y = aa_num_option_num(some_num,B2) )
               => aa_option_num_o(aa_opt3964967581558639985_num_o(P,X2),Y) ) )
         => aa_option_num_o(aa_opt3964967581558639985_num_o(P,X2),Y) ) ) ) ).

% combine_options_cases
tff(fact_107_combine__options__cases,axiom,
    ! [X2: option8956607266484857688it_nat,P: fun_op1633239139951409690_nat_o,Y: option8956607266484857688it_nat] :
      ( ( ( X2 = none_P9117596204409417319it_nat )
       => aa_opt8360315729766332930_nat_o(aa_opt6948326687743049987_nat_o(P,X2),Y) )
     => ( ( ( Y = none_P9117596204409417319it_nat )
         => aa_opt8360315729766332930_nat_o(aa_opt6948326687743049987_nat_o(P,X2),Y) )
       => ( ! [A3: produc8664842809031399944it_nat,B2: produc8664842809031399944it_nat] :
              ( ( X2 = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,A3) )
             => ( ( Y = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,B2) )
               => aa_opt8360315729766332930_nat_o(aa_opt6948326687743049987_nat_o(P,X2),Y) ) )
         => aa_opt8360315729766332930_nat_o(aa_opt6948326687743049987_nat_o(P,X2),Y) ) ) ) ).

% combine_options_cases
tff(fact_108_success__effectE,axiom,
    ! [C: heap_T5738788834812785303t_unit,Ha: heap_e7401611519738050253t_unit] :
      ( aa_hea7994211679605476167unit_o(heap_T584514906347983379t_unit(C),Ha)
     => ~ ! [R: product_unit,H2: heap_e7401611519738050253t_unit,N: nat] : ~ aa_nat_o(heap_T6553295506729943825t_unit(C,Ha,H2,R),N) ) ).

% success_effectE
tff(fact_109_success__effectE,axiom,
    ! [C: heap_T6362127782908069795rray_a,Ha: heap_e7401611519738050253t_unit] :
      ( aa_hea7994211679605476167unit_o(heap_T6932021131025641745rray_a(C),Ha)
     => ~ ! [R: array_a,H2: heap_e7401611519738050253t_unit,N: nat] : ~ aa_nat_o(heap_T5830633491639066771rray_a(C,Ha,H2,R),N) ) ).

% success_effectE
tff(fact_110_effect__success,axiom,
    ! [C: heap_T5738788834812785303t_unit,Ha: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit,R2: product_unit,N2: nat] :
      ( aa_nat_o(heap_T6553295506729943825t_unit(C,Ha,H3,R2),N2)
     => aa_hea7994211679605476167unit_o(heap_T584514906347983379t_unit(C),Ha) ) ).

% effect_success
tff(fact_111_effect__success,axiom,
    ! [C: heap_T6362127782908069795rray_a,Ha: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit,R2: array_a,N2: nat] :
      ( aa_nat_o(heap_T5830633491639066771rray_a(C,Ha,H3,R2),N2)
     => aa_hea7994211679605476167unit_o(heap_T6932021131025641745rray_a(C),Ha) ) ).

% effect_success
tff(fact_112_effect__raiseE,axiom,
    ! [X2: list_char,Ha: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit,R2: product_unit,N2: nat] : ~ aa_nat_o(heap_T6553295506729943825t_unit(heap_T2927564422264180874t_unit(X2),Ha,H3,R2),N2) ).

% effect_raiseE
tff(fact_113_effect__raiseE,axiom,
    ! [X2: list_char,Ha: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit,R2: array_a,N2: nat] : ~ aa_nat_o(heap_T5830633491639066771rray_a(heap_T1552190017797416154rray_a(X2),Ha,H3,R2),N2) ).

% effect_raiseE
tff(fact_114_the__default_Osimps_I1_J,axiom,
    ! [Uu: num,X2: num] : aa_option_num_num(the_default_num(Uu),aa_num_option_num(some_num,X2)) = X2 ).

% the_default.simps(1)
tff(fact_115_the__default_Osimps_I1_J,axiom,
    ! [Uu: produc8664842809031399944it_nat,X2: produc8664842809031399944it_nat] : the_de2487931475039285041it_nat(Uu,aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X2)) = X2 ).

% the_default.simps(1)
tff(fact_116_Heap__cases,axiom,
    ! [F: heap_T6362127782908069795rray_a,Ha: heap_e7401611519738050253t_unit] :
      ( ! [X3: array_a,H2: produc6653097349344004940it_nat] : aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(F),Ha) != aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,produc1733996804261680252it_nat(X3,H2))
     => ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(F),Ha) = none_P2587165478634041381it_nat ) ) ).

% Heap_cases
tff(fact_117_Heap__cases,axiom,
    ! [F: heap_T5738788834812785303t_unit,Ha: heap_e7401611519738050253t_unit] :
      ( ! [X3: product_unit,H2: produc6653097349344004940it_nat] : aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(F),Ha) != aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(X3,H2))
     => ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(F),Ha) = none_P9117596204409417319it_nat ) ) ).

% Heap_cases
tff(fact_118_successE,axiom,
    ! [F: heap_T5738788834812785303t_unit,Ha: heap_e7401611519738050253t_unit] :
      ( aa_hea7994211679605476167unit_o(heap_T584514906347983379t_unit(F),Ha)
     => ~ ! [R: product_unit,H2: produc6653097349344004940it_nat] : aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(F),Ha) != aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(R,H2)) ) ).

% successE
tff(fact_119_successE,axiom,
    ! [F: heap_T6362127782908069795rray_a,Ha: heap_e7401611519738050253t_unit] :
      ( aa_hea7994211679605476167unit_o(heap_T6932021131025641745rray_a(F),Ha)
     => ~ ! [R: array_a,H2: produc6653097349344004940it_nat] : aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(F),Ha) != aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,produc1733996804261680252it_nat(R,H2)) ) ).

% successE
tff(fact_120_execute__heap,axiom,
    ! [F: fun_he281446669002384250it_nat] : heap_T5591663578999710211rray_a(heap_T7473999186002612558rray_a(F)) = comp_P2097125496263478628t_unit(some_P6105628898608307625it_nat,F) ).

% execute_heap
tff(fact_121_execute__heap,axiom,
    ! [F: fun_he4944555133437423336it_nat] : heap_T875086893843062177t_unit(heap_T6927113302350381334t_unit(F)) = comp_P3118722334806803912t_unit(some_P1914260805536162275it_nat,F) ).

% execute_heap
tff(fact_122_some__opt__sym__eq__trivial,axiom,
    ! [X2: num] : eps_Opt_num(aa_num_fun_num_o(fequal_num,X2)) = aa_num_option_num(some_num,X2) ).

% some_opt_sym_eq_trivial
tff(fact_123_some__opt__sym__eq__trivial,axiom,
    ! [X2: produc8664842809031399944it_nat] : eps_Op3393321821070424684it_nat(fequal1407654770548522611it_nat(X2)) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X2) ).

% some_opt_sym_eq_trivial
tff(fact_124_success__newI,axiom,
    ! [N2: nat,X2: a,Ha: heap_e7401611519738050253t_unit] : aa_hea7994211679605476167unit_o(heap_T6932021131025641745rray_a(array_new_a(N2,X2)),Ha) ).

% success_newI
tff(fact_125_success__makeI,axiom,
    ! [N2: nat,F: fun_nat_a,Ha: heap_e7401611519738050253t_unit] : aa_hea7994211679605476167unit_o(heap_T6932021131025641745rray_a(array_make_a(N2,F)),Ha) ).

% success_makeI
tff(fact_126_mmupd__in__upd,axiom,
    ! [K: produc3843707927480180839at_nat,K2: set_Pr4329608150637261639at_nat,M: fun_Pr6553355248451873380on_num,V: num] :
      ( member8757157785044589968at_nat(K,K2)
     => ( aa_Pro6040048559569557on_num(map_mm2124855372588256220at_num(M,K2,V),K) = aa_num_option_num(some_num,V) ) ) ).

% mmupd_in_upd
tff(fact_127_mmupd__in__upd,axiom,
    ! [K: product_prod_nat_nat,K2: set_Pr1261947904930325089at_nat,M: fun_Pr7397166214287566974on_num,V: num] :
      ( member8440522571783428010at_nat(K,K2)
     => ( aa_Pro7308558959993556143on_num(map_mm6272435474268545910at_num(M,K2,V),K) = aa_num_option_num(some_num,V) ) ) ).

% mmupd_in_upd
tff(fact_128_mmupd__in__upd,axiom,
    ! [K: $o,K2: set_o,M: fun_o_option_num,V: num] :
      ( member_o((K),K2)
     => ( aa_o_option_num(map_mmupd_o_num(M,K2,V),(K)) = aa_num_option_num(some_num,V) ) ) ).

% mmupd_in_upd
tff(fact_129_mmupd__in__upd,axiom,
    ! [K: nat,K2: set_nat,M: fun_nat_option_num,V: num] :
      ( member_nat(K,K2)
     => ( aa_nat_option_num(map_mmupd_nat_num(M,K2,V),K) = aa_num_option_num(some_num,V) ) ) ).

% mmupd_in_upd
tff(fact_130_mmupd__in__upd,axiom,
    ! [K: int,K2: set_int,M: fun_int_option_num,V: num] :
      ( member_int(K,K2)
     => ( aa_int_option_num(map_mmupd_int_num(M,K2,V),K) = aa_num_option_num(some_num,V) ) ) ).

% mmupd_in_upd
tff(fact_131_mmupd__in__upd,axiom,
    ! [K: produc3843707927480180839at_nat,K2: set_Pr4329608150637261639at_nat,M: fun_Pr6865292569827446866it_nat,V: produc8664842809031399944it_nat] :
      ( member8757157785044589968at_nat(K,K2)
     => ( aa_Pro6559690566658787203it_nat(map_mm6227321356191524810it_nat(M,K2,V),K) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,V) ) ) ).

% mmupd_in_upd
tff(fact_132_mmupd__in__upd,axiom,
    ! [K: product_prod_nat_nat,K2: set_Pr1261947904930325089at_nat,M: fun_Pr6624299372562097772it_nat,V: produc8664842809031399944it_nat] :
      ( member8440522571783428010at_nat(K,K2)
     => ( aa_Pro5591324840913351069it_nat(map_mm8925508573636269924it_nat(M,K2,V),K) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,V) ) ) ).

% mmupd_in_upd
tff(fact_133_mmupd__in__upd,axiom,
    ! [K: $o,K2: set_o,M: fun_o_7229649064035662211it_nat,V: produc8664842809031399944it_nat] :
      ( member_o((K),K2)
     => ( aa_o_o5708127299350256820it_nat(map_mm4340940675810032635it_nat(M,K2,V),(K)) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,V) ) ) ).

% mmupd_in_upd
tff(fact_134_mmupd__in__upd,axiom,
    ! [K: nat,K2: set_nat,M: fun_na5667031169817407269it_nat,V: produc8664842809031399944it_nat] :
      ( member_nat(K,K2)
     => ( aa_nat3804989708481012326it_nat(map_mm4316137065318800191it_nat(M,K2,V),K) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,V) ) ) ).

% mmupd_in_upd
tff(fact_135_mmupd__in__upd,axiom,
    ! [K: int,K2: set_int,M: fun_in8543325783774419841it_nat,V: produc8664842809031399944it_nat] :
      ( member_int(K,K2)
     => ( aa_int6681284322438024898it_nat(map_mm5942422175790858651it_nat(M,K2,V),K) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,V) ) ) ).

% mmupd_in_upd
tff(fact_136_option_Ocollapse,axiom,
    ! [Option: option3216581401566546698it_nat] :
      ( ( Option != none_P2587165478634041381it_nat )
     => ( aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,aa_opt2040853179424174198it_nat(the_Pr5856008525237892824it_nat,Option)) = Option ) ) ).

% option.collapse
tff(fact_137_option_Ocollapse,axiom,
    ! [Option: option_num] :
      ( ( Option != none_num )
     => ( aa_num_option_num(some_num,aa_option_num_num(the_num,Option)) = Option ) ) ).

% option.collapse
tff(fact_138_option_Ocollapse,axiom,
    ! [Option: option8956607266484857688it_nat] :
      ( ( Option != none_P9117596204409417319it_nat )
     => ( aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,aa_opt6779208767223616030it_nat(the_Pr7776125533777466484it_nat,Option)) = Option ) ) ).

% option.collapse
tff(fact_139_not__Some__eq2,axiom,
    ! [V: option983905398058327270nteger] :
      ( ! [X4: fun_Pr5098669352780829690e_term,Y3: produc8923325533196201883nteger] : V != some_P7453818414240362097nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X4),Y3))
    <=> ( V = none_P612323165605163765nteger ) ) ).

% not_Some_eq2
tff(fact_140_not__Some__eq2,axiom,
    ! [V: option4955102875562834416et_nat] :
      ( ! [X4: fun_Pr6460944699146269935_nat_o,Y3: produc3658429121746597890et_nat] : V != some_P994283844982041979et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X4),Y3))
    <=> ( V = none_P7891021755743879167et_nat ) ) ).

% not_Some_eq2
tff(fact_141_not__Some__eq2,axiom,
    ! [V: option5899113203645146382et_nat] :
      ( ! [X4: fun_Pr6460944699146269935_nat_o,Y3: produc8799533983703829792et_nat] : V != some_P3006888012174695577et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X4),Y3))
    <=> ( V = none_P2758821087663475997et_nat ) ) ).

% not_Some_eq2
tff(fact_142_not__Some__eq2,axiom,
    ! [V: option1544258867535432659nt_int] :
      ( ! [X4: fun_Pr7763680713840462443e_term,Y3: product_prod_int_int] : V != some_P9145269820779039710nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X4),Y3))
    <=> ( V = none_P3112835510759997538nt_int ) ) ).

% not_Some_eq2
tff(fact_143_not__Some__eq2,axiom,
    ! [V: option6186025235080601855nt_int] :
      ( ! [X4: fun_in5730379987311621695e_term,Y3: product_prod_int_int] : V != some_P8798507657793832714nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X4),Y3))
    <=> ( V = none_P1716269551890668430nt_int ) ) ).

% not_Some_eq2
tff(fact_144_not__Some__eq2,axiom,
    ! [V: option3216581401566546698it_nat] :
      ( ! [X4: array_a,Y3: produc6653097349344004940it_nat] : V != aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,produc1733996804261680252it_nat(X4,Y3))
    <=> ( V = none_P2587165478634041381it_nat ) ) ).

% not_Some_eq2
tff(fact_145_not__Some__eq2,axiom,
    ! [V: option8956607266484857688it_nat] :
      ( ! [X4: product_unit,Y3: produc6653097349344004940it_nat] : V != aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(X4,Y3))
    <=> ( V = none_P9117596204409417319it_nat ) ) ).

% not_Some_eq2
tff(fact_146_effect__assertI,axiom,
    ! [P: fun_Product_unit_o,X2: product_unit,H3: heap_e7401611519738050253t_unit,Ha: heap_e7401611519738050253t_unit,R2: product_unit,N2: nat] :
      ( aa_Product_unit_o(P,X2)
     => ( ( H3 = Ha )
       => ( ( R2 = X2 )
         => ( ( N2 = one_one_nat )
           => aa_nat_o(heap_T6553295506729943825t_unit(aa_Pro1108561329362217960t_unit(heap_T4208721593536448476t_unit(P),X2),Ha,H3,R2),N2) ) ) ) ) ).

% effect_assertI
tff(fact_147_effect__assertI,axiom,
    ! [P: fun_array_a_o,X2: array_a,H3: heap_e7401611519738050253t_unit,Ha: heap_e7401611519738050253t_unit,R2: array_a,N2: nat] :
      ( aa_array_a_o(P,X2)
     => ( ( H3 = Ha )
       => ( ( R2 = X2 )
         => ( ( N2 = one_one_nat )
           => aa_nat_o(heap_T5830633491639066771rray_a(aa_arr1142863274018860686rray_a(heap_T7971689983404357896rray_a(P),X2),Ha,H3,R2),N2) ) ) ) ) ).

% effect_assertI
tff(fact_148_fun__comp__eq__conv,axiom,
    ! [F: fun_Co8499238673658658103nteger,G: fun_num_Code_integer,Fg: fun_num_Code_integer] :
      ( ( aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),G) = Fg )
    <=> ! [X4: num] : aa_Cod1783974652533396728nteger(F,aa_num_Code_integer(G,X4)) = aa_num_Code_integer(Fg,X4) ) ).

% fun_comp_eq_conv
tff(fact_149_fun__comp__eq__conv,axiom,
    ! [F: fun_Co1561183069634336733nteger,G: fun_Co8499238673658658103nteger,Fg: fun_Co1561183069634336733nteger] :
      ( ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),G) = Fg )
    <=> ! [X4: code_integer] : aa_Cod1978467581589928094nteger(F,aa_Cod1783974652533396728nteger(G,X4)) = aa_Cod1978467581589928094nteger(Fg,X4) ) ).

% fun_comp_eq_conv
tff(fact_150_fun__comp__eq__conv,axiom,
    ! [F: fun_fu4800041728187187127nteger,G: fun_Co1981900195452921617nteger,Fg: fun_Co1561183069634336733nteger] :
      ( ( comp_f6739083541385432444nteger(F,G) = Fg )
    <=> ! [X4: code_integer] : aa_fun2509385170507305080nteger(F,aa_Cod4161879620478718930nteger(G,X4)) = aa_Cod1978467581589928094nteger(Fg,X4) ) ).

% fun_comp_eq_conv
tff(fact_151_fun__comp__eq__conv,axiom,
    ! [F: fun_nat_num,G: fun_int_nat,Fg: fun_int_num] :
      ( ( aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),G) = Fg )
    <=> ! [X4: int] : aa_nat_num(F,aa_int_nat(G,X4)) = aa_int_num(Fg,X4) ) ).

% fun_comp_eq_conv
tff(fact_152_comp__cong__right,axiom,
    ! [X2: fun_num_Code_integer,Y: fun_num_Code_integer,F: fun_Co8499238673658658103nteger] :
      ( ( X2 = Y )
     => ( aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),X2) = aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),Y) ) ) ).

% comp_cong_right
tff(fact_153_comp__cong__right,axiom,
    ! [X2: fun_Co8499238673658658103nteger,Y: fun_Co8499238673658658103nteger,F: fun_Co1561183069634336733nteger] :
      ( ( X2 = Y )
     => ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),X2) = aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),Y) ) ) ).

% comp_cong_right
tff(fact_154_comp__cong__right,axiom,
    ! [X2: fun_Co1981900195452921617nteger,Y: fun_Co1981900195452921617nteger,F: fun_fu4800041728187187127nteger] :
      ( ( X2 = Y )
     => ( comp_f6739083541385432444nteger(F,X2) = comp_f6739083541385432444nteger(F,Y) ) ) ).

% comp_cong_right
tff(fact_155_comp__cong__right,axiom,
    ! [X2: fun_int_nat,Y: fun_int_nat,F: fun_nat_num] :
      ( ( X2 = Y )
     => ( aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),X2) = aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),Y) ) ) ).

% comp_cong_right
tff(fact_156_comp__cong__left,axiom,
    ! [X2: fun_Co8499238673658658103nteger,Y: fun_Co8499238673658658103nteger,F: fun_num_Code_integer] :
      ( ( X2 = Y )
     => ( aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,X2),F) = aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,Y),F) ) ) ).

% comp_cong_left
tff(fact_157_comp__cong__left,axiom,
    ! [X2: fun_Co1561183069634336733nteger,Y: fun_Co1561183069634336733nteger,F: fun_Co8499238673658658103nteger] :
      ( ( X2 = Y )
     => ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,X2),F) = aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,Y),F) ) ) ).

% comp_cong_left
tff(fact_158_comp__cong__left,axiom,
    ! [X2: fun_fu4800041728187187127nteger,Y: fun_fu4800041728187187127nteger,F: fun_Co1981900195452921617nteger] :
      ( ( X2 = Y )
     => ( comp_f6739083541385432444nteger(X2,F) = comp_f6739083541385432444nteger(Y,F) ) ) ).

% comp_cong_left
tff(fact_159_comp__cong__left,axiom,
    ! [X2: fun_nat_num,Y: fun_nat_num,F: fun_int_nat] :
      ( ( X2 = Y )
     => ( aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,X2),F) = aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,Y),F) ) ) ).

% comp_cong_left
tff(fact_160_bex2I,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,S2: set_Pr4329608150637261639at_nat,P: fun_se5639961202347202350_nat_o] :
      ( member8757157785044589968at_nat(produc2922128104949294807at_nat(A,B),S2)
     => ( ( member8757157785044589968at_nat(produc2922128104949294807at_nat(A,B),S2)
         => aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(P,A),B) )
       => ? [A3: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
            ( member8757157785044589968at_nat(produc2922128104949294807at_nat(A3,B2),S2)
            & aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(P,A3),B2) ) ) ) ).

% bex2I
tff(fact_161_bex2I,axiom,
    ! [A: nat,B: nat,S2: set_Pr1261947904930325089at_nat,P: fun_nat_fun_nat_o] :
      ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B),S2)
     => ( ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B),S2)
         => aa_nat_o(aa_nat_fun_nat_o(P,A),B) )
       => ? [A3: nat,B2: nat] :
            ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A3),B2),S2)
            & aa_nat_o(aa_nat_fun_nat_o(P,A3),B2) ) ) ) ).

% bex2I
tff(fact_162_bex2I,axiom,
    ! [A: fun_Pr5098669352780829690e_term,B: produc8923325533196201883nteger,S2: set_Pr3486312109254157132nteger,P: fun_fu7695273699059480439eger_o] :
      ( member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A),B),S2)
     => ( ( member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A),B),S2)
         => aa_Pro4926521453222654329eger_o(aa_fun4505422719058378424eger_o(P,A),B) )
       => ? [A3: fun_Pr5098669352780829690e_term,B2: produc8923325533196201883nteger] :
            ( member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A3),B2),S2)
            & aa_Pro4926521453222654329eger_o(aa_fun4505422719058378424eger_o(P,A3),B2) ) ) ) ).

% bex2I
tff(fact_163_bex2I,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,B: produc3658429121746597890et_nat,S2: set_Pr1312406793078187350et_nat,P: fun_fu8419763957888848259_nat_o] :
      ( member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A),B),S2)
     => ( ( member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A),B),S2)
         => aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(P,A),B) )
       => ? [A3: fun_Pr6460944699146269935_nat_o,B2: produc3658429121746597890et_nat] :
            ( member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A3),B2),S2)
            & aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(P,A3),B2) ) ) ) ).

% bex2I
tff(fact_164_bex2I,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,B: produc8799533983703829792et_nat,S2: set_Pr4040394263813967220et_nat,P: fun_fu2611741329380808165_nat_o] :
      ( member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A),B),S2)
     => ( ( member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A),B),S2)
         => aa_Pro5643009357358181178_nat_o(aa_fun912680268133416158_nat_o(P,A),B) )
       => ? [A3: fun_Pr6460944699146269935_nat_o,B2: produc8799533983703829792et_nat] :
            ( member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A3),B2),S2)
            & aa_Pro5643009357358181178_nat_o(aa_fun912680268133416158_nat_o(P,A3),B2) ) ) ) ).

% bex2I
tff(fact_165_bex2I,axiom,
    ! [A: fun_Pr7763680713840462443e_term,B: product_prod_int_int,S2: set_Pr6700895561065273913nt_int,P: fun_fu6865642474282033866_int_o] :
      ( member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,A),B),S2)
     => ( ( member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,A),B),S2)
         => aa_Pro4592068669816069595_int_o(aa_fun3538162476766722827_int_o(P,A),B) )
       => ? [A3: fun_Pr7763680713840462443e_term,B2: product_prod_int_int] :
            ( member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,A3),B2),S2)
            & aa_Pro4592068669816069595_int_o(aa_fun3538162476766722827_int_o(P,A3),B2) ) ) ) ).

% bex2I
tff(fact_166_bex2I,axiom,
    ! [A: fun_in5730379987311621695e_term,B: product_prod_int_int,S2: set_Pr4166680992137330533nt_int,P: fun_fu2978539155105838238_int_o] :
      ( member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A),B),S2)
     => ( ( member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A),B),S2)
         => aa_Pro4592068669816069595_int_o(aa_fun586359091965693151_int_o(P,A),B) )
       => ? [A3: fun_in5730379987311621695e_term,B2: product_prod_int_int] :
            ( member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A3),B2),S2)
            & aa_Pro4592068669816069595_int_o(aa_fun586359091965693151_int_o(P,A3),B2) ) ) ) ).

% bex2I
tff(fact_167_pairself_Ocases,axiom,
    ! [X2: produc4788131091073775919nt_int] :
      ~ ! [F2: fun_in5730379987311621695e_term,A3: int,B2: int] : X2 != aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,F2),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A3),B2)) ).

% pairself.cases
tff(fact_168_fails__array__new,axiom,
    ! [N2: nat,X2: a,Ha: heap_e7401611519738050253t_unit] : ~ aa_hea7994211679605476167unit_o(time_fails_array_a(array_new_a(N2,X2)),Ha) ).

% fails_array_new
tff(fact_169_timeFrame_Ocases,axiom,
    ! [X2: produc2867611627572283311it_nat] :
      ( ! [N: nat,R: array_a,H: heap_e7401611519738050253t_unit,N3: nat] : X2 != produc3378006678175723489it_nat(N,aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,produc1733996804261680252it_nat(R,produc584006145561248582it_nat(H,N3))))
     => ~ ! [N: nat] : X2 != produc3378006678175723489it_nat(N,none_P2587165478634041381it_nat) ) ).

% timeFrame.cases
tff(fact_170_timeFrame_Ocases,axiom,
    ! [X2: produc3911288613690379145it_nat] :
      ( ! [N: nat,R: product_unit,H: heap_e7401611519738050253t_unit,N3: nat] : X2 != produc638857205735767105it_nat(N,aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(R,produc584006145561248582it_nat(H,N3))))
     => ~ ! [N: nat] : X2 != produc638857205735767105it_nat(N,none_P9117596204409417319it_nat) ) ).

% timeFrame.cases
tff(fact_171_execute__assert_I1_J,axiom,
    ! [P: fun_array_a_o,X2: array_a,Ha: heap_e7401611519738050253t_unit] :
      ( aa_array_a_o(P,X2)
     => ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(aa_arr1142863274018860686rray_a(heap_T7971689983404357896rray_a(P),X2)),Ha) = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,produc1733996804261680252it_nat(X2,produc584006145561248582it_nat(Ha,one_one_nat))) ) ) ).

% execute_assert(1)
tff(fact_172_execute__assert_I1_J,axiom,
    ! [P: fun_Product_unit_o,X2: product_unit,Ha: heap_e7401611519738050253t_unit] :
      ( aa_Product_unit_o(P,X2)
     => ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(aa_Pro1108561329362217960t_unit(heap_T4208721593536448476t_unit(P),X2)),Ha) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(X2,produc584006145561248582it_nat(Ha,one_one_nat))) ) ) ).

% execute_assert(1)
tff(fact_173_execute__tap,axiom,
    ! [F: fun_he7369252872201260279rray_a,Ha: heap_e7401611519738050253t_unit] : aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(heap_T2055650868554030641rray_a(F)),Ha) = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,produc1733996804261680252it_nat(aa_hea3268681801748734376rray_a(F,Ha),produc584006145561248582it_nat(Ha,one_one_nat))) ).

% execute_tap
tff(fact_174_execute__tap,axiom,
    ! [F: fun_he5123621388056232515t_unit,Ha: heap_e7401611519738050253t_unit] : aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(heap_T560649228465745139t_unit(F)),Ha) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(aa_hea4146273921685161788t_unit(F,Ha),produc584006145561248582it_nat(Ha,one_one_nat))) ).

% execute_tap
tff(fact_175_option_Osel,axiom,
    ! [X22: num] : aa_option_num_num(the_num,aa_num_option_num(some_num,X22)) = X22 ).

% option.sel
tff(fact_176_option_Osel,axiom,
    ! [X22: produc8664842809031399944it_nat] : aa_opt6779208767223616030it_nat(the_Pr7776125533777466484it_nat,aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X22)) = X22 ).

% option.sel
tff(fact_177_option_Oexpand,axiom,
    ! [Option: option3216581401566546698it_nat,Option2: option3216581401566546698it_nat] :
      ( ( ( Option = none_P2587165478634041381it_nat )
      <=> ( Option2 = none_P2587165478634041381it_nat ) )
     => ( ( ( Option != none_P2587165478634041381it_nat )
         => ( ( Option2 != none_P2587165478634041381it_nat )
           => ( aa_opt2040853179424174198it_nat(the_Pr5856008525237892824it_nat,Option) = aa_opt2040853179424174198it_nat(the_Pr5856008525237892824it_nat,Option2) ) ) )
       => ( Option = Option2 ) ) ) ).

% option.expand
tff(fact_178_option_Oexpand,axiom,
    ! [Option: option_num,Option2: option_num] :
      ( ( ( Option = none_num )
      <=> ( Option2 = none_num ) )
     => ( ( ( Option != none_num )
         => ( ( Option2 != none_num )
           => ( aa_option_num_num(the_num,Option) = aa_option_num_num(the_num,Option2) ) ) )
       => ( Option = Option2 ) ) ) ).

% option.expand
tff(fact_179_option_Oexpand,axiom,
    ! [Option: option8956607266484857688it_nat,Option2: option8956607266484857688it_nat] :
      ( ( ( Option = none_P9117596204409417319it_nat )
      <=> ( Option2 = none_P9117596204409417319it_nat ) )
     => ( ( ( Option != none_P9117596204409417319it_nat )
         => ( ( Option2 != none_P9117596204409417319it_nat )
           => ( aa_opt6779208767223616030it_nat(the_Pr7776125533777466484it_nat,Option) = aa_opt6779208767223616030it_nat(the_Pr7776125533777466484it_nat,Option2) ) ) )
       => ( Option = Option2 ) ) ) ).

% option.expand
tff(fact_180_effect__def,axiom,
    ! [C: heap_T6362127782908069795rray_a,Ha: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit,R2: array_a,N2: nat] :
      ( aa_nat_o(heap_T5830633491639066771rray_a(C,Ha,H3,R2),N2)
    <=> ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(C),Ha) = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,produc1733996804261680252it_nat(R2,produc584006145561248582it_nat(H3,N2))) ) ) ).

% effect_def
tff(fact_181_effect__def,axiom,
    ! [C: heap_T5738788834812785303t_unit,Ha: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit,R2: product_unit,N2: nat] :
      ( aa_nat_o(heap_T6553295506729943825t_unit(C,Ha,H3,R2),N2)
    <=> ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(C),Ha) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(R2,produc584006145561248582it_nat(H3,N2))) ) ) ).

% effect_def
tff(fact_182_effectI,axiom,
    ! [C: heap_T6362127782908069795rray_a,Ha: heap_e7401611519738050253t_unit,R2: array_a,H3: heap_e7401611519738050253t_unit,N2: nat] :
      ( ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(C),Ha) = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,produc1733996804261680252it_nat(R2,produc584006145561248582it_nat(H3,N2))) )
     => aa_nat_o(heap_T5830633491639066771rray_a(C,Ha,H3,R2),N2) ) ).

% effectI
tff(fact_183_effectI,axiom,
    ! [C: heap_T5738788834812785303t_unit,Ha: heap_e7401611519738050253t_unit,R2: product_unit,H3: heap_e7401611519738050253t_unit,N2: nat] :
      ( ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(C),Ha) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(R2,produc584006145561248582it_nat(H3,N2))) )
     => aa_nat_o(heap_T6553295506729943825t_unit(C,Ha,H3,R2),N2) ) ).

% effectI
tff(fact_184_map__mmupd__def,axiom,
    ! [M: fun_Pr6553355248451873380on_num,K2: set_Pr4329608150637261639at_nat,V: num,K: produc3843707927480180839at_nat] :
      aa_Pro6040048559569557on_num(map_mm2124855372588256220at_num(M,K2,V),K) = $ite(member8757157785044589968at_nat(K,K2),aa_num_option_num(some_num,V),aa_Pro6040048559569557on_num(M,K)) ).

% map_mmupd_def
tff(fact_185_map__mmupd__def,axiom,
    ! [M: fun_Pr7397166214287566974on_num,K2: set_Pr1261947904930325089at_nat,V: num,K: product_prod_nat_nat] :
      aa_Pro7308558959993556143on_num(map_mm6272435474268545910at_num(M,K2,V),K) = $ite(member8440522571783428010at_nat(K,K2),aa_num_option_num(some_num,V),aa_Pro7308558959993556143on_num(M,K)) ).

% map_mmupd_def
tff(fact_186_map__mmupd__def,axiom,
    ! [M: fun_o_option_num,K2: set_o,V: num,K: $o] :
      aa_o_option_num(map_mmupd_o_num(M,K2,V),(K)) = $ite(member_o((K),K2),aa_num_option_num(some_num,V),aa_o_option_num(M,(K))) ).

% map_mmupd_def
tff(fact_187_map__mmupd__def,axiom,
    ! [M: fun_nat_option_num,K2: set_nat,V: num,K: nat] :
      aa_nat_option_num(map_mmupd_nat_num(M,K2,V),K) = $ite(member_nat(K,K2),aa_num_option_num(some_num,V),aa_nat_option_num(M,K)) ).

% map_mmupd_def
tff(fact_188_map__mmupd__def,axiom,
    ! [M: fun_int_option_num,K2: set_int,V: num,K: int] :
      aa_int_option_num(map_mmupd_int_num(M,K2,V),K) = $ite(member_int(K,K2),aa_num_option_num(some_num,V),aa_int_option_num(M,K)) ).

% map_mmupd_def
tff(fact_189_map__mmupd__def,axiom,
    ! [M: fun_Pr6865292569827446866it_nat,K2: set_Pr4329608150637261639at_nat,V: produc8664842809031399944it_nat,K: produc3843707927480180839at_nat] :
      aa_Pro6559690566658787203it_nat(map_mm6227321356191524810it_nat(M,K2,V),K) = $ite(member8757157785044589968at_nat(K,K2),aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,V),aa_Pro6559690566658787203it_nat(M,K)) ).

% map_mmupd_def
tff(fact_190_map__mmupd__def,axiom,
    ! [M: fun_Pr6624299372562097772it_nat,K2: set_Pr1261947904930325089at_nat,V: produc8664842809031399944it_nat,K: product_prod_nat_nat] :
      aa_Pro5591324840913351069it_nat(map_mm8925508573636269924it_nat(M,K2,V),K) = $ite(member8440522571783428010at_nat(K,K2),aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,V),aa_Pro5591324840913351069it_nat(M,K)) ).

% map_mmupd_def
tff(fact_191_map__mmupd__def,axiom,
    ! [M: fun_o_7229649064035662211it_nat,K2: set_o,V: produc8664842809031399944it_nat,K: $o] :
      aa_o_o5708127299350256820it_nat(map_mm4340940675810032635it_nat(M,K2,V),(K)) = $ite(member_o((K),K2),aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,V),aa_o_o5708127299350256820it_nat(M,(K))) ).

% map_mmupd_def
tff(fact_192_map__mmupd__def,axiom,
    ! [M: fun_na5667031169817407269it_nat,K2: set_nat,V: produc8664842809031399944it_nat,K: nat] :
      aa_nat3804989708481012326it_nat(map_mm4316137065318800191it_nat(M,K2,V),K) = $ite(member_nat(K,K2),aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,V),aa_nat3804989708481012326it_nat(M,K)) ).

% map_mmupd_def
tff(fact_193_map__mmupd__def,axiom,
    ! [M: fun_in8543325783774419841it_nat,K2: set_int,V: produc8664842809031399944it_nat,K: int] :
      aa_int6681284322438024898it_nat(map_mm5942422175790858651it_nat(M,K2,V),K) = $ite(member_int(K,K2),aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,V),aa_int6681284322438024898it_nat(M,K)) ).

% map_mmupd_def
tff(fact_194_map__mmupdE,axiom,
    ! [M: fun_Pr6553355248451873380on_num,K2: set_Pr4329608150637261639at_nat,V: num,K: produc3843707927480180839at_nat,X2: num] :
      ( ( aa_Pro6040048559569557on_num(map_mm2124855372588256220at_num(M,K2,V),K) = aa_num_option_num(some_num,X2) )
     => ( ( ~ member8757157785044589968at_nat(K,K2)
         => ( aa_Pro6040048559569557on_num(M,K) != aa_num_option_num(some_num,X2) ) )
       => ~ ( member8757157785044589968at_nat(K,K2)
           => ( X2 != V ) ) ) ) ).

% map_mmupdE
tff(fact_195_map__mmupdE,axiom,
    ! [M: fun_Pr7397166214287566974on_num,K2: set_Pr1261947904930325089at_nat,V: num,K: product_prod_nat_nat,X2: num] :
      ( ( aa_Pro7308558959993556143on_num(map_mm6272435474268545910at_num(M,K2,V),K) = aa_num_option_num(some_num,X2) )
     => ( ( ~ member8440522571783428010at_nat(K,K2)
         => ( aa_Pro7308558959993556143on_num(M,K) != aa_num_option_num(some_num,X2) ) )
       => ~ ( member8440522571783428010at_nat(K,K2)
           => ( X2 != V ) ) ) ) ).

% map_mmupdE
tff(fact_196_map__mmupdE,axiom,
    ! [M: fun_o_option_num,K2: set_o,V: num,K: $o,X2: num] :
      ( ( aa_o_option_num(map_mmupd_o_num(M,K2,V),(K)) = aa_num_option_num(some_num,X2) )
     => ( ( ~ member_o((K),K2)
         => ( aa_o_option_num(M,(K)) != aa_num_option_num(some_num,X2) ) )
       => ~ ( member_o((K),K2)
           => ( X2 != V ) ) ) ) ).

% map_mmupdE
tff(fact_197_map__mmupdE,axiom,
    ! [M: fun_nat_option_num,K2: set_nat,V: num,K: nat,X2: num] :
      ( ( aa_nat_option_num(map_mmupd_nat_num(M,K2,V),K) = aa_num_option_num(some_num,X2) )
     => ( ( ~ member_nat(K,K2)
         => ( aa_nat_option_num(M,K) != aa_num_option_num(some_num,X2) ) )
       => ~ ( member_nat(K,K2)
           => ( X2 != V ) ) ) ) ).

% map_mmupdE
tff(fact_198_map__mmupdE,axiom,
    ! [M: fun_int_option_num,K2: set_int,V: num,K: int,X2: num] :
      ( ( aa_int_option_num(map_mmupd_int_num(M,K2,V),K) = aa_num_option_num(some_num,X2) )
     => ( ( ~ member_int(K,K2)
         => ( aa_int_option_num(M,K) != aa_num_option_num(some_num,X2) ) )
       => ~ ( member_int(K,K2)
           => ( X2 != V ) ) ) ) ).

% map_mmupdE
tff(fact_199_map__mmupdE,axiom,
    ! [M: fun_Pr6865292569827446866it_nat,K2: set_Pr4329608150637261639at_nat,V: produc8664842809031399944it_nat,K: produc3843707927480180839at_nat,X2: produc8664842809031399944it_nat] :
      ( ( aa_Pro6559690566658787203it_nat(map_mm6227321356191524810it_nat(M,K2,V),K) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X2) )
     => ( ( ~ member8757157785044589968at_nat(K,K2)
         => ( aa_Pro6559690566658787203it_nat(M,K) != aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X2) ) )
       => ~ ( member8757157785044589968at_nat(K,K2)
           => ( X2 != V ) ) ) ) ).

% map_mmupdE
tff(fact_200_map__mmupdE,axiom,
    ! [M: fun_Pr6624299372562097772it_nat,K2: set_Pr1261947904930325089at_nat,V: produc8664842809031399944it_nat,K: product_prod_nat_nat,X2: produc8664842809031399944it_nat] :
      ( ( aa_Pro5591324840913351069it_nat(map_mm8925508573636269924it_nat(M,K2,V),K) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X2) )
     => ( ( ~ member8440522571783428010at_nat(K,K2)
         => ( aa_Pro5591324840913351069it_nat(M,K) != aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X2) ) )
       => ~ ( member8440522571783428010at_nat(K,K2)
           => ( X2 != V ) ) ) ) ).

% map_mmupdE
tff(fact_201_map__mmupdE,axiom,
    ! [M: fun_o_7229649064035662211it_nat,K2: set_o,V: produc8664842809031399944it_nat,K: $o,X2: produc8664842809031399944it_nat] :
      ( ( aa_o_o5708127299350256820it_nat(map_mm4340940675810032635it_nat(M,K2,V),(K)) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X2) )
     => ( ( ~ member_o((K),K2)
         => ( aa_o_o5708127299350256820it_nat(M,(K)) != aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X2) ) )
       => ~ ( member_o((K),K2)
           => ( X2 != V ) ) ) ) ).

% map_mmupdE
tff(fact_202_map__mmupdE,axiom,
    ! [M: fun_na5667031169817407269it_nat,K2: set_nat,V: produc8664842809031399944it_nat,K: nat,X2: produc8664842809031399944it_nat] :
      ( ( aa_nat3804989708481012326it_nat(map_mm4316137065318800191it_nat(M,K2,V),K) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X2) )
     => ( ( ~ member_nat(K,K2)
         => ( aa_nat3804989708481012326it_nat(M,K) != aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X2) ) )
       => ~ ( member_nat(K,K2)
           => ( X2 != V ) ) ) ) ).

% map_mmupdE
tff(fact_203_map__mmupdE,axiom,
    ! [M: fun_in8543325783774419841it_nat,K2: set_int,V: produc8664842809031399944it_nat,K: int,X2: produc8664842809031399944it_nat] :
      ( ( aa_int6681284322438024898it_nat(map_mm5942422175790858651it_nat(M,K2,V),K) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X2) )
     => ( ( ~ member_int(K,K2)
         => ( aa_int6681284322438024898it_nat(M,K) != aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X2) ) )
       => ~ ( member_int(K,K2)
           => ( X2 != V ) ) ) ) ).

% map_mmupdE
tff(fact_204_success__bind__executeI,axiom,
    ! [F: heap_T6362127782908069795rray_a,Ha: heap_e7401611519738050253t_unit,X2: array_a,H3: heap_e7401611519738050253t_unit,N2: nat,G: fun_ar1074044450438384043t_unit] :
      ( ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(F),Ha) = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,produc1733996804261680252it_nat(X2,produc584006145561248582it_nat(H3,N2))) )
     => ( aa_hea7994211679605476167unit_o(heap_T584514906347983379t_unit(aa_arr7999650297717212780t_unit(G,X2)),H3)
       => aa_hea7994211679605476167unit_o(heap_T584514906347983379t_unit(heap_T7324619625323989613t_unit(F,G)),Ha) ) ) ).

% success_bind_executeI
tff(fact_205_success__bind__executeI,axiom,
    ! [F: heap_T5738788834812785303t_unit,Ha: heap_e7401611519738050253t_unit,X2: product_unit,H3: heap_e7401611519738050253t_unit,N2: nat,G: fun_Pr292408699144966967t_unit] :
      ( ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(F),Ha) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(X2,produc584006145561248582it_nat(H3,N2))) )
     => ( aa_hea7994211679605476167unit_o(heap_T584514906347983379t_unit(aa_Pro1108561329362217960t_unit(G,X2)),H3)
       => aa_hea7994211679605476167unit_o(heap_T584514906347983379t_unit(heap_T2633723481742716231t_unit(F,G)),Ha) ) ) ).

% success_bind_executeI
tff(fact_206_success__bind__executeI,axiom,
    ! [F: heap_T6362127782908069795rray_a,Ha: heap_e7401611519738050253t_unit,X2: array_a,H3: heap_e7401611519738050253t_unit,N2: nat,G: fun_ar3891948820113774757rray_a] :
      ( ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(F),Ha) = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,produc1733996804261680252it_nat(X2,produc584006145561248582it_nat(H3,N2))) )
     => ( aa_hea7994211679605476167unit_o(heap_T6932021131025641745rray_a(aa_arr1142863274018860686rray_a(G,X2)),H3)
       => aa_hea7994211679605476167unit_o(heap_T6932021131025641745rray_a(heap_T2407400398799471159rray_a(F,G)),Ha) ) ) ).

% success_bind_executeI
tff(fact_207_success__bind__executeI,axiom,
    ! [F: heap_T5738788834812785303t_unit,Ha: heap_e7401611519738050253t_unit,X2: product_unit,H3: heap_e7401611519738050253t_unit,N2: nat,G: fun_Pr5924905948197006361rray_a] :
      ( ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(F),Ha) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(X2,produc584006145561248582it_nat(H3,N2))) )
     => ( aa_hea7994211679605476167unit_o(heap_T6932021131025641745rray_a(aa_Pro755961224256580114rray_a(G,X2)),H3)
       => aa_hea7994211679605476167unit_o(heap_T6932021131025641745rray_a(heap_T7158140910958840029rray_a(F,G)),Ha) ) ) ).

% success_bind_executeI
tff(fact_208_Eps__Opt__eq__Some__implies,axiom,
    ! [P: fun_num_o,X2: num] :
      ( ( eps_Opt_num(P) = aa_num_option_num(some_num,X2) )
     => aa_num_o(P,X2) ) ).

% Eps_Opt_eq_Some_implies
tff(fact_209_Eps__Opt__eq__Some__implies,axiom,
    ! [P: fun_Pr8032424337255632745_nat_o,X2: produc8664842809031399944it_nat] :
      ( ( eps_Op3393321821070424684it_nat(P) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X2) )
     => aa_Pro4744234731172327378_nat_o(P,X2) ) ).

% Eps_Opt_eq_Some_implies
tff(fact_210_Eps__Opt__eq__Some,axiom,
    ! [P: fun_num_o,X2: num] :
      ( ! [X5: num] :
          ( aa_num_o(P,X2)
         => ( aa_num_o(P,X5)
           => ( X5 = X2 ) ) )
     => ( ( eps_Opt_num(P) = aa_num_option_num(some_num,X2) )
      <=> aa_num_o(P,X2) ) ) ).

% Eps_Opt_eq_Some
tff(fact_211_Eps__Opt__eq__Some,axiom,
    ! [P: fun_Pr8032424337255632745_nat_o,X2: produc8664842809031399944it_nat] :
      ( ! [X5: produc8664842809031399944it_nat] :
          ( aa_Pro4744234731172327378_nat_o(P,X2)
         => ( aa_Pro4744234731172327378_nat_o(P,X5)
           => ( X5 = X2 ) ) )
     => ( ( eps_Op3393321821070424684it_nat(P) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X2) )
      <=> aa_Pro4744234731172327378_nat_o(P,X2) ) ) ).

% Eps_Opt_eq_Some
tff(fact_212_option_Oexhaust__sel,axiom,
    ! [Option: option3216581401566546698it_nat] :
      ( ( Option != none_P2587165478634041381it_nat )
     => ( Option = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,aa_opt2040853179424174198it_nat(the_Pr5856008525237892824it_nat,Option)) ) ) ).

% option.exhaust_sel
tff(fact_213_option_Oexhaust__sel,axiom,
    ! [Option: option_num] :
      ( ( Option != none_num )
     => ( Option = aa_num_option_num(some_num,aa_option_num_num(the_num,Option)) ) ) ).

% option.exhaust_sel
tff(fact_214_option_Oexhaust__sel,axiom,
    ! [Option: option8956607266484857688it_nat] :
      ( ( Option != none_P9117596204409417319it_nat )
     => ( Option = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,aa_opt6779208767223616030it_nat(the_Pr7776125533777466484it_nat,Option)) ) ) ).

% option.exhaust_sel
tff(fact_215_effect__assertE,axiom,
    ! [P: fun_Product_unit_o,X2: product_unit,Ha: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit,R2: product_unit,N2: nat] :
      ( aa_nat_o(heap_T6553295506729943825t_unit(aa_Pro1108561329362217960t_unit(heap_T4208721593536448476t_unit(P),X2),Ha,H3,R2),N2)
     => ~ ( aa_Product_unit_o(P,X2)
         => ( ( R2 = X2 )
           => ( ( H3 = Ha )
             => ( N2 != one_one_nat ) ) ) ) ) ).

% effect_assertE
tff(fact_216_effect__assertE,axiom,
    ! [P: fun_array_a_o,X2: array_a,Ha: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit,R2: array_a,N2: nat] :
      ( aa_nat_o(heap_T5830633491639066771rray_a(aa_arr1142863274018860686rray_a(heap_T7971689983404357896rray_a(P),X2),Ha,H3,R2),N2)
     => ~ ( aa_array_a_o(P,X2)
         => ( ( R2 = X2 )
           => ( ( H3 = Ha )
             => ( N2 != one_one_nat ) ) ) ) ) ).

% effect_assertE
tff(fact_217_comp__apply,axiom,
    ! [F: fun_Co8499238673658658103nteger,G: fun_num_Code_integer,X2: num] : aa_num_Code_integer(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),G),X2) = aa_Cod1783974652533396728nteger(F,aa_num_Code_integer(G,X2)) ).

% comp_apply
tff(fact_218_comp__apply,axiom,
    ! [F: fun_Co1561183069634336733nteger,G: fun_Co8499238673658658103nteger,X2: code_integer] : aa_Cod1978467581589928094nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),G),X2) = aa_Cod1978467581589928094nteger(F,aa_Cod1783974652533396728nteger(G,X2)) ).

% comp_apply
tff(fact_219_comp__apply,axiom,
    ! [F: fun_fu4800041728187187127nteger,G: fun_Co1981900195452921617nteger,X2: code_integer] : aa_Cod1978467581589928094nteger(comp_f6739083541385432444nteger(F,G),X2) = aa_fun2509385170507305080nteger(F,aa_Cod4161879620478718930nteger(G,X2)) ).

% comp_apply
tff(fact_220_comp__apply,axiom,
    ! [F: fun_nat_num,G: fun_int_nat,X2: int] : aa_int_num(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),G),X2) = aa_nat_num(F,aa_int_nat(G,X2)) ).

% comp_apply
tff(fact_221_prod_Oinject,axiom,
    ! [X1: fun_Pr5098669352780829690e_term,X22: produc8923325533196201883nteger,Y1: fun_Pr5098669352780829690e_term,Y2: produc8923325533196201883nteger] :
      ( ( aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X1),X22) = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,Y1),Y2) )
    <=> ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% prod.inject
tff(fact_222_prod_Oinject,axiom,
    ! [X1: fun_Pr6460944699146269935_nat_o,X22: produc3658429121746597890et_nat,Y1: fun_Pr6460944699146269935_nat_o,Y2: produc3658429121746597890et_nat] :
      ( ( aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X1),X22) = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,Y1),Y2) )
    <=> ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% prod.inject
tff(fact_223_prod_Oinject,axiom,
    ! [X1: fun_Pr6460944699146269935_nat_o,X22: produc8799533983703829792et_nat,Y1: fun_Pr6460944699146269935_nat_o,Y2: produc8799533983703829792et_nat] :
      ( ( aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X1),X22) = aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,Y1),Y2) )
    <=> ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% prod.inject
tff(fact_224_prod_Oinject,axiom,
    ! [X1: fun_Pr7763680713840462443e_term,X22: product_prod_int_int,Y1: fun_Pr7763680713840462443e_term,Y2: product_prod_int_int] :
      ( ( aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X1),X22) = aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,Y1),Y2) )
    <=> ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% prod.inject
tff(fact_225_prod_Oinject,axiom,
    ! [X1: fun_in5730379987311621695e_term,X22: product_prod_int_int,Y1: fun_in5730379987311621695e_term,Y2: product_prod_int_int] :
      ( ( aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X1),X22) = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,Y1),Y2) )
    <=> ( ( X1 = Y1 )
        & ( X22 = Y2 ) ) ) ).

% prod.inject
tff(fact_226_old_Oprod_Oinject,axiom,
    ! [A: fun_Pr5098669352780829690e_term,B: produc8923325533196201883nteger,A4: fun_Pr5098669352780829690e_term,B3: produc8923325533196201883nteger] :
      ( ( aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A),B) = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A4),B3) )
    <=> ( ( A = A4 )
        & ( B = B3 ) ) ) ).

% old.prod.inject
tff(fact_227_old_Oprod_Oinject,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,B: produc3658429121746597890et_nat,A4: fun_Pr6460944699146269935_nat_o,B3: produc3658429121746597890et_nat] :
      ( ( aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A),B) = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A4),B3) )
    <=> ( ( A = A4 )
        & ( B = B3 ) ) ) ).

% old.prod.inject
tff(fact_228_old_Oprod_Oinject,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,B: produc8799533983703829792et_nat,A4: fun_Pr6460944699146269935_nat_o,B3: produc8799533983703829792et_nat] :
      ( ( aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A),B) = aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A4),B3) )
    <=> ( ( A = A4 )
        & ( B = B3 ) ) ) ).

% old.prod.inject
tff(fact_229_old_Oprod_Oinject,axiom,
    ! [A: fun_Pr7763680713840462443e_term,B: product_prod_int_int,A4: fun_Pr7763680713840462443e_term,B3: product_prod_int_int] :
      ( ( aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,A),B) = aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,A4),B3) )
    <=> ( ( A = A4 )
        & ( B = B3 ) ) ) ).

% old.prod.inject
tff(fact_230_old_Oprod_Oinject,axiom,
    ! [A: fun_in5730379987311621695e_term,B: product_prod_int_int,A4: fun_in5730379987311621695e_term,B3: product_prod_int_int] :
      ( ( aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A),B) = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A4),B3) )
    <=> ( ( A = A4 )
        & ( B = B3 ) ) ) ).

% old.prod.inject
tff(fact_231_execute__bind_I1_J,axiom,
    ! [F: heap_T6362127782908069795rray_a,Ha: heap_e7401611519738050253t_unit,X2: array_a,H3: heap_e7401611519738050253t_unit,N2: nat,G: fun_ar3891948820113774757rray_a] :
      ( ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(F),Ha) = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,produc1733996804261680252it_nat(X2,produc584006145561248582it_nat(H3,N2))) )
     => ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(heap_T2407400398799471159rray_a(F,G)),Ha) = heap_T531568236820715630rray_a(N2,aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(aa_arr1142863274018860686rray_a(G,X2)),H3)) ) ) ).

% execute_bind(1)
tff(fact_232_execute__bind_I1_J,axiom,
    ! [F: heap_T6362127782908069795rray_a,Ha: heap_e7401611519738050253t_unit,X2: array_a,H3: heap_e7401611519738050253t_unit,N2: nat,G: fun_ar1074044450438384043t_unit] :
      ( ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(F),Ha) = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,produc1733996804261680252it_nat(X2,produc584006145561248582it_nat(H3,N2))) )
     => ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(heap_T7324619625323989613t_unit(F,G)),Ha) = heap_T3616969660504097270t_unit(N2,aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(aa_arr7999650297717212780t_unit(G,X2)),H3)) ) ) ).

% execute_bind(1)
tff(fact_233_execute__bind_I1_J,axiom,
    ! [F: heap_T5738788834812785303t_unit,Ha: heap_e7401611519738050253t_unit,X2: product_unit,H3: heap_e7401611519738050253t_unit,N2: nat,G: fun_Pr5924905948197006361rray_a] :
      ( ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(F),Ha) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(X2,produc584006145561248582it_nat(H3,N2))) )
     => ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(heap_T7158140910958840029rray_a(F,G)),Ha) = heap_T531568236820715630rray_a(N2,aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(aa_Pro755961224256580114rray_a(G,X2)),H3)) ) ) ).

% execute_bind(1)
tff(fact_234_execute__bind_I1_J,axiom,
    ! [F: heap_T5738788834812785303t_unit,Ha: heap_e7401611519738050253t_unit,X2: product_unit,H3: heap_e7401611519738050253t_unit,N2: nat,G: fun_Pr292408699144966967t_unit] :
      ( ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(F),Ha) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(X2,produc584006145561248582it_nat(H3,N2))) )
     => ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(heap_T2633723481742716231t_unit(F,G)),Ha) = heap_T3616969660504097270t_unit(N2,aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(aa_Pro1108561329362217960t_unit(G,X2)),H3)) ) ) ).

% execute_bind(1)
tff(fact_235_prod__cases3,axiom,
    ! [Y: produc2453742332425399446nteger] :
      ~ ! [A3: fun_Pr5098669352780829690e_term,B2: code_integer,C2: code_integer] : Y != aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A3),aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(B2),C2)) ).

% prod_cases3
tff(fact_236_prod__cases3,axiom,
    ! [Y: produc8799533983703829792et_nat] :
      ~ ! [A3: fun_Pr6460944699146269935_nat_o,B2: heap_e7401611519738050253t_unit,C2: set_nat] : Y != aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A3),produc7507926704131184380et_nat(B2,C2)) ).

% prod_cases3
tff(fact_237_prod__cases3,axiom,
    ! [Y: produc3112576180687729086et_nat] :
      ~ ! [A3: fun_Pr6460944699146269935_nat_o,B2: fun_Pr6460944699146269935_nat_o,C2: produc3658429121746597890et_nat] : Y != aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A3),aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,B2),C2)) ).

% prod_cases3
tff(fact_238_prod__cases3,axiom,
    ! [Y: produc3043004577601930755nt_int] :
      ~ ! [A3: fun_Pr7763680713840462443e_term,B2: int,C2: int] : Y != aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,A3),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,B2),C2)) ).

% prod_cases3
tff(fact_239_prod__cases3,axiom,
    ! [Y: produc4788131091073775919nt_int] :
      ~ ! [A3: fun_in5730379987311621695e_term,B2: int,C2: int] : Y != aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A3),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,B2),C2)) ).

% prod_cases3
tff(fact_240_prod__cases4,axiom,
    ! [Y: produc3112576180687729086et_nat] :
      ~ ! [A3: fun_Pr6460944699146269935_nat_o,B2: fun_Pr6460944699146269935_nat_o,C2: heap_e7401611519738050253t_unit,D: set_nat] : Y != aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A3),aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,B2),produc7507926704131184380et_nat(C2,D))) ).

% prod_cases4
tff(fact_241_prod__induct3,axiom,
    ! [P: fun_Pr7015759342434529115eger_o,X2: produc2453742332425399446nteger] :
      ( ! [A3: fun_Pr5098669352780829690e_term,B2: code_integer,C2: code_integer] : aa_Pro4148064003102580676eger_o(P,aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A3),aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(B2),C2)))
     => aa_Pro4148064003102580676eger_o(P,X2) ) ).

% prod_induct3
tff(fact_242_prod__induct3,axiom,
    ! [P: fun_Pr2620521676128474833_nat_o,X2: produc8799533983703829792et_nat] :
      ( ! [A3: fun_Pr6460944699146269935_nat_o,B2: heap_e7401611519738050253t_unit,C2: set_nat] : aa_Pro5643009357358181178_nat_o(P,aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A3),produc7507926704131184380et_nat(B2,C2)))
     => aa_Pro5643009357358181178_nat_o(P,X2) ) ).

% prod_induct3
tff(fact_243_prod__induct3,axiom,
    ! [P: fun_Pr1227177680593602867_nat_o,X2: produc3112576180687729086et_nat] :
      ( ! [A3: fun_Pr6460944699146269935_nat_o,B2: fun_Pr6460944699146269935_nat_o,C2: produc3658429121746597890et_nat] : aa_Pro2671238023309943196_nat_o(P,aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A3),aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,B2),C2)))
     => aa_Pro2671238023309943196_nat_o(P,X2) ) ).

% prod_induct3
tff(fact_244_prod__induct3,axiom,
    ! [P: fun_Pr3540825087398332590_int_o,X2: produc3043004577601930755nt_int] :
      ( ! [A3: fun_Pr7763680713840462443e_term,B2: int,C2: int] : aa_Pro2601676399929874711_int_o(P,aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,A3),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,B2),C2)))
     => aa_Pro2601676399929874711_int_o(P,X2) ) ).

% prod_induct3
tff(fact_245_prod__induct3,axiom,
    ! [P: fun_Pr1196100989263358594_int_o,X2: produc4788131091073775919nt_int] :
      ( ! [A3: fun_in5730379987311621695e_term,B2: int,C2: int] : aa_Pro5451197003417746155_int_o(P,aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A3),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,B2),C2)))
     => aa_Pro5451197003417746155_int_o(P,X2) ) ).

% prod_induct3
tff(fact_246_prod__induct4,axiom,
    ! [P: fun_Pr1227177680593602867_nat_o,X2: produc3112576180687729086et_nat] :
      ( ! [A3: fun_Pr6460944699146269935_nat_o,B2: fun_Pr6460944699146269935_nat_o,C2: heap_e7401611519738050253t_unit,D: set_nat] : aa_Pro2671238023309943196_nat_o(P,aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A3),aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,B2),produc7507926704131184380et_nat(C2,D))))
     => aa_Pro2671238023309943196_nat_o(P,X2) ) ).

% prod_induct4
tff(fact_247_timeFrame_Osimps_I2_J,axiom,
    ! [N2: nat] : heap_T531568236820715630rray_a(N2,none_P2587165478634041381it_nat) = none_P2587165478634041381it_nat ).

% timeFrame.simps(2)
tff(fact_248_timeFrame_Osimps_I2_J,axiom,
    ! [N2: nat] : heap_T3616969660504097270t_unit(N2,none_P9117596204409417319it_nat) = none_P9117596204409417319it_nat ).

% timeFrame.simps(2)
tff(fact_249_Pair__inject,axiom,
    ! [A: fun_Pr5098669352780829690e_term,B: produc8923325533196201883nteger,A4: fun_Pr5098669352780829690e_term,B3: produc8923325533196201883nteger] :
      ( ( aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A),B) = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A4),B3) )
     => ~ ( ( A = A4 )
         => ( B != B3 ) ) ) ).

% Pair_inject
tff(fact_250_Pair__inject,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,B: produc3658429121746597890et_nat,A4: fun_Pr6460944699146269935_nat_o,B3: produc3658429121746597890et_nat] :
      ( ( aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A),B) = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A4),B3) )
     => ~ ( ( A = A4 )
         => ( B != B3 ) ) ) ).

% Pair_inject
tff(fact_251_Pair__inject,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,B: produc8799533983703829792et_nat,A4: fun_Pr6460944699146269935_nat_o,B3: produc8799533983703829792et_nat] :
      ( ( aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A),B) = aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A4),B3) )
     => ~ ( ( A = A4 )
         => ( B != B3 ) ) ) ).

% Pair_inject
tff(fact_252_Pair__inject,axiom,
    ! [A: fun_Pr7763680713840462443e_term,B: product_prod_int_int,A4: fun_Pr7763680713840462443e_term,B3: product_prod_int_int] :
      ( ( aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,A),B) = aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,A4),B3) )
     => ~ ( ( A = A4 )
         => ( B != B3 ) ) ) ).

% Pair_inject
tff(fact_253_Pair__inject,axiom,
    ! [A: fun_in5730379987311621695e_term,B: product_prod_int_int,A4: fun_in5730379987311621695e_term,B3: product_prod_int_int] :
      ( ( aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A),B) = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A4),B3) )
     => ~ ( ( A = A4 )
         => ( B != B3 ) ) ) ).

% Pair_inject
tff(fact_254_prod__cases,axiom,
    ! [P: fun_Pr7015759342434529115eger_o,P2: produc2453742332425399446nteger] :
      ( ! [A3: fun_Pr5098669352780829690e_term,B2: produc8923325533196201883nteger] : aa_Pro4148064003102580676eger_o(P,aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A3),B2))
     => aa_Pro4148064003102580676eger_o(P,P2) ) ).

% prod_cases
tff(fact_255_prod__cases,axiom,
    ! [P: fun_Pr2620521676128474833_nat_o,P2: produc8799533983703829792et_nat] :
      ( ! [A3: fun_Pr6460944699146269935_nat_o,B2: produc3658429121746597890et_nat] : aa_Pro5643009357358181178_nat_o(P,aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A3),B2))
     => aa_Pro5643009357358181178_nat_o(P,P2) ) ).

% prod_cases
tff(fact_256_prod__cases,axiom,
    ! [P: fun_Pr1227177680593602867_nat_o,P2: produc3112576180687729086et_nat] :
      ( ! [A3: fun_Pr6460944699146269935_nat_o,B2: produc8799533983703829792et_nat] : aa_Pro2671238023309943196_nat_o(P,aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A3),B2))
     => aa_Pro2671238023309943196_nat_o(P,P2) ) ).

% prod_cases
tff(fact_257_prod__cases,axiom,
    ! [P: fun_Pr3540825087398332590_int_o,P2: produc3043004577601930755nt_int] :
      ( ! [A3: fun_Pr7763680713840462443e_term,B2: product_prod_int_int] : aa_Pro2601676399929874711_int_o(P,aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,A3),B2))
     => aa_Pro2601676399929874711_int_o(P,P2) ) ).

% prod_cases
tff(fact_258_prod__cases,axiom,
    ! [P: fun_Pr1196100989263358594_int_o,P2: produc4788131091073775919nt_int] :
      ( ! [A3: fun_in5730379987311621695e_term,B2: product_prod_int_int] : aa_Pro5451197003417746155_int_o(P,aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A3),B2))
     => aa_Pro5451197003417746155_int_o(P,P2) ) ).

% prod_cases
tff(fact_259_surj__pair,axiom,
    ! [P2: produc2453742332425399446nteger] :
    ? [X3: fun_Pr5098669352780829690e_term,Y4: produc8923325533196201883nteger] : P2 = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X3),Y4) ).

% surj_pair
tff(fact_260_surj__pair,axiom,
    ! [P2: produc8799533983703829792et_nat] :
    ? [X3: fun_Pr6460944699146269935_nat_o,Y4: produc3658429121746597890et_nat] : P2 = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X3),Y4) ).

% surj_pair
tff(fact_261_surj__pair,axiom,
    ! [P2: produc3112576180687729086et_nat] :
    ? [X3: fun_Pr6460944699146269935_nat_o,Y4: produc8799533983703829792et_nat] : P2 = aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X3),Y4) ).

% surj_pair
tff(fact_262_surj__pair,axiom,
    ! [P2: produc3043004577601930755nt_int] :
    ? [X3: fun_Pr7763680713840462443e_term,Y4: product_prod_int_int] : P2 = aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X3),Y4) ).

% surj_pair
tff(fact_263_surj__pair,axiom,
    ! [P2: produc4788131091073775919nt_int] :
    ? [X3: fun_in5730379987311621695e_term,Y4: product_prod_int_int] : P2 = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X3),Y4) ).

% surj_pair
tff(fact_264_old_Oprod_Oexhaust,axiom,
    ! [Y: produc2453742332425399446nteger] :
      ~ ! [A3: fun_Pr5098669352780829690e_term,B2: produc8923325533196201883nteger] : Y != aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A3),B2) ).

% old.prod.exhaust
tff(fact_265_old_Oprod_Oexhaust,axiom,
    ! [Y: produc8799533983703829792et_nat] :
      ~ ! [A3: fun_Pr6460944699146269935_nat_o,B2: produc3658429121746597890et_nat] : Y != aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A3),B2) ).

% old.prod.exhaust
tff(fact_266_old_Oprod_Oexhaust,axiom,
    ! [Y: produc3112576180687729086et_nat] :
      ~ ! [A3: fun_Pr6460944699146269935_nat_o,B2: produc8799533983703829792et_nat] : Y != aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A3),B2) ).

% old.prod.exhaust
tff(fact_267_old_Oprod_Oexhaust,axiom,
    ! [Y: produc3043004577601930755nt_int] :
      ~ ! [A3: fun_Pr7763680713840462443e_term,B2: product_prod_int_int] : Y != aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,A3),B2) ).

% old.prod.exhaust
tff(fact_268_old_Oprod_Oexhaust,axiom,
    ! [Y: produc4788131091073775919nt_int] :
      ~ ! [A3: fun_in5730379987311621695e_term,B2: product_prod_int_int] : Y != aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A3),B2) ).

% old.prod.exhaust
tff(fact_269_one__reorient,axiom,
    ! [X2: code_integer] :
      ( ( one_one_Code_integer = X2 )
    <=> ( X2 = one_one_Code_integer ) ) ).

% one_reorient
tff(fact_270_one__reorient,axiom,
    ! [X2: assn] :
      ( ( one_one_assn = X2 )
    <=> ( X2 = one_one_assn ) ) ).

% one_reorient
tff(fact_271_one__reorient,axiom,
    ! [X2: rat] :
      ( ( one_one_rat = X2 )
    <=> ( X2 = one_one_rat ) ) ).

% one_reorient
tff(fact_272_one__reorient,axiom,
    ! [X2: nat] :
      ( ( one_one_nat = X2 )
    <=> ( X2 = one_one_nat ) ) ).

% one_reorient
tff(fact_273_one__reorient,axiom,
    ! [X2: int] :
      ( ( one_one_int = X2 )
    <=> ( X2 = one_one_int ) ) ).

% one_reorient
tff(fact_274_comp__eq__dest__lhs,axiom,
    ! [A: fun_Co8499238673658658103nteger,B: fun_num_Code_integer,C: fun_num_Code_integer,V: num] :
      ( ( aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,A),B) = C )
     => ( aa_Cod1783974652533396728nteger(A,aa_num_Code_integer(B,V)) = aa_num_Code_integer(C,V) ) ) ).

% comp_eq_dest_lhs
tff(fact_275_comp__eq__dest__lhs,axiom,
    ! [A: fun_Co1561183069634336733nteger,B: fun_Co8499238673658658103nteger,C: fun_Co1561183069634336733nteger,V: code_integer] :
      ( ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,A),B) = C )
     => ( aa_Cod1978467581589928094nteger(A,aa_Cod1783974652533396728nteger(B,V)) = aa_Cod1978467581589928094nteger(C,V) ) ) ).

% comp_eq_dest_lhs
tff(fact_276_comp__eq__dest__lhs,axiom,
    ! [A: fun_fu4800041728187187127nteger,B: fun_Co1981900195452921617nteger,C: fun_Co1561183069634336733nteger,V: code_integer] :
      ( ( comp_f6739083541385432444nteger(A,B) = C )
     => ( aa_fun2509385170507305080nteger(A,aa_Cod4161879620478718930nteger(B,V)) = aa_Cod1978467581589928094nteger(C,V) ) ) ).

% comp_eq_dest_lhs
tff(fact_277_comp__eq__dest__lhs,axiom,
    ! [A: fun_nat_num,B: fun_int_nat,C: fun_int_num,V: int] :
      ( ( aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,A),B) = C )
     => ( aa_nat_num(A,aa_int_nat(B,V)) = aa_int_num(C,V) ) ) ).

% comp_eq_dest_lhs
tff(fact_278_comp__eq__elim,axiom,
    ! [A: fun_Co8499238673658658103nteger,B: fun_num_Code_integer,C: fun_Co8499238673658658103nteger,D2: fun_num_Code_integer] :
      ( ( aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,A),B) = aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,C),D2) )
     => ! [V2: num] : aa_Cod1783974652533396728nteger(A,aa_num_Code_integer(B,V2)) = aa_Cod1783974652533396728nteger(C,aa_num_Code_integer(D2,V2)) ) ).

% comp_eq_elim
tff(fact_279_comp__eq__elim,axiom,
    ! [A: fun_Co1561183069634336733nteger,B: fun_Co8499238673658658103nteger,C: fun_Co1561183069634336733nteger,D2: fun_Co8499238673658658103nteger] :
      ( ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,A),B) = aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,C),D2) )
     => ! [V2: code_integer] : aa_Cod1978467581589928094nteger(A,aa_Cod1783974652533396728nteger(B,V2)) = aa_Cod1978467581589928094nteger(C,aa_Cod1783974652533396728nteger(D2,V2)) ) ).

% comp_eq_elim
tff(fact_280_comp__eq__elim,axiom,
    ! [A: fun_Co1561183069634336733nteger,B: fun_Co8499238673658658103nteger,C: fun_fu4800041728187187127nteger,D2: fun_Co1981900195452921617nteger] :
      ( ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,A),B) = comp_f6739083541385432444nteger(C,D2) )
     => ! [V2: code_integer] : aa_Cod1978467581589928094nteger(A,aa_Cod1783974652533396728nteger(B,V2)) = aa_fun2509385170507305080nteger(C,aa_Cod4161879620478718930nteger(D2,V2)) ) ).

% comp_eq_elim
tff(fact_281_comp__eq__elim,axiom,
    ! [A: fun_fu4800041728187187127nteger,B: fun_Co1981900195452921617nteger,C: fun_Co1561183069634336733nteger,D2: fun_Co8499238673658658103nteger] :
      ( ( comp_f6739083541385432444nteger(A,B) = aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,C),D2) )
     => ! [V2: code_integer] : aa_fun2509385170507305080nteger(A,aa_Cod4161879620478718930nteger(B,V2)) = aa_Cod1978467581589928094nteger(C,aa_Cod1783974652533396728nteger(D2,V2)) ) ).

% comp_eq_elim
tff(fact_282_comp__eq__elim,axiom,
    ! [A: fun_fu4800041728187187127nteger,B: fun_Co1981900195452921617nteger,C: fun_fu4800041728187187127nteger,D2: fun_Co1981900195452921617nteger] :
      ( ( comp_f6739083541385432444nteger(A,B) = comp_f6739083541385432444nteger(C,D2) )
     => ! [V2: code_integer] : aa_fun2509385170507305080nteger(A,aa_Cod4161879620478718930nteger(B,V2)) = aa_fun2509385170507305080nteger(C,aa_Cod4161879620478718930nteger(D2,V2)) ) ).

% comp_eq_elim
tff(fact_283_comp__eq__elim,axiom,
    ! [A: fun_nat_num,B: fun_int_nat,C: fun_nat_num,D2: fun_int_nat] :
      ( ( aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,A),B) = aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,C),D2) )
     => ! [V2: int] : aa_nat_num(A,aa_int_nat(B,V2)) = aa_nat_num(C,aa_int_nat(D2,V2)) ) ).

% comp_eq_elim
tff(fact_284_comp__eq__dest,axiom,
    ! [A: fun_Co8499238673658658103nteger,B: fun_num_Code_integer,C: fun_Co8499238673658658103nteger,D2: fun_num_Code_integer,V: num] :
      ( ( aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,A),B) = aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,C),D2) )
     => ( aa_Cod1783974652533396728nteger(A,aa_num_Code_integer(B,V)) = aa_Cod1783974652533396728nteger(C,aa_num_Code_integer(D2,V)) ) ) ).

% comp_eq_dest
tff(fact_285_comp__eq__dest,axiom,
    ! [A: fun_Co1561183069634336733nteger,B: fun_Co8499238673658658103nteger,C: fun_Co1561183069634336733nteger,D2: fun_Co8499238673658658103nteger,V: code_integer] :
      ( ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,A),B) = aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,C),D2) )
     => ( aa_Cod1978467581589928094nteger(A,aa_Cod1783974652533396728nteger(B,V)) = aa_Cod1978467581589928094nteger(C,aa_Cod1783974652533396728nteger(D2,V)) ) ) ).

% comp_eq_dest
tff(fact_286_comp__eq__dest,axiom,
    ! [A: fun_Co1561183069634336733nteger,B: fun_Co8499238673658658103nteger,C: fun_fu4800041728187187127nteger,D2: fun_Co1981900195452921617nteger,V: code_integer] :
      ( ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,A),B) = comp_f6739083541385432444nteger(C,D2) )
     => ( aa_Cod1978467581589928094nteger(A,aa_Cod1783974652533396728nteger(B,V)) = aa_fun2509385170507305080nteger(C,aa_Cod4161879620478718930nteger(D2,V)) ) ) ).

% comp_eq_dest
tff(fact_287_comp__eq__dest,axiom,
    ! [A: fun_fu4800041728187187127nteger,B: fun_Co1981900195452921617nteger,C: fun_Co1561183069634336733nteger,D2: fun_Co8499238673658658103nteger,V: code_integer] :
      ( ( comp_f6739083541385432444nteger(A,B) = aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,C),D2) )
     => ( aa_fun2509385170507305080nteger(A,aa_Cod4161879620478718930nteger(B,V)) = aa_Cod1978467581589928094nteger(C,aa_Cod1783974652533396728nteger(D2,V)) ) ) ).

% comp_eq_dest
tff(fact_288_comp__eq__dest,axiom,
    ! [A: fun_fu4800041728187187127nteger,B: fun_Co1981900195452921617nteger,C: fun_fu4800041728187187127nteger,D2: fun_Co1981900195452921617nteger,V: code_integer] :
      ( ( comp_f6739083541385432444nteger(A,B) = comp_f6739083541385432444nteger(C,D2) )
     => ( aa_fun2509385170507305080nteger(A,aa_Cod4161879620478718930nteger(B,V)) = aa_fun2509385170507305080nteger(C,aa_Cod4161879620478718930nteger(D2,V)) ) ) ).

% comp_eq_dest
tff(fact_289_comp__eq__dest,axiom,
    ! [A: fun_nat_num,B: fun_int_nat,C: fun_nat_num,D2: fun_int_nat,V: int] :
      ( ( aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,A),B) = aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,C),D2) )
     => ( aa_nat_num(A,aa_int_nat(B,V)) = aa_nat_num(C,aa_int_nat(D2,V)) ) ) ).

% comp_eq_dest
tff(fact_290_comp__assoc,axiom,
    ! [F: fun_Co8499238673658658103nteger,G: fun_num_Code_integer,Ha: fun_num_num] : comp_n6909714581898973814er_num(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),G),Ha) = aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),comp_n6909714581898973814er_num(G,Ha)) ).

% comp_assoc
tff(fact_291_comp__assoc,axiom,
    ! [F: fun_nat_num,G: fun_int_nat,Ha: fun_int_int] : comp_int_num_int(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),G),Ha) = aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),comp_int_nat_int(G,Ha)) ).

% comp_assoc
tff(fact_292_comp__assoc,axiom,
    ! [F: fun_Co8499238673658658103nteger,G: fun_Co8499238673658658103nteger,Ha: fun_num_Code_integer] : aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,aa_fun4435975922079263404nteger(comp_C7449957260575251196nteger(F),G)),Ha) = aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),Ha)) ).

% comp_assoc
tff(fact_293_comp__assoc,axiom,
    ! [F: fun_num_num,G: fun_nat_num,Ha: fun_int_nat] : aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,comp_num_num_nat(F,G)),Ha) = comp_num_num_int(F,aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,G),Ha)) ).

% comp_assoc
tff(fact_294_comp__assoc,axiom,
    ! [F: fun_nat_num,G: fun_nat_nat,Ha: fun_int_nat] : aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,comp_nat_num_nat(F,G)),Ha) = aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),comp_nat_nat_int(G,Ha)) ).

% comp_assoc
tff(fact_295_comp__assoc,axiom,
    ! [F: fun_Co1561183069634336733nteger,G: fun_Co8499238673658658103nteger,Ha: fun_num_Code_integer] : comp_C2151251282054683487er_num(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),G),Ha) = comp_C2151251282054683487er_num(F,aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),Ha)) ).

% comp_assoc
tff(fact_296_comp__assoc,axiom,
    ! [F: fun_Co1561183069634336733nteger,G: fun_Co8499238673658658103nteger,Ha: fun_Co8499238673658658103nteger] : aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),G)),Ha) = aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),aa_fun4435975922079263404nteger(comp_C7449957260575251196nteger(G),Ha)) ).

% comp_assoc
tff(fact_297_comp__assoc,axiom,
    ! [F: fun_fu4800041728187187127nteger,G: fun_Co1981900195452921617nteger,Ha: fun_Co8499238673658658103nteger] : aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,comp_f6739083541385432444nteger(F,G)),Ha) = comp_f6739083541385432444nteger(F,comp_C7233611567195229654nteger(G,Ha)) ).

% comp_assoc
tff(fact_298_comp__assoc,axiom,
    ! [F: fun_Co1561183069634336733nteger,G: fun_fu5689865433563736081nteger,Ha: fun_Co1981900195452921617nteger] : comp_f6739083541385432444nteger(comp_C7827331287018003580nteger(F,G),Ha) = aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),comp_f2642788907534428630nteger(G,Ha)) ).

% comp_assoc
tff(fact_299_comp__assoc,axiom,
    ! [F: fun_fu4800041728187187127nteger,G: fun_fu1763652423599918571nteger,Ha: fun_Co1981900195452921617nteger] : comp_f6739083541385432444nteger(comp_f3848972703483044950nteger(F,G),Ha) = comp_f6739083541385432444nteger(F,comp_f228016600672082096nteger(G,Ha)) ).

% comp_assoc
tff(fact_300_comp__def,axiom,
    ! [F: fun_Co8499238673658658103nteger,G: fun_num_Code_integer,X: num] : aa_num_Code_integer(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),G),X) = aa_Cod1783974652533396728nteger(F,aa_num_Code_integer(G,X)) ).

% comp_def
tff(fact_301_comp__def,axiom,
    ! [F: fun_Co1561183069634336733nteger,G: fun_Co8499238673658658103nteger,X: code_integer] : aa_Cod1978467581589928094nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),G),X) = aa_Cod1978467581589928094nteger(F,aa_Cod1783974652533396728nteger(G,X)) ).

% comp_def
tff(fact_302_comp__def,axiom,
    ! [F: fun_fu4800041728187187127nteger,G: fun_Co1981900195452921617nteger,X: code_integer] : aa_Cod1978467581589928094nteger(comp_f6739083541385432444nteger(F,G),X) = aa_fun2509385170507305080nteger(F,aa_Cod4161879620478718930nteger(G,X)) ).

% comp_def
tff(fact_303_comp__def,axiom,
    ! [F: fun_nat_num,G: fun_int_nat,X: int] : aa_int_num(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),G),X) = aa_nat_num(F,aa_int_nat(G,X)) ).

% comp_def
tff(fact_304_timeFrame_Oelims,axiom,
    ! [X2: nat,Xa: option3216581401566546698it_nat,Y: option3216581401566546698it_nat] :
      ( ( heap_T531568236820715630rray_a(X2,Xa) = Y )
     => ( ! [R: array_a,H: heap_e7401611519738050253t_unit,N3: nat] :
            ( ( Xa = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,produc1733996804261680252it_nat(R,produc584006145561248582it_nat(H,N3))) )
           => ( Y != aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,produc1733996804261680252it_nat(R,produc584006145561248582it_nat(H,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X2),N3)))) ) )
       => ~ ( ( Xa = none_P2587165478634041381it_nat )
           => ( Y != none_P2587165478634041381it_nat ) ) ) ) ).

% timeFrame.elims
tff(fact_305_timeFrame_Oelims,axiom,
    ! [X2: nat,Xa: option8956607266484857688it_nat,Y: option8956607266484857688it_nat] :
      ( ( heap_T3616969660504097270t_unit(X2,Xa) = Y )
     => ( ! [R: product_unit,H: heap_e7401611519738050253t_unit,N3: nat] :
            ( ( Xa = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(R,produc584006145561248582it_nat(H,N3))) )
           => ( Y != aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(R,produc584006145561248582it_nat(H,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X2),N3)))) ) )
       => ~ ( ( Xa = none_P9117596204409417319it_nat )
           => ( Y != none_P9117596204409417319it_nat ) ) ) ) ).

% timeFrame.elims
tff(fact_306_execute__bind__eq__SomeI,axiom,
    ! [F: heap_T6362127782908069795rray_a,Ha: heap_e7401611519738050253t_unit,X2: array_a,H3: heap_e7401611519738050253t_unit,N2: nat,G: fun_ar3891948820113774757rray_a,Y: array_a,H4: heap_e7401611519738050253t_unit,N4: nat] :
      ( ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(F),Ha) = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,produc1733996804261680252it_nat(X2,produc584006145561248582it_nat(H3,N2))) )
     => ( ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(aa_arr1142863274018860686rray_a(G,X2)),H3) = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,produc1733996804261680252it_nat(Y,produc584006145561248582it_nat(H4,N4))) )
       => ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(heap_T2407400398799471159rray_a(F,G)),Ha) = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,produc1733996804261680252it_nat(Y,produc584006145561248582it_nat(H4,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),N4)))) ) ) ) ).

% execute_bind_eq_SomeI
tff(fact_307_execute__bind__eq__SomeI,axiom,
    ! [F: heap_T6362127782908069795rray_a,Ha: heap_e7401611519738050253t_unit,X2: array_a,H3: heap_e7401611519738050253t_unit,N2: nat,G: fun_ar1074044450438384043t_unit,Y: product_unit,H4: heap_e7401611519738050253t_unit,N4: nat] :
      ( ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(F),Ha) = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,produc1733996804261680252it_nat(X2,produc584006145561248582it_nat(H3,N2))) )
     => ( ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(aa_arr7999650297717212780t_unit(G,X2)),H3) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(Y,produc584006145561248582it_nat(H4,N4))) )
       => ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(heap_T7324619625323989613t_unit(F,G)),Ha) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(Y,produc584006145561248582it_nat(H4,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),N4)))) ) ) ) ).

% execute_bind_eq_SomeI
tff(fact_308_execute__bind__eq__SomeI,axiom,
    ! [F: heap_T5738788834812785303t_unit,Ha: heap_e7401611519738050253t_unit,X2: product_unit,H3: heap_e7401611519738050253t_unit,N2: nat,G: fun_Pr5924905948197006361rray_a,Y: array_a,H4: heap_e7401611519738050253t_unit,N4: nat] :
      ( ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(F),Ha) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(X2,produc584006145561248582it_nat(H3,N2))) )
     => ( ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(aa_Pro755961224256580114rray_a(G,X2)),H3) = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,produc1733996804261680252it_nat(Y,produc584006145561248582it_nat(H4,N4))) )
       => ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(heap_T7158140910958840029rray_a(F,G)),Ha) = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,produc1733996804261680252it_nat(Y,produc584006145561248582it_nat(H4,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),N4)))) ) ) ) ).

% execute_bind_eq_SomeI
tff(fact_309_execute__bind__eq__SomeI,axiom,
    ! [F: heap_T5738788834812785303t_unit,Ha: heap_e7401611519738050253t_unit,X2: product_unit,H3: heap_e7401611519738050253t_unit,N2: nat,G: fun_Pr292408699144966967t_unit,Y: product_unit,H4: heap_e7401611519738050253t_unit,N4: nat] :
      ( ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(F),Ha) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(X2,produc584006145561248582it_nat(H3,N2))) )
     => ( ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(aa_Pro1108561329362217960t_unit(G,X2)),H3) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(Y,produc584006145561248582it_nat(H4,N4))) )
       => ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(heap_T2633723481742716231t_unit(F,G)),Ha) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(Y,produc584006145561248582it_nat(H4,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),N4)))) ) ) ) ).

% execute_bind_eq_SomeI
tff(fact_310_timeFrame_Osimps_I1_J,axiom,
    ! [N2: nat,R2: product_unit,Ha: heap_e7401611519738050253t_unit,N4: nat] : heap_T3616969660504097270t_unit(N2,aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(R2,produc584006145561248582it_nat(Ha,N4)))) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(R2,produc584006145561248582it_nat(Ha,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),N4)))) ).

% timeFrame.simps(1)
tff(fact_311_heap__def,axiom,
    ! [F: fun_he4944555133437423336it_nat] : heap_T6927113302350381334t_unit(F) = heap_T6183433275982383450t_unit(comp_P3118722334806803912t_unit(some_P1914260805536162275it_nat,F)) ).

% heap_def
tff(fact_312_option_Osplit__sel,axiom,
    ! [P: fun_int_o,F1: int,F22: fun_num_int,Option: option_num] :
      ( aa_int_o(P,aa_option_num_int(case_option_int_num(F1,F22),Option))
    <=> ( ( ( Option = none_num )
         => aa_int_o(P,F1) )
        & ( ( Option = aa_num_option_num(some_num,aa_option_num_num(the_num,Option)) )
         => aa_int_o(P,aa_num_int(F22,aa_option_num_num(the_num,Option))) ) ) ) ).

% option.split_sel
tff(fact_313_option_Osplit__sel,axiom,
    ! [P: fun_option_num_o,F1: option_num,F22: fun_num_option_num,Option: option_num] :
      ( aa_option_num_o(P,aa_opt5369159329878751634on_num(case_o6005452278849405969um_num(F1,F22),Option))
    <=> ( ( ( Option = none_num )
         => aa_option_num_o(P,F1) )
        & ( ( Option = aa_num_option_num(some_num,aa_option_num_num(the_num,Option)) )
         => aa_option_num_o(P,aa_num_option_num(F22,aa_option_num_num(the_num,Option))) ) ) ) ).

% option.split_sel
tff(fact_314_option_Osplit__sel,axiom,
    ! [P: fun_num_o,F1: num,F22: fun_num_num,Option: option_num] :
      ( aa_num_o(P,aa_option_num_num(case_option_num_num(F1,F22),Option))
    <=> ( ( ( Option = none_num )
         => aa_num_o(P,F1) )
        & ( ( Option = aa_num_option_num(some_num,aa_option_num_num(the_num,Option)) )
         => aa_num_o(P,aa_num_num(F22,aa_option_num_num(the_num,Option))) ) ) ) ).

% option.split_sel
tff(fact_315_option_Osplit__sel__asm,axiom,
    ! [P: fun_int_o,F1: int,F22: fun_num_int,Option: option_num] :
      ( aa_int_o(P,aa_option_num_int(case_option_int_num(F1,F22),Option))
    <=> ~ ( ( ( Option = none_num )
            & ~ aa_int_o(P,F1) )
          | ( ( Option = aa_num_option_num(some_num,aa_option_num_num(the_num,Option)) )
            & ~ aa_int_o(P,aa_num_int(F22,aa_option_num_num(the_num,Option))) ) ) ) ).

% option.split_sel_asm
tff(fact_316_option_Osplit__sel__asm,axiom,
    ! [P: fun_option_num_o,F1: option_num,F22: fun_num_option_num,Option: option_num] :
      ( aa_option_num_o(P,aa_opt5369159329878751634on_num(case_o6005452278849405969um_num(F1,F22),Option))
    <=> ~ ( ( ( Option = none_num )
            & ~ aa_option_num_o(P,F1) )
          | ( ( Option = aa_num_option_num(some_num,aa_option_num_num(the_num,Option)) )
            & ~ aa_option_num_o(P,aa_num_option_num(F22,aa_option_num_num(the_num,Option))) ) ) ) ).

% option.split_sel_asm
tff(fact_317_option_Osplit__sel__asm,axiom,
    ! [P: fun_num_o,F1: num,F22: fun_num_num,Option: option_num] :
      ( aa_num_o(P,aa_option_num_num(case_option_num_num(F1,F22),Option))
    <=> ~ ( ( ( Option = none_num )
            & ~ aa_num_o(P,F1) )
          | ( ( Option = aa_num_option_num(some_num,aa_option_num_num(the_num,Option)) )
            & ~ aa_num_o(P,aa_num_num(F22,aa_option_num_num(the_num,Option))) ) ) ) ).

% option.split_sel_asm
tff(fact_318_one__natural_Orsp,axiom,
    one_one_nat = one_one_nat ).

% one_natural.rsp
tff(fact_319_timeFrame_Opelims,axiom,
    ! [X2: nat,Xa: option3216581401566546698it_nat,Y: option3216581401566546698it_nat] :
      ( ( heap_T531568236820715630rray_a(X2,Xa) = Y )
     => ( accp_P8948468358075348838it_nat(heap_T6578553156929092987rray_a,produc3378006678175723489it_nat(X2,Xa))
       => ( ! [R: array_a,H: heap_e7401611519738050253t_unit,N3: nat] :
              ( ( Xa = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,produc1733996804261680252it_nat(R,produc584006145561248582it_nat(H,N3))) )
             => ( ( Y = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,produc1733996804261680252it_nat(R,produc584006145561248582it_nat(H,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X2),N3)))) )
               => ~ accp_P8948468358075348838it_nat(heap_T6578553156929092987rray_a,produc3378006678175723489it_nat(X2,aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,produc1733996804261680252it_nat(R,produc584006145561248582it_nat(H,N3))))) ) )
         => ~ ( ( Xa = none_P2587165478634041381it_nat )
             => ( ( Y = none_P2587165478634041381it_nat )
               => ~ accp_P8948468358075348838it_nat(heap_T6578553156929092987rray_a,produc3378006678175723489it_nat(X2,none_P2587165478634041381it_nat)) ) ) ) ) ) ).

% timeFrame.pelims
tff(fact_320_timeFrame_Opelims,axiom,
    ! [X2: nat,Xa: option8956607266484857688it_nat,Y: option8956607266484857688it_nat] :
      ( ( heap_T3616969660504097270t_unit(X2,Xa) = Y )
     => ( accp_P414730952086964626it_nat(heap_T996182799752388649t_unit,produc638857205735767105it_nat(X2,Xa))
       => ( ! [R: product_unit,H: heap_e7401611519738050253t_unit,N3: nat] :
              ( ( Xa = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(R,produc584006145561248582it_nat(H,N3))) )
             => ( ( Y = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(R,produc584006145561248582it_nat(H,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X2),N3)))) )
               => ~ accp_P414730952086964626it_nat(heap_T996182799752388649t_unit,produc638857205735767105it_nat(X2,aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(R,produc584006145561248582it_nat(H,N3))))) ) )
         => ~ ( ( Xa = none_P9117596204409417319it_nat )
             => ( ( Y = none_P9117596204409417319it_nat )
               => ~ accp_P414730952086964626it_nat(heap_T996182799752388649t_unit,produc638857205735767105it_nat(X2,none_P9117596204409417319it_nat)) ) ) ) ) ) ).

% timeFrame.pelims
tff(fact_321_add__right__cancel,axiom,
    ! [B: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
      ( ( aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(B),A) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(C),A) )
    <=> ( B = C ) ) ).

% add_right_cancel
tff(fact_322_add__right__cancel,axiom,
    ! [B: rat,A: rat,C: rat] :
      ( ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),A) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,C),A) )
    <=> ( B = C ) ) ).

% add_right_cancel
tff(fact_323_add__right__cancel,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),A) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,C),A) )
    <=> ( B = C ) ) ).

% add_right_cancel
tff(fact_324_add__right__cancel,axiom,
    ! [B: int,A: int,C: int] :
      ( ( aa_int_int(aa_int_fun_int_int(plus_plus_int,B),A) = aa_int_int(aa_int_fun_int_int(plus_plus_int,C),A) )
    <=> ( B = C ) ) ).

% add_right_cancel
tff(fact_325_add__left__cancel,axiom,
    ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
      ( ( aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(A),B) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(A),C) )
    <=> ( B = C ) ) ).

% add_left_cancel
tff(fact_326_add__left__cancel,axiom,
    ! [A: rat,B: rat,C: rat] :
      ( ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),C) )
    <=> ( B = C ) ) ).

% add_left_cancel
tff(fact_327_add__left__cancel,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C) )
    <=> ( B = C ) ) ).

% add_left_cancel
tff(fact_328_add__left__cancel,axiom,
    ! [A: int,B: int,C: int] :
      ( ( aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B) = aa_int_int(aa_int_fun_int_int(plus_plus_int,A),C) )
    <=> ( B = C ) ) ).

% add_left_cancel
tff(fact_329_Heap_Oinject,axiom,
    ! [X2: fun_he5234484606919320760it_nat,Ya: fun_he5234484606919320760it_nat] :
      ( ( heap_T6183433275982383450t_unit(X2) = heap_T6183433275982383450t_unit(Ya) )
    <=> ( X2 = Ya ) ) ).

% Heap.inject
tff(fact_330_Heap__execute,axiom,
    ! [F: heap_T6362127782908069795rray_a] : heap_T1488828001306802186rray_a(heap_T5591663578999710211rray_a(F)) = F ).

% Heap_execute
tff(fact_331_Heap__execute,axiom,
    ! [F: heap_T5738788834812785303t_unit] : heap_T6183433275982383450t_unit(heap_T875086893843062177t_unit(F)) = F ).

% Heap_execute
tff(fact_332_add__right__imp__eq,axiom,
    ! [B: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
      ( ( aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(B),A) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(C),A) )
     => ( B = C ) ) ).

% add_right_imp_eq
tff(fact_333_add__right__imp__eq,axiom,
    ! [B: rat,A: rat,C: rat] :
      ( ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),A) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,C),A) )
     => ( B = C ) ) ).

% add_right_imp_eq
tff(fact_334_add__right__imp__eq,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),A) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,C),A) )
     => ( B = C ) ) ).

% add_right_imp_eq
tff(fact_335_add__right__imp__eq,axiom,
    ! [B: int,A: int,C: int] :
      ( ( aa_int_int(aa_int_fun_int_int(plus_plus_int,B),A) = aa_int_int(aa_int_fun_int_int(plus_plus_int,C),A) )
     => ( B = C ) ) ).

% add_right_imp_eq
tff(fact_336_add__left__imp__eq,axiom,
    ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] :
      ( ( aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(A),B) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(A),C) )
     => ( B = C ) ) ).

% add_left_imp_eq
tff(fact_337_add__left__imp__eq,axiom,
    ! [A: rat,B: rat,C: rat] :
      ( ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),C) )
     => ( B = C ) ) ).

% add_left_imp_eq
tff(fact_338_add__left__imp__eq,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C) )
     => ( B = C ) ) ).

% add_left_imp_eq
tff(fact_339_add__left__imp__eq,axiom,
    ! [A: int,B: int,C: int] :
      ( ( aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B) = aa_int_int(aa_int_fun_int_int(plus_plus_int,A),C) )
     => ( B = C ) ) ).

% add_left_imp_eq
tff(fact_340_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
    ! [B: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] : aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(B),aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(A),C)) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(A),aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(B),C)) ).

% ab_semigroup_add_class.add.left_commute
tff(fact_341_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
    ! [B: rat,A: rat,C: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),C)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),C)) ).

% ab_semigroup_add_class.add.left_commute
tff(fact_342_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
    ! [B: nat,A: nat,C: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),C)) ).

% ab_semigroup_add_class.add.left_commute
tff(fact_343_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
    ! [B: int,A: int,C: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,B),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),C)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),C)) ).

% ab_semigroup_add_class.add.left_commute
tff(fact_344_ab__semigroup__add__class_Oadd_Ocommute,axiom,
    ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] : aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(A),B) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(B),A) ).

% ab_semigroup_add_class.add.commute
tff(fact_345_ab__semigroup__add__class_Oadd_Ocommute,axiom,
    ! [A: rat,B: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),A) ).

% ab_semigroup_add_class.add.commute
tff(fact_346_ab__semigroup__add__class_Oadd_Ocommute,axiom,
    ! [A: nat,B: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),A) ).

% ab_semigroup_add_class.add.commute
tff(fact_347_ab__semigroup__add__class_Oadd_Ocommute,axiom,
    ! [A: int,B: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B) = aa_int_int(aa_int_fun_int_int(plus_plus_int,B),A) ).

% ab_semigroup_add_class.add.commute
tff(fact_348_add_Oright__cancel,axiom,
    ! [B: rat,A: rat,C: rat] :
      ( ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),A) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,C),A) )
    <=> ( B = C ) ) ).

% add.right_cancel
tff(fact_349_add_Oright__cancel,axiom,
    ! [B: int,A: int,C: int] :
      ( ( aa_int_int(aa_int_fun_int_int(plus_plus_int,B),A) = aa_int_int(aa_int_fun_int_int(plus_plus_int,C),A) )
    <=> ( B = C ) ) ).

% add.right_cancel
tff(fact_350_add_Oleft__cancel,axiom,
    ! [A: rat,B: rat,C: rat] :
      ( ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),C) )
    <=> ( B = C ) ) ).

% add.left_cancel
tff(fact_351_add_Oleft__cancel,axiom,
    ! [A: int,B: int,C: int] :
      ( ( aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B) = aa_int_int(aa_int_fun_int_int(plus_plus_int,A),C) )
    <=> ( B = C ) ) ).

% add.left_cancel
tff(fact_352_add_Oassoc,axiom,
    ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] : aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(A),B)),C) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(A),aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(B),C)) ).

% add.assoc
tff(fact_353_add_Oassoc,axiom,
    ! [A: rat,B: rat,C: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),C) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),C)) ).

% add.assoc
tff(fact_354_add_Oassoc,axiom,
    ! [A: nat,B: nat,C: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),C) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),C)) ).

% add.assoc
tff(fact_355_add_Oassoc,axiom,
    ! [A: int,B: int,C: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),C) = aa_int_int(aa_int_fun_int_int(plus_plus_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),C)) ).

% add.assoc
tff(fact_356_group__cancel_Oadd2,axiom,
    ! [B4: multis2468970476368604999at_nat,K: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat] :
      ( ( B4 = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(K),B) )
     => ( aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(A),B4) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(K),aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(A),B)) ) ) ).

% group_cancel.add2
tff(fact_357_group__cancel_Oadd2,axiom,
    ! [B4: rat,K: rat,B: rat,A: rat] :
      ( ( B4 = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,K),B) )
     => ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B4) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,K),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)) ) ) ).

% group_cancel.add2
tff(fact_358_group__cancel_Oadd2,axiom,
    ! [B4: nat,K: nat,B: nat,A: nat] :
      ( ( B4 = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,K),B) )
     => ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B4) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,K),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)) ) ) ).

% group_cancel.add2
tff(fact_359_group__cancel_Oadd2,axiom,
    ! [B4: int,K: int,B: int,A: int] :
      ( ( B4 = aa_int_int(aa_int_fun_int_int(plus_plus_int,K),B) )
     => ( aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B4) = aa_int_int(aa_int_fun_int_int(plus_plus_int,K),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)) ) ) ).

% group_cancel.add2
tff(fact_360_group__cancel_Oadd1,axiom,
    ! [A2: multis2468970476368604999at_nat,K: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
      ( ( A2 = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(K),A) )
     => ( aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(A2),B) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(K),aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(A),B)) ) ) ).

% group_cancel.add1
tff(fact_361_group__cancel_Oadd1,axiom,
    ! [A2: rat,K: rat,A: rat,B: rat] :
      ( ( A2 = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,K),A) )
     => ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A2),B) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,K),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)) ) ) ).

% group_cancel.add1
tff(fact_362_group__cancel_Oadd1,axiom,
    ! [A2: nat,K: nat,A: nat,B: nat] :
      ( ( A2 = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,K),A) )
     => ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A2),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,K),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)) ) ) ).

% group_cancel.add1
tff(fact_363_group__cancel_Oadd1,axiom,
    ! [A2: int,K: int,A: int,B: int] :
      ( ( A2 = aa_int_int(aa_int_fun_int_int(plus_plus_int,K),A) )
     => ( aa_int_int(aa_int_fun_int_int(plus_plus_int,A2),B) = aa_int_int(aa_int_fun_int_int(plus_plus_int,K),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)) ) ) ).

% group_cancel.add1
tff(fact_364_add__mono__thms__linordered__semiring_I4_J,axiom,
    ! [I: rat,J: rat,K: rat,L: rat] :
      ( ( ( I = J )
        & ( K = L ) )
     => ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,I),K) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,J),L) ) ) ).

% add_mono_thms_linordered_semiring(4)
tff(fact_365_add__mono__thms__linordered__semiring_I4_J,axiom,
    ! [I: nat,J: nat,K: nat,L: nat] :
      ( ( ( I = J )
        & ( K = L ) )
     => ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),L) ) ) ).

% add_mono_thms_linordered_semiring(4)
tff(fact_366_add__mono__thms__linordered__semiring_I4_J,axiom,
    ! [I: int,J: int,K: int,L: int] :
      ( ( ( I = J )
        & ( K = L ) )
     => ( aa_int_int(aa_int_fun_int_int(plus_plus_int,I),K) = aa_int_int(aa_int_fun_int_int(plus_plus_int,J),L) ) ) ).

% add_mono_thms_linordered_semiring(4)
tff(fact_367_Heap_Oexhaust,axiom,
    ! [Y: heap_T5738788834812785303t_unit] :
      ~ ! [X3: fun_he5234484606919320760it_nat] : Y != heap_T6183433275982383450t_unit(X3) ).

% Heap.exhaust
tff(fact_368_execute_Osimps,axiom,
    ! [F: fun_he1504492240061592256it_nat] : heap_T5591663578999710211rray_a(heap_T1488828001306802186rray_a(F)) = F ).

% execute.simps
tff(fact_369_execute_Osimps,axiom,
    ! [F: fun_he5234484606919320760it_nat] : heap_T875086893843062177t_unit(heap_T6183433275982383450t_unit(F)) = F ).

% execute.simps
tff(fact_370_option_Osimps_I5_J,axiom,
    ! [F1: int,F22: fun_num_int,X22: num] : aa_option_num_int(case_option_int_num(F1,F22),aa_num_option_num(some_num,X22)) = aa_num_int(F22,X22) ).

% option.simps(5)
tff(fact_371_option_Osimps_I5_J,axiom,
    ! [F1: option_num,F22: fun_num_option_num,X22: num] : aa_opt5369159329878751634on_num(case_o6005452278849405969um_num(F1,F22),aa_num_option_num(some_num,X22)) = aa_num_option_num(F22,X22) ).

% option.simps(5)
tff(fact_372_option_Osimps_I5_J,axiom,
    ! [F1: num,F22: fun_num_num,X22: num] : aa_option_num_num(case_option_num_num(F1,F22),aa_num_option_num(some_num,X22)) = aa_num_num(F22,X22) ).

% option.simps(5)
tff(fact_373_option_Osimps_I4_J,axiom,
    ! [F1: int,F22: fun_num_int] : aa_option_num_int(case_option_int_num(F1,F22),none_num) = F1 ).

% option.simps(4)
tff(fact_374_option_Osimps_I4_J,axiom,
    ! [F1: option_num,F22: fun_num_option_num] : aa_opt5369159329878751634on_num(case_o6005452278849405969um_num(F1,F22),none_num) = F1 ).

% option.simps(4)
tff(fact_375_option_Osimps_I4_J,axiom,
    ! [F1: num,F22: fun_num_num] : aa_option_num_num(case_option_num_num(F1,F22),none_num) = F1 ).

% option.simps(4)
tff(fact_376_option_Ocase__eq__if,axiom,
    ! [F1: int,F22: fun_num_int,Option: option_num] :
      aa_option_num_int(case_option_int_num(F1,F22),Option) = $ite(Option = none_num,F1,aa_num_int(F22,aa_option_num_num(the_num,Option))) ).

% option.case_eq_if
tff(fact_377_option_Ocase__eq__if,axiom,
    ! [F1: option_num,F22: fun_num_option_num,Option: option_num] :
      aa_opt5369159329878751634on_num(case_o6005452278849405969um_num(F1,F22),Option) = $ite(Option = none_num,F1,aa_num_option_num(F22,aa_option_num_num(the_num,Option))) ).

% option.case_eq_if
tff(fact_378_option_Ocase__eq__if,axiom,
    ! [F1: num,F22: fun_num_num,Option: option_num] :
      aa_option_num_num(case_option_num_num(F1,F22),Option) = $ite(Option = none_num,F1,aa_num_num(F22,aa_option_num_num(the_num,Option))) ).

% option.case_eq_if
tff(fact_379_accp_Ocases,axiom,
    ! [R2: fun_Pr2028404973800837934_nat_o,A: product_prod_nat_nat] :
      ( aa_Pro6150637604445964947_nat_o(accp_P4275260045618599050at_nat(R2),A)
     => ! [Y5: product_prod_nat_nat] :
          ( aa_Pro6150637604445964947_nat_o(aa_Pro989595756709598047_nat_o(R2,Y5),A)
         => aa_Pro6150637604445964947_nat_o(accp_P4275260045618599050at_nat(R2),Y5) ) ) ).

% accp.cases
tff(fact_380_accp_Ocases,axiom,
    ! [R2: fun_Pr9018117161326028078_int_o,A: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(accp_P1096762738010456898nt_int(R2),A)
     => ! [Y5: product_prod_int_int] :
          ( aa_Pro4592068669816069595_int_o(aa_Pro3952998155787061599_int_o(R2,Y5),A)
         => aa_Pro4592068669816069595_int_o(accp_P1096762738010456898nt_int(R2),Y5) ) ) ).

% accp.cases
tff(fact_381_accp_Ocases,axiom,
    ! [R2: fun_Pr3358449090565925198_nat_o,A: produc3112576180687729086et_nat] :
      ( aa_Pro2671238023309943196_nat_o(accp_P1394777952347926645et_nat(R2),A)
     => ! [Y5: produc3112576180687729086et_nat] :
          ( aa_Pro2671238023309943196_nat_o(aa_Pro4671852207856306999_nat_o(R2,Y5),A)
         => aa_Pro2671238023309943196_nat_o(accp_P1394777952347926645et_nat(R2),Y5) ) ) ).

% accp.cases
tff(fact_382_accp_Ocases,axiom,
    ! [R2: fun_li1025265955262268170_nat_o,A: list_nat] :
      ( aa_list_nat_o(accp_list_nat(R2),A)
     => ! [Y5: list_nat] :
          ( aa_list_nat_o(aa_lis557685189327716851_nat_o(R2,Y5),A)
         => aa_list_nat_o(accp_list_nat(R2),Y5) ) ) ).

% accp.cases
tff(fact_383_accp_Ocases,axiom,
    ! [R2: fun_nat_fun_nat_o,A: nat] :
      ( aa_nat_o(accp_nat(R2),A)
     => ! [Y5: nat] :
          ( aa_nat_o(aa_nat_fun_nat_o(R2,Y5),A)
         => aa_nat_o(accp_nat(R2),Y5) ) ) ).

% accp.cases
tff(fact_384_accp_Osimps,axiom,
    ! [R2: fun_Pr2028404973800837934_nat_o,A: product_prod_nat_nat] :
      ( aa_Pro6150637604445964947_nat_o(accp_P4275260045618599050at_nat(R2),A)
    <=> ? [X4: product_prod_nat_nat] :
          ( ( A = X4 )
          & ! [Xa2: product_prod_nat_nat] :
              ( aa_Pro6150637604445964947_nat_o(aa_Pro989595756709598047_nat_o(R2,Xa2),X4)
             => aa_Pro6150637604445964947_nat_o(accp_P4275260045618599050at_nat(R2),Xa2) ) ) ) ).

% accp.simps
tff(fact_385_accp_Osimps,axiom,
    ! [R2: fun_Pr9018117161326028078_int_o,A: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(accp_P1096762738010456898nt_int(R2),A)
    <=> ? [X4: product_prod_int_int] :
          ( ( A = X4 )
          & ! [Xa2: product_prod_int_int] :
              ( aa_Pro4592068669816069595_int_o(aa_Pro3952998155787061599_int_o(R2,Xa2),X4)
             => aa_Pro4592068669816069595_int_o(accp_P1096762738010456898nt_int(R2),Xa2) ) ) ) ).

% accp.simps
tff(fact_386_accp_Osimps,axiom,
    ! [R2: fun_Pr3358449090565925198_nat_o,A: produc3112576180687729086et_nat] :
      ( aa_Pro2671238023309943196_nat_o(accp_P1394777952347926645et_nat(R2),A)
    <=> ? [X4: produc3112576180687729086et_nat] :
          ( ( A = X4 )
          & ! [Xa2: produc3112576180687729086et_nat] :
              ( aa_Pro2671238023309943196_nat_o(aa_Pro4671852207856306999_nat_o(R2,Xa2),X4)
             => aa_Pro2671238023309943196_nat_o(accp_P1394777952347926645et_nat(R2),Xa2) ) ) ) ).

% accp.simps
tff(fact_387_accp_Osimps,axiom,
    ! [R2: fun_li1025265955262268170_nat_o,A: list_nat] :
      ( aa_list_nat_o(accp_list_nat(R2),A)
    <=> ? [X4: list_nat] :
          ( ( A = X4 )
          & ! [Xa2: list_nat] :
              ( aa_list_nat_o(aa_lis557685189327716851_nat_o(R2,Xa2),X4)
             => aa_list_nat_o(accp_list_nat(R2),Xa2) ) ) ) ).

% accp.simps
tff(fact_388_accp_Osimps,axiom,
    ! [R2: fun_nat_fun_nat_o,A: nat] :
      ( aa_nat_o(accp_nat(R2),A)
    <=> ? [X4: nat] :
          ( ( A = X4 )
          & ! [Xa2: nat] :
              ( aa_nat_o(aa_nat_fun_nat_o(R2,Xa2),X4)
             => aa_nat_o(accp_nat(R2),Xa2) ) ) ) ).

% accp.simps
tff(fact_389_accpI,axiom,
    ! [R2: fun_Pr2028404973800837934_nat_o,X2: product_prod_nat_nat] :
      ( ! [Y4: product_prod_nat_nat] :
          ( aa_Pro6150637604445964947_nat_o(aa_Pro989595756709598047_nat_o(R2,Y4),X2)
         => aa_Pro6150637604445964947_nat_o(accp_P4275260045618599050at_nat(R2),Y4) )
     => aa_Pro6150637604445964947_nat_o(accp_P4275260045618599050at_nat(R2),X2) ) ).

% accpI
tff(fact_390_accpI,axiom,
    ! [R2: fun_Pr9018117161326028078_int_o,X2: product_prod_int_int] :
      ( ! [Y4: product_prod_int_int] :
          ( aa_Pro4592068669816069595_int_o(aa_Pro3952998155787061599_int_o(R2,Y4),X2)
         => aa_Pro4592068669816069595_int_o(accp_P1096762738010456898nt_int(R2),Y4) )
     => aa_Pro4592068669816069595_int_o(accp_P1096762738010456898nt_int(R2),X2) ) ).

% accpI
tff(fact_391_accpI,axiom,
    ! [R2: fun_Pr3358449090565925198_nat_o,X2: produc3112576180687729086et_nat] :
      ( ! [Y4: produc3112576180687729086et_nat] :
          ( aa_Pro2671238023309943196_nat_o(aa_Pro4671852207856306999_nat_o(R2,Y4),X2)
         => aa_Pro2671238023309943196_nat_o(accp_P1394777952347926645et_nat(R2),Y4) )
     => aa_Pro2671238023309943196_nat_o(accp_P1394777952347926645et_nat(R2),X2) ) ).

% accpI
tff(fact_392_accpI,axiom,
    ! [R2: fun_li1025265955262268170_nat_o,X2: list_nat] :
      ( ! [Y4: list_nat] :
          ( aa_list_nat_o(aa_lis557685189327716851_nat_o(R2,Y4),X2)
         => aa_list_nat_o(accp_list_nat(R2),Y4) )
     => aa_list_nat_o(accp_list_nat(R2),X2) ) ).

% accpI
tff(fact_393_accpI,axiom,
    ! [R2: fun_nat_fun_nat_o,X2: nat] :
      ( ! [Y4: nat] :
          ( aa_nat_o(aa_nat_fun_nat_o(R2,Y4),X2)
         => aa_nat_o(accp_nat(R2),Y4) )
     => aa_nat_o(accp_nat(R2),X2) ) ).

% accpI
tff(fact_394_accp__induct,axiom,
    ! [R2: fun_Pr2028404973800837934_nat_o,A: product_prod_nat_nat,P: fun_Pr4796943543331071514_nat_o] :
      ( aa_Pro6150637604445964947_nat_o(accp_P4275260045618599050at_nat(R2),A)
     => ( ! [X3: product_prod_nat_nat] :
            ( aa_Pro6150637604445964947_nat_o(accp_P4275260045618599050at_nat(R2),X3)
           => ( ! [Y5: product_prod_nat_nat] :
                  ( aa_Pro6150637604445964947_nat_o(aa_Pro989595756709598047_nat_o(R2,Y5),X3)
                 => aa_Pro6150637604445964947_nat_o(P,Y5) )
             => aa_Pro6150637604445964947_nat_o(P,X3) ) )
       => aa_Pro6150637604445964947_nat_o(P,A) ) ) ).

% accp_induct
tff(fact_395_accp__induct,axiom,
    ! [R2: fun_Pr9018117161326028078_int_o,A: product_prod_int_int,P: fun_Pr3238374608701176162_int_o] :
      ( aa_Pro4592068669816069595_int_o(accp_P1096762738010456898nt_int(R2),A)
     => ( ! [X3: product_prod_int_int] :
            ( aa_Pro4592068669816069595_int_o(accp_P1096762738010456898nt_int(R2),X3)
           => ( ! [Y5: product_prod_int_int] :
                  ( aa_Pro4592068669816069595_int_o(aa_Pro3952998155787061599_int_o(R2,Y5),X3)
                 => aa_Pro4592068669816069595_int_o(P,Y5) )
             => aa_Pro4592068669816069595_int_o(P,X3) ) )
       => aa_Pro4592068669816069595_int_o(P,A) ) ) ).

% accp_induct
tff(fact_396_accp__induct,axiom,
    ! [R2: fun_Pr3358449090565925198_nat_o,A: produc3112576180687729086et_nat,P: fun_Pr1227177680593602867_nat_o] :
      ( aa_Pro2671238023309943196_nat_o(accp_P1394777952347926645et_nat(R2),A)
     => ( ! [X3: produc3112576180687729086et_nat] :
            ( aa_Pro2671238023309943196_nat_o(accp_P1394777952347926645et_nat(R2),X3)
           => ( ! [Y5: produc3112576180687729086et_nat] :
                  ( aa_Pro2671238023309943196_nat_o(aa_Pro4671852207856306999_nat_o(R2,Y5),X3)
                 => aa_Pro2671238023309943196_nat_o(P,Y5) )
             => aa_Pro2671238023309943196_nat_o(P,X3) ) )
       => aa_Pro2671238023309943196_nat_o(P,A) ) ) ).

% accp_induct
tff(fact_397_accp__induct,axiom,
    ! [R2: fun_li1025265955262268170_nat_o,A: list_nat,P: fun_list_nat_o] :
      ( aa_list_nat_o(accp_list_nat(R2),A)
     => ( ! [X3: list_nat] :
            ( aa_list_nat_o(accp_list_nat(R2),X3)
           => ( ! [Y5: list_nat] :
                  ( aa_list_nat_o(aa_lis557685189327716851_nat_o(R2,Y5),X3)
                 => aa_list_nat_o(P,Y5) )
             => aa_list_nat_o(P,X3) ) )
       => aa_list_nat_o(P,A) ) ) ).

% accp_induct
tff(fact_398_accp__induct,axiom,
    ! [R2: fun_nat_fun_nat_o,A: nat,P: fun_nat_o] :
      ( aa_nat_o(accp_nat(R2),A)
     => ( ! [X3: nat] :
            ( aa_nat_o(accp_nat(R2),X3)
           => ( ! [Y5: nat] :
                  ( aa_nat_o(aa_nat_fun_nat_o(R2,Y5),X3)
                 => aa_nat_o(P,Y5) )
             => aa_nat_o(P,X3) ) )
       => aa_nat_o(P,A) ) ) ).

% accp_induct
tff(fact_399_accp__downward,axiom,
    ! [R2: fun_Pr2028404973800837934_nat_o,B: product_prod_nat_nat,A: product_prod_nat_nat] :
      ( aa_Pro6150637604445964947_nat_o(accp_P4275260045618599050at_nat(R2),B)
     => ( aa_Pro6150637604445964947_nat_o(aa_Pro989595756709598047_nat_o(R2,A),B)
       => aa_Pro6150637604445964947_nat_o(accp_P4275260045618599050at_nat(R2),A) ) ) ).

% accp_downward
tff(fact_400_accp__downward,axiom,
    ! [R2: fun_Pr9018117161326028078_int_o,B: product_prod_int_int,A: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(accp_P1096762738010456898nt_int(R2),B)
     => ( aa_Pro4592068669816069595_int_o(aa_Pro3952998155787061599_int_o(R2,A),B)
       => aa_Pro4592068669816069595_int_o(accp_P1096762738010456898nt_int(R2),A) ) ) ).

% accp_downward
tff(fact_401_accp__downward,axiom,
    ! [R2: fun_Pr3358449090565925198_nat_o,B: produc3112576180687729086et_nat,A: produc3112576180687729086et_nat] :
      ( aa_Pro2671238023309943196_nat_o(accp_P1394777952347926645et_nat(R2),B)
     => ( aa_Pro2671238023309943196_nat_o(aa_Pro4671852207856306999_nat_o(R2,A),B)
       => aa_Pro2671238023309943196_nat_o(accp_P1394777952347926645et_nat(R2),A) ) ) ).

% accp_downward
tff(fact_402_accp__downward,axiom,
    ! [R2: fun_li1025265955262268170_nat_o,B: list_nat,A: list_nat] :
      ( aa_list_nat_o(accp_list_nat(R2),B)
     => ( aa_list_nat_o(aa_lis557685189327716851_nat_o(R2,A),B)
       => aa_list_nat_o(accp_list_nat(R2),A) ) ) ).

% accp_downward
tff(fact_403_accp__downward,axiom,
    ! [R2: fun_nat_fun_nat_o,B: nat,A: nat] :
      ( aa_nat_o(accp_nat(R2),B)
     => ( aa_nat_o(aa_nat_fun_nat_o(R2,A),B)
       => aa_nat_o(accp_nat(R2),A) ) ) ).

% accp_downward
tff(fact_404_not__accp__down,axiom,
    ! [R3: fun_Pr2028404973800837934_nat_o,X2: product_prod_nat_nat] :
      ( ~ aa_Pro6150637604445964947_nat_o(accp_P4275260045618599050at_nat(R3),X2)
     => ~ ! [Z2: product_prod_nat_nat] :
            ( aa_Pro6150637604445964947_nat_o(aa_Pro989595756709598047_nat_o(R3,Z2),X2)
           => aa_Pro6150637604445964947_nat_o(accp_P4275260045618599050at_nat(R3),Z2) ) ) ).

% not_accp_down
tff(fact_405_not__accp__down,axiom,
    ! [R3: fun_Pr9018117161326028078_int_o,X2: product_prod_int_int] :
      ( ~ aa_Pro4592068669816069595_int_o(accp_P1096762738010456898nt_int(R3),X2)
     => ~ ! [Z2: product_prod_int_int] :
            ( aa_Pro4592068669816069595_int_o(aa_Pro3952998155787061599_int_o(R3,Z2),X2)
           => aa_Pro4592068669816069595_int_o(accp_P1096762738010456898nt_int(R3),Z2) ) ) ).

% not_accp_down
tff(fact_406_not__accp__down,axiom,
    ! [R3: fun_Pr3358449090565925198_nat_o,X2: produc3112576180687729086et_nat] :
      ( ~ aa_Pro2671238023309943196_nat_o(accp_P1394777952347926645et_nat(R3),X2)
     => ~ ! [Z2: produc3112576180687729086et_nat] :
            ( aa_Pro2671238023309943196_nat_o(aa_Pro4671852207856306999_nat_o(R3,Z2),X2)
           => aa_Pro2671238023309943196_nat_o(accp_P1394777952347926645et_nat(R3),Z2) ) ) ).

% not_accp_down
tff(fact_407_not__accp__down,axiom,
    ! [R3: fun_li1025265955262268170_nat_o,X2: list_nat] :
      ( ~ aa_list_nat_o(accp_list_nat(R3),X2)
     => ~ ! [Z2: list_nat] :
            ( aa_list_nat_o(aa_lis557685189327716851_nat_o(R3,Z2),X2)
           => aa_list_nat_o(accp_list_nat(R3),Z2) ) ) ).

% not_accp_down
tff(fact_408_not__accp__down,axiom,
    ! [R3: fun_nat_fun_nat_o,X2: nat] :
      ( ~ aa_nat_o(accp_nat(R3),X2)
     => ~ ! [Z2: nat] :
            ( aa_nat_o(aa_nat_fun_nat_o(R3,Z2),X2)
           => aa_nat_o(accp_nat(R3),Z2) ) ) ).

% not_accp_down
tff(fact_409_accp__induct__rule,axiom,
    ! [R2: fun_Pr2028404973800837934_nat_o,A: product_prod_nat_nat,P: fun_Pr4796943543331071514_nat_o] :
      ( aa_Pro6150637604445964947_nat_o(accp_P4275260045618599050at_nat(R2),A)
     => ( ! [X3: product_prod_nat_nat] :
            ( aa_Pro6150637604445964947_nat_o(accp_P4275260045618599050at_nat(R2),X3)
           => ( ! [Y5: product_prod_nat_nat] :
                  ( aa_Pro6150637604445964947_nat_o(aa_Pro989595756709598047_nat_o(R2,Y5),X3)
                 => aa_Pro6150637604445964947_nat_o(P,Y5) )
             => aa_Pro6150637604445964947_nat_o(P,X3) ) )
       => aa_Pro6150637604445964947_nat_o(P,A) ) ) ).

% accp_induct_rule
tff(fact_410_accp__induct__rule,axiom,
    ! [R2: fun_Pr9018117161326028078_int_o,A: product_prod_int_int,P: fun_Pr3238374608701176162_int_o] :
      ( aa_Pro4592068669816069595_int_o(accp_P1096762738010456898nt_int(R2),A)
     => ( ! [X3: product_prod_int_int] :
            ( aa_Pro4592068669816069595_int_o(accp_P1096762738010456898nt_int(R2),X3)
           => ( ! [Y5: product_prod_int_int] :
                  ( aa_Pro4592068669816069595_int_o(aa_Pro3952998155787061599_int_o(R2,Y5),X3)
                 => aa_Pro4592068669816069595_int_o(P,Y5) )
             => aa_Pro4592068669816069595_int_o(P,X3) ) )
       => aa_Pro4592068669816069595_int_o(P,A) ) ) ).

% accp_induct_rule
tff(fact_411_accp__induct__rule,axiom,
    ! [R2: fun_Pr3358449090565925198_nat_o,A: produc3112576180687729086et_nat,P: fun_Pr1227177680593602867_nat_o] :
      ( aa_Pro2671238023309943196_nat_o(accp_P1394777952347926645et_nat(R2),A)
     => ( ! [X3: produc3112576180687729086et_nat] :
            ( aa_Pro2671238023309943196_nat_o(accp_P1394777952347926645et_nat(R2),X3)
           => ( ! [Y5: produc3112576180687729086et_nat] :
                  ( aa_Pro2671238023309943196_nat_o(aa_Pro4671852207856306999_nat_o(R2,Y5),X3)
                 => aa_Pro2671238023309943196_nat_o(P,Y5) )
             => aa_Pro2671238023309943196_nat_o(P,X3) ) )
       => aa_Pro2671238023309943196_nat_o(P,A) ) ) ).

% accp_induct_rule
tff(fact_412_accp__induct__rule,axiom,
    ! [R2: fun_li1025265955262268170_nat_o,A: list_nat,P: fun_list_nat_o] :
      ( aa_list_nat_o(accp_list_nat(R2),A)
     => ( ! [X3: list_nat] :
            ( aa_list_nat_o(accp_list_nat(R2),X3)
           => ( ! [Y5: list_nat] :
                  ( aa_list_nat_o(aa_lis557685189327716851_nat_o(R2,Y5),X3)
                 => aa_list_nat_o(P,Y5) )
             => aa_list_nat_o(P,X3) ) )
       => aa_list_nat_o(P,A) ) ) ).

% accp_induct_rule
tff(fact_413_accp__induct__rule,axiom,
    ! [R2: fun_nat_fun_nat_o,A: nat,P: fun_nat_o] :
      ( aa_nat_o(accp_nat(R2),A)
     => ( ! [X3: nat] :
            ( aa_nat_o(accp_nat(R2),X3)
           => ( ! [Y5: nat] :
                  ( aa_nat_o(aa_nat_fun_nat_o(R2,Y5),X3)
                 => aa_nat_o(P,Y5) )
             => aa_nat_o(P,X3) ) )
       => aa_nat_o(P,A) ) ) ).

% accp_induct_rule
tff(fact_414_fun_Omap__comp,axiom,
    ! [G: fun_num_num,F: fun_nat_num,V: fun_int_nat] : comp_num_num_int(G,aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),V)) = aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,comp_num_num_nat(G,F)),V) ).

% fun.map_comp
tff(fact_415_fun_Omap__comp,axiom,
    ! [G: fun_Co8499238673658658103nteger,F: fun_num_Code_integer,V: fun_num_num] : aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),comp_n6909714581898973814er_num(F,V)) = comp_n6909714581898973814er_num(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),F),V) ).

% fun.map_comp
tff(fact_416_fun_Omap__comp,axiom,
    ! [G: fun_Co8499238673658658103nteger,F: fun_Co8499238673658658103nteger,V: fun_num_Code_integer] : aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),V)) = aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,aa_fun4435975922079263404nteger(comp_C7449957260575251196nteger(G),F)),V) ).

% fun.map_comp
tff(fact_417_fun_Omap__comp,axiom,
    ! [G: fun_nat_num,F: fun_int_nat,V: fun_int_int] : aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,G),comp_int_nat_int(F,V)) = comp_int_num_int(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,G),F),V) ).

% fun.map_comp
tff(fact_418_fun_Omap__comp,axiom,
    ! [G: fun_nat_num,F: fun_nat_nat,V: fun_int_nat] : aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,G),comp_nat_nat_int(F,V)) = aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,comp_nat_num_nat(G,F)),V) ).

% fun.map_comp
tff(fact_419_fun_Omap__comp,axiom,
    ! [G: fun_Co1561183069634336733nteger,F: fun_Co8499238673658658103nteger,V: fun_num_Code_integer] : comp_C2151251282054683487er_num(G,aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),V)) = comp_C2151251282054683487er_num(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,G),F),V) ).

% fun.map_comp
tff(fact_420_fun_Omap__comp,axiom,
    ! [G: fun_Co1561183069634336733nteger,F: fun_Co8499238673658658103nteger,V: fun_Co8499238673658658103nteger] : aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,G),aa_fun4435975922079263404nteger(comp_C7449957260575251196nteger(F),V)) = aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,G),F)),V) ).

% fun.map_comp
tff(fact_421_fun_Omap__comp,axiom,
    ! [G: fun_Co1561183069634336733nteger,F: fun_fu5689865433563736081nteger,V: fun_Co1981900195452921617nteger] : aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,G),comp_f2642788907534428630nteger(F,V)) = comp_f6739083541385432444nteger(comp_C7827331287018003580nteger(G,F),V) ).

% fun.map_comp
tff(fact_422_fun_Omap__comp,axiom,
    ! [G: fun_fu4800041728187187127nteger,F: fun_Co1981900195452921617nteger,V: fun_Co8499238673658658103nteger] : comp_f6739083541385432444nteger(G,comp_C7233611567195229654nteger(F,V)) = aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,comp_f6739083541385432444nteger(G,F)),V) ).

% fun.map_comp
tff(fact_423_fun_Omap__comp,axiom,
    ! [G: fun_fu4800041728187187127nteger,F: fun_fu1763652423599918571nteger,V: fun_Co1981900195452921617nteger] : comp_f6739083541385432444nteger(G,comp_f228016600672082096nteger(F,V)) = comp_f6739083541385432444nteger(comp_f3848972703483044950nteger(G,F),V) ).

% fun.map_comp
tff(fact_424_comp__cong,axiom,
    ! [F: fun_Co8499238673658658103nteger,G: fun_num_Code_integer,X2: num,F3: fun_Co8499238673658658103nteger,G2: fun_num_Code_integer,X6: num] :
      ( ( aa_Cod1783974652533396728nteger(F,aa_num_Code_integer(G,X2)) = aa_Cod1783974652533396728nteger(F3,aa_num_Code_integer(G2,X6)) )
     => ( aa_num_Code_integer(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),G),X2) = aa_num_Code_integer(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F3),G2),X6) ) ) ).

% comp_cong
tff(fact_425_comp__cong,axiom,
    ! [F: fun_Co1561183069634336733nteger,G: fun_Co8499238673658658103nteger,X2: code_integer,F3: fun_Co1561183069634336733nteger,G2: fun_Co8499238673658658103nteger,X6: code_integer] :
      ( ( aa_Cod1978467581589928094nteger(F,aa_Cod1783974652533396728nteger(G,X2)) = aa_Cod1978467581589928094nteger(F3,aa_Cod1783974652533396728nteger(G2,X6)) )
     => ( aa_Cod1978467581589928094nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),G),X2) = aa_Cod1978467581589928094nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F3),G2),X6) ) ) ).

% comp_cong
tff(fact_426_comp__cong,axiom,
    ! [F: fun_Co1561183069634336733nteger,G: fun_Co8499238673658658103nteger,X2: code_integer,F3: fun_fu4800041728187187127nteger,G2: fun_Co1981900195452921617nteger,X6: code_integer] :
      ( ( aa_Cod1978467581589928094nteger(F,aa_Cod1783974652533396728nteger(G,X2)) = aa_fun2509385170507305080nteger(F3,aa_Cod4161879620478718930nteger(G2,X6)) )
     => ( aa_Cod1978467581589928094nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),G),X2) = aa_Cod1978467581589928094nteger(comp_f6739083541385432444nteger(F3,G2),X6) ) ) ).

% comp_cong
tff(fact_427_comp__cong,axiom,
    ! [F: fun_fu4800041728187187127nteger,G: fun_Co1981900195452921617nteger,X2: code_integer,F3: fun_Co1561183069634336733nteger,G2: fun_Co8499238673658658103nteger,X6: code_integer] :
      ( ( aa_fun2509385170507305080nteger(F,aa_Cod4161879620478718930nteger(G,X2)) = aa_Cod1978467581589928094nteger(F3,aa_Cod1783974652533396728nteger(G2,X6)) )
     => ( aa_Cod1978467581589928094nteger(comp_f6739083541385432444nteger(F,G),X2) = aa_Cod1978467581589928094nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F3),G2),X6) ) ) ).

% comp_cong
tff(fact_428_comp__cong,axiom,
    ! [F: fun_fu4800041728187187127nteger,G: fun_Co1981900195452921617nteger,X2: code_integer,F3: fun_fu4800041728187187127nteger,G2: fun_Co1981900195452921617nteger,X6: code_integer] :
      ( ( aa_fun2509385170507305080nteger(F,aa_Cod4161879620478718930nteger(G,X2)) = aa_fun2509385170507305080nteger(F3,aa_Cod4161879620478718930nteger(G2,X6)) )
     => ( aa_Cod1978467581589928094nteger(comp_f6739083541385432444nteger(F,G),X2) = aa_Cod1978467581589928094nteger(comp_f6739083541385432444nteger(F3,G2),X6) ) ) ).

% comp_cong
tff(fact_429_comp__cong,axiom,
    ! [F: fun_nat_num,G: fun_int_nat,X2: int,F3: fun_nat_num,G2: fun_int_nat,X6: int] :
      ( ( aa_nat_num(F,aa_int_nat(G,X2)) = aa_nat_num(F3,aa_int_nat(G2,X6)) )
     => ( aa_int_num(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),G),X2) = aa_int_num(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F3),G2),X6) ) ) ).

% comp_cong
tff(fact_430_curryI,axiom,
    ! [F: fun_Pr7015759342434529115eger_o,A: fun_Pr5098669352780829690e_term,B: produc8923325533196201883nteger] :
      ( aa_Pro4148064003102580676eger_o(F,aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A),B))
     => aa_Pro4926521453222654329eger_o(aa_fun4505422719058378424eger_o(produc177509963858859394eger_o(F),A),B) ) ).

% curryI
tff(fact_431_curryI,axiom,
    ! [F: fun_Pr2620521676128474833_nat_o,A: fun_Pr6460944699146269935_nat_o,B: produc3658429121746597890et_nat] :
      ( aa_Pro5643009357358181178_nat_o(F,aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A),B))
     => aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(produc4701769847872139056_nat_o(F),A),B) ) ).

% curryI
tff(fact_432_curryI,axiom,
    ! [F: fun_Pr1227177680593602867_nat_o,A: fun_Pr6460944699146269935_nat_o,B: produc8799533983703829792et_nat] :
      ( aa_Pro2671238023309943196_nat_o(F,aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A),B))
     => aa_Pro5643009357358181178_nat_o(aa_fun912680268133416158_nat_o(produc3333590387107866898_nat_o(F),A),B) ) ).

% curryI
tff(fact_433_curryI,axiom,
    ! [F: fun_Pr3540825087398332590_int_o,A: fun_Pr7763680713840462443e_term,B: product_prod_int_int] :
      ( aa_Pro2601676399929874711_int_o(F,aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,A),B))
     => aa_Pro4592068669816069595_int_o(aa_fun3538162476766722827_int_o(produc443495763101479893_int_o(F),A),B) ) ).

% curryI
tff(fact_434_curryI,axiom,
    ! [F: fun_Pr1196100989263358594_int_o,A: fun_in5730379987311621695e_term,B: product_prod_int_int] :
      ( aa_Pro5451197003417746155_int_o(F,aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A),B))
     => aa_Pro4592068669816069595_int_o(aa_fun586359091965693151_int_o(produc2168430993391648169_int_o(F),A),B) ) ).

% curryI
tff(fact_435_curryE,axiom,
    ! [F: fun_Pr7015759342434529115eger_o,A: fun_Pr5098669352780829690e_term,B: produc8923325533196201883nteger] :
      ( aa_Pro4926521453222654329eger_o(aa_fun4505422719058378424eger_o(produc177509963858859394eger_o(F),A),B)
     => aa_Pro4148064003102580676eger_o(F,aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A),B)) ) ).

% curryE
tff(fact_436_curryE,axiom,
    ! [F: fun_Pr2620521676128474833_nat_o,A: fun_Pr6460944699146269935_nat_o,B: produc3658429121746597890et_nat] :
      ( aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(produc4701769847872139056_nat_o(F),A),B)
     => aa_Pro5643009357358181178_nat_o(F,aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A),B)) ) ).

% curryE
tff(fact_437_curryE,axiom,
    ! [F: fun_Pr1227177680593602867_nat_o,A: fun_Pr6460944699146269935_nat_o,B: produc8799533983703829792et_nat] :
      ( aa_Pro5643009357358181178_nat_o(aa_fun912680268133416158_nat_o(produc3333590387107866898_nat_o(F),A),B)
     => aa_Pro2671238023309943196_nat_o(F,aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A),B)) ) ).

% curryE
tff(fact_438_curryE,axiom,
    ! [F: fun_Pr3540825087398332590_int_o,A: fun_Pr7763680713840462443e_term,B: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(aa_fun3538162476766722827_int_o(produc443495763101479893_int_o(F),A),B)
     => aa_Pro2601676399929874711_int_o(F,aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,A),B)) ) ).

% curryE
tff(fact_439_curryE,axiom,
    ! [F: fun_Pr1196100989263358594_int_o,A: fun_in5730379987311621695e_term,B: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(aa_fun586359091965693151_int_o(produc2168430993391648169_int_o(F),A),B)
     => aa_Pro5451197003417746155_int_o(F,aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A),B)) ) ).

% curryE
tff(fact_440_curryD,axiom,
    ! [F: fun_Pr7015759342434529115eger_o,A: fun_Pr5098669352780829690e_term,B: produc8923325533196201883nteger] :
      ( aa_Pro4926521453222654329eger_o(aa_fun4505422719058378424eger_o(produc177509963858859394eger_o(F),A),B)
     => aa_Pro4148064003102580676eger_o(F,aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A),B)) ) ).

% curryD
tff(fact_441_curryD,axiom,
    ! [F: fun_Pr2620521676128474833_nat_o,A: fun_Pr6460944699146269935_nat_o,B: produc3658429121746597890et_nat] :
      ( aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(produc4701769847872139056_nat_o(F),A),B)
     => aa_Pro5643009357358181178_nat_o(F,aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A),B)) ) ).

% curryD
tff(fact_442_curryD,axiom,
    ! [F: fun_Pr1227177680593602867_nat_o,A: fun_Pr6460944699146269935_nat_o,B: produc8799533983703829792et_nat] :
      ( aa_Pro5643009357358181178_nat_o(aa_fun912680268133416158_nat_o(produc3333590387107866898_nat_o(F),A),B)
     => aa_Pro2671238023309943196_nat_o(F,aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A),B)) ) ).

% curryD
tff(fact_443_curryD,axiom,
    ! [F: fun_Pr3540825087398332590_int_o,A: fun_Pr7763680713840462443e_term,B: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(aa_fun3538162476766722827_int_o(produc443495763101479893_int_o(F),A),B)
     => aa_Pro2601676399929874711_int_o(F,aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,A),B)) ) ).

% curryD
tff(fact_444_curryD,axiom,
    ! [F: fun_Pr1196100989263358594_int_o,A: fun_in5730379987311621695e_term,B: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(aa_fun586359091965693151_int_o(produc2168430993391648169_int_o(F),A),B)
     => aa_Pro5451197003417746155_int_o(F,aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A),B)) ) ).

% curryD
tff(fact_445_in__lex__prod,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,R2: set_Pr4329608150637261639at_nat,S: set_Pr4329608150637261639at_nat] :
      ( member6009668390874684176at_nat(produc2335810615602371415at_nat(produc2922128104949294807at_nat(A,B),produc2922128104949294807at_nat(A4,B3)),lex_pr8000699672184251119at_nat(R2,S))
    <=> ( member8757157785044589968at_nat(produc2922128104949294807at_nat(A,A4),R2)
        | ( ( A = A4 )
          & member8757157785044589968at_nat(produc2922128104949294807at_nat(B,B3),S) ) ) ) ).

% in_lex_prod
tff(fact_446_in__lex__prod,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: nat,A4: set_Pr1261947904930325089at_nat,B3: nat,R2: set_Pr4329608150637261639at_nat,S: set_Pr1261947904930325089at_nat] :
      ( member3480088626692287306at_nat(produc3585720979125124569at_nat(produc3149970401713881818at_nat(A,B),produc3149970401713881818at_nat(A4,B3)),lex_pr1951919194703979714at_nat(R2,S))
    <=> ( member8757157785044589968at_nat(produc2922128104949294807at_nat(A,A4),R2)
        | ( ( A = A4 )
          & member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,B),B3),S) ) ) ) ).

% in_lex_prod
tff(fact_447_in__lex__prod,axiom,
    ! [A: nat,B: set_Pr1261947904930325089at_nat,A4: nat,B3: set_Pr1261947904930325089at_nat,R2: set_Pr1261947904930325089at_nat,S: set_Pr4329608150637261639at_nat] :
      ( member4107301959146914710at_nat(produc8824474337961625893at_nat(produc5463602008962177208at_nat(A,B),produc5463602008962177208at_nat(A4,B3)),lex_pr4265550801952275104at_nat(R2,S))
    <=> ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),A4),R2)
        | ( ( A = A4 )
          & member8757157785044589968at_nat(produc2922128104949294807at_nat(B,B3),S) ) ) ) ).

% in_lex_prod
tff(fact_448_in__lex__prod,axiom,
    ! [A: nat,B: nat,A4: nat,B3: nat,R2: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
      ( member8206827879206165904at_nat(produc6161850002892822231at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A4),B3)),lex_prod_nat_nat(R2,S))
    <=> ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),A4),R2)
        | ( ( A = A4 )
          & member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,B),B3),S) ) ) ) ).

% in_lex_prod
tff(fact_449_in__lex__prod,axiom,
    ! [A: fun_Pr5098669352780829690e_term,B: produc8923325533196201883nteger,A4: fun_Pr5098669352780829690e_term,B3: produc8923325533196201883nteger,R2: set_Pr2514328457256655413e_term,S: set_Pr5052581263052047815nteger] :
      ( member5045372342328489014nteger(produc2269347123789068741nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A),B),aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A4),B3)),lex_pr1401158619140779824nteger(R2,S))
    <=> ( member6921354900009420158e_term(produc2518349463292777741e_term(A,A4),R2)
        | ( ( A = A4 )
          & member335077259223437328nteger(produc4911887526399440471nteger(B,B3),S) ) ) ) ).

% in_lex_prod
tff(fact_450_in__lex__prod,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,B: produc3658429121746597890et_nat,A4: fun_Pr6460944699146269935_nat_o,B3: produc3658429121746597890et_nat,R2: set_Pr2890355626087285447_nat_o,S: set_Pr719794911490849221et_nat] :
      ( member2216856746449346506et_nat(produc8050396023069295193et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A),B),aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A4),B3)),lex_pr6479962325641483138et_nat(R2,S))
    <=> ( member3012145478770660624_nat_o(produc4714251849521319255_nat_o(A,A4),R2)
        | ( ( A = A4 )
          & member6099555550032318734et_nat(produc8199053930788261021et_nat(B,B3),S) ) ) ) ).

% in_lex_prod
tff(fact_451_in__lex__prod,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,B: produc8799533983703829792et_nat,A4: fun_Pr6460944699146269935_nat_o,B3: produc8799533983703829792et_nat,R2: set_Pr2890355626087285447_nat_o,S: set_Pr9066344408807579265et_nat] :
      ( member2136425100634443654et_nat(produc7768440062179809557et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A),B),aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A4),B3)),lex_pr1264321499788159136et_nat(R2,S))
    <=> ( member3012145478770660624_nat_o(produc4714251849521319255_nat_o(A,A4),R2)
        | ( ( A = A4 )
          & member2216856746449346506et_nat(produc8050396023069295193et_nat(B,B3),S) ) ) ) ).

% in_lex_prod
tff(fact_452_in__lex__prod,axiom,
    ! [A: fun_Pr7763680713840462443e_term,B: product_prod_int_int,A4: fun_Pr7763680713840462443e_term,B3: product_prod_int_int,R2: set_Pr257197284073945367e_term,S: set_Pr2560585780119916871nt_int] :
      ( member8789097660028509840nt_int(produc5411871556384885407nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,A),B),aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,A4),B3)),lex_pr7544126028092883869nt_int(R2,S))
    <=> ( member8891660375229322592e_term(produc6823973692863303023e_term(A,A4),R2)
        | ( ( A = A4 )
          & member8566619992076573584nt_int(produc3646306378393792727nt_int(B,B3),S) ) ) ) ).

% in_lex_prod
tff(fact_453_in__lex__prod,axiom,
    ! [A: fun_in5730379987311621695e_term,B: product_prod_int_int,A4: fun_in5730379987311621695e_term,B3: product_prod_int_int,R2: set_Pr7847555563209246911e_term,S: set_Pr2560585780119916871nt_int] :
      ( member9155761383210387176nt_int(produc4613263410003446007nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A),B),aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A4),B3)),lex_pr421891345023438537nt_int(R2,S))
    <=> ( member4035412867189635336e_term(produc5508588179030252311e_term(A,A4),R2)
        | ( ( A = A4 )
          & member8566619992076573584nt_int(produc3646306378393792727nt_int(B,B3),S) ) ) ) ).

% in_lex_prod
tff(fact_454_rewriteR__comp__comp2,axiom,
    ! [G: fun_int_nat,Ha: fun_int_int,R1: fun_nat_nat,R22: fun_int_nat,F: fun_nat_num,L: fun_nat_num] :
      ( ( comp_int_nat_int(G,Ha) = comp_nat_nat_int(R1,R22) )
     => ( ( comp_nat_num_nat(F,R1) = L )
       => ( comp_int_num_int(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),G),Ha) = aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,L),R22) ) ) ) ).

% rewriteR_comp_comp2
tff(fact_455_rewriteR__comp__comp2,axiom,
    ! [G: fun_nat_nat,Ha: fun_int_nat,R1: fun_int_nat,R22: fun_int_int,F: fun_nat_num,L: fun_int_num] :
      ( ( comp_nat_nat_int(G,Ha) = comp_int_nat_int(R1,R22) )
     => ( ( aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),R1) = L )
       => ( aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,comp_nat_num_nat(F,G)),Ha) = comp_int_num_int(L,R22) ) ) ) ).

% rewriteR_comp_comp2
tff(fact_456_rewriteR__comp__comp2,axiom,
    ! [G: fun_num_Code_integer,Ha: fun_num_num,R1: fun_Co8499238673658658103nteger,R22: fun_num_Code_integer,F: fun_Co8499238673658658103nteger,L: fun_Co8499238673658658103nteger] :
      ( ( comp_n6909714581898973814er_num(G,Ha) = aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,R1),R22) )
     => ( ( aa_fun4435975922079263404nteger(comp_C7449957260575251196nteger(F),R1) = L )
       => ( comp_n6909714581898973814er_num(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),G),Ha) = aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,L),R22) ) ) ) ).

% rewriteR_comp_comp2
tff(fact_457_rewriteR__comp__comp2,axiom,
    ! [G: fun_Co8499238673658658103nteger,Ha: fun_num_Code_integer,R1: fun_num_Code_integer,R22: fun_num_num,F: fun_Co8499238673658658103nteger,L: fun_num_Code_integer] :
      ( ( aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),Ha) = comp_n6909714581898973814er_num(R1,R22) )
     => ( ( aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),R1) = L )
       => ( aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,aa_fun4435975922079263404nteger(comp_C7449957260575251196nteger(F),G)),Ha) = comp_n6909714581898973814er_num(L,R22) ) ) ) ).

% rewriteR_comp_comp2
tff(fact_458_rewriteR__comp__comp2,axiom,
    ! [G: fun_Co8499238673658658103nteger,Ha: fun_num_Code_integer,R1: fun_Co8499238673658658103nteger,R22: fun_num_Code_integer,F: fun_Co8499238673658658103nteger,L: fun_Co8499238673658658103nteger] :
      ( ( aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),Ha) = aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,R1),R22) )
     => ( ( aa_fun4435975922079263404nteger(comp_C7449957260575251196nteger(F),R1) = L )
       => ( aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,aa_fun4435975922079263404nteger(comp_C7449957260575251196nteger(F),G)),Ha) = aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,L),R22) ) ) ) ).

% rewriteR_comp_comp2
tff(fact_459_rewriteR__comp__comp2,axiom,
    ! [G: fun_nat_num,Ha: fun_int_nat,R1: fun_nat_num,R22: fun_int_nat,F: fun_num_num,L: fun_nat_num] :
      ( ( aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,G),Ha) = aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,R1),R22) )
     => ( ( comp_num_num_nat(F,R1) = L )
       => ( aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,comp_num_num_nat(F,G)),Ha) = aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,L),R22) ) ) ) ).

% rewriteR_comp_comp2
tff(fact_460_rewriteR__comp__comp2,axiom,
    ! [G: fun_Co8499238673658658103nteger,Ha: fun_Co8499238673658658103nteger,R1: fun_Co8499238673658658103nteger,R22: fun_Co8499238673658658103nteger,F: fun_Co1561183069634336733nteger,L: fun_Co1561183069634336733nteger] :
      ( ( aa_fun4435975922079263404nteger(comp_C7449957260575251196nteger(G),Ha) = aa_fun4435975922079263404nteger(comp_C7449957260575251196nteger(R1),R22) )
     => ( ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),R1) = L )
       => ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),G)),Ha) = aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,L),R22) ) ) ) ).

% rewriteR_comp_comp2
tff(fact_461_rewriteR__comp__comp2,axiom,
    ! [G: fun_Co8499238673658658103nteger,Ha: fun_num_Code_integer,R1: fun_Co8499238673658658103nteger,R22: fun_num_Code_integer,F: fun_Co1561183069634336733nteger,L: fun_Co1561183069634336733nteger] :
      ( ( aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),Ha) = aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,R1),R22) )
     => ( ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),R1) = L )
       => ( comp_C2151251282054683487er_num(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),G),Ha) = comp_C2151251282054683487er_num(L,R22) ) ) ) ).

% rewriteR_comp_comp2
tff(fact_462_rewriteR__comp__comp2,axiom,
    ! [G: fun_Co8499238673658658103nteger,Ha: fun_Co8499238673658658103nteger,R1: fun_fu5689865433563736081nteger,R22: fun_Co1981900195452921617nteger,F: fun_Co1561183069634336733nteger,L: fun_fu4800041728187187127nteger] :
      ( ( aa_fun4435975922079263404nteger(comp_C7449957260575251196nteger(G),Ha) = comp_f2642788907534428630nteger(R1,R22) )
     => ( ( comp_C7827331287018003580nteger(F,R1) = L )
       => ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),G)),Ha) = comp_f6739083541385432444nteger(L,R22) ) ) ) ).

% rewriteR_comp_comp2
tff(fact_463_rewriteR__comp__comp2,axiom,
    ! [G: fun_fu5689865433563736081nteger,Ha: fun_Co1981900195452921617nteger,R1: fun_Co8499238673658658103nteger,R22: fun_Co8499238673658658103nteger,F: fun_Co1561183069634336733nteger,L: fun_Co1561183069634336733nteger] :
      ( ( comp_f2642788907534428630nteger(G,Ha) = aa_fun4435975922079263404nteger(comp_C7449957260575251196nteger(R1),R22) )
     => ( ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),R1) = L )
       => ( comp_f6739083541385432444nteger(comp_C7827331287018003580nteger(F,G),Ha) = aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,L),R22) ) ) ) ).

% rewriteR_comp_comp2
tff(fact_464_rewriteL__comp__comp2,axiom,
    ! [F: fun_num_num,G: fun_nat_num,L1: fun_nat_num,L2: fun_nat_nat,Ha: fun_int_nat,R2: fun_int_nat] :
      ( ( comp_num_num_nat(F,G) = comp_nat_num_nat(L1,L2) )
     => ( ( comp_nat_nat_int(L2,Ha) = R2 )
       => ( comp_num_num_int(F,aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,G),Ha)) = aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,L1),R2) ) ) ) ).

% rewriteL_comp_comp2
tff(fact_465_rewriteL__comp__comp2,axiom,
    ! [F: fun_Co8499238673658658103nteger,G: fun_Co8499238673658658103nteger,L1: fun_Co8499238673658658103nteger,L2: fun_Co8499238673658658103nteger,Ha: fun_num_Code_integer,R2: fun_num_Code_integer] :
      ( ( aa_fun4435975922079263404nteger(comp_C7449957260575251196nteger(F),G) = aa_fun4435975922079263404nteger(comp_C7449957260575251196nteger(L1),L2) )
     => ( ( aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,L2),Ha) = R2 )
       => ( aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),Ha)) = aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,L1),R2) ) ) ) ).

% rewriteL_comp_comp2
tff(fact_466_rewriteL__comp__comp2,axiom,
    ! [F: fun_nat_num,G: fun_nat_nat,L1: fun_num_num,L2: fun_nat_num,Ha: fun_int_nat,R2: fun_int_num] :
      ( ( comp_nat_num_nat(F,G) = comp_num_num_nat(L1,L2) )
     => ( ( aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,L2),Ha) = R2 )
       => ( aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),comp_nat_nat_int(G,Ha)) = comp_num_num_int(L1,R2) ) ) ) ).

% rewriteL_comp_comp2
tff(fact_467_rewriteL__comp__comp2,axiom,
    ! [F: fun_Co8499238673658658103nteger,G: fun_num_Code_integer,L1: fun_Co8499238673658658103nteger,L2: fun_num_Code_integer,Ha: fun_num_num,R2: fun_num_Code_integer] :
      ( ( aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),G) = aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,L1),L2) )
     => ( ( comp_n6909714581898973814er_num(L2,Ha) = R2 )
       => ( aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),comp_n6909714581898973814er_num(G,Ha)) = aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,L1),R2) ) ) ) ).

% rewriteL_comp_comp2
tff(fact_468_rewriteL__comp__comp2,axiom,
    ! [F: fun_nat_num,G: fun_int_nat,L1: fun_nat_num,L2: fun_int_nat,Ha: fun_int_int,R2: fun_int_nat] :
      ( ( aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),G) = aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,L1),L2) )
     => ( ( comp_int_nat_int(L2,Ha) = R2 )
       => ( aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),comp_int_nat_int(G,Ha)) = aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,L1),R2) ) ) ) ).

% rewriteL_comp_comp2
tff(fact_469_rewriteL__comp__comp2,axiom,
    ! [F: fun_Co1561183069634336733nteger,G: fun_Co8499238673658658103nteger,L1: fun_Co1561183069634336733nteger,L2: fun_Co8499238673658658103nteger,Ha: fun_Co8499238673658658103nteger,R2: fun_Co8499238673658658103nteger] :
      ( ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),G) = aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,L1),L2) )
     => ( ( aa_fun4435975922079263404nteger(comp_C7449957260575251196nteger(L2),Ha) = R2 )
       => ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),aa_fun4435975922079263404nteger(comp_C7449957260575251196nteger(G),Ha)) = aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,L1),R2) ) ) ) ).

% rewriteL_comp_comp2
tff(fact_470_rewriteL__comp__comp2,axiom,
    ! [F: fun_Co1561183069634336733nteger,G: fun_Co8499238673658658103nteger,L1: fun_Co1561183069634336733nteger,L2: fun_Co8499238673658658103nteger,Ha: fun_num_Code_integer,R2: fun_num_Code_integer] :
      ( ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),G) = aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,L1),L2) )
     => ( ( aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,L2),Ha) = R2 )
       => ( comp_C2151251282054683487er_num(F,aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),Ha)) = comp_C2151251282054683487er_num(L1,R2) ) ) ) ).

% rewriteL_comp_comp2
tff(fact_471_rewriteL__comp__comp2,axiom,
    ! [F: fun_Co1561183069634336733nteger,G: fun_Co8499238673658658103nteger,L1: fun_fu4800041728187187127nteger,L2: fun_Co1981900195452921617nteger,Ha: fun_num_Code_integer,R2: fun_nu1287335591331657422nteger] :
      ( ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),G) = comp_f6739083541385432444nteger(L1,L2) )
     => ( ( comp_C6573007665814501267er_num(L2,Ha) = R2 )
       => ( comp_C2151251282054683487er_num(F,aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),Ha)) = comp_f6099540932654157625er_num(L1,R2) ) ) ) ).

% rewriteL_comp_comp2
tff(fact_472_rewriteL__comp__comp2,axiom,
    ! [F: fun_Co1561183069634336733nteger,G: fun_Co8499238673658658103nteger,L1: fun_fu4800041728187187127nteger,L2: fun_Co1981900195452921617nteger,Ha: fun_Co8499238673658658103nteger,R2: fun_Co1981900195452921617nteger] :
      ( ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),G) = comp_f6739083541385432444nteger(L1,L2) )
     => ( ( comp_C7233611567195229654nteger(L2,Ha) = R2 )
       => ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),aa_fun4435975922079263404nteger(comp_C7449957260575251196nteger(G),Ha)) = comp_f6739083541385432444nteger(L1,R2) ) ) ) ).

% rewriteL_comp_comp2
tff(fact_473_rewriteL__comp__comp2,axiom,
    ! [F: fun_fu4800041728187187127nteger,G: fun_Co1981900195452921617nteger,L1: fun_Co1561183069634336733nteger,L2: fun_Co8499238673658658103nteger,Ha: fun_Co8499238673658658103nteger,R2: fun_Co8499238673658658103nteger] :
      ( ( comp_f6739083541385432444nteger(F,G) = aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,L1),L2) )
     => ( ( aa_fun4435975922079263404nteger(comp_C7449957260575251196nteger(L2),Ha) = R2 )
       => ( comp_f6739083541385432444nteger(F,comp_C7233611567195229654nteger(G,Ha)) = aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,L1),R2) ) ) ) ).

% rewriteL_comp_comp2
tff(fact_474_rewriteR__comp__comp,axiom,
    ! [G: fun_num_Code_integer,Ha: fun_num_num,R2: fun_num_Code_integer,F: fun_Co8499238673658658103nteger] :
      ( ( comp_n6909714581898973814er_num(G,Ha) = R2 )
     => ( comp_n6909714581898973814er_num(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),G),Ha) = aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),R2) ) ) ).

% rewriteR_comp_comp
tff(fact_475_rewriteR__comp__comp,axiom,
    ! [G: fun_int_nat,Ha: fun_int_int,R2: fun_int_nat,F: fun_nat_num] :
      ( ( comp_int_nat_int(G,Ha) = R2 )
     => ( comp_int_num_int(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),G),Ha) = aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),R2) ) ) ).

% rewriteR_comp_comp
tff(fact_476_rewriteR__comp__comp,axiom,
    ! [G: fun_nat_nat,Ha: fun_int_nat,R2: fun_int_nat,F: fun_nat_num] :
      ( ( comp_nat_nat_int(G,Ha) = R2 )
     => ( aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,comp_nat_num_nat(F,G)),Ha) = aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),R2) ) ) ).

% rewriteR_comp_comp
tff(fact_477_rewriteR__comp__comp,axiom,
    ! [G: fun_Co8499238673658658103nteger,Ha: fun_num_Code_integer,R2: fun_num_Code_integer,F: fun_Co8499238673658658103nteger] :
      ( ( aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),Ha) = R2 )
     => ( aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,aa_fun4435975922079263404nteger(comp_C7449957260575251196nteger(F),G)),Ha) = aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),R2) ) ) ).

% rewriteR_comp_comp
tff(fact_478_rewriteR__comp__comp,axiom,
    ! [G: fun_nat_num,Ha: fun_int_nat,R2: fun_int_num,F: fun_num_num] :
      ( ( aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,G),Ha) = R2 )
     => ( aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,comp_num_num_nat(F,G)),Ha) = comp_num_num_int(F,R2) ) ) ).

% rewriteR_comp_comp
tff(fact_479_rewriteR__comp__comp,axiom,
    ! [G: fun_Co8499238673658658103nteger,Ha: fun_Co8499238673658658103nteger,R2: fun_Co8499238673658658103nteger,F: fun_Co1561183069634336733nteger] :
      ( ( aa_fun4435975922079263404nteger(comp_C7449957260575251196nteger(G),Ha) = R2 )
     => ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),G)),Ha) = aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),R2) ) ) ).

% rewriteR_comp_comp
tff(fact_480_rewriteR__comp__comp,axiom,
    ! [G: fun_Co8499238673658658103nteger,Ha: fun_num_Code_integer,R2: fun_num_Code_integer,F: fun_Co1561183069634336733nteger] :
      ( ( aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),Ha) = R2 )
     => ( comp_C2151251282054683487er_num(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),G),Ha) = comp_C2151251282054683487er_num(F,R2) ) ) ).

% rewriteR_comp_comp
tff(fact_481_rewriteR__comp__comp,axiom,
    ! [G: fun_Co1981900195452921617nteger,Ha: fun_Co8499238673658658103nteger,R2: fun_Co1981900195452921617nteger,F: fun_fu4800041728187187127nteger] :
      ( ( comp_C7233611567195229654nteger(G,Ha) = R2 )
     => ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,comp_f6739083541385432444nteger(F,G)),Ha) = comp_f6739083541385432444nteger(F,R2) ) ) ).

% rewriteR_comp_comp
tff(fact_482_rewriteR__comp__comp,axiom,
    ! [G: fun_fu5689865433563736081nteger,Ha: fun_Co1981900195452921617nteger,R2: fun_Co8499238673658658103nteger,F: fun_Co1561183069634336733nteger] :
      ( ( comp_f2642788907534428630nteger(G,Ha) = R2 )
     => ( comp_f6739083541385432444nteger(comp_C7827331287018003580nteger(F,G),Ha) = aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),R2) ) ) ).

% rewriteR_comp_comp
tff(fact_483_rewriteR__comp__comp,axiom,
    ! [G: fun_fu1763652423599918571nteger,Ha: fun_Co1981900195452921617nteger,R2: fun_Co1981900195452921617nteger,F: fun_fu4800041728187187127nteger] :
      ( ( comp_f228016600672082096nteger(G,Ha) = R2 )
     => ( comp_f6739083541385432444nteger(comp_f3848972703483044950nteger(F,G),Ha) = comp_f6739083541385432444nteger(F,R2) ) ) ).

% rewriteR_comp_comp
tff(fact_484_rewriteL__comp__comp,axiom,
    ! [F: fun_num_num,G: fun_nat_num,L: fun_nat_num,Ha: fun_int_nat] :
      ( ( comp_num_num_nat(F,G) = L )
     => ( comp_num_num_int(F,aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,G),Ha)) = aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,L),Ha) ) ) ).

% rewriteL_comp_comp
tff(fact_485_rewriteL__comp__comp,axiom,
    ! [F: fun_Co8499238673658658103nteger,G: fun_Co8499238673658658103nteger,L: fun_Co8499238673658658103nteger,Ha: fun_num_Code_integer] :
      ( ( aa_fun4435975922079263404nteger(comp_C7449957260575251196nteger(F),G) = L )
     => ( aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),Ha)) = aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,L),Ha) ) ) ).

% rewriteL_comp_comp
tff(fact_486_rewriteL__comp__comp,axiom,
    ! [F: fun_nat_num,G: fun_nat_nat,L: fun_nat_num,Ha: fun_int_nat] :
      ( ( comp_nat_num_nat(F,G) = L )
     => ( aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),comp_nat_nat_int(G,Ha)) = aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,L),Ha) ) ) ).

% rewriteL_comp_comp
tff(fact_487_rewriteL__comp__comp,axiom,
    ! [F: fun_Co8499238673658658103nteger,G: fun_num_Code_integer,L: fun_num_Code_integer,Ha: fun_num_num] :
      ( ( aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),G) = L )
     => ( aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),comp_n6909714581898973814er_num(G,Ha)) = comp_n6909714581898973814er_num(L,Ha) ) ) ).

% rewriteL_comp_comp
tff(fact_488_rewriteL__comp__comp,axiom,
    ! [F: fun_nat_num,G: fun_int_nat,L: fun_int_num,Ha: fun_int_int] :
      ( ( aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),G) = L )
     => ( aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),comp_int_nat_int(G,Ha)) = comp_int_num_int(L,Ha) ) ) ).

% rewriteL_comp_comp
tff(fact_489_rewriteL__comp__comp,axiom,
    ! [F: fun_Co1561183069634336733nteger,G: fun_Co8499238673658658103nteger,L: fun_Co1561183069634336733nteger,Ha: fun_num_Code_integer] :
      ( ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),G) = L )
     => ( comp_C2151251282054683487er_num(F,aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),Ha)) = comp_C2151251282054683487er_num(L,Ha) ) ) ).

% rewriteL_comp_comp
tff(fact_490_rewriteL__comp__comp,axiom,
    ! [F: fun_Co1561183069634336733nteger,G: fun_Co8499238673658658103nteger,L: fun_Co1561183069634336733nteger,Ha: fun_Co8499238673658658103nteger] :
      ( ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),G) = L )
     => ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),aa_fun4435975922079263404nteger(comp_C7449957260575251196nteger(G),Ha)) = aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,L),Ha) ) ) ).

% rewriteL_comp_comp
tff(fact_491_rewriteL__comp__comp,axiom,
    ! [F: fun_Co1561183069634336733nteger,G: fun_fu5689865433563736081nteger,L: fun_fu4800041728187187127nteger,Ha: fun_Co1981900195452921617nteger] :
      ( ( comp_C7827331287018003580nteger(F,G) = L )
     => ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),comp_f2642788907534428630nteger(G,Ha)) = comp_f6739083541385432444nteger(L,Ha) ) ) ).

% rewriteL_comp_comp
tff(fact_492_rewriteL__comp__comp,axiom,
    ! [F: fun_fu4800041728187187127nteger,G: fun_Co1981900195452921617nteger,L: fun_Co1561183069634336733nteger,Ha: fun_Co8499238673658658103nteger] :
      ( ( comp_f6739083541385432444nteger(F,G) = L )
     => ( comp_f6739083541385432444nteger(F,comp_C7233611567195229654nteger(G,Ha)) = aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,L),Ha) ) ) ).

% rewriteL_comp_comp
tff(fact_493_rewriteL__comp__comp,axiom,
    ! [F: fun_fu4800041728187187127nteger,G: fun_fu1763652423599918571nteger,L: fun_fu4800041728187187127nteger,Ha: fun_Co1981900195452921617nteger] :
      ( ( comp_f3848972703483044950nteger(F,G) = L )
     => ( comp_f6739083541385432444nteger(F,comp_f228016600672082096nteger(G,Ha)) = comp_f6739083541385432444nteger(L,Ha) ) ) ).

% rewriteL_comp_comp
tff(fact_494_type__copy__map__cong0,axiom,
    ! [M2: fun_num_Code_integer,G: fun_num_num,X2: num,N5: fun_Co8499238673658658103nteger,Ha: fun_num_Code_integer,F: fun_Co8499238673658658103nteger] :
      ( ( aa_num_Code_integer(M2,aa_num_num(G,X2)) = aa_Cod1783974652533396728nteger(N5,aa_num_Code_integer(Ha,X2)) )
     => ( aa_num_Code_integer(comp_n6909714581898973814er_num(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),M2),G),X2) = aa_num_Code_integer(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,aa_fun4435975922079263404nteger(comp_C7449957260575251196nteger(F),N5)),Ha),X2) ) ) ).

% type_copy_map_cong0
tff(fact_495_type__copy__map__cong0,axiom,
    ! [M2: fun_int_nat,G: fun_int_int,X2: int,N5: fun_nat_nat,Ha: fun_int_nat,F: fun_nat_num] :
      ( ( aa_int_nat(M2,aa_int_int(G,X2)) = aa_nat_nat(N5,aa_int_nat(Ha,X2)) )
     => ( aa_int_num(comp_int_num_int(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),M2),G),X2) = aa_int_num(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,comp_nat_num_nat(F,N5)),Ha),X2) ) ) ).

% type_copy_map_cong0
tff(fact_496_type__copy__map__cong0,axiom,
    ! [M2: fun_Co8499238673658658103nteger,G: fun_num_Code_integer,X2: num,N5: fun_num_Code_integer,Ha: fun_num_num,F: fun_Co8499238673658658103nteger] :
      ( ( aa_Cod1783974652533396728nteger(M2,aa_num_Code_integer(G,X2)) = aa_num_Code_integer(N5,aa_num_num(Ha,X2)) )
     => ( aa_num_Code_integer(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,aa_fun4435975922079263404nteger(comp_C7449957260575251196nteger(F),M2)),G),X2) = aa_num_Code_integer(comp_n6909714581898973814er_num(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),N5),Ha),X2) ) ) ).

% type_copy_map_cong0
tff(fact_497_type__copy__map__cong0,axiom,
    ! [M2: fun_Co8499238673658658103nteger,G: fun_Co8499238673658658103nteger,X2: code_integer,N5: fun_Co8499238673658658103nteger,Ha: fun_Co8499238673658658103nteger,F: fun_Co1561183069634336733nteger] :
      ( ( aa_Cod1783974652533396728nteger(M2,aa_Cod1783974652533396728nteger(G,X2)) = aa_Cod1783974652533396728nteger(N5,aa_Cod1783974652533396728nteger(Ha,X2)) )
     => ( aa_Cod1978467581589928094nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),M2)),G),X2) = aa_Cod1978467581589928094nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),N5)),Ha),X2) ) ) ).

% type_copy_map_cong0
tff(fact_498_type__copy__map__cong0,axiom,
    ! [M2: fun_Co8499238673658658103nteger,G: fun_Co8499238673658658103nteger,X2: code_integer,N5: fun_fu5689865433563736081nteger,Ha: fun_Co1981900195452921617nteger,F: fun_Co1561183069634336733nteger] :
      ( ( aa_Cod1783974652533396728nteger(M2,aa_Cod1783974652533396728nteger(G,X2)) = aa_fun2937960011630702546nteger(N5,aa_Cod4161879620478718930nteger(Ha,X2)) )
     => ( aa_Cod1978467581589928094nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),M2)),G),X2) = aa_Cod1978467581589928094nteger(comp_f6739083541385432444nteger(comp_C7827331287018003580nteger(F,N5),Ha),X2) ) ) ).

% type_copy_map_cong0
tff(fact_499_type__copy__map__cong0,axiom,
    ! [M2: fun_Co1981900195452921617nteger,G: fun_Co8499238673658658103nteger,X2: code_integer,N5: fun_Co1981900195452921617nteger,Ha: fun_Co8499238673658658103nteger,F: fun_fu4800041728187187127nteger] :
      ( ( aa_Cod4161879620478718930nteger(M2,aa_Cod1783974652533396728nteger(G,X2)) = aa_Cod4161879620478718930nteger(N5,aa_Cod1783974652533396728nteger(Ha,X2)) )
     => ( aa_Cod1978467581589928094nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,comp_f6739083541385432444nteger(F,M2)),G),X2) = aa_Cod1978467581589928094nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,comp_f6739083541385432444nteger(F,N5)),Ha),X2) ) ) ).

% type_copy_map_cong0
tff(fact_500_type__copy__map__cong0,axiom,
    ! [M2: fun_Co1981900195452921617nteger,G: fun_Co8499238673658658103nteger,X2: code_integer,N5: fun_fu1763652423599918571nteger,Ha: fun_Co1981900195452921617nteger,F: fun_fu4800041728187187127nteger] :
      ( ( aa_Cod4161879620478718930nteger(M2,aa_Cod1783974652533396728nteger(G,X2)) = aa_fun4435975922079263404nteger(N5,aa_Cod4161879620478718930nteger(Ha,X2)) )
     => ( aa_Cod1978467581589928094nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,comp_f6739083541385432444nteger(F,M2)),G),X2) = aa_Cod1978467581589928094nteger(comp_f6739083541385432444nteger(comp_f3848972703483044950nteger(F,N5),Ha),X2) ) ) ).

% type_copy_map_cong0
tff(fact_501_type__copy__map__cong0,axiom,
    ! [M2: fun_fu5689865433563736081nteger,G: fun_Co1981900195452921617nteger,X2: code_integer,N5: fun_Co8499238673658658103nteger,Ha: fun_Co8499238673658658103nteger,F: fun_Co1561183069634336733nteger] :
      ( ( aa_fun2937960011630702546nteger(M2,aa_Cod4161879620478718930nteger(G,X2)) = aa_Cod1783974652533396728nteger(N5,aa_Cod1783974652533396728nteger(Ha,X2)) )
     => ( aa_Cod1978467581589928094nteger(comp_f6739083541385432444nteger(comp_C7827331287018003580nteger(F,M2),G),X2) = aa_Cod1978467581589928094nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),N5)),Ha),X2) ) ) ).

% type_copy_map_cong0
tff(fact_502_type__copy__map__cong0,axiom,
    ! [M2: fun_fu1763652423599918571nteger,G: fun_Co1981900195452921617nteger,X2: code_integer,N5: fun_Co1981900195452921617nteger,Ha: fun_Co8499238673658658103nteger,F: fun_fu4800041728187187127nteger] :
      ( ( aa_fun4435975922079263404nteger(M2,aa_Cod4161879620478718930nteger(G,X2)) = aa_Cod4161879620478718930nteger(N5,aa_Cod1783974652533396728nteger(Ha,X2)) )
     => ( aa_Cod1978467581589928094nteger(comp_f6739083541385432444nteger(comp_f3848972703483044950nteger(F,M2),G),X2) = aa_Cod1978467581589928094nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,comp_f6739083541385432444nteger(F,N5)),Ha),X2) ) ) ).

% type_copy_map_cong0
tff(fact_503_type__copy__map__cong0,axiom,
    ! [M2: fun_nat_nat,G: fun_int_nat,X2: int,N5: fun_int_nat,Ha: fun_int_int,F: fun_nat_num] :
      ( ( aa_nat_nat(M2,aa_int_nat(G,X2)) = aa_int_nat(N5,aa_int_int(Ha,X2)) )
     => ( aa_int_num(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,comp_nat_num_nat(F,M2)),G),X2) = aa_int_num(comp_int_num_int(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),N5),Ha),X2) ) ) ).

% type_copy_map_cong0
tff(fact_504_comp__apply__eq,axiom,
    ! [F: fun_Co8499238673658658103nteger,G: fun_num_Code_integer,X2: num,Ha: fun_Co8499238673658658103nteger,K: fun_num_Code_integer] :
      ( ( aa_Cod1783974652533396728nteger(F,aa_num_Code_integer(G,X2)) = aa_Cod1783974652533396728nteger(Ha,aa_num_Code_integer(K,X2)) )
     => ( aa_num_Code_integer(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),G),X2) = aa_num_Code_integer(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,Ha),K),X2) ) ) ).

% comp_apply_eq
tff(fact_505_comp__apply__eq,axiom,
    ! [F: fun_Co1561183069634336733nteger,G: fun_Co8499238673658658103nteger,X2: code_integer,Ha: fun_Co1561183069634336733nteger,K: fun_Co8499238673658658103nteger] :
      ( ( aa_Cod1978467581589928094nteger(F,aa_Cod1783974652533396728nteger(G,X2)) = aa_Cod1978467581589928094nteger(Ha,aa_Cod1783974652533396728nteger(K,X2)) )
     => ( aa_Cod1978467581589928094nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),G),X2) = aa_Cod1978467581589928094nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,Ha),K),X2) ) ) ).

% comp_apply_eq
tff(fact_506_comp__apply__eq,axiom,
    ! [F: fun_Co1561183069634336733nteger,G: fun_Co8499238673658658103nteger,X2: code_integer,Ha: fun_fu4800041728187187127nteger,K: fun_Co1981900195452921617nteger] :
      ( ( aa_Cod1978467581589928094nteger(F,aa_Cod1783974652533396728nteger(G,X2)) = aa_fun2509385170507305080nteger(Ha,aa_Cod4161879620478718930nteger(K,X2)) )
     => ( aa_Cod1978467581589928094nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),G),X2) = aa_Cod1978467581589928094nteger(comp_f6739083541385432444nteger(Ha,K),X2) ) ) ).

% comp_apply_eq
tff(fact_507_comp__apply__eq,axiom,
    ! [F: fun_fu4800041728187187127nteger,G: fun_Co1981900195452921617nteger,X2: code_integer,Ha: fun_Co1561183069634336733nteger,K: fun_Co8499238673658658103nteger] :
      ( ( aa_fun2509385170507305080nteger(F,aa_Cod4161879620478718930nteger(G,X2)) = aa_Cod1978467581589928094nteger(Ha,aa_Cod1783974652533396728nteger(K,X2)) )
     => ( aa_Cod1978467581589928094nteger(comp_f6739083541385432444nteger(F,G),X2) = aa_Cod1978467581589928094nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,Ha),K),X2) ) ) ).

% comp_apply_eq
tff(fact_508_comp__apply__eq,axiom,
    ! [F: fun_fu4800041728187187127nteger,G: fun_Co1981900195452921617nteger,X2: code_integer,Ha: fun_fu4800041728187187127nteger,K: fun_Co1981900195452921617nteger] :
      ( ( aa_fun2509385170507305080nteger(F,aa_Cod4161879620478718930nteger(G,X2)) = aa_fun2509385170507305080nteger(Ha,aa_Cod4161879620478718930nteger(K,X2)) )
     => ( aa_Cod1978467581589928094nteger(comp_f6739083541385432444nteger(F,G),X2) = aa_Cod1978467581589928094nteger(comp_f6739083541385432444nteger(Ha,K),X2) ) ) ).

% comp_apply_eq
tff(fact_509_comp__apply__eq,axiom,
    ! [F: fun_nat_num,G: fun_int_nat,X2: int,Ha: fun_nat_num,K: fun_int_nat] :
      ( ( aa_nat_num(F,aa_int_nat(G,X2)) = aa_nat_num(Ha,aa_int_nat(K,X2)) )
     => ( aa_int_num(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),G),X2) = aa_int_num(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,Ha),K),X2) ) ) ).

% comp_apply_eq
tff(fact_510_add_Oright__commute,axiom,
    ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] : aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(A),B)),C) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(A),C)),B) ).

% add.right_commute
tff(fact_511_add_Oright__commute,axiom,
    ! [A: rat,B: rat,C: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),C) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),C)),B) ).

% add.right_commute
tff(fact_512_add_Oright__commute,axiom,
    ! [A: nat,B: nat,C: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),C) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C)),B) ).

% add.right_commute
tff(fact_513_add_Oright__commute,axiom,
    ! [A: int,B: int,C: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),C) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),C)),B) ).

% add.right_commute
tff(fact_514_add__less__cancel__right,axiom,
    ! [A: code_integer,C: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),C)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,B),C))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),B) ) ).

% add_less_cancel_right
tff(fact_515_add__less__cancel__right,axiom,
    ! [A: rat,C: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),C)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),C))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B) ) ).

% add_less_cancel_right
tff(fact_516_add__less__cancel__right,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),C))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),B) ) ).

% add_less_cancel_right
tff(fact_517_add__less__cancel__right,axiom,
    ! [A: int,C: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),C)),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),C))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,A),B) ) ).

% add_less_cancel_right
tff(fact_518_add__less__cancel__left,axiom,
    ! [C: code_integer,A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,C),A)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,C),B))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),B) ) ).

% add_less_cancel_left
tff(fact_519_add__less__cancel__left,axiom,
    ! [C: rat,A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,C),A)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,C),B))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B) ) ).

% add_less_cancel_left
tff(fact_520_add__less__cancel__left,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,C),A)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,C),B))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),B) ) ).

% add_less_cancel_left
tff(fact_521_add__less__cancel__left,axiom,
    ! [C: int,A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,C),A)),aa_int_int(aa_int_fun_int_int(plus_plus_int,C),B))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,A),B) ) ).

% add_less_cancel_left
tff(fact_522_add__less__imp__less__right,axiom,
    ! [A: code_integer,C: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),C)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,B),C))
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),B) ) ).

% add_less_imp_less_right
tff(fact_523_add__less__imp__less__right,axiom,
    ! [A: rat,C: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),C)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),C))
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B) ) ).

% add_less_imp_less_right
tff(fact_524_add__less__imp__less__right,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),C))
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),B) ) ).

% add_less_imp_less_right
tff(fact_525_add__less__imp__less__right,axiom,
    ! [A: int,C: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),C)),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),C))
     => aa_int_o(aa_int_fun_int_o(ord_less_int,A),B) ) ).

% add_less_imp_less_right
tff(fact_526_add__less__imp__less__left,axiom,
    ! [C: code_integer,A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,C),A)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,C),B))
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),B) ) ).

% add_less_imp_less_left
tff(fact_527_add__less__imp__less__left,axiom,
    ! [C: rat,A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,C),A)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,C),B))
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B) ) ).

% add_less_imp_less_left
tff(fact_528_add__less__imp__less__left,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,C),A)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,C),B))
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),B) ) ).

% add_less_imp_less_left
tff(fact_529_add__less__imp__less__left,axiom,
    ! [C: int,A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,C),A)),aa_int_int(aa_int_fun_int_int(plus_plus_int,C),B))
     => aa_int_o(aa_int_fun_int_o(ord_less_int,A),B) ) ).

% add_less_imp_less_left
tff(fact_530_add__strict__right__mono,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),B)
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),C)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,B),C)) ) ).

% add_strict_right_mono
tff(fact_531_add__strict__right__mono,axiom,
    ! [A: rat,B: rat,C: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B)
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),C)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),C)) ) ).

% add_strict_right_mono
tff(fact_532_add__strict__right__mono,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),B)
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),C)) ) ).

% add_strict_right_mono
tff(fact_533_add__strict__right__mono,axiom,
    ! [A: int,B: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,A),B)
     => aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),C)),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),C)) ) ).

% add_strict_right_mono
tff(fact_534_add__strict__left__mono,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),B)
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,C),A)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,C),B)) ) ).

% add_strict_left_mono
tff(fact_535_add__strict__left__mono,axiom,
    ! [A: rat,B: rat,C: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B)
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,C),A)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,C),B)) ) ).

% add_strict_left_mono
tff(fact_536_add__strict__left__mono,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),B)
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,C),A)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,C),B)) ) ).

% add_strict_left_mono
tff(fact_537_add__strict__left__mono,axiom,
    ! [A: int,B: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,A),B)
     => aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,C),A)),aa_int_int(aa_int_fun_int_int(plus_plus_int,C),B)) ) ).

% add_strict_left_mono
tff(fact_538_add__strict__mono,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),B)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,C),D2)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),C)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,B),D2)) ) ) ).

% add_strict_mono
tff(fact_539_add__strict__mono,axiom,
    ! [A: rat,B: rat,C: rat,D2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,C),D2)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),C)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),D2)) ) ) ).

% add_strict_mono
tff(fact_540_add__strict__mono,axiom,
    ! [A: nat,B: nat,C: nat,D2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),B)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,C),D2)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),D2)) ) ) ).

% add_strict_mono
tff(fact_541_add__strict__mono,axiom,
    ! [A: int,B: int,C: int,D2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,A),B)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,C),D2)
       => aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),C)),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),D2)) ) ) ).

% add_strict_mono
tff(fact_542_add__mono__thms__linordered__field_I1_J,axiom,
    ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
      ( ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,I),J)
        & ( K = L ) )
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,I),K)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,J),L)) ) ).

% add_mono_thms_linordered_field(1)
tff(fact_543_add__mono__thms__linordered__field_I1_J,axiom,
    ! [I: rat,J: rat,K: rat,L: rat] :
      ( ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,I),J)
        & ( K = L ) )
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,I),K)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,J),L)) ) ).

% add_mono_thms_linordered_field(1)
tff(fact_544_add__mono__thms__linordered__field_I1_J,axiom,
    ! [I: nat,J: nat,K: nat,L: nat] :
      ( ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,I),J)
        & ( K = L ) )
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),L)) ) ).

% add_mono_thms_linordered_field(1)
tff(fact_545_add__mono__thms__linordered__field_I1_J,axiom,
    ! [I: int,J: int,K: int,L: int] :
      ( ( aa_int_o(aa_int_fun_int_o(ord_less_int,I),J)
        & ( K = L ) )
     => aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,I),K)),aa_int_int(aa_int_fun_int_int(plus_plus_int,J),L)) ) ).

% add_mono_thms_linordered_field(1)
tff(fact_546_add__mono__thms__linordered__field_I2_J,axiom,
    ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
      ( ( ( I = J )
        & aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,K),L) )
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,I),K)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,J),L)) ) ).

% add_mono_thms_linordered_field(2)
tff(fact_547_add__mono__thms__linordered__field_I2_J,axiom,
    ! [I: rat,J: rat,K: rat,L: rat] :
      ( ( ( I = J )
        & aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,K),L) )
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,I),K)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,J),L)) ) ).

% add_mono_thms_linordered_field(2)
tff(fact_548_add__mono__thms__linordered__field_I2_J,axiom,
    ! [I: nat,J: nat,K: nat,L: nat] :
      ( ( ( I = J )
        & aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,K),L) )
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),L)) ) ).

% add_mono_thms_linordered_field(2)
tff(fact_549_add__mono__thms__linordered__field_I2_J,axiom,
    ! [I: int,J: int,K: int,L: int] :
      ( ( ( I = J )
        & aa_int_o(aa_int_fun_int_o(ord_less_int,K),L) )
     => aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,I),K)),aa_int_int(aa_int_fun_int_int(plus_plus_int,J),L)) ) ).

% add_mono_thms_linordered_field(2)
tff(fact_550_add__mono__thms__linordered__field_I5_J,axiom,
    ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
      ( ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,I),J)
        & aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,K),L) )
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,I),K)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,J),L)) ) ).

% add_mono_thms_linordered_field(5)
tff(fact_551_add__mono__thms__linordered__field_I5_J,axiom,
    ! [I: rat,J: rat,K: rat,L: rat] :
      ( ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,I),J)
        & aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,K),L) )
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,I),K)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,J),L)) ) ).

% add_mono_thms_linordered_field(5)
tff(fact_552_add__mono__thms__linordered__field_I5_J,axiom,
    ! [I: nat,J: nat,K: nat,L: nat] :
      ( ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,I),J)
        & aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,K),L) )
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),L)) ) ).

% add_mono_thms_linordered_field(5)
tff(fact_553_add__mono__thms__linordered__field_I5_J,axiom,
    ! [I: int,J: int,K: int,L: int] :
      ( ( aa_int_o(aa_int_fun_int_o(ord_less_int,I),J)
        & aa_int_o(aa_int_fun_int_o(ord_less_int,K),L) )
     => aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,I),K)),aa_int_int(aa_int_fun_int_int(plus_plus_int,J),L)) ) ).

% add_mono_thms_linordered_field(5)
tff(fact_554_success__returnI,axiom,
    ! [X2: product_unit,Ha: heap_e7401611519738050253t_unit] : aa_hea7994211679605476167unit_o(heap_T584514906347983379t_unit(aa_Pro1108561329362217960t_unit(heap_T7507251653302230130t_unit,X2)),Ha) ).

% success_returnI
tff(fact_555_success__returnI,axiom,
    ! [X2: array_a,Ha: heap_e7401611519738050253t_unit] : aa_hea7994211679605476167unit_o(heap_T6932021131025641745rray_a(aa_arr1142863274018860686rray_a(heap_T4896204969850773234rray_a,X2)),Ha) ).

% success_returnI
tff(fact_556_fails__return,axiom,
    ! [X2: product_unit,Ha: heap_e7401611519738050253t_unit] : ~ aa_hea7994211679605476167unit_o(time_f8834461667527620124t_unit(aa_Pro1108561329362217960t_unit(heap_T7507251653302230130t_unit,X2)),Ha) ).

% fails_return
tff(fact_557_fails__return,axiom,
    ! [X2: array_a,Ha: heap_e7401611519738050253t_unit] : ~ aa_hea7994211679605476167unit_o(time_fails_array_a(aa_arr1142863274018860686rray_a(heap_T4896204969850773234rray_a,X2)),Ha) ).

% fails_return
tff(fact_558_add_Oright__assoc,axiom,
    ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] : aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(A),B)),C) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(A),aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(B),C)) ).

% add.right_assoc
tff(fact_559_add_Oright__assoc,axiom,
    ! [A: rat,B: rat,C: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),C) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),C)) ).

% add.right_assoc
tff(fact_560_add_Oright__assoc,axiom,
    ! [A: nat,B: nat,C: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),C) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),C)) ).

% add.right_assoc
tff(fact_561_add_Oright__assoc,axiom,
    ! [A: int,B: int,C: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),C) = aa_int_int(aa_int_fun_int_int(plus_plus_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),C)) ).

% add.right_assoc
tff(fact_562_nat__add__left__cancel__less,axiom,
    ! [K: nat,M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,K),M)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,K),N2))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M),N2) ) ).

% nat_add_left_cancel_less
tff(fact_563_less__option__Some,axiom,
    ! [X2: code_integer,Y: code_integer] :
      ( ord_le7113747843092208513nteger(aa_Cod5017737808611256136nteger(some_Code_integer,X2),aa_Cod5017737808611256136nteger(some_Code_integer,Y))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,X2),Y) ) ).

% less_option_Some
tff(fact_564_less__option__Some,axiom,
    ! [X2: rat,Y: rat] :
      ( ord_less_option_rat(some_rat(X2),some_rat(Y))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,X2),Y) ) ).

% less_option_Some
tff(fact_565_less__option__Some,axiom,
    ! [X2: num,Y: num] :
      ( aa_option_num_o(aa_opt8674010985164783839_num_o(ord_less_option_num,aa_num_option_num(some_num,X2)),aa_num_option_num(some_num,Y))
    <=> aa_num_o(aa_num_fun_num_o(ord_less_num,X2),Y) ) ).

% less_option_Some
tff(fact_566_less__option__Some,axiom,
    ! [X2: nat,Y: nat] :
      ( ord_less_option_nat(aa_nat_option_nat(some_nat,X2),aa_nat_option_nat(some_nat,Y))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,X2),Y) ) ).

% less_option_Some
tff(fact_567_less__option__Some,axiom,
    ! [X2: int,Y: int] :
      ( ord_less_option_int(aa_int_option_int(some_int,X2),aa_int_option_int(some_int,Y))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,X2),Y) ) ).

% less_option_Some
tff(fact_568_fold__atLeastAtMost__nat_Opelims,axiom,
    ! [X2: fun_nat_fun_nat_nat,Xa: nat,Xb: nat,Xc: nat,Y: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(set_fo2584398358068434914at_nat(X2,Xa),Xb),Xc) = Y )
     => ( accp_P4694664897847628410at_nat(set_fo3699595496184130361el_nat,produc2818902965508115497at_nat(X2,produc487386426758144856at_nat(Xa,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Xb),Xc))))
       => ~ ( ( Y = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,Xb),Xa),Xc,aa_nat_nat(aa_nat_fun_nat_nat(set_fo2584398358068434914at_nat(X2,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Xa),one_one_nat)),Xb),aa_nat_nat(aa_nat_fun_nat_nat(X2,Xa),Xc))) )
           => ~ accp_P4694664897847628410at_nat(set_fo3699595496184130361el_nat,produc2818902965508115497at_nat(X2,produc487386426758144856at_nat(Xa,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Xb),Xc)))) ) ) ) ).

% fold_atLeastAtMost_nat.pelims
tff(fact_569_fold__atLeastAtMost__nat_Opsimps,axiom,
    ! [F: fun_nat_fun_nat_nat,A: nat,B: nat,Acc: nat] :
      ( accp_P4694664897847628410at_nat(set_fo3699595496184130361el_nat,produc2818902965508115497at_nat(F,produc487386426758144856at_nat(A,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,B),Acc))))
     => ( aa_nat_nat(aa_nat_fun_nat_nat(set_fo2584398358068434914at_nat(F,A),B),Acc) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,B),A),Acc,aa_nat_nat(aa_nat_fun_nat_nat(set_fo2584398358068434914at_nat(F,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),one_one_nat)),B),aa_nat_nat(aa_nat_fun_nat_nat(F,A),Acc))) ) ) ).

% fold_atLeastAtMost_nat.psimps
tff(fact_570_in__measure,axiom,
    ! [X2: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,F: fun_se4097146774670233028at_nat] :
      ( member8757157785044589968at_nat(produc2922128104949294807at_nat(X2,Y),measur1827424007717751593at_nat(F))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_set4749074711808745205at_nat(F,X2)),aa_set4749074711808745205at_nat(F,Y)) ) ).

% in_measure
tff(fact_571_in__measure,axiom,
    ! [X2: nat,Y: nat,F: fun_nat_nat] :
      ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X2),Y),measure_nat(F))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(F,X2)),aa_nat_nat(F,Y)) ) ).

% in_measure
tff(fact_572_less__add__one,axiom,
    ! [A: code_integer] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),one_one_Code_integer)) ).

% less_add_one
tff(fact_573_less__add__one,axiom,
    ! [A: rat] : aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),one_one_rat)) ).

% less_add_one
tff(fact_574_less__add__one,axiom,
    ! [A: nat] : aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),one_one_nat)) ).

% less_add_one
tff(fact_575_less__add__one,axiom,
    ! [A: int] : aa_int_o(aa_int_fun_int_o(ord_less_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),one_one_int)) ).

% less_add_one
tff(fact_576_add__mono1,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),B)
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),one_one_Code_integer)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,B),one_one_Code_integer)) ) ).

% add_mono1
tff(fact_577_add__mono1,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B)
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),one_one_rat)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),one_one_rat)) ) ).

% add_mono1
tff(fact_578_add__mono1,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),B)
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),one_one_nat)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),one_one_nat)) ) ).

% add_mono1
tff(fact_579_add__mono1,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,A),B)
     => aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),one_one_int)),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),one_one_int)) ) ).

% add_mono1
tff(fact_580_add__lessD1,axiom,
    ! [I: nat,J: nat,K: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),J)),K)
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,I),K) ) ).

% add_lessD1
tff(fact_581_add__less__mono,axiom,
    ! [I: nat,J: nat,K: nat,L: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,I),J)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,K),L)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),L)) ) ) ).

% add_less_mono
tff(fact_582_not__add__less1,axiom,
    ! [I: nat,J: nat] : ~ aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),J)),I) ).

% not_add_less1
tff(fact_583_less__option__None,axiom,
    ! [X2: option_num] : ~ aa_option_num_o(aa_opt8674010985164783839_num_o(ord_less_option_num,X2),none_num) ).

% less_option_None
tff(fact_584_less__option__None__Some__code,axiom,
    ! [X2: num] : aa_option_num_o(aa_opt8674010985164783839_num_o(ord_less_option_num,none_num),aa_num_option_num(some_num,X2)) ).

% less_option_None_Some_code
tff(fact_585_less__option__None__Some,axiom,
    ! [X2: num] : aa_option_num_o(aa_opt8674010985164783839_num_o(ord_less_option_num,none_num),aa_num_option_num(some_num,X2)) ).

% less_option_None_Some
tff(fact_586_less__option__None__is__Some,axiom,
    ! [X2: option_num] :
      ( aa_option_num_o(aa_opt8674010985164783839_num_o(ord_less_option_num,none_num),X2)
     => ? [Z2: num] : X2 = aa_num_option_num(some_num,Z2) ) ).

% less_option_None_is_Some
tff(fact_587_fold__atLeastAtMost__nat_Osimps,axiom,
    ! [F: fun_nat_fun_nat_nat,A: nat,B: nat,Acc: nat] :
      aa_nat_nat(aa_nat_fun_nat_nat(set_fo2584398358068434914at_nat(F,A),B),Acc) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,B),A),Acc,aa_nat_nat(aa_nat_fun_nat_nat(set_fo2584398358068434914at_nat(F,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),one_one_nat)),B),aa_nat_nat(aa_nat_fun_nat_nat(F,A),Acc))) ).

% fold_atLeastAtMost_nat.simps
tff(fact_588_fold__atLeastAtMost__nat_Oelims,axiom,
    ! [X2: fun_nat_fun_nat_nat,Xa: nat,Xb: nat,Xc: nat,Y: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(set_fo2584398358068434914at_nat(X2,Xa),Xb),Xc) = Y )
     => ( Y = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,Xb),Xa),Xc,aa_nat_nat(aa_nat_fun_nat_nat(set_fo2584398358068434914at_nat(X2,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Xa),one_one_nat)),Xb),aa_nat_nat(aa_nat_fun_nat_nat(X2,Xa),Xc))) ) ) ).

% fold_atLeastAtMost_nat.elims
tff(fact_589_less__add__eq__less,axiom,
    ! [K: nat,L: nat,M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,K),L)
     => ( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),L) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,K),N2) )
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M),N2) ) ) ).

% less_add_eq_less
tff(fact_590_trans__less__add2,axiom,
    ! [I: nat,J: nat,M: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,I),J)
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,I),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),J)) ) ).

% trans_less_add2
tff(fact_591_trans__less__add1,axiom,
    ! [I: nat,J: nat,M: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,I),J)
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,I),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),M)) ) ).

% trans_less_add1
tff(fact_592_add__less__mono1,axiom,
    ! [I: nat,J: nat,K: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,I),J)
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),K)) ) ).

% add_less_mono1
tff(fact_593_not__add__less2,axiom,
    ! [J: nat,I: nat] : ~ aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),I)),I) ).

% not_add_less2
tff(fact_594_less__numeral__extra_I4_J,axiom,
    ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),one_one_Code_integer) ).

% less_numeral_extra(4)
tff(fact_595_less__numeral__extra_I4_J,axiom,
    ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),one_one_rat) ).

% less_numeral_extra(4)
tff(fact_596_less__numeral__extra_I4_J,axiom,
    ~ aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,one_one_nat),one_one_nat) ).

% less_numeral_extra(4)
tff(fact_597_less__numeral__extra_I4_J,axiom,
    ~ aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),one_one_int) ).

% less_numeral_extra(4)
tff(fact_598_mlex__iff,axiom,
    ! [X2: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,F: fun_se4097146774670233028at_nat,R3: set_Pr4329608150637261639at_nat] :
      ( member8757157785044589968at_nat(produc2922128104949294807at_nat(X2,Y),mlex_p3502713205431853936at_nat(F,R3))
    <=> ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_set4749074711808745205at_nat(F,X2)),aa_set4749074711808745205at_nat(F,Y))
        | ( ( aa_set4749074711808745205at_nat(F,X2) = aa_set4749074711808745205at_nat(F,Y) )
          & member8757157785044589968at_nat(produc2922128104949294807at_nat(X2,Y),R3) ) ) ) ).

% mlex_iff
tff(fact_599_mlex__iff,axiom,
    ! [X2: nat,Y: nat,F: fun_nat_nat,R3: set_Pr1261947904930325089at_nat] :
      ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X2),Y),aa_set8868280134176360700at_nat(mlex_prod_nat(F),R3))
    <=> ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(F,X2)),aa_nat_nat(F,Y))
        | ( ( aa_nat_nat(F,X2) = aa_nat_nat(F,Y) )
          & member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X2),Y),R3) ) ) ) ).

% mlex_iff
tff(fact_600_mlex__less,axiom,
    ! [F: fun_se4097146774670233028at_nat,X2: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,R3: set_Pr4329608150637261639at_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_set4749074711808745205at_nat(F,X2)),aa_set4749074711808745205at_nat(F,Y))
     => member8757157785044589968at_nat(produc2922128104949294807at_nat(X2,Y),mlex_p3502713205431853936at_nat(F,R3)) ) ).

% mlex_less
tff(fact_601_mlex__less,axiom,
    ! [F: fun_nat_nat,X2: nat,Y: nat,R3: set_Pr1261947904930325089at_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(F,X2)),aa_nat_nat(F,Y))
     => member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X2),Y),aa_set8868280134176360700at_nat(mlex_prod_nat(F),R3)) ) ).

% mlex_less
tff(fact_602_pairself_Opelims,axiom,
    ! [X2: fun_in5730379987311621695e_term,Xa: product_prod_int_int,Y: produc6576344331059438605e_term] :
      ( ( pairse3534876335208825186e_term(X2,Xa) = Y )
     => ( aa_Pro5451197003417746155_int_o(accp_P3253464921323968230nt_int(pairse6848479906795794847e_term),aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X2),Xa))
       => ~ ! [A3: int,B2: int] :
              ( ( Xa = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A3),B2) )
             => ( ( Y = produc5950683997804057413e_term(aa_int3262262799336221824e_term(X2,A3),aa_int3262262799336221824e_term(X2,B2)) )
               => ~ aa_Pro5451197003417746155_int_o(accp_P3253464921323968230nt_int(pairse6848479906795794847e_term),aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X2),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A3),B2))) ) ) ) ) ).

% pairself.pelims
tff(fact_603_execute__return,axiom,
    ! [X2: array_a] : heap_T5591663578999710211rray_a(aa_arr1142863274018860686rray_a(heap_T4896204969850773234rray_a,X2)) = comp_P2097125496263478628t_unit(some_P6105628898608307625it_nat,aTP_Lamm_af(X2)) ).

% execute_return
tff(fact_604_execute__return,axiom,
    ! [X2: product_unit] : heap_T875086893843062177t_unit(aa_Pro1108561329362217960t_unit(heap_T7507251653302230130t_unit,X2)) = comp_P3118722334806803912t_unit(some_P1914260805536162275it_nat,aTP_Lamm_ag(X2)) ).

% execute_return
tff(fact_605_same__fstI,axiom,
    ! [P: fun_fu4736795817735658359term_o,X2: fun_Pr5098669352780829690e_term,Y6: produc8923325533196201883nteger,Y: produc8923325533196201883nteger,R3: fun_fu8543582513329703974nteger] :
      ( aa_fun7993445754732355552term_o(P,X2)
     => ( member335077259223437328nteger(produc4911887526399440471nteger(Y6,Y),aa_fun435912938702255631nteger(R3,X2))
       => member5045372342328489014nteger(produc2269347123789068741nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X2),Y6),aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X2),Y)),same_f8215626710265358387nteger(P,R3)) ) ) ).

% same_fstI
tff(fact_606_same__fstI,axiom,
    ! [P: fun_fu5135969500543783852at_o_o,X2: fun_Pr6460944699146269935_nat_o,Y6: produc3658429121746597890et_nat,Y: produc3658429121746597890et_nat,R3: fun_fu5004560472337415769et_nat] :
      ( aa_fun1675921005893230629at_o_o(P,X2)
     => ( member6099555550032318734et_nat(produc8199053930788261021et_nat(Y6,Y),aa_fun8297425419345108306et_nat(R3,X2))
       => member2216856746449346506et_nat(produc8050396023069295193et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X2),Y6),aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X2),Y)),same_f842378046369478405et_nat(P,R3)) ) ) ).

% same_fstI
tff(fact_607_same__fstI,axiom,
    ! [P: fun_fu5135969500543783852at_o_o,X2: fun_Pr6460944699146269935_nat_o,Y6: produc8799533983703829792et_nat,Y: produc8799533983703829792et_nat,R3: fun_fu951349246861503509et_nat] :
      ( aa_fun1675921005893230629at_o_o(P,X2)
     => ( member2216856746449346506et_nat(produc8050396023069295193et_nat(Y6,Y),aa_fun313470179692725518et_nat(R3,X2))
       => member2136425100634443654et_nat(produc7768440062179809557et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X2),Y6),aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X2),Y)),same_f7796809703074202275et_nat(P,R3)) ) ) ).

% same_fstI
tff(fact_608_same__fstI,axiom,
    ! [P: fun_fu6378075912484669126term_o,X2: fun_Pr7763680713840462443e_term,Y6: product_prod_int_int,Y: product_prod_int_int,R3: fun_fu4812223801888690549nt_int] :
      ( aa_fun7650857933016935215term_o(P,X2)
     => ( member8566619992076573584nt_int(produc3646306378393792727nt_int(Y6,Y),aa_fun5011775822604196702nt_int(R3,X2))
       => member8789097660028509840nt_int(produc5411871556384885407nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X2),Y6),aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X2),Y)),same_f9192169231508103328nt_int(P,R3)) ) ) ).

% same_fstI
tff(fact_609_same__fstI,axiom,
    ! [P: fun_fu3265955482920998386term_o,X2: fun_in5730379987311621695e_term,Y6: product_prod_int_int,Y: product_prod_int_int,R3: fun_fu786557078278636193nt_int] :
      ( aa_fun3020711759848831579term_o(P,X2)
     => ( member8566619992076573584nt_int(produc3646306378393792727nt_int(Y6,Y),aa_fun4587069911532227722nt_int(R3,X2))
       => member9155761383210387176nt_int(produc4613263410003446007nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X2),Y6),aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X2),Y)),same_f1121446225334236108nt_int(P,R3)) ) ) ).

% same_fstI
tff(fact_610_zero__less__two,axiom,
    aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,one_one_Code_integer),one_one_Code_integer)) ).

% zero_less_two
tff(fact_611_zero__less__two,axiom,
    aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,one_one_rat),one_one_rat)) ).

% zero_less_two
tff(fact_612_zero__less__two,axiom,
    aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)) ).

% zero_less_two
tff(fact_613_zero__less__two,axiom,
    aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)) ).

% zero_less_two
tff(fact_614_is__num__normalize_I1_J,axiom,
    ! [A: rat,B: rat,C: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),C) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),C)) ).

% is_num_normalize(1)
tff(fact_615_is__num__normalize_I1_J,axiom,
    ! [A: int,B: int,C: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),C) = aa_int_int(aa_int_fun_int_int(plus_plus_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),C)) ).

% is_num_normalize(1)
tff(fact_616_add_Osafe__commute,axiom,
    ! [X2: multis2468970476368604999at_nat,Y: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
      ( syntax5084084251851430274at_nat(aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(X2),Y),A)
     => ( aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(A),B) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(B),A) ) ) ).

% add.safe_commute
tff(fact_617_add_Osafe__commute,axiom,
    ! [X2: rat,Y: rat,A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(syntax3730441303064801268at_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),Y)),A)
     => ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),A) ) ) ).

% add.safe_commute
tff(fact_618_add_Osafe__commute,axiom,
    ! [X2: nat,Y: nat,A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(syntax4682126007086162916at_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X2),Y)),A)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),A) ) ) ).

% add.safe_commute
tff(fact_619_add_Osafe__commute,axiom,
    ! [X2: int,Y: int,A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(syntax5678989248478167196nt_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),Y)),A)
     => ( aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B) = aa_int_int(aa_int_fun_int_int(plus_plus_int,B),A) ) ) ).

% add.safe_commute
tff(fact_620_bijective__def,axiom,
    ! [R3: set_Pr4329608150637261639at_nat] :
      ( biject3388518990857851981at_nat(R3)
    <=> ( ! [X4: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] :
            ( ( member8757157785044589968at_nat(produc2922128104949294807at_nat(X4,Y3),R3)
              & member8757157785044589968at_nat(produc2922128104949294807at_nat(X4,Z3),R3) )
           => ( Y3 = Z3 ) )
        & ! [X4: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] :
            ( ( member8757157785044589968at_nat(produc2922128104949294807at_nat(X4,Z3),R3)
              & member8757157785044589968at_nat(produc2922128104949294807at_nat(Y3,Z3),R3) )
           => ( X4 = Y3 ) ) ) ) ).

% bijective_def
tff(fact_621_bijective__def,axiom,
    ! [R3: set_Pr1261947904930325089at_nat] :
      ( bijective_nat_nat(R3)
    <=> ( ! [X4: nat,Y3: nat,Z3: nat] :
            ( ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X4),Y3),R3)
              & member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X4),Z3),R3) )
           => ( Y3 = Z3 ) )
        & ! [X4: nat,Y3: nat,Z3: nat] :
            ( ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X4),Z3),R3)
              & member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Y3),Z3),R3) )
           => ( X4 = Y3 ) ) ) ) ).

% bijective_def
tff(fact_622_bijective__def,axiom,
    ! [R3: set_Pr3486312109254157132nteger] :
      ( biject6040901034283248210nteger(R3)
    <=> ( ! [X4: fun_Pr5098669352780829690e_term,Y3: produc8923325533196201883nteger,Z3: produc8923325533196201883nteger] :
            ( ( member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X4),Y3),R3)
              & member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X4),Z3),R3) )
           => ( Y3 = Z3 ) )
        & ! [X4: fun_Pr5098669352780829690e_term,Y3: fun_Pr5098669352780829690e_term,Z3: produc8923325533196201883nteger] :
            ( ( member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X4),Z3),R3)
              & member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,Y3),Z3),R3) )
           => ( X4 = Y3 ) ) ) ) ).

% bijective_def
tff(fact_623_bijective__def,axiom,
    ! [R3: set_Pr1312406793078187350et_nat] :
      ( biject6574446902887564708et_nat(R3)
    <=> ( ! [X4: fun_Pr6460944699146269935_nat_o,Y3: produc3658429121746597890et_nat,Z3: produc3658429121746597890et_nat] :
            ( ( member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X4),Y3),R3)
              & member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X4),Z3),R3) )
           => ( Y3 = Z3 ) )
        & ! [X4: fun_Pr6460944699146269935_nat_o,Y3: fun_Pr6460944699146269935_nat_o,Z3: produc3658429121746597890et_nat] :
            ( ( member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X4),Z3),R3)
              & member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,Y3),Z3),R3) )
           => ( X4 = Y3 ) ) ) ) ).

% bijective_def
tff(fact_624_bijective__def,axiom,
    ! [R3: set_Pr4040394263813967220et_nat] :
      ( biject4066639966817638850et_nat(R3)
    <=> ( ! [X4: fun_Pr6460944699146269935_nat_o,Y3: produc8799533983703829792et_nat,Z3: produc8799533983703829792et_nat] :
            ( ( member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X4),Y3),R3)
              & member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X4),Z3),R3) )
           => ( Y3 = Z3 ) )
        & ! [X4: fun_Pr6460944699146269935_nat_o,Y3: fun_Pr6460944699146269935_nat_o,Z3: produc8799533983703829792et_nat] :
            ( ( member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X4),Z3),R3)
              & member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,Y3),Z3),R3) )
           => ( X4 = Y3 ) ) ) ) ).

% bijective_def
tff(fact_625_bijective__def,axiom,
    ! [R3: set_Pr6700895561065273913nt_int] :
      ( biject1579208791189821119nt_int(R3)
    <=> ( ! [X4: fun_Pr7763680713840462443e_term,Y3: product_prod_int_int,Z3: product_prod_int_int] :
            ( ( member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X4),Y3),R3)
              & member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X4),Z3),R3) )
           => ( Y3 = Z3 ) )
        & ! [X4: fun_Pr7763680713840462443e_term,Y3: fun_Pr7763680713840462443e_term,Z3: product_prod_int_int] :
            ( ( member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X4),Z3),R3)
              & member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,Y3),Z3),R3) )
           => ( X4 = Y3 ) ) ) ) ).

% bijective_def
tff(fact_626_bijective__def,axiom,
    ! [R3: set_Pr4166680992137330533nt_int] :
      ( biject9165800892491502059nt_int(R3)
    <=> ( ! [X4: fun_in5730379987311621695e_term,Y3: product_prod_int_int,Z3: product_prod_int_int] :
            ( ( member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X4),Y3),R3)
              & member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X4),Z3),R3) )
           => ( Y3 = Z3 ) )
        & ! [X4: fun_in5730379987311621695e_term,Y3: fun_in5730379987311621695e_term,Z3: product_prod_int_int] :
            ( ( member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X4),Z3),R3)
              & member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,Y3),Z3),R3) )
           => ( X4 = Y3 ) ) ) ) ).

% bijective_def
tff(fact_627_ssubst__Pair__rhs,axiom,
    ! [R2: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat,R3: set_Pr4329608150637261639at_nat,S3: set_Pr1261947904930325089at_nat] :
      ( member8757157785044589968at_nat(produc2922128104949294807at_nat(R2,S),R3)
     => ( ( S3 = S )
       => member8757157785044589968at_nat(produc2922128104949294807at_nat(R2,S3),R3) ) ) ).

% ssubst_Pair_rhs
tff(fact_628_ssubst__Pair__rhs,axiom,
    ! [R2: nat,S: nat,R3: set_Pr1261947904930325089at_nat,S3: nat] :
      ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,R2),S),R3)
     => ( ( S3 = S )
       => member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,R2),S3),R3) ) ) ).

% ssubst_Pair_rhs
tff(fact_629_ssubst__Pair__rhs,axiom,
    ! [R2: fun_Pr5098669352780829690e_term,S: produc8923325533196201883nteger,R3: set_Pr3486312109254157132nteger,S3: produc8923325533196201883nteger] :
      ( member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,R2),S),R3)
     => ( ( S3 = S )
       => member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,R2),S3),R3) ) ) ).

% ssubst_Pair_rhs
tff(fact_630_ssubst__Pair__rhs,axiom,
    ! [R2: fun_Pr6460944699146269935_nat_o,S: produc3658429121746597890et_nat,R3: set_Pr1312406793078187350et_nat,S3: produc3658429121746597890et_nat] :
      ( member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,R2),S),R3)
     => ( ( S3 = S )
       => member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,R2),S3),R3) ) ) ).

% ssubst_Pair_rhs
tff(fact_631_ssubst__Pair__rhs,axiom,
    ! [R2: fun_Pr6460944699146269935_nat_o,S: produc8799533983703829792et_nat,R3: set_Pr4040394263813967220et_nat,S3: produc8799533983703829792et_nat] :
      ( member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,R2),S),R3)
     => ( ( S3 = S )
       => member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,R2),S3),R3) ) ) ).

% ssubst_Pair_rhs
tff(fact_632_ssubst__Pair__rhs,axiom,
    ! [R2: fun_Pr7763680713840462443e_term,S: product_prod_int_int,R3: set_Pr6700895561065273913nt_int,S3: product_prod_int_int] :
      ( member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,R2),S),R3)
     => ( ( S3 = S )
       => member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,R2),S3),R3) ) ) ).

% ssubst_Pair_rhs
tff(fact_633_ssubst__Pair__rhs,axiom,
    ! [R2: fun_in5730379987311621695e_term,S: product_prod_int_int,R3: set_Pr4166680992137330533nt_int,S3: product_prod_int_int] :
      ( member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,R2),S),R3)
     => ( ( S3 = S )
       => member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,R2),S3),R3) ) ) ).

% ssubst_Pair_rhs
tff(fact_634_add__is__0,axiom,
    ! [M: nat,N2: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2) = zero_zero_nat )
    <=> ( ( M = zero_zero_nat )
        & ( N2 = zero_zero_nat ) ) ) ).

% add_is_0
tff(fact_635_Nat_Oadd__0__right,axiom,
    ! [M: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),zero_zero_nat) = M ).

% Nat.add_0_right
tff(fact_636_not__gr__zero,axiom,
    ! [N2: nat] :
      ( ~ aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
    <=> ( N2 = zero_zero_nat ) ) ).

% not_gr_zero
tff(fact_637_add__0,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,zero_z3403309356797280102nteger),A) = A ).

% add_0
tff(fact_638_add__0,axiom,
    ! [A: multis2468970476368604999at_nat] : aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(zero_z1048942125864253310at_nat),A) = A ).

% add_0
tff(fact_639_add__0,axiom,
    ! [A: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,zero_zero_rat),A) = A ).

% add_0
tff(fact_640_add__0,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),A) = A ).

% add_0
tff(fact_641_add__0,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,zero_zero_int),A) = A ).

% add_0
tff(fact_642_zero__eq__add__iff__both__eq__0,axiom,
    ! [X2: nat,Y: nat] :
      ( ( zero_zero_nat = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X2),Y) )
    <=> ( ( X2 = zero_zero_nat )
        & ( Y = zero_zero_nat ) ) ) ).

% zero_eq_add_iff_both_eq_0
tff(fact_643_add__eq__0__iff__both__eq__0,axiom,
    ! [X2: nat,Y: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X2),Y) = zero_zero_nat )
    <=> ( ( X2 = zero_zero_nat )
        & ( Y = zero_zero_nat ) ) ) ).

% add_eq_0_iff_both_eq_0
tff(fact_644_add__cancel__right__right,axiom,
    ! [A: code_integer,B: code_integer] :
      ( ( A = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B) )
    <=> ( B = zero_z3403309356797280102nteger ) ) ).

% add_cancel_right_right
tff(fact_645_add__cancel__right__right,axiom,
    ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
      ( ( A = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(A),B) )
    <=> ( B = zero_z1048942125864253310at_nat ) ) ).

% add_cancel_right_right
tff(fact_646_add__cancel__right__right,axiom,
    ! [A: rat,B: rat] :
      ( ( A = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B) )
    <=> ( B = zero_zero_rat ) ) ).

% add_cancel_right_right
tff(fact_647_add__cancel__right__right,axiom,
    ! [A: nat,B: nat] :
      ( ( A = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) )
    <=> ( B = zero_zero_nat ) ) ).

% add_cancel_right_right
tff(fact_648_add__cancel__right__right,axiom,
    ! [A: int,B: int] :
      ( ( A = aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B) )
    <=> ( B = zero_zero_int ) ) ).

% add_cancel_right_right
tff(fact_649_add__cancel__right__left,axiom,
    ! [A: code_integer,B: code_integer] :
      ( ( A = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,B),A) )
    <=> ( B = zero_z3403309356797280102nteger ) ) ).

% add_cancel_right_left
tff(fact_650_add__cancel__right__left,axiom,
    ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
      ( ( A = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(B),A) )
    <=> ( B = zero_z1048942125864253310at_nat ) ) ).

% add_cancel_right_left
tff(fact_651_add__cancel__right__left,axiom,
    ! [A: rat,B: rat] :
      ( ( A = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),A) )
    <=> ( B = zero_zero_rat ) ) ).

% add_cancel_right_left
tff(fact_652_add__cancel__right__left,axiom,
    ! [A: nat,B: nat] :
      ( ( A = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),A) )
    <=> ( B = zero_zero_nat ) ) ).

% add_cancel_right_left
tff(fact_653_add__cancel__right__left,axiom,
    ! [A: int,B: int] :
      ( ( A = aa_int_int(aa_int_fun_int_int(plus_plus_int,B),A) )
    <=> ( B = zero_zero_int ) ) ).

% add_cancel_right_left
tff(fact_654_add__cancel__left__right,axiom,
    ! [A: code_integer,B: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B) = A )
    <=> ( B = zero_z3403309356797280102nteger ) ) ).

% add_cancel_left_right
tff(fact_655_add__cancel__left__right,axiom,
    ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
      ( ( aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(A),B) = A )
    <=> ( B = zero_z1048942125864253310at_nat ) ) ).

% add_cancel_left_right
tff(fact_656_add__cancel__left__right,axiom,
    ! [A: rat,B: rat] :
      ( ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B) = A )
    <=> ( B = zero_zero_rat ) ) ).

% add_cancel_left_right
tff(fact_657_add__cancel__left__right,axiom,
    ! [A: nat,B: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = A )
    <=> ( B = zero_zero_nat ) ) ).

% add_cancel_left_right
tff(fact_658_add__cancel__left__right,axiom,
    ! [A: int,B: int] :
      ( ( aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B) = A )
    <=> ( B = zero_zero_int ) ) ).

% add_cancel_left_right
tff(fact_659_add__cancel__left__left,axiom,
    ! [B: code_integer,A: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,B),A) = A )
    <=> ( B = zero_z3403309356797280102nteger ) ) ).

% add_cancel_left_left
tff(fact_660_add__cancel__left__left,axiom,
    ! [B: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat] :
      ( ( aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(B),A) = A )
    <=> ( B = zero_z1048942125864253310at_nat ) ) ).

% add_cancel_left_left
tff(fact_661_add__cancel__left__left,axiom,
    ! [B: rat,A: rat] :
      ( ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),A) = A )
    <=> ( B = zero_zero_rat ) ) ).

% add_cancel_left_left
tff(fact_662_add__cancel__left__left,axiom,
    ! [B: nat,A: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),A) = A )
    <=> ( B = zero_zero_nat ) ) ).

% add_cancel_left_left
tff(fact_663_add__cancel__left__left,axiom,
    ! [B: int,A: int] :
      ( ( aa_int_int(aa_int_fun_int_int(plus_plus_int,B),A) = A )
    <=> ( B = zero_zero_int ) ) ).

% add_cancel_left_left
tff(fact_664_double__zero__sym,axiom,
    ! [A: code_integer] :
      ( ( zero_z3403309356797280102nteger = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),A) )
    <=> ( A = zero_z3403309356797280102nteger ) ) ).

% double_zero_sym
tff(fact_665_double__zero__sym,axiom,
    ! [A: rat] :
      ( ( zero_zero_rat = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),A) )
    <=> ( A = zero_zero_rat ) ) ).

% double_zero_sym
tff(fact_666_double__zero__sym,axiom,
    ! [A: int] :
      ( ( zero_zero_int = aa_int_int(aa_int_fun_int_int(plus_plus_int,A),A) )
    <=> ( A = zero_zero_int ) ) ).

% double_zero_sym
tff(fact_667_add_Oright__neutral,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),zero_z3403309356797280102nteger) = A ).

% add.right_neutral
tff(fact_668_add_Oright__neutral,axiom,
    ! [A: multis2468970476368604999at_nat] : aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(A),zero_z1048942125864253310at_nat) = A ).

% add.right_neutral
tff(fact_669_add_Oright__neutral,axiom,
    ! [A: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),zero_zero_rat) = A ).

% add.right_neutral
tff(fact_670_add_Oright__neutral,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),zero_zero_nat) = A ).

% add.right_neutral
tff(fact_671_add_Oright__neutral,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,A),zero_zero_int) = A ).

% add.right_neutral
tff(fact_672_add__gr__0,axiom,
    ! [M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2))
    <=> ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),M)
        | aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2) ) ) ).

% add_gr_0
tff(fact_673_less__one,axiom,
    ! [N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),one_one_nat)
    <=> ( N2 = zero_zero_nat ) ) ).

% less_one
tff(fact_674_some__opt__eq__trivial,axiom,
    ! [X2: num] : eps_Opt_num(aa_num_fun_num_o(aTP_Lamm_ah,X2)) = aa_num_option_num(some_num,X2) ).

% some_opt_eq_trivial
tff(fact_675_some__opt__eq__trivial,axiom,
    ! [X2: produc8664842809031399944it_nat] : eps_Op3393321821070424684it_nat(aTP_Lamm_ai(X2)) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X2) ).

% some_opt_eq_trivial
tff(fact_676_zero__less__double__add__iff__zero__less__single__add,axiom,
    ! [A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),A))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),A) ) ).

% zero_less_double_add_iff_zero_less_single_add
tff(fact_677_zero__less__double__add__iff__zero__less__single__add,axiom,
    ! [A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),A))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),A) ) ).

% zero_less_double_add_iff_zero_less_single_add
tff(fact_678_zero__less__double__add__iff__zero__less__single__add,axiom,
    ! [A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),A))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),A) ) ).

% zero_less_double_add_iff_zero_less_single_add
tff(fact_679_double__add__less__zero__iff__single__add__less__zero,axiom,
    ! [A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),A)),zero_z3403309356797280102nteger)
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),zero_z3403309356797280102nteger) ) ).

% double_add_less_zero_iff_single_add_less_zero
tff(fact_680_double__add__less__zero__iff__single__add__less__zero,axiom,
    ! [A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),A)),zero_zero_rat)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),zero_zero_rat) ) ).

% double_add_less_zero_iff_single_add_less_zero
tff(fact_681_double__add__less__zero__iff__single__add__less__zero,axiom,
    ! [A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),A)),zero_zero_int)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,A),zero_zero_int) ) ).

% double_add_less_zero_iff_single_add_less_zero
tff(fact_682_less__add__same__cancel2,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,B),A))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),B) ) ).

% less_add_same_cancel2
tff(fact_683_less__add__same__cancel2,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),A))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),B) ) ).

% less_add_same_cancel2
tff(fact_684_less__add__same__cancel2,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),A))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),B) ) ).

% less_add_same_cancel2
tff(fact_685_less__add__same__cancel2,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),A))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),B) ) ).

% less_add_same_cancel2
tff(fact_686_less__add__same__cancel1,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),B) ) ).

% less_add_same_cancel1
tff(fact_687_less__add__same__cancel1,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),B) ) ).

% less_add_same_cancel1
tff(fact_688_less__add__same__cancel1,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),B) ) ).

% less_add_same_cancel1
tff(fact_689_less__add__same__cancel1,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),B) ) ).

% less_add_same_cancel1
tff(fact_690_add__less__same__cancel2,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)),B)
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),zero_z3403309356797280102nteger) ) ).

% add_less_same_cancel2
tff(fact_691_add__less__same__cancel2,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),B)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),zero_zero_rat) ) ).

% add_less_same_cancel2
tff(fact_692_add__less__same__cancel2,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),B)
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),zero_zero_nat) ) ).

% add_less_same_cancel2
tff(fact_693_add__less__same__cancel2,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),B)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,A),zero_zero_int) ) ).

% add_less_same_cancel2
tff(fact_694_add__less__same__cancel1,axiom,
    ! [B: code_integer,A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,B),A)),B)
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),zero_z3403309356797280102nteger) ) ).

% add_less_same_cancel1
tff(fact_695_add__less__same__cancel1,axiom,
    ! [B: rat,A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),A)),B)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),zero_zero_rat) ) ).

% add_less_same_cancel1
tff(fact_696_add__less__same__cancel1,axiom,
    ! [B: nat,A: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),A)),B)
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),zero_zero_nat) ) ).

% add_less_same_cancel1
tff(fact_697_add__less__same__cancel1,axiom,
    ! [B: int,A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,B),A)),B)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,A),zero_zero_int) ) ).

% add_less_same_cancel1
tff(fact_698_some__opt__false__trivial,axiom,
    eps_Op1141264490366522080it_nat(aTP_Lamm_aj) = none_P2587165478634041381it_nat ).

% some_opt_false_trivial
tff(fact_699_some__opt__false__trivial,axiom,
    eps_Opt_num(aTP_Lamm_ak) = none_num ).

% some_opt_false_trivial
tff(fact_700_some__opt__false__trivial,axiom,
    eps_Op3393321821070424684it_nat(aTP_Lamm_al) = none_P9117596204409417319it_nat ).

% some_opt_false_trivial
tff(fact_701_zero__reorient,axiom,
    ! [X2: code_integer] :
      ( ( zero_z3403309356797280102nteger = X2 )
    <=> ( X2 = zero_z3403309356797280102nteger ) ) ).

% zero_reorient
tff(fact_702_zero__reorient,axiom,
    ! [X2: multis2468970476368604999at_nat] :
      ( ( zero_z1048942125864253310at_nat = X2 )
    <=> ( X2 = zero_z1048942125864253310at_nat ) ) ).

% zero_reorient
tff(fact_703_zero__reorient,axiom,
    ! [X2: rat] :
      ( ( zero_zero_rat = X2 )
    <=> ( X2 = zero_zero_rat ) ) ).

% zero_reorient
tff(fact_704_zero__reorient,axiom,
    ! [X2: nat] :
      ( ( zero_zero_nat = X2 )
    <=> ( X2 = zero_zero_nat ) ) ).

% zero_reorient
tff(fact_705_zero__reorient,axiom,
    ! [X2: int] :
      ( ( zero_zero_int = X2 )
    <=> ( X2 = zero_zero_int ) ) ).

% zero_reorient
tff(fact_706_fun_Omap__ident,axiom,
    ! [T: fun_num_Code_integer] : aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,aTP_Lamm_am),T) = T ).

% fun.map_ident
tff(fact_707_option_Odisc__eq__case_I2_J,axiom,
    ! [Option: option3216581401566546698it_nat] :
      ( ( Option != none_P2587165478634041381it_nat )
    <=> aa_opt4809530629565672394_nat_o(case_o2169478532838437047it_nat($false,aTP_Lamm_an),Option) ) ).

% option.disc_eq_case(2)
tff(fact_708_option_Odisc__eq__case_I2_J,axiom,
    ! [Option: option_num] :
      ( ( Option != none_num )
    <=> aa_option_num_o(case_option_o_num($false,aTP_Lamm_ao),Option) ) ).

% option.disc_eq_case(2)
tff(fact_709_option_Odisc__eq__case_I2_J,axiom,
    ! [Option: option8956607266484857688it_nat] :
      ( ( Option != none_P9117596204409417319it_nat )
    <=> aa_opt8360315729766332930_nat_o(case_o2686588417244861013it_nat($false,aTP_Lamm_ap),Option) ) ).

% option.disc_eq_case(2)
tff(fact_710_option_Odisc__eq__case_I1_J,axiom,
    ! [Option: option3216581401566546698it_nat] :
      ( ( Option = none_P2587165478634041381it_nat )
    <=> aa_opt4809530629565672394_nat_o(case_o2169478532838437047it_nat($true,aTP_Lamm_aj),Option) ) ).

% option.disc_eq_case(1)
tff(fact_711_option_Odisc__eq__case_I1_J,axiom,
    ! [Option: option_num] :
      ( ( Option = none_num )
    <=> aa_option_num_o(case_option_o_num($true,aTP_Lamm_ak),Option) ) ).

% option.disc_eq_case(1)
tff(fact_712_option_Odisc__eq__case_I1_J,axiom,
    ! [Option: option8956607266484857688it_nat] :
      ( ( Option = none_P9117596204409417319it_nat )
    <=> aa_opt8360315729766332930_nat_o(case_o2686588417244861013it_nat($true,aTP_Lamm_al),Option) ) ).

% option.disc_eq_case(1)
tff(fact_713_option_Ocase__distrib,axiom,
    ! [Ha: fun_int_int,F1: int,F22: fun_num_int,Option: option_num] : aa_int_int(Ha,aa_option_num_int(case_option_int_num(F1,F22),Option)) = aa_option_num_int(case_option_int_num(aa_int_int(Ha,F1),aa_fun329774391934724804um_int(aTP_Lamm_aq(Ha),F22)),Option) ).

% option.case_distrib
tff(fact_714_option_Ocase__distrib,axiom,
    ! [Ha: fun_int_option_num,F1: int,F22: fun_num_int,Option: option_num] : aa_int_option_num(Ha,aa_option_num_int(case_option_int_num(F1,F22),Option)) = aa_opt5369159329878751634on_num(case_o6005452278849405969um_num(aa_int_option_num(Ha,F1),aa_fun3858197967482829954on_num(aTP_Lamm_ar(Ha),F22)),Option) ).

% option.case_distrib
tff(fact_715_option_Ocase__distrib,axiom,
    ! [Ha: fun_int_num,F1: int,F22: fun_num_int,Option: option_num] : aa_int_num(Ha,aa_option_num_int(case_option_int_num(F1,F22),Option)) = aa_option_num_num(case_option_num_num(aa_int_num(Ha,F1),aa_fun5215869348392759218um_num(aTP_Lamm_as(Ha),F22)),Option) ).

% option.case_distrib
tff(fact_716_option_Ocase__distrib,axiom,
    ! [Ha: fun_option_num_int,F1: option_num,F22: fun_num_option_num,Option: option_num] : aa_option_num_int(Ha,aa_opt5369159329878751634on_num(case_o6005452278849405969um_num(F1,F22),Option)) = aa_option_num_int(case_option_int_num(aa_option_num_int(Ha,F1),aa_fun2256179333612926594um_int(aTP_Lamm_at(Ha),F22)),Option) ).

% option.case_distrib
tff(fact_717_option_Ocase__distrib,axiom,
    ! [Ha: fun_op8989173174992673105on_num,F1: option_num,F22: fun_num_option_num,Option: option_num] : aa_opt5369159329878751634on_num(Ha,aa_opt5369159329878751634on_num(case_o6005452278849405969um_num(F1,F22),Option)) = aa_opt5369159329878751634on_num(case_o6005452278849405969um_num(aa_opt5369159329878751634on_num(Ha,F1),aa_fun3636977833914307392on_num(aTP_Lamm_au(Ha),F22)),Option) ).

% option.case_distrib
tff(fact_718_option_Ocase__distrib,axiom,
    ! [Ha: fun_option_num_num,F1: option_num,F22: fun_num_option_num,Option: option_num] : aa_option_num_num(Ha,aa_opt5369159329878751634on_num(case_o6005452278849405969um_num(F1,F22),Option)) = aa_option_num_num(case_option_num_num(aa_option_num_num(Ha,F1),aa_fun7142274290070961008um_num(aTP_Lamm_av(Ha),F22)),Option) ).

% option.case_distrib
tff(fact_719_option_Ocase__distrib,axiom,
    ! [Ha: fun_num_int,F1: num,F22: fun_num_num,Option: option_num] : aa_num_int(Ha,aa_option_num_num(case_option_num_num(F1,F22),Option)) = aa_option_num_int(case_option_int_num(aa_num_int(Ha,F1),aa_fun3162900327506486194um_int(aTP_Lamm_aw(Ha),F22)),Option) ).

% option.case_distrib
tff(fact_720_option_Ocase__distrib,axiom,
    ! [Ha: fun_num_option_num,F1: num,F22: fun_num_num,Option: option_num] : aa_num_option_num(Ha,aa_option_num_num(case_option_num_num(F1,F22),Option)) = aa_opt5369159329878751634on_num(case_o6005452278849405969um_num(aa_num_option_num(Ha,F1),aa_fun612943910911948912on_num(aTP_Lamm_ax(Ha),F22)),Option) ).

% option.case_distrib
tff(fact_721_option_Ocase__distrib,axiom,
    ! [Ha: fun_num_num,F1: num,F22: fun_num_num,Option: option_num] : aa_num_num(Ha,aa_option_num_num(case_option_num_num(F1,F22),Option)) = aa_option_num_num(case_option_num_num(aa_num_num(Ha,F1),aa_fun8048995283964520608um_num(aTP_Lamm_ay(Ha),F22)),Option) ).

% option.case_distrib
tff(fact_722_case__optionE,axiom,
    ! [P: $o,Q: fun_Pr7068637894315934487_nat_o,X2: option3216581401566546698it_nat] :
      ( aa_opt4809530629565672394_nat_o(case_o2169478532838437047it_nat((P),Q),X2)
     => ( ( ( X2 = none_P2587165478634041381it_nat )
         => ~ (P) )
       => ~ ! [Y4: produc6714399278180371524it_nat] :
              ( ( X2 = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,Y4) )
             => ~ aa_Pro7528120012624322448_nat_o(Q,Y4) ) ) ) ).

% case_optionE
tff(fact_723_case__optionE,axiom,
    ! [P: $o,Q: fun_num_o,X2: option_num] :
      ( aa_option_num_o(case_option_o_num((P),Q),X2)
     => ( ( ( X2 = none_num )
         => ~ (P) )
       => ~ ! [Y4: num] :
              ( ( X2 = aa_num_option_num(some_num,Y4) )
             => ~ aa_num_o(Q,Y4) ) ) ) ).

% case_optionE
tff(fact_724_case__optionE,axiom,
    ! [P: $o,Q: fun_Pr8032424337255632745_nat_o,X2: option8956607266484857688it_nat] :
      ( aa_opt8360315729766332930_nat_o(case_o2686588417244861013it_nat((P),Q),X2)
     => ( ( ( X2 = none_P9117596204409417319it_nat )
         => ~ (P) )
       => ~ ! [Y4: produc8664842809031399944it_nat] :
              ( ( X2 = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,Y4) )
             => ~ aa_Pro4744234731172327378_nat_o(Q,Y4) ) ) ) ).

% case_optionE
tff(fact_725_combine__options__def,axiom,
    ! [F: fun_Pr1003294667014919570it_nat,X2: option8956607266484857688it_nat,Y: option8956607266484857688it_nat] : combin4318129983670048329it_nat(F,X2,Y) = case_o2963978774867076333it_nat(Y,aa_opt7728438819757478003it_nat(aTP_Lamm_ba(F),Y),X2) ).

% combine_options_def
tff(fact_726_combine__options__def,axiom,
    ! [F: fun_num_fun_num_num,X2: option_num,Y: option_num] : aa_opt5369159329878751634on_num(combine_options_num(F,X2),Y) = aa_opt5369159329878751634on_num(case_o6005452278849405969um_num(Y,aa_opt8899475237019873193on_num(aTP_Lamm_bc(F),Y)),X2) ).

% combine_options_def
tff(fact_727_less__option__def,axiom,
    ! [X2: option_Code_integer,Y: option_Code_integer] :
      ( ord_le7113747843092208513nteger(X2,Y)
    <=> case_o43118980978444458nteger($false,aTP_Lamm_be(X2),Y) ) ).

% less_option_def
tff(fact_728_less__option__def,axiom,
    ! [X2: option_rat,Y: option_rat] :
      ( ord_less_option_rat(X2,Y)
    <=> case_option_o_rat($false,aTP_Lamm_bg(X2),Y) ) ).

% less_option_def
tff(fact_729_less__option__def,axiom,
    ! [X2: option_num,Y: option_num] :
      ( aa_option_num_o(aa_opt8674010985164783839_num_o(ord_less_option_num,X2),Y)
    <=> aa_option_num_o(case_option_o_num($false,aTP_Lamm_bi(X2)),Y) ) ).

% less_option_def
tff(fact_730_less__option__def,axiom,
    ! [X2: option_nat,Y: option_nat] :
      ( ord_less_option_nat(X2,Y)
    <=> case_option_o_nat($false,aTP_Lamm_bk(X2),Y) ) ).

% less_option_def
tff(fact_731_less__option__def,axiom,
    ! [X2: option_int,Y: option_int] :
      ( ord_less_option_int(X2,Y)
    <=> case_option_o_int($false,aTP_Lamm_bm(X2),Y) ) ).

% less_option_def
tff(fact_732_zero__less__iff__neq__zero,axiom,
    ! [N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
    <=> ( N2 != zero_zero_nat ) ) ).

% zero_less_iff_neq_zero
tff(fact_733_gr__implies__not__zero,axiom,
    ! [M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M),N2)
     => ( N2 != zero_zero_nat ) ) ).

% gr_implies_not_zero
tff(fact_734_not__less__zero,axiom,
    ! [N2: nat] : ~ aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),zero_zero_nat) ).

% not_less_zero
tff(fact_735_gr__zeroI,axiom,
    ! [N2: nat] :
      ( ( N2 != zero_zero_nat )
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2) ) ).

% gr_zeroI
tff(fact_736_add_Ogroup__left__neutral,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,zero_z3403309356797280102nteger),A) = A ).

% add.group_left_neutral
tff(fact_737_add_Ogroup__left__neutral,axiom,
    ! [A: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,zero_zero_rat),A) = A ).

% add.group_left_neutral
tff(fact_738_add_Ogroup__left__neutral,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,zero_zero_int),A) = A ).

% add.group_left_neutral
tff(fact_739_add_Ocomm__neutral,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),zero_z3403309356797280102nteger) = A ).

% add.comm_neutral
tff(fact_740_add_Ocomm__neutral,axiom,
    ! [A: multis2468970476368604999at_nat] : aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(A),zero_z1048942125864253310at_nat) = A ).

% add.comm_neutral
tff(fact_741_add_Ocomm__neutral,axiom,
    ! [A: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),zero_zero_rat) = A ).

% add.comm_neutral
tff(fact_742_add_Ocomm__neutral,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),zero_zero_nat) = A ).

% add.comm_neutral
tff(fact_743_add_Ocomm__neutral,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,A),zero_zero_int) = A ).

% add.comm_neutral
tff(fact_744_comm__monoid__add__class_Oadd__0,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,zero_z3403309356797280102nteger),A) = A ).

% comm_monoid_add_class.add_0
tff(fact_745_comm__monoid__add__class_Oadd__0,axiom,
    ! [A: multis2468970476368604999at_nat] : aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(zero_z1048942125864253310at_nat),A) = A ).

% comm_monoid_add_class.add_0
tff(fact_746_comm__monoid__add__class_Oadd__0,axiom,
    ! [A: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,zero_zero_rat),A) = A ).

% comm_monoid_add_class.add_0
tff(fact_747_comm__monoid__add__class_Oadd__0,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),A) = A ).

% comm_monoid_add_class.add_0
tff(fact_748_comm__monoid__add__class_Oadd__0,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,zero_zero_int),A) = A ).

% comm_monoid_add_class.add_0
tff(fact_749_zero__neq__one,axiom,
    zero_z3403309356797280102nteger != one_one_Code_integer ).

% zero_neq_one
tff(fact_750_zero__neq__one,axiom,
    zero_zero_rat != one_one_rat ).

% zero_neq_one
tff(fact_751_zero__neq__one,axiom,
    zero_zero_nat != one_one_nat ).

% zero_neq_one
tff(fact_752_zero__neq__one,axiom,
    zero_zero_int != one_one_int ).

% zero_neq_one
tff(fact_753_plus__nat_Oadd__0,axiom,
    ! [N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),N2) = N2 ).

% plus_nat.add_0
tff(fact_754_add__eq__self__zero,axiom,
    ! [M: nat,N2: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2) = M )
     => ( N2 = zero_zero_nat ) ) ).

% add_eq_self_zero
tff(fact_755_less__numeral__extra_I1_J,axiom,
    aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),one_one_Code_integer) ).

% less_numeral_extra(1)
tff(fact_756_less__numeral__extra_I1_J,axiom,
    aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),one_one_rat) ).

% less_numeral_extra(1)
tff(fact_757_less__numeral__extra_I1_J,axiom,
    aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),one_one_nat) ).

% less_numeral_extra(1)
tff(fact_758_less__numeral__extra_I1_J,axiom,
    aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),one_one_int) ).

% less_numeral_extra(1)
tff(fact_759_raise__def,axiom,
    ! [S: list_char] : heap_T1552190017797416154rray_a(S) = heap_T1488828001306802186rray_a(aTP_Lamm_bn) ).

% raise_def
tff(fact_760_raise__def,axiom,
    ! [S: list_char] : heap_T2927564422264180874t_unit(S) = heap_T6183433275982383450t_unit(aTP_Lamm_bo) ).

% raise_def
tff(fact_761_guard__def,axiom,
    ! [P: fun_he8413527710729349838unit_o,F: fun_he281446669002384250it_nat] : heap_T7685628758766326643rray_a(P,F) = heap_T1488828001306802186rray_a(aa_fun3106883476453902712it_nat(aTP_Lamm_bp(P),F)) ).

% guard_def
tff(fact_762_guard__def,axiom,
    ! [P: fun_he8413527710729349838unit_o,F: fun_he4944555133437423336it_nat] : heap_T8440541562793052209t_unit(P,F) = heap_T6183433275982383450t_unit(aa_fun2986507860694160780it_nat(aTP_Lamm_bq(P),F)) ).

% guard_def
tff(fact_763_pos__add__strict,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),A)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,B),C)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,B),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),C)) ) ) ).

% pos_add_strict
tff(fact_764_pos__add__strict,axiom,
    ! [A: rat,B: rat,C: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),A)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,B),C)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,B),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),C)) ) ) ).

% pos_add_strict
tff(fact_765_pos__add__strict,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,B),C)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,B),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C)) ) ) ).

% pos_add_strict
tff(fact_766_pos__add__strict,axiom,
    ! [A: int,B: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),A)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,B),C)
       => aa_int_o(aa_int_fun_int_o(ord_less_int,B),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),C)) ) ) ).

% pos_add_strict
tff(fact_767_canonically__ordered__monoid__add__class_OlessE,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),B)
     => ~ ! [C2: nat] :
            ( ( B = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C2) )
           => ( C2 = zero_zero_nat ) ) ) ).

% canonically_ordered_monoid_add_class.lessE
tff(fact_768_add__pos__pos,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),A)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),B)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)) ) ) ).

% add_pos_pos
tff(fact_769_add__pos__pos,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),A)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),B)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)) ) ) ).

% add_pos_pos
tff(fact_770_add__pos__pos,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),B)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)) ) ) ).

% add_pos_pos
tff(fact_771_add__pos__pos,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),A)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),B)
       => aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)) ) ) ).

% add_pos_pos
tff(fact_772_add__neg__neg,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),zero_z3403309356797280102nteger)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,B),zero_z3403309356797280102nteger)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)),zero_z3403309356797280102nteger) ) ) ).

% add_neg_neg
tff(fact_773_add__neg__neg,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),zero_zero_rat)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,B),zero_zero_rat)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),zero_zero_rat) ) ) ).

% add_neg_neg
tff(fact_774_add__neg__neg,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),zero_zero_nat)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,B),zero_zero_nat)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),zero_zero_nat) ) ) ).

% add_neg_neg
tff(fact_775_add__neg__neg,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,A),zero_zero_int)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,B),zero_zero_int)
       => aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),zero_zero_int) ) ) ).

% add_neg_neg
tff(fact_776_add__less__zeroD,axiom,
    ! [X2: code_integer,Y: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X2),Y)),zero_z3403309356797280102nteger)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,X2),zero_z3403309356797280102nteger)
        | aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,Y),zero_z3403309356797280102nteger) ) ) ).

% add_less_zeroD
tff(fact_777_add__less__zeroD,axiom,
    ! [X2: rat,Y: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),Y)),zero_zero_rat)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,X2),zero_zero_rat)
        | aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,Y),zero_zero_rat) ) ) ).

% add_less_zeroD
tff(fact_778_add__less__zeroD,axiom,
    ! [X2: int,Y: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),Y)),zero_zero_int)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,X2),zero_zero_int)
        | aa_int_o(aa_int_fun_int_o(ord_less_int,Y),zero_zero_int) ) ) ).

% add_less_zeroD
tff(fact_779_zero__less__one,axiom,
    aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),one_one_Code_integer) ).

% zero_less_one
tff(fact_780_zero__less__one,axiom,
    aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),one_one_rat) ).

% zero_less_one
tff(fact_781_zero__less__one,axiom,
    aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),one_one_nat) ).

% zero_less_one
tff(fact_782_zero__less__one,axiom,
    aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),one_one_int) ).

% zero_less_one
tff(fact_783_not__one__less__zero,axiom,
    ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),zero_z3403309356797280102nteger) ).

% not_one_less_zero
tff(fact_784_not__one__less__zero,axiom,
    ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),zero_zero_rat) ).

% not_one_less_zero
tff(fact_785_not__one__less__zero,axiom,
    ~ aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,one_one_nat),zero_zero_nat) ).

% not_one_less_zero
tff(fact_786_not__one__less__zero,axiom,
    ~ aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),zero_zero_int) ).

% not_one_less_zero
tff(fact_787_execute__ureturn,axiom,
    ! [X2: array_a] : heap_T5591663578999710211rray_a(aa_arr1142863274018860686rray_a(heap_T4328122439115681491rray_a,X2)) = comp_P2097125496263478628t_unit(some_P6105628898608307625it_nat,aTP_Lamm_br(X2)) ).

% execute_ureturn
tff(fact_788_execute__ureturn,axiom,
    ! [X2: product_unit] : heap_T875086893843062177t_unit(aa_Pro1108561329362217960t_unit(heap_T4284346855313245393t_unit,X2)) = comp_P3118722334806803912t_unit(some_P1914260805536162275it_nat,aTP_Lamm_bs(X2)) ).

% execute_ureturn
tff(fact_789_less__imp__add__positive,axiom,
    ! [I: nat,J: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,I),J)
     => ? [K3: nat] :
          ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),K3)
          & ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K3) = J ) ) ) ).

% less_imp_add_positive
tff(fact_790_tap__def,axiom,
    ! [F: fun_he5123621388056232515t_unit] : heap_T560649228465745139t_unit(F) = heap_T6183433275982383450t_unit(aTP_Lamm_bt(F)) ).

% tap_def
tff(fact_791_double__eq__0__iff,axiom,
    ! [A: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),A) = zero_z3403309356797280102nteger )
    <=> ( A = zero_z3403309356797280102nteger ) ) ).

% double_eq_0_iff
tff(fact_792_double__eq__0__iff,axiom,
    ! [A: rat] :
      ( ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),A) = zero_zero_rat )
    <=> ( A = zero_zero_rat ) ) ).

% double_eq_0_iff
tff(fact_793_double__eq__0__iff,axiom,
    ! [A: int] :
      ( ( aa_int_int(aa_int_fun_int_int(plus_plus_int,A),A) = zero_zero_int )
    <=> ( A = zero_zero_int ) ) ).

% double_eq_0_iff
tff(fact_794_add__0__iff,axiom,
    ! [B: code_integer,A: code_integer] :
      ( ( B = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,B),A) )
    <=> ( A = zero_z3403309356797280102nteger ) ) ).

% add_0_iff
tff(fact_795_add__0__iff,axiom,
    ! [B: rat,A: rat] :
      ( ( B = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),A) )
    <=> ( A = zero_zero_rat ) ) ).

% add_0_iff
tff(fact_796_add__0__iff,axiom,
    ! [B: nat,A: nat] :
      ( ( B = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),A) )
    <=> ( A = zero_zero_nat ) ) ).

% add_0_iff
tff(fact_797_add__0__iff,axiom,
    ! [B: int,A: int] :
      ( ( B = aa_int_int(aa_int_fun_int_int(plus_plus_int,B),A) )
    <=> ( A = zero_zero_int ) ) ).

% add_0_iff
tff(fact_798_verit__sum__simplify,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),zero_z3403309356797280102nteger) = A ).

% verit_sum_simplify
tff(fact_799_verit__sum__simplify,axiom,
    ! [A: multis2468970476368604999at_nat] : aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(A),zero_z1048942125864253310at_nat) = A ).

% verit_sum_simplify
tff(fact_800_verit__sum__simplify,axiom,
    ! [A: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),zero_zero_rat) = A ).

% verit_sum_simplify
tff(fact_801_verit__sum__simplify,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),zero_zero_nat) = A ).

% verit_sum_simplify
tff(fact_802_verit__sum__simplify,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,A),zero_zero_int) = A ).

% verit_sum_simplify
tff(fact_803_dbl__inc__simps_I2_J,axiom,
    aa_Cod1783974652533396728nteger(neg_nu5831290666863070958nteger,zero_z3403309356797280102nteger) = one_one_Code_integer ).

% dbl_inc_simps(2)
tff(fact_804_dbl__inc__simps_I2_J,axiom,
    aa_rat_rat(neg_nu5219082963157363817nc_rat,zero_zero_rat) = one_one_rat ).

% dbl_inc_simps(2)
tff(fact_805_dbl__inc__simps_I2_J,axiom,
    aa_int_int(neg_nu5851722552734809277nc_int,zero_zero_int) = one_one_int ).

% dbl_inc_simps(2)
tff(fact_806_disjE__realizer2,axiom,
    ! [P: $o,Q: fun_num_o,X2: option_num,R3: fun_int_o,F: int,G: fun_num_int] :
      ( aa_option_num_o(case_option_o_num((P),Q),X2)
     => ( ( (P)
         => aa_int_o(R3,F) )
       => ( ! [Q2: num] :
              ( aa_num_o(Q,Q2)
             => aa_int_o(R3,aa_num_int(G,Q2)) )
         => aa_int_o(R3,aa_option_num_int(case_option_int_num(F,G),X2)) ) ) ) ).

% disjE_realizer2
tff(fact_807_disjE__realizer2,axiom,
    ! [P: $o,Q: fun_num_o,X2: option_num,R3: fun_option_num_o,F: option_num,G: fun_num_option_num] :
      ( aa_option_num_o(case_option_o_num((P),Q),X2)
     => ( ( (P)
         => aa_option_num_o(R3,F) )
       => ( ! [Q2: num] :
              ( aa_num_o(Q,Q2)
             => aa_option_num_o(R3,aa_num_option_num(G,Q2)) )
         => aa_option_num_o(R3,aa_opt5369159329878751634on_num(case_o6005452278849405969um_num(F,G),X2)) ) ) ) ).

% disjE_realizer2
tff(fact_808_disjE__realizer2,axiom,
    ! [P: $o,Q: fun_num_o,X2: option_num,R3: fun_num_o,F: num,G: fun_num_num] :
      ( aa_option_num_o(case_option_o_num((P),Q),X2)
     => ( ( (P)
         => aa_num_o(R3,F) )
       => ( ! [Q2: num] :
              ( aa_num_o(Q,Q2)
             => aa_num_o(R3,aa_num_num(G,Q2)) )
         => aa_num_o(R3,aa_option_num_num(case_option_num_num(F,G),X2)) ) ) ) ).

% disjE_realizer2
tff(fact_809_set__to__map__def,axiom,
    ! [S2: set_Pr4329608150637261639at_nat,K: set_Pr1261947904930325089at_nat] : aa_set2934564513904597954at_nat(set_to4447731662395764663at_nat(S2),K) = eps_Op994234036888646909at_nat(aa_set7675215768510388063_nat_o(aa_set5605188905385065315_nat_o(aTP_Lamm_bu,S2),K)) ).

% set_to_map_def
tff(fact_810_set__to__map__def,axiom,
    ! [S2: set_Pr1261947904930325089at_nat,K: nat] : aa_nat_option_nat(set_to_map_nat_nat(S2),K) = eps_Opt_nat(aa_nat_fun_nat_o(aa_set2634951030311766213_nat_o(aTP_Lamm_bv,S2),K)) ).

% set_to_map_def
tff(fact_811_set__to__map__def,axiom,
    ! [S2: set_Pr3486312109254157132nteger,K: fun_Pr5098669352780829690e_term] : aa_fun1271726682903785001nteger(set_to765696221487571048nteger(S2),K) = eps_Op9034888937550303799nteger(aa_fun4505422719058378424eger_o(aa_set282680696547864321eger_o(aTP_Lamm_bw,S2),K)) ).

% set_to_map_def
tff(fact_812_set__to__map__def,axiom,
    ! [S2: set_Pr1312406793078187350et_nat,K: fun_Pr6460944699146269935_nat_o] : aa_fun5824947343344787589et_nat(set_to2037224588991580346et_nat(S2),K) = aa_fun5824947343344787589et_nat(eps_Op2013419657081471078et_nat,aa_fun2638059832795814268_nat_o(aa_set6295625606485646487_nat_o(aTP_Lamm_bx,S2),K)) ).

% set_to_map_def
tff(fact_813_set__to__map__def,axiom,
    ! [S2: set_Pr4040394263813967220et_nat,K: fun_Pr6460944699146269935_nat_o] : aa_fun1716447855799474851et_nat(set_to3162555076294590936et_nat(S2),K) = eps_Op5936278548196508548et_nat(aa_fun912680268133416158_nat_o(aa_set2269662337286943895_nat_o(aTP_Lamm_by,S2),K)) ).

% set_to_map_def
tff(fact_814_set__to__map__def,axiom,
    ! [S2: set_Pr6700895561065273913nt_int,K: fun_Pr7763680713840462443e_term] : aa_fun251074914522852630nt_int(set_to8251664086025573589nt_int(S2),K) = eps_Op2446201859369042517nt_int(aa_fun3538162476766722827_int_o(aa_set8857007276572228673_int_o(aTP_Lamm_bz,S2),K)) ).

% set_to_map_def
tff(fact_815_set__to__map__def,axiom,
    ! [S2: set_Pr4166680992137330533nt_int,K: fun_in5730379987311621695e_term] : aa_fun3970441718214872642nt_int(set_to2016340311434469377nt_int(S2),K) = eps_Op2446201859369042517nt_int(aa_fun586359091965693151_int_o(aa_set6932945912113297217_int_o(aTP_Lamm_ca,S2),K)) ).

% set_to_map_def
tff(fact_816_K__record__comp,axiom,
    ! [C: code_integer,F: fun_num_Code_integer,X: num] : aa_num_Code_integer(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,aa_Cod4161879620478718930nteger(aTP_Lamm_cb,C)),F),X) = C ).

% K_record_comp
tff(fact_817_K__record__comp,axiom,
    ! [C: fun_Pr5876161306168176259nteger,F: fun_Co8499238673658658103nteger,X: code_integer] : aa_Cod1978467581589928094nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,aTP_Lamm_cc(C)),F),X) = C ).

% K_record_comp
tff(fact_818_K__record__comp,axiom,
    ! [C: fun_Pr5876161306168176259nteger,F: fun_Co1981900195452921617nteger,X: code_integer] : aa_Cod1978467581589928094nteger(comp_f6739083541385432444nteger(aTP_Lamm_cd(C),F),X) = C ).

% K_record_comp
tff(fact_819_K__record__comp,axiom,
    ! [C: num,F: fun_int_nat,X: int] : aa_int_num(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,aTP_Lamm_ce(C)),F),X) = C ).

% K_record_comp
tff(fact_820_pred__equals__eq2,axiom,
    ! [R3: set_Pr4329608150637261639at_nat,S2: set_Pr4329608150637261639at_nat] :
      ( ! [X4: set_Pr1261947904930325089at_nat,Xa2: set_Pr1261947904930325089at_nat] :
          ( member8757157785044589968at_nat(produc2922128104949294807at_nat(X4,Xa2),R3)
        <=> member8757157785044589968at_nat(produc2922128104949294807at_nat(X4,Xa2),S2) )
    <=> ( R3 = S2 ) ) ).

% pred_equals_eq2
tff(fact_821_pred__equals__eq2,axiom,
    ! [R3: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
      ( ! [X4: nat,Xa2: nat] :
          ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X4),Xa2),R3)
        <=> member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X4),Xa2),S2) )
    <=> ( R3 = S2 ) ) ).

% pred_equals_eq2
tff(fact_822_pred__equals__eq2,axiom,
    ! [R3: set_Pr3486312109254157132nteger,S2: set_Pr3486312109254157132nteger] :
      ( ! [X4: fun_Pr5098669352780829690e_term,Xa2: produc8923325533196201883nteger] :
          ( member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X4),Xa2),R3)
        <=> member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X4),Xa2),S2) )
    <=> ( R3 = S2 ) ) ).

% pred_equals_eq2
tff(fact_823_pred__equals__eq2,axiom,
    ! [R3: set_Pr1312406793078187350et_nat,S2: set_Pr1312406793078187350et_nat] :
      ( ! [X4: fun_Pr6460944699146269935_nat_o,Xa2: produc3658429121746597890et_nat] :
          ( member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X4),Xa2),R3)
        <=> member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X4),Xa2),S2) )
    <=> ( R3 = S2 ) ) ).

% pred_equals_eq2
tff(fact_824_pred__equals__eq2,axiom,
    ! [R3: set_Pr4040394263813967220et_nat,S2: set_Pr4040394263813967220et_nat] :
      ( ! [X4: fun_Pr6460944699146269935_nat_o,Xa2: produc8799533983703829792et_nat] :
          ( member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X4),Xa2),R3)
        <=> member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X4),Xa2),S2) )
    <=> ( R3 = S2 ) ) ).

% pred_equals_eq2
tff(fact_825_pred__equals__eq2,axiom,
    ! [R3: set_Pr6700895561065273913nt_int,S2: set_Pr6700895561065273913nt_int] :
      ( ! [X4: fun_Pr7763680713840462443e_term,Xa2: product_prod_int_int] :
          ( member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X4),Xa2),R3)
        <=> member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X4),Xa2),S2) )
    <=> ( R3 = S2 ) ) ).

% pred_equals_eq2
tff(fact_826_pred__equals__eq2,axiom,
    ! [R3: set_Pr4166680992137330533nt_int,S2: set_Pr4166680992137330533nt_int] :
      ( ! [X4: fun_in5730379987311621695e_term,Xa2: product_prod_int_int] :
          ( member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X4),Xa2),R3)
        <=> member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X4),Xa2),S2) )
    <=> ( R3 = S2 ) ) ).

% pred_equals_eq2
tff(fact_827_dbl__inc__def,axiom,
    ! [X2: code_integer] : aa_Cod1783974652533396728nteger(neg_nu5831290666863070958nteger,X2) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X2),X2)),one_one_Code_integer) ).

% dbl_inc_def
tff(fact_828_dbl__inc__def,axiom,
    ! [X2: rat] : aa_rat_rat(neg_nu5219082963157363817nc_rat,X2) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),X2)),one_one_rat) ).

% dbl_inc_def
tff(fact_829_dbl__inc__def,axiom,
    ! [X2: int] : aa_int_int(neg_nu5851722552734809277nc_int,X2) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),X2)),one_one_int) ).

% dbl_inc_def
tff(fact_830_zero__natural_Orsp,axiom,
    zero_zero_nat = zero_zero_nat ).

% zero_natural.rsp
tff(fact_831_fails__wait,axiom,
    ! [X2: nat,Ha: heap_e7401611519738050253t_unit] : ~ aa_hea7994211679605476167unit_o(time_f8834461667527620124t_unit(heap_Time_wait(X2)),Ha) ).

% fails_wait
tff(fact_832_Euclid__induct,axiom,
    ! [P: fun_nat_fun_nat_o,A: nat,B: nat] :
      ( ! [A3: nat,B2: nat] :
          ( aa_nat_o(aa_nat_fun_nat_o(P,A3),B2)
        <=> aa_nat_o(aa_nat_fun_nat_o(P,B2),A3) )
     => ( ! [A3: nat] : aa_nat_o(aa_nat_fun_nat_o(P,A3),zero_zero_nat)
       => ( ! [A3: nat,B2: nat] :
              ( aa_nat_o(aa_nat_fun_nat_o(P,A3),B2)
             => aa_nat_o(aa_nat_fun_nat_o(P,A3),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A3),B2)) )
         => aa_nat_o(aa_nat_fun_nat_o(P,A),B) ) ) ) ).

% Euclid_induct
tff(fact_833_Ints__odd__less__0,axiom,
    ! [A: code_integer] :
      ( member_Code_integer(A,ring_11222124179247155820nteger)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,one_one_Code_integer),A)),A)),zero_z3403309356797280102nteger)
      <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),zero_z3403309356797280102nteger) ) ) ).

% Ints_odd_less_0
tff(fact_834_Ints__odd__less__0,axiom,
    ! [A: rat] :
      ( member_rat(A,ring_1_Ints_rat)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,one_one_rat),A)),A)),zero_zero_rat)
      <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),zero_zero_rat) ) ) ).

% Ints_odd_less_0
tff(fact_835_Ints__odd__less__0,axiom,
    ! [A: int] :
      ( member_int(A,ring_1_Ints_int)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),A)),A)),zero_zero_int)
      <=> aa_int_o(aa_int_fun_int_o(ord_less_int,A),zero_zero_int) ) ) ).

% Ints_odd_less_0
tff(fact_836_num__of__nat__plus__distrib,axiom,
    ! [M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),M)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
       => ( aa_nat_num(num_of_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)) = aa_num_num(aa_num_fun_num_num(plus_plus_num,aa_nat_num(num_of_nat,M)),aa_nat_num(num_of_nat,N2)) ) ) ) ).

% num_of_nat_plus_distrib
tff(fact_837_divides__aux__eq,axiom,
    ! [Q3: code_integer,R2: code_integer] :
      ( aa_Pro4926521453222654329eger_o(unique5706413561485394159nteger,aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(Q3),R2))
    <=> ( R2 = zero_z3403309356797280102nteger ) ) ).

% divides_aux_eq
tff(fact_838_divides__aux__eq,axiom,
    ! [Q3: nat,R2: nat] :
      ( aa_Pro6150637604445964947_nat_o(unique6322359934112328802ux_nat,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Q3),R2))
    <=> ( R2 = zero_zero_nat ) ) ).

% divides_aux_eq
tff(fact_839_divides__aux__eq,axiom,
    ! [Q3: int,R2: int] :
      ( aa_Pro4592068669816069595_int_o(unique6319869463603278526ux_int,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Q3),R2))
    <=> ( R2 = zero_zero_int ) ) ).

% divides_aux_eq
tff(fact_840_sgn__pos,axiom,
    ! [A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),A)
     => ( aa_Cod1783974652533396728nteger(sgn_sgn_Code_integer,A) = one_one_Code_integer ) ) ).

% sgn_pos
tff(fact_841_sgn__pos,axiom,
    ! [A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),A)
     => ( aa_rat_rat(sgn_sgn_rat,A) = one_one_rat ) ) ).

% sgn_pos
tff(fact_842_sgn__pos,axiom,
    ! [A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),A)
     => ( aa_int_int(sgn_sgn_int,A) = one_one_int ) ) ).

% sgn_pos
tff(fact_843_abs__add__one__gt__zero,axiom,
    ! [X2: code_integer] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,one_one_Code_integer),aa_Cod1783974652533396728nteger(abs_abs_Code_integer,X2))) ).

% abs_add_one_gt_zero
tff(fact_844_abs__add__one__gt__zero,axiom,
    ! [X2: rat] : aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,one_one_rat),aa_rat_rat(abs_abs_rat,X2))) ).

% abs_add_one_gt_zero
tff(fact_845_abs__add__one__gt__zero,axiom,
    ! [X2: int] : aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_int_int(abs_abs_int,X2))) ).

% abs_add_one_gt_zero
tff(fact_846_map__option__case,axiom,
    ! [F: fun_num_num,Y: option_num] : aa_opt5369159329878751634on_num(map_option_num_num(F),Y) = aa_opt5369159329878751634on_num(case_o6005452278849405969um_num(none_num,aTP_Lamm_cf(F)),Y) ).

% map_option_case
tff(fact_847_add__neg__numeral__special_I7_J,axiom,
    aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_int_int(uminus_uminus_int,one_one_int)) = zero_zero_int ).

% add_neg_numeral_special(7)
tff(fact_848_add__neg__numeral__special_I7_J,axiom,
    aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,one_one_Code_integer),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) = zero_z3403309356797280102nteger ).

% add_neg_numeral_special(7)
tff(fact_849_add__neg__numeral__special_I7_J,axiom,
    aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,one_one_rat),aa_rat_rat(uminus_uminus_rat,one_one_rat)) = zero_zero_rat ).

% add_neg_numeral_special(7)
tff(fact_850_add__neg__numeral__special_I8_J,axiom,
    aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(uminus_uminus_int,one_one_int)),one_one_int) = zero_zero_int ).

% add_neg_numeral_special(8)
tff(fact_851_add__neg__numeral__special_I8_J,axiom,
    aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),one_one_Code_integer) = zero_z3403309356797280102nteger ).

% add_neg_numeral_special(8)
tff(fact_852_add__neg__numeral__special_I8_J,axiom,
    aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),one_one_rat) = zero_zero_rat ).

% add_neg_numeral_special(8)
tff(fact_853_dbl__dec__simps_I3_J,axiom,
    aa_Cod1783974652533396728nteger(neg_nu7757733837767384882nteger,one_one_Code_integer) = one_one_Code_integer ).

% dbl_dec_simps(3)
tff(fact_854_dbl__dec__simps_I3_J,axiom,
    aa_rat_rat(neg_nu3179335615603231917ec_rat,one_one_rat) = one_one_rat ).

% dbl_dec_simps(3)
tff(fact_855_dbl__dec__simps_I3_J,axiom,
    aa_int_int(neg_nu3811975205180677377ec_int,one_one_int) = one_one_int ).

% dbl_dec_simps(3)
tff(fact_856_neg__equal__iff__equal,axiom,
    ! [A: int,B: int] :
      ( ( aa_int_int(uminus_uminus_int,A) = aa_int_int(uminus_uminus_int,B) )
    <=> ( A = B ) ) ).

% neg_equal_iff_equal
tff(fact_857_neg__equal__iff__equal,axiom,
    ! [A: code_integer,B: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,B) )
    <=> ( A = B ) ) ).

% neg_equal_iff_equal
tff(fact_858_neg__equal__iff__equal,axiom,
    ! [A: rat,B: rat] :
      ( ( aa_rat_rat(uminus_uminus_rat,A) = aa_rat_rat(uminus_uminus_rat,B) )
    <=> ( A = B ) ) ).

% neg_equal_iff_equal
tff(fact_859_add_Oinverse__inverse,axiom,
    ! [A: int] : aa_int_int(uminus_uminus_int,aa_int_int(uminus_uminus_int,A)) = A ).

% add.inverse_inverse
tff(fact_860_add_Oinverse__inverse,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A)) = A ).

% add.inverse_inverse
tff(fact_861_add_Oinverse__inverse,axiom,
    ! [A: rat] : aa_rat_rat(uminus_uminus_rat,aa_rat_rat(uminus_uminus_rat,A)) = A ).

% add.inverse_inverse
tff(fact_862_abs__idempotent,axiom,
    ! [A: int] : aa_int_int(abs_abs_int,aa_int_int(abs_abs_int,A)) = aa_int_int(abs_abs_int,A) ).

% abs_idempotent
tff(fact_863_abs__idempotent,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A)) = aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A) ).

% abs_idempotent
tff(fact_864_abs__idempotent,axiom,
    ! [A: rat] : aa_rat_rat(abs_abs_rat,aa_rat_rat(abs_abs_rat,A)) = aa_rat_rat(abs_abs_rat,A) ).

% abs_idempotent
tff(fact_865_neg__equal__zero,axiom,
    ! [A: int] :
      ( ( aa_int_int(uminus_uminus_int,A) = A )
    <=> ( A = zero_zero_int ) ) ).

% neg_equal_zero
tff(fact_866_neg__equal__zero,axiom,
    ! [A: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A) = A )
    <=> ( A = zero_z3403309356797280102nteger ) ) ).

% neg_equal_zero
tff(fact_867_neg__equal__zero,axiom,
    ! [A: rat] :
      ( ( aa_rat_rat(uminus_uminus_rat,A) = A )
    <=> ( A = zero_zero_rat ) ) ).

% neg_equal_zero
tff(fact_868_equal__neg__zero,axiom,
    ! [A: int] :
      ( ( A = aa_int_int(uminus_uminus_int,A) )
    <=> ( A = zero_zero_int ) ) ).

% equal_neg_zero
tff(fact_869_equal__neg__zero,axiom,
    ! [A: code_integer] :
      ( ( A = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A) )
    <=> ( A = zero_z3403309356797280102nteger ) ) ).

% equal_neg_zero
tff(fact_870_equal__neg__zero,axiom,
    ! [A: rat] :
      ( ( A = aa_rat_rat(uminus_uminus_rat,A) )
    <=> ( A = zero_zero_rat ) ) ).

% equal_neg_zero
tff(fact_871_neg__equal__0__iff__equal,axiom,
    ! [A: int] :
      ( ( aa_int_int(uminus_uminus_int,A) = zero_zero_int )
    <=> ( A = zero_zero_int ) ) ).

% neg_equal_0_iff_equal
tff(fact_872_neg__equal__0__iff__equal,axiom,
    ! [A: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A) = zero_z3403309356797280102nteger )
    <=> ( A = zero_z3403309356797280102nteger ) ) ).

% neg_equal_0_iff_equal
tff(fact_873_neg__equal__0__iff__equal,axiom,
    ! [A: rat] :
      ( ( aa_rat_rat(uminus_uminus_rat,A) = zero_zero_rat )
    <=> ( A = zero_zero_rat ) ) ).

% neg_equal_0_iff_equal
tff(fact_874_neg__0__equal__iff__equal,axiom,
    ! [A: int] :
      ( ( zero_zero_int = aa_int_int(uminus_uminus_int,A) )
    <=> ( zero_zero_int = A ) ) ).

% neg_0_equal_iff_equal
tff(fact_875_neg__0__equal__iff__equal,axiom,
    ! [A: code_integer] :
      ( ( zero_z3403309356797280102nteger = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A) )
    <=> ( zero_z3403309356797280102nteger = A ) ) ).

% neg_0_equal_iff_equal
tff(fact_876_neg__0__equal__iff__equal,axiom,
    ! [A: rat] :
      ( ( zero_zero_rat = aa_rat_rat(uminus_uminus_rat,A) )
    <=> ( zero_zero_rat = A ) ) ).

% neg_0_equal_iff_equal
tff(fact_877_add_Oinverse__neutral,axiom,
    aa_int_int(uminus_uminus_int,zero_zero_int) = zero_zero_int ).

% add.inverse_neutral
tff(fact_878_add_Oinverse__neutral,axiom,
    aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,zero_z3403309356797280102nteger) = zero_z3403309356797280102nteger ).

% add.inverse_neutral
tff(fact_879_add_Oinverse__neutral,axiom,
    aa_rat_rat(uminus_uminus_rat,zero_zero_rat) = zero_zero_rat ).

% add.inverse_neutral
tff(fact_880_neg__less__iff__less,axiom,
    ! [B: int,A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(uminus_uminus_int,B)),aa_int_int(uminus_uminus_int,A))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,A),B) ) ).

% neg_less_iff_less
tff(fact_881_neg__less__iff__less,axiom,
    ! [B: code_integer,A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,B)),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),B) ) ).

% neg_less_iff_less
tff(fact_882_neg__less__iff__less,axiom,
    ! [B: rat,A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(uminus_uminus_rat,B)),aa_rat_rat(uminus_uminus_rat,A))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B) ) ).

% neg_less_iff_less
tff(fact_883_minus__add__distrib,axiom,
    ! [A: int,B: int] : aa_int_int(uminus_uminus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(uminus_uminus_int,A)),aa_int_int(uminus_uminus_int,B)) ).

% minus_add_distrib
tff(fact_884_minus__add__distrib,axiom,
    ! [A: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A)),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,B)) ).

% minus_add_distrib
tff(fact_885_minus__add__distrib,axiom,
    ! [A: rat,B: rat] : aa_rat_rat(uminus_uminus_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,A)),aa_rat_rat(uminus_uminus_rat,B)) ).

% minus_add_distrib
tff(fact_886_minus__add__cancel,axiom,
    ! [A: int,B: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(uminus_uminus_int,A)),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)) = B ).

% minus_add_cancel
tff(fact_887_minus__add__cancel,axiom,
    ! [A: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)) = B ).

% minus_add_cancel
tff(fact_888_minus__add__cancel,axiom,
    ! [A: rat,B: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,A)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)) = B ).

% minus_add_cancel
tff(fact_889_add__minus__cancel,axiom,
    ! [A: int,B: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(uminus_uminus_int,A)),B)) = B ).

% add_minus_cancel
tff(fact_890_add__minus__cancel,axiom,
    ! [A: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A)),B)) = B ).

% add_minus_cancel
tff(fact_891_add__minus__cancel,axiom,
    ! [A: rat,B: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,A)),B)) = B ).

% add_minus_cancel
tff(fact_892_abs__zero,axiom,
    aa_Cod1783974652533396728nteger(abs_abs_Code_integer,zero_z3403309356797280102nteger) = zero_z3403309356797280102nteger ).

% abs_zero
tff(fact_893_abs__zero,axiom,
    aa_rat_rat(abs_abs_rat,zero_zero_rat) = zero_zero_rat ).

% abs_zero
tff(fact_894_abs__zero,axiom,
    aa_int_int(abs_abs_int,zero_zero_int) = zero_zero_int ).

% abs_zero
tff(fact_895_abs__eq__0,axiom,
    ! [A: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A) = zero_z3403309356797280102nteger )
    <=> ( A = zero_z3403309356797280102nteger ) ) ).

% abs_eq_0
tff(fact_896_abs__eq__0,axiom,
    ! [A: rat] :
      ( ( aa_rat_rat(abs_abs_rat,A) = zero_zero_rat )
    <=> ( A = zero_zero_rat ) ) ).

% abs_eq_0
tff(fact_897_abs__eq__0,axiom,
    ! [A: int] :
      ( ( aa_int_int(abs_abs_int,A) = zero_zero_int )
    <=> ( A = zero_zero_int ) ) ).

% abs_eq_0
tff(fact_898_abs__0__eq,axiom,
    ! [A: code_integer] :
      ( ( zero_z3403309356797280102nteger = aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A) )
    <=> ( A = zero_z3403309356797280102nteger ) ) ).

% abs_0_eq
tff(fact_899_abs__0__eq,axiom,
    ! [A: rat] :
      ( ( zero_zero_rat = aa_rat_rat(abs_abs_rat,A) )
    <=> ( A = zero_zero_rat ) ) ).

% abs_0_eq
tff(fact_900_abs__0__eq,axiom,
    ! [A: int] :
      ( ( zero_zero_int = aa_int_int(abs_abs_int,A) )
    <=> ( A = zero_zero_int ) ) ).

% abs_0_eq
tff(fact_901_abs__add__abs,axiom,
    ! [A: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A)),aa_Cod1783974652533396728nteger(abs_abs_Code_integer,B))) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A)),aa_Cod1783974652533396728nteger(abs_abs_Code_integer,B)) ).

% abs_add_abs
tff(fact_902_abs__add__abs,axiom,
    ! [A: rat,B: rat] : aa_rat_rat(abs_abs_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(abs_abs_rat,A)),aa_rat_rat(abs_abs_rat,B))) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(abs_abs_rat,A)),aa_rat_rat(abs_abs_rat,B)) ).

% abs_add_abs
tff(fact_903_abs__add__abs,axiom,
    ! [A: int,B: int] : aa_int_int(abs_abs_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(abs_abs_int,A)),aa_int_int(abs_abs_int,B))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(abs_abs_int,A)),aa_int_int(abs_abs_int,B)) ).

% abs_add_abs
tff(fact_904_abs__1,axiom,
    aa_Cod1783974652533396728nteger(abs_abs_Code_integer,one_one_Code_integer) = one_one_Code_integer ).

% abs_1
tff(fact_905_abs__1,axiom,
    aa_rat_rat(abs_abs_rat,one_one_rat) = one_one_rat ).

% abs_1
tff(fact_906_abs__1,axiom,
    aa_int_int(abs_abs_int,one_one_int) = one_one_int ).

% abs_1
tff(fact_907_abs__minus__cancel,axiom,
    ! [A: int] : aa_int_int(abs_abs_int,aa_int_int(uminus_uminus_int,A)) = aa_int_int(abs_abs_int,A) ).

% abs_minus_cancel
tff(fact_908_abs__minus__cancel,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A)) = aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A) ).

% abs_minus_cancel
tff(fact_909_abs__minus__cancel,axiom,
    ! [A: rat] : aa_rat_rat(abs_abs_rat,aa_rat_rat(uminus_uminus_rat,A)) = aa_rat_rat(abs_abs_rat,A) ).

% abs_minus_cancel
tff(fact_910_sgn__1,axiom,
    aa_int_int(sgn_sgn_int,one_one_int) = one_one_int ).

% sgn_1
tff(fact_911_sgn__1,axiom,
    aa_Cod1783974652533396728nteger(sgn_sgn_Code_integer,one_one_Code_integer) = one_one_Code_integer ).

% sgn_1
tff(fact_912_sgn__1,axiom,
    aa_rat_rat(sgn_sgn_rat,one_one_rat) = one_one_rat ).

% sgn_1
tff(fact_913_map__option__eq__Some,axiom,
    ! [F: fun_Pr1075626608990047775at_num,Xo: option8956607266484857688it_nat,Y: num] :
      ( ( map_op2731889312448867759at_num(F,Xo) = aa_num_option_num(some_num,Y) )
    <=> ? [Z3: produc8664842809031399944it_nat] :
          ( ( Xo = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,Z3) )
          & ( aa_Pro1785383075579372640at_num(F,Z3) = Y ) ) ) ).

% map_option_eq_Some
tff(fact_914_map__option__eq__Some,axiom,
    ! [F: fun_nu5234077238548837151it_nat,Xo: option_num,Y: produc8664842809031399944it_nat] :
      ( ( map_op8118133509425879471it_nat(F,Xo) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,Y) )
    <=> ? [Z3: num] :
          ( ( Xo = aa_num_option_num(some_num,Z3) )
          & ( aa_num7171627272556384352it_nat(F,Z3) = Y ) ) ) ).

% map_option_eq_Some
tff(fact_915_map__option__eq__Some,axiom,
    ! [F: fun_Pr1033138224055104269it_nat,Xo: option8956607266484857688it_nat,Y: produc8664842809031399944it_nat] :
      ( ( map_op8673683442680995229it_nat(F,Xo) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,Y) )
    <=> ? [Z3: produc8664842809031399944it_nat] :
          ( ( Xo = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,Z3) )
          & ( aa_Pro550487673543749710it_nat(F,Z3) = Y ) ) ) ).

% map_option_eq_Some
tff(fact_916_map__option__eq__Some,axiom,
    ! [F: fun_num_num,Xo: option_num,Y: num] :
      ( ( aa_opt5369159329878751634on_num(map_option_num_num(F),Xo) = aa_num_option_num(some_num,Y) )
    <=> ? [Z3: num] :
          ( ( Xo = aa_num_option_num(some_num,Z3) )
          & ( aa_num_num(F,Z3) = Y ) ) ) ).

% map_option_eq_Some
tff(fact_917_None__eq__map__option__iff,axiom,
    ! [F: fun_Pr3819237756034508227it_nat,X2: option3216581401566546698it_nat] :
      ( ( none_P2587165478634041381it_nat = map_op6002829699023054091it_nat(F,X2) )
    <=> ( X2 = none_P2587165478634041381it_nat ) ) ).

% None_eq_map_option_iff
tff(fact_918_None__eq__map__option__iff,axiom,
    ! [F: fun_nu2241728722996109699it_nat,X2: option_num] :
      ( ( none_P2587165478634041381it_nat = map_op6598675229099881181it_nat(F,X2) )
    <=> ( X2 = none_num ) ) ).

% None_eq_map_option_iff
tff(fact_919_None__eq__map__option__iff,axiom,
    ! [F: fun_Pr3908927074708932117it_nat,X2: option8956607266484857688it_nat] :
      ( ( none_P2587165478634041381it_nat = map_op7916408704904942447it_nat(F,X2) )
    <=> ( X2 = none_P9117596204409417319it_nat ) ) ).

% None_eq_map_option_iff
tff(fact_920_None__eq__map__option__iff,axiom,
    ! [F: fun_Pr1223581030874358257at_num,X2: option3216581401566546698it_nat] :
      ( ( none_num = map_op8228268515680064275at_num(F,X2) )
    <=> ( X2 = none_P2587165478634041381it_nat ) ) ).

% None_eq_map_option_iff
tff(fact_921_None__eq__map__option__iff,axiom,
    ! [F: fun_Pr1075626608990047775at_num,X2: option8956607266484857688it_nat] :
      ( ( none_num = map_op2731889312448867759at_num(F,X2) )
    <=> ( X2 = none_P9117596204409417319it_nat ) ) ).

% None_eq_map_option_iff
tff(fact_922_None__eq__map__option__iff,axiom,
    ! [F: fun_Pr2014882013869309663it_nat,X2: option3216581401566546698it_nat] :
      ( ( none_P9117596204409417319it_nat = map_op674526153330701057it_nat(F,X2) )
    <=> ( X2 = none_P2587165478634041381it_nat ) ) ).

% None_eq_map_option_iff
tff(fact_923_None__eq__map__option__iff,axiom,
    ! [F: fun_nu5234077238548837151it_nat,X2: option_num] :
      ( ( none_P9117596204409417319it_nat = map_op8118133509425879471it_nat(F,X2) )
    <=> ( X2 = none_num ) ) ).

% None_eq_map_option_iff
tff(fact_924_None__eq__map__option__iff,axiom,
    ! [F: fun_Pr1033138224055104269it_nat,X2: option8956607266484857688it_nat] :
      ( ( none_P9117596204409417319it_nat = map_op8673683442680995229it_nat(F,X2) )
    <=> ( X2 = none_P9117596204409417319it_nat ) ) ).

% None_eq_map_option_iff
tff(fact_925_None__eq__map__option__iff,axiom,
    ! [F: fun_num_num,X2: option_num] :
      ( ( none_num = aa_opt5369159329878751634on_num(map_option_num_num(F),X2) )
    <=> ( X2 = none_num ) ) ).

% None_eq_map_option_iff
tff(fact_926_map__option__is__None,axiom,
    ! [F: fun_Pr3819237756034508227it_nat,Opt: option3216581401566546698it_nat] :
      ( ( map_op6002829699023054091it_nat(F,Opt) = none_P2587165478634041381it_nat )
    <=> ( Opt = none_P2587165478634041381it_nat ) ) ).

% map_option_is_None
tff(fact_927_map__option__is__None,axiom,
    ! [F: fun_nu2241728722996109699it_nat,Opt: option_num] :
      ( ( map_op6598675229099881181it_nat(F,Opt) = none_P2587165478634041381it_nat )
    <=> ( Opt = none_num ) ) ).

% map_option_is_None
tff(fact_928_map__option__is__None,axiom,
    ! [F: fun_Pr3908927074708932117it_nat,Opt: option8956607266484857688it_nat] :
      ( ( map_op7916408704904942447it_nat(F,Opt) = none_P2587165478634041381it_nat )
    <=> ( Opt = none_P9117596204409417319it_nat ) ) ).

% map_option_is_None
tff(fact_929_map__option__is__None,axiom,
    ! [F: fun_Pr1223581030874358257at_num,Opt: option3216581401566546698it_nat] :
      ( ( map_op8228268515680064275at_num(F,Opt) = none_num )
    <=> ( Opt = none_P2587165478634041381it_nat ) ) ).

% map_option_is_None
tff(fact_930_map__option__is__None,axiom,
    ! [F: fun_Pr1075626608990047775at_num,Opt: option8956607266484857688it_nat] :
      ( ( map_op2731889312448867759at_num(F,Opt) = none_num )
    <=> ( Opt = none_P9117596204409417319it_nat ) ) ).

% map_option_is_None
tff(fact_931_map__option__is__None,axiom,
    ! [F: fun_Pr2014882013869309663it_nat,Opt: option3216581401566546698it_nat] :
      ( ( map_op674526153330701057it_nat(F,Opt) = none_P9117596204409417319it_nat )
    <=> ( Opt = none_P2587165478634041381it_nat ) ) ).

% map_option_is_None
tff(fact_932_map__option__is__None,axiom,
    ! [F: fun_nu5234077238548837151it_nat,Opt: option_num] :
      ( ( map_op8118133509425879471it_nat(F,Opt) = none_P9117596204409417319it_nat )
    <=> ( Opt = none_num ) ) ).

% map_option_is_None
tff(fact_933_map__option__is__None,axiom,
    ! [F: fun_Pr1033138224055104269it_nat,Opt: option8956607266484857688it_nat] :
      ( ( map_op8673683442680995229it_nat(F,Opt) = none_P9117596204409417319it_nat )
    <=> ( Opt = none_P9117596204409417319it_nat ) ) ).

% map_option_is_None
tff(fact_934_map__option__is__None,axiom,
    ! [F: fun_num_num,Opt: option_num] :
      ( ( aa_opt5369159329878751634on_num(map_option_num_num(F),Opt) = none_num )
    <=> ( Opt = none_num ) ) ).

% map_option_is_None
tff(fact_935_option_Omap__disc__iff,axiom,
    ! [F: fun_Pr3819237756034508227it_nat,A: option3216581401566546698it_nat] :
      ( ( map_op6002829699023054091it_nat(F,A) = none_P2587165478634041381it_nat )
    <=> ( A = none_P2587165478634041381it_nat ) ) ).

% option.map_disc_iff
tff(fact_936_option_Omap__disc__iff,axiom,
    ! [F: fun_nu2241728722996109699it_nat,A: option_num] :
      ( ( map_op6598675229099881181it_nat(F,A) = none_P2587165478634041381it_nat )
    <=> ( A = none_num ) ) ).

% option.map_disc_iff
tff(fact_937_option_Omap__disc__iff,axiom,
    ! [F: fun_Pr3908927074708932117it_nat,A: option8956607266484857688it_nat] :
      ( ( map_op7916408704904942447it_nat(F,A) = none_P2587165478634041381it_nat )
    <=> ( A = none_P9117596204409417319it_nat ) ) ).

% option.map_disc_iff
tff(fact_938_option_Omap__disc__iff,axiom,
    ! [F: fun_Pr1223581030874358257at_num,A: option3216581401566546698it_nat] :
      ( ( map_op8228268515680064275at_num(F,A) = none_num )
    <=> ( A = none_P2587165478634041381it_nat ) ) ).

% option.map_disc_iff
tff(fact_939_option_Omap__disc__iff,axiom,
    ! [F: fun_Pr1075626608990047775at_num,A: option8956607266484857688it_nat] :
      ( ( map_op2731889312448867759at_num(F,A) = none_num )
    <=> ( A = none_P9117596204409417319it_nat ) ) ).

% option.map_disc_iff
tff(fact_940_option_Omap__disc__iff,axiom,
    ! [F: fun_Pr2014882013869309663it_nat,A: option3216581401566546698it_nat] :
      ( ( map_op674526153330701057it_nat(F,A) = none_P9117596204409417319it_nat )
    <=> ( A = none_P2587165478634041381it_nat ) ) ).

% option.map_disc_iff
tff(fact_941_option_Omap__disc__iff,axiom,
    ! [F: fun_nu5234077238548837151it_nat,A: option_num] :
      ( ( map_op8118133509425879471it_nat(F,A) = none_P9117596204409417319it_nat )
    <=> ( A = none_num ) ) ).

% option.map_disc_iff
tff(fact_942_option_Omap__disc__iff,axiom,
    ! [F: fun_Pr1033138224055104269it_nat,A: option8956607266484857688it_nat] :
      ( ( map_op8673683442680995229it_nat(F,A) = none_P9117596204409417319it_nat )
    <=> ( A = none_P9117596204409417319it_nat ) ) ).

% option.map_disc_iff
tff(fact_943_option_Omap__disc__iff,axiom,
    ! [F: fun_num_num,A: option_num] :
      ( ( aa_opt5369159329878751634on_num(map_option_num_num(F),A) = none_num )
    <=> ( A = none_num ) ) ).

% option.map_disc_iff
tff(fact_944_neg__less__0__iff__less,axiom,
    ! [A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(uminus_uminus_int,A)),zero_zero_int)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),A) ) ).

% neg_less_0_iff_less
tff(fact_945_neg__less__0__iff__less,axiom,
    ! [A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A)),zero_z3403309356797280102nteger)
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),A) ) ).

% neg_less_0_iff_less
tff(fact_946_neg__less__0__iff__less,axiom,
    ! [A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(uminus_uminus_rat,A)),zero_zero_rat)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),A) ) ).

% neg_less_0_iff_less
tff(fact_947_neg__0__less__iff__less,axiom,
    ! [A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),aa_int_int(uminus_uminus_int,A))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,A),zero_zero_int) ) ).

% neg_0_less_iff_less
tff(fact_948_neg__0__less__iff__less,axiom,
    ! [A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),zero_z3403309356797280102nteger) ) ).

% neg_0_less_iff_less
tff(fact_949_neg__0__less__iff__less,axiom,
    ! [A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),aa_rat_rat(uminus_uminus_rat,A))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),zero_zero_rat) ) ).

% neg_0_less_iff_less
tff(fact_950_neg__less__pos,axiom,
    ! [A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(uminus_uminus_int,A)),A)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),A) ) ).

% neg_less_pos
tff(fact_951_neg__less__pos,axiom,
    ! [A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A)),A)
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),A) ) ).

% neg_less_pos
tff(fact_952_neg__less__pos,axiom,
    ! [A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(uminus_uminus_rat,A)),A)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),A) ) ).

% neg_less_pos
tff(fact_953_less__neg__neg,axiom,
    ! [A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,A),aa_int_int(uminus_uminus_int,A))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,A),zero_zero_int) ) ).

% less_neg_neg
tff(fact_954_less__neg__neg,axiom,
    ! [A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),zero_z3403309356797280102nteger) ) ).

% less_neg_neg
tff(fact_955_less__neg__neg,axiom,
    ! [A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),aa_rat_rat(uminus_uminus_rat,A))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),zero_zero_rat) ) ).

% less_neg_neg
tff(fact_956_ab__left__minus,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(uminus_uminus_int,A)),A) = zero_zero_int ).

% ab_left_minus
tff(fact_957_ab__left__minus,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A)),A) = zero_z3403309356797280102nteger ).

% ab_left_minus
tff(fact_958_ab__left__minus,axiom,
    ! [A: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,A)),A) = zero_zero_rat ).

% ab_left_minus
tff(fact_959_add_Oright__inverse,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,A),aa_int_int(uminus_uminus_int,A)) = zero_zero_int ).

% add.right_inverse
tff(fact_960_add_Oright__inverse,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A)) = zero_z3403309356797280102nteger ).

% add.right_inverse
tff(fact_961_add_Oright__inverse,axiom,
    ! [A: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),aa_rat_rat(uminus_uminus_rat,A)) = zero_zero_rat ).

% add.right_inverse
tff(fact_962_zero__less__abs__iff,axiom,
    ! [A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A))
    <=> ( A != zero_z3403309356797280102nteger ) ) ).

% zero_less_abs_iff
tff(fact_963_zero__less__abs__iff,axiom,
    ! [A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),aa_rat_rat(abs_abs_rat,A))
    <=> ( A != zero_zero_rat ) ) ).

% zero_less_abs_iff
tff(fact_964_zero__less__abs__iff,axiom,
    ! [A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),aa_int_int(abs_abs_int,A))
    <=> ( A != zero_zero_int ) ) ).

% zero_less_abs_iff
tff(fact_965_abs__neg__one,axiom,
    aa_int_int(abs_abs_int,aa_int_int(uminus_uminus_int,one_one_int)) = one_one_int ).

% abs_neg_one
tff(fact_966_abs__neg__one,axiom,
    aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) = one_one_Code_integer ).

% abs_neg_one
tff(fact_967_abs__neg__one,axiom,
    aa_rat_rat(abs_abs_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)) = one_one_rat ).

% abs_neg_one
tff(fact_968_case__map__option,axiom,
    ! [G: code_integer,Ha: fun_Co8499238673658658103nteger,F: fun_num_Code_integer,X2: option_num] : case_o9049918639272118855nteger(G,Ha,aa_opt692344247527444053nteger(map_op2849635639313731588nteger(F),X2)) = case_o356765784539232260er_num(G,aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,Ha),F),X2) ).

% case_map_option
tff(fact_969_case__map__option,axiom,
    ! [G: fun_Pr5876161306168176259nteger,Ha: fun_Co1561183069634336733nteger,F: fun_Co8499238673658658103nteger,X2: option_Code_integer] : case_o6517734911099809389nteger(G,Ha,aa_opt5394215800039610008nteger(map_op3669829223712506439nteger(F),X2)) = case_o6517734911099809389nteger(G,aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,Ha),F),X2) ).

% case_map_option
tff(fact_970_case__map__option,axiom,
    ! [G: fun_Pr5876161306168176259nteger,Ha: fun_fu4800041728187187127nteger,F: fun_Co1981900195452921617nteger,X2: option_Code_integer] : case_o4513113946662230855nteger(G,Ha,aa_opt6635412093559109234nteger(map_op3919597019539041057nteger(F),X2)) = case_o6517734911099809389nteger(G,comp_f6739083541385432444nteger(Ha,F),X2) ).

% case_map_option
tff(fact_971_case__map__option,axiom,
    ! [G: num,Ha: fun_nat_num,F: fun_int_nat,X2: option_int] : case_option_num_nat(G,Ha,aa_opt7293503039907056730on_nat(map_option_int_nat(F),X2)) = case_option_num_int(G,aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,Ha),F),X2) ).

% case_map_option
tff(fact_972_case__map__option,axiom,
    ! [G: int,Ha: fun_num_int,F: fun_num_num,X2: option_num] : aa_option_num_int(case_option_int_num(G,Ha),aa_opt5369159329878751634on_num(map_option_num_num(F),X2)) = aa_option_num_int(case_option_int_num(G,comp_num_int_num(Ha,F)),X2) ).

% case_map_option
tff(fact_973_case__map__option,axiom,
    ! [G: option_num,Ha: fun_num_option_num,F: fun_num_num,X2: option_num] : aa_opt5369159329878751634on_num(case_o6005452278849405969um_num(G,Ha),aa_opt5369159329878751634on_num(map_option_num_num(F),X2)) = aa_opt5369159329878751634on_num(case_o6005452278849405969um_num(G,comp_n6731957995704128387um_num(Ha,F)),X2) ).

% case_map_option
tff(fact_974_case__map__option,axiom,
    ! [G: num,Ha: fun_num_num,F: fun_num_num,X2: option_num] : aa_option_num_num(case_option_num_num(G,Ha),aa_opt5369159329878751634on_num(map_option_num_num(F),X2)) = aa_option_num_num(case_option_num_num(G,comp_num_num_num(Ha,F)),X2) ).

% case_map_option
tff(fact_975_dbl__inc__simps_I4_J,axiom,
    aa_int_int(neg_nu5851722552734809277nc_int,aa_int_int(uminus_uminus_int,one_one_int)) = aa_int_int(uminus_uminus_int,one_one_int) ).

% dbl_inc_simps(4)
tff(fact_976_dbl__inc__simps_I4_J,axiom,
    aa_Cod1783974652533396728nteger(neg_nu5831290666863070958nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) ).

% dbl_inc_simps(4)
tff(fact_977_dbl__inc__simps_I4_J,axiom,
    aa_rat_rat(neg_nu5219082963157363817nc_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)) = aa_rat_rat(uminus_uminus_rat,one_one_rat) ).

% dbl_inc_simps(4)
tff(fact_978_abs__sgn__eq__1,axiom,
    ! [A: code_integer] :
      ( ( A != zero_z3403309356797280102nteger )
     => ( aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(sgn_sgn_Code_integer,A)) = one_one_Code_integer ) ) ).

% abs_sgn_eq_1
tff(fact_979_abs__sgn__eq__1,axiom,
    ! [A: rat] :
      ( ( A != zero_zero_rat )
     => ( aa_rat_rat(abs_abs_rat,aa_rat_rat(sgn_sgn_rat,A)) = one_one_rat ) ) ).

% abs_sgn_eq_1
tff(fact_980_abs__sgn__eq__1,axiom,
    ! [A: int] :
      ( ( A != zero_zero_int )
     => ( aa_int_int(abs_abs_int,aa_int_int(sgn_sgn_int,A)) = one_one_int ) ) ).

% abs_sgn_eq_1
tff(fact_981_dbl__dec__simps_I2_J,axiom,
    aa_int_int(neg_nu3811975205180677377ec_int,zero_zero_int) = aa_int_int(uminus_uminus_int,one_one_int) ).

% dbl_dec_simps(2)
tff(fact_982_dbl__dec__simps_I2_J,axiom,
    aa_Cod1783974652533396728nteger(neg_nu7757733837767384882nteger,zero_z3403309356797280102nteger) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) ).

% dbl_dec_simps(2)
tff(fact_983_dbl__dec__simps_I2_J,axiom,
    aa_rat_rat(neg_nu3179335615603231917ec_rat,zero_zero_rat) = aa_rat_rat(uminus_uminus_rat,one_one_rat) ).

% dbl_dec_simps(2)
tff(fact_984_sgn__neg,axiom,
    ! [A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,A),zero_zero_int)
     => ( aa_int_int(sgn_sgn_int,A) = aa_int_int(uminus_uminus_int,one_one_int) ) ) ).

% sgn_neg
tff(fact_985_sgn__neg,axiom,
    ! [A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),zero_z3403309356797280102nteger)
     => ( aa_Cod1783974652533396728nteger(sgn_sgn_Code_integer,A) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) ) ) ).

% sgn_neg
tff(fact_986_sgn__neg,axiom,
    ! [A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),zero_zero_rat)
     => ( aa_rat_rat(sgn_sgn_rat,A) = aa_rat_rat(uminus_uminus_rat,one_one_rat) ) ) ).

% sgn_neg
tff(fact_987_minus__equation__iff,axiom,
    ! [A: int,B: int] :
      ( ( aa_int_int(uminus_uminus_int,A) = B )
    <=> ( aa_int_int(uminus_uminus_int,B) = A ) ) ).

% minus_equation_iff
tff(fact_988_minus__equation__iff,axiom,
    ! [A: code_integer,B: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A) = B )
    <=> ( aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,B) = A ) ) ).

% minus_equation_iff
tff(fact_989_minus__equation__iff,axiom,
    ! [A: rat,B: rat] :
      ( ( aa_rat_rat(uminus_uminus_rat,A) = B )
    <=> ( aa_rat_rat(uminus_uminus_rat,B) = A ) ) ).

% minus_equation_iff
tff(fact_990_equation__minus__iff,axiom,
    ! [A: int,B: int] :
      ( ( A = aa_int_int(uminus_uminus_int,B) )
    <=> ( B = aa_int_int(uminus_uminus_int,A) ) ) ).

% equation_minus_iff
tff(fact_991_equation__minus__iff,axiom,
    ! [A: code_integer,B: code_integer] :
      ( ( A = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,B) )
    <=> ( B = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A) ) ) ).

% equation_minus_iff
tff(fact_992_equation__minus__iff,axiom,
    ! [A: rat,B: rat] :
      ( ( A = aa_rat_rat(uminus_uminus_rat,B) )
    <=> ( B = aa_rat_rat(uminus_uminus_rat,A) ) ) ).

% equation_minus_iff
tff(fact_993_same__sgn__abs__add,axiom,
    ! [B: code_integer,A: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(sgn_sgn_Code_integer,B) = aa_Cod1783974652533396728nteger(sgn_sgn_Code_integer,A) )
     => ( aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A)),aa_Cod1783974652533396728nteger(abs_abs_Code_integer,B)) ) ) ).

% same_sgn_abs_add
tff(fact_994_same__sgn__abs__add,axiom,
    ! [B: rat,A: rat] :
      ( ( aa_rat_rat(sgn_sgn_rat,B) = aa_rat_rat(sgn_sgn_rat,A) )
     => ( aa_rat_rat(abs_abs_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(abs_abs_rat,A)),aa_rat_rat(abs_abs_rat,B)) ) ) ).

% same_sgn_abs_add
tff(fact_995_same__sgn__abs__add,axiom,
    ! [B: int,A: int] :
      ( ( aa_int_int(sgn_sgn_int,B) = aa_int_int(sgn_sgn_int,A) )
     => ( aa_int_int(abs_abs_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(abs_abs_int,A)),aa_int_int(abs_abs_int,B)) ) ) ).

% same_sgn_abs_add
tff(fact_996_sgn__minus__1,axiom,
    aa_int_int(sgn_sgn_int,aa_int_int(uminus_uminus_int,one_one_int)) = aa_int_int(uminus_uminus_int,one_one_int) ).

% sgn_minus_1
tff(fact_997_sgn__minus__1,axiom,
    aa_Cod1783974652533396728nteger(sgn_sgn_Code_integer,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) ).

% sgn_minus_1
tff(fact_998_sgn__minus__1,axiom,
    aa_rat_rat(sgn_sgn_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)) = aa_rat_rat(uminus_uminus_rat,one_one_rat) ).

% sgn_minus_1
tff(fact_999_option_Omap__ident,axiom,
    ! [T: option_num] : aa_opt5369159329878751634on_num(map_option_num_num(aTP_Lamm_cg),T) = T ).

% option.map_ident
tff(fact_1000_abs__of__neg,axiom,
    ! [A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,A),zero_zero_int)
     => ( aa_int_int(abs_abs_int,A) = aa_int_int(uminus_uminus_int,A) ) ) ).

% abs_of_neg
tff(fact_1001_abs__of__neg,axiom,
    ! [A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),zero_z3403309356797280102nteger)
     => ( aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A) ) ) ).

% abs_of_neg
tff(fact_1002_abs__of__neg,axiom,
    ! [A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),zero_zero_rat)
     => ( aa_rat_rat(abs_abs_rat,A) = aa_rat_rat(uminus_uminus_rat,A) ) ) ).

% abs_of_neg
tff(fact_1003_abs__sgn__eq,axiom,
    ! [A: code_integer] :
      aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(sgn_sgn_Code_integer,A)) = $ite(A = zero_z3403309356797280102nteger,zero_z3403309356797280102nteger,one_one_Code_integer) ).

% abs_sgn_eq
tff(fact_1004_abs__sgn__eq,axiom,
    ! [A: rat] :
      aa_rat_rat(abs_abs_rat,aa_rat_rat(sgn_sgn_rat,A)) = $ite(A = zero_zero_rat,zero_zero_rat,one_one_rat) ).

% abs_sgn_eq
tff(fact_1005_abs__sgn__eq,axiom,
    ! [A: int] :
      aa_int_int(abs_abs_int,aa_int_int(sgn_sgn_int,A)) = $ite(A = zero_zero_int,zero_zero_int,one_one_int) ).

% abs_sgn_eq
tff(fact_1006_abs__one,axiom,
    aa_Cod1783974652533396728nteger(abs_abs_Code_integer,one_one_Code_integer) = one_one_Code_integer ).

% abs_one
tff(fact_1007_abs__one,axiom,
    aa_rat_rat(abs_abs_rat,one_one_rat) = one_one_rat ).

% abs_one
tff(fact_1008_abs__one,axiom,
    aa_int_int(abs_abs_int,one_one_int) = one_one_int ).

% abs_one
tff(fact_1009_map__option_Ocompositionality,axiom,
    ! [F: fun_Co8499238673658658103nteger,G: fun_num_Code_integer,Option: option_num] : aa_opt5394215800039610008nteger(map_op3669829223712506439nteger(F),aa_opt692344247527444053nteger(map_op2849635639313731588nteger(G),Option)) = aa_opt692344247527444053nteger(map_op2849635639313731588nteger(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),G)),Option) ).

% map_option.compositionality
tff(fact_1010_map__option_Ocompositionality,axiom,
    ! [F: fun_Co1561183069634336733nteger,G: fun_Co8499238673658658103nteger,Option: option_Code_integer] : aa_opt8008171047296870846nteger(map_op3703932585503671661nteger(F),aa_opt5394215800039610008nteger(map_op3669829223712506439nteger(G),Option)) = aa_opt8008171047296870846nteger(map_op3703932585503671661nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),G)),Option) ).

% map_option.compositionality
tff(fact_1011_map__option_Ocompositionality,axiom,
    ! [F: fun_fu4800041728187187127nteger,G: fun_Co1981900195452921617nteger,Option: option_Code_integer] : aa_opt235805188696355736nteger(map_op7435587552923436871nteger(F),aa_opt6635412093559109234nteger(map_op3919597019539041057nteger(G),Option)) = aa_opt8008171047296870846nteger(map_op3703932585503671661nteger(comp_f6739083541385432444nteger(F,G)),Option) ).

% map_option.compositionality
tff(fact_1012_map__option_Ocompositionality,axiom,
    ! [F: fun_nat_num,G: fun_int_nat,Option: option_int] : aa_opt2590664795152431944on_num(map_option_nat_num(F),aa_opt7293503039907056730on_nat(map_option_int_nat(G),Option)) = aa_opt8001746976855894436on_num(map_option_int_num(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),G)),Option) ).

% map_option.compositionality
tff(fact_1013_map__option_Ocompositionality,axiom,
    ! [F: fun_num_num,G: fun_num_num,Option: option_num] : aa_opt5369159329878751634on_num(map_option_num_num(F),aa_opt5369159329878751634on_num(map_option_num_num(G),Option)) = aa_opt5369159329878751634on_num(map_option_num_num(comp_num_num_num(F,G)),Option) ).

% map_option.compositionality
tff(fact_1014_option_Omap__comp,axiom,
    ! [G: fun_Co8499238673658658103nteger,F: fun_num_Code_integer,V: option_num] : aa_opt5394215800039610008nteger(map_op3669829223712506439nteger(G),aa_opt692344247527444053nteger(map_op2849635639313731588nteger(F),V)) = aa_opt692344247527444053nteger(map_op2849635639313731588nteger(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),F)),V) ).

% option.map_comp
tff(fact_1015_option_Omap__comp,axiom,
    ! [G: fun_Co1561183069634336733nteger,F: fun_Co8499238673658658103nteger,V: option_Code_integer] : aa_opt8008171047296870846nteger(map_op3703932585503671661nteger(G),aa_opt5394215800039610008nteger(map_op3669829223712506439nteger(F),V)) = aa_opt8008171047296870846nteger(map_op3703932585503671661nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,G),F)),V) ).

% option.map_comp
tff(fact_1016_option_Omap__comp,axiom,
    ! [G: fun_fu4800041728187187127nteger,F: fun_Co1981900195452921617nteger,V: option_Code_integer] : aa_opt235805188696355736nteger(map_op7435587552923436871nteger(G),aa_opt6635412093559109234nteger(map_op3919597019539041057nteger(F),V)) = aa_opt8008171047296870846nteger(map_op3703932585503671661nteger(comp_f6739083541385432444nteger(G,F)),V) ).

% option.map_comp
tff(fact_1017_option_Omap__comp,axiom,
    ! [G: fun_nat_num,F: fun_int_nat,V: option_int] : aa_opt2590664795152431944on_num(map_option_nat_num(G),aa_opt7293503039907056730on_nat(map_option_int_nat(F),V)) = aa_opt8001746976855894436on_num(map_option_int_num(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,G),F)),V) ).

% option.map_comp
tff(fact_1018_option_Omap__comp,axiom,
    ! [G: fun_num_num,F: fun_num_num,V: option_num] : aa_opt5369159329878751634on_num(map_option_num_num(G),aa_opt5369159329878751634on_num(map_option_num_num(F),V)) = aa_opt5369159329878751634on_num(map_option_num_num(comp_num_num_num(G,F)),V) ).

% option.map_comp
tff(fact_1019_map__option_Ocomp,axiom,
    ! [F: fun_Co8499238673658658103nteger,G: fun_num_Code_integer] : comp_o5321900959263616553on_num(map_op3669829223712506439nteger(F),map_op2849635639313731588nteger(G)) = map_op2849635639313731588nteger(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),G)) ).

% map_option.comp
tff(fact_1020_map__option_Ocomp,axiom,
    ! [F: fun_Co1561183069634336733nteger,G: fun_Co8499238673658658103nteger] : comp_o1169693055247830034nteger(map_op3703932585503671661nteger(F),map_op3669829223712506439nteger(G)) = map_op3703932585503671661nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),G)) ).

% map_option.comp
tff(fact_1021_map__option_Ocomp,axiom,
    ! [F: fun_fu4800041728187187127nteger,G: fun_Co1981900195452921617nteger] : comp_o7605500609165425388nteger(map_op7435587552923436871nteger(F),map_op3919597019539041057nteger(G)) = map_op3703932585503671661nteger(comp_f6739083541385432444nteger(F,G)) ).

% map_option.comp
tff(fact_1022_map__option_Ocomp,axiom,
    ! [F: fun_nat_num,G: fun_int_nat] : comp_o3128663659858294251on_int(map_option_nat_num(F),map_option_int_nat(G)) = map_option_int_num(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),G)) ).

% map_option.comp
tff(fact_1023_map__option_Ocomp,axiom,
    ! [F: fun_num_num,G: fun_num_num] : comp_o8931257242830428707on_num(map_option_num_num(F),map_option_num_num(G)) = map_option_num_num(comp_num_num_num(F,G)) ).

% map_option.comp
tff(fact_1024_minus__less__iff,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(uminus_uminus_int,A)),B)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(uminus_uminus_int,B)),A) ) ).

% minus_less_iff
tff(fact_1025_minus__less__iff,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A)),B)
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,B)),A) ) ).

% minus_less_iff
tff(fact_1026_minus__less__iff,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(uminus_uminus_rat,A)),B)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(uminus_uminus_rat,B)),A) ) ).

% minus_less_iff
tff(fact_1027_less__minus__iff,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,A),aa_int_int(uminus_uminus_int,B))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,B),aa_int_int(uminus_uminus_int,A)) ) ).

% less_minus_iff
tff(fact_1028_less__minus__iff,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,B))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,B),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A)) ) ).

% less_minus_iff
tff(fact_1029_less__minus__iff,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),aa_rat_rat(uminus_uminus_rat,B))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,B),aa_rat_rat(uminus_uminus_rat,A)) ) ).

% less_minus_iff
tff(fact_1030_is__num__normalize_I8_J,axiom,
    ! [A: int,B: int] : aa_int_int(uminus_uminus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(uminus_uminus_int,B)),aa_int_int(uminus_uminus_int,A)) ).

% is_num_normalize(8)
tff(fact_1031_is__num__normalize_I8_J,axiom,
    ! [A: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,B)),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A)) ).

% is_num_normalize(8)
tff(fact_1032_is__num__normalize_I8_J,axiom,
    ! [A: rat,B: rat] : aa_rat_rat(uminus_uminus_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,B)),aa_rat_rat(uminus_uminus_rat,A)) ).

% is_num_normalize(8)
tff(fact_1033_add_Oinverse__distrib__swap,axiom,
    ! [A: int,B: int] : aa_int_int(uminus_uminus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(uminus_uminus_int,B)),aa_int_int(uminus_uminus_int,A)) ).

% add.inverse_distrib_swap
tff(fact_1034_add_Oinverse__distrib__swap,axiom,
    ! [A: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,B)),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A)) ).

% add.inverse_distrib_swap
tff(fact_1035_add_Oinverse__distrib__swap,axiom,
    ! [A: rat,B: rat] : aa_rat_rat(uminus_uminus_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,B)),aa_rat_rat(uminus_uminus_rat,A)) ).

% add.inverse_distrib_swap
tff(fact_1036_group__cancel_Oneg1,axiom,
    ! [A2: int,K: int,A: int] :
      ( ( A2 = aa_int_int(aa_int_fun_int_int(plus_plus_int,K),A) )
     => ( aa_int_int(uminus_uminus_int,A2) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(uminus_uminus_int,K)),aa_int_int(uminus_uminus_int,A)) ) ) ).

% group_cancel.neg1
tff(fact_1037_group__cancel_Oneg1,axiom,
    ! [A2: code_integer,K: code_integer,A: code_integer] :
      ( ( A2 = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,K),A) )
     => ( aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A2) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,K)),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A)) ) ) ).

% group_cancel.neg1
tff(fact_1038_group__cancel_Oneg1,axiom,
    ! [A2: rat,K: rat,A: rat] :
      ( ( A2 = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,K),A) )
     => ( aa_rat_rat(uminus_uminus_rat,A2) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,K)),aa_rat_rat(uminus_uminus_rat,A)) ) ) ).

% group_cancel.neg1
tff(fact_1039_one__neq__neg__one,axiom,
    one_one_int != aa_int_int(uminus_uminus_int,one_one_int) ).

% one_neq_neg_one
tff(fact_1040_one__neq__neg__one,axiom,
    one_one_Code_integer != aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) ).

% one_neq_neg_one
tff(fact_1041_one__neq__neg__one,axiom,
    one_one_rat != aa_rat_rat(uminus_uminus_rat,one_one_rat) ).

% one_neq_neg_one
tff(fact_1042_map__option__cong,axiom,
    ! [X2: option_num,Y: option_num,F: fun_num_num,G: fun_num_num] :
      ( ( X2 = Y )
     => ( ! [A3: num] :
            ( ( Y = aa_num_option_num(some_num,A3) )
           => ( aa_num_num(F,A3) = aa_num_num(G,A3) ) )
       => ( aa_opt5369159329878751634on_num(map_option_num_num(F),X2) = aa_opt5369159329878751634on_num(map_option_num_num(G),Y) ) ) ) ).

% map_option_cong
tff(fact_1043_option_Osimps_I9_J,axiom,
    ! [F: fun_nu5234077238548837151it_nat,X22: num] : map_op8118133509425879471it_nat(F,aa_num_option_num(some_num,X22)) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,aa_num7171627272556384352it_nat(F,X22)) ).

% option.simps(9)
tff(fact_1044_option_Osimps_I9_J,axiom,
    ! [F: fun_Pr1075626608990047775at_num,X22: produc8664842809031399944it_nat] : map_op2731889312448867759at_num(F,aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X22)) = aa_num_option_num(some_num,aa_Pro1785383075579372640at_num(F,X22)) ).

% option.simps(9)
tff(fact_1045_option_Osimps_I9_J,axiom,
    ! [F: fun_Pr1033138224055104269it_nat,X22: produc8664842809031399944it_nat] : map_op8673683442680995229it_nat(F,aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X22)) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,aa_Pro550487673543749710it_nat(F,X22)) ).

% option.simps(9)
tff(fact_1046_option_Osimps_I9_J,axiom,
    ! [F: fun_num_num,X22: num] : aa_opt5369159329878751634on_num(map_option_num_num(F),aa_num_option_num(some_num,X22)) = aa_num_option_num(some_num,aa_num_num(F,X22)) ).

% option.simps(9)
tff(fact_1047_option_Osimps_I8_J,axiom,
    ! [F: fun_Pr3819237756034508227it_nat] : map_op6002829699023054091it_nat(F,none_P2587165478634041381it_nat) = none_P2587165478634041381it_nat ).

% option.simps(8)
tff(fact_1048_option_Osimps_I8_J,axiom,
    ! [F: fun_Pr1223581030874358257at_num] : map_op8228268515680064275at_num(F,none_P2587165478634041381it_nat) = none_num ).

% option.simps(8)
tff(fact_1049_option_Osimps_I8_J,axiom,
    ! [F: fun_Pr2014882013869309663it_nat] : map_op674526153330701057it_nat(F,none_P2587165478634041381it_nat) = none_P9117596204409417319it_nat ).

% option.simps(8)
tff(fact_1050_option_Osimps_I8_J,axiom,
    ! [F: fun_nu2241728722996109699it_nat] : map_op6598675229099881181it_nat(F,none_num) = none_P2587165478634041381it_nat ).

% option.simps(8)
tff(fact_1051_option_Osimps_I8_J,axiom,
    ! [F: fun_nu5234077238548837151it_nat] : map_op8118133509425879471it_nat(F,none_num) = none_P9117596204409417319it_nat ).

% option.simps(8)
tff(fact_1052_option_Osimps_I8_J,axiom,
    ! [F: fun_Pr3908927074708932117it_nat] : map_op7916408704904942447it_nat(F,none_P9117596204409417319it_nat) = none_P2587165478634041381it_nat ).

% option.simps(8)
tff(fact_1053_option_Osimps_I8_J,axiom,
    ! [F: fun_Pr1075626608990047775at_num] : map_op2731889312448867759at_num(F,none_P9117596204409417319it_nat) = none_num ).

% option.simps(8)
tff(fact_1054_option_Osimps_I8_J,axiom,
    ! [F: fun_Pr1033138224055104269it_nat] : map_op8673683442680995229it_nat(F,none_P9117596204409417319it_nat) = none_P9117596204409417319it_nat ).

% option.simps(8)
tff(fact_1055_option_Osimps_I8_J,axiom,
    ! [F: fun_num_num] : aa_opt5369159329878751634on_num(map_option_num_num(F),none_num) = none_num ).

% option.simps(8)
tff(fact_1056_same__sgn__sgn__add,axiom,
    ! [B: code_integer,A: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(sgn_sgn_Code_integer,B) = aa_Cod1783974652533396728nteger(sgn_sgn_Code_integer,A) )
     => ( aa_Cod1783974652533396728nteger(sgn_sgn_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)) = aa_Cod1783974652533396728nteger(sgn_sgn_Code_integer,A) ) ) ).

% same_sgn_sgn_add
tff(fact_1057_same__sgn__sgn__add,axiom,
    ! [B: rat,A: rat] :
      ( ( aa_rat_rat(sgn_sgn_rat,B) = aa_rat_rat(sgn_sgn_rat,A) )
     => ( aa_rat_rat(sgn_sgn_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)) = aa_rat_rat(sgn_sgn_rat,A) ) ) ).

% same_sgn_sgn_add
tff(fact_1058_same__sgn__sgn__add,axiom,
    ! [B: int,A: int] :
      ( ( aa_int_int(sgn_sgn_int,B) = aa_int_int(sgn_sgn_int,A) )
     => ( aa_int_int(sgn_sgn_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)) = aa_int_int(sgn_sgn_int,A) ) ) ).

% same_sgn_sgn_add
tff(fact_1059_Ints__add,axiom,
    ! [A: rat,B: rat] :
      ( member_rat(A,ring_1_Ints_rat)
     => ( member_rat(B,ring_1_Ints_rat)
       => member_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B),ring_1_Ints_rat) ) ) ).

% Ints_add
tff(fact_1060_Ints__add,axiom,
    ! [A: int,B: int] :
      ( member_int(A,ring_1_Ints_int)
     => ( member_int(B,ring_1_Ints_int)
       => member_int(aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B),ring_1_Ints_int) ) ) ).

% Ints_add
tff(fact_1061_success__lookupI,axiom,
    ! [R2: ref_Product_unit,Ha: heap_e7401611519738050253t_unit] : aa_hea7994211679605476167unit_o(heap_T584514906347983379t_unit(ref_lo7930775386976318366t_unit(R2)),Ha) ).

% success_lookupI
tff(fact_1062_success__lookupI,axiom,
    ! [R2: ref_array_a,Ha: heap_e7401611519738050253t_unit] : aa_hea7994211679605476167unit_o(heap_T6932021131025641745rray_a(ref_lookup_array_a(R2)),Ha) ).

% success_lookupI
tff(fact_1063_Ints__1,axiom,
    member_Code_integer(one_one_Code_integer,ring_11222124179247155820nteger) ).

% Ints_1
tff(fact_1064_Ints__1,axiom,
    member_rat(one_one_rat,ring_1_Ints_rat) ).

% Ints_1
tff(fact_1065_Ints__1,axiom,
    member_int(one_one_int,ring_1_Ints_int) ).

% Ints_1
tff(fact_1066_Ints__nonzero__abs__less1,axiom,
    ! [X2: code_integer] :
      ( member_Code_integer(X2,ring_11222124179247155820nteger)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,X2)),one_one_Code_integer)
       => ( X2 = zero_z3403309356797280102nteger ) ) ) ).

% Ints_nonzero_abs_less1
tff(fact_1067_Ints__nonzero__abs__less1,axiom,
    ! [X2: rat] :
      ( member_rat(X2,ring_1_Ints_rat)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(abs_abs_rat,X2)),one_one_rat)
       => ( X2 = zero_zero_rat ) ) ) ).

% Ints_nonzero_abs_less1
tff(fact_1068_Ints__nonzero__abs__less1,axiom,
    ! [X2: int] :
      ( member_int(X2,ring_1_Ints_int)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(abs_abs_int,X2)),one_one_int)
       => ( X2 = zero_zero_int ) ) ) ).

% Ints_nonzero_abs_less1
tff(fact_1069_sgn__if,axiom,
    ! [X2: int] :
      aa_int_int(sgn_sgn_int,X2) = $ite(
        X2 = zero_zero_int,
        zero_zero_int,
        $ite(aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),X2),one_one_int,aa_int_int(uminus_uminus_int,one_one_int)) ) ).

% sgn_if
tff(fact_1070_sgn__if,axiom,
    ! [X2: code_integer] :
      aa_Cod1783974652533396728nteger(sgn_sgn_Code_integer,X2) = $ite(
        X2 = zero_z3403309356797280102nteger,
        zero_z3403309356797280102nteger,
        $ite(aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),X2),one_one_Code_integer,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) ) ).

% sgn_if
tff(fact_1071_sgn__if,axiom,
    ! [X2: rat] :
      aa_rat_rat(sgn_sgn_rat,X2) = $ite(
        X2 = zero_zero_rat,
        zero_zero_rat,
        $ite(aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),X2),one_one_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)) ) ).

% sgn_if
tff(fact_1072_sgn__1__neg,axiom,
    ! [A: int] :
      ( ( aa_int_int(sgn_sgn_int,A) = aa_int_int(uminus_uminus_int,one_one_int) )
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,A),zero_zero_int) ) ).

% sgn_1_neg
tff(fact_1073_sgn__1__neg,axiom,
    ! [A: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(sgn_sgn_Code_integer,A) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) )
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),zero_z3403309356797280102nteger) ) ).

% sgn_1_neg
tff(fact_1074_sgn__1__neg,axiom,
    ! [A: rat] :
      ( ( aa_rat_rat(sgn_sgn_rat,A) = aa_rat_rat(uminus_uminus_rat,one_one_rat) )
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),zero_zero_rat) ) ).

% sgn_1_neg
tff(fact_1075_abs__not__less__zero,axiom,
    ! [A: code_integer] : ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A)),zero_z3403309356797280102nteger) ).

% abs_not_less_zero
tff(fact_1076_abs__not__less__zero,axiom,
    ! [A: rat] : ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(abs_abs_rat,A)),zero_zero_rat) ).

% abs_not_less_zero
tff(fact_1077_abs__not__less__zero,axiom,
    ! [A: int] : ~ aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(abs_abs_int,A)),zero_zero_int) ).

% abs_not_less_zero
tff(fact_1078_abs__of__pos,axiom,
    ! [A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),A)
     => ( aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A) = A ) ) ).

% abs_of_pos
tff(fact_1079_abs__of__pos,axiom,
    ! [A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),A)
     => ( aa_rat_rat(abs_abs_rat,A) = A ) ) ).

% abs_of_pos
tff(fact_1080_abs__of__pos,axiom,
    ! [A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),A)
     => ( aa_int_int(abs_abs_int,A) = A ) ) ).

% abs_of_pos
tff(fact_1081_neg__eq__iff__add__eq__0,axiom,
    ! [A: int,B: int] :
      ( ( aa_int_int(uminus_uminus_int,A) = B )
    <=> ( aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B) = zero_zero_int ) ) ).

% neg_eq_iff_add_eq_0
tff(fact_1082_neg__eq__iff__add__eq__0,axiom,
    ! [A: code_integer,B: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A) = B )
    <=> ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B) = zero_z3403309356797280102nteger ) ) ).

% neg_eq_iff_add_eq_0
tff(fact_1083_neg__eq__iff__add__eq__0,axiom,
    ! [A: rat,B: rat] :
      ( ( aa_rat_rat(uminus_uminus_rat,A) = B )
    <=> ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B) = zero_zero_rat ) ) ).

% neg_eq_iff_add_eq_0
tff(fact_1084_eq__neg__iff__add__eq__0,axiom,
    ! [A: int,B: int] :
      ( ( A = aa_int_int(uminus_uminus_int,B) )
    <=> ( aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B) = zero_zero_int ) ) ).

% eq_neg_iff_add_eq_0
tff(fact_1085_eq__neg__iff__add__eq__0,axiom,
    ! [A: code_integer,B: code_integer] :
      ( ( A = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,B) )
    <=> ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B) = zero_z3403309356797280102nteger ) ) ).

% eq_neg_iff_add_eq_0
tff(fact_1086_eq__neg__iff__add__eq__0,axiom,
    ! [A: rat,B: rat] :
      ( ( A = aa_rat_rat(uminus_uminus_rat,B) )
    <=> ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B) = zero_zero_rat ) ) ).

% eq_neg_iff_add_eq_0
tff(fact_1087_add_Oinverse__unique,axiom,
    ! [A: int,B: int] :
      ( ( aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B) = zero_zero_int )
     => ( aa_int_int(uminus_uminus_int,A) = B ) ) ).

% add.inverse_unique
tff(fact_1088_add_Oinverse__unique,axiom,
    ! [A: code_integer,B: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B) = zero_z3403309356797280102nteger )
     => ( aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A) = B ) ) ).

% add.inverse_unique
tff(fact_1089_add_Oinverse__unique,axiom,
    ! [A: rat,B: rat] :
      ( ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B) = zero_zero_rat )
     => ( aa_rat_rat(uminus_uminus_rat,A) = B ) ) ).

% add.inverse_unique
tff(fact_1090_ab__group__add__class_Oab__left__minus,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(uminus_uminus_int,A)),A) = zero_zero_int ).

% ab_group_add_class.ab_left_minus
tff(fact_1091_ab__group__add__class_Oab__left__minus,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A)),A) = zero_z3403309356797280102nteger ).

% ab_group_add_class.ab_left_minus
tff(fact_1092_ab__group__add__class_Oab__left__minus,axiom,
    ! [A: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,A)),A) = zero_zero_rat ).

% ab_group_add_class.ab_left_minus
tff(fact_1093_add__eq__0__iff,axiom,
    ! [A: int,B: int] :
      ( ( aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B) = zero_zero_int )
    <=> ( B = aa_int_int(uminus_uminus_int,A) ) ) ).

% add_eq_0_iff
tff(fact_1094_add__eq__0__iff,axiom,
    ! [A: code_integer,B: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B) = zero_z3403309356797280102nteger )
    <=> ( B = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A) ) ) ).

% add_eq_0_iff
tff(fact_1095_add__eq__0__iff,axiom,
    ! [A: rat,B: rat] :
      ( ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B) = zero_zero_rat )
    <=> ( B = aa_rat_rat(uminus_uminus_rat,A) ) ) ).

% add_eq_0_iff
tff(fact_1096_zero__neq__neg__one,axiom,
    zero_zero_int != aa_int_int(uminus_uminus_int,one_one_int) ).

% zero_neq_neg_one
tff(fact_1097_zero__neq__neg__one,axiom,
    zero_z3403309356797280102nteger != aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) ).

% zero_neq_neg_one
tff(fact_1098_zero__neq__neg__one,axiom,
    zero_zero_rat != aa_rat_rat(uminus_uminus_rat,one_one_rat) ).

% zero_neq_neg_one
tff(fact_1099_less__minus__one__simps_I4_J,axiom,
    ~ aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),aa_int_int(uminus_uminus_int,one_one_int)) ).

% less_minus_one_simps(4)
tff(fact_1100_less__minus__one__simps_I4_J,axiom,
    ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) ).

% less_minus_one_simps(4)
tff(fact_1101_less__minus__one__simps_I4_J,axiom,
    ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),aa_rat_rat(uminus_uminus_rat,one_one_rat)) ).

% less_minus_one_simps(4)
tff(fact_1102_less__minus__one__simps_I2_J,axiom,
    aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(uminus_uminus_int,one_one_int)),one_one_int) ).

% less_minus_one_simps(2)
tff(fact_1103_less__minus__one__simps_I2_J,axiom,
    aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),one_one_Code_integer) ).

% less_minus_one_simps(2)
tff(fact_1104_less__minus__one__simps_I2_J,axiom,
    aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),one_one_rat) ).

% less_minus_one_simps(2)
tff(fact_1105_option_Omap__sel,axiom,
    ! [A: option_num,F: fun_num_num] :
      ( ( A != none_num )
     => ( aa_option_num_num(the_num,aa_opt5369159329878751634on_num(map_option_num_num(F),A)) = aa_num_num(F,aa_option_num_num(the_num,A)) ) ) ).

% option.map_sel
tff(fact_1106_Ints__double__eq__0__iff,axiom,
    ! [A: code_integer] :
      ( member_Code_integer(A,ring_11222124179247155820nteger)
     => ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),A) = zero_z3403309356797280102nteger )
      <=> ( A = zero_z3403309356797280102nteger ) ) ) ).

% Ints_double_eq_0_iff
tff(fact_1107_Ints__double__eq__0__iff,axiom,
    ! [A: rat] :
      ( member_rat(A,ring_1_Ints_rat)
     => ( ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),A) = zero_zero_rat )
      <=> ( A = zero_zero_rat ) ) ) ).

% Ints_double_eq_0_iff
tff(fact_1108_Ints__double__eq__0__iff,axiom,
    ! [A: int] :
      ( member_int(A,ring_1_Ints_int)
     => ( ( aa_int_int(aa_int_fun_int_int(plus_plus_int,A),A) = zero_zero_int )
      <=> ( A = zero_zero_int ) ) ) ).

% Ints_double_eq_0_iff
tff(fact_1109_less__minus__one__simps_I3_J,axiom,
    ~ aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),aa_int_int(uminus_uminus_int,one_one_int)) ).

% less_minus_one_simps(3)
tff(fact_1110_less__minus__one__simps_I3_J,axiom,
    ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) ).

% less_minus_one_simps(3)
tff(fact_1111_less__minus__one__simps_I3_J,axiom,
    ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),aa_rat_rat(uminus_uminus_rat,one_one_rat)) ).

% less_minus_one_simps(3)
tff(fact_1112_less__minus__one__simps_I1_J,axiom,
    aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(uminus_uminus_int,one_one_int)),zero_zero_int) ).

% less_minus_one_simps(1)
tff(fact_1113_less__minus__one__simps_I1_J,axiom,
    aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),zero_z3403309356797280102nteger) ).

% less_minus_one_simps(1)
tff(fact_1114_less__minus__one__simps_I1_J,axiom,
    aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),zero_zero_rat) ).

% less_minus_one_simps(1)
tff(fact_1115_sgn__1__pos,axiom,
    ! [A: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(sgn_sgn_Code_integer,A) = one_one_Code_integer )
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),A) ) ).

% sgn_1_pos
tff(fact_1116_sgn__1__pos,axiom,
    ! [A: rat] :
      ( ( aa_rat_rat(sgn_sgn_rat,A) = one_one_rat )
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),A) ) ).

% sgn_1_pos
tff(fact_1117_sgn__1__pos,axiom,
    ! [A: int] :
      ( ( aa_int_int(sgn_sgn_int,A) = one_one_int )
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),A) ) ).

% sgn_1_pos
tff(fact_1118_Ints__odd__nonzero,axiom,
    ! [A: code_integer] :
      ( member_Code_integer(A,ring_11222124179247155820nteger)
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,one_one_Code_integer),A)),A) != zero_z3403309356797280102nteger ) ) ).

% Ints_odd_nonzero
tff(fact_1119_Ints__odd__nonzero,axiom,
    ! [A: rat] :
      ( member_rat(A,ring_1_Ints_rat)
     => ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,one_one_rat),A)),A) != zero_zero_rat ) ) ).

% Ints_odd_nonzero
tff(fact_1120_Ints__odd__nonzero,axiom,
    ! [A: int] :
      ( member_int(A,ring_1_Ints_int)
     => ( aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),A)),A) != zero_zero_int ) ) ).

% Ints_odd_nonzero
tff(fact_1121_execute__lookup,axiom,
    ! [R2: ref_array_a,Ha: heap_e7401611519738050253t_unit] : aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(ref_lookup_array_a(R2)),Ha) = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,produc1733996804261680252it_nat(ref_get_array_a(Ha,R2),produc584006145561248582it_nat(Ha,one_one_nat))) ).

% execute_lookup
tff(fact_1122_execute__lookup,axiom,
    ! [R2: ref_Product_unit,Ha: heap_e7401611519738050253t_unit] : aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(ref_lo7930775386976318366t_unit(R2)),Ha) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(ref_get_Product_unit(Ha,R2),produc584006145561248582it_nat(Ha,one_one_nat))) ).

% execute_lookup
tff(fact_1123_fails__assert_H,axiom,
    ! [P: $o,Ha: heap_e7401611519738050253t_unit] :
      ( aa_hea7994211679605476167unit_o(time_f8834461667527620124t_unit(refine_Imp_assert((P))),Ha)
    <=> ~ (P) ) ).

% fails_assert'
tff(fact_1124_add_Ogroup__axioms,axiom,
    group_int(plus_plus_int,zero_zero_int,uminus_uminus_int) ).

% add.group_axioms
tff(fact_1125_add_Ogroup__axioms,axiom,
    group_Code_integer(plus_p5714425477246183910nteger,zero_z3403309356797280102nteger,uminus1351360451143612070nteger) ).

% add.group_axioms
tff(fact_1126_add_Ogroup__axioms,axiom,
    group_rat(plus_plus_rat,zero_zero_rat,uminus_uminus_rat) ).

% add.group_axioms
tff(fact_1127_num__of__nat__double,axiom,
    ! [N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => ( aa_nat_num(num_of_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),N2)) = aa_num_num(bit0,aa_nat_num(num_of_nat,N2)) ) ) ).

% num_of_nat_double
tff(fact_1128_Ints__nonzero__abs__ge1,axiom,
    ! [X2: code_integer] :
      ( member_Code_integer(X2,ring_11222124179247155820nteger)
     => ( ( X2 != zero_z3403309356797280102nteger )
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),aa_Cod1783974652533396728nteger(abs_abs_Code_integer,X2)) ) ) ).

% Ints_nonzero_abs_ge1
tff(fact_1129_Ints__nonzero__abs__ge1,axiom,
    ! [X2: rat] :
      ( member_rat(X2,ring_1_Ints_rat)
     => ( ( X2 != zero_zero_rat )
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),aa_rat_rat(abs_abs_rat,X2)) ) ) ).

% Ints_nonzero_abs_ge1
tff(fact_1130_Ints__nonzero__abs__ge1,axiom,
    ! [X2: int] :
      ( member_int(X2,ring_1_Ints_int)
     => ( ( X2 != zero_zero_int )
       => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,one_one_int),aa_int_int(abs_abs_int,X2)) ) ) ).

% Ints_nonzero_abs_ge1
tff(fact_1131_map__conv__bind__option,axiom,
    ! [F: fun_num_num,X2: option_num] : aa_opt5369159329878751634on_num(map_option_num_num(F),X2) = bind_num_num(X2,comp_n6731957995704128387um_num(some_num,F)) ).

% map_conv_bind_option
tff(fact_1132_nat__add__left__cancel__le,axiom,
    ! [K: nat,M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,K),M)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,K),N2))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2) ) ).

% nat_add_left_cancel_le
tff(fact_1133_less__eq__option__None__code,axiom,
    ! [X2: option_num] : aa_option_num_o(aa_opt8674010985164783839_num_o(ord_le6622620407824499402on_num,none_num),X2) ).

% less_eq_option_None_code
tff(fact_1134_le__zero__eq,axiom,
    ! [N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),zero_zero_nat)
    <=> ( N2 = zero_zero_nat ) ) ).

% le_zero_eq
tff(fact_1135_add__le__cancel__left,axiom,
    ! [C: rat,A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,C),A)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,C),B))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),B) ) ).

% add_le_cancel_left
tff(fact_1136_add__le__cancel__left,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,C),A)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,C),B))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B) ) ).

% add_le_cancel_left
tff(fact_1137_add__le__cancel__left,axiom,
    ! [C: int,A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,C),A)),aa_int_int(aa_int_fun_int_int(plus_plus_int,C),B))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),B) ) ).

% add_le_cancel_left
tff(fact_1138_add__le__cancel__right,axiom,
    ! [A: rat,C: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),C)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),C))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),B) ) ).

% add_le_cancel_right
tff(fact_1139_add__le__cancel__right,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),C))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B) ) ).

% add_le_cancel_right
tff(fact_1140_add__le__cancel__right,axiom,
    ! [A: int,C: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),C)),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),C))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),B) ) ).

% add_le_cancel_right
tff(fact_1141_neg__le__iff__le,axiom,
    ! [B: code_integer,A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,B)),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),B) ) ).

% neg_le_iff_le
tff(fact_1142_neg__le__iff__le,axiom,
    ! [B: rat,A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(uminus_uminus_rat,B)),aa_rat_rat(uminus_uminus_rat,A))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),B) ) ).

% neg_le_iff_le
tff(fact_1143_neg__le__iff__le,axiom,
    ! [B: int,A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(uminus_uminus_int,B)),aa_int_int(uminus_uminus_int,A))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),B) ) ).

% neg_le_iff_le
tff(fact_1144_less__eq__option__Some,axiom,
    ! [X2: set_nat,Y: set_nat] :
      ( ord_le2843612097646854710et_nat(aa_set6119337032432945050et_nat(some_set_nat,X2),aa_set6119337032432945050et_nat(some_set_nat,Y))
    <=> aa_set_nat_o(ord_less_eq_set_nat(X2),Y) ) ).

% less_eq_option_Some
tff(fact_1145_less__eq__option__Some,axiom,
    ! [X2: rat,Y: rat] :
      ( ord_le2406147912482264968on_rat(some_rat(X2),some_rat(Y))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,X2),Y) ) ).

% less_eq_option_Some
tff(fact_1146_less__eq__option__Some,axiom,
    ! [X2: num,Y: num] :
      ( aa_option_num_o(aa_opt8674010985164783839_num_o(ord_le6622620407824499402on_num,aa_num_option_num(some_num,X2)),aa_num_option_num(some_num,Y))
    <=> aa_num_o(aa_num_fun_num_o(ord_less_eq_num,X2),Y) ) ).

% less_eq_option_Some
tff(fact_1147_less__eq__option__Some,axiom,
    ! [X2: nat,Y: nat] :
      ( ord_le5914376470875661696on_nat(aa_nat_option_nat(some_nat,X2),aa_nat_option_nat(some_nat,Y))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,X2),Y) ) ).

% less_eq_option_Some
tff(fact_1148_less__eq__option__Some,axiom,
    ! [X2: int,Y: int] :
      ( ord_le1736525451366464988on_int(aa_int_option_int(some_int,X2),aa_int_option_int(some_int,Y))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,X2),Y) ) ).

% less_eq_option_Some
tff(fact_1149_less__eq__option__Some__None,axiom,
    ! [X2: num] : ~ aa_option_num_o(aa_opt8674010985164783839_num_o(ord_le6622620407824499402on_num,aa_num_option_num(some_num,X2)),none_num) ).

% less_eq_option_Some_None
tff(fact_1150_bind__runit,axiom,
    ! [X2: option_num] : bind_num_num(X2,some_num) = X2 ).

% bind_runit
tff(fact_1151_bind__runit,axiom,
    ! [X2: option8956607266484857688it_nat] : bind_P7351952464966851536it_nat(X2,some_P1914260805536162275it_nat) = X2 ).

% bind_runit
tff(fact_1152_add__le__same__cancel1,axiom,
    ! [B: code_integer,A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,B),A)),B)
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),zero_z3403309356797280102nteger) ) ).

% add_le_same_cancel1
tff(fact_1153_add__le__same__cancel1,axiom,
    ! [B: rat,A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),A)),B)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),zero_zero_rat) ) ).

% add_le_same_cancel1
tff(fact_1154_add__le__same__cancel1,axiom,
    ! [B: nat,A: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),A)),B)
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),zero_zero_nat) ) ).

% add_le_same_cancel1
tff(fact_1155_add__le__same__cancel1,axiom,
    ! [B: int,A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,B),A)),B)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),zero_zero_int) ) ).

% add_le_same_cancel1
tff(fact_1156_add__le__same__cancel2,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)),B)
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),zero_z3403309356797280102nteger) ) ).

% add_le_same_cancel2
tff(fact_1157_add__le__same__cancel2,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),B)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),zero_zero_rat) ) ).

% add_le_same_cancel2
tff(fact_1158_add__le__same__cancel2,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),B)
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),zero_zero_nat) ) ).

% add_le_same_cancel2
tff(fact_1159_add__le__same__cancel2,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),B)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),zero_zero_int) ) ).

% add_le_same_cancel2
tff(fact_1160_le__add__same__cancel1,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),B) ) ).

% le_add_same_cancel1
tff(fact_1161_le__add__same__cancel1,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),B) ) ).

% le_add_same_cancel1
tff(fact_1162_le__add__same__cancel1,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),B) ) ).

% le_add_same_cancel1
tff(fact_1163_le__add__same__cancel1,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),B) ) ).

% le_add_same_cancel1
tff(fact_1164_le__add__same__cancel2,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,B),A))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),B) ) ).

% le_add_same_cancel2
tff(fact_1165_le__add__same__cancel2,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),A))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),B) ) ).

% le_add_same_cancel2
tff(fact_1166_le__add__same__cancel2,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),A))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),B) ) ).

% le_add_same_cancel2
tff(fact_1167_le__add__same__cancel2,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),A))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),B) ) ).

% le_add_same_cancel2
tff(fact_1168_double__add__le__zero__iff__single__add__le__zero,axiom,
    ! [A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),A)),zero_z3403309356797280102nteger)
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),zero_z3403309356797280102nteger) ) ).

% double_add_le_zero_iff_single_add_le_zero
tff(fact_1169_double__add__le__zero__iff__single__add__le__zero,axiom,
    ! [A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),A)),zero_zero_rat)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),zero_zero_rat) ) ).

% double_add_le_zero_iff_single_add_le_zero
tff(fact_1170_double__add__le__zero__iff__single__add__le__zero,axiom,
    ! [A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),A)),zero_zero_int)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),zero_zero_int) ) ).

% double_add_le_zero_iff_single_add_le_zero
tff(fact_1171_zero__le__double__add__iff__zero__le__single__add,axiom,
    ! [A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),A))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),A) ) ).

% zero_le_double_add_iff_zero_le_single_add
tff(fact_1172_zero__le__double__add__iff__zero__le__single__add,axiom,
    ! [A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),A))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),A) ) ).

% zero_le_double_add_iff_zero_le_single_add
tff(fact_1173_zero__le__double__add__iff__zero__le__single__add,axiom,
    ! [A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),A))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),A) ) ).

% zero_le_double_add_iff_zero_le_single_add
tff(fact_1174_neg__0__le__iff__le,axiom,
    ! [A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),zero_z3403309356797280102nteger) ) ).

% neg_0_le_iff_le
tff(fact_1175_neg__0__le__iff__le,axiom,
    ! [A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),aa_rat_rat(uminus_uminus_rat,A))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),zero_zero_rat) ) ).

% neg_0_le_iff_le
tff(fact_1176_neg__0__le__iff__le,axiom,
    ! [A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),aa_int_int(uminus_uminus_int,A))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),zero_zero_int) ) ).

% neg_0_le_iff_le
tff(fact_1177_neg__le__0__iff__le,axiom,
    ! [A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A)),zero_z3403309356797280102nteger)
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),A) ) ).

% neg_le_0_iff_le
tff(fact_1178_neg__le__0__iff__le,axiom,
    ! [A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(uminus_uminus_rat,A)),zero_zero_rat)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),A) ) ).

% neg_le_0_iff_le
tff(fact_1179_neg__le__0__iff__le,axiom,
    ! [A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(uminus_uminus_int,A)),zero_zero_int)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),A) ) ).

% neg_le_0_iff_le
tff(fact_1180_less__eq__neg__nonpos,axiom,
    ! [A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),zero_z3403309356797280102nteger) ) ).

% less_eq_neg_nonpos
tff(fact_1181_less__eq__neg__nonpos,axiom,
    ! [A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),aa_rat_rat(uminus_uminus_rat,A))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),zero_zero_rat) ) ).

% less_eq_neg_nonpos
tff(fact_1182_less__eq__neg__nonpos,axiom,
    ! [A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),aa_int_int(uminus_uminus_int,A))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),zero_zero_int) ) ).

% less_eq_neg_nonpos
tff(fact_1183_neg__less__eq__nonneg,axiom,
    ! [A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A)),A)
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),A) ) ).

% neg_less_eq_nonneg
tff(fact_1184_neg__less__eq__nonneg,axiom,
    ! [A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(uminus_uminus_rat,A)),A)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),A) ) ).

% neg_less_eq_nonneg
tff(fact_1185_neg__less__eq__nonneg,axiom,
    ! [A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(uminus_uminus_int,A)),A)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),A) ) ).

% neg_less_eq_nonneg
tff(fact_1186_abs__of__nonneg,axiom,
    ! [A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),A)
     => ( aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A) = A ) ) ).

% abs_of_nonneg
tff(fact_1187_abs__of__nonneg,axiom,
    ! [A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),A)
     => ( aa_rat_rat(abs_abs_rat,A) = A ) ) ).

% abs_of_nonneg
tff(fact_1188_abs__of__nonneg,axiom,
    ! [A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),A)
     => ( aa_int_int(abs_abs_int,A) = A ) ) ).

% abs_of_nonneg
tff(fact_1189_abs__le__self__iff,axiom,
    ! [A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A)),A)
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),A) ) ).

% abs_le_self_iff
tff(fact_1190_abs__le__self__iff,axiom,
    ! [A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(abs_abs_rat,A)),A)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),A) ) ).

% abs_le_self_iff
tff(fact_1191_abs__le__self__iff,axiom,
    ! [A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(abs_abs_int,A)),A)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),A) ) ).

% abs_le_self_iff
tff(fact_1192_abs__le__zero__iff,axiom,
    ! [A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A)),zero_z3403309356797280102nteger)
    <=> ( A = zero_z3403309356797280102nteger ) ) ).

% abs_le_zero_iff
tff(fact_1193_abs__le__zero__iff,axiom,
    ! [A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(abs_abs_rat,A)),zero_zero_rat)
    <=> ( A = zero_zero_rat ) ) ).

% abs_le_zero_iff
tff(fact_1194_abs__le__zero__iff,axiom,
    ! [A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(abs_abs_int,A)),zero_zero_int)
    <=> ( A = zero_zero_int ) ) ).

% abs_le_zero_iff
tff(fact_1195_abs__of__nonpos,axiom,
    ! [A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),zero_z3403309356797280102nteger)
     => ( aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A) ) ) ).

% abs_of_nonpos
tff(fact_1196_abs__of__nonpos,axiom,
    ! [A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),zero_zero_rat)
     => ( aa_rat_rat(abs_abs_rat,A) = aa_rat_rat(uminus_uminus_rat,A) ) ) ).

% abs_of_nonpos
tff(fact_1197_abs__of__nonpos,axiom,
    ! [A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),zero_zero_int)
     => ( aa_int_int(abs_abs_int,A) = aa_int_int(uminus_uminus_int,A) ) ) ).

% abs_of_nonpos
tff(fact_1198_ord__eq__le__eq__trans,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat,D2: set_nat] :
      ( ( A = B )
     => ( aa_set_nat_o(ord_less_eq_set_nat(B),C)
       => ( ( C = D2 )
         => aa_set_nat_o(ord_less_eq_set_nat(A),D2) ) ) ) ).

% ord_eq_le_eq_trans
tff(fact_1199_ord__eq__le__eq__trans,axiom,
    ! [A: rat,B: rat,C: rat,D2: rat] :
      ( ( A = B )
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),C)
       => ( ( C = D2 )
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),D2) ) ) ) ).

% ord_eq_le_eq_trans
tff(fact_1200_ord__eq__le__eq__trans,axiom,
    ! [A: num,B: num,C: num,D2: num] :
      ( ( A = B )
     => ( aa_num_o(aa_num_fun_num_o(ord_less_eq_num,B),C)
       => ( ( C = D2 )
         => aa_num_o(aa_num_fun_num_o(ord_less_eq_num,A),D2) ) ) ) ).

% ord_eq_le_eq_trans
tff(fact_1201_ord__eq__le__eq__trans,axiom,
    ! [A: nat,B: nat,C: nat,D2: nat] :
      ( ( A = B )
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,B),C)
       => ( ( C = D2 )
         => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),D2) ) ) ) ).

% ord_eq_le_eq_trans
tff(fact_1202_ord__eq__le__eq__trans,axiom,
    ! [A: int,B: int,C: int,D2: int] :
      ( ( A = B )
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,B),C)
       => ( ( C = D2 )
         => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),D2) ) ) ) ).

% ord_eq_le_eq_trans
tff(fact_1203_accp__subset,axiom,
    ! [R12: fun_Pr2028404973800837934_nat_o,R23: fun_Pr2028404973800837934_nat_o] :
      ( ord_le3650406611588909774_nat_o(R12,R23)
     => aa_fun8408151826566693824at_o_o(ord_le1572679713340831354_nat_o(accp_P4275260045618599050at_nat(R23)),accp_P4275260045618599050at_nat(R12)) ) ).

% accp_subset
tff(fact_1204_accp__subset,axiom,
    ! [R12: fun_Pr9018117161326028078_int_o,R23: fun_Pr9018117161326028078_int_o] :
      ( ord_le1416746762259324110_int_o(R12,R23)
     => ord_le14110778710936002_int_o(accp_P1096762738010456898nt_int(R23),accp_P1096762738010456898nt_int(R12)) ) ).

% accp_subset
tff(fact_1205_accp__subset,axiom,
    ! [R12: fun_Pr3358449090565925198_nat_o,R23: fun_Pr3358449090565925198_nat_o] :
      ( ord_le6446978100474826990_nat_o(R12,R23)
     => ord_le3896530374514135251_nat_o(accp_P1394777952347926645et_nat(R23),accp_P1394777952347926645et_nat(R12)) ) ).

% accp_subset
tff(fact_1206_accp__subset,axiom,
    ! [R12: fun_li1025265955262268170_nat_o,R23: fun_li1025265955262268170_nat_o] :
      ( ord_le4470944457981725354_nat_o(R12,R23)
     => ord_le4972187363741583025_nat_o(accp_list_nat(R23),accp_list_nat(R12)) ) ).

% accp_subset
tff(fact_1207_accp__subset,axiom,
    ! [R12: fun_nat_fun_nat_o,R23: fun_nat_fun_nat_o] :
      ( ord_le768339454706049738_nat_o(R12,R23)
     => aa_fun_nat_o_o(aa_fun4840518763754620511at_o_o(ord_le7240017405068453697_nat_o,accp_nat(R23)),accp_nat(R12)) ) ).

% accp_subset
tff(fact_1208_le__some__optE,axiom,
    ! [M: set_nat,X2: option_set_nat] :
      ( ord_le2843612097646854710et_nat(aa_set6119337032432945050et_nat(some_set_nat,M),X2)
     => ~ ! [M3: set_nat] :
            ( ( X2 = aa_set6119337032432945050et_nat(some_set_nat,M3) )
           => ~ aa_set_nat_o(ord_less_eq_set_nat(M),M3) ) ) ).

% le_some_optE
tff(fact_1209_le__some__optE,axiom,
    ! [M: rat,X2: option_rat] :
      ( ord_le2406147912482264968on_rat(some_rat(M),X2)
     => ~ ! [M3: rat] :
            ( ( X2 = some_rat(M3) )
           => ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,M),M3) ) ) ).

% le_some_optE
tff(fact_1210_le__some__optE,axiom,
    ! [M: num,X2: option_num] :
      ( aa_option_num_o(aa_opt8674010985164783839_num_o(ord_le6622620407824499402on_num,aa_num_option_num(some_num,M)),X2)
     => ~ ! [M3: num] :
            ( ( X2 = aa_num_option_num(some_num,M3) )
           => ~ aa_num_o(aa_num_fun_num_o(ord_less_eq_num,M),M3) ) ) ).

% le_some_optE
tff(fact_1211_le__some__optE,axiom,
    ! [M: nat,X2: option_nat] :
      ( ord_le5914376470875661696on_nat(aa_nat_option_nat(some_nat,M),X2)
     => ~ ! [M3: nat] :
            ( ( X2 = aa_nat_option_nat(some_nat,M3) )
           => ~ aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),M3) ) ) ).

% le_some_optE
tff(fact_1212_le__some__optE,axiom,
    ! [M: int,X2: option_int] :
      ( ord_le1736525451366464988on_int(aa_int_option_int(some_int,M),X2)
     => ~ ! [M3: int] :
            ( ( X2 = aa_int_option_int(some_int,M3) )
           => ~ aa_int_o(aa_int_fun_int_o(ord_less_eq_int,M),M3) ) ) ).

% le_some_optE
tff(fact_1213_pred__subset__eq2,axiom,
    ! [R3: set_Pr4329608150637261639at_nat,S2: set_Pr4329608150637261639at_nat] :
      ( ord_le5606610691101069006_nat_o(aa_set5605188905385065315_nat_o(aTP_Lamm_bu,R3),aa_set5605188905385065315_nat_o(aTP_Lamm_bu,S2))
    <=> ord_le1268244103169919719at_nat(R3,S2) ) ).

% pred_subset_eq2
tff(fact_1214_pred__subset__eq2,axiom,
    ! [R3: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
      ( ord_le768339454706049738_nat_o(aa_set2634951030311766213_nat_o(aTP_Lamm_bv,R3),aa_set2634951030311766213_nat_o(aTP_Lamm_bv,S2))
    <=> aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(ord_le3146513528884898305at_nat,R3),S2) ) ).

% pred_subset_eq2
tff(fact_1215_pred__subset__eq2,axiom,
    ! [R3: set_Pr3486312109254157132nteger,S2: set_Pr3486312109254157132nteger] :
      ( ord_le4825817444062779351eger_o(aa_set282680696547864321eger_o(aTP_Lamm_bw,R3),aa_set282680696547864321eger_o(aTP_Lamm_bw,S2))
    <=> ord_le2932375828722672556nteger(R3,S2) ) ).

% pred_subset_eq2
tff(fact_1216_pred__subset__eq2,axiom,
    ! [R3: set_Pr1312406793078187350et_nat,S2: set_Pr1312406793078187350et_nat] :
      ( ord_le3580378406483493347_nat_o(aa_set6295625606485646487_nat_o(aTP_Lamm_bx,R3),aa_set6295625606485646487_nat_o(aTP_Lamm_bx,S2))
    <=> ord_le3919382008627836342et_nat(R3,S2) ) ).

% pred_subset_eq2
tff(fact_1217_pred__subset__eq2,axiom,
    ! [R3: set_Pr4040394263813967220et_nat,S2: set_Pr4040394263813967220et_nat] :
      ( ord_le2834457679758710341_nat_o(aa_set2269662337286943895_nat_o(aTP_Lamm_by,R3),aa_set2269662337286943895_nat_o(aTP_Lamm_by,S2))
    <=> ord_le5189643068899110356et_nat(R3,S2) ) ).

% pred_subset_eq2
tff(fact_1218_pred__subset__eq2,axiom,
    ! [R3: set_Pr6700895561065273913nt_int,S2: set_Pr6700895561065273913nt_int] :
      ( ord_le4806730579060245290_int_o(aa_set8857007276572228673_int_o(aTP_Lamm_bz,R3),aa_set8857007276572228673_int_o(aTP_Lamm_bz,S2))
    <=> ord_le3990897393281686169nt_int(R3,S2) ) ).

% pred_subset_eq2
tff(fact_1219_pred__subset__eq2,axiom,
    ! [R3: set_Pr4166680992137330533nt_int,S2: set_Pr4166680992137330533nt_int] :
      ( ord_le2876595303158420734_int_o(aa_set6932945912113297217_int_o(aTP_Lamm_ca,R3),aa_set6932945912113297217_int_o(aTP_Lamm_ca,S2))
    <=> ord_le3197784583289274309nt_int(R3,S2) ) ).

% pred_subset_eq2
tff(fact_1220_less__eq__option__def,axiom,
    ! [X2: option_set_nat,Y: option_set_nat] :
      ( ord_le2843612097646854710et_nat(X2,Y)
    <=> case_o4401850862724306899et_nat($true,aTP_Lamm_ch(Y),X2) ) ).

% less_eq_option_def
tff(fact_1221_less__eq__option__def,axiom,
    ! [X2: option_rat,Y: option_rat] :
      ( ord_le2406147912482264968on_rat(X2,Y)
    <=> case_option_o_rat($true,aTP_Lamm_ci(Y),X2) ) ).

% less_eq_option_def
tff(fact_1222_less__eq__option__def,axiom,
    ! [X2: option_num,Y: option_num] :
      ( aa_option_num_o(aa_opt8674010985164783839_num_o(ord_le6622620407824499402on_num,X2),Y)
    <=> aa_option_num_o(case_option_o_num($true,aTP_Lamm_cj(Y)),X2) ) ).

% less_eq_option_def
tff(fact_1223_less__eq__option__def,axiom,
    ! [X2: option_nat,Y: option_nat] :
      ( ord_le5914376470875661696on_nat(X2,Y)
    <=> case_option_o_nat($true,aTP_Lamm_ck(Y),X2) ) ).

% less_eq_option_def
tff(fact_1224_less__eq__option__def,axiom,
    ! [X2: option_int,Y: option_int] :
      ( ord_le1736525451366464988on_int(X2,Y)
    <=> case_option_o_int($true,aTP_Lamm_cl(Y),X2) ) ).

% less_eq_option_def
tff(fact_1225_zero__le,axiom,
    ! [X2: nat] : aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),X2) ).

% zero_le
tff(fact_1226_add__mono__thms__linordered__semiring_I3_J,axiom,
    ! [I: rat,J: rat,K: rat,L: rat] :
      ( ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,I),J)
        & ( K = L ) )
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,I),K)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,J),L)) ) ).

% add_mono_thms_linordered_semiring(3)
tff(fact_1227_add__mono__thms__linordered__semiring_I3_J,axiom,
    ! [I: nat,J: nat,K: nat,L: nat] :
      ( ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,I),J)
        & ( K = L ) )
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),L)) ) ).

% add_mono_thms_linordered_semiring(3)
tff(fact_1228_add__mono__thms__linordered__semiring_I3_J,axiom,
    ! [I: int,J: int,K: int,L: int] :
      ( ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,I),J)
        & ( K = L ) )
     => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,I),K)),aa_int_int(aa_int_fun_int_int(plus_plus_int,J),L)) ) ).

% add_mono_thms_linordered_semiring(3)
tff(fact_1229_add__mono__thms__linordered__semiring_I2_J,axiom,
    ! [I: rat,J: rat,K: rat,L: rat] :
      ( ( ( I = J )
        & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,K),L) )
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,I),K)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,J),L)) ) ).

% add_mono_thms_linordered_semiring(2)
tff(fact_1230_add__mono__thms__linordered__semiring_I2_J,axiom,
    ! [I: nat,J: nat,K: nat,L: nat] :
      ( ( ( I = J )
        & aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),L) )
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),L)) ) ).

% add_mono_thms_linordered_semiring(2)
tff(fact_1231_add__mono__thms__linordered__semiring_I2_J,axiom,
    ! [I: int,J: int,K: int,L: int] :
      ( ( ( I = J )
        & aa_int_o(aa_int_fun_int_o(ord_less_eq_int,K),L) )
     => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,I),K)),aa_int_int(aa_int_fun_int_int(plus_plus_int,J),L)) ) ).

% add_mono_thms_linordered_semiring(2)
tff(fact_1232_add__mono__thms__linordered__semiring_I1_J,axiom,
    ! [I: rat,J: rat,K: rat,L: rat] :
      ( ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,I),J)
        & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,K),L) )
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,I),K)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,J),L)) ) ).

% add_mono_thms_linordered_semiring(1)
tff(fact_1233_add__mono__thms__linordered__semiring_I1_J,axiom,
    ! [I: nat,J: nat,K: nat,L: nat] :
      ( ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,I),J)
        & aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),L) )
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),L)) ) ).

% add_mono_thms_linordered_semiring(1)
tff(fact_1234_add__mono__thms__linordered__semiring_I1_J,axiom,
    ! [I: int,J: int,K: int,L: int] :
      ( ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,I),J)
        & aa_int_o(aa_int_fun_int_o(ord_less_eq_int,K),L) )
     => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,I),K)),aa_int_int(aa_int_fun_int_int(plus_plus_int,J),L)) ) ).

% add_mono_thms_linordered_semiring(1)
tff(fact_1235_add__mono,axiom,
    ! [A: rat,B: rat,C: rat,D2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),B)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,C),D2)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),C)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),D2)) ) ) ).

% add_mono
tff(fact_1236_add__mono,axiom,
    ! [A: nat,B: nat,C: nat,D2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,C),D2)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),D2)) ) ) ).

% add_mono
tff(fact_1237_add__mono,axiom,
    ! [A: int,B: int,C: int,D2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),B)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,C),D2)
       => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),C)),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),D2)) ) ) ).

% add_mono
tff(fact_1238_add__left__mono,axiom,
    ! [A: rat,B: rat,C: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),B)
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,C),A)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,C),B)) ) ).

% add_left_mono
tff(fact_1239_add__left__mono,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,C),A)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,C),B)) ) ).

% add_left_mono
tff(fact_1240_add__left__mono,axiom,
    ! [A: int,B: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),B)
     => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,C),A)),aa_int_int(aa_int_fun_int_int(plus_plus_int,C),B)) ) ).

% add_left_mono
tff(fact_1241_less__eqE,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
     => ~ ! [C2: nat] : B != aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C2) ) ).

% less_eqE
tff(fact_1242_add__right__mono,axiom,
    ! [A: rat,B: rat,C: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),B)
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),C)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),C)) ) ).

% add_right_mono
tff(fact_1243_add__right__mono,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),C)) ) ).

% add_right_mono
tff(fact_1244_add__right__mono,axiom,
    ! [A: int,B: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),B)
     => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),C)),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),C)) ) ).

% add_right_mono
tff(fact_1245_le__iff__add,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
    <=> ? [C3: nat] : B = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C3) ) ).

% le_iff_add
tff(fact_1246_add__le__imp__le__left,axiom,
    ! [C: rat,A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,C),A)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,C),B))
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),B) ) ).

% add_le_imp_le_left
tff(fact_1247_add__le__imp__le__left,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,C),A)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,C),B))
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B) ) ).

% add_le_imp_le_left
tff(fact_1248_add__le__imp__le__left,axiom,
    ! [C: int,A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,C),A)),aa_int_int(aa_int_fun_int_int(plus_plus_int,C),B))
     => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),B) ) ).

% add_le_imp_le_left
tff(fact_1249_add__le__imp__le__right,axiom,
    ! [A: rat,C: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),C)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),C))
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),B) ) ).

% add_le_imp_le_right
tff(fact_1250_add__le__imp__le__right,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),C))
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B) ) ).

% add_le_imp_le_right
tff(fact_1251_add__le__imp__le__right,axiom,
    ! [A: int,C: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),C)),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),C))
     => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),B) ) ).

% add_le_imp_le_right
tff(fact_1252_accp__subset__induct,axiom,
    ! [D3: fun_Pr4796943543331071514_nat_o,R3: fun_Pr2028404973800837934_nat_o,X2: product_prod_nat_nat,P: fun_Pr4796943543331071514_nat_o] :
      ( aa_fun8408151826566693824at_o_o(ord_le1572679713340831354_nat_o(D3),accp_P4275260045618599050at_nat(R3))
     => ( ! [X3: product_prod_nat_nat,Z2: product_prod_nat_nat] :
            ( aa_Pro6150637604445964947_nat_o(D3,X3)
           => ( aa_Pro6150637604445964947_nat_o(aa_Pro989595756709598047_nat_o(R3,Z2),X3)
             => aa_Pro6150637604445964947_nat_o(D3,Z2) ) )
       => ( aa_Pro6150637604445964947_nat_o(D3,X2)
         => ( ! [X3: product_prod_nat_nat] :
                ( aa_Pro6150637604445964947_nat_o(D3,X3)
               => ( ! [Z4: product_prod_nat_nat] :
                      ( aa_Pro6150637604445964947_nat_o(aa_Pro989595756709598047_nat_o(R3,Z4),X3)
                     => aa_Pro6150637604445964947_nat_o(P,Z4) )
                 => aa_Pro6150637604445964947_nat_o(P,X3) ) )
           => aa_Pro6150637604445964947_nat_o(P,X2) ) ) ) ) ).

% accp_subset_induct
tff(fact_1253_accp__subset__induct,axiom,
    ! [D3: fun_Pr3238374608701176162_int_o,R3: fun_Pr9018117161326028078_int_o,X2: product_prod_int_int,P: fun_Pr3238374608701176162_int_o] :
      ( ord_le14110778710936002_int_o(D3,accp_P1096762738010456898nt_int(R3))
     => ( ! [X3: product_prod_int_int,Z2: product_prod_int_int] :
            ( aa_Pro4592068669816069595_int_o(D3,X3)
           => ( aa_Pro4592068669816069595_int_o(aa_Pro3952998155787061599_int_o(R3,Z2),X3)
             => aa_Pro4592068669816069595_int_o(D3,Z2) ) )
       => ( aa_Pro4592068669816069595_int_o(D3,X2)
         => ( ! [X3: product_prod_int_int] :
                ( aa_Pro4592068669816069595_int_o(D3,X3)
               => ( ! [Z4: product_prod_int_int] :
                      ( aa_Pro4592068669816069595_int_o(aa_Pro3952998155787061599_int_o(R3,Z4),X3)
                     => aa_Pro4592068669816069595_int_o(P,Z4) )
                 => aa_Pro4592068669816069595_int_o(P,X3) ) )
           => aa_Pro4592068669816069595_int_o(P,X2) ) ) ) ) ).

% accp_subset_induct
tff(fact_1254_accp__subset__induct,axiom,
    ! [D3: fun_Pr1227177680593602867_nat_o,R3: fun_Pr3358449090565925198_nat_o,X2: produc3112576180687729086et_nat,P: fun_Pr1227177680593602867_nat_o] :
      ( ord_le3896530374514135251_nat_o(D3,accp_P1394777952347926645et_nat(R3))
     => ( ! [X3: produc3112576180687729086et_nat,Z2: produc3112576180687729086et_nat] :
            ( aa_Pro2671238023309943196_nat_o(D3,X3)
           => ( aa_Pro2671238023309943196_nat_o(aa_Pro4671852207856306999_nat_o(R3,Z2),X3)
             => aa_Pro2671238023309943196_nat_o(D3,Z2) ) )
       => ( aa_Pro2671238023309943196_nat_o(D3,X2)
         => ( ! [X3: produc3112576180687729086et_nat] :
                ( aa_Pro2671238023309943196_nat_o(D3,X3)
               => ( ! [Z4: produc3112576180687729086et_nat] :
                      ( aa_Pro2671238023309943196_nat_o(aa_Pro4671852207856306999_nat_o(R3,Z4),X3)
                     => aa_Pro2671238023309943196_nat_o(P,Z4) )
                 => aa_Pro2671238023309943196_nat_o(P,X3) ) )
           => aa_Pro2671238023309943196_nat_o(P,X2) ) ) ) ) ).

% accp_subset_induct
tff(fact_1255_accp__subset__induct,axiom,
    ! [D3: fun_list_nat_o,R3: fun_li1025265955262268170_nat_o,X2: list_nat,P: fun_list_nat_o] :
      ( ord_le4972187363741583025_nat_o(D3,accp_list_nat(R3))
     => ( ! [X3: list_nat,Z2: list_nat] :
            ( aa_list_nat_o(D3,X3)
           => ( aa_list_nat_o(aa_lis557685189327716851_nat_o(R3,Z2),X3)
             => aa_list_nat_o(D3,Z2) ) )
       => ( aa_list_nat_o(D3,X2)
         => ( ! [X3: list_nat] :
                ( aa_list_nat_o(D3,X3)
               => ( ! [Z4: list_nat] :
                      ( aa_list_nat_o(aa_lis557685189327716851_nat_o(R3,Z4),X3)
                     => aa_list_nat_o(P,Z4) )
                 => aa_list_nat_o(P,X3) ) )
           => aa_list_nat_o(P,X2) ) ) ) ) ).

% accp_subset_induct
tff(fact_1256_accp__subset__induct,axiom,
    ! [D3: fun_nat_o,R3: fun_nat_fun_nat_o,X2: nat,P: fun_nat_o] :
      ( aa_fun_nat_o_o(aa_fun4840518763754620511at_o_o(ord_le7240017405068453697_nat_o,D3),accp_nat(R3))
     => ( ! [X3: nat,Z2: nat] :
            ( aa_nat_o(D3,X3)
           => ( aa_nat_o(aa_nat_fun_nat_o(R3,Z2),X3)
             => aa_nat_o(D3,Z2) ) )
       => ( aa_nat_o(D3,X2)
         => ( ! [X3: nat] :
                ( aa_nat_o(D3,X3)
               => ( ! [Z4: nat] :
                      ( aa_nat_o(aa_nat_fun_nat_o(R3,Z4),X3)
                     => aa_nat_o(P,Z4) )
                 => aa_nat_o(P,X3) ) )
           => aa_nat_o(P,X2) ) ) ) ) ).

% accp_subset_induct
tff(fact_1257_le__numeral__extra_I4_J,axiom,
    aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),one_one_Code_integer) ).

% le_numeral_extra(4)
tff(fact_1258_le__numeral__extra_I4_J,axiom,
    aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),one_one_rat) ).

% le_numeral_extra(4)
tff(fact_1259_le__numeral__extra_I4_J,axiom,
    aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),one_one_nat) ).

% le_numeral_extra(4)
tff(fact_1260_le__numeral__extra_I4_J,axiom,
    aa_int_o(aa_int_fun_int_o(ord_less_eq_int,one_one_int),one_one_int) ).

% le_numeral_extra(4)
tff(fact_1261_subrelI,axiom,
    ! [R2: set_Pr4329608150637261639at_nat,S: set_Pr4329608150637261639at_nat] :
      ( ! [X3: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] :
          ( member8757157785044589968at_nat(produc2922128104949294807at_nat(X3,Y4),R2)
         => member8757157785044589968at_nat(produc2922128104949294807at_nat(X3,Y4),S) )
     => ord_le1268244103169919719at_nat(R2,S) ) ).

% subrelI
tff(fact_1262_subrelI,axiom,
    ! [R2: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
      ( ! [X3: nat,Y4: nat] :
          ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),Y4),R2)
         => member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),Y4),S) )
     => aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(ord_le3146513528884898305at_nat,R2),S) ) ).

% subrelI
tff(fact_1263_subrelI,axiom,
    ! [R2: set_Pr3486312109254157132nteger,S: set_Pr3486312109254157132nteger] :
      ( ! [X3: fun_Pr5098669352780829690e_term,Y4: produc8923325533196201883nteger] :
          ( member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X3),Y4),R2)
         => member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X3),Y4),S) )
     => ord_le2932375828722672556nteger(R2,S) ) ).

% subrelI
tff(fact_1264_subrelI,axiom,
    ! [R2: set_Pr1312406793078187350et_nat,S: set_Pr1312406793078187350et_nat] :
      ( ! [X3: fun_Pr6460944699146269935_nat_o,Y4: produc3658429121746597890et_nat] :
          ( member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X3),Y4),R2)
         => member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X3),Y4),S) )
     => ord_le3919382008627836342et_nat(R2,S) ) ).

% subrelI
tff(fact_1265_subrelI,axiom,
    ! [R2: set_Pr4040394263813967220et_nat,S: set_Pr4040394263813967220et_nat] :
      ( ! [X3: fun_Pr6460944699146269935_nat_o,Y4: produc8799533983703829792et_nat] :
          ( member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X3),Y4),R2)
         => member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X3),Y4),S) )
     => ord_le5189643068899110356et_nat(R2,S) ) ).

% subrelI
tff(fact_1266_subrelI,axiom,
    ! [R2: set_Pr6700895561065273913nt_int,S: set_Pr6700895561065273913nt_int] :
      ( ! [X3: fun_Pr7763680713840462443e_term,Y4: product_prod_int_int] :
          ( member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X3),Y4),R2)
         => member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X3),Y4),S) )
     => ord_le3990897393281686169nt_int(R2,S) ) ).

% subrelI
tff(fact_1267_subrelI,axiom,
    ! [R2: set_Pr4166680992137330533nt_int,S: set_Pr4166680992137330533nt_int] :
      ( ! [X3: fun_in5730379987311621695e_term,Y4: product_prod_int_int] :
          ( member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X3),Y4),R2)
         => member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X3),Y4),S) )
     => ord_le3197784583289274309nt_int(R2,S) ) ).

% subrelI
tff(fact_1268_le__minus__iff,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,B))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,B),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A)) ) ).

% le_minus_iff
tff(fact_1269_le__minus__iff,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),aa_rat_rat(uminus_uminus_rat,B))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),aa_rat_rat(uminus_uminus_rat,A)) ) ).

% le_minus_iff
tff(fact_1270_le__minus__iff,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),aa_int_int(uminus_uminus_int,B))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,B),aa_int_int(uminus_uminus_int,A)) ) ).

% le_minus_iff
tff(fact_1271_minus__le__iff,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A)),B)
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,B)),A) ) ).

% minus_le_iff
tff(fact_1272_minus__le__iff,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(uminus_uminus_rat,A)),B)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(uminus_uminus_rat,B)),A) ) ).

% minus_le_iff
tff(fact_1273_minus__le__iff,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(uminus_uminus_int,A)),B)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(uminus_uminus_int,B)),A) ) ).

% minus_le_iff
tff(fact_1274_le__imp__neg__le,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),B)
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,B)),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A)) ) ).

% le_imp_neg_le
tff(fact_1275_le__imp__neg__le,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),B)
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(uminus_uminus_rat,B)),aa_rat_rat(uminus_uminus_rat,A)) ) ).

% le_imp_neg_le
tff(fact_1276_le__imp__neg__le,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),B)
     => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(uminus_uminus_int,B)),aa_int_int(uminus_uminus_int,A)) ) ).

% le_imp_neg_le
tff(fact_1277_exists__leI,axiom,
    ! [N2: nat,P: fun_nat_o] :
      ( ( ! [N6: nat] :
            ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N6),N2)
           => ~ aa_nat_o(P,N6) )
       => aa_nat_o(P,N2) )
     => ? [N3: nat] :
          ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N3),N2)
          & aa_nat_o(P,N3) ) ) ).

% exists_leI
tff(fact_1278_nat__le__iff__add,axiom,
    ! [M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
    <=> ? [K4: nat] : N2 = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),K4) ) ).

% nat_le_iff_add
tff(fact_1279_trans__le__add2,axiom,
    ! [I: nat,J: nat,M: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,I),J)
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,I),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),J)) ) ).

% trans_le_add2
tff(fact_1280_trans__le__add1,axiom,
    ! [I: nat,J: nat,M: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,I),J)
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,I),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),M)) ) ).

% trans_le_add1
tff(fact_1281_add__le__mono1,axiom,
    ! [I: nat,J: nat,K: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,I),J)
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),K)) ) ).

% add_le_mono1
tff(fact_1282_add__le__mono,axiom,
    ! [I: nat,J: nat,K: nat,L: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,I),J)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),L)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),L)) ) ) ).

% add_le_mono
tff(fact_1283_le__Suc__ex,axiom,
    ! [K: nat,L: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),L)
     => ? [N: nat] : L = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,K),N) ) ).

% le_Suc_ex
tff(fact_1284_add__leD2,axiom,
    ! [M: nat,K: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),K)),N2)
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),N2) ) ).

% add_leD2
tff(fact_1285_add__leD1,axiom,
    ! [M: nat,K: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),K)),N2)
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2) ) ).

% add_leD1
tff(fact_1286_le__add2,axiom,
    ! [N2: nat,M: nat] : aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)) ).

% le_add2
tff(fact_1287_le__add1,axiom,
    ! [N2: nat,M: nat] : aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),M)) ).

% le_add1
tff(fact_1288_add__leE,axiom,
    ! [M: nat,K: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),K)),N2)
     => ~ ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
         => ~ aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),N2) ) ) ).

% add_leE
tff(fact_1289_abs__le__D1,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A)),B)
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),B) ) ).

% abs_le_D1
tff(fact_1290_abs__le__D1,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(abs_abs_rat,A)),B)
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),B) ) ).

% abs_le_D1
tff(fact_1291_abs__le__D1,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(abs_abs_int,A)),B)
     => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),B) ) ).

% abs_le_D1
tff(fact_1292_abs__ge__self,axiom,
    ! [A: code_integer] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A)) ).

% abs_ge_self
tff(fact_1293_abs__ge__self,axiom,
    ! [A: rat] : aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),aa_rat_rat(abs_abs_rat,A)) ).

% abs_ge_self
tff(fact_1294_abs__ge__self,axiom,
    ! [A: int] : aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),aa_int_int(abs_abs_int,A)) ).

% abs_ge_self
tff(fact_1295_less__eq__option__None,axiom,
    ! [X2: option_num] : aa_option_num_o(aa_opt8674010985164783839_num_o(ord_le6622620407824499402on_num,none_num),X2) ).

% less_eq_option_None
tff(fact_1296_less__eq__option__None__is__None,axiom,
    ! [X2: option_num] :
      ( aa_option_num_o(aa_opt8674010985164783839_num_o(ord_le6622620407824499402on_num,X2),none_num)
     => ( X2 = none_num ) ) ).

% less_eq_option_None_is_None
tff(fact_1297_bind__eq__Some__conv,axiom,
    ! [F: option_num,G: fun_num_option_num,X2: num] :
      ( ( bind_num_num(F,G) = aa_num_option_num(some_num,X2) )
    <=> ? [Y3: num] :
          ( ( F = aa_num_option_num(some_num,Y3) )
          & ( aa_num_option_num(G,Y3) = aa_num_option_num(some_num,X2) ) ) ) ).

% bind_eq_Some_conv
tff(fact_1298_bind__eq__Some__conv,axiom,
    ! [F: option8956607266484857688it_nat,G: fun_Pr1661544312997278575on_num,X2: num] :
      ( ( bind_P4387644102537648098at_num(F,G) = aa_num_option_num(some_num,X2) )
    <=> ? [Y3: produc8664842809031399944it_nat] :
          ( ( F = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,Y3) )
          & ( aa_Pro8341797174369656752on_num(G,Y3) = aa_num_option_num(some_num,X2) ) ) ) ).

% bind_eq_Some_conv
tff(fact_1299_bind__eq__Some__conv,axiom,
    ! [F: option_num,G: fun_nu8356290101743979119it_nat,X2: produc8664842809031399944it_nat] :
      ( ( bind_n550516262659884002it_nat(F,G) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X2) )
    <=> ? [Y3: num] :
          ( ( F = aa_num_option_num(some_num,Y3) )
          & ( aa_num6494248640407584176it_nat(G,Y3) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X2) ) ) ) ).

% bind_eq_Some_conv
tff(fact_1300_bind__eq__Some__conv,axiom,
    ! [F: option8956607266484857688it_nat,G: fun_Pr7644814098969791837it_nat,X2: produc8664842809031399944it_nat] :
      ( ( bind_P7351952464966851536it_nat(F,G) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X2) )
    <=> ? [Y3: produc8664842809031399944it_nat] :
          ( ( F = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,Y3) )
          & ( aa_Pro8996696869555642526it_nat(G,Y3) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X2) ) ) ) ).

% bind_eq_Some_conv
tff(fact_1301_bind_Obind__lzero,axiom,
    ! [F: fun_Pr8118912048244921225it_nat] : bind_P1787608729393679550it_nat(none_P2587165478634041381it_nat,F) = none_P2587165478634041381it_nat ).

% bind.bind_lzero
tff(fact_1302_bind_Obind__lzero,axiom,
    ! [F: fun_Pr2994431579521131585on_num] : bind_P7816469540982926368at_num(none_P2587165478634041381it_nat,F) = none_num ).

% bind.bind_lzero
tff(fact_1303_bind_Obind__lzero,axiom,
    ! [F: fun_Pr245379829043246639it_nat] : bind_P3087804342168909838it_nat(none_P2587165478634041381it_nat,F) = none_P9117596204409417319it_nat ).

% bind.bind_lzero
tff(fact_1304_bind_Obind__lzero,axiom,
    ! [F: fun_nu5903705430729240393it_nat] : bind_n6186876254402743274it_nat(none_num,F) = none_P2587165478634041381it_nat ).

% bind.bind_lzero
tff(fact_1305_bind_Obind__lzero,axiom,
    ! [F: fun_num_option_num] : bind_num_num(none_num,F) = none_num ).

% bind.bind_lzero
tff(fact_1306_bind_Obind__lzero,axiom,
    ! [F: fun_nu8356290101743979119it_nat] : bind_n550516262659884002it_nat(none_num,F) = none_P9117596204409417319it_nat ).

% bind.bind_lzero
tff(fact_1307_bind_Obind__lzero,axiom,
    ! [F: fun_Pr7518090501403545819it_nat] : bind_P1106314856888375420it_nat(none_P9117596204409417319it_nat,F) = none_P2587165478634041381it_nat ).

% bind.bind_lzero
tff(fact_1308_bind_Obind__lzero,axiom,
    ! [F: fun_Pr1661544312997278575on_num] : bind_P4387644102537648098at_num(none_P9117596204409417319it_nat,F) = none_num ).

% bind.bind_lzero
tff(fact_1309_bind_Obind__lzero,axiom,
    ! [F: fun_Pr7644814098969791837it_nat] : bind_P7351952464966851536it_nat(none_P9117596204409417319it_nat,F) = none_P9117596204409417319it_nat ).

% bind.bind_lzero
tff(fact_1310_add__decreasing,axiom,
    ! [A: code_integer,C: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),zero_z3403309356797280102nteger)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,C),B)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),C)),B) ) ) ).

% add_decreasing
tff(fact_1311_add__decreasing,axiom,
    ! [A: rat,C: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),zero_zero_rat)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,C),B)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),C)),B) ) ) ).

% add_decreasing
tff(fact_1312_add__decreasing,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),zero_zero_nat)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,C),B)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C)),B) ) ) ).

% add_decreasing
tff(fact_1313_add__decreasing,axiom,
    ! [A: int,C: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),zero_zero_int)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,C),B)
       => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),C)),B) ) ) ).

% add_decreasing
tff(fact_1314_add__increasing,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),A)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,B),C)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,B),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),C)) ) ) ).

% add_increasing
tff(fact_1315_add__increasing,axiom,
    ! [A: rat,B: rat,C: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),A)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),C)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),C)) ) ) ).

% add_increasing
tff(fact_1316_add__increasing,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,B),C)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,B),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C)) ) ) ).

% add_increasing
tff(fact_1317_add__increasing,axiom,
    ! [A: int,B: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),A)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,B),C)
       => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,B),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),C)) ) ) ).

% add_increasing
tff(fact_1318_add__decreasing2,axiom,
    ! [C: code_integer,A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,C),zero_z3403309356797280102nteger)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),B)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),C)),B) ) ) ).

% add_decreasing2
tff(fact_1319_add__decreasing2,axiom,
    ! [C: rat,A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,C),zero_zero_rat)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),B)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),C)),B) ) ) ).

% add_decreasing2
tff(fact_1320_add__decreasing2,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,C),zero_zero_nat)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C)),B) ) ) ).

% add_decreasing2
tff(fact_1321_add__decreasing2,axiom,
    ! [C: int,A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,C),zero_zero_int)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),B)
       => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),C)),B) ) ) ).

% add_decreasing2
tff(fact_1322_add__increasing2,axiom,
    ! [C: code_integer,B: code_integer,A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),C)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,B),A)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,B),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),C)) ) ) ).

% add_increasing2
tff(fact_1323_add__increasing2,axiom,
    ! [C: rat,B: rat,A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),C)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),A)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),C)) ) ) ).

% add_increasing2
tff(fact_1324_add__increasing2,axiom,
    ! [C: nat,B: nat,A: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),C)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,B),A)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,B),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C)) ) ) ).

% add_increasing2
tff(fact_1325_add__increasing2,axiom,
    ! [C: int,B: int,A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),C)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,B),A)
       => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,B),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),C)) ) ) ).

% add_increasing2
tff(fact_1326_add__nonneg__nonneg,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),A)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),B)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)) ) ) ).

% add_nonneg_nonneg
tff(fact_1327_add__nonneg__nonneg,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),A)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),B)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)) ) ) ).

% add_nonneg_nonneg
tff(fact_1328_add__nonneg__nonneg,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),B)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)) ) ) ).

% add_nonneg_nonneg
tff(fact_1329_add__nonneg__nonneg,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),A)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),B)
       => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)) ) ) ).

% add_nonneg_nonneg
tff(fact_1330_add__nonpos__nonpos,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),zero_z3403309356797280102nteger)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,B),zero_z3403309356797280102nteger)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)),zero_z3403309356797280102nteger) ) ) ).

% add_nonpos_nonpos
tff(fact_1331_add__nonpos__nonpos,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),zero_zero_rat)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),zero_zero_rat)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),zero_zero_rat) ) ) ).

% add_nonpos_nonpos
tff(fact_1332_add__nonpos__nonpos,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),zero_zero_nat)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,B),zero_zero_nat)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),zero_zero_nat) ) ) ).

% add_nonpos_nonpos
tff(fact_1333_add__nonpos__nonpos,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),zero_zero_int)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,B),zero_zero_int)
       => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),zero_zero_int) ) ) ).

% add_nonpos_nonpos
tff(fact_1334_add__nonneg__eq__0__iff,axiom,
    ! [X2: code_integer,Y: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),X2)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),Y)
       => ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X2),Y) = zero_z3403309356797280102nteger )
        <=> ( ( X2 = zero_z3403309356797280102nteger )
            & ( Y = zero_z3403309356797280102nteger ) ) ) ) ) ).

% add_nonneg_eq_0_iff
tff(fact_1335_add__nonneg__eq__0__iff,axiom,
    ! [X2: rat,Y: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),X2)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),Y)
       => ( ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),Y) = zero_zero_rat )
        <=> ( ( X2 = zero_zero_rat )
            & ( Y = zero_zero_rat ) ) ) ) ) ).

% add_nonneg_eq_0_iff
tff(fact_1336_add__nonneg__eq__0__iff,axiom,
    ! [X2: nat,Y: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),X2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),Y)
       => ( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X2),Y) = zero_zero_nat )
        <=> ( ( X2 = zero_zero_nat )
            & ( Y = zero_zero_nat ) ) ) ) ) ).

% add_nonneg_eq_0_iff
tff(fact_1337_add__nonneg__eq__0__iff,axiom,
    ! [X2: int,Y: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),X2)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),Y)
       => ( ( aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),Y) = zero_zero_int )
        <=> ( ( X2 = zero_zero_int )
            & ( Y = zero_zero_int ) ) ) ) ) ).

% add_nonneg_eq_0_iff
tff(fact_1338_add__nonpos__eq__0__iff,axiom,
    ! [X2: code_integer,Y: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,X2),zero_z3403309356797280102nteger)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,Y),zero_z3403309356797280102nteger)
       => ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X2),Y) = zero_z3403309356797280102nteger )
        <=> ( ( X2 = zero_z3403309356797280102nteger )
            & ( Y = zero_z3403309356797280102nteger ) ) ) ) ) ).

% add_nonpos_eq_0_iff
tff(fact_1339_add__nonpos__eq__0__iff,axiom,
    ! [X2: rat,Y: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,X2),zero_zero_rat)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,Y),zero_zero_rat)
       => ( ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),Y) = zero_zero_rat )
        <=> ( ( X2 = zero_zero_rat )
            & ( Y = zero_zero_rat ) ) ) ) ) ).

% add_nonpos_eq_0_iff
tff(fact_1340_add__nonpos__eq__0__iff,axiom,
    ! [X2: nat,Y: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,X2),zero_zero_nat)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,Y),zero_zero_nat)
       => ( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X2),Y) = zero_zero_nat )
        <=> ( ( X2 = zero_zero_nat )
            & ( Y = zero_zero_nat ) ) ) ) ) ).

% add_nonpos_eq_0_iff
tff(fact_1341_add__nonpos__eq__0__iff,axiom,
    ! [X2: int,Y: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,X2),zero_zero_int)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,Y),zero_zero_int)
       => ( ( aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),Y) = zero_zero_int )
        <=> ( ( X2 = zero_zero_int )
            & ( Y = zero_zero_int ) ) ) ) ) ).

% add_nonpos_eq_0_iff
tff(fact_1342_not__one__le__zero,axiom,
    ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),zero_z3403309356797280102nteger) ).

% not_one_le_zero
tff(fact_1343_not__one__le__zero,axiom,
    ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),zero_zero_rat) ).

% not_one_le_zero
tff(fact_1344_not__one__le__zero,axiom,
    ~ aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),zero_zero_nat) ).

% not_one_le_zero
tff(fact_1345_not__one__le__zero,axiom,
    ~ aa_int_o(aa_int_fun_int_o(ord_less_eq_int,one_one_int),zero_zero_int) ).

% not_one_le_zero
tff(fact_1346_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
    aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),one_one_Code_integer) ).

% linordered_nonzero_semiring_class.zero_le_one
tff(fact_1347_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
    aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),one_one_rat) ).

% linordered_nonzero_semiring_class.zero_le_one
tff(fact_1348_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
    aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),one_one_nat) ).

% linordered_nonzero_semiring_class.zero_le_one
tff(fact_1349_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
    aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),one_one_int) ).

% linordered_nonzero_semiring_class.zero_le_one
tff(fact_1350_zero__less__one__class_Ozero__le__one,axiom,
    aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),one_one_Code_integer) ).

% zero_less_one_class.zero_le_one
tff(fact_1351_zero__less__one__class_Ozero__le__one,axiom,
    aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),one_one_rat) ).

% zero_less_one_class.zero_le_one
tff(fact_1352_zero__less__one__class_Ozero__le__one,axiom,
    aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),one_one_nat) ).

% zero_less_one_class.zero_le_one
tff(fact_1353_zero__less__one__class_Ozero__le__one,axiom,
    aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),one_one_int) ).

% zero_less_one_class.zero_le_one
tff(fact_1354_add__mono__thms__linordered__field_I4_J,axiom,
    ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
      ( ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,I),J)
        & aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,K),L) )
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,I),K)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,J),L)) ) ).

% add_mono_thms_linordered_field(4)
tff(fact_1355_add__mono__thms__linordered__field_I4_J,axiom,
    ! [I: rat,J: rat,K: rat,L: rat] :
      ( ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,I),J)
        & aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,K),L) )
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,I),K)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,J),L)) ) ).

% add_mono_thms_linordered_field(4)
tff(fact_1356_add__mono__thms__linordered__field_I4_J,axiom,
    ! [I: nat,J: nat,K: nat,L: nat] :
      ( ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,I),J)
        & aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,K),L) )
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),L)) ) ).

% add_mono_thms_linordered_field(4)
tff(fact_1357_add__mono__thms__linordered__field_I4_J,axiom,
    ! [I: int,J: int,K: int,L: int] :
      ( ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,I),J)
        & aa_int_o(aa_int_fun_int_o(ord_less_int,K),L) )
     => aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,I),K)),aa_int_int(aa_int_fun_int_int(plus_plus_int,J),L)) ) ).

% add_mono_thms_linordered_field(4)
tff(fact_1358_add__mono__thms__linordered__field_I3_J,axiom,
    ! [I: code_integer,J: code_integer,K: code_integer,L: code_integer] :
      ( ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,I),J)
        & aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,K),L) )
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,I),K)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,J),L)) ) ).

% add_mono_thms_linordered_field(3)
tff(fact_1359_add__mono__thms__linordered__field_I3_J,axiom,
    ! [I: rat,J: rat,K: rat,L: rat] :
      ( ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,I),J)
        & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,K),L) )
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,I),K)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,J),L)) ) ).

% add_mono_thms_linordered_field(3)
tff(fact_1360_add__mono__thms__linordered__field_I3_J,axiom,
    ! [I: nat,J: nat,K: nat,L: nat] :
      ( ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,I),J)
        & aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),L) )
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),L)) ) ).

% add_mono_thms_linordered_field(3)
tff(fact_1361_add__mono__thms__linordered__field_I3_J,axiom,
    ! [I: int,J: int,K: int,L: int] :
      ( ( aa_int_o(aa_int_fun_int_o(ord_less_int,I),J)
        & aa_int_o(aa_int_fun_int_o(ord_less_eq_int,K),L) )
     => aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,I),K)),aa_int_int(aa_int_fun_int_int(plus_plus_int,J),L)) ) ).

% add_mono_thms_linordered_field(3)
tff(fact_1362_add__le__less__mono,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),B)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,C),D2)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),C)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,B),D2)) ) ) ).

% add_le_less_mono
tff(fact_1363_add__le__less__mono,axiom,
    ! [A: rat,B: rat,C: rat,D2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),B)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,C),D2)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),C)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),D2)) ) ) ).

% add_le_less_mono
tff(fact_1364_add__le__less__mono,axiom,
    ! [A: nat,B: nat,C: nat,D2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,C),D2)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),D2)) ) ) ).

% add_le_less_mono
tff(fact_1365_add__le__less__mono,axiom,
    ! [A: int,B: int,C: int,D2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),B)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,C),D2)
       => aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),C)),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),D2)) ) ) ).

% add_le_less_mono
tff(fact_1366_add__less__le__mono,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),B)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,C),D2)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),C)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,B),D2)) ) ) ).

% add_less_le_mono
tff(fact_1367_add__less__le__mono,axiom,
    ! [A: rat,B: rat,C: rat,D2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,C),D2)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),C)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),D2)) ) ) ).

% add_less_le_mono
tff(fact_1368_add__less__le__mono,axiom,
    ! [A: nat,B: nat,C: nat,D2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),B)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,C),D2)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),D2)) ) ) ).

% add_less_le_mono
tff(fact_1369_add__less__le__mono,axiom,
    ! [A: int,B: int,C: int,D2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,A),B)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,C),D2)
       => aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),C)),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),D2)) ) ) ).

% add_less_le_mono
tff(fact_1370_le__minus__one__simps_I2_J,axiom,
    aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),one_one_Code_integer) ).

% le_minus_one_simps(2)
tff(fact_1371_le__minus__one__simps_I2_J,axiom,
    aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),one_one_rat) ).

% le_minus_one_simps(2)
tff(fact_1372_le__minus__one__simps_I2_J,axiom,
    aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(uminus_uminus_int,one_one_int)),one_one_int) ).

% le_minus_one_simps(2)
tff(fact_1373_le__minus__one__simps_I4_J,axiom,
    ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) ).

% le_minus_one_simps(4)
tff(fact_1374_le__minus__one__simps_I4_J,axiom,
    ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),aa_rat_rat(uminus_uminus_rat,one_one_rat)) ).

% le_minus_one_simps(4)
tff(fact_1375_le__minus__one__simps_I4_J,axiom,
    ~ aa_int_o(aa_int_fun_int_o(ord_less_eq_int,one_one_int),aa_int_int(uminus_uminus_int,one_one_int)) ).

% le_minus_one_simps(4)
tff(fact_1376_abs__ge__zero,axiom,
    ! [A: code_integer] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A)) ).

% abs_ge_zero
tff(fact_1377_abs__ge__zero,axiom,
    ! [A: rat] : aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),aa_rat_rat(abs_abs_rat,A)) ).

% abs_ge_zero
tff(fact_1378_abs__ge__zero,axiom,
    ! [A: int] : aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),aa_int_int(abs_abs_int,A)) ).

% abs_ge_zero
tff(fact_1379_abs__triangle__ineq,axiom,
    ! [A: code_integer,B: code_integer] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A)),aa_Cod1783974652533396728nteger(abs_abs_Code_integer,B))) ).

% abs_triangle_ineq
tff(fact_1380_abs__triangle__ineq,axiom,
    ! [A: rat,B: rat] : aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(abs_abs_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B))),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(abs_abs_rat,A)),aa_rat_rat(abs_abs_rat,B))) ).

% abs_triangle_ineq
tff(fact_1381_abs__triangle__ineq,axiom,
    ! [A: int,B: int] : aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(abs_abs_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B))),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(abs_abs_int,A)),aa_int_int(abs_abs_int,B))) ).

% abs_triangle_ineq
tff(fact_1382_abs__leI,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),B)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A)),B)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A)),B) ) ) ).

% abs_leI
tff(fact_1383_abs__leI,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),B)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(uminus_uminus_rat,A)),B)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(abs_abs_rat,A)),B) ) ) ).

% abs_leI
tff(fact_1384_abs__leI,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),B)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(uminus_uminus_int,A)),B)
       => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(abs_abs_int,A)),B) ) ) ).

% abs_leI
tff(fact_1385_abs__le__D2,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A)),B)
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A)),B) ) ).

% abs_le_D2
tff(fact_1386_abs__le__D2,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(abs_abs_rat,A)),B)
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(uminus_uminus_rat,A)),B) ) ).

% abs_le_D2
tff(fact_1387_abs__le__D2,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(abs_abs_int,A)),B)
     => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(uminus_uminus_int,A)),B) ) ).

% abs_le_D2
tff(fact_1388_abs__le__iff,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A)),B)
    <=> ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),B)
        & aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A)),B) ) ) ).

% abs_le_iff
tff(fact_1389_abs__le__iff,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(abs_abs_rat,A)),B)
    <=> ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),B)
        & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(uminus_uminus_rat,A)),B) ) ) ).

% abs_le_iff
tff(fact_1390_abs__le__iff,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(abs_abs_int,A)),B)
    <=> ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),B)
        & aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(uminus_uminus_int,A)),B) ) ) ).

% abs_le_iff
tff(fact_1391_abs__ge__minus__self,axiom,
    ! [A: code_integer] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A)),aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A)) ).

% abs_ge_minus_self
tff(fact_1392_abs__ge__minus__self,axiom,
    ! [A: rat] : aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(uminus_uminus_rat,A)),aa_rat_rat(abs_abs_rat,A)) ).

% abs_ge_minus_self
tff(fact_1393_abs__ge__minus__self,axiom,
    ! [A: int] : aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(uminus_uminus_int,A)),aa_int_int(abs_abs_int,A)) ).

% abs_ge_minus_self
tff(fact_1394_mono__nat__linear__lb,axiom,
    ! [F: fun_nat_nat,M: nat,K: nat] :
      ( ! [M4: nat,N: nat] :
          ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M4),N)
         => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(F,M4)),aa_nat_nat(F,N)) )
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(F,M)),K)),aa_nat_nat(F,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),K))) ) ).

% mono_nat_linear_lb
tff(fact_1395_nat__geq__1__eq__neqz,axiom,
    ! [X2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),X2)
    <=> ( X2 != zero_zero_nat ) ) ).

% nat_geq_1_eq_neqz
tff(fact_1396_bind__split__asm,axiom,
    ! [P: fun_op4751157287140997969_nat_o,M: option3216581401566546698it_nat,F: fun_Pr8118912048244921225it_nat] :
      ( aa_opt4809530629565672394_nat_o(P,bind_P1787608729393679550it_nat(M,F))
    <=> ~ ( ( ( M = none_P2587165478634041381it_nat )
            & ~ aa_opt4809530629565672394_nat_o(P,none_P2587165478634041381it_nat) )
          | ? [X4: produc6714399278180371524it_nat] :
              ( ( M = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,X4) )
              & ~ aa_opt4809530629565672394_nat_o(P,aa_Pro1291033051762305794it_nat(F,X4)) ) ) ) ).

% bind_split_asm
tff(fact_1397_bind__split__asm,axiom,
    ! [P: fun_option_num_o,M: option3216581401566546698it_nat,F: fun_Pr2994431579521131585on_num] :
      ( aa_option_num_o(P,bind_P7816469540982926368at_num(M,F))
    <=> ~ ( ( ( M = none_P2587165478634041381it_nat )
            & ~ aa_option_num_o(P,none_num) )
          | ? [X4: produc6714399278180371524it_nat] :
              ( ( M = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,X4) )
              & ~ aa_option_num_o(P,aa_Pro976347780353151090on_num(F,X4)) ) ) ) ).

% bind_split_asm
tff(fact_1398_bind__split__asm,axiom,
    ! [P: fun_op479301348043730329_nat_o,M: option3216581401566546698it_nat,F: fun_Pr245379829043246639it_nat] :
      ( aa_opt8360315729766332930_nat_o(P,bind_P3087804342168909838it_nat(M,F))
    <=> ~ ( ( ( M = none_P2587165478634041381it_nat )
            & ~ aa_opt8360315729766332930_nat_o(P,none_P9117596204409417319it_nat) )
          | ? [X4: produc6714399278180371524it_nat] :
              ( ( M = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,X4) )
              & ~ aa_opt8360315729766332930_nat_o(P,aa_Pro8990453184240486752it_nat(F,X4)) ) ) ) ).

% bind_split_asm
tff(fact_1399_bind__split__asm,axiom,
    ! [P: fun_op4751157287140997969_nat_o,M: option_num,F: fun_nu5903705430729240393it_nat] :
      ( aa_opt4809530629565672394_nat_o(P,bind_n6186876254402743274it_nat(M,F))
    <=> ~ ( ( ( M = none_num )
            & ~ aa_opt4809530629565672394_nat_o(P,none_P2587165478634041381it_nat) )
          | ? [X4: num] :
              ( ( M = aa_num_option_num(some_num,X4) )
              & ~ aa_opt4809530629565672394_nat_o(P,aa_num7625411027033842354it_nat(F,X4)) ) ) ) ).

% bind_split_asm
tff(fact_1400_bind__split__asm,axiom,
    ! [P: fun_option_num_o,M: option_num,F: fun_num_option_num] :
      ( aa_option_num_o(P,bind_num_num(M,F))
    <=> ~ ( ( ( M = none_num )
            & ~ aa_option_num_o(P,none_num) )
          | ? [X4: num] :
              ( ( M = aa_num_option_num(some_num,X4) )
              & ~ aa_option_num_o(P,aa_num_option_num(F,X4)) ) ) ) ).

% bind_split_asm
tff(fact_1401_bind__split__asm,axiom,
    ! [P: fun_op479301348043730329_nat_o,M: option_num,F: fun_nu8356290101743979119it_nat] :
      ( aa_opt8360315729766332930_nat_o(P,bind_n550516262659884002it_nat(M,F))
    <=> ~ ( ( ( M = none_num )
            & ~ aa_opt8360315729766332930_nat_o(P,none_P9117596204409417319it_nat) )
          | ? [X4: num] :
              ( ( M = aa_num_option_num(some_num,X4) )
              & ~ aa_opt8360315729766332930_nat_o(P,aa_num6494248640407584176it_nat(F,X4)) ) ) ) ).

% bind_split_asm
tff(fact_1402_bind__split__asm,axiom,
    ! [P: fun_op4751157287140997969_nat_o,M: option8956607266484857688it_nat,F: fun_Pr7518090501403545819it_nat] :
      ( aa_opt4809530629565672394_nat_o(P,bind_P1106314856888375420it_nat(M,F))
    <=> ~ ( ( ( M = none_P9117596204409417319it_nat )
            & ~ aa_opt4809530629565672394_nat_o(P,none_P2587165478634041381it_nat) )
          | ? [X4: produc8664842809031399944it_nat] :
              ( ( M = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X4) )
              & ~ aa_opt4809530629565672394_nat_o(P,aa_Pro875131464217814084it_nat(F,X4)) ) ) ) ).

% bind_split_asm
tff(fact_1403_bind__split__asm,axiom,
    ! [P: fun_option_num_o,M: option8956607266484857688it_nat,F: fun_Pr1661544312997278575on_num] :
      ( aa_option_num_o(P,bind_P4387644102537648098at_num(M,F))
    <=> ~ ( ( ( M = none_P9117596204409417319it_nat )
            & ~ aa_option_num_o(P,none_num) )
          | ? [X4: produc8664842809031399944it_nat] :
              ( ( M = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X4) )
              & ~ aa_option_num_o(P,aa_Pro8341797174369656752on_num(F,X4)) ) ) ) ).

% bind_split_asm
tff(fact_1404_bind__split__asm,axiom,
    ! [P: fun_op479301348043730329_nat_o,M: option8956607266484857688it_nat,F: fun_Pr7644814098969791837it_nat] :
      ( aa_opt8360315729766332930_nat_o(P,bind_P7351952464966851536it_nat(M,F))
    <=> ~ ( ( ( M = none_P9117596204409417319it_nat )
            & ~ aa_opt8360315729766332930_nat_o(P,none_P9117596204409417319it_nat) )
          | ? [X4: produc8664842809031399944it_nat] :
              ( ( M = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X4) )
              & ~ aa_opt8360315729766332930_nat_o(P,aa_Pro8996696869555642526it_nat(F,X4)) ) ) ) ).

% bind_split_asm
tff(fact_1405_bind__split,axiom,
    ! [P: fun_op4751157287140997969_nat_o,M: option3216581401566546698it_nat,F: fun_Pr8118912048244921225it_nat] :
      ( aa_opt4809530629565672394_nat_o(P,bind_P1787608729393679550it_nat(M,F))
    <=> ( ( ( M = none_P2587165478634041381it_nat )
         => aa_opt4809530629565672394_nat_o(P,none_P2587165478634041381it_nat) )
        & ! [V3: produc6714399278180371524it_nat] :
            ( ( M = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,V3) )
           => aa_opt4809530629565672394_nat_o(P,aa_Pro1291033051762305794it_nat(F,V3)) ) ) ) ).

% bind_split
tff(fact_1406_bind__split,axiom,
    ! [P: fun_option_num_o,M: option3216581401566546698it_nat,F: fun_Pr2994431579521131585on_num] :
      ( aa_option_num_o(P,bind_P7816469540982926368at_num(M,F))
    <=> ( ( ( M = none_P2587165478634041381it_nat )
         => aa_option_num_o(P,none_num) )
        & ! [V3: produc6714399278180371524it_nat] :
            ( ( M = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,V3) )
           => aa_option_num_o(P,aa_Pro976347780353151090on_num(F,V3)) ) ) ) ).

% bind_split
tff(fact_1407_bind__split,axiom,
    ! [P: fun_op479301348043730329_nat_o,M: option3216581401566546698it_nat,F: fun_Pr245379829043246639it_nat] :
      ( aa_opt8360315729766332930_nat_o(P,bind_P3087804342168909838it_nat(M,F))
    <=> ( ( ( M = none_P2587165478634041381it_nat )
         => aa_opt8360315729766332930_nat_o(P,none_P9117596204409417319it_nat) )
        & ! [V3: produc6714399278180371524it_nat] :
            ( ( M = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,V3) )
           => aa_opt8360315729766332930_nat_o(P,aa_Pro8990453184240486752it_nat(F,V3)) ) ) ) ).

% bind_split
tff(fact_1408_bind__split,axiom,
    ! [P: fun_op4751157287140997969_nat_o,M: option_num,F: fun_nu5903705430729240393it_nat] :
      ( aa_opt4809530629565672394_nat_o(P,bind_n6186876254402743274it_nat(M,F))
    <=> ( ( ( M = none_num )
         => aa_opt4809530629565672394_nat_o(P,none_P2587165478634041381it_nat) )
        & ! [V3: num] :
            ( ( M = aa_num_option_num(some_num,V3) )
           => aa_opt4809530629565672394_nat_o(P,aa_num7625411027033842354it_nat(F,V3)) ) ) ) ).

% bind_split
tff(fact_1409_bind__split,axiom,
    ! [P: fun_option_num_o,M: option_num,F: fun_num_option_num] :
      ( aa_option_num_o(P,bind_num_num(M,F))
    <=> ( ( ( M = none_num )
         => aa_option_num_o(P,none_num) )
        & ! [V3: num] :
            ( ( M = aa_num_option_num(some_num,V3) )
           => aa_option_num_o(P,aa_num_option_num(F,V3)) ) ) ) ).

% bind_split
tff(fact_1410_bind__split,axiom,
    ! [P: fun_op479301348043730329_nat_o,M: option_num,F: fun_nu8356290101743979119it_nat] :
      ( aa_opt8360315729766332930_nat_o(P,bind_n550516262659884002it_nat(M,F))
    <=> ( ( ( M = none_num )
         => aa_opt8360315729766332930_nat_o(P,none_P9117596204409417319it_nat) )
        & ! [V3: num] :
            ( ( M = aa_num_option_num(some_num,V3) )
           => aa_opt8360315729766332930_nat_o(P,aa_num6494248640407584176it_nat(F,V3)) ) ) ) ).

% bind_split
tff(fact_1411_bind__split,axiom,
    ! [P: fun_op4751157287140997969_nat_o,M: option8956607266484857688it_nat,F: fun_Pr7518090501403545819it_nat] :
      ( aa_opt4809530629565672394_nat_o(P,bind_P1106314856888375420it_nat(M,F))
    <=> ( ( ( M = none_P9117596204409417319it_nat )
         => aa_opt4809530629565672394_nat_o(P,none_P2587165478634041381it_nat) )
        & ! [V3: produc8664842809031399944it_nat] :
            ( ( M = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,V3) )
           => aa_opt4809530629565672394_nat_o(P,aa_Pro875131464217814084it_nat(F,V3)) ) ) ) ).

% bind_split
tff(fact_1412_bind__split,axiom,
    ! [P: fun_option_num_o,M: option8956607266484857688it_nat,F: fun_Pr1661544312997278575on_num] :
      ( aa_option_num_o(P,bind_P4387644102537648098at_num(M,F))
    <=> ( ( ( M = none_P9117596204409417319it_nat )
         => aa_option_num_o(P,none_num) )
        & ! [V3: produc8664842809031399944it_nat] :
            ( ( M = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,V3) )
           => aa_option_num_o(P,aa_Pro8341797174369656752on_num(F,V3)) ) ) ) ).

% bind_split
tff(fact_1413_bind__split,axiom,
    ! [P: fun_op479301348043730329_nat_o,M: option8956607266484857688it_nat,F: fun_Pr7644814098969791837it_nat] :
      ( aa_opt8360315729766332930_nat_o(P,bind_P7351952464966851536it_nat(M,F))
    <=> ( ( ( M = none_P9117596204409417319it_nat )
         => aa_opt8360315729766332930_nat_o(P,none_P9117596204409417319it_nat) )
        & ! [V3: produc8664842809031399944it_nat] :
            ( ( M = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,V3) )
           => aa_opt8360315729766332930_nat_o(P,aa_Pro8996696869555642526it_nat(F,V3)) ) ) ) ).

% bind_split
tff(fact_1414_mlex__leq,axiom,
    ! [F: fun_se4097146774670233028at_nat,X2: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,R3: set_Pr4329608150637261639at_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_set4749074711808745205at_nat(F,X2)),aa_set4749074711808745205at_nat(F,Y))
     => ( member8757157785044589968at_nat(produc2922128104949294807at_nat(X2,Y),R3)
       => member8757157785044589968at_nat(produc2922128104949294807at_nat(X2,Y),mlex_p3502713205431853936at_nat(F,R3)) ) ) ).

% mlex_leq
tff(fact_1415_mlex__leq,axiom,
    ! [F: fun_nat_nat,X2: nat,Y: nat,R3: set_Pr1261947904930325089at_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(F,X2)),aa_nat_nat(F,Y))
     => ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X2),Y),R3)
       => member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X2),Y),aa_set8868280134176360700at_nat(mlex_prod_nat(F),R3)) ) ) ).

% mlex_leq
tff(fact_1416_bind__eq__None__conv,axiom,
    ! [A: option3216581401566546698it_nat,F: fun_Pr8118912048244921225it_nat] :
      ( ( bind_P1787608729393679550it_nat(A,F) = none_P2587165478634041381it_nat )
    <=> ( ( A = none_P2587165478634041381it_nat )
        | ( aa_Pro1291033051762305794it_nat(F,aa_opt2040853179424174198it_nat(the_Pr5856008525237892824it_nat,A)) = none_P2587165478634041381it_nat ) ) ) ).

% bind_eq_None_conv
tff(fact_1417_bind__eq__None__conv,axiom,
    ! [A: option_num,F: fun_nu5903705430729240393it_nat] :
      ( ( bind_n6186876254402743274it_nat(A,F) = none_P2587165478634041381it_nat )
    <=> ( ( A = none_num )
        | ( aa_num7625411027033842354it_nat(F,aa_option_num_num(the_num,A)) = none_P2587165478634041381it_nat ) ) ) ).

% bind_eq_None_conv
tff(fact_1418_bind__eq__None__conv,axiom,
    ! [A: option8956607266484857688it_nat,F: fun_Pr7518090501403545819it_nat] :
      ( ( bind_P1106314856888375420it_nat(A,F) = none_P2587165478634041381it_nat )
    <=> ( ( A = none_P9117596204409417319it_nat )
        | ( aa_Pro875131464217814084it_nat(F,aa_opt6779208767223616030it_nat(the_Pr7776125533777466484it_nat,A)) = none_P2587165478634041381it_nat ) ) ) ).

% bind_eq_None_conv
tff(fact_1419_bind__eq__None__conv,axiom,
    ! [A: option3216581401566546698it_nat,F: fun_Pr2994431579521131585on_num] :
      ( ( bind_P7816469540982926368at_num(A,F) = none_num )
    <=> ( ( A = none_P2587165478634041381it_nat )
        | ( aa_Pro976347780353151090on_num(F,aa_opt2040853179424174198it_nat(the_Pr5856008525237892824it_nat,A)) = none_num ) ) ) ).

% bind_eq_None_conv
tff(fact_1420_bind__eq__None__conv,axiom,
    ! [A: option_num,F: fun_num_option_num] :
      ( ( bind_num_num(A,F) = none_num )
    <=> ( ( A = none_num )
        | ( aa_num_option_num(F,aa_option_num_num(the_num,A)) = none_num ) ) ) ).

% bind_eq_None_conv
tff(fact_1421_bind__eq__None__conv,axiom,
    ! [A: option8956607266484857688it_nat,F: fun_Pr1661544312997278575on_num] :
      ( ( bind_P4387644102537648098at_num(A,F) = none_num )
    <=> ( ( A = none_P9117596204409417319it_nat )
        | ( aa_Pro8341797174369656752on_num(F,aa_opt6779208767223616030it_nat(the_Pr7776125533777466484it_nat,A)) = none_num ) ) ) ).

% bind_eq_None_conv
tff(fact_1422_bind__eq__None__conv,axiom,
    ! [A: option3216581401566546698it_nat,F: fun_Pr245379829043246639it_nat] :
      ( ( bind_P3087804342168909838it_nat(A,F) = none_P9117596204409417319it_nat )
    <=> ( ( A = none_P2587165478634041381it_nat )
        | ( aa_Pro8990453184240486752it_nat(F,aa_opt2040853179424174198it_nat(the_Pr5856008525237892824it_nat,A)) = none_P9117596204409417319it_nat ) ) ) ).

% bind_eq_None_conv
tff(fact_1423_bind__eq__None__conv,axiom,
    ! [A: option_num,F: fun_nu8356290101743979119it_nat] :
      ( ( bind_n550516262659884002it_nat(A,F) = none_P9117596204409417319it_nat )
    <=> ( ( A = none_num )
        | ( aa_num6494248640407584176it_nat(F,aa_option_num_num(the_num,A)) = none_P9117596204409417319it_nat ) ) ) ).

% bind_eq_None_conv
tff(fact_1424_bind__eq__None__conv,axiom,
    ! [A: option8956607266484857688it_nat,F: fun_Pr7644814098969791837it_nat] :
      ( ( bind_P7351952464966851536it_nat(A,F) = none_P9117596204409417319it_nat )
    <=> ( ( A = none_P9117596204409417319it_nat )
        | ( aa_Pro8996696869555642526it_nat(F,aa_opt6779208767223616030it_nat(the_Pr7776125533777466484it_nat,A)) = none_P9117596204409417319it_nat ) ) ) ).

% bind_eq_None_conv
tff(fact_1425_add__neg__nonpos,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),zero_z3403309356797280102nteger)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,B),zero_z3403309356797280102nteger)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)),zero_z3403309356797280102nteger) ) ) ).

% add_neg_nonpos
tff(fact_1426_add__neg__nonpos,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),zero_zero_rat)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),zero_zero_rat)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),zero_zero_rat) ) ) ).

% add_neg_nonpos
tff(fact_1427_add__neg__nonpos,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),zero_zero_nat)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,B),zero_zero_nat)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),zero_zero_nat) ) ) ).

% add_neg_nonpos
tff(fact_1428_add__neg__nonpos,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,A),zero_zero_int)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,B),zero_zero_int)
       => aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),zero_zero_int) ) ) ).

% add_neg_nonpos
tff(fact_1429_add__nonneg__pos,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),A)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),B)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)) ) ) ).

% add_nonneg_pos
tff(fact_1430_add__nonneg__pos,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),A)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),B)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)) ) ) ).

% add_nonneg_pos
tff(fact_1431_add__nonneg__pos,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),B)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)) ) ) ).

% add_nonneg_pos
tff(fact_1432_add__nonneg__pos,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),A)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),B)
       => aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)) ) ) ).

% add_nonneg_pos
tff(fact_1433_add__nonpos__neg,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),zero_z3403309356797280102nteger)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,B),zero_z3403309356797280102nteger)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)),zero_z3403309356797280102nteger) ) ) ).

% add_nonpos_neg
tff(fact_1434_add__nonpos__neg,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),zero_zero_rat)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,B),zero_zero_rat)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),zero_zero_rat) ) ) ).

% add_nonpos_neg
tff(fact_1435_add__nonpos__neg,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),zero_zero_nat)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,B),zero_zero_nat)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),zero_zero_nat) ) ) ).

% add_nonpos_neg
tff(fact_1436_add__nonpos__neg,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),zero_zero_int)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,B),zero_zero_int)
       => aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),zero_zero_int) ) ) ).

% add_nonpos_neg
tff(fact_1437_add__pos__nonneg,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),A)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),B)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)) ) ) ).

% add_pos_nonneg
tff(fact_1438_add__pos__nonneg,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),A)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),B)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)) ) ) ).

% add_pos_nonneg
tff(fact_1439_add__pos__nonneg,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),B)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)) ) ) ).

% add_pos_nonneg
tff(fact_1440_add__pos__nonneg,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),A)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),B)
       => aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)) ) ) ).

% add_pos_nonneg
tff(fact_1441_add__strict__increasing,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),A)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,B),C)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,B),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),C)) ) ) ).

% add_strict_increasing
tff(fact_1442_add__strict__increasing,axiom,
    ! [A: rat,B: rat,C: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),A)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),C)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,B),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),C)) ) ) ).

% add_strict_increasing
tff(fact_1443_add__strict__increasing,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,B),C)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,B),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C)) ) ) ).

% add_strict_increasing
tff(fact_1444_add__strict__increasing,axiom,
    ! [A: int,B: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),A)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,B),C)
       => aa_int_o(aa_int_fun_int_o(ord_less_int,B),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),C)) ) ) ).

% add_strict_increasing
tff(fact_1445_add__strict__increasing2,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),A)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,B),C)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,B),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),C)) ) ) ).

% add_strict_increasing2
tff(fact_1446_add__strict__increasing2,axiom,
    ! [A: rat,B: rat,C: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),A)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,B),C)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,B),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),C)) ) ) ).

% add_strict_increasing2
tff(fact_1447_add__strict__increasing2,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,B),C)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,B),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C)) ) ) ).

% add_strict_increasing2
tff(fact_1448_add__strict__increasing2,axiom,
    ! [A: int,B: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),A)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,B),C)
       => aa_int_o(aa_int_fun_int_o(ord_less_int,B),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),C)) ) ) ).

% add_strict_increasing2
tff(fact_1449_discrete,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),B)
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),one_one_Code_integer)),B) ) ).

% discrete
tff(fact_1450_discrete,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),B)
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),one_one_nat)),B) ) ).

% discrete
tff(fact_1451_discrete,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,A),B)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),one_one_int)),B) ) ).

% discrete
tff(fact_1452_le__minus__one__simps_I1_J,axiom,
    aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),zero_z3403309356797280102nteger) ).

% le_minus_one_simps(1)
tff(fact_1453_le__minus__one__simps_I1_J,axiom,
    aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),zero_zero_rat) ).

% le_minus_one_simps(1)
tff(fact_1454_le__minus__one__simps_I1_J,axiom,
    aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(uminus_uminus_int,one_one_int)),zero_zero_int) ).

% le_minus_one_simps(1)
tff(fact_1455_le__minus__one__simps_I3_J,axiom,
    ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) ).

% le_minus_one_simps(3)
tff(fact_1456_le__minus__one__simps_I3_J,axiom,
    ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),aa_rat_rat(uminus_uminus_rat,one_one_rat)) ).

% le_minus_one_simps(3)
tff(fact_1457_le__minus__one__simps_I3_J,axiom,
    ~ aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),aa_int_int(uminus_uminus_int,one_one_int)) ).

% le_minus_one_simps(3)
tff(fact_1458_dense__eq0__I,axiom,
    ! [X2: rat] :
      ( ! [E2: rat] :
          ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),E2)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(abs_abs_rat,X2)),E2) )
     => ( X2 = zero_zero_rat ) ) ).

% dense_eq0_I
tff(fact_1459_abs__minus__le__zero,axiom,
    ! [A: code_integer] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A))),zero_z3403309356797280102nteger) ).

% abs_minus_le_zero
tff(fact_1460_abs__minus__le__zero,axiom,
    ! [A: rat] : aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(uminus_uminus_rat,aa_rat_rat(abs_abs_rat,A))),zero_zero_rat) ).

% abs_minus_le_zero
tff(fact_1461_abs__minus__le__zero,axiom,
    ! [A: int] : aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(uminus_uminus_int,aa_int_int(abs_abs_int,A))),zero_zero_int) ).

% abs_minus_le_zero
tff(fact_1462_success__changeI,axiom,
    ! [F: fun_Pr2191293291710260995t_unit,R2: ref_Product_unit,Ha: heap_e7401611519738050253t_unit] : aa_hea7994211679605476167unit_o(heap_T584514906347983379t_unit(ref_ch7259622376331601608t_unit(F,R2)),Ha) ).

% success_changeI
tff(fact_1463_success__changeI,axiom,
    ! [F: fun_array_a_array_a,R2: ref_array_a,Ha: heap_e7401611519738050253t_unit] : aa_hea7994211679605476167unit_o(heap_T6932021131025641745rray_a(ref_change_array_a(F,R2)),Ha) ).

% success_changeI
tff(fact_1464_semiring__norm_I6_J,axiom,
    ! [M: num,N2: num] : aa_num_num(aa_num_fun_num_num(plus_plus_num,aa_num_num(bit0,M)),aa_num_num(bit0,N2)) = aa_num_num(bit0,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2)) ).

% semiring_norm(6)
tff(fact_1465_field__le__epsilon,axiom,
    ! [X2: rat,Y: rat] :
      ( ! [E2: rat] :
          ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),E2)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,X2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,Y),E2)) )
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,X2),Y) ) ).

% field_le_epsilon
tff(fact_1466_convex__bound__lt,axiom,
    ! [X2: code_integer,A: code_integer,Y: code_integer,U: code_integer,V: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,X2),A)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,Y),A)
       => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),U)
         => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),V)
           => ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,U),V) = one_one_Code_integer )
             => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,U),X2)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,V),Y))),A) ) ) ) ) ) ).

% convex_bound_lt
tff(fact_1467_convex__bound__lt,axiom,
    ! [X2: rat,A: rat,Y: rat,U: rat,V: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,X2),A)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,Y),A)
       => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),U)
         => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),V)
           => ( ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,U),V) = one_one_rat )
             => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,U),X2)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,V),Y))),A) ) ) ) ) ) ).

% convex_bound_lt
tff(fact_1468_convex__bound__lt,axiom,
    ! [X2: int,A: int,Y: int,U: int,V: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,X2),A)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,Y),A)
       => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),U)
         => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),V)
           => ( ( aa_int_int(aa_int_fun_int_int(plus_plus_int,U),V) = one_one_int )
             => aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,U),X2)),aa_int_int(aa_int_fun_int_int(times_times_int,V),Y))),A) ) ) ) ) ) ).

% convex_bound_lt
tff(fact_1469_Ints__eq__abs__less1,axiom,
    ! [X2: code_integer,Y: code_integer] :
      ( member_Code_integer(X2,ring_11222124179247155820nteger)
     => ( member_Code_integer(Y,ring_11222124179247155820nteger)
       => ( ( X2 = Y )
        <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,X2),Y))),one_one_Code_integer) ) ) ) ).

% Ints_eq_abs_less1
tff(fact_1470_Ints__eq__abs__less1,axiom,
    ! [X2: rat,Y: rat] :
      ( member_rat(X2,ring_1_Ints_rat)
     => ( member_rat(Y,ring_1_Ints_rat)
       => ( ( X2 = Y )
        <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(abs_abs_rat,aa_rat_rat(minus_minus_rat(X2),Y))),one_one_rat) ) ) ) ).

% Ints_eq_abs_less1
tff(fact_1471_Ints__eq__abs__less1,axiom,
    ! [X2: int,Y: int] :
      ( member_int(X2,ring_1_Ints_int)
     => ( member_int(Y,ring_1_Ints_int)
       => ( ( X2 = Y )
        <=> aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(abs_abs_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,X2),Y))),one_one_int) ) ) ) ).

% Ints_eq_abs_less1
tff(fact_1472_nat0__intermed__int__val,axiom,
    ! [N2: nat,F: fun_nat_int,K: int] :
      ( ! [I2: nat] :
          ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,I2),N2)
         => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(abs_abs_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(F,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I2),one_one_nat))),aa_nat_int(F,I2)))),one_one_int) )
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_nat_int(F,zero_zero_nat)),K)
       => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,K),aa_nat_int(F,N2))
         => ? [I2: nat] :
              ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,I2),N2)
              & ( aa_nat_int(F,I2) = K ) ) ) ) ) ).

% nat0_intermed_int_val
tff(fact_1473_diff__diff__left,axiom,
    ! [I: nat,J: nat,K: nat] : aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,I),J)),K) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,I),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),K)) ).

% diff_diff_left
tff(fact_1474_nat__1__eq__mult__iff,axiom,
    ! [M: nat,N2: nat] :
      ( ( one_one_nat = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,M),N2) )
    <=> ( ( M = one_one_nat )
        & ( N2 = one_one_nat ) ) ) ).

% nat_1_eq_mult_iff
tff(fact_1475_nat__mult__eq__1__iff,axiom,
    ! [M: nat,N2: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,M),N2) = one_one_nat )
    <=> ( ( M = one_one_nat )
        & ( N2 = one_one_nat ) ) ) ).

% nat_mult_eq_1_iff
tff(fact_1476_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
    ! [A: multis2468970476368604999at_nat] : minus_4286766774447292334at_nat(A,A) = zero_z1048942125864253310at_nat ).

% cancel_comm_monoid_add_class.diff_cancel
tff(fact_1477_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),A) = zero_z3403309356797280102nteger ).

% cancel_comm_monoid_add_class.diff_cancel
tff(fact_1478_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
    ! [A: rat] : aa_rat_rat(minus_minus_rat(A),A) = zero_zero_rat ).

% cancel_comm_monoid_add_class.diff_cancel
tff(fact_1479_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,A),A) = zero_zero_nat ).

% cancel_comm_monoid_add_class.diff_cancel
tff(fact_1480_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(minus_minus_int,A),A) = zero_zero_int ).

% cancel_comm_monoid_add_class.diff_cancel
tff(fact_1481_diff__zero,axiom,
    ! [A: multis2468970476368604999at_nat] : minus_4286766774447292334at_nat(A,zero_z1048942125864253310at_nat) = A ).

% diff_zero
tff(fact_1482_diff__zero,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),zero_z3403309356797280102nteger) = A ).

% diff_zero
tff(fact_1483_diff__zero,axiom,
    ! [A: rat] : aa_rat_rat(minus_minus_rat(A),zero_zero_rat) = A ).

% diff_zero
tff(fact_1484_diff__zero,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,A),zero_zero_nat) = A ).

% diff_zero
tff(fact_1485_diff__zero,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(minus_minus_int,A),zero_zero_int) = A ).

% diff_zero
tff(fact_1486_zero__diff,axiom,
    ! [A: multis2468970476368604999at_nat] : minus_4286766774447292334at_nat(zero_z1048942125864253310at_nat,A) = zero_z1048942125864253310at_nat ).

% zero_diff
tff(fact_1487_zero__diff,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,zero_zero_nat),A) = zero_zero_nat ).

% zero_diff
tff(fact_1488_diff__0__right,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),zero_z3403309356797280102nteger) = A ).

% diff_0_right
tff(fact_1489_diff__0__right,axiom,
    ! [A: rat] : aa_rat_rat(minus_minus_rat(A),zero_zero_rat) = A ).

% diff_0_right
tff(fact_1490_diff__0__right,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(minus_minus_int,A),zero_zero_int) = A ).

% diff_0_right
tff(fact_1491_diff__self,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),A) = zero_z3403309356797280102nteger ).

% diff_self
tff(fact_1492_diff__self,axiom,
    ! [A: rat] : aa_rat_rat(minus_minus_rat(A),A) = zero_zero_rat ).

% diff_self
tff(fact_1493_diff__self,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(minus_minus_int,A),A) = zero_zero_int ).

% diff_self
tff(fact_1494_mult_Oright__neutral,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),one_one_Code_integer) = A ).

% mult.right_neutral
tff(fact_1495_mult_Oright__neutral,axiom,
    ! [A: assn] : aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,A),one_one_assn) = A ).

% mult.right_neutral
tff(fact_1496_mult_Oright__neutral,axiom,
    ! [A: rat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),one_one_rat) = A ).

% mult.right_neutral
tff(fact_1497_mult_Oright__neutral,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),one_one_nat) = A ).

% mult.right_neutral
tff(fact_1498_mult_Oright__neutral,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(times_times_int,A),one_one_int) = A ).

% mult.right_neutral
tff(fact_1499_mult__1,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,one_one_Code_integer),A) = A ).

% mult_1
tff(fact_1500_mult__1,axiom,
    ! [A: assn] : aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,one_one_assn),A) = A ).

% mult_1
tff(fact_1501_mult__1,axiom,
    ! [A: rat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,one_one_rat),A) = A ).

% mult_1
tff(fact_1502_mult__1,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,one_one_nat),A) = A ).

% mult_1
tff(fact_1503_mult__1,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(times_times_int,one_one_int),A) = A ).

% mult_1
tff(fact_1504_add__diff__cancel__right_H,axiom,
    ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] : minus_4286766774447292334at_nat(aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(A),B),B) = A ).

% add_diff_cancel_right'
tff(fact_1505_add__diff__cancel__right_H,axiom,
    ! [A: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)),B) = A ).

% add_diff_cancel_right'
tff(fact_1506_add__diff__cancel__right_H,axiom,
    ! [A: rat,B: rat] : aa_rat_rat(minus_minus_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),B) = A ).

% add_diff_cancel_right'
tff(fact_1507_add__diff__cancel__right_H,axiom,
    ! [A: nat,B: nat] : aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),B) = A ).

% add_diff_cancel_right'
tff(fact_1508_add__diff__cancel__right_H,axiom,
    ! [A: int,B: int] : aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),B) = A ).

% add_diff_cancel_right'
tff(fact_1509_add__diff__cancel__right,axiom,
    ! [A: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] : minus_4286766774447292334at_nat(aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(A),C),aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(B),C)) = minus_4286766774447292334at_nat(A,B) ).

% add_diff_cancel_right
tff(fact_1510_add__diff__cancel__right,axiom,
    ! [A: code_integer,C: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),C)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,B),C)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B) ).

% add_diff_cancel_right
tff(fact_1511_add__diff__cancel__right,axiom,
    ! [A: rat,C: rat,B: rat] : aa_rat_rat(minus_minus_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),C)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),C)) = aa_rat_rat(minus_minus_rat(A),B) ).

% add_diff_cancel_right
tff(fact_1512_add__diff__cancel__right,axiom,
    ! [A: nat,C: nat,B: nat] : aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),C)) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,A),B) ).

% add_diff_cancel_right
tff(fact_1513_add__diff__cancel__right,axiom,
    ! [A: int,C: int,B: int] : aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),C)),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),C)) = aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B) ).

% add_diff_cancel_right
tff(fact_1514_add__diff__cancel__left_H,axiom,
    ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] : minus_4286766774447292334at_nat(aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(A),B),A) = B ).

% add_diff_cancel_left'
tff(fact_1515_add__diff__cancel__left_H,axiom,
    ! [A: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)),A) = B ).

% add_diff_cancel_left'
tff(fact_1516_add__diff__cancel__left_H,axiom,
    ! [A: rat,B: rat] : aa_rat_rat(minus_minus_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),A) = B ).

% add_diff_cancel_left'
tff(fact_1517_add__diff__cancel__left_H,axiom,
    ! [A: nat,B: nat] : aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),A) = B ).

% add_diff_cancel_left'
tff(fact_1518_add__diff__cancel__left_H,axiom,
    ! [A: int,B: int] : aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),A) = B ).

% add_diff_cancel_left'
tff(fact_1519_add__diff__cancel__left,axiom,
    ! [C: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] : minus_4286766774447292334at_nat(aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(C),A),aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(C),B)) = minus_4286766774447292334at_nat(A,B) ).

% add_diff_cancel_left
tff(fact_1520_add__diff__cancel__left,axiom,
    ! [C: code_integer,A: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,C),A)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,C),B)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B) ).

% add_diff_cancel_left
tff(fact_1521_add__diff__cancel__left,axiom,
    ! [C: rat,A: rat,B: rat] : aa_rat_rat(minus_minus_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,C),A)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,C),B)) = aa_rat_rat(minus_minus_rat(A),B) ).

% add_diff_cancel_left
tff(fact_1522_add__diff__cancel__left,axiom,
    ! [C: nat,A: nat,B: nat] : aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,C),A)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,C),B)) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,A),B) ).

% add_diff_cancel_left
tff(fact_1523_add__diff__cancel__left,axiom,
    ! [C: int,A: int,B: int] : aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,C),A)),aa_int_int(aa_int_fun_int_int(plus_plus_int,C),B)) = aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B) ).

% add_diff_cancel_left
tff(fact_1524_diff__add__cancel,axiom,
    ! [A: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B)),B) = A ).

% diff_add_cancel
tff(fact_1525_diff__add__cancel,axiom,
    ! [A: rat,B: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(minus_minus_rat(A),B)),B) = A ).

% diff_add_cancel
tff(fact_1526_diff__add__cancel,axiom,
    ! [A: int,B: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B)),B) = A ).

% diff_add_cancel
tff(fact_1527_add__diff__cancel,axiom,
    ! [A: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)),B) = A ).

% add_diff_cancel
tff(fact_1528_add__diff__cancel,axiom,
    ! [A: rat,B: rat] : aa_rat_rat(minus_minus_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),B) = A ).

% add_diff_cancel
tff(fact_1529_add__diff__cancel,axiom,
    ! [A: int,B: int] : aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),B) = A ).

% add_diff_cancel
tff(fact_1530_minus__diff__eq,axiom,
    ! [A: int,B: int] : aa_int_int(uminus_uminus_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B)) = aa_int_int(aa_int_fun_int_int(minus_minus_int,B),A) ).

% minus_diff_eq
tff(fact_1531_minus__diff__eq,axiom,
    ! [A: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,B),A) ).

% minus_diff_eq
tff(fact_1532_minus__diff__eq,axiom,
    ! [A: rat,B: rat] : aa_rat_rat(uminus_uminus_rat,aa_rat_rat(minus_minus_rat(A),B)) = aa_rat_rat(minus_minus_rat(B),A) ).

% minus_diff_eq
tff(fact_1533_Nat_Oadd__diff__assoc,axiom,
    ! [K: nat,J: nat,I: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),J)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,J),K)) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),J)),K) ) ) ).

% Nat.add_diff_assoc
tff(fact_1534_Nat_Oadd__diff__assoc2,axiom,
    ! [K: nat,J: nat,I: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),J)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,J),K)),I) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),I)),K) ) ) ).

% Nat.add_diff_assoc2
tff(fact_1535_Nat_Odiff__diff__right,axiom,
    ! [K: nat,J: nat,I: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),J)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,I),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,J),K)) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K)),J) ) ) ).

% Nat.diff_diff_right
tff(fact_1536_zle__add1__eq__le,axiom,
    ! [W: int,Z: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,W),aa_int_int(aa_int_fun_int_int(plus_plus_int,Z),one_one_int))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,W),Z) ) ).

% zle_add1_eq_le
tff(fact_1537_diff__ge__0__iff__ge,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,B),A) ) ).

% diff_ge_0_iff_ge
tff(fact_1538_diff__ge__0__iff__ge,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),aa_rat_rat(minus_minus_rat(A),B))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),A) ) ).

% diff_ge_0_iff_ge
tff(fact_1539_diff__ge__0__iff__ge,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,B),A) ) ).

% diff_ge_0_iff_ge
tff(fact_1540_zero__comp__diff__simps_I1_J,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,B),A) ) ).

% zero_comp_diff_simps(1)
tff(fact_1541_zero__comp__diff__simps_I1_J,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),aa_rat_rat(minus_minus_rat(A),B))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),A) ) ).

% zero_comp_diff_simps(1)
tff(fact_1542_zero__comp__diff__simps_I1_J,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,B),A) ) ).

% zero_comp_diff_simps(1)
tff(fact_1543_diff__gt__0__iff__gt,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,B),A) ) ).

% diff_gt_0_iff_gt
tff(fact_1544_diff__gt__0__iff__gt,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),aa_rat_rat(minus_minus_rat(A),B))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,B),A) ) ).

% diff_gt_0_iff_gt
tff(fact_1545_diff__gt__0__iff__gt,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,B),A) ) ).

% diff_gt_0_iff_gt
tff(fact_1546_zero__comp__diff__simps_I2_J,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,B),A) ) ).

% zero_comp_diff_simps(2)
tff(fact_1547_zero__comp__diff__simps_I2_J,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),aa_rat_rat(minus_minus_rat(A),B))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,B),A) ) ).

% zero_comp_diff_simps(2)
tff(fact_1548_zero__comp__diff__simps_I2_J,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,B),A) ) ).

% zero_comp_diff_simps(2)
tff(fact_1549_le__add__diff__inverse,axiom,
    ! [B: code_integer,A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,B),A)
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,B),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B)) = A ) ) ).

% le_add_diff_inverse
tff(fact_1550_le__add__diff__inverse,axiom,
    ! [B: rat,A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),A)
     => ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),aa_rat_rat(minus_minus_rat(A),B)) = A ) ) ).

% le_add_diff_inverse
tff(fact_1551_le__add__diff__inverse,axiom,
    ! [B: nat,A: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,B),A)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,A),B)) = A ) ) ).

% le_add_diff_inverse
tff(fact_1552_le__add__diff__inverse,axiom,
    ! [B: int,A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,B),A)
     => ( aa_int_int(aa_int_fun_int_int(plus_plus_int,B),aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B)) = A ) ) ).

% le_add_diff_inverse
tff(fact_1553_le__add__diff__inverse2,axiom,
    ! [B: code_integer,A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,B),A)
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B)),B) = A ) ) ).

% le_add_diff_inverse2
tff(fact_1554_le__add__diff__inverse2,axiom,
    ! [B: rat,A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),A)
     => ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(minus_minus_rat(A),B)),B) = A ) ) ).

% le_add_diff_inverse2
tff(fact_1555_le__add__diff__inverse2,axiom,
    ! [B: nat,A: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,B),A)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,A),B)),B) = A ) ) ).

% le_add_diff_inverse2
tff(fact_1556_le__add__diff__inverse2,axiom,
    ! [B: int,A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,B),A)
     => ( aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B)),B) = A ) ) ).

% le_add_diff_inverse2
tff(fact_1557_mult__cancel__left1,axiom,
    ! [C: code_integer,B: code_integer] :
      ( ( C = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,C),B) )
    <=> ( ( C = zero_z3403309356797280102nteger )
        | ( B = one_one_Code_integer ) ) ) ).

% mult_cancel_left1
tff(fact_1558_mult__cancel__left1,axiom,
    ! [C: rat,B: rat] :
      ( ( C = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,C),B) )
    <=> ( ( C = zero_zero_rat )
        | ( B = one_one_rat ) ) ) ).

% mult_cancel_left1
tff(fact_1559_mult__cancel__left1,axiom,
    ! [C: int,B: int] :
      ( ( C = aa_int_int(aa_int_fun_int_int(times_times_int,C),B) )
    <=> ( ( C = zero_zero_int )
        | ( B = one_one_int ) ) ) ).

% mult_cancel_left1
tff(fact_1560_mult__cancel__left2,axiom,
    ! [C: code_integer,A: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,C),A) = C )
    <=> ( ( C = zero_z3403309356797280102nteger )
        | ( A = one_one_Code_integer ) ) ) ).

% mult_cancel_left2
tff(fact_1561_mult__cancel__left2,axiom,
    ! [C: rat,A: rat] :
      ( ( aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,C),A) = C )
    <=> ( ( C = zero_zero_rat )
        | ( A = one_one_rat ) ) ) ).

% mult_cancel_left2
tff(fact_1562_mult__cancel__left2,axiom,
    ! [C: int,A: int] :
      ( ( aa_int_int(aa_int_fun_int_int(times_times_int,C),A) = C )
    <=> ( ( C = zero_zero_int )
        | ( A = one_one_int ) ) ) ).

% mult_cancel_left2
tff(fact_1563_mult__cancel__right1,axiom,
    ! [C: code_integer,B: code_integer] :
      ( ( C = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,B),C) )
    <=> ( ( C = zero_z3403309356797280102nteger )
        | ( B = one_one_Code_integer ) ) ) ).

% mult_cancel_right1
tff(fact_1564_mult__cancel__right1,axiom,
    ! [C: rat,B: rat] :
      ( ( C = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,B),C) )
    <=> ( ( C = zero_zero_rat )
        | ( B = one_one_rat ) ) ) ).

% mult_cancel_right1
tff(fact_1565_mult__cancel__right1,axiom,
    ! [C: int,B: int] :
      ( ( C = aa_int_int(aa_int_fun_int_int(times_times_int,B),C) )
    <=> ( ( C = zero_zero_int )
        | ( B = one_one_int ) ) ) ).

% mult_cancel_right1
tff(fact_1566_mult__cancel__right2,axiom,
    ! [A: code_integer,C: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),C) = C )
    <=> ( ( C = zero_z3403309356797280102nteger )
        | ( A = one_one_Code_integer ) ) ) ).

% mult_cancel_right2
tff(fact_1567_mult__cancel__right2,axiom,
    ! [A: rat,C: rat] :
      ( ( aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),C) = C )
    <=> ( ( C = zero_zero_rat )
        | ( A = one_one_rat ) ) ) ).

% mult_cancel_right2
tff(fact_1568_mult__cancel__right2,axiom,
    ! [A: int,C: int] :
      ( ( aa_int_int(aa_int_fun_int_int(times_times_int,A),C) = C )
    <=> ( ( C = zero_zero_int )
        | ( A = one_one_int ) ) ) ).

% mult_cancel_right2
tff(fact_1569_diff__add__zero,axiom,
    ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] : minus_4286766774447292334at_nat(A,aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(A),B)) = zero_z1048942125864253310at_nat ).

% diff_add_zero
tff(fact_1570_diff__add__zero,axiom,
    ! [A: nat,B: nat] : aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)) = zero_zero_nat ).

% diff_add_zero
tff(fact_1571_diff__numeral__special_I9_J,axiom,
    aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,one_one_Code_integer),one_one_Code_integer) = zero_z3403309356797280102nteger ).

% diff_numeral_special(9)
tff(fact_1572_diff__numeral__special_I9_J,axiom,
    aa_rat_rat(minus_minus_rat(one_one_rat),one_one_rat) = zero_zero_rat ).

% diff_numeral_special(9)
tff(fact_1573_diff__numeral__special_I9_J,axiom,
    aa_int_int(aa_int_fun_int_int(minus_minus_int,one_one_int),one_one_int) = zero_zero_int ).

% diff_numeral_special(9)
tff(fact_1574_diff__0,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(minus_minus_int,zero_zero_int),A) = aa_int_int(uminus_uminus_int,A) ).

% diff_0
tff(fact_1575_diff__0,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,zero_z3403309356797280102nteger),A) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A) ).

% diff_0
tff(fact_1576_diff__0,axiom,
    ! [A: rat] : aa_rat_rat(minus_minus_rat(zero_zero_rat),A) = aa_rat_rat(uminus_uminus_rat,A) ).

% diff_0
tff(fact_1577_mult__minus1,axiom,
    ! [Z: int] : aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(uminus_uminus_int,one_one_int)),Z) = aa_int_int(uminus_uminus_int,Z) ).

% mult_minus1
tff(fact_1578_mult__minus1,axiom,
    ! [Z: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),Z) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,Z) ).

% mult_minus1
tff(fact_1579_mult__minus1,axiom,
    ! [Z: rat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),Z) = aa_rat_rat(uminus_uminus_rat,Z) ).

% mult_minus1
tff(fact_1580_mult__minus1__right,axiom,
    ! [Z: int] : aa_int_int(aa_int_fun_int_int(times_times_int,Z),aa_int_int(uminus_uminus_int,one_one_int)) = aa_int_int(uminus_uminus_int,Z) ).

% mult_minus1_right
tff(fact_1581_mult__minus1__right,axiom,
    ! [Z: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,Z),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,Z) ).

% mult_minus1_right
tff(fact_1582_mult__minus1__right,axiom,
    ! [Z: rat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,Z),aa_rat_rat(uminus_uminus_rat,one_one_rat)) = aa_rat_rat(uminus_uminus_rat,Z) ).

% mult_minus1_right
tff(fact_1583_uminus__add__conv__diff,axiom,
    ! [A: int,B: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(uminus_uminus_int,A)),B) = aa_int_int(aa_int_fun_int_int(minus_minus_int,B),A) ).

% uminus_add_conv_diff
tff(fact_1584_uminus__add__conv__diff,axiom,
    ! [A: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A)),B) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,B),A) ).

% uminus_add_conv_diff
tff(fact_1585_uminus__add__conv__diff,axiom,
    ! [A: rat,B: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,A)),B) = aa_rat_rat(minus_minus_rat(B),A) ).

% uminus_add_conv_diff
tff(fact_1586_diff__minus__eq__add,axiom,
    ! [A: int,B: int] : aa_int_int(aa_int_fun_int_int(minus_minus_int,A),aa_int_int(uminus_uminus_int,B)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B) ).

% diff_minus_eq_add
tff(fact_1587_diff__minus__eq__add,axiom,
    ! [A: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,B)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B) ).

% diff_minus_eq_add
tff(fact_1588_diff__minus__eq__add,axiom,
    ! [A: rat,B: rat] : aa_rat_rat(minus_minus_rat(A),aa_rat_rat(uminus_uminus_rat,B)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B) ).

% diff_minus_eq_add
tff(fact_1589_diff__numeral__special_I12_J,axiom,
    aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(uminus_uminus_int,one_one_int)),aa_int_int(uminus_uminus_int,one_one_int)) = zero_zero_int ).

% diff_numeral_special(12)
tff(fact_1590_diff__numeral__special_I12_J,axiom,
    aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) = zero_z3403309356797280102nteger ).

% diff_numeral_special(12)
tff(fact_1591_diff__numeral__special_I12_J,axiom,
    aa_rat_rat(minus_minus_rat(aa_rat_rat(uminus_uminus_rat,one_one_rat)),aa_rat_rat(uminus_uminus_rat,one_one_rat)) = zero_zero_rat ).

% diff_numeral_special(12)
tff(fact_1592_le__imp__0__less,axiom,
    ! [Z: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),Z)
     => aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),Z)) ) ).

% le_imp_0_less
tff(fact_1593_q__pos__lemma,axiom,
    ! [B3: int,Q4: int,R4: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,B3),Q4)),R4))
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,R4),B3)
       => ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),B3)
         => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),Q4) ) ) ) ).

% q_pos_lemma
tff(fact_1594_zdiv__mono2__lemma,axiom,
    ! [B: int,Q3: int,R2: int,B3: int,Q4: int,R4: int] :
      ( ( aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,B),Q3)),R2) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,B3),Q4)),R4) )
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,B3),Q4)),R4))
       => ( aa_int_o(aa_int_fun_int_o(ord_less_int,R4),B3)
         => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),R2)
           => ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),B3)
             => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,B3),B)
               => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,Q3),Q4) ) ) ) ) ) ) ).

% zdiv_mono2_lemma
tff(fact_1595_zdiv__mono2__neg__lemma,axiom,
    ! [B: int,Q3: int,R2: int,B3: int,Q4: int,R4: int] :
      ( ( aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,B),Q3)),R2) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,B3),Q4)),R4) )
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,B3),Q4)),R4)),zero_zero_int)
       => ( aa_int_o(aa_int_fun_int_o(ord_less_int,R2),B)
         => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),R4)
           => ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),B3)
             => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,B3),B)
               => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,Q4),Q3) ) ) ) ) ) ) ).

% zdiv_mono2_neg_lemma
tff(fact_1596_unique__quotient__lemma,axiom,
    ! [B: int,Q4: int,R4: int,Q3: int,R2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,B),Q4)),R4)),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,B),Q3)),R2))
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),R4)
       => ( aa_int_o(aa_int_fun_int_o(ord_less_int,R4),B)
         => ( aa_int_o(aa_int_fun_int_o(ord_less_int,R2),B)
           => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,Q4),Q3) ) ) ) ) ).

% unique_quotient_lemma
tff(fact_1597_unique__quotient__lemma__neg,axiom,
    ! [B: int,Q4: int,R4: int,Q3: int,R2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,B),Q4)),R4)),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,B),Q3)),R2))
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,R2),zero_zero_int)
       => ( aa_int_o(aa_int_fun_int_o(ord_less_int,B),R2)
         => ( aa_int_o(aa_int_fun_int_o(ord_less_int,B),R4)
           => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,Q3),Q4) ) ) ) ) ).

% unique_quotient_lemma_neg
tff(fact_1598_int__ge__induct,axiom,
    ! [K: int,I: int,P: fun_int_o] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,K),I)
     => ( aa_int_o(P,K)
       => ( ! [I2: int] :
              ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,K),I2)
             => ( aa_int_o(P,I2)
               => aa_int_o(P,aa_int_int(aa_int_fun_int_int(plus_plus_int,I2),one_one_int)) ) )
         => aa_int_o(P,I) ) ) ) ).

% int_ge_induct
tff(fact_1599_int__induct,axiom,
    ! [P: fun_int_o,K: int,I: int] :
      ( aa_int_o(P,K)
     => ( ! [I2: int] :
            ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,K),I2)
           => ( aa_int_o(P,I2)
             => aa_int_o(P,aa_int_int(aa_int_fun_int_int(plus_plus_int,I2),one_one_int)) ) )
       => ( ! [I2: int] :
              ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,I2),K)
             => ( aa_int_o(P,I2)
               => aa_int_o(P,aa_int_int(aa_int_fun_int_int(minus_minus_int,I2),one_one_int)) ) )
         => aa_int_o(P,I) ) ) ) ).

% int_induct
tff(fact_1600_zless__imp__add1__zle,axiom,
    ! [W: int,Z: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,W),Z)
     => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,W),one_one_int)),Z) ) ).

% zless_imp_add1_zle
tff(fact_1601_add1__zle__eq,axiom,
    ! [W: int,Z: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,W),one_one_int)),Z)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,W),Z) ) ).

% add1_zle_eq
tff(fact_1602_nat__eq__add__iff1,axiom,
    ! [J: nat,I: nat,U: nat,M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,J),I)
     => ( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,I),U)),M) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,J),U)),N2) )
      <=> ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,I),J)),U)),M) = N2 ) ) ) ).

% nat_eq_add_iff1
tff(fact_1603_nat__eq__add__iff2,axiom,
    ! [I: nat,J: nat,U: nat,M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,I),J)
     => ( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,I),U)),M) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,J),U)),N2) )
      <=> ( M = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,J),I)),U)),N2) ) ) ) ).

% nat_eq_add_iff2
tff(fact_1604_nat__le__add__iff1,axiom,
    ! [J: nat,I: nat,U: nat,M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,J),I)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,I),U)),M)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,J),U)),N2))
      <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,I),J)),U)),M)),N2) ) ) ).

% nat_le_add_iff1
tff(fact_1605_nat__le__add__iff2,axiom,
    ! [I: nat,J: nat,U: nat,M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,I),J)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,I),U)),M)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,J),U)),N2))
      <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,J),I)),U)),N2)) ) ) ).

% nat_le_add_iff2
tff(fact_1606_nat__diff__add__eq1,axiom,
    ! [J: nat,I: nat,U: nat,M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,J),I)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,I),U)),M)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,J),U)),N2)) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,I),J)),U)),M)),N2) ) ) ).

% nat_diff_add_eq1
tff(fact_1607_nat__diff__add__eq2,axiom,
    ! [I: nat,J: nat,U: nat,M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,I),J)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,I),U)),M)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,J),U)),N2)) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,J),I)),U)),N2)) ) ) ).

% nat_diff_add_eq2
tff(fact_1608_bounded__Max__nat,axiom,
    ! [P: fun_nat_o,X2: nat,M2: nat] :
      ( aa_nat_o(P,X2)
     => ( ! [X3: nat] :
            ( aa_nat_o(P,X3)
           => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,X3),M2) )
       => ~ ! [M4: nat] :
              ( aa_nat_o(P,M4)
             => ~ ! [X: nat] :
                    ( aa_nat_o(P,X)
                   => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,X),M4) ) ) ) ) ).

% bounded_Max_nat
tff(fact_1609_subset__Collect__conv,axiom,
    ! [S2: set_list_nat,P: fun_list_nat_o] :
      ( ord_le6045566169113846134st_nat(S2,collect_list_nat(P))
    <=> ! [X4: list_nat] :
          ( member_list_nat(X4,S2)
         => aa_list_nat_o(P,X4) ) ) ).

% subset_Collect_conv
tff(fact_1610_subset__Collect__conv,axiom,
    ! [S2: set_nat,P: fun_nat_o] :
      ( aa_set_nat_o(ord_less_eq_set_nat(S2),collect_nat(P))
    <=> ! [X4: nat] :
          ( member_nat(X4,S2)
         => aa_nat_o(P,X4) ) ) ).

% subset_Collect_conv
tff(fact_1611_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
    ! [A: code_integer,C: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),C)),B) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B)),C) ).

% cancel_ab_semigroup_add_class.diff_right_commute
tff(fact_1612_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
    ! [A: rat,C: rat,B: rat] : aa_rat_rat(minus_minus_rat(aa_rat_rat(minus_minus_rat(A),C)),B) = aa_rat_rat(minus_minus_rat(aa_rat_rat(minus_minus_rat(A),B)),C) ).

% cancel_ab_semigroup_add_class.diff_right_commute
tff(fact_1613_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
    ! [A: nat,C: nat,B: nat] : aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,A),C)),B) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,A),B)),C) ).

% cancel_ab_semigroup_add_class.diff_right_commute
tff(fact_1614_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
    ! [A: int,C: int,B: int] : aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),C)),B) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B)),C) ).

% cancel_ab_semigroup_add_class.diff_right_commute
tff(fact_1615_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
    ! [B: assn,A: assn,C: assn] : aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,B),aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,A),C)) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,A),aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,B),C)) ).

% ab_semigroup_mult_class.mult.left_commute
tff(fact_1616_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
    ! [B: rat,A: rat,C: rat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,B),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),C)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,B),C)) ).

% ab_semigroup_mult_class.mult.left_commute
tff(fact_1617_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
    ! [B: nat,A: nat,C: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),C)) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),C)) ).

% ab_semigroup_mult_class.mult.left_commute
tff(fact_1618_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
    ! [B: int,A: int,C: int] : aa_int_int(aa_int_fun_int_int(times_times_int,B),aa_int_int(aa_int_fun_int_int(times_times_int,A),C)) = aa_int_int(aa_int_fun_int_int(times_times_int,A),aa_int_int(aa_int_fun_int_int(times_times_int,B),C)) ).

% ab_semigroup_mult_class.mult.left_commute
tff(fact_1619_ab__semigroup__mult__class_Omult_Ocommute,axiom,
    ! [A: assn,B: assn] : aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,A),B) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,B),A) ).

% ab_semigroup_mult_class.mult.commute
tff(fact_1620_ab__semigroup__mult__class_Omult_Ocommute,axiom,
    ! [A: rat,B: rat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),B) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,B),A) ).

% ab_semigroup_mult_class.mult.commute
tff(fact_1621_ab__semigroup__mult__class_Omult_Ocommute,axiom,
    ! [A: nat,B: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),A) ).

% ab_semigroup_mult_class.mult.commute
tff(fact_1622_ab__semigroup__mult__class_Omult_Ocommute,axiom,
    ! [A: int,B: int] : aa_int_int(aa_int_fun_int_int(times_times_int,A),B) = aa_int_int(aa_int_fun_int_int(times_times_int,B),A) ).

% ab_semigroup_mult_class.mult.commute
tff(fact_1623_mult_Oassoc,axiom,
    ! [A: assn,B: assn,C: assn] : aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,A),B)),C) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,A),aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,B),C)) ).

% mult.assoc
tff(fact_1624_mult_Oassoc,axiom,
    ! [A: rat,B: rat,C: rat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),B)),C) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,B),C)) ).

% mult.assoc
tff(fact_1625_mult_Oassoc,axiom,
    ! [A: nat,B: nat,C: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),B)),C) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),C)) ).

% mult.assoc
tff(fact_1626_mult_Oassoc,axiom,
    ! [A: int,B: int,C: int] : aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),B)),C) = aa_int_int(aa_int_fun_int_int(times_times_int,A),aa_int_int(aa_int_fun_int_int(times_times_int,B),C)) ).

% mult.assoc
tff(fact_1627_diff__eq__diff__eq,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,C),D2) )
     => ( ( A = B )
      <=> ( C = D2 ) ) ) ).

% diff_eq_diff_eq
tff(fact_1628_diff__eq__diff__eq,axiom,
    ! [A: rat,B: rat,C: rat,D2: rat] :
      ( ( aa_rat_rat(minus_minus_rat(A),B) = aa_rat_rat(minus_minus_rat(C),D2) )
     => ( ( A = B )
      <=> ( C = D2 ) ) ) ).

% diff_eq_diff_eq
tff(fact_1629_diff__eq__diff__eq,axiom,
    ! [A: int,B: int,C: int,D2: int] :
      ( ( aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B) = aa_int_int(aa_int_fun_int_int(minus_minus_int,C),D2) )
     => ( ( A = B )
      <=> ( C = D2 ) ) ) ).

% diff_eq_diff_eq
tff(fact_1630_one__integer_Orsp,axiom,
    one_one_int = one_one_int ).

% one_integer.rsp
tff(fact_1631_int__gr__induct,axiom,
    ! [K: int,I: int,P: fun_int_o] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,K),I)
     => ( aa_int_o(P,aa_int_int(aa_int_fun_int_int(plus_plus_int,K),one_one_int))
       => ( ! [I2: int] :
              ( aa_int_o(aa_int_fun_int_o(ord_less_int,K),I2)
             => ( aa_int_o(P,I2)
               => aa_int_o(P,aa_int_int(aa_int_fun_int_int(plus_plus_int,I2),one_one_int)) ) )
         => aa_int_o(P,I) ) ) ) ).

% int_gr_induct
tff(fact_1632_zless__add1__eq,axiom,
    ! [W: int,Z: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,W),aa_int_int(aa_int_fun_int_int(plus_plus_int,Z),one_one_int))
    <=> ( aa_int_o(aa_int_fun_int_o(ord_less_int,W),Z)
        | ( W = Z ) ) ) ).

% zless_add1_eq
tff(fact_1633_odd__nonzero,axiom,
    ! [Z: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),Z)),Z) != zero_zero_int ).

% odd_nonzero
tff(fact_1634_odd__less__0__iff,axiom,
    ! [Z: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),Z)),Z)),zero_zero_int)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,Z),zero_zero_int) ) ).

% odd_less_0_iff
tff(fact_1635_eq__add__iff1,axiom,
    ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),E)),C) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,B),E)),D2) )
    <=> ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B)),E)),C) = D2 ) ) ).

% eq_add_iff1
tff(fact_1636_eq__add__iff1,axiom,
    ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
      ( ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),E)),C) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,B),E)),D2) )
    <=> ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(minus_minus_rat(A),B)),E)),C) = D2 ) ) ).

% eq_add_iff1
tff(fact_1637_eq__add__iff1,axiom,
    ! [A: int,E: int,C: int,B: int,D2: int] :
      ( ( aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),E)),C) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,B),E)),D2) )
    <=> ( aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B)),E)),C) = D2 ) ) ).

% eq_add_iff1
tff(fact_1638_eq__add__iff2,axiom,
    ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),E)),C) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,B),E)),D2) )
    <=> ( C = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,B),A)),E)),D2) ) ) ).

% eq_add_iff2
tff(fact_1639_eq__add__iff2,axiom,
    ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
      ( ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),E)),C) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,B),E)),D2) )
    <=> ( C = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(minus_minus_rat(B),A)),E)),D2) ) ) ).

% eq_add_iff2
tff(fact_1640_eq__add__iff2,axiom,
    ! [A: int,E: int,C: int,B: int,D2: int] :
      ( ( aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),E)),C) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,B),E)),D2) )
    <=> ( C = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,B),A)),E)),D2) ) ) ).

% eq_add_iff2
tff(fact_1641_square__diff__square__factored,axiom,
    ! [X2: code_integer,Y: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,X2),X2)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,Y),Y)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X2),Y)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,X2),Y)) ).

% square_diff_square_factored
tff(fact_1642_square__diff__square__factored,axiom,
    ! [X2: rat,Y: rat] : aa_rat_rat(minus_minus_rat(aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,X2),X2)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,Y),Y)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),Y)),aa_rat_rat(minus_minus_rat(X2),Y)) ).

% square_diff_square_factored
tff(fact_1643_square__diff__square__factored,axiom,
    ! [X2: int,Y: int] : aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(aa_int_fun_int_int(times_times_int,X2),X2)),aa_int_int(aa_int_fun_int_int(times_times_int,Y),Y)) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),Y)),aa_int_int(aa_int_fun_int_int(minus_minus_int,X2),Y)) ).

% square_diff_square_factored
tff(fact_1644_left__add__mult__distrib,axiom,
    ! [I: nat,U: nat,J: nat,K: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,I),U)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,J),U)),K)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),J)),U)),K) ).

% left_add_mult_distrib
tff(fact_1645_nat__less__add__iff1,axiom,
    ! [J: nat,I: nat,U: nat,M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,J),I)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,I),U)),M)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,J),U)),N2))
      <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,I),J)),U)),M)),N2) ) ) ).

% nat_less_add_iff1
tff(fact_1646_nat__less__add__iff2,axiom,
    ! [I: nat,J: nat,U: nat,M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,I),J)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,I),U)),M)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,J),U)),N2))
      <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,J),I)),U)),N2)) ) ) ).

% nat_less_add_iff2
tff(fact_1647_le__add__iff1,axiom,
    ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),E)),C)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,B),E)),D2))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B)),E)),C)),D2) ) ).

% le_add_iff1
tff(fact_1648_le__add__iff1,axiom,
    ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),E)),C)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,B),E)),D2))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(minus_minus_rat(A),B)),E)),C)),D2) ) ).

% le_add_iff1
tff(fact_1649_le__add__iff1,axiom,
    ! [A: int,E: int,C: int,B: int,D2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),E)),C)),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,B),E)),D2))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B)),E)),C)),D2) ) ).

% le_add_iff1
tff(fact_1650_le__add__iff2,axiom,
    ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),E)),C)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,B),E)),D2))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,C),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,B),A)),E)),D2)) ) ).

% le_add_iff2
tff(fact_1651_le__add__iff2,axiom,
    ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),E)),C)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,B),E)),D2))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,C),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(minus_minus_rat(B),A)),E)),D2)) ) ).

% le_add_iff2
tff(fact_1652_le__add__iff2,axiom,
    ! [A: int,E: int,C: int,B: int,D2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),E)),C)),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,B),E)),D2))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,C),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,B),A)),E)),D2)) ) ).

% le_add_iff2
tff(fact_1653_less__add__iff1,axiom,
    ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),E)),C)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,B),E)),D2))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B)),E)),C)),D2) ) ).

% less_add_iff1
tff(fact_1654_less__add__iff1,axiom,
    ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),E)),C)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,B),E)),D2))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(minus_minus_rat(A),B)),E)),C)),D2) ) ).

% less_add_iff1
tff(fact_1655_less__add__iff1,axiom,
    ! [A: int,E: int,C: int,B: int,D2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),E)),C)),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,B),E)),D2))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B)),E)),C)),D2) ) ).

% less_add_iff1
tff(fact_1656_less__add__iff2,axiom,
    ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),E)),C)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,B),E)),D2))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,C),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,B),A)),E)),D2)) ) ).

% less_add_iff2
tff(fact_1657_less__add__iff2,axiom,
    ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),E)),C)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,B),E)),D2))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,C),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(minus_minus_rat(B),A)),E)),D2)) ) ).

% less_add_iff2
tff(fact_1658_less__add__iff2,axiom,
    ! [A: int,E: int,C: int,B: int,D2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),E)),C)),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,B),E)),D2))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,C),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,B),A)),E)),D2)) ) ).

% less_add_iff2
tff(fact_1659_square__diff__one__factored,axiom,
    ! [X2: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,X2),X2)),one_one_Code_integer) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X2),one_one_Code_integer)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,X2),one_one_Code_integer)) ).

% square_diff_one_factored
tff(fact_1660_square__diff__one__factored,axiom,
    ! [X2: rat] : aa_rat_rat(minus_minus_rat(aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,X2),X2)),one_one_rat) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),one_one_rat)),aa_rat_rat(minus_minus_rat(X2),one_one_rat)) ).

% square_diff_one_factored
tff(fact_1661_square__diff__one__factored,axiom,
    ! [X2: int] : aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(aa_int_fun_int_int(times_times_int,X2),X2)),one_one_int) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),one_one_int)),aa_int_int(aa_int_fun_int_int(minus_minus_int,X2),one_one_int)) ).

% square_diff_one_factored
tff(fact_1662_diff__eq__diff__less__eq,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,C),D2) )
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),B)
      <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,C),D2) ) ) ).

% diff_eq_diff_less_eq
tff(fact_1663_diff__eq__diff__less__eq,axiom,
    ! [A: rat,B: rat,C: rat,D2: rat] :
      ( ( aa_rat_rat(minus_minus_rat(A),B) = aa_rat_rat(minus_minus_rat(C),D2) )
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),B)
      <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,C),D2) ) ) ).

% diff_eq_diff_less_eq
tff(fact_1664_diff__eq__diff__less__eq,axiom,
    ! [A: int,B: int,C: int,D2: int] :
      ( ( aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B) = aa_int_int(aa_int_fun_int_int(minus_minus_int,C),D2) )
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),B)
      <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,C),D2) ) ) ).

% diff_eq_diff_less_eq
tff(fact_1665_diff__right__mono,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),B)
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),C)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,B),C)) ) ).

% diff_right_mono
tff(fact_1666_diff__right__mono,axiom,
    ! [A: rat,B: rat,C: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),B)
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(minus_minus_rat(A),C)),aa_rat_rat(minus_minus_rat(B),C)) ) ).

% diff_right_mono
tff(fact_1667_diff__right__mono,axiom,
    ! [A: int,B: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),B)
     => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),C)),aa_int_int(aa_int_fun_int_int(minus_minus_int,B),C)) ) ).

% diff_right_mono
tff(fact_1668_diff__left__mono,axiom,
    ! [B: code_integer,A: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,B),A)
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,C),A)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,C),B)) ) ).

% diff_left_mono
tff(fact_1669_diff__left__mono,axiom,
    ! [B: rat,A: rat,C: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),A)
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(minus_minus_rat(C),A)),aa_rat_rat(minus_minus_rat(C),B)) ) ).

% diff_left_mono
tff(fact_1670_diff__left__mono,axiom,
    ! [B: int,A: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,B),A)
     => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,C),A)),aa_int_int(aa_int_fun_int_int(minus_minus_int,C),B)) ) ).

% diff_left_mono
tff(fact_1671_diff__mono,axiom,
    ! [A: code_integer,B: code_integer,D2: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),B)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,D2),C)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),C)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,B),D2)) ) ) ).

% diff_mono
tff(fact_1672_diff__mono,axiom,
    ! [A: rat,B: rat,D2: rat,C: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),B)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,D2),C)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(minus_minus_rat(A),C)),aa_rat_rat(minus_minus_rat(B),D2)) ) ) ).

% diff_mono
tff(fact_1673_diff__mono,axiom,
    ! [A: int,B: int,D2: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),B)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,D2),C)
       => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),C)),aa_int_int(aa_int_fun_int_int(minus_minus_int,B),D2)) ) ) ).

% diff_mono
tff(fact_1674_eq__iff__diff__eq__0,axiom,
    ! [A: code_integer,B: code_integer] :
      ( ( A = B )
    <=> ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B) = zero_z3403309356797280102nteger ) ) ).

% eq_iff_diff_eq_0
tff(fact_1675_eq__iff__diff__eq__0,axiom,
    ! [A: rat,B: rat] :
      ( ( A = B )
    <=> ( aa_rat_rat(minus_minus_rat(A),B) = zero_zero_rat ) ) ).

% eq_iff_diff_eq_0
tff(fact_1676_eq__iff__diff__eq__0,axiom,
    ! [A: int,B: int] :
      ( ( A = B )
    <=> ( aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B) = zero_zero_int ) ) ).

% eq_iff_diff_eq_0
tff(fact_1677_diff__strict__right__mono,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),B)
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),C)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,B),C)) ) ).

% diff_strict_right_mono
tff(fact_1678_diff__strict__right__mono,axiom,
    ! [A: rat,B: rat,C: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B)
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(minus_minus_rat(A),C)),aa_rat_rat(minus_minus_rat(B),C)) ) ).

% diff_strict_right_mono
tff(fact_1679_diff__strict__right__mono,axiom,
    ! [A: int,B: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,A),B)
     => aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),C)),aa_int_int(aa_int_fun_int_int(minus_minus_int,B),C)) ) ).

% diff_strict_right_mono
tff(fact_1680_diff__strict__left__mono,axiom,
    ! [B: code_integer,A: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,B),A)
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,C),A)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,C),B)) ) ).

% diff_strict_left_mono
tff(fact_1681_diff__strict__left__mono,axiom,
    ! [B: rat,A: rat,C: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,B),A)
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(minus_minus_rat(C),A)),aa_rat_rat(minus_minus_rat(C),B)) ) ).

% diff_strict_left_mono
tff(fact_1682_diff__strict__left__mono,axiom,
    ! [B: int,A: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,B),A)
     => aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,C),A)),aa_int_int(aa_int_fun_int_int(minus_minus_int,C),B)) ) ).

% diff_strict_left_mono
tff(fact_1683_diff__eq__diff__less,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,C),D2) )
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),B)
      <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,C),D2) ) ) ).

% diff_eq_diff_less
tff(fact_1684_diff__eq__diff__less,axiom,
    ! [A: rat,B: rat,C: rat,D2: rat] :
      ( ( aa_rat_rat(minus_minus_rat(A),B) = aa_rat_rat(minus_minus_rat(C),D2) )
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B)
      <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,C),D2) ) ) ).

% diff_eq_diff_less
tff(fact_1685_diff__eq__diff__less,axiom,
    ! [A: int,B: int,C: int,D2: int] :
      ( ( aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B) = aa_int_int(aa_int_fun_int_int(minus_minus_int,C),D2) )
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,A),B)
      <=> aa_int_o(aa_int_fun_int_o(ord_less_int,C),D2) ) ) ).

% diff_eq_diff_less
tff(fact_1686_diff__strict__mono,axiom,
    ! [A: code_integer,B: code_integer,D2: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),B)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,D2),C)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),C)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,B),D2)) ) ) ).

% diff_strict_mono
tff(fact_1687_diff__strict__mono,axiom,
    ! [A: rat,B: rat,D2: rat,C: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,D2),C)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(minus_minus_rat(A),C)),aa_rat_rat(minus_minus_rat(B),D2)) ) ) ).

% diff_strict_mono
tff(fact_1688_diff__strict__mono,axiom,
    ! [A: int,B: int,D2: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,A),B)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,D2),C)
       => aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),C)),aa_int_int(aa_int_fun_int_int(minus_minus_int,B),D2)) ) ) ).

% diff_strict_mono
tff(fact_1689_diff__diff__eq,axiom,
    ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,C: multis2468970476368604999at_nat] : minus_4286766774447292334at_nat(minus_4286766774447292334at_nat(A,B),C) = minus_4286766774447292334at_nat(A,aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(B),C)) ).

% diff_diff_eq
tff(fact_1690_diff__diff__eq,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B)),C) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,B),C)) ).

% diff_diff_eq
tff(fact_1691_diff__diff__eq,axiom,
    ! [A: rat,B: rat,C: rat] : aa_rat_rat(minus_minus_rat(aa_rat_rat(minus_minus_rat(A),B)),C) = aa_rat_rat(minus_minus_rat(A),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),C)) ).

% diff_diff_eq
tff(fact_1692_diff__diff__eq,axiom,
    ! [A: nat,B: nat,C: nat] : aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,A),B)),C) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),C)) ).

% diff_diff_eq
tff(fact_1693_diff__diff__eq,axiom,
    ! [A: int,B: int,C: int] : aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B)),C) = aa_int_int(aa_int_fun_int_int(minus_minus_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),C)) ).

% diff_diff_eq
tff(fact_1694_add__implies__diff,axiom,
    ! [C: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat] :
      ( ( aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(C),B) = A )
     => ( C = minus_4286766774447292334at_nat(A,B) ) ) ).

% add_implies_diff
tff(fact_1695_add__implies__diff,axiom,
    ! [C: code_integer,B: code_integer,A: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,C),B) = A )
     => ( C = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B) ) ) ).

% add_implies_diff
tff(fact_1696_add__implies__diff,axiom,
    ! [C: rat,B: rat,A: rat] :
      ( ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,C),B) = A )
     => ( C = aa_rat_rat(minus_minus_rat(A),B) ) ) ).

% add_implies_diff
tff(fact_1697_add__implies__diff,axiom,
    ! [C: nat,B: nat,A: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,C),B) = A )
     => ( C = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,A),B) ) ) ).

% add_implies_diff
tff(fact_1698_add__implies__diff,axiom,
    ! [C: int,B: int,A: int] :
      ( ( aa_int_int(aa_int_fun_int_int(plus_plus_int,C),B) = A )
     => ( C = aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B) ) ) ).

% add_implies_diff
tff(fact_1699_diff__add__eq__diff__diff__swap,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,B),C)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),C)),B) ).

% diff_add_eq_diff_diff_swap
tff(fact_1700_diff__add__eq__diff__diff__swap,axiom,
    ! [A: rat,B: rat,C: rat] : aa_rat_rat(minus_minus_rat(A),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),C)) = aa_rat_rat(minus_minus_rat(aa_rat_rat(minus_minus_rat(A),C)),B) ).

% diff_add_eq_diff_diff_swap
tff(fact_1701_diff__add__eq__diff__diff__swap,axiom,
    ! [A: int,B: int,C: int] : aa_int_int(aa_int_fun_int_int(minus_minus_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),C)) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),C)),B) ).

% diff_add_eq_diff_diff_swap
tff(fact_1702_diff__add__eq,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B)),C) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),C)),B) ).

% diff_add_eq
tff(fact_1703_diff__add__eq,axiom,
    ! [A: rat,B: rat,C: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(minus_minus_rat(A),B)),C) = aa_rat_rat(minus_minus_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),C)),B) ).

% diff_add_eq
tff(fact_1704_diff__add__eq,axiom,
    ! [A: int,B: int,C: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B)),C) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),C)),B) ).

% diff_add_eq
tff(fact_1705_diff__diff__eq2,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,B),C)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),C)),B) ).

% diff_diff_eq2
tff(fact_1706_diff__diff__eq2,axiom,
    ! [A: rat,B: rat,C: rat] : aa_rat_rat(minus_minus_rat(A),aa_rat_rat(minus_minus_rat(B),C)) = aa_rat_rat(minus_minus_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),C)),B) ).

% diff_diff_eq2
tff(fact_1707_diff__diff__eq2,axiom,
    ! [A: int,B: int,C: int] : aa_int_int(aa_int_fun_int_int(minus_minus_int,A),aa_int_int(aa_int_fun_int_int(minus_minus_int,B),C)) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),C)),B) ).

% diff_diff_eq2
tff(fact_1708_add__diff__eq,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,B),C)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)),C) ).

% add_diff_eq
tff(fact_1709_add__diff__eq,axiom,
    ! [A: rat,B: rat,C: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),aa_rat_rat(minus_minus_rat(B),C)) = aa_rat_rat(minus_minus_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),C) ).

% add_diff_eq
tff(fact_1710_add__diff__eq,axiom,
    ! [A: int,B: int,C: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,A),aa_int_int(aa_int_fun_int_int(minus_minus_int,B),C)) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),C) ).

% add_diff_eq
tff(fact_1711_eq__diff__eq,axiom,
    ! [A: code_integer,C: code_integer,B: code_integer] :
      ( ( A = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,C),B) )
    <=> ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B) = C ) ) ).

% eq_diff_eq
tff(fact_1712_eq__diff__eq,axiom,
    ! [A: rat,C: rat,B: rat] :
      ( ( A = aa_rat_rat(minus_minus_rat(C),B) )
    <=> ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B) = C ) ) ).

% eq_diff_eq
tff(fact_1713_eq__diff__eq,axiom,
    ! [A: int,C: int,B: int] :
      ( ( A = aa_int_int(aa_int_fun_int_int(minus_minus_int,C),B) )
    <=> ( aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B) = C ) ) ).

% eq_diff_eq
tff(fact_1714_diff__eq__eq,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B) = C )
    <=> ( A = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,C),B) ) ) ).

% diff_eq_eq
tff(fact_1715_diff__eq__eq,axiom,
    ! [A: rat,B: rat,C: rat] :
      ( ( aa_rat_rat(minus_minus_rat(A),B) = C )
    <=> ( A = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,C),B) ) ) ).

% diff_eq_eq
tff(fact_1716_diff__eq__eq,axiom,
    ! [A: int,B: int,C: int] :
      ( ( aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B) = C )
    <=> ( A = aa_int_int(aa_int_fun_int_int(plus_plus_int,C),B) ) ) ).

% diff_eq_eq
tff(fact_1717_group__cancel_Osub1,axiom,
    ! [A2: code_integer,K: code_integer,A: code_integer,B: code_integer] :
      ( ( A2 = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,K),A) )
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A2),B) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,K),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B)) ) ) ).

% group_cancel.sub1
tff(fact_1718_group__cancel_Osub1,axiom,
    ! [A2: rat,K: rat,A: rat,B: rat] :
      ( ( A2 = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,K),A) )
     => ( aa_rat_rat(minus_minus_rat(A2),B) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,K),aa_rat_rat(minus_minus_rat(A),B)) ) ) ).

% group_cancel.sub1
tff(fact_1719_group__cancel_Osub1,axiom,
    ! [A2: int,K: int,A: int,B: int] :
      ( ( A2 = aa_int_int(aa_int_fun_int_int(plus_plus_int,K),A) )
     => ( aa_int_int(aa_int_fun_int_int(minus_minus_int,A2),B) = aa_int_int(aa_int_fun_int_int(plus_plus_int,K),aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B)) ) ) ).

% group_cancel.sub1
tff(fact_1720_minus__diff__commute,axiom,
    ! [B: int,A: int] : aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(uminus_uminus_int,B)),A) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(uminus_uminus_int,A)),B) ).

% minus_diff_commute
tff(fact_1721_minus__diff__commute,axiom,
    ! [B: code_integer,A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,B)),A) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A)),B) ).

% minus_diff_commute
tff(fact_1722_minus__diff__commute,axiom,
    ! [B: rat,A: rat] : aa_rat_rat(minus_minus_rat(aa_rat_rat(uminus_uminus_rat,B)),A) = aa_rat_rat(minus_minus_rat(aa_rat_rat(uminus_uminus_rat,A)),B) ).

% minus_diff_commute
tff(fact_1723_ring__class_Oring__distribs_I2_J,axiom,
    ! [A: rat,B: rat,C: rat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),C) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),C)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,B),C)) ).

% ring_class.ring_distribs(2)
tff(fact_1724_ring__class_Oring__distribs_I2_J,axiom,
    ! [A: int,B: int,C: int] : aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),C) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),C)),aa_int_int(aa_int_fun_int_int(times_times_int,B),C)) ).

% ring_class.ring_distribs(2)
tff(fact_1725_ring__class_Oring__distribs_I1_J,axiom,
    ! [A: rat,B: rat,C: rat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),C)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),B)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),C)) ).

% ring_class.ring_distribs(1)
tff(fact_1726_ring__class_Oring__distribs_I1_J,axiom,
    ! [A: int,B: int,C: int] : aa_int_int(aa_int_fun_int_int(times_times_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),C)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),B)),aa_int_int(aa_int_fun_int_int(times_times_int,A),C)) ).

% ring_class.ring_distribs(1)
tff(fact_1727_comm__semiring__class_Odistrib,axiom,
    ! [A: rat,B: rat,C: rat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),C) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),C)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,B),C)) ).

% comm_semiring_class.distrib
tff(fact_1728_comm__semiring__class_Odistrib,axiom,
    ! [A: nat,B: nat,C: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),C) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),C)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),C)) ).

% comm_semiring_class.distrib
tff(fact_1729_comm__semiring__class_Odistrib,axiom,
    ! [A: int,B: int,C: int] : aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),C) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),C)),aa_int_int(aa_int_fun_int_int(times_times_int,B),C)) ).

% comm_semiring_class.distrib
tff(fact_1730_distrib__left,axiom,
    ! [A: rat,B: rat,C: rat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),C)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),B)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),C)) ).

% distrib_left
tff(fact_1731_distrib__left,axiom,
    ! [A: nat,B: nat,C: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),C)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),B)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),C)) ).

% distrib_left
tff(fact_1732_distrib__left,axiom,
    ! [A: int,B: int,C: int] : aa_int_int(aa_int_fun_int_int(times_times_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),C)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),B)),aa_int_int(aa_int_fun_int_int(times_times_int,A),C)) ).

% distrib_left
tff(fact_1733_distrib__right,axiom,
    ! [A: rat,B: rat,C: rat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),C) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),C)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,B),C)) ).

% distrib_right
tff(fact_1734_distrib__right,axiom,
    ! [A: nat,B: nat,C: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),C) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),C)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),C)) ).

% distrib_right
tff(fact_1735_distrib__right,axiom,
    ! [A: int,B: int,C: int] : aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),C) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),C)),aa_int_int(aa_int_fun_int_int(times_times_int,B),C)) ).

% distrib_right
tff(fact_1736_combine__common__factor,axiom,
    ! [A: rat,E: rat,B: rat,C: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),E)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,B),E)),C)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),E)),C) ).

% combine_common_factor
tff(fact_1737_combine__common__factor,axiom,
    ! [A: nat,E: nat,B: nat,C: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),E)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),E)),C)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),E)),C) ).

% combine_common_factor
tff(fact_1738_combine__common__factor,axiom,
    ! [A: int,E: int,B: int,C: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),E)),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,B),E)),C)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),E)),C) ).

% combine_common_factor
tff(fact_1739_crossproduct__eq,axiom,
    ! [W: rat,Y: rat,X2: rat,Z: rat] :
      ( ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,W),Y)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,X2),Z)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,W),Z)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,X2),Y)) )
    <=> ( ( W = X2 )
        | ( Y = Z ) ) ) ).

% crossproduct_eq
tff(fact_1740_crossproduct__eq,axiom,
    ! [W: nat,Y: nat,X2: nat,Z: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,W),Y)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X2),Z)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,W),Z)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X2),Y)) )
    <=> ( ( W = X2 )
        | ( Y = Z ) ) ) ).

% crossproduct_eq
tff(fact_1741_crossproduct__eq,axiom,
    ! [W: int,Y: int,X2: int,Z: int] :
      ( ( aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,W),Y)),aa_int_int(aa_int_fun_int_int(times_times_int,X2),Z)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,W),Z)),aa_int_int(aa_int_fun_int_int(times_times_int,X2),Y)) )
    <=> ( ( W = X2 )
        | ( Y = Z ) ) ) ).

% crossproduct_eq
tff(fact_1742_crossproduct__noteq,axiom,
    ! [A: rat,B: rat,C: rat,D2: rat] :
      ( ( ( A != B )
        & ( C != D2 ) )
    <=> ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),C)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,B),D2)) != aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),D2)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,B),C)) ) ) ).

% crossproduct_noteq
tff(fact_1743_crossproduct__noteq,axiom,
    ! [A: nat,B: nat,C: nat,D2: nat] :
      ( ( ( A != B )
        & ( C != D2 ) )
    <=> ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),C)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),D2)) != aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),D2)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),C)) ) ) ).

% crossproduct_noteq
tff(fact_1744_crossproduct__noteq,axiom,
    ! [A: int,B: int,C: int,D2: int] :
      ( ( ( A != B )
        & ( C != D2 ) )
    <=> ( aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),C)),aa_int_int(aa_int_fun_int_int(times_times_int,B),D2)) != aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),D2)),aa_int_int(aa_int_fun_int_int(times_times_int,B),C)) ) ) ).

% crossproduct_noteq
tff(fact_1745_comm__monoid__mult__class_Omult__1,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,one_one_Code_integer),A) = A ).

% comm_monoid_mult_class.mult_1
tff(fact_1746_comm__monoid__mult__class_Omult__1,axiom,
    ! [A: assn] : aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,one_one_assn),A) = A ).

% comm_monoid_mult_class.mult_1
tff(fact_1747_comm__monoid__mult__class_Omult__1,axiom,
    ! [A: rat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,one_one_rat),A) = A ).

% comm_monoid_mult_class.mult_1
tff(fact_1748_comm__monoid__mult__class_Omult__1,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,one_one_nat),A) = A ).

% comm_monoid_mult_class.mult_1
tff(fact_1749_comm__monoid__mult__class_Omult__1,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(times_times_int,one_one_int),A) = A ).

% comm_monoid_mult_class.mult_1
tff(fact_1750_mult_Ocomm__neutral,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),one_one_Code_integer) = A ).

% mult.comm_neutral
tff(fact_1751_mult_Ocomm__neutral,axiom,
    ! [A: assn] : aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,A),one_one_assn) = A ).

% mult.comm_neutral
tff(fact_1752_mult_Ocomm__neutral,axiom,
    ! [A: rat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),one_one_rat) = A ).

% mult.comm_neutral
tff(fact_1753_mult_Ocomm__neutral,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),one_one_nat) = A ).

% mult.comm_neutral
tff(fact_1754_mult_Ocomm__neutral,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(times_times_int,A),one_one_int) = A ).

% mult.comm_neutral
tff(fact_1755_abs__minus__commute,axiom,
    ! [A: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B)) = aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,B),A)) ).

% abs_minus_commute
tff(fact_1756_abs__minus__commute,axiom,
    ! [A: rat,B: rat] : aa_rat_rat(abs_abs_rat,aa_rat_rat(minus_minus_rat(A),B)) = aa_rat_rat(abs_abs_rat,aa_rat_rat(minus_minus_rat(B),A)) ).

% abs_minus_commute
tff(fact_1757_abs__minus__commute,axiom,
    ! [A: int,B: int] : aa_int_int(abs_abs_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B)) = aa_int_int(abs_abs_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,B),A)) ).

% abs_minus_commute
tff(fact_1758_Nat_Odiff__cancel,axiom,
    ! [K: nat,M: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,K),M)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,K),N2)) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),N2) ).

% Nat.diff_cancel
tff(fact_1759_diff__cancel2,axiom,
    ! [M: nat,K: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),K)) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),N2) ).

% diff_cancel2
tff(fact_1760_diff__add__inverse,axiom,
    ! [N2: nat,M: nat] : aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),M)),N2) = M ).

% diff_add_inverse
tff(fact_1761_diff__add__inverse2,axiom,
    ! [M: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)),N2) = M ).

% diff_add_inverse2
tff(fact_1762_le__diff__conv,axiom,
    ! [J: nat,K: nat,I: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,J),K)),I)
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,J),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K)) ) ).

% le_diff_conv
tff(fact_1763_Nat_Ole__diff__conv2,axiom,
    ! [K: nat,J: nat,I: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),J)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,I),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,J),K))
      <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K)),J) ) ) ).

% Nat.le_diff_conv2
tff(fact_1764_Nat_Odiff__add__assoc,axiom,
    ! [K: nat,J: nat,I: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),J)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),J)),K) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,J),K)) ) ) ).

% Nat.diff_add_assoc
tff(fact_1765_Nat_Odiff__add__assoc2,axiom,
    ! [K: nat,J: nat,I: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),J)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),I)),K) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,J),K)),I) ) ) ).

% Nat.diff_add_assoc2
tff(fact_1766_Nat_Ole__imp__diff__is__add,axiom,
    ! [I: nat,J: nat,K: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,I),J)
     => ( ( aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,J),I) = K )
      <=> ( J = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,K),I) ) ) ) ).

% Nat.le_imp_diff_is_add
tff(fact_1767_add__mult__distrib,axiom,
    ! [M: nat,N2: nat,K: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)),K) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,M),K)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,N2),K)) ).

% add_mult_distrib
tff(fact_1768_add__mult__distrib2,axiom,
    ! [K: nat,M: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,K),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,K),M)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,K),N2)) ).

% add_mult_distrib2
tff(fact_1769_mlex__leI,axiom,
    ! [A: nat,A4: nat,B: nat,B3: nat,N5: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),A4)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,B),B3)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),N5)),B)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A4),N5)),B3)) ) ) ).

% mlex_leI
tff(fact_1770_nat__mult__1,axiom,
    ! [N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,one_one_nat),N2) = N2 ).

% nat_mult_1
tff(fact_1771_nat__mult__1__right,axiom,
    ! [N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,N2),one_one_nat) = N2 ).

% nat_mult_1_right
tff(fact_1772_mult__eq__if,axiom,
    ! [M: nat,N2: nat] :
      aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,M),N2) = $ite(M = zero_zero_nat,zero_zero_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),one_one_nat)),N2))) ).

% mult_eq_if
tff(fact_1773_lambda__one,axiom,
    aTP_Lamm_am = aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,one_one_Code_integer) ).

% lambda_one
tff(fact_1774_lambda__one,axiom,
    aTP_Lamm_cm = aa_ass954072293579886259n_assn(times_times_assn,one_one_assn) ).

% lambda_one
tff(fact_1775_lambda__one,axiom,
    aTP_Lamm_cn = aa_rat_fun_rat_rat(times_times_rat,one_one_rat) ).

% lambda_one
tff(fact_1776_lambda__one,axiom,
    aTP_Lamm_co = aa_nat_fun_nat_nat(times_times_nat,one_one_nat) ).

% lambda_one
tff(fact_1777_lambda__one,axiom,
    aTP_Lamm_cp = aa_int_fun_int_int(times_times_int,one_one_int) ).

% lambda_one
tff(fact_1778_is__num__normalize_I6_J,axiom,
    ! [X2: rat,Y: rat] :
      ( aa_rat_o(neg_nu6808929389511037909um_rat,X2)
     => ( aa_rat_o(neg_nu6808929389511037909um_rat,Y)
       => aa_rat_o(neg_nu6808929389511037909um_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),Y)) ) ) ).

% is_num_normalize(6)
tff(fact_1779_is__num__normalize_I6_J,axiom,
    ! [X2: int,Y: int] :
      ( aa_int_o(neg_nu7441568979088483369um_int,X2)
     => ( aa_int_o(neg_nu7441568979088483369um_int,Y)
       => aa_int_o(neg_nu7441568979088483369um_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),Y)) ) ) ).

% is_num_normalize(6)
tff(fact_1780_is__num__add__commute,axiom,
    ! [X2: rat,Y: rat] :
      ( aa_rat_o(neg_nu6808929389511037909um_rat,X2)
     => ( aa_rat_o(neg_nu6808929389511037909um_rat,Y)
       => ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),Y) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,Y),X2) ) ) ) ).

% is_num_add_commute
tff(fact_1781_is__num__add__commute,axiom,
    ! [X2: int,Y: int] :
      ( aa_int_o(neg_nu7441568979088483369um_int,X2)
     => ( aa_int_o(neg_nu7441568979088483369um_int,Y)
       => ( aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),Y) = aa_int_int(aa_int_fun_int_int(plus_plus_int,Y),X2) ) ) ) ).

% is_num_add_commute
tff(fact_1782_is__num__add__left__commute,axiom,
    ! [X2: rat,Y: rat,Z: rat] :
      ( aa_rat_o(neg_nu6808929389511037909um_rat,X2)
     => ( aa_rat_o(neg_nu6808929389511037909um_rat,Y)
       => ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,Y),Z)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,Y),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),Z)) ) ) ) ).

% is_num_add_left_commute
tff(fact_1783_is__num__add__left__commute,axiom,
    ! [X2: int,Y: int,Z: int] :
      ( aa_int_o(neg_nu7441568979088483369um_int,X2)
     => ( aa_int_o(neg_nu7441568979088483369um_int,Y)
       => ( aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),aa_int_int(aa_int_fun_int_int(plus_plus_int,Y),Z)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,Y),aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),Z)) ) ) ) ).

% is_num_add_left_commute
tff(fact_1784_is__num__normalize_I4_J,axiom,
    aa_Code_integer_o(neg_nu2435721316971906650nteger,one_one_Code_integer) ).

% is_num_normalize(4)
tff(fact_1785_is__num__normalize_I4_J,axiom,
    aa_rat_o(neg_nu6808929389511037909um_rat,one_one_rat) ).

% is_num_normalize(4)
tff(fact_1786_is__num__normalize_I4_J,axiom,
    aa_int_o(neg_nu7441568979088483369um_int,one_one_int) ).

% is_num_normalize(4)
tff(fact_1787_le__iff__diff__le__0,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),B)
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B)),zero_z3403309356797280102nteger) ) ).

% le_iff_diff_le_0
tff(fact_1788_le__iff__diff__le__0,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),B)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(minus_minus_rat(A),B)),zero_zero_rat) ) ).

% le_iff_diff_le_0
tff(fact_1789_le__iff__diff__le__0,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),B)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B)),zero_zero_int) ) ).

% le_iff_diff_le_0
tff(fact_1790_less__iff__diff__less__0,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),B)
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B)),zero_z3403309356797280102nteger) ) ).

% less_iff_diff_less_0
tff(fact_1791_less__iff__diff__less__0,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(minus_minus_rat(A),B)),zero_zero_rat) ) ).

% less_iff_diff_less_0
tff(fact_1792_less__iff__diff__less__0,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,A),B)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B)),zero_zero_int) ) ).

% less_iff_diff_less_0
tff(fact_1793_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
       => ( ( aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,B),A) = C )
        <=> ( B = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,C),A) ) ) ) ) ).

% ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
tff(fact_1794_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,B),A)) = B ) ) ).

% ordered_cancel_comm_monoid_diff_class.add_diff_inverse
tff(fact_1795_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,C),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,B),A)) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,C),A)),B) ) ) ).

% ordered_cancel_comm_monoid_diff_class.diff_diff_right
tff(fact_1796_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),C)),A) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,B),A)),C) ) ) ).

% ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
tff(fact_1797_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,B),A)),C) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),C)),A) ) ) ).

% ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
tff(fact_1798_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,C),B)),A) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,C),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,B),A)) ) ) ).

% ordered_cancel_comm_monoid_diff_class.diff_add_assoc
tff(fact_1799_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,C),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,B),A)) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,C),B)),A) ) ) ).

% ordered_cancel_comm_monoid_diff_class.add_diff_assoc
tff(fact_1800_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,C),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,B),A))
      <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,C),A)),B) ) ) ).

% ordered_cancel_comm_monoid_diff_class.le_diff_conv2
tff(fact_1801_le__add__diff,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,C),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),C)),A)) ) ).

% le_add_diff
tff(fact_1802_ordered__cancel__comm__monoid__diff__class_Odiff__add,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,B),A)),A) = B ) ) ).

% ordered_cancel_comm_monoid_diff_class.diff_add
tff(fact_1803_le__diff__eq,axiom,
    ! [A: code_integer,C: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,C),B))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)),C) ) ).

% le_diff_eq
tff(fact_1804_le__diff__eq,axiom,
    ! [A: rat,C: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),aa_rat_rat(minus_minus_rat(C),B))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),C) ) ).

% le_diff_eq
tff(fact_1805_le__diff__eq,axiom,
    ! [A: int,C: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),aa_int_int(aa_int_fun_int_int(minus_minus_int,C),B))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),C) ) ).

% le_diff_eq
tff(fact_1806_diff__le__eq,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B)),C)
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,C),B)) ) ).

% diff_le_eq
tff(fact_1807_diff__le__eq,axiom,
    ! [A: rat,B: rat,C: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(minus_minus_rat(A),B)),C)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,C),B)) ) ).

% diff_le_eq
tff(fact_1808_diff__le__eq,axiom,
    ! [A: int,B: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B)),C)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,C),B)) ) ).

% diff_le_eq
tff(fact_1809_add__le__imp__le__diff,axiom,
    ! [I: code_integer,K: code_integer,N2: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,I),K)),N2)
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,I),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,N2),K)) ) ).

% add_le_imp_le_diff
tff(fact_1810_add__le__imp__le__diff,axiom,
    ! [I: rat,K: rat,N2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,I),K)),N2)
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,I),aa_rat_rat(minus_minus_rat(N2),K)) ) ).

% add_le_imp_le_diff
tff(fact_1811_add__le__imp__le__diff,axiom,
    ! [I: nat,K: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K)),N2)
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,I),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),K)) ) ).

% add_le_imp_le_diff
tff(fact_1812_add__le__imp__le__diff,axiom,
    ! [I: int,K: int,N2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,I),K)),N2)
     => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,I),aa_int_int(aa_int_fun_int_int(minus_minus_int,N2),K)) ) ).

% add_le_imp_le_diff
tff(fact_1813_add__le__add__imp__diff__le,axiom,
    ! [I: code_integer,K: code_integer,N2: code_integer,J: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,I),K)),N2)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,N2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,J),K))
       => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,I),K)),N2)
         => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,N2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,J),K))
           => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,N2),K)),J) ) ) ) ) ).

% add_le_add_imp_diff_le
tff(fact_1814_add__le__add__imp__diff__le,axiom,
    ! [I: rat,K: rat,N2: rat,J: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,I),K)),N2)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,N2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,J),K))
       => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,I),K)),N2)
         => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,N2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,J),K))
           => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(minus_minus_rat(N2),K)),J) ) ) ) ) ).

% add_le_add_imp_diff_le
tff(fact_1815_add__le__add__imp__diff__le,axiom,
    ! [I: nat,K: nat,N2: nat,J: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K)),N2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),K))
       => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K)),N2)
         => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),K))
           => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),K)),J) ) ) ) ) ).

% add_le_add_imp_diff_le
tff(fact_1816_add__le__add__imp__diff__le,axiom,
    ! [I: int,K: int,N2: int,J: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,I),K)),N2)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,N2),aa_int_int(aa_int_fun_int_int(plus_plus_int,J),K))
       => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,I),K)),N2)
         => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,N2),aa_int_int(aa_int_fun_int_int(plus_plus_int,J),K))
           => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,N2),K)),J) ) ) ) ) ).

% add_le_add_imp_diff_le
tff(fact_1817_less__diff__eq,axiom,
    ! [A: code_integer,C: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,C),B))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)),C) ) ).

% less_diff_eq
tff(fact_1818_less__diff__eq,axiom,
    ! [A: rat,C: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),aa_rat_rat(minus_minus_rat(C),B))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),C) ) ).

% less_diff_eq
tff(fact_1819_less__diff__eq,axiom,
    ! [A: int,C: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,A),aa_int_int(aa_int_fun_int_int(minus_minus_int,C),B))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),C) ) ).

% less_diff_eq
tff(fact_1820_diff__less__eq,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B)),C)
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,C),B)) ) ).

% diff_less_eq
tff(fact_1821_diff__less__eq,axiom,
    ! [A: rat,B: rat,C: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(minus_minus_rat(A),B)),C)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,C),B)) ) ).

% diff_less_eq
tff(fact_1822_diff__less__eq,axiom,
    ! [A: int,B: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B)),C)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,C),B)) ) ).

% diff_less_eq
tff(fact_1823_linordered__semidom__class_Oadd__diff__inverse,axiom,
    ! [A: code_integer,B: code_integer] :
      ( ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),B)
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,B),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B)) = A ) ) ).

% linordered_semidom_class.add_diff_inverse
tff(fact_1824_linordered__semidom__class_Oadd__diff__inverse,axiom,
    ! [A: rat,B: rat] :
      ( ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B)
     => ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),aa_rat_rat(minus_minus_rat(A),B)) = A ) ) ).

% linordered_semidom_class.add_diff_inverse
tff(fact_1825_linordered__semidom__class_Oadd__diff__inverse,axiom,
    ! [A: nat,B: nat] :
      ( ~ aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),B)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,A),B)) = A ) ) ).

% linordered_semidom_class.add_diff_inverse
tff(fact_1826_linordered__semidom__class_Oadd__diff__inverse,axiom,
    ! [A: int,B: int] :
      ( ~ aa_int_o(aa_int_fun_int_o(ord_less_int,A),B)
     => ( aa_int_int(aa_int_fun_int_int(plus_plus_int,B),aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B)) = A ) ) ).

% linordered_semidom_class.add_diff_inverse
tff(fact_1827_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
    ! [A: int,B: int] : aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B) = aa_int_int(aa_int_fun_int_int(plus_plus_int,A),aa_int_int(uminus_uminus_int,B)) ).

% ab_group_add_class.ab_diff_conv_add_uminus
tff(fact_1828_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
    ! [A: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,B)) ).

% ab_group_add_class.ab_diff_conv_add_uminus
tff(fact_1829_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
    ! [A: rat,B: rat] : aa_rat_rat(minus_minus_rat(A),B) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),aa_rat_rat(uminus_uminus_rat,B)) ).

% ab_group_add_class.ab_diff_conv_add_uminus
tff(fact_1830_diff__conv__add__uminus,axiom,
    ! [A: int,B: int] : aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B) = aa_int_int(aa_int_fun_int_int(plus_plus_int,A),aa_int_int(uminus_uminus_int,B)) ).

% diff_conv_add_uminus
tff(fact_1831_diff__conv__add__uminus,axiom,
    ! [A: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,B)) ).

% diff_conv_add_uminus
tff(fact_1832_diff__conv__add__uminus,axiom,
    ! [A: rat,B: rat] : aa_rat_rat(minus_minus_rat(A),B) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),aa_rat_rat(uminus_uminus_rat,B)) ).

% diff_conv_add_uminus
tff(fact_1833_group__cancel_Osub2,axiom,
    ! [B4: int,K: int,B: int,A: int] :
      ( ( B4 = aa_int_int(aa_int_fun_int_int(plus_plus_int,K),B) )
     => ( aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B4) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(uminus_uminus_int,K)),aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B)) ) ) ).

% group_cancel.sub2
tff(fact_1834_group__cancel_Osub2,axiom,
    ! [B4: code_integer,K: code_integer,B: code_integer,A: code_integer] :
      ( ( B4 = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,K),B) )
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B4) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,K)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B)) ) ) ).

% group_cancel.sub2
tff(fact_1835_group__cancel_Osub2,axiom,
    ! [B4: rat,K: rat,B: rat,A: rat] :
      ( ( B4 = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,K),B) )
     => ( aa_rat_rat(minus_minus_rat(A),B4) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,K)),aa_rat_rat(minus_minus_rat(A),B)) ) ) ).

% group_cancel.sub2
tff(fact_1836_abs__triangle__ineq2__sym,axiom,
    ! [A: code_integer,B: code_integer] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A)),aa_Cod1783974652533396728nteger(abs_abs_Code_integer,B))),aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,B),A))) ).

% abs_triangle_ineq2_sym
tff(fact_1837_abs__triangle__ineq2__sym,axiom,
    ! [A: rat,B: rat] : aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(minus_minus_rat(aa_rat_rat(abs_abs_rat,A)),aa_rat_rat(abs_abs_rat,B))),aa_rat_rat(abs_abs_rat,aa_rat_rat(minus_minus_rat(B),A))) ).

% abs_triangle_ineq2_sym
tff(fact_1838_abs__triangle__ineq2__sym,axiom,
    ! [A: int,B: int] : aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(abs_abs_int,A)),aa_int_int(abs_abs_int,B))),aa_int_int(abs_abs_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,B),A))) ).

% abs_triangle_ineq2_sym
tff(fact_1839_abs__triangle__ineq3,axiom,
    ! [A: code_integer,B: code_integer] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A)),aa_Cod1783974652533396728nteger(abs_abs_Code_integer,B)))),aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B))) ).

% abs_triangle_ineq3
tff(fact_1840_abs__triangle__ineq3,axiom,
    ! [A: rat,B: rat] : aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(abs_abs_rat,aa_rat_rat(minus_minus_rat(aa_rat_rat(abs_abs_rat,A)),aa_rat_rat(abs_abs_rat,B)))),aa_rat_rat(abs_abs_rat,aa_rat_rat(minus_minus_rat(A),B))) ).

% abs_triangle_ineq3
tff(fact_1841_abs__triangle__ineq3,axiom,
    ! [A: int,B: int] : aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(abs_abs_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(abs_abs_int,A)),aa_int_int(abs_abs_int,B)))),aa_int_int(abs_abs_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B))) ).

% abs_triangle_ineq3
tff(fact_1842_abs__triangle__ineq2,axiom,
    ! [A: code_integer,B: code_integer] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A)),aa_Cod1783974652533396728nteger(abs_abs_Code_integer,B))),aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B))) ).

% abs_triangle_ineq2
tff(fact_1843_abs__triangle__ineq2,axiom,
    ! [A: rat,B: rat] : aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(minus_minus_rat(aa_rat_rat(abs_abs_rat,A)),aa_rat_rat(abs_abs_rat,B))),aa_rat_rat(abs_abs_rat,aa_rat_rat(minus_minus_rat(A),B))) ).

% abs_triangle_ineq2
tff(fact_1844_abs__triangle__ineq2,axiom,
    ! [A: int,B: int] : aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(abs_abs_int,A)),aa_int_int(abs_abs_int,B))),aa_int_int(abs_abs_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B))) ).

% abs_triangle_ineq2
tff(fact_1845_add__scale__eq__noteq,axiom,
    ! [R2: code_integer,A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
      ( ( R2 != zero_z3403309356797280102nteger )
     => ( ( ( A = B )
          & ( C != D2 ) )
       => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,R2),C)) != aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,B),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,R2),D2)) ) ) ) ).

% add_scale_eq_noteq
tff(fact_1846_add__scale__eq__noteq,axiom,
    ! [R2: rat,A: rat,B: rat,C: rat,D2: rat] :
      ( ( R2 != zero_zero_rat )
     => ( ( ( A = B )
          & ( C != D2 ) )
       => ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,R2),C)) != aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,R2),D2)) ) ) ) ).

% add_scale_eq_noteq
tff(fact_1847_add__scale__eq__noteq,axiom,
    ! [R2: nat,A: nat,B: nat,C: nat,D2: nat] :
      ( ( R2 != zero_zero_nat )
     => ( ( ( A = B )
          & ( C != D2 ) )
       => ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,R2),C)) != aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,R2),D2)) ) ) ) ).

% add_scale_eq_noteq
tff(fact_1848_add__scale__eq__noteq,axiom,
    ! [R2: int,A: int,B: int,C: int,D2: int] :
      ( ( R2 != zero_zero_int )
     => ( ( ( A = B )
          & ( C != D2 ) )
       => ( aa_int_int(aa_int_fun_int_int(plus_plus_int,A),aa_int_int(aa_int_fun_int_int(times_times_int,R2),C)) != aa_int_int(aa_int_fun_int_int(plus_plus_int,B),aa_int_int(aa_int_fun_int_int(times_times_int,R2),D2)) ) ) ) ).

% add_scale_eq_noteq
tff(fact_1849_less__1__mult,axiom,
    ! [M: code_integer,N2: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),M)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),N2)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,M),N2)) ) ) ).

% less_1_mult
tff(fact_1850_less__1__mult,axiom,
    ! [M: rat,N2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),M)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),N2)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,M),N2)) ) ) ).

% less_1_mult
tff(fact_1851_less__1__mult,axiom,
    ! [M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,one_one_nat),M)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,one_one_nat),N2)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,M),N2)) ) ) ).

% less_1_mult
tff(fact_1852_less__1__mult,axiom,
    ! [M: int,N2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),M)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),N2)
       => aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),aa_int_int(aa_int_fun_int_int(times_times_int,M),N2)) ) ) ).

% less_1_mult
tff(fact_1853_square__eq__1__iff,axiom,
    ! [X2: int] :
      ( ( aa_int_int(aa_int_fun_int_int(times_times_int,X2),X2) = one_one_int )
    <=> ( ( X2 = one_one_int )
        | ( X2 = aa_int_int(uminus_uminus_int,one_one_int) ) ) ) ).

% square_eq_1_iff
tff(fact_1854_square__eq__1__iff,axiom,
    ! [X2: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,X2),X2) = one_one_Code_integer )
    <=> ( ( X2 = one_one_Code_integer )
        | ( X2 = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) ) ) ) ).

% square_eq_1_iff
tff(fact_1855_square__eq__1__iff,axiom,
    ! [X2: rat] :
      ( ( aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,X2),X2) = one_one_rat )
    <=> ( ( X2 = one_one_rat )
        | ( X2 = aa_rat_rat(uminus_uminus_rat,one_one_rat) ) ) ) ).

% square_eq_1_iff
tff(fact_1856_diff__add__0,axiom,
    ! [N2: nat,M: nat] : aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),M)) = zero_zero_nat ).

% diff_add_0
tff(fact_1857_less__diff__conv,axiom,
    ! [I: nat,J: nat,K: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,I),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,J),K))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K)),J) ) ).

% less_diff_conv
tff(fact_1858_add__diff__inverse__nat,axiom,
    ! [M: nat,N2: nat] :
      ( ~ aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M),N2)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),N2)) = M ) ) ).

% add_diff_inverse_nat
tff(fact_1859_less__diff__conv2,axiom,
    ! [K: nat,J: nat,I: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),J)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,J),K)),I)
      <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,J),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K)) ) ) ).

% less_diff_conv2
tff(fact_1860_mlex__snd__decrI,axiom,
    ! [A: nat,A4: nat,B: nat,B3: nat,N5: nat] :
      ( ( A = A4 )
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,B),B3)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),N5)),B)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A4),N5)),B3)) ) ) ).

% mlex_snd_decrI
tff(fact_1861_mlex__fst__decrI,axiom,
    ! [A: nat,A4: nat,B: nat,N5: nat,B3: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),A4)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,B),N5)
       => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,B3),N5)
         => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),N5)),B)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A4),N5)),B3)) ) ) ) ).

% mlex_fst_decrI
tff(fact_1862_mlex__bound,axiom,
    ! [A: nat,A2: nat,B: nat,N5: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),A2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,B),N5)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),N5)),B)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A2),N5)) ) ) ).

% mlex_bound
tff(fact_1863_mult__eq__self__implies__10,axiom,
    ! [M: nat,N2: nat] :
      ( ( M = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,M),N2) )
     => ( ( N2 = one_one_nat )
        | ( M = zero_zero_nat ) ) ) ).

% mult_eq_self_implies_10
tff(fact_1864_field__le__mult__one__interval,axiom,
    ! [X2: rat,Y: rat] :
      ( ! [Z2: rat] :
          ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),Z2)
         => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,Z2),one_one_rat)
           => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,Z2),X2)),Y) ) )
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,X2),Y) ) ).

% field_le_mult_one_interval
tff(fact_1865_abs__diff__le__iff,axiom,
    ! [X2: code_integer,A: code_integer,R2: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,X2),A))),R2)
    <=> ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),R2)),X2)
        & aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,X2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),R2)) ) ) ).

% abs_diff_le_iff
tff(fact_1866_abs__diff__le__iff,axiom,
    ! [X2: rat,A: rat,R2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(abs_abs_rat,aa_rat_rat(minus_minus_rat(X2),A))),R2)
    <=> ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(minus_minus_rat(A),R2)),X2)
        & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,X2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),R2)) ) ) ).

% abs_diff_le_iff
tff(fact_1867_abs__diff__le__iff,axiom,
    ! [X2: int,A: int,R2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(abs_abs_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,X2),A))),R2)
    <=> ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),R2)),X2)
        & aa_int_o(aa_int_fun_int_o(ord_less_eq_int,X2),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),R2)) ) ) ).

% abs_diff_le_iff
tff(fact_1868_abs__diff__triangle__ineq,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,C),D2)))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),C))),aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,B),D2)))) ).

% abs_diff_triangle_ineq
tff(fact_1869_abs__diff__triangle__ineq,axiom,
    ! [A: rat,B: rat,C: rat,D2: rat] : aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(abs_abs_rat,aa_rat_rat(minus_minus_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,C),D2)))),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(abs_abs_rat,aa_rat_rat(minus_minus_rat(A),C))),aa_rat_rat(abs_abs_rat,aa_rat_rat(minus_minus_rat(B),D2)))) ).

% abs_diff_triangle_ineq
tff(fact_1870_abs__diff__triangle__ineq,axiom,
    ! [A: int,B: int,C: int,D2: int] : aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(abs_abs_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),aa_int_int(aa_int_fun_int_int(plus_plus_int,C),D2)))),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(abs_abs_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),C))),aa_int_int(abs_abs_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,B),D2)))) ).

% abs_diff_triangle_ineq
tff(fact_1871_abs__triangle__ineq4,axiom,
    ! [A: code_integer,B: code_integer] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,A)),aa_Cod1783974652533396728nteger(abs_abs_Code_integer,B))) ).

% abs_triangle_ineq4
tff(fact_1872_abs__triangle__ineq4,axiom,
    ! [A: rat,B: rat] : aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(abs_abs_rat,aa_rat_rat(minus_minus_rat(A),B))),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(abs_abs_rat,A)),aa_rat_rat(abs_abs_rat,B))) ).

% abs_triangle_ineq4
tff(fact_1873_abs__triangle__ineq4,axiom,
    ! [A: int,B: int] : aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(abs_abs_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B))),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(abs_abs_int,A)),aa_int_int(abs_abs_int,B))) ).

% abs_triangle_ineq4
tff(fact_1874_abs__diff__less__iff,axiom,
    ! [X2: code_integer,A: code_integer,R2: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,X2),A))),R2)
    <=> ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),R2)),X2)
        & aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,X2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),R2)) ) ) ).

% abs_diff_less_iff
tff(fact_1875_abs__diff__less__iff,axiom,
    ! [X2: rat,A: rat,R2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(abs_abs_rat,aa_rat_rat(minus_minus_rat(X2),A))),R2)
    <=> ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(minus_minus_rat(A),R2)),X2)
        & aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,X2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),R2)) ) ) ).

% abs_diff_less_iff
tff(fact_1876_abs__diff__less__iff,axiom,
    ! [X2: int,A: int,R2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(abs_abs_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,X2),A))),R2)
    <=> ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),R2)),X2)
        & aa_int_o(aa_int_fun_int_o(ord_less_int,X2),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),R2)) ) ) ).

% abs_diff_less_iff
tff(fact_1877_sum__squares__ge__zero,axiom,
    ! [X2: code_integer,Y: code_integer] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,X2),X2)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,Y),Y))) ).

% sum_squares_ge_zero
tff(fact_1878_sum__squares__ge__zero,axiom,
    ! [X2: rat,Y: rat] : aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,X2),X2)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,Y),Y))) ).

% sum_squares_ge_zero
tff(fact_1879_sum__squares__ge__zero,axiom,
    ! [X2: int,Y: int] : aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,X2),X2)),aa_int_int(aa_int_fun_int_int(times_times_int,Y),Y))) ).

% sum_squares_ge_zero
tff(fact_1880_mult__left__le,axiom,
    ! [C: code_integer,A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,C),one_one_Code_integer)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),A)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),C)),A) ) ) ).

% mult_left_le
tff(fact_1881_mult__left__le,axiom,
    ! [C: rat,A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,C),one_one_rat)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),A)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),C)),A) ) ) ).

% mult_left_le
tff(fact_1882_mult__left__le,axiom,
    ! [C: nat,A: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,C),one_one_nat)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),A)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),C)),A) ) ) ).

% mult_left_le
tff(fact_1883_mult__left__le,axiom,
    ! [C: int,A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,C),one_one_int)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),A)
       => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),C)),A) ) ) ).

% mult_left_le
tff(fact_1884_mult__le__one,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),one_one_Code_integer)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),B)
       => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,B),one_one_Code_integer)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),B)),one_one_Code_integer) ) ) ) ).

% mult_le_one
tff(fact_1885_mult__le__one,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),one_one_rat)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),B)
       => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),one_one_rat)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),B)),one_one_rat) ) ) ) ).

% mult_le_one
tff(fact_1886_mult__le__one,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),one_one_nat)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),B)
       => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,B),one_one_nat)
         => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),B)),one_one_nat) ) ) ) ).

% mult_le_one
tff(fact_1887_mult__le__one,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),one_one_int)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),B)
       => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,B),one_one_int)
         => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),B)),one_one_int) ) ) ) ).

% mult_le_one
tff(fact_1888_mult__right__le__one__le,axiom,
    ! [X2: code_integer,Y: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),X2)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),Y)
       => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,Y),one_one_Code_integer)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,X2),Y)),X2) ) ) ) ).

% mult_right_le_one_le
tff(fact_1889_mult__right__le__one__le,axiom,
    ! [X2: rat,Y: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),X2)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),Y)
       => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,Y),one_one_rat)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,X2),Y)),X2) ) ) ) ).

% mult_right_le_one_le
tff(fact_1890_mult__right__le__one__le,axiom,
    ! [X2: int,Y: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),X2)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),Y)
       => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,Y),one_one_int)
         => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(times_times_int,X2),Y)),X2) ) ) ) ).

% mult_right_le_one_le
tff(fact_1891_mult__left__le__one__le,axiom,
    ! [X2: code_integer,Y: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),X2)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),Y)
       => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,Y),one_one_Code_integer)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,Y),X2)),X2) ) ) ) ).

% mult_left_le_one_le
tff(fact_1892_mult__left__le__one__le,axiom,
    ! [X2: rat,Y: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),X2)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),Y)
       => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,Y),one_one_rat)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,Y),X2)),X2) ) ) ) ).

% mult_left_le_one_le
tff(fact_1893_mult__left__le__one__le,axiom,
    ! [X2: int,Y: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),X2)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),Y)
       => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,Y),one_one_int)
         => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(times_times_int,Y),X2)),X2) ) ) ) ).

% mult_left_le_one_le
tff(fact_1894_not__sum__squares__lt__zero,axiom,
    ! [X2: code_integer,Y: code_integer] : ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,X2),X2)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,Y),Y))),zero_z3403309356797280102nteger) ).

% not_sum_squares_lt_zero
tff(fact_1895_not__sum__squares__lt__zero,axiom,
    ! [X2: rat,Y: rat] : ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,X2),X2)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,Y),Y))),zero_zero_rat) ).

% not_sum_squares_lt_zero
tff(fact_1896_not__sum__squares__lt__zero,axiom,
    ! [X2: int,Y: int] : ~ aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,X2),X2)),aa_int_int(aa_int_fun_int_int(times_times_int,Y),Y))),zero_zero_int) ).

% not_sum_squares_lt_zero
tff(fact_1897_nat__diff__split,axiom,
    ! [P: fun_nat_o,A: nat,B: nat] :
      ( aa_nat_o(P,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,A),B))
    <=> ( ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),B)
         => aa_nat_o(P,zero_zero_nat) )
        & ! [D4: nat] :
            ( ( A = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),D4) )
           => aa_nat_o(P,D4) ) ) ) ).

% nat_diff_split
tff(fact_1898_nat__diff__split__asm,axiom,
    ! [P: fun_nat_o,A: nat,B: nat] :
      ( aa_nat_o(P,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,A),B))
    <=> ~ ( ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),B)
            & ~ aa_nat_o(P,zero_zero_nat) )
          | ? [D4: nat] :
              ( ( A = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),D4) )
              & ~ aa_nat_o(P,D4) ) ) ) ).

% nat_diff_split_asm
tff(fact_1899_dbl__dec__def,axiom,
    ! [X2: code_integer] : aa_Cod1783974652533396728nteger(neg_nu7757733837767384882nteger,X2) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X2),X2)),one_one_Code_integer) ).

% dbl_dec_def
tff(fact_1900_dbl__dec__def,axiom,
    ! [X2: rat] : aa_rat_rat(neg_nu3179335615603231917ec_rat,X2) = aa_rat_rat(minus_minus_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),X2)),one_one_rat) ).

% dbl_dec_def
tff(fact_1901_dbl__dec__def,axiom,
    ! [X2: int] : aa_int_int(neg_nu3811975205180677377ec_int,X2) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),X2)),one_one_int) ).

% dbl_dec_def
tff(fact_1902_mult__le__cancel__left1,axiom,
    ! [C: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,C),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,C),B))
    <=> ( ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),C)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),B) )
        & ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,C),zero_z3403309356797280102nteger)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,B),one_one_Code_integer) ) ) ) ).

% mult_le_cancel_left1
tff(fact_1903_mult__le__cancel__left1,axiom,
    ! [C: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,C),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,C),B))
    <=> ( ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),C)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),B) )
        & ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,C),zero_zero_rat)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),one_one_rat) ) ) ) ).

% mult_le_cancel_left1
tff(fact_1904_mult__le__cancel__left1,axiom,
    ! [C: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,C),aa_int_int(aa_int_fun_int_int(times_times_int,C),B))
    <=> ( ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),C)
         => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,one_one_int),B) )
        & ( aa_int_o(aa_int_fun_int_o(ord_less_int,C),zero_zero_int)
         => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,B),one_one_int) ) ) ) ).

% mult_le_cancel_left1
tff(fact_1905_mult__le__cancel__left2,axiom,
    ! [C: code_integer,A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,C),A)),C)
    <=> ( ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),C)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),one_one_Code_integer) )
        & ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,C),zero_z3403309356797280102nteger)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),A) ) ) ) ).

% mult_le_cancel_left2
tff(fact_1906_mult__le__cancel__left2,axiom,
    ! [C: rat,A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,C),A)),C)
    <=> ( ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),C)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),one_one_rat) )
        & ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,C),zero_zero_rat)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),A) ) ) ) ).

% mult_le_cancel_left2
tff(fact_1907_mult__le__cancel__left2,axiom,
    ! [C: int,A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(times_times_int,C),A)),C)
    <=> ( ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),C)
         => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),one_one_int) )
        & ( aa_int_o(aa_int_fun_int_o(ord_less_int,C),zero_zero_int)
         => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,one_one_int),A) ) ) ) ).

% mult_le_cancel_left2
tff(fact_1908_mult__le__cancel__right1,axiom,
    ! [C: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,C),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,B),C))
    <=> ( ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),C)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),B) )
        & ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,C),zero_z3403309356797280102nteger)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,B),one_one_Code_integer) ) ) ) ).

% mult_le_cancel_right1
tff(fact_1909_mult__le__cancel__right1,axiom,
    ! [C: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,C),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,B),C))
    <=> ( ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),C)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),B) )
        & ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,C),zero_zero_rat)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),one_one_rat) ) ) ) ).

% mult_le_cancel_right1
tff(fact_1910_mult__le__cancel__right1,axiom,
    ! [C: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,C),aa_int_int(aa_int_fun_int_int(times_times_int,B),C))
    <=> ( ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),C)
         => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,one_one_int),B) )
        & ( aa_int_o(aa_int_fun_int_o(ord_less_int,C),zero_zero_int)
         => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,B),one_one_int) ) ) ) ).

% mult_le_cancel_right1
tff(fact_1911_mult__le__cancel__right2,axiom,
    ! [A: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),C)),C)
    <=> ( ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),C)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),one_one_Code_integer) )
        & ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,C),zero_z3403309356797280102nteger)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),A) ) ) ) ).

% mult_le_cancel_right2
tff(fact_1912_mult__le__cancel__right2,axiom,
    ! [A: rat,C: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),C)),C)
    <=> ( ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),C)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),one_one_rat) )
        & ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,C),zero_zero_rat)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),A) ) ) ) ).

% mult_le_cancel_right2
tff(fact_1913_mult__le__cancel__right2,axiom,
    ! [A: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),C)),C)
    <=> ( ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),C)
         => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),one_one_int) )
        & ( aa_int_o(aa_int_fun_int_o(ord_less_int,C),zero_zero_int)
         => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,one_one_int),A) ) ) ) ).

% mult_le_cancel_right2
tff(fact_1914_mult__less__cancel__left1,axiom,
    ! [C: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,C),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,C),B))
    <=> ( ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),C)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),B) )
        & ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,C),zero_z3403309356797280102nteger)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,B),one_one_Code_integer) ) ) ) ).

% mult_less_cancel_left1
tff(fact_1915_mult__less__cancel__left1,axiom,
    ! [C: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,C),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,C),B))
    <=> ( ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),C)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),B) )
        & ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,C),zero_zero_rat)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,B),one_one_rat) ) ) ) ).

% mult_less_cancel_left1
tff(fact_1916_mult__less__cancel__left1,axiom,
    ! [C: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,C),aa_int_int(aa_int_fun_int_int(times_times_int,C),B))
    <=> ( ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),C)
         => aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),B) )
        & ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,C),zero_zero_int)
         => aa_int_o(aa_int_fun_int_o(ord_less_int,B),one_one_int) ) ) ) ).

% mult_less_cancel_left1
tff(fact_1917_mult__less__cancel__left2,axiom,
    ! [C: code_integer,A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,C),A)),C)
    <=> ( ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),C)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),one_one_Code_integer) )
        & ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,C),zero_z3403309356797280102nteger)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),A) ) ) ) ).

% mult_less_cancel_left2
tff(fact_1918_mult__less__cancel__left2,axiom,
    ! [C: rat,A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,C),A)),C)
    <=> ( ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),C)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),one_one_rat) )
        & ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,C),zero_zero_rat)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),A) ) ) ) ).

% mult_less_cancel_left2
tff(fact_1919_mult__less__cancel__left2,axiom,
    ! [C: int,A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(times_times_int,C),A)),C)
    <=> ( ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),C)
         => aa_int_o(aa_int_fun_int_o(ord_less_int,A),one_one_int) )
        & ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,C),zero_zero_int)
         => aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),A) ) ) ) ).

% mult_less_cancel_left2
tff(fact_1920_mult__less__cancel__right1,axiom,
    ! [C: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,C),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,B),C))
    <=> ( ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),C)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),B) )
        & ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,C),zero_z3403309356797280102nteger)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,B),one_one_Code_integer) ) ) ) ).

% mult_less_cancel_right1
tff(fact_1921_mult__less__cancel__right1,axiom,
    ! [C: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,C),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,B),C))
    <=> ( ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),C)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),B) )
        & ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,C),zero_zero_rat)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,B),one_one_rat) ) ) ) ).

% mult_less_cancel_right1
tff(fact_1922_mult__less__cancel__right1,axiom,
    ! [C: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,C),aa_int_int(aa_int_fun_int_int(times_times_int,B),C))
    <=> ( ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),C)
         => aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),B) )
        & ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,C),zero_zero_int)
         => aa_int_o(aa_int_fun_int_o(ord_less_int,B),one_one_int) ) ) ) ).

% mult_less_cancel_right1
tff(fact_1923_mult__less__cancel__right2,axiom,
    ! [A: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),C)),C)
    <=> ( ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),C)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),one_one_Code_integer) )
        & ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,C),zero_z3403309356797280102nteger)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),A) ) ) ) ).

% mult_less_cancel_right2
tff(fact_1924_mult__less__cancel__right2,axiom,
    ! [A: rat,C: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),C)),C)
    <=> ( ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),C)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),one_one_rat) )
        & ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,C),zero_zero_rat)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),A) ) ) ) ).

% mult_less_cancel_right2
tff(fact_1925_mult__less__cancel__right2,axiom,
    ! [A: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),C)),C)
    <=> ( ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),C)
         => aa_int_o(aa_int_fun_int_o(ord_less_int,A),one_one_int) )
        & ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,C),zero_zero_int)
         => aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),A) ) ) ) ).

% mult_less_cancel_right2
tff(fact_1926_convex__bound__le,axiom,
    ! [X2: code_integer,A: code_integer,Y: code_integer,U: code_integer,V: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,X2),A)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,Y),A)
       => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),U)
         => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),V)
           => ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,U),V) = one_one_Code_integer )
             => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,U),X2)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,V),Y))),A) ) ) ) ) ) ).

% convex_bound_le
tff(fact_1927_convex__bound__le,axiom,
    ! [X2: rat,A: rat,Y: rat,U: rat,V: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,X2),A)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,Y),A)
       => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),U)
         => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),V)
           => ( ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,U),V) = one_one_rat )
             => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,U),X2)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,V),Y))),A) ) ) ) ) ) ).

% convex_bound_le
tff(fact_1928_convex__bound__le,axiom,
    ! [X2: int,A: int,Y: int,U: int,V: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,X2),A)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,Y),A)
       => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),U)
         => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),V)
           => ( ( aa_int_int(aa_int_fun_int_int(plus_plus_int,U),V) = one_one_int )
             => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,U),X2)),aa_int_int(aa_int_fun_int_int(times_times_int,V),Y))),A) ) ) ) ) ) ).

% convex_bound_le
tff(fact_1929_is__num_Ocases,axiom,
    ! [A: int] :
      ( aa_int_o(neg_nu7441568979088483369um_int,A)
     => ( ( A != one_one_int )
       => ( ! [X3: int] :
              ( ( A = aa_int_int(uminus_uminus_int,X3) )
             => ~ aa_int_o(neg_nu7441568979088483369um_int,X3) )
         => ~ ! [X3: int,Y4: int] :
                ( ( A = aa_int_int(aa_int_fun_int_int(plus_plus_int,X3),Y4) )
               => ( aa_int_o(neg_nu7441568979088483369um_int,X3)
                 => ~ aa_int_o(neg_nu7441568979088483369um_int,Y4) ) ) ) ) ) ).

% is_num.cases
tff(fact_1930_is__num_Ocases,axiom,
    ! [A: code_integer] :
      ( aa_Code_integer_o(neg_nu2435721316971906650nteger,A)
     => ( ( A != one_one_Code_integer )
       => ( ! [X3: code_integer] :
              ( ( A = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,X3) )
             => ~ aa_Code_integer_o(neg_nu2435721316971906650nteger,X3) )
         => ~ ! [X3: code_integer,Y4: code_integer] :
                ( ( A = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X3),Y4) )
               => ( aa_Code_integer_o(neg_nu2435721316971906650nteger,X3)
                 => ~ aa_Code_integer_o(neg_nu2435721316971906650nteger,Y4) ) ) ) ) ) ).

% is_num.cases
tff(fact_1931_is__num_Ocases,axiom,
    ! [A: rat] :
      ( aa_rat_o(neg_nu6808929389511037909um_rat,A)
     => ( ( A != one_one_rat )
       => ( ! [X3: rat] :
              ( ( A = aa_rat_rat(uminus_uminus_rat,X3) )
             => ~ aa_rat_o(neg_nu6808929389511037909um_rat,X3) )
         => ~ ! [X3: rat,Y4: rat] :
                ( ( A = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X3),Y4) )
               => ( aa_rat_o(neg_nu6808929389511037909um_rat,X3)
                 => ~ aa_rat_o(neg_nu6808929389511037909um_rat,Y4) ) ) ) ) ) ).

% is_num.cases
tff(fact_1932_is__num_Osimps,axiom,
    ! [A: int] :
      ( aa_int_o(neg_nu7441568979088483369um_int,A)
    <=> ( ( A = one_one_int )
        | ? [X4: int] :
            ( ( A = aa_int_int(uminus_uminus_int,X4) )
            & aa_int_o(neg_nu7441568979088483369um_int,X4) )
        | ? [X4: int,Y3: int] :
            ( ( A = aa_int_int(aa_int_fun_int_int(plus_plus_int,X4),Y3) )
            & aa_int_o(neg_nu7441568979088483369um_int,X4)
            & aa_int_o(neg_nu7441568979088483369um_int,Y3) ) ) ) ).

% is_num.simps
tff(fact_1933_is__num_Osimps,axiom,
    ! [A: code_integer] :
      ( aa_Code_integer_o(neg_nu2435721316971906650nteger,A)
    <=> ( ( A = one_one_Code_integer )
        | ? [X4: code_integer] :
            ( ( A = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,X4) )
            & aa_Code_integer_o(neg_nu2435721316971906650nteger,X4) )
        | ? [X4: code_integer,Y3: code_integer] :
            ( ( A = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X4),Y3) )
            & aa_Code_integer_o(neg_nu2435721316971906650nteger,X4)
            & aa_Code_integer_o(neg_nu2435721316971906650nteger,Y3) ) ) ) ).

% is_num.simps
tff(fact_1934_is__num_Osimps,axiom,
    ! [A: rat] :
      ( aa_rat_o(neg_nu6808929389511037909um_rat,A)
    <=> ( ( A = one_one_rat )
        | ? [X4: rat] :
            ( ( A = aa_rat_rat(uminus_uminus_rat,X4) )
            & aa_rat_o(neg_nu6808929389511037909um_rat,X4) )
        | ? [X4: rat,Y3: rat] :
            ( ( A = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X4),Y3) )
            & aa_rat_o(neg_nu6808929389511037909um_rat,X4)
            & aa_rat_o(neg_nu6808929389511037909um_rat,Y3) ) ) ) ).

% is_num.simps
tff(fact_1935_sum__squares__gt__zero__iff,axiom,
    ! [X2: code_integer,Y: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,X2),X2)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,Y),Y)))
    <=> ( ( X2 != zero_z3403309356797280102nteger )
        | ( Y != zero_z3403309356797280102nteger ) ) ) ).

% sum_squares_gt_zero_iff
tff(fact_1936_sum__squares__gt__zero__iff,axiom,
    ! [X2: rat,Y: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,X2),X2)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,Y),Y)))
    <=> ( ( X2 != zero_zero_rat )
        | ( Y != zero_zero_rat ) ) ) ).

% sum_squares_gt_zero_iff
tff(fact_1937_sum__squares__gt__zero__iff,axiom,
    ! [X2: int,Y: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,X2),X2)),aa_int_int(aa_int_fun_int_int(times_times_int,Y),Y)))
    <=> ( ( X2 != zero_zero_int )
        | ( Y != zero_zero_int ) ) ) ).

% sum_squares_gt_zero_iff
tff(fact_1938_sum__squares__le__zero__iff,axiom,
    ! [X2: code_integer,Y: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,X2),X2)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,Y),Y))),zero_z3403309356797280102nteger)
    <=> ( ( X2 = zero_z3403309356797280102nteger )
        & ( Y = zero_z3403309356797280102nteger ) ) ) ).

% sum_squares_le_zero_iff
tff(fact_1939_sum__squares__le__zero__iff,axiom,
    ! [X2: rat,Y: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,X2),X2)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,Y),Y))),zero_zero_rat)
    <=> ( ( X2 = zero_zero_rat )
        & ( Y = zero_zero_rat ) ) ) ).

% sum_squares_le_zero_iff
tff(fact_1940_sum__squares__le__zero__iff,axiom,
    ! [X2: int,Y: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,X2),X2)),aa_int_int(aa_int_fun_int_int(times_times_int,Y),Y))),zero_zero_int)
    <=> ( ( X2 = zero_zero_int )
        & ( Y = zero_zero_int ) ) ) ).

% sum_squares_le_zero_iff
tff(fact_1941_incr__lemma,axiom,
    ! [D2: int,Z: int,X2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),D2)
     => aa_int_o(aa_int_fun_int_o(ord_less_int,Z),aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(abs_abs_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,X2),Z))),one_one_int)),D2))) ) ).

% incr_lemma
tff(fact_1942_decr__lemma,axiom,
    ! [D2: int,X2: int,Z: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),D2)
     => aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,X2),aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(abs_abs_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,X2),Z))),one_one_int)),D2))),Z) ) ).

% decr_lemma
tff(fact_1943_sum__squares__eq__zero__iff,axiom,
    ! [X2: code_integer,Y: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,X2),X2)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,Y),Y)) = zero_z3403309356797280102nteger )
    <=> ( ( X2 = zero_z3403309356797280102nteger )
        & ( Y = zero_z3403309356797280102nteger ) ) ) ).

% sum_squares_eq_zero_iff
tff(fact_1944_sum__squares__eq__zero__iff,axiom,
    ! [X2: rat,Y: rat] :
      ( ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,X2),X2)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,Y),Y)) = zero_zero_rat )
    <=> ( ( X2 = zero_zero_rat )
        & ( Y = zero_zero_rat ) ) ) ).

% sum_squares_eq_zero_iff
tff(fact_1945_sum__squares__eq__zero__iff,axiom,
    ! [X2: int,Y: int] :
      ( ( aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,X2),X2)),aa_int_int(aa_int_fun_int_int(times_times_int,Y),Y)) = zero_zero_int )
    <=> ( ( X2 = zero_zero_int )
        & ( Y = zero_zero_int ) ) ) ).

% sum_squares_eq_zero_iff
tff(fact_1946_frac__unique__iff,axiom,
    ! [X2: rat,A: rat] :
      ( ( aa_rat_rat(archimedean_frac_rat,X2) = A )
    <=> ( member_rat(aa_rat_rat(minus_minus_rat(X2),A),ring_1_Ints_rat)
        & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),A)
        & aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),one_one_rat) ) ) ).

% frac_unique_iff
tff(fact_1947_scaling__mono,axiom,
    ! [U: rat,V: rat,R2: rat,S: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,U),V)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),R2)
       => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,R2),S)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,U),aa_rat_rat(divide_divide_rat(aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,R2),aa_rat_rat(minus_minus_rat(V),U))),S))),V) ) ) ) ).

% scaling_mono
tff(fact_1948_divide__le__eq__1__neg,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),zero_zero_rat)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(divide_divide_rat(B),A)),one_one_rat)
      <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),B) ) ) ).

% divide_le_eq_1_neg
tff(fact_1949_divide__le__eq__1__pos,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),A)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(divide_divide_rat(B),A)),one_one_rat)
      <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),A) ) ) ).

% divide_le_eq_1_pos
tff(fact_1950_div__by__1,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(divide_divide_int,A),one_one_int) = A ).

% div_by_1
tff(fact_1951_div__by__1,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),one_one_nat) = A ).

% div_by_1
tff(fact_1952_div__by__1,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),one_one_Code_integer) = A ).

% div_by_1
tff(fact_1953_div__by__1,axiom,
    ! [A: rat] : aa_rat_rat(divide_divide_rat(A),one_one_rat) = A ).

% div_by_1
tff(fact_1954_div__by__1,axiom,
    ! [A: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),one_one_Code_natural) = A ).

% div_by_1
tff(fact_1955_div__self,axiom,
    ! [A: int] :
      ( ( A != zero_zero_int )
     => ( aa_int_int(aa_int_fun_int_int(divide_divide_int,A),A) = one_one_int ) ) ).

% div_self
tff(fact_1956_div__self,axiom,
    ! [A: nat] :
      ( ( A != zero_zero_nat )
     => ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),A) = one_one_nat ) ) ).

% div_self
tff(fact_1957_div__self,axiom,
    ! [A: code_integer] :
      ( ( A != zero_z3403309356797280102nteger )
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),A) = one_one_Code_integer ) ) ).

% div_self
tff(fact_1958_div__self,axiom,
    ! [A: rat] :
      ( ( A != zero_zero_rat )
     => ( aa_rat_rat(divide_divide_rat(A),A) = one_one_rat ) ) ).

% div_self
tff(fact_1959_div__self,axiom,
    ! [A: code_natural] :
      ( ( A != zero_z2226904508553997617atural )
     => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),A) = one_one_Code_natural ) ) ).

% div_self
tff(fact_1960_zero__eq__1__divide__iff,axiom,
    ! [A: rat] :
      ( ( zero_zero_rat = aa_rat_rat(divide_divide_rat(one_one_rat),A) )
    <=> ( A = zero_zero_rat ) ) ).

% zero_eq_1_divide_iff
tff(fact_1961_one__divide__eq__0__iff,axiom,
    ! [A: rat] :
      ( ( aa_rat_rat(divide_divide_rat(one_one_rat),A) = zero_zero_rat )
    <=> ( A = zero_zero_rat ) ) ).

% one_divide_eq_0_iff
tff(fact_1962_eq__divide__eq__1,axiom,
    ! [B: rat,A: rat] :
      ( ( one_one_rat = aa_rat_rat(divide_divide_rat(B),A) )
    <=> ( ( A != zero_zero_rat )
        & ( A = B ) ) ) ).

% eq_divide_eq_1
tff(fact_1963_divide__eq__eq__1,axiom,
    ! [B: rat,A: rat] :
      ( ( aa_rat_rat(divide_divide_rat(B),A) = one_one_rat )
    <=> ( ( A != zero_zero_rat )
        & ( A = B ) ) ) ).

% divide_eq_eq_1
tff(fact_1964_divide__self__if,axiom,
    ! [A: rat] :
      aa_rat_rat(divide_divide_rat(A),A) = $ite(A = zero_zero_rat,zero_zero_rat,one_one_rat) ).

% divide_self_if
tff(fact_1965_divide__self,axiom,
    ! [A: rat] :
      ( ( A != zero_zero_rat )
     => ( aa_rat_rat(divide_divide_rat(A),A) = one_one_rat ) ) ).

% divide_self
tff(fact_1966_one__eq__divide__iff,axiom,
    ! [A: rat,B: rat] :
      ( ( one_one_rat = aa_rat_rat(divide_divide_rat(A),B) )
    <=> ( ( B != zero_zero_rat )
        & ( A = B ) ) ) ).

% one_eq_divide_iff
tff(fact_1967_divide__eq__1__iff,axiom,
    ! [A: rat,B: rat] :
      ( ( aa_rat_rat(divide_divide_rat(A),B) = one_one_rat )
    <=> ( ( B != zero_zero_rat )
        & ( A = B ) ) ) ).

% divide_eq_1_iff
tff(fact_1968_divide__minus1,axiom,
    ! [X2: rat] : aa_rat_rat(divide_divide_rat(X2),aa_rat_rat(uminus_uminus_rat,one_one_rat)) = aa_rat_rat(uminus_uminus_rat,X2) ).

% divide_minus1
tff(fact_1969_zero__le__divide__1__iff,axiom,
    ! [A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),aa_rat_rat(divide_divide_rat(one_one_rat),A))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),A) ) ).

% zero_le_divide_1_iff
tff(fact_1970_divide__le__0__1__iff,axiom,
    ! [A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(divide_divide_rat(one_one_rat),A)),zero_zero_rat)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),zero_zero_rat) ) ).

% divide_le_0_1_iff
tff(fact_1971_zero__less__divide__1__iff,axiom,
    ! [A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),aa_rat_rat(divide_divide_rat(one_one_rat),A))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),A) ) ).

% zero_less_divide_1_iff
tff(fact_1972_less__divide__eq__1__pos,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),A)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),aa_rat_rat(divide_divide_rat(B),A))
      <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B) ) ) ).

% less_divide_eq_1_pos
tff(fact_1973_less__divide__eq__1__neg,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),zero_zero_rat)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),aa_rat_rat(divide_divide_rat(B),A))
      <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,B),A) ) ) ).

% less_divide_eq_1_neg
tff(fact_1974_divide__less__eq__1__pos,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),A)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(divide_divide_rat(B),A)),one_one_rat)
      <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,B),A) ) ) ).

% divide_less_eq_1_pos
tff(fact_1975_divide__less__eq__1__neg,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),zero_zero_rat)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(divide_divide_rat(B),A)),one_one_rat)
      <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B) ) ) ).

% divide_less_eq_1_neg
tff(fact_1976_divide__less__0__1__iff,axiom,
    ! [A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(divide_divide_rat(one_one_rat),A)),zero_zero_rat)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),zero_zero_rat) ) ).

% divide_less_0_1_iff
tff(fact_1977_nonzero__divide__mult__cancel__right,axiom,
    ! [B: rat,A: rat] :
      ( ( B != zero_zero_rat )
     => ( aa_rat_rat(divide_divide_rat(B),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),B)) = aa_rat_rat(divide_divide_rat(one_one_rat),A) ) ) ).

% nonzero_divide_mult_cancel_right
tff(fact_1978_nonzero__divide__mult__cancel__left,axiom,
    ! [A: rat,B: rat] :
      ( ( A != zero_zero_rat )
     => ( aa_rat_rat(divide_divide_rat(A),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),B)) = aa_rat_rat(divide_divide_rat(one_one_rat),B) ) ) ).

% nonzero_divide_mult_cancel_left
tff(fact_1979_le__divide__eq__1__pos,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),A)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),aa_rat_rat(divide_divide_rat(B),A))
      <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),B) ) ) ).

% le_divide_eq_1_pos
tff(fact_1980_le__divide__eq__1__neg,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),zero_zero_rat)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),aa_rat_rat(divide_divide_rat(B),A))
      <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),A) ) ) ).

% le_divide_eq_1_neg
tff(fact_1981_int__distrib_I2_J,axiom,
    ! [W: int,Z1: int,Z22: int] : aa_int_int(aa_int_fun_int_int(times_times_int,W),aa_int_int(aa_int_fun_int_int(plus_plus_int,Z1),Z22)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,W),Z1)),aa_int_int(aa_int_fun_int_int(times_times_int,W),Z22)) ).

% int_distrib(2)
tff(fact_1982_int__distrib_I1_J,axiom,
    ! [Z1: int,Z22: int,W: int] : aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,Z1),Z22)),W) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,Z1),W)),aa_int_int(aa_int_fun_int_int(times_times_int,Z22),W)) ).

% int_distrib(1)
tff(fact_1983_plus__int__code_I2_J,axiom,
    ! [L: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,zero_zero_int),L) = L ).

% plus_int_code(2)
tff(fact_1984_plus__int__code_I1_J,axiom,
    ! [K: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,K),zero_zero_int) = K ).

% plus_int_code(1)
tff(fact_1985_zero__integer_Orsp,axiom,
    zero_zero_int = zero_zero_int ).

% zero_integer.rsp
tff(fact_1986_add__divide__distrib,axiom,
    ! [A: rat,B: rat,C: rat] : aa_rat_rat(divide_divide_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),C) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(divide_divide_rat(A),C)),aa_rat_rat(divide_divide_rat(B),C)) ).

% add_divide_distrib
tff(fact_1987_int__div__pos__eq,axiom,
    ! [A: int,B: int,Q3: int,R2: int] :
      ( ( A = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,B),Q3)),R2) )
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),R2)
       => ( aa_int_o(aa_int_fun_int_o(ord_less_int,R2),B)
         => ( aa_int_int(aa_int_fun_int_int(divide_divide_int,A),B) = Q3 ) ) ) ) ).

% int_div_pos_eq
tff(fact_1988_int__div__neg__eq,axiom,
    ! [A: int,B: int,Q3: int,R2: int] :
      ( ( A = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,B),Q3)),R2) )
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,R2),zero_zero_int)
       => ( aa_int_o(aa_int_fun_int_o(ord_less_int,B),R2)
         => ( aa_int_int(aa_int_fun_int_int(divide_divide_int,A),B) = Q3 ) ) ) ) ).

% int_div_neg_eq
tff(fact_1989_split__zdiv,axiom,
    ! [P: fun_int_o,N2: int,K: int] :
      ( aa_int_o(P,aa_int_int(aa_int_fun_int_int(divide_divide_int,N2),K))
    <=> ( ( ( K = zero_zero_int )
         => aa_int_o(P,zero_zero_int) )
        & ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),K)
         => ! [I3: int,J2: int] :
              ( ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),J2)
                & aa_int_o(aa_int_fun_int_o(ord_less_int,J2),K)
                & ( N2 = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,K),I3)),J2) ) )
             => aa_int_o(P,I3) ) )
        & ( aa_int_o(aa_int_fun_int_o(ord_less_int,K),zero_zero_int)
         => ! [I3: int,J2: int] :
              ( ( aa_int_o(aa_int_fun_int_o(ord_less_int,K),J2)
                & aa_int_o(aa_int_fun_int_o(ord_less_eq_int,J2),zero_zero_int)
                & ( N2 = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,K),I3)),J2) ) )
             => aa_int_o(P,I3) ) ) ) ) ).

% split_zdiv
tff(fact_1990_frac__lt__1,axiom,
    ! [X2: rat] : aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(archimedean_frac_rat,X2)),one_one_rat) ).

% frac_lt_1
tff(fact_1991_frac__1__eq,axiom,
    ! [X2: rat] : aa_rat_rat(archimedean_frac_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),one_one_rat)) = aa_rat_rat(archimedean_frac_rat,X2) ).

% frac_1_eq
tff(fact_1992_right__inverse__eq,axiom,
    ! [B: rat,A: rat] :
      ( ( B != zero_zero_rat )
     => ( ( aa_rat_rat(divide_divide_rat(A),B) = one_one_rat )
      <=> ( A = B ) ) ) ).

% right_inverse_eq
tff(fact_1993_less__divide__eq__1,axiom,
    ! [B: rat,A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),aa_rat_rat(divide_divide_rat(B),A))
    <=> ( ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),A)
          & aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B) )
        | ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),zero_zero_rat)
          & aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,B),A) ) ) ) ).

% less_divide_eq_1
tff(fact_1994_divide__less__eq__1,axiom,
    ! [B: rat,A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(divide_divide_rat(B),A)),one_one_rat)
    <=> ( ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),A)
          & aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,B),A) )
        | ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),zero_zero_rat)
          & aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B) )
        | ( A = zero_zero_rat ) ) ) ).

% divide_less_eq_1
tff(fact_1995_divide__add__eq__iff,axiom,
    ! [Z: rat,X2: rat,Y: rat] :
      ( ( Z != zero_zero_rat )
     => ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(divide_divide_rat(X2),Z)),Y) = aa_rat_rat(divide_divide_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,Y),Z))),Z) ) ) ).

% divide_add_eq_iff
tff(fact_1996_add__divide__eq__iff,axiom,
    ! [Z: rat,X2: rat,Y: rat] :
      ( ( Z != zero_zero_rat )
     => ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),aa_rat_rat(divide_divide_rat(Y),Z)) = aa_rat_rat(divide_divide_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,X2),Z)),Y)),Z) ) ) ).

% add_divide_eq_iff
tff(fact_1997_add__num__frac,axiom,
    ! [Y: rat,Z: rat,X2: rat] :
      ( ( Y != zero_zero_rat )
     => ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,Z),aa_rat_rat(divide_divide_rat(X2),Y)) = aa_rat_rat(divide_divide_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,Z),Y))),Y) ) ) ).

% add_num_frac
tff(fact_1998_add__frac__num,axiom,
    ! [Y: rat,X2: rat,Z: rat] :
      ( ( Y != zero_zero_rat )
     => ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(divide_divide_rat(X2),Y)),Z) = aa_rat_rat(divide_divide_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,Z),Y))),Y) ) ) ).

% add_frac_num
tff(fact_1999_add__frac__eq,axiom,
    ! [Y: rat,Z: rat,X2: rat,W: rat] :
      ( ( Y != zero_zero_rat )
     => ( ( Z != zero_zero_rat )
       => ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(divide_divide_rat(X2),Y)),aa_rat_rat(divide_divide_rat(W),Z)) = aa_rat_rat(divide_divide_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,X2),Z)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,W),Y))),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,Y),Z)) ) ) ) ).

% add_frac_eq
tff(fact_2000_add__divide__eq__if__simps_I1_J,axiom,
    ! [A: rat,B: rat,Z: rat] :
      aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),aa_rat_rat(divide_divide_rat(B),Z)) = $ite(Z = zero_zero_rat,A,aa_rat_rat(divide_divide_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),Z)),B)),Z)) ).

% add_divide_eq_if_simps(1)
tff(fact_2001_add__divide__eq__if__simps_I2_J,axiom,
    ! [A: rat,Z: rat,B: rat] :
      aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(divide_divide_rat(A),Z)),B) = $ite(Z = zero_zero_rat,B,aa_rat_rat(divide_divide_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,B),Z))),Z)) ).

% add_divide_eq_if_simps(2)
tff(fact_2002_less__half__sum,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B)
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),aa_rat_rat(divide_divide_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,one_one_rat),one_one_rat))) ) ).

% less_half_sum
tff(fact_2003_gt__half__sum,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B)
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(divide_divide_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,one_one_rat),one_one_rat))),B) ) ).

% gt_half_sum
tff(fact_2004_divide__eq__minus__1__iff,axiom,
    ! [A: rat,B: rat] :
      ( ( aa_rat_rat(divide_divide_rat(A),B) = aa_rat_rat(uminus_uminus_rat,one_one_rat) )
    <=> ( ( B != zero_zero_rat )
        & ( A = aa_rat_rat(uminus_uminus_rat,B) ) ) ) ).

% divide_eq_minus_1_iff
tff(fact_2005_div__pos__geq,axiom,
    ! [L: int,K: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),L)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,L),K)
       => ( aa_int_int(aa_int_fun_int_int(divide_divide_int,K),L) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,K),L)),L)),one_one_int) ) ) ) ).

% div_pos_geq
tff(fact_2006_frac__eq,axiom,
    ! [X2: rat] :
      ( ( aa_rat_rat(archimedean_frac_rat,X2) = X2 )
    <=> ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),X2)
        & aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,X2),one_one_rat) ) ) ).

% frac_eq
tff(fact_2007_frac__add,axiom,
    ! [X2: rat,Y: rat] :
      aa_rat_rat(archimedean_frac_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),Y)) = $ite(aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(archimedean_frac_rat,X2)),aa_rat_rat(archimedean_frac_rat,Y))),one_one_rat),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(archimedean_frac_rat,X2)),aa_rat_rat(archimedean_frac_rat,Y)),aa_rat_rat(minus_minus_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(archimedean_frac_rat,X2)),aa_rat_rat(archimedean_frac_rat,Y))),one_one_rat)) ).

% frac_add
tff(fact_2008_incr__mult__lemma,axiom,
    ! [D2: int,P: fun_int_o,K: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),D2)
     => ( ! [X3: int] :
            ( aa_int_o(P,X3)
           => aa_int_o(P,aa_int_int(aa_int_fun_int_int(plus_plus_int,X3),D2)) )
       => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),K)
         => ! [X: int] :
              ( aa_int_o(P,X)
             => aa_int_o(P,aa_int_int(aa_int_fun_int_int(plus_plus_int,X),aa_int_int(aa_int_fun_int_int(times_times_int,K),D2))) ) ) ) ) ).

% incr_mult_lemma
tff(fact_2009_divide__le__eq__1,axiom,
    ! [B: rat,A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(divide_divide_rat(B),A)),one_one_rat)
    <=> ( ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),A)
          & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),A) )
        | ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),zero_zero_rat)
          & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),B) )
        | ( A = zero_zero_rat ) ) ) ).

% divide_le_eq_1
tff(fact_2010_le__divide__eq__1,axiom,
    ! [B: rat,A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),aa_rat_rat(divide_divide_rat(B),A))
    <=> ( ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),A)
          & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),B) )
        | ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),zero_zero_rat)
          & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),A) ) ) ) ).

% le_divide_eq_1
tff(fact_2011_minus__divide__add__eq__iff,axiom,
    ! [Z: rat,X2: rat,Y: rat] :
      ( ( Z != zero_zero_rat )
     => ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,aa_rat_rat(divide_divide_rat(X2),Z))),Y) = aa_rat_rat(divide_divide_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,X2)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,Y),Z))),Z) ) ) ).

% minus_divide_add_eq_iff
tff(fact_2012_add__divide__eq__if__simps_I3_J,axiom,
    ! [A: rat,Z: rat,B: rat] :
      aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,aa_rat_rat(divide_divide_rat(A),Z))),B) = $ite(Z = zero_zero_rat,B,aa_rat_rat(divide_divide_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,A)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,B),Z))),Z)) ).

% add_divide_eq_if_simps(3)
tff(fact_2013_frac__neg,axiom,
    ! [X2: rat] :
      aa_rat_rat(archimedean_frac_rat,aa_rat_rat(uminus_uminus_rat,X2)) = $ite(member_rat(X2,ring_1_Ints_rat),zero_zero_rat,aa_rat_rat(minus_minus_rat(one_one_rat),aa_rat_rat(archimedean_frac_rat,X2))) ).

% frac_neg
tff(fact_2014_div__mult__self4,axiom,
    ! [B: int,C: int,A: int] :
      ( ( B != zero_zero_int )
     => ( aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,B),C)),A)),B) = aa_int_int(aa_int_fun_int_int(plus_plus_int,C),aa_int_int(aa_int_fun_int_int(divide_divide_int,A),B)) ) ) ).

% div_mult_self4
tff(fact_2015_div__mult__self4,axiom,
    ! [B: nat,C: nat,A: nat] :
      ( ( B != zero_zero_nat )
     => ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),C)),A)),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,C),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),B)) ) ) ).

% div_mult_self4
tff(fact_2016_div__mult__self4,axiom,
    ! [B: code_integer,C: code_integer,A: code_integer] :
      ( ( B != zero_z3403309356797280102nteger )
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,B),C)),A)),B) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,C),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),B)) ) ) ).

% div_mult_self4
tff(fact_2017_div__mult__self4,axiom,
    ! [B: code_natural,C: code_natural,A: code_natural] :
      ( ( B != zero_z2226904508553997617atural )
     => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,B),C)),A)),B) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,C),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),B)) ) ) ).

% div_mult_self4
tff(fact_2018_div__mult__self3,axiom,
    ! [B: int,C: int,A: int] :
      ( ( B != zero_zero_int )
     => ( aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,C),B)),A)),B) = aa_int_int(aa_int_fun_int_int(plus_plus_int,C),aa_int_int(aa_int_fun_int_int(divide_divide_int,A),B)) ) ) ).

% div_mult_self3
tff(fact_2019_div__mult__self3,axiom,
    ! [B: nat,C: nat,A: nat] :
      ( ( B != zero_zero_nat )
     => ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,C),B)),A)),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,C),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),B)) ) ) ).

% div_mult_self3
tff(fact_2020_div__mult__self3,axiom,
    ! [B: code_integer,C: code_integer,A: code_integer] :
      ( ( B != zero_z3403309356797280102nteger )
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,C),B)),A)),B) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,C),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),B)) ) ) ).

% div_mult_self3
tff(fact_2021_div__mult__self3,axiom,
    ! [B: code_natural,C: code_natural,A: code_natural] :
      ( ( B != zero_z2226904508553997617atural )
     => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,C),B)),A)),B) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,C),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),B)) ) ) ).

% div_mult_self3
tff(fact_2022_div__mult__self2,axiom,
    ! [B: int,A: int,C: int] :
      ( ( B != zero_zero_int )
     => ( aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),aa_int_int(aa_int_fun_int_int(times_times_int,B),C))),B) = aa_int_int(aa_int_fun_int_int(plus_plus_int,C),aa_int_int(aa_int_fun_int_int(divide_divide_int,A),B)) ) ) ).

% div_mult_self2
tff(fact_2023_div__mult__self2,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( ( B != zero_zero_nat )
     => ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),C))),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,C),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),B)) ) ) ).

% div_mult_self2
tff(fact_2024_div__mult__self2,axiom,
    ! [B: code_integer,A: code_integer,C: code_integer] :
      ( ( B != zero_z3403309356797280102nteger )
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,B),C))),B) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,C),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),B)) ) ) ).

% div_mult_self2
tff(fact_2025_div__mult__self2,axiom,
    ! [B: code_natural,A: code_natural,C: code_natural] :
      ( ( B != zero_z2226904508553997617atural )
     => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,B),C))),B) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,C),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),B)) ) ) ).

% div_mult_self2
tff(fact_2026_div__mult__self1,axiom,
    ! [B: int,A: int,C: int] :
      ( ( B != zero_zero_int )
     => ( aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),aa_int_int(aa_int_fun_int_int(times_times_int,C),B))),B) = aa_int_int(aa_int_fun_int_int(plus_plus_int,C),aa_int_int(aa_int_fun_int_int(divide_divide_int,A),B)) ) ) ).

% div_mult_self1
tff(fact_2027_div__mult__self1,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( ( B != zero_zero_nat )
     => ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,C),B))),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,C),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),B)) ) ) ).

% div_mult_self1
tff(fact_2028_div__mult__self1,axiom,
    ! [B: code_integer,A: code_integer,C: code_integer] :
      ( ( B != zero_z3403309356797280102nteger )
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,C),B))),B) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,C),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),B)) ) ) ).

% div_mult_self1
tff(fact_2029_div__mult__self1,axiom,
    ! [B: code_natural,A: code_natural,C: code_natural] :
      ( ( B != zero_z2226904508553997617atural )
     => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,C),B))),B) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,C),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),B)) ) ) ).

% div_mult_self1
tff(fact_2030_div__minus1__right,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_int_int(uminus_uminus_int,one_one_int)) = aa_int_int(uminus_uminus_int,A) ).

% div_minus1_right
tff(fact_2031_div__minus1__right,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A) ).

% div_minus1_right
tff(fact_2032_div__pos__neg__trivial,axiom,
    ! [K: int,L: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),K)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,K),L)),zero_zero_int)
       => ( aa_int_int(aa_int_fun_int_int(divide_divide_int,K),L) = aa_int_int(uminus_uminus_int,one_one_int) ) ) ) ).

% div_pos_neg_trivial
tff(fact_2033_bits__div__by__1,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(divide_divide_int,A),one_one_int) = A ).

% bits_div_by_1
tff(fact_2034_bits__div__by__1,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),one_one_nat) = A ).

% bits_div_by_1
tff(fact_2035_bits__div__by__1,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),one_one_Code_integer) = A ).

% bits_div_by_1
tff(fact_2036_bits__div__by__1,axiom,
    ! [A: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),one_one_Code_natural) = A ).

% bits_div_by_1
tff(fact_2037_dividend__less__times__div,axiom,
    ! [N2: nat,M: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,M),N2)))) ) ).

% dividend_less_times_div
tff(fact_2038_dividend__less__div__times,axiom,
    ! [N2: nat,M: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,M),N2)),N2))) ) ).

% dividend_less_div_times
tff(fact_2039_split__div,axiom,
    ! [P: fun_nat_o,M: nat,N2: nat] :
      ( aa_nat_o(P,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,M),N2))
    <=> ( ( ( N2 = zero_zero_nat )
         => aa_nat_o(P,zero_zero_nat) )
        & ( ( N2 != zero_zero_nat )
         => ! [I3: nat,J2: nat] :
              ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,J2),N2)
             => ( ( M = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,N2),I3)),J2) )
               => aa_nat_o(P,I3) ) ) ) ) ) ).

% split_div
tff(fact_2040_div__less__dividend,axiom,
    ! [N2: nat,M: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,one_one_nat),N2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),M)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,M),N2)),M) ) ) ).

% div_less_dividend
tff(fact_2041_div__eq__dividend__iff,axiom,
    ! [M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),M)
     => ( ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,M),N2) = M )
      <=> ( N2 = one_one_nat ) ) ) ).

% div_eq_dividend_iff
tff(fact_2042_div__add__self1,axiom,
    ! [B: int,A: int] :
      ( ( B != zero_zero_int )
     => ( aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,B),A)),B) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,A),B)),one_one_int) ) ) ).

% div_add_self1
tff(fact_2043_div__add__self1,axiom,
    ! [B: nat,A: nat] :
      ( ( B != zero_zero_nat )
     => ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),A)),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),B)),one_one_nat) ) ) ).

% div_add_self1
tff(fact_2044_div__add__self1,axiom,
    ! [B: code_integer,A: code_integer] :
      ( ( B != zero_z3403309356797280102nteger )
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,B),A)),B) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),B)),one_one_Code_integer) ) ) ).

% div_add_self1
tff(fact_2045_div__add__self1,axiom,
    ! [B: code_natural,A: code_natural] :
      ( ( B != zero_z2226904508553997617atural )
     => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,B),A)),B) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),B)),one_one_Code_natural) ) ) ).

% div_add_self1
tff(fact_2046_div__add__self2,axiom,
    ! [B: int,A: int] :
      ( ( B != zero_zero_int )
     => ( aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),B) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,A),B)),one_one_int) ) ) ).

% div_add_self2
tff(fact_2047_div__add__self2,axiom,
    ! [B: nat,A: nat] :
      ( ( B != zero_zero_nat )
     => ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),B) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),B)),one_one_nat) ) ) ).

% div_add_self2
tff(fact_2048_div__add__self2,axiom,
    ! [B: code_integer,A: code_integer] :
      ( ( B != zero_z3403309356797280102nteger )
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)),B) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),B)),one_one_Code_integer) ) ) ).

% div_add_self2
tff(fact_2049_div__add__self2,axiom,
    ! [B: code_natural,A: code_natural] :
      ( ( B != zero_z2226904508553997617atural )
     => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),B)),B) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),B)),one_one_Code_natural) ) ) ).

% div_add_self2
tff(fact_2050_upto_Opinduct,axiom,
    ! [A0: int,A1: int,P: fun_int_fun_int_o] :
      ( aa_Pro4592068669816069595_int_o(accp_P1096762738010456898nt_int(upto_rel),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A0),A1))
     => ( ! [I2: int,J3: int] :
            ( aa_Pro4592068669816069595_int_o(accp_P1096762738010456898nt_int(upto_rel),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,I2),J3))
           => ( ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,I2),J3)
               => aa_int_o(aa_int_fun_int_o(P,aa_int_int(aa_int_fun_int_int(plus_plus_int,I2),one_one_int)),J3) )
             => aa_int_o(aa_int_fun_int_o(P,I2),J3) ) )
       => aa_int_o(aa_int_fun_int_o(P,A0),A1) ) ) ).

% upto.pinduct
tff(fact_2051_eucl__rel__int_Osimps,axiom,
    ! [A1: int,A22: int,A32: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(eucl_rel_int(A1,A22),A32)
    <=> ( ? [K4: int] :
            ( ( A1 = K4 )
            & ( A22 = zero_zero_int )
            & ( A32 = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,zero_zero_int),K4) ) )
        | ? [L3: int,K4: int,Q5: int] :
            ( ( A1 = K4 )
            & ( A22 = L3 )
            & ( A32 = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Q5),zero_zero_int) )
            & ( L3 != zero_zero_int )
            & ( K4 = aa_int_int(aa_int_fun_int_int(times_times_int,Q5),L3) ) )
        | ? [R5: int,L3: int,K4: int,Q5: int] :
            ( ( A1 = K4 )
            & ( A22 = L3 )
            & ( A32 = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Q5),R5) )
            & ( aa_int_int(sgn_sgn_int,R5) = aa_int_int(sgn_sgn_int,L3) )
            & aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(abs_abs_int,R5)),aa_int_int(abs_abs_int,L3))
            & ( K4 = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,Q5),L3)),R5) ) ) ) ) ).

% eucl_rel_int.simps
tff(fact_2052_eucl__rel__int_Ocases,axiom,
    ! [A1: int,A22: int,A32: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(eucl_rel_int(A1,A22),A32)
     => ( ( ( A22 = zero_zero_int )
         => ( A32 != aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,zero_zero_int),A1) ) )
       => ( ! [Q2: int] :
              ( ( A32 = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Q2),zero_zero_int) )
             => ( ( A22 != zero_zero_int )
               => ( A1 != aa_int_int(aa_int_fun_int_int(times_times_int,Q2),A22) ) ) )
         => ~ ! [R: int,Q2: int] :
                ( ( A32 = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Q2),R) )
               => ( ( aa_int_int(sgn_sgn_int,R) = aa_int_int(sgn_sgn_int,A22) )
                 => ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(abs_abs_int,R)),aa_int_int(abs_abs_int,A22))
                   => ( A1 != aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,Q2),A22)),R) ) ) ) ) ) ) ) ).

% eucl_rel_int.cases
tff(fact_2053_eucl__rel__int__iff,axiom,
    ! [K: int,L: int,Q3: int,R2: int] :
      ( aa_Pro4592068669816069595_int_o(eucl_rel_int(K,L),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Q3),R2))
    <=> ( ( K = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,L),Q3)),R2) )
        & $ite(
            aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),L),
            ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),R2)
            & aa_int_o(aa_int_fun_int_o(ord_less_int,R2),L) ),
            $ite(
              aa_int_o(aa_int_fun_int_o(ord_less_int,L),zero_zero_int),
              ( aa_int_o(aa_int_fun_int_o(ord_less_int,L),R2)
              & aa_int_o(aa_int_fun_int_o(ord_less_eq_int,R2),zero_zero_int) ),
              Q3 = zero_zero_int ) ) ) ) ).

% eucl_rel_int_iff
tff(fact_2054_split__neg__lemma,axiom,
    ! [K: int,P: fun_int_fun_int_o,N2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,K),zero_zero_int)
     => ( aa_int_o(aa_int_fun_int_o(P,aa_int_int(aa_int_fun_int_int(divide_divide_int,N2),K)),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,N2),K))
      <=> ! [I3: int,J2: int] :
            ( ( aa_int_o(aa_int_fun_int_o(ord_less_int,K),J2)
              & aa_int_o(aa_int_fun_int_o(ord_less_eq_int,J2),zero_zero_int)
              & ( N2 = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,K),I3)),J2) ) )
           => aa_int_o(aa_int_fun_int_o(P,I3),J2) ) ) ) ).

% split_neg_lemma
tff(fact_2055_split__pos__lemma,axiom,
    ! [K: int,P: fun_int_fun_int_o,N2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),K)
     => ( aa_int_o(aa_int_fun_int_o(P,aa_int_int(aa_int_fun_int_int(divide_divide_int,N2),K)),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,N2),K))
      <=> ! [I3: int,J2: int] :
            ( ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),J2)
              & aa_int_o(aa_int_fun_int_o(ord_less_int,J2),K)
              & ( N2 = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,K),I3)),J2) ) )
           => aa_int_o(aa_int_fun_int_o(P,I3),J2) ) ) ) ).

% split_pos_lemma
tff(fact_2056_mod__add__self2,axiom,
    ! [A: int,B: int] : aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),B) = aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),B) ).

% mod_add_self2
tff(fact_2057_mod__add__self2,axiom,
    ! [A: nat,B: nat] : aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),B) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),B) ).

% mod_add_self2
tff(fact_2058_mod__add__self2,axiom,
    ! [A: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)),B) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),B) ).

% mod_add_self2
tff(fact_2059_mod__add__self2,axiom,
    ! [A: code_natural,B: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),B)),B) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),B) ).

% mod_add_self2
tff(fact_2060_mod__add__self1,axiom,
    ! [B: int,A: int] : aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,B),A)),B) = aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),B) ).

% mod_add_self1
tff(fact_2061_mod__add__self1,axiom,
    ! [B: nat,A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),A)),B) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),B) ).

% mod_add_self1
tff(fact_2062_mod__add__self1,axiom,
    ! [B: code_integer,A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,B),A)),B) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),B) ).

% mod_add_self1
tff(fact_2063_mod__add__self1,axiom,
    ! [B: code_natural,A: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,B),A)),B) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),B) ).

% mod_add_self1
tff(fact_2064_mod__by__1,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),one_one_int) = zero_zero_int ).

% mod_by_1
tff(fact_2065_mod__by__1,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),one_one_nat) = zero_zero_nat ).

% mod_by_1
tff(fact_2066_mod__by__1,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),one_one_Code_integer) = zero_z3403309356797280102nteger ).

% mod_by_1
tff(fact_2067_mod__by__1,axiom,
    ! [A: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),one_one_Code_natural) = zero_z2226904508553997617atural ).

% mod_by_1
tff(fact_2068_bits__mod__by__1,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),one_one_int) = zero_zero_int ).

% bits_mod_by_1
tff(fact_2069_bits__mod__by__1,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),one_one_nat) = zero_zero_nat ).

% bits_mod_by_1
tff(fact_2070_bits__mod__by__1,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),one_one_Code_integer) = zero_z3403309356797280102nteger ).

% bits_mod_by_1
tff(fact_2071_bits__mod__by__1,axiom,
    ! [A: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),one_one_Code_natural) = zero_z2226904508553997617atural ).

% bits_mod_by_1
tff(fact_2072_mod__mult__self1,axiom,
    ! [A: int,C: int,B: int] : aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),aa_int_int(aa_int_fun_int_int(times_times_int,C),B))),B) = aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),B) ).

% mod_mult_self1
tff(fact_2073_mod__mult__self1,axiom,
    ! [A: nat,C: nat,B: nat] : aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,C),B))),B) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),B) ).

% mod_mult_self1
tff(fact_2074_mod__mult__self1,axiom,
    ! [A: code_integer,C: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,C),B))),B) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),B) ).

% mod_mult_self1
tff(fact_2075_mod__mult__self1,axiom,
    ! [A: code_natural,C: code_natural,B: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,C),B))),B) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),B) ).

% mod_mult_self1
tff(fact_2076_mod__mult__self2,axiom,
    ! [A: int,B: int,C: int] : aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),aa_int_int(aa_int_fun_int_int(times_times_int,B),C))),B) = aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),B) ).

% mod_mult_self2
tff(fact_2077_mod__mult__self2,axiom,
    ! [A: nat,B: nat,C: nat] : aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),C))),B) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),B) ).

% mod_mult_self2
tff(fact_2078_mod__mult__self2,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,B),C))),B) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),B) ).

% mod_mult_self2
tff(fact_2079_mod__mult__self2,axiom,
    ! [A: code_natural,B: code_natural,C: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,B),C))),B) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),B) ).

% mod_mult_self2
tff(fact_2080_mod__mult__self3,axiom,
    ! [C: int,B: int,A: int] : aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,C),B)),A)),B) = aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),B) ).

% mod_mult_self3
tff(fact_2081_mod__mult__self3,axiom,
    ! [C: nat,B: nat,A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,C),B)),A)),B) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),B) ).

% mod_mult_self3
tff(fact_2082_mod__mult__self3,axiom,
    ! [C: code_integer,B: code_integer,A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,C),B)),A)),B) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),B) ).

% mod_mult_self3
tff(fact_2083_mod__mult__self3,axiom,
    ! [C: code_natural,B: code_natural,A: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,C),B)),A)),B) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),B) ).

% mod_mult_self3
tff(fact_2084_mod__mult__self4,axiom,
    ! [B: int,C: int,A: int] : aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,B),C)),A)),B) = aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),B) ).

% mod_mult_self4
tff(fact_2085_mod__mult__self4,axiom,
    ! [B: nat,C: nat,A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),C)),A)),B) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),B) ).

% mod_mult_self4
tff(fact_2086_mod__mult__self4,axiom,
    ! [B: code_integer,C: code_integer,A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,B),C)),A)),B) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),B) ).

% mod_mult_self4
tff(fact_2087_mod__mult__self4,axiom,
    ! [B: code_natural,C: code_natural,A: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,B),C)),A)),B) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),B) ).

% mod_mult_self4
tff(fact_2088_mod__minus1__right,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),aa_int_int(uminus_uminus_int,one_one_int)) = zero_zero_int ).

% mod_minus1_right
tff(fact_2089_mod__minus1__right,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) = zero_z3403309356797280102nteger ).

% mod_minus1_right
tff(fact_2090_mod__int__unique,axiom,
    ! [K: int,L: int,Q3: int,R2: int] :
      ( aa_Pro4592068669816069595_int_o(eucl_rel_int(K,L),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Q3),R2))
     => ( aa_int_int(aa_int_fun_int_int(modulo_modulo_int,K),L) = R2 ) ) ).

% mod_int_unique
tff(fact_2091_unique__quotient,axiom,
    ! [A: int,B: int,Q3: int,R2: int,Q4: int,R4: int] :
      ( aa_Pro4592068669816069595_int_o(eucl_rel_int(A,B),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Q3),R2))
     => ( aa_Pro4592068669816069595_int_o(eucl_rel_int(A,B),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Q4),R4))
       => ( Q3 = Q4 ) ) ) ).

% unique_quotient
tff(fact_2092_unique__remainder,axiom,
    ! [A: int,B: int,Q3: int,R2: int,Q4: int,R4: int] :
      ( aa_Pro4592068669816069595_int_o(eucl_rel_int(A,B),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Q3),R2))
     => ( aa_Pro4592068669816069595_int_o(eucl_rel_int(A,B),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Q4),R4))
       => ( R2 = R4 ) ) ) ).

% unique_remainder
tff(fact_2093_full__exhaustive__int_H_Ocases,axiom,
    ! [X2: produc3043004577601930755nt_int] :
      ~ ! [F2: fun_Pr7763680713840462443e_term,D: int,I2: int] : X2 != aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,F2),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,D),I2)) ).

% full_exhaustive_int'.cases
tff(fact_2094_exhaustive__int_H_Ocases,axiom,
    ! [X2: produc4788131091073775919nt_int] :
      ~ ! [F2: fun_in5730379987311621695e_term,D: int,I2: int] : X2 != aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,F2),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,D),I2)) ).

% exhaustive_int'.cases
tff(fact_2095_small__lazy_H_Ocases,axiom,
    ! [X2: product_prod_int_int] :
      ~ ! [D: int,I2: int] : X2 != aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,D),I2) ).

% small_lazy'.cases
tff(fact_2096_eucl__rel__int,axiom,
    ! [K: int,L: int] : aa_Pro4592068669816069595_int_o(eucl_rel_int(K,L),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,K),L)),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,K),L))) ).

% eucl_rel_int
tff(fact_2097_mod__add__right__eq,axiom,
    ! [A: int,B: int,C: int] : aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,B),C))),C) = aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),C) ).

% mod_add_right_eq
tff(fact_2098_mod__add__right__eq,axiom,
    ! [A: nat,B: nat,C: nat] : aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,B),C))),C) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),C) ).

% mod_add_right_eq
tff(fact_2099_mod__add__right__eq,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,B),C))),C) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)),C) ).

% mod_add_right_eq
tff(fact_2100_mod__add__right__eq,axiom,
    ! [A: code_natural,B: code_natural,C: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,B),C))),C) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),B)),C) ).

% mod_add_right_eq
tff(fact_2101_mod__add__left__eq,axiom,
    ! [A: int,C: int,B: int] : aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),C)),B)),C) = aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),C) ).

% mod_add_left_eq
tff(fact_2102_mod__add__left__eq,axiom,
    ! [A: nat,C: nat,B: nat] : aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),C)),B)),C) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),C) ).

% mod_add_left_eq
tff(fact_2103_mod__add__left__eq,axiom,
    ! [A: code_integer,C: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),C)),B)),C) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)),C) ).

% mod_add_left_eq
tff(fact_2104_mod__add__left__eq,axiom,
    ! [A: code_natural,C: code_natural,B: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),C)),B)),C) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),B)),C) ).

% mod_add_left_eq
tff(fact_2105_mod__add__cong,axiom,
    ! [A: int,C: int,A4: int,B: int,B3: int] :
      ( ( aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),C) = aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A4),C) )
     => ( ( aa_int_int(aa_int_fun_int_int(modulo_modulo_int,B),C) = aa_int_int(aa_int_fun_int_int(modulo_modulo_int,B3),C) )
       => ( aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),C) = aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A4),B3)),C) ) ) ) ).

% mod_add_cong
tff(fact_2106_mod__add__cong,axiom,
    ! [A: nat,C: nat,A4: nat,B: nat,B3: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),C) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A4),C) )
     => ( ( aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,B),C) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,B3),C) )
       => ( aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),C) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A4),B3)),C) ) ) ) ).

% mod_add_cong
tff(fact_2107_mod__add__cong,axiom,
    ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B3: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),C) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A4),C) )
     => ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,B),C) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,B3),C) )
       => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)),C) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A4),B3)),C) ) ) ) ).

% mod_add_cong
tff(fact_2108_mod__add__cong,axiom,
    ! [A: code_natural,C: code_natural,A4: code_natural,B: code_natural,B3: code_natural] :
      ( ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),C) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A4),C) )
     => ( ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,B),C) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,B3),C) )
       => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),B)),C) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A4),B3)),C) ) ) ) ).

% mod_add_cong
tff(fact_2109_mod__add__eq,axiom,
    ! [A: int,C: int,B: int] : aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),C)),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,B),C))),C) = aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),C) ).

% mod_add_eq
tff(fact_2110_mod__add__eq,axiom,
    ! [A: nat,C: nat,B: nat] : aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),C)),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,B),C))),C) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),C) ).

% mod_add_eq
tff(fact_2111_mod__add__eq,axiom,
    ! [A: code_integer,C: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),C)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,B),C))),C) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)),C) ).

% mod_add_eq
tff(fact_2112_mod__add__eq,axiom,
    ! [A: code_natural,C: code_natural,B: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),C)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,B),C))),C) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),B)),C) ).

% mod_add_eq
tff(fact_2113_eucl__rel__int__by0,axiom,
    ! [K: int] : aa_Pro4592068669816069595_int_o(eucl_rel_int(K,zero_zero_int),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,zero_zero_int),K)) ).

% eucl_rel_int_by0
tff(fact_2114_div__int__unique,axiom,
    ! [K: int,L: int,Q3: int,R2: int] :
      ( aa_Pro4592068669816069595_int_o(eucl_rel_int(K,L),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Q3),R2))
     => ( aa_int_int(aa_int_fun_int_int(divide_divide_int,K),L) = Q3 ) ) ).

% div_int_unique
tff(fact_2115_mod__eqE,axiom,
    ! [A: int,C: int,B: int] :
      ( ( aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),C) = aa_int_int(aa_int_fun_int_int(modulo_modulo_int,B),C) )
     => ~ ! [D: int] : B != aa_int_int(aa_int_fun_int_int(plus_plus_int,A),aa_int_int(aa_int_fun_int_int(times_times_int,C),D)) ) ).

% mod_eqE
tff(fact_2116_mod__eqE,axiom,
    ! [A: code_integer,C: code_integer,B: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),C) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,B),C) )
     => ~ ! [D: code_integer] : B != aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,C),D)) ) ).

% mod_eqE
tff(fact_2117_div__add1__eq,axiom,
    ! [A: int,B: int,C: int] : aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),C) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,A),C)),aa_int_int(aa_int_fun_int_int(divide_divide_int,B),C))),aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),C)),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,B),C))),C)) ).

% div_add1_eq
tff(fact_2118_div__add1__eq,axiom,
    ! [A: nat,B: nat,C: nat] : aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),C) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),C)),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,B),C))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),C)),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,B),C))),C)) ).

% div_add1_eq
tff(fact_2119_div__add1__eq,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)),C) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),C)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,B),C))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),C)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,B),C))),C)) ).

% div_add1_eq
tff(fact_2120_div__add1__eq,axiom,
    ! [A: code_natural,B: code_natural,C: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),B)),C) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),C)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,B),C))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),C)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,B),C))),C)) ).

% div_add1_eq
tff(fact_2121_mult__div__mod__eq,axiom,
    ! [B: int,A: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,B),aa_int_int(aa_int_fun_int_int(divide_divide_int,A),B))),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),B)) = A ).

% mult_div_mod_eq
tff(fact_2122_mult__div__mod__eq,axiom,
    ! [B: nat,A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),B))),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),B)) = A ).

% mult_div_mod_eq
tff(fact_2123_mult__div__mod__eq,axiom,
    ! [B: code_integer,A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,B),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),B))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),B)) = A ).

% mult_div_mod_eq
tff(fact_2124_mult__div__mod__eq,axiom,
    ! [B: code_natural,A: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,B),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),B))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),B)) = A ).

% mult_div_mod_eq
tff(fact_2125_mod__mult__div__eq,axiom,
    ! [A: int,B: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),B)),aa_int_int(aa_int_fun_int_int(times_times_int,B),aa_int_int(aa_int_fun_int_int(divide_divide_int,A),B))) = A ).

% mod_mult_div_eq
tff(fact_2126_mod__mult__div__eq,axiom,
    ! [A: nat,B: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),B)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),B))) = A ).

% mod_mult_div_eq
tff(fact_2127_mod__mult__div__eq,axiom,
    ! [A: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),B)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,B),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),B))) = A ).

% mod_mult_div_eq
tff(fact_2128_mod__mult__div__eq,axiom,
    ! [A: code_natural,B: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),B)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,B),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),B))) = A ).

% mod_mult_div_eq
tff(fact_2129_mod__div__mult__eq,axiom,
    ! [A: int,B: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),B)),aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,A),B)),B)) = A ).

% mod_div_mult_eq
tff(fact_2130_mod__div__mult__eq,axiom,
    ! [A: nat,B: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),B)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),B)),B)) = A ).

% mod_div_mult_eq
tff(fact_2131_mod__div__mult__eq,axiom,
    ! [A: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),B)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),B)),B)) = A ).

% mod_div_mult_eq
tff(fact_2132_mod__div__mult__eq,axiom,
    ! [A: code_natural,B: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),B)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),B)),B)) = A ).

% mod_div_mult_eq
tff(fact_2133_div__mult__mod__eq,axiom,
    ! [A: int,B: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,A),B)),B)),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),B)) = A ).

% div_mult_mod_eq
tff(fact_2134_div__mult__mod__eq,axiom,
    ! [A: nat,B: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),B)),B)),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),B)) = A ).

% div_mult_mod_eq
tff(fact_2135_div__mult__mod__eq,axiom,
    ! [A: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),B)),B)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),B)) = A ).

% div_mult_mod_eq
tff(fact_2136_div__mult__mod__eq,axiom,
    ! [A: code_natural,B: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),B)),B)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),B)) = A ).

% div_mult_mod_eq
tff(fact_2137_mod__div__decomp,axiom,
    ! [A: int,B: int] : A = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,A),B)),B)),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),B)) ).

% mod_div_decomp
tff(fact_2138_mod__div__decomp,axiom,
    ! [A: nat,B: nat] : A = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),B)),B)),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),B)) ).

% mod_div_decomp
tff(fact_2139_mod__div__decomp,axiom,
    ! [A: code_integer,B: code_integer] : A = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),B)),B)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),B)) ).

% mod_div_decomp
tff(fact_2140_mod__div__decomp,axiom,
    ! [A: code_natural,B: code_natural] : A = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),B)),B)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),B)) ).

% mod_div_decomp
tff(fact_2141_cancel__div__mod__rules_I1_J,axiom,
    ! [A: int,B: int,C: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,A),B)),B)),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),B))),C) = aa_int_int(aa_int_fun_int_int(plus_plus_int,A),C) ).

% cancel_div_mod_rules(1)
tff(fact_2142_cancel__div__mod__rules_I1_J,axiom,
    ! [A: nat,B: nat,C: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),B)),B)),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),B))),C) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C) ).

% cancel_div_mod_rules(1)
tff(fact_2143_cancel__div__mod__rules_I1_J,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),B)),B)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),B))),C) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),C) ).

% cancel_div_mod_rules(1)
tff(fact_2144_cancel__div__mod__rules_I1_J,axiom,
    ! [A: code_natural,B: code_natural,C: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),B)),B)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),B))),C) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),C) ).

% cancel_div_mod_rules(1)
tff(fact_2145_cancel__div__mod__rules_I2_J,axiom,
    ! [B: int,A: int,C: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,B),aa_int_int(aa_int_fun_int_int(divide_divide_int,A),B))),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),B))),C) = aa_int_int(aa_int_fun_int_int(plus_plus_int,A),C) ).

% cancel_div_mod_rules(2)
tff(fact_2146_cancel__div__mod__rules_I2_J,axiom,
    ! [B: nat,A: nat,C: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),B))),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),B))),C) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),C) ).

% cancel_div_mod_rules(2)
tff(fact_2147_cancel__div__mod__rules_I2_J,axiom,
    ! [B: code_integer,A: code_integer,C: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,B),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),B))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),B))),C) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),C) ).

% cancel_div_mod_rules(2)
tff(fact_2148_cancel__div__mod__rules_I2_J,axiom,
    ! [B: code_natural,A: code_natural,C: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,B),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),B))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),B))),C) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),C) ).

% cancel_div_mod_rules(2)
tff(fact_2149_div__mult1__eq,axiom,
    ! [A: int,B: int,C: int] : aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),B)),C) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),aa_int_int(aa_int_fun_int_int(divide_divide_int,B),C))),aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,B),C))),C)) ).

% div_mult1_eq
tff(fact_2150_div__mult1__eq,axiom,
    ! [A: nat,B: nat,C: nat] : aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),B)),C) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,B),C))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,B),C))),C)) ).

% div_mult1_eq
tff(fact_2151_div__mult1__eq,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),B)),C) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,B),C))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,B),C))),C)) ).

% div_mult1_eq
tff(fact_2152_div__mult1__eq,axiom,
    ! [A: code_natural,B: code_natural,C: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,A),B)),C) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,A),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,B),C))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,A),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,B),C))),C)) ).

% div_mult1_eq
tff(fact_2153_eucl__rel__int__dividesI,axiom,
    ! [L: int,K: int,Q3: int] :
      ( ( L != zero_zero_int )
     => ( ( K = aa_int_int(aa_int_fun_int_int(times_times_int,Q3),L) )
       => aa_Pro4592068669816069595_int_o(eucl_rel_int(K,L),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Q3),zero_zero_int)) ) ) ).

% eucl_rel_int_dividesI
tff(fact_2154_div__mod__decomp__int,axiom,
    ! [A2: int,N2: int] : A2 = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,A2),N2)),N2)),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A2),N2)) ).

% div_mod_decomp_int
tff(fact_2155_mod__pos__neg__trivial,axiom,
    ! [K: int,L: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),K)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,K),L)),zero_zero_int)
       => ( aa_int_int(aa_int_fun_int_int(modulo_modulo_int,K),L) = aa_int_int(aa_int_fun_int_int(plus_plus_int,K),L) ) ) ) ).

% mod_pos_neg_trivial
tff(fact_2156_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
    ! [C: code_integer,A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),C)
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,B),C)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,B),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),B)),C))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),B)) ) ) ).

% unique_euclidean_semiring_numeral_class.mod_mult2_eq
tff(fact_2157_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),C)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),C)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),B)),C))),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),B)) ) ) ).

% unique_euclidean_semiring_numeral_class.mod_mult2_eq
tff(fact_2158_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
    ! [C: int,A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),C)
     => ( aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),aa_int_int(aa_int_fun_int_int(times_times_int,B),C)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,B),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,A),B)),C))),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),B)) ) ) ).

% unique_euclidean_semiring_numeral_class.mod_mult2_eq
tff(fact_2159_int__mod__pos__eq,axiom,
    ! [A: int,B: int,Q3: int,R2: int] :
      ( ( A = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,B),Q3)),R2) )
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),R2)
       => ( aa_int_o(aa_int_fun_int_o(ord_less_int,R2),B)
         => ( aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),B) = R2 ) ) ) ) ).

% int_mod_pos_eq
tff(fact_2160_int__mod__neg__eq,axiom,
    ! [A: int,B: int,Q3: int,R2: int] :
      ( ( A = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,B),Q3)),R2) )
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,R2),zero_zero_int)
       => ( aa_int_o(aa_int_fun_int_o(ord_less_int,B),R2)
         => ( aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),B) = R2 ) ) ) ) ).

% int_mod_neg_eq
tff(fact_2161_split__zmod,axiom,
    ! [P: fun_int_o,N2: int,K: int] :
      ( aa_int_o(P,aa_int_int(aa_int_fun_int_int(modulo_modulo_int,N2),K))
    <=> ( ( ( K = zero_zero_int )
         => aa_int_o(P,N2) )
        & ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),K)
         => ! [I3: int,J2: int] :
              ( ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),J2)
                & aa_int_o(aa_int_fun_int_o(ord_less_int,J2),K)
                & ( N2 = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,K),I3)),J2) ) )
             => aa_int_o(P,J2) ) )
        & ( aa_int_o(aa_int_fun_int_o(ord_less_int,K),zero_zero_int)
         => ! [I3: int,J2: int] :
              ( ( aa_int_o(aa_int_fun_int_o(ord_less_int,K),J2)
                & aa_int_o(aa_int_fun_int_o(ord_less_eq_int,J2),zero_zero_int)
                & ( N2 = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,K),I3)),J2) ) )
             => aa_int_o(P,J2) ) ) ) ) ).

% split_zmod
tff(fact_2162_zmod__zmult2__eq,axiom,
    ! [C: int,A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),C)
     => ( aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),aa_int_int(aa_int_fun_int_int(times_times_int,B),C)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,B),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,A),B)),C))),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),B)) ) ) ).

% zmod_zmult2_eq
tff(fact_2163_zminus1__lemma,axiom,
    ! [A: int,B: int,Q3: int,R2: int] :
      ( aa_Pro4592068669816069595_int_o(eucl_rel_int(A,B),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Q3),R2))
     => ( ( B != zero_zero_int )
       => aa_Pro4592068669816069595_int_o(eucl_rel_int(aa_int_int(uminus_uminus_int,A),B),
            aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,
                $ite(R2 = zero_zero_int,aa_int_int(uminus_uminus_int,Q3),aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(uminus_uminus_int,Q3)),one_one_int))),
              $ite(R2 = zero_zero_int,zero_zero_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,B),R2)))) ) ) ).

% zminus1_lemma
tff(fact_2164_eucl__rel__int__remainderI,axiom,
    ! [R2: int,L: int,K: int,Q3: int] :
      ( ( aa_int_int(sgn_sgn_int,R2) = aa_int_int(sgn_sgn_int,L) )
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(abs_abs_int,R2)),aa_int_int(abs_abs_int,L))
       => ( ( K = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,Q3),L)),R2) )
         => aa_Pro4592068669816069595_int_o(eucl_rel_int(K,L),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Q3),R2)) ) ) ) ).

% eucl_rel_int_remainderI
tff(fact_2165_verit__le__mono__div__int,axiom,
    ! [A2: int,B4: int,N2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,A2),B4)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),N2)
       => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,
              aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,A2),N2)),
                $ite(aa_int_int(aa_int_fun_int_int(modulo_modulo_int,B4),N2) = zero_zero_int,one_one_int,zero_zero_int))),aa_int_int(aa_int_fun_int_int(divide_divide_int,B4),N2)) ) ) ).

% verit_le_mono_div_int
tff(fact_2166_bezw__0,axiom,
    ! [X2: nat] : aa_nat4424723855478970923nt_int(bezw(X2),zero_zero_nat) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,one_one_int),zero_zero_int) ).

% bezw_0
tff(fact_2167_verit__le__mono__div,axiom,
    ! [A2: nat,B4: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A2),B4)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,
              aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A2),N2)),
                $ite(aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,B4),N2) = zero_zero_nat,one_one_nat,zero_zero_nat))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,B4),N2)) ) ) ).

% verit_le_mono_div
tff(fact_2168_zero__le__ceiling,axiom,
    ! [X2: rat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),archim2889992004027027881ng_rat(X2))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),X2) ) ).

% zero_le_ceiling
tff(fact_2169_ceiling__less__zero,axiom,
    ! [X2: rat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,archim2889992004027027881ng_rat(X2)),zero_zero_int)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,X2),aa_rat_rat(uminus_uminus_rat,one_one_rat)) ) ).

% ceiling_less_zero
tff(fact_2170_floor__add,axiom,
    ! [X2: rat,Y: rat] :
      archim3151403230148437115or_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),Y)) = $ite(aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(archimedean_frac_rat,X2)),aa_rat_rat(archimedean_frac_rat,Y))),one_one_rat),aa_int_int(aa_int_fun_int_int(plus_plus_int,archim3151403230148437115or_rat(X2)),archim3151403230148437115or_rat(Y)),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,archim3151403230148437115or_rat(X2)),archim3151403230148437115or_rat(Y))),one_one_int)) ).

% floor_add
tff(fact_2171_cpmi,axiom,
    ! [D3: int,P: fun_int_o,P3: fun_int_o,B4: set_int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),D3)
     => ( ? [Z4: int] :
          ! [X3: int] :
            ( aa_int_o(aa_int_fun_int_o(ord_less_int,X3),Z4)
           => ( aa_int_o(P,X3)
            <=> aa_int_o(P3,X3) ) )
       => ( ! [X3: int] :
              ( ! [Xa3: int] :
                  ( member_int(Xa3,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
                 => ! [Xb2: int] :
                      ( member_int(Xb2,B4)
                     => ( X3 != aa_int_int(aa_int_fun_int_int(plus_plus_int,Xb2),Xa3) ) ) )
             => ( aa_int_o(P,X3)
               => aa_int_o(P,aa_int_int(aa_int_fun_int_int(minus_minus_int,X3),D3)) ) )
         => ( ! [X3: int,K3: int] :
                ( aa_int_o(P3,X3)
              <=> aa_int_o(P3,aa_int_int(aa_int_fun_int_int(minus_minus_int,X3),aa_int_int(aa_int_fun_int_int(times_times_int,K3),D3))) )
           => ( ? [X_1: int] : aa_int_o(P,X_1)
            <=> ( ? [X4: int] :
                    ( member_int(X4,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
                    & aa_int_o(P3,X4) )
                | ? [X4: int] :
                    ( member_int(X4,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
                    & ? [Xa2: int] :
                        ( member_int(Xa2,B4)
                        & aa_int_o(P,aa_int_int(aa_int_fun_int_int(plus_plus_int,Xa2),X4)) ) ) ) ) ) ) ) ) ).

% cpmi
tff(fact_2172_cppi,axiom,
    ! [D3: int,P: fun_int_o,P3: fun_int_o,A2: set_int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),D3)
     => ( ? [Z4: int] :
          ! [X3: int] :
            ( aa_int_o(aa_int_fun_int_o(ord_less_int,Z4),X3)
           => ( aa_int_o(P,X3)
            <=> aa_int_o(P3,X3) ) )
       => ( ! [X3: int] :
              ( ! [Xa3: int] :
                  ( member_int(Xa3,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
                 => ! [Xb2: int] :
                      ( member_int(Xb2,A2)
                     => ( X3 != aa_int_int(aa_int_fun_int_int(minus_minus_int,Xb2),Xa3) ) ) )
             => ( aa_int_o(P,X3)
               => aa_int_o(P,aa_int_int(aa_int_fun_int_int(plus_plus_int,X3),D3)) ) )
         => ( ! [X3: int,K3: int] :
                ( aa_int_o(P3,X3)
              <=> aa_int_o(P3,aa_int_int(aa_int_fun_int_int(minus_minus_int,X3),aa_int_int(aa_int_fun_int_int(times_times_int,K3),D3))) )
           => ( ? [X_1: int] : aa_int_o(P,X_1)
            <=> ( ? [X4: int] :
                    ( member_int(X4,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
                    & aa_int_o(P3,X4) )
                | ? [X4: int] :
                    ( member_int(X4,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
                    & ? [Xa2: int] :
                        ( member_int(Xa2,A2)
                        & aa_int_o(P,aa_int_int(aa_int_fun_int_int(minus_minus_int,Xa2),X4)) ) ) ) ) ) ) ) ) ).

% cppi
tff(fact_2173_bset_I6_J,axiom,
    ! [D3: int,B4: set_int,T: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),D3)
     => ! [X: int] :
          ( ! [Xa4: int] :
              ( member_int(Xa4,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
             => ! [Xb3: int] :
                  ( member_int(Xb3,B4)
                 => ( X != aa_int_int(aa_int_fun_int_int(plus_plus_int,Xb3),Xa4) ) ) )
         => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,X),T)
           => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,X),D3)),T) ) ) ) ).

% bset(6)
tff(fact_2174_bset_I8_J,axiom,
    ! [D3: int,T: int,B4: set_int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),D3)
     => ( member_int(aa_int_int(aa_int_fun_int_int(minus_minus_int,T),one_one_int),B4)
       => ! [X: int] :
            ( ! [Xa4: int] :
                ( member_int(Xa4,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
               => ! [Xb3: int] :
                    ( member_int(Xb3,B4)
                   => ( X != aa_int_int(aa_int_fun_int_int(plus_plus_int,Xb3),Xa4) ) ) )
           => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,T),X)
             => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,T),aa_int_int(aa_int_fun_int_int(minus_minus_int,X),D3)) ) ) ) ) ).

% bset(8)
tff(fact_2175_aset_I6_J,axiom,
    ! [D3: int,T: int,A2: set_int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),D3)
     => ( member_int(aa_int_int(aa_int_fun_int_int(plus_plus_int,T),one_one_int),A2)
       => ! [X: int] :
            ( ! [Xa4: int] :
                ( member_int(Xa4,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
               => ! [Xb3: int] :
                    ( member_int(Xb3,A2)
                   => ( X != aa_int_int(aa_int_fun_int_int(minus_minus_int,Xb3),Xa4) ) ) )
           => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,X),T)
             => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,X),D3)),T) ) ) ) ) ).

% aset(6)
tff(fact_2176_atLeastAtMost__iff,axiom,
    ! [I: $o,L: $o,U: $o] :
      ( member_o((I),aa_o_set_o(set_or8904488021354931149Most_o((L)),(U)))
    <=> ( aa_o_o(aa_o_fun_o_o(ord_less_eq_o,(L)),(I))
        & aa_o_o(aa_o_fun_o_o(ord_less_eq_o,(I)),(U)) ) ) ).

% atLeastAtMost_iff
tff(fact_2177_atLeastAtMost__iff,axiom,
    ! [I: set_nat,L: set_nat,U: set_nat] :
      ( member_set_nat(I,set_or4548717258645045905et_nat(L,U))
    <=> ( aa_set_nat_o(ord_less_eq_set_nat(L),I)
        & aa_set_nat_o(ord_less_eq_set_nat(I),U) ) ) ).

% atLeastAtMost_iff
tff(fact_2178_atLeastAtMost__iff,axiom,
    ! [I: rat,L: rat,U: rat] :
      ( member_rat(I,set_or633870826150836451st_rat(L,U))
    <=> ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,L),I)
        & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,I),U) ) ) ).

% atLeastAtMost_iff
tff(fact_2179_atLeastAtMost__iff,axiom,
    ! [I: num,L: num,U: num] :
      ( member_num(I,set_or7049704709247886629st_num(L,U))
    <=> ( aa_num_o(aa_num_fun_num_o(ord_less_eq_num,L),I)
        & aa_num_o(aa_num_fun_num_o(ord_less_eq_num,I),U) ) ) ).

% atLeastAtMost_iff
tff(fact_2180_atLeastAtMost__iff,axiom,
    ! [I: int,L: int,U: int] :
      ( member_int(I,aa_int_set_int(set_or1266510415728281911st_int(L),U))
    <=> ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,L),I)
        & aa_int_o(aa_int_fun_int_o(ord_less_eq_int,I),U) ) ) ).

% atLeastAtMost_iff
tff(fact_2181_atLeastAtMost__iff,axiom,
    ! [I: nat,L: nat,U: nat] :
      ( member_nat(I,aa_nat_set_nat(set_or1269000886237332187st_nat(L),U))
    <=> ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,L),I)
        & aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,I),U) ) ) ).

% atLeastAtMost_iff
tff(fact_2182_atLeastAtMost__iff,axiom,
    ! [I: code_integer,L: code_integer,U: code_integer] :
      ( member_Code_integer(I,aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(L),U))
    <=> ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,L),I)
        & aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,I),U) ) ) ).

% atLeastAtMost_iff
tff(fact_2183_Icc__eq__Icc,axiom,
    ! [L: set_nat,Ha: set_nat,L4: set_nat,H3: set_nat] :
      ( ( set_or4548717258645045905et_nat(L,Ha) = set_or4548717258645045905et_nat(L4,H3) )
    <=> ( ( ( L = L4 )
          & ( Ha = H3 ) )
        | ( ~ aa_set_nat_o(ord_less_eq_set_nat(L),Ha)
          & ~ aa_set_nat_o(ord_less_eq_set_nat(L4),H3) ) ) ) ).

% Icc_eq_Icc
tff(fact_2184_Icc__eq__Icc,axiom,
    ! [L: rat,Ha: rat,L4: rat,H3: rat] :
      ( ( set_or633870826150836451st_rat(L,Ha) = set_or633870826150836451st_rat(L4,H3) )
    <=> ( ( ( L = L4 )
          & ( Ha = H3 ) )
        | ( ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,L),Ha)
          & ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,L4),H3) ) ) ) ).

% Icc_eq_Icc
tff(fact_2185_Icc__eq__Icc,axiom,
    ! [L: num,Ha: num,L4: num,H3: num] :
      ( ( set_or7049704709247886629st_num(L,Ha) = set_or7049704709247886629st_num(L4,H3) )
    <=> ( ( ( L = L4 )
          & ( Ha = H3 ) )
        | ( ~ aa_num_o(aa_num_fun_num_o(ord_less_eq_num,L),Ha)
          & ~ aa_num_o(aa_num_fun_num_o(ord_less_eq_num,L4),H3) ) ) ) ).

% Icc_eq_Icc
tff(fact_2186_Icc__eq__Icc,axiom,
    ! [L: int,Ha: int,L4: int,H3: int] :
      ( ( aa_int_set_int(set_or1266510415728281911st_int(L),Ha) = aa_int_set_int(set_or1266510415728281911st_int(L4),H3) )
    <=> ( ( ( L = L4 )
          & ( Ha = H3 ) )
        | ( ~ aa_int_o(aa_int_fun_int_o(ord_less_eq_int,L),Ha)
          & ~ aa_int_o(aa_int_fun_int_o(ord_less_eq_int,L4),H3) ) ) ) ).

% Icc_eq_Icc
tff(fact_2187_Icc__eq__Icc,axiom,
    ! [L: nat,Ha: nat,L4: nat,H3: nat] :
      ( ( aa_nat_set_nat(set_or1269000886237332187st_nat(L),Ha) = aa_nat_set_nat(set_or1269000886237332187st_nat(L4),H3) )
    <=> ( ( ( L = L4 )
          & ( Ha = H3 ) )
        | ( ~ aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,L),Ha)
          & ~ aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,L4),H3) ) ) ) ).

% Icc_eq_Icc
tff(fact_2188_Icc__eq__Icc,axiom,
    ! [L: code_integer,Ha: code_integer,L4: code_integer,H3: code_integer] :
      ( ( aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(L),Ha) = aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(L4),H3) )
    <=> ( ( ( L = L4 )
          & ( Ha = H3 ) )
        | ( ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,L),Ha)
          & ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,L4),H3) ) ) ) ).

% Icc_eq_Icc
tff(fact_2189_atLeastatMost__subset__iff,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat,D2: set_nat] :
      ( ord_le6893508408891458716et_nat(set_or4548717258645045905et_nat(A,B),set_or4548717258645045905et_nat(C,D2))
    <=> ( ~ aa_set_nat_o(ord_less_eq_set_nat(A),B)
        | ( aa_set_nat_o(ord_less_eq_set_nat(C),A)
          & aa_set_nat_o(ord_less_eq_set_nat(B),D2) ) ) ) ).

% atLeastatMost_subset_iff
tff(fact_2190_atLeastatMost__subset__iff,axiom,
    ! [A: rat,B: rat,C: rat,D2: rat] :
      ( ord_less_eq_set_rat(set_or633870826150836451st_rat(A,B),set_or633870826150836451st_rat(C,D2))
    <=> ( ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),B)
        | ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,C),A)
          & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),D2) ) ) ) ).

% atLeastatMost_subset_iff
tff(fact_2191_atLeastatMost__subset__iff,axiom,
    ! [A: num,B: num,C: num,D2: num] :
      ( ord_less_eq_set_num(set_or7049704709247886629st_num(A,B),set_or7049704709247886629st_num(C,D2))
    <=> ( ~ aa_num_o(aa_num_fun_num_o(ord_less_eq_num,A),B)
        | ( aa_num_o(aa_num_fun_num_o(ord_less_eq_num,C),A)
          & aa_num_o(aa_num_fun_num_o(ord_less_eq_num,B),D2) ) ) ) ).

% atLeastatMost_subset_iff
tff(fact_2192_atLeastatMost__subset__iff,axiom,
    ! [A: int,B: int,C: int,D2: int] :
      ( ord_less_eq_set_int(aa_int_set_int(set_or1266510415728281911st_int(A),B),aa_int_set_int(set_or1266510415728281911st_int(C),D2))
    <=> ( ~ aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),B)
        | ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,C),A)
          & aa_int_o(aa_int_fun_int_o(ord_less_eq_int,B),D2) ) ) ) ).

% atLeastatMost_subset_iff
tff(fact_2193_atLeastatMost__subset__iff,axiom,
    ! [A: nat,B: nat,C: nat,D2: nat] :
      ( aa_set_nat_o(ord_less_eq_set_nat(aa_nat_set_nat(set_or1269000886237332187st_nat(A),B)),aa_nat_set_nat(set_or1269000886237332187st_nat(C),D2))
    <=> ( ~ aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
        | ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,C),A)
          & aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,B),D2) ) ) ) ).

% atLeastatMost_subset_iff
tff(fact_2194_atLeastatMost__subset__iff,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
      ( ord_le7084787975880047091nteger(aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(A),B),aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(C),D2))
    <=> ( ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),B)
        | ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,C),A)
          & aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,B),D2) ) ) ) ).

% atLeastatMost_subset_iff
tff(fact_2195_floor__one,axiom,
    archim3151403230148437115or_rat(one_one_rat) = one_one_int ).

% floor_one
tff(fact_2196_ceiling__one,axiom,
    archim2889992004027027881ng_rat(one_one_rat) = one_one_int ).

% ceiling_one
tff(fact_2197_floor__add2,axiom,
    ! [X2: rat,Y: rat] :
      ( ( member_rat(X2,ring_1_Ints_rat)
        | member_rat(Y,ring_1_Ints_rat) )
     => ( archim3151403230148437115or_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),Y)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,archim3151403230148437115or_rat(X2)),archim3151403230148437115or_rat(Y)) ) ) ).

% floor_add2
tff(fact_2198_zero__less__floor,axiom,
    ! [X2: rat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),archim3151403230148437115or_rat(X2))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),X2) ) ).

% zero_less_floor
tff(fact_2199_floor__le__zero,axiom,
    ! [X2: rat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,archim3151403230148437115or_rat(X2)),zero_zero_int)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,X2),one_one_rat) ) ).

% floor_le_zero
tff(fact_2200_one__le__floor,axiom,
    ! [X2: rat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,one_one_int),archim3151403230148437115or_rat(X2))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),X2) ) ).

% one_le_floor
tff(fact_2201_floor__less__one,axiom,
    ! [X2: rat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,archim3151403230148437115or_rat(X2)),one_one_int)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,X2),one_one_rat) ) ).

% floor_less_one
tff(fact_2202_ceiling__le__one,axiom,
    ! [X2: rat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,archim2889992004027027881ng_rat(X2)),one_one_int)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,X2),one_one_rat) ) ).

% ceiling_le_one
tff(fact_2203_one__less__ceiling,axiom,
    ! [X2: rat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),archim2889992004027027881ng_rat(X2))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),X2) ) ).

% one_less_ceiling
tff(fact_2204_ceiling__add__one,axiom,
    ! [X2: rat] : archim2889992004027027881ng_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),one_one_rat)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,archim2889992004027027881ng_rat(X2)),one_one_int) ).

% ceiling_add_one
tff(fact_2205_floor__diff__one,axiom,
    ! [X2: rat] : archim3151403230148437115or_rat(aa_rat_rat(minus_minus_rat(X2),one_one_rat)) = aa_int_int(aa_int_fun_int_int(minus_minus_int,archim3151403230148437115or_rat(X2)),one_one_int) ).

% floor_diff_one
tff(fact_2206_ceiling__diff__one,axiom,
    ! [X2: rat] : archim2889992004027027881ng_rat(aa_rat_rat(minus_minus_rat(X2),one_one_rat)) = aa_int_int(aa_int_fun_int_int(minus_minus_int,archim2889992004027027881ng_rat(X2)),one_one_int) ).

% ceiling_diff_one
tff(fact_2207_atLeastatMost__psubset__iff,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat,D2: set_nat] :
      ( ord_less_set_set_nat(set_or4548717258645045905et_nat(A,B),set_or4548717258645045905et_nat(C,D2))
    <=> ( ( ~ aa_set_nat_o(ord_less_eq_set_nat(A),B)
          | ( aa_set_nat_o(ord_less_eq_set_nat(C),A)
            & aa_set_nat_o(ord_less_eq_set_nat(B),D2)
            & ( ord_less_set_nat(C,A)
              | ord_less_set_nat(B,D2) ) ) )
        & aa_set_nat_o(ord_less_eq_set_nat(C),D2) ) ) ).

% atLeastatMost_psubset_iff
tff(fact_2208_atLeastatMost__psubset__iff,axiom,
    ! [A: rat,B: rat,C: rat,D2: rat] :
      ( ord_less_set_rat(set_or633870826150836451st_rat(A,B),set_or633870826150836451st_rat(C,D2))
    <=> ( ( ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),B)
          | ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,C),A)
            & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),D2)
            & ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,C),A)
              | aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,B),D2) ) ) )
        & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,C),D2) ) ) ).

% atLeastatMost_psubset_iff
tff(fact_2209_atLeastatMost__psubset__iff,axiom,
    ! [A: num,B: num,C: num,D2: num] :
      ( ord_less_set_num(set_or7049704709247886629st_num(A,B),set_or7049704709247886629st_num(C,D2))
    <=> ( ( ~ aa_num_o(aa_num_fun_num_o(ord_less_eq_num,A),B)
          | ( aa_num_o(aa_num_fun_num_o(ord_less_eq_num,C),A)
            & aa_num_o(aa_num_fun_num_o(ord_less_eq_num,B),D2)
            & ( aa_num_o(aa_num_fun_num_o(ord_less_num,C),A)
              | aa_num_o(aa_num_fun_num_o(ord_less_num,B),D2) ) ) )
        & aa_num_o(aa_num_fun_num_o(ord_less_eq_num,C),D2) ) ) ).

% atLeastatMost_psubset_iff
tff(fact_2210_atLeastatMost__psubset__iff,axiom,
    ! [A: int,B: int,C: int,D2: int] :
      ( ord_less_set_int(aa_int_set_int(set_or1266510415728281911st_int(A),B),aa_int_set_int(set_or1266510415728281911st_int(C),D2))
    <=> ( ( ~ aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),B)
          | ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,C),A)
            & aa_int_o(aa_int_fun_int_o(ord_less_eq_int,B),D2)
            & ( aa_int_o(aa_int_fun_int_o(ord_less_int,C),A)
              | aa_int_o(aa_int_fun_int_o(ord_less_int,B),D2) ) ) )
        & aa_int_o(aa_int_fun_int_o(ord_less_eq_int,C),D2) ) ) ).

% atLeastatMost_psubset_iff
tff(fact_2211_atLeastatMost__psubset__iff,axiom,
    ! [A: nat,B: nat,C: nat,D2: nat] :
      ( ord_less_set_nat(aa_nat_set_nat(set_or1269000886237332187st_nat(A),B),aa_nat_set_nat(set_or1269000886237332187st_nat(C),D2))
    <=> ( ( ~ aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
          | ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,C),A)
            & aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,B),D2)
            & ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,C),A)
              | aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,B),D2) ) ) )
        & aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,C),D2) ) ) ).

% atLeastatMost_psubset_iff
tff(fact_2212_atLeastatMost__psubset__iff,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
      ( ord_le1307284697595431911nteger(aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(A),B),aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(C),D2))
    <=> ( ( ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),B)
          | ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,C),A)
            & aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,B),D2)
            & ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,C),A)
              | aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,B),D2) ) ) )
        & aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,C),D2) ) ) ).

% atLeastatMost_psubset_iff
tff(fact_2213_nat__mod__eq__iff,axiom,
    ! [X2: nat,N2: nat,Y: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X2),N2) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,Y),N2) )
    <=> ? [Q1: nat,Q22: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X2),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,N2),Q1)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Y),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,N2),Q22)) ) ).

% nat_mod_eq_iff
tff(fact_2214_le__floor__add,axiom,
    ! [X2: rat,Y: rat] : aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,archim3151403230148437115or_rat(X2)),archim3151403230148437115or_rat(Y))),archim3151403230148437115or_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),Y))) ).

% le_floor_add
tff(fact_2215_bset_I1_J,axiom,
    ! [D3: int,B4: set_int,P: fun_int_o,Q: fun_int_o] :
      ( ! [X3: int] :
          ( ! [Xa3: int] :
              ( member_int(Xa3,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
             => ! [Xb2: int] :
                  ( member_int(Xb2,B4)
                 => ( X3 != aa_int_int(aa_int_fun_int_int(plus_plus_int,Xb2),Xa3) ) ) )
         => ( aa_int_o(P,X3)
           => aa_int_o(P,aa_int_int(aa_int_fun_int_int(minus_minus_int,X3),D3)) ) )
     => ( ! [X3: int] :
            ( ! [Xa3: int] :
                ( member_int(Xa3,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
               => ! [Xb2: int] :
                    ( member_int(Xb2,B4)
                   => ( X3 != aa_int_int(aa_int_fun_int_int(plus_plus_int,Xb2),Xa3) ) ) )
           => ( aa_int_o(Q,X3)
             => aa_int_o(Q,aa_int_int(aa_int_fun_int_int(minus_minus_int,X3),D3)) ) )
       => ! [X: int] :
            ( ! [Xa4: int] :
                ( member_int(Xa4,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
               => ! [Xb3: int] :
                    ( member_int(Xb3,B4)
                   => ( X != aa_int_int(aa_int_fun_int_int(plus_plus_int,Xb3),Xa4) ) ) )
           => ( ( aa_int_o(P,X)
                & aa_int_o(Q,X) )
             => ( aa_int_o(P,aa_int_int(aa_int_fun_int_int(minus_minus_int,X),D3))
                & aa_int_o(Q,aa_int_int(aa_int_fun_int_int(minus_minus_int,X),D3)) ) ) ) ) ) ).

% bset(1)
tff(fact_2216_bset_I2_J,axiom,
    ! [D3: int,B4: set_int,P: fun_int_o,Q: fun_int_o] :
      ( ! [X3: int] :
          ( ! [Xa3: int] :
              ( member_int(Xa3,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
             => ! [Xb2: int] :
                  ( member_int(Xb2,B4)
                 => ( X3 != aa_int_int(aa_int_fun_int_int(plus_plus_int,Xb2),Xa3) ) ) )
         => ( aa_int_o(P,X3)
           => aa_int_o(P,aa_int_int(aa_int_fun_int_int(minus_minus_int,X3),D3)) ) )
     => ( ! [X3: int] :
            ( ! [Xa3: int] :
                ( member_int(Xa3,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
               => ! [Xb2: int] :
                    ( member_int(Xb2,B4)
                   => ( X3 != aa_int_int(aa_int_fun_int_int(plus_plus_int,Xb2),Xa3) ) ) )
           => ( aa_int_o(Q,X3)
             => aa_int_o(Q,aa_int_int(aa_int_fun_int_int(minus_minus_int,X3),D3)) ) )
       => ! [X: int] :
            ( ! [Xa4: int] :
                ( member_int(Xa4,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
               => ! [Xb3: int] :
                    ( member_int(Xb3,B4)
                   => ( X != aa_int_int(aa_int_fun_int_int(plus_plus_int,Xb3),Xa4) ) ) )
           => ( ( aa_int_o(P,X)
                | aa_int_o(Q,X) )
             => ( aa_int_o(P,aa_int_int(aa_int_fun_int_int(minus_minus_int,X),D3))
                | aa_int_o(Q,aa_int_int(aa_int_fun_int_int(minus_minus_int,X),D3)) ) ) ) ) ) ).

% bset(2)
tff(fact_2217_aset_I1_J,axiom,
    ! [D3: int,A2: set_int,P: fun_int_o,Q: fun_int_o] :
      ( ! [X3: int] :
          ( ! [Xa3: int] :
              ( member_int(Xa3,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
             => ! [Xb2: int] :
                  ( member_int(Xb2,A2)
                 => ( X3 != aa_int_int(aa_int_fun_int_int(minus_minus_int,Xb2),Xa3) ) ) )
         => ( aa_int_o(P,X3)
           => aa_int_o(P,aa_int_int(aa_int_fun_int_int(plus_plus_int,X3),D3)) ) )
     => ( ! [X3: int] :
            ( ! [Xa3: int] :
                ( member_int(Xa3,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
               => ! [Xb2: int] :
                    ( member_int(Xb2,A2)
                   => ( X3 != aa_int_int(aa_int_fun_int_int(minus_minus_int,Xb2),Xa3) ) ) )
           => ( aa_int_o(Q,X3)
             => aa_int_o(Q,aa_int_int(aa_int_fun_int_int(plus_plus_int,X3),D3)) ) )
       => ! [X: int] :
            ( ! [Xa4: int] :
                ( member_int(Xa4,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
               => ! [Xb3: int] :
                    ( member_int(Xb3,A2)
                   => ( X != aa_int_int(aa_int_fun_int_int(minus_minus_int,Xb3),Xa4) ) ) )
           => ( ( aa_int_o(P,X)
                & aa_int_o(Q,X) )
             => ( aa_int_o(P,aa_int_int(aa_int_fun_int_int(plus_plus_int,X),D3))
                & aa_int_o(Q,aa_int_int(aa_int_fun_int_int(plus_plus_int,X),D3)) ) ) ) ) ) ).

% aset(1)
tff(fact_2218_aset_I2_J,axiom,
    ! [D3: int,A2: set_int,P: fun_int_o,Q: fun_int_o] :
      ( ! [X3: int] :
          ( ! [Xa3: int] :
              ( member_int(Xa3,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
             => ! [Xb2: int] :
                  ( member_int(Xb2,A2)
                 => ( X3 != aa_int_int(aa_int_fun_int_int(minus_minus_int,Xb2),Xa3) ) ) )
         => ( aa_int_o(P,X3)
           => aa_int_o(P,aa_int_int(aa_int_fun_int_int(plus_plus_int,X3),D3)) ) )
     => ( ! [X3: int] :
            ( ! [Xa3: int] :
                ( member_int(Xa3,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
               => ! [Xb2: int] :
                    ( member_int(Xb2,A2)
                   => ( X3 != aa_int_int(aa_int_fun_int_int(minus_minus_int,Xb2),Xa3) ) ) )
           => ( aa_int_o(Q,X3)
             => aa_int_o(Q,aa_int_int(aa_int_fun_int_int(plus_plus_int,X3),D3)) ) )
       => ! [X: int] :
            ( ! [Xa4: int] :
                ( member_int(Xa4,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
               => ! [Xb3: int] :
                    ( member_int(Xb3,A2)
                   => ( X != aa_int_int(aa_int_fun_int_int(minus_minus_int,Xb3),Xa4) ) ) )
           => ( ( aa_int_o(P,X)
                | aa_int_o(Q,X) )
             => ( aa_int_o(P,aa_int_int(aa_int_fun_int_int(plus_plus_int,X),D3))
                | aa_int_o(Q,aa_int_int(aa_int_fun_int_int(plus_plus_int,X),D3)) ) ) ) ) ) ).

% aset(2)
tff(fact_2219_nat__mod__eq__lemma,axiom,
    ! [X2: nat,N2: nat,Y: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X2),N2) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,Y),N2) )
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,Y),X2)
       => ? [Q2: nat] : X2 = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Y),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,N2),Q2)) ) ) ).

% nat_mod_eq_lemma
tff(fact_2220_mod__eq__nat2E,axiom,
    ! [M: nat,Q3: nat,N2: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,M),Q3) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,N2),Q3) )
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
       => ~ ! [S4: nat] : N2 != aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,Q3),S4)) ) ) ).

% mod_eq_nat2E
tff(fact_2221_mod__eq__nat1E,axiom,
    ! [M: nat,Q3: nat,N2: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,M),Q3) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,N2),Q3) )
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),M)
       => ~ ! [S4: nat] : M != aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,Q3),S4)) ) ) ).

% mod_eq_nat1E
tff(fact_2222_ceiling__add__le,axiom,
    ! [X2: rat,Y: rat] : aa_int_o(aa_int_fun_int_o(ord_less_eq_int,archim2889992004027027881ng_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),Y))),aa_int_int(aa_int_fun_int_int(plus_plus_int,archim2889992004027027881ng_rat(X2)),archim2889992004027027881ng_rat(Y))) ).

% ceiling_add_le
tff(fact_2223_mod__mult2__eq,axiom,
    ! [M: nat,N2: nat,Q3: nat] : aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,N2),Q3)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,M),N2)),Q3))),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,M),N2)) ).

% mod_mult2_eq
tff(fact_2224_div__mod__decomp,axiom,
    ! [A2: nat,N2: nat] : A2 = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A2),N2)),N2)),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A2),N2)) ).

% div_mod_decomp
tff(fact_2225_one__add__floor,axiom,
    ! [X2: rat] : aa_int_int(aa_int_fun_int_int(plus_plus_int,archim3151403230148437115or_rat(X2)),one_one_int) = archim3151403230148437115or_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),one_one_rat)) ).

% one_add_floor
tff(fact_2226_split__mod,axiom,
    ! [P: fun_nat_o,M: nat,N2: nat] :
      ( aa_nat_o(P,aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,M),N2))
    <=> ( ( ( N2 = zero_zero_nat )
         => aa_nat_o(P,M) )
        & ( ( N2 != zero_zero_nat )
         => ! [I3: nat,J2: nat] :
              ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,J2),N2)
             => ( ( M = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,N2),I3)),J2) )
               => aa_nat_o(P,J2) ) ) ) ) ) ).

% split_mod
tff(fact_2227_bset_I3_J,axiom,
    ! [D3: int,T: int,B4: set_int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),D3)
     => ( member_int(aa_int_int(aa_int_fun_int_int(minus_minus_int,T),one_one_int),B4)
       => ! [X: int] :
            ( ! [Xa4: int] :
                ( member_int(Xa4,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
               => ! [Xb3: int] :
                    ( member_int(Xb3,B4)
                   => ( X != aa_int_int(aa_int_fun_int_int(plus_plus_int,Xb3),Xa4) ) ) )
           => ( ( X = T )
             => ( aa_int_int(aa_int_fun_int_int(minus_minus_int,X),D3) = T ) ) ) ) ) ).

% bset(3)
tff(fact_2228_bset_I4_J,axiom,
    ! [D3: int,T: int,B4: set_int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),D3)
     => ( member_int(T,B4)
       => ! [X: int] :
            ( ! [Xa4: int] :
                ( member_int(Xa4,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
               => ! [Xb3: int] :
                    ( member_int(Xb3,B4)
                   => ( X != aa_int_int(aa_int_fun_int_int(plus_plus_int,Xb3),Xa4) ) ) )
           => ( ( X != T )
             => ( aa_int_int(aa_int_fun_int_int(minus_minus_int,X),D3) != T ) ) ) ) ) ).

% bset(4)
tff(fact_2229_bset_I5_J,axiom,
    ! [D3: int,B4: set_int,T: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),D3)
     => ! [X: int] :
          ( ! [Xa4: int] :
              ( member_int(Xa4,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
             => ! [Xb3: int] :
                  ( member_int(Xb3,B4)
                 => ( X != aa_int_int(aa_int_fun_int_int(plus_plus_int,Xb3),Xa4) ) ) )
         => ( aa_int_o(aa_int_fun_int_o(ord_less_int,X),T)
           => aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,X),D3)),T) ) ) ) ).

% bset(5)
tff(fact_2230_bset_I7_J,axiom,
    ! [D3: int,T: int,B4: set_int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),D3)
     => ( member_int(T,B4)
       => ! [X: int] :
            ( ! [Xa4: int] :
                ( member_int(Xa4,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
               => ! [Xb3: int] :
                    ( member_int(Xb3,B4)
                   => ( X != aa_int_int(aa_int_fun_int_int(plus_plus_int,Xb3),Xa4) ) ) )
           => ( aa_int_o(aa_int_fun_int_o(ord_less_int,T),X)
             => aa_int_o(aa_int_fun_int_o(ord_less_int,T),aa_int_int(aa_int_fun_int_int(minus_minus_int,X),D3)) ) ) ) ) ).

% bset(7)
tff(fact_2231_aset_I3_J,axiom,
    ! [D3: int,T: int,A2: set_int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),D3)
     => ( member_int(aa_int_int(aa_int_fun_int_int(plus_plus_int,T),one_one_int),A2)
       => ! [X: int] :
            ( ! [Xa4: int] :
                ( member_int(Xa4,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
               => ! [Xb3: int] :
                    ( member_int(Xb3,A2)
                   => ( X != aa_int_int(aa_int_fun_int_int(minus_minus_int,Xb3),Xa4) ) ) )
           => ( ( X = T )
             => ( aa_int_int(aa_int_fun_int_int(plus_plus_int,X),D3) = T ) ) ) ) ) ).

% aset(3)
tff(fact_2232_aset_I4_J,axiom,
    ! [D3: int,T: int,A2: set_int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),D3)
     => ( member_int(T,A2)
       => ! [X: int] :
            ( ! [Xa4: int] :
                ( member_int(Xa4,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
               => ! [Xb3: int] :
                    ( member_int(Xb3,A2)
                   => ( X != aa_int_int(aa_int_fun_int_int(minus_minus_int,Xb3),Xa4) ) ) )
           => ( ( X != T )
             => ( aa_int_int(aa_int_fun_int_int(plus_plus_int,X),D3) != T ) ) ) ) ) ).

% aset(4)
tff(fact_2233_aset_I5_J,axiom,
    ! [D3: int,T: int,A2: set_int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),D3)
     => ( member_int(T,A2)
       => ! [X: int] :
            ( ! [Xa4: int] :
                ( member_int(Xa4,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
               => ! [Xb3: int] :
                    ( member_int(Xb3,A2)
                   => ( X != aa_int_int(aa_int_fun_int_int(minus_minus_int,Xb3),Xa4) ) ) )
           => ( aa_int_o(aa_int_fun_int_o(ord_less_int,X),T)
             => aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,X),D3)),T) ) ) ) ) ).

% aset(5)
tff(fact_2234_aset_I7_J,axiom,
    ! [D3: int,A2: set_int,T: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),D3)
     => ! [X: int] :
          ( ! [Xa4: int] :
              ( member_int(Xa4,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
             => ! [Xb3: int] :
                  ( member_int(Xb3,A2)
                 => ( X != aa_int_int(aa_int_fun_int_int(minus_minus_int,Xb3),Xa4) ) ) )
         => ( aa_int_o(aa_int_fun_int_o(ord_less_int,T),X)
           => aa_int_o(aa_int_fun_int_o(ord_less_int,T),aa_int_int(aa_int_fun_int_int(plus_plus_int,X),D3)) ) ) ) ).

% aset(7)
tff(fact_2235_aset_I8_J,axiom,
    ! [D3: int,A2: set_int,T: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),D3)
     => ! [X: int] :
          ( ! [Xa4: int] :
              ( member_int(Xa4,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
             => ! [Xb3: int] :
                  ( member_int(Xb3,A2)
                 => ( X != aa_int_int(aa_int_fun_int_int(minus_minus_int,Xb3),Xa4) ) ) )
         => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,T),X)
           => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,T),aa_int_int(aa_int_fun_int_int(plus_plus_int,X),D3)) ) ) ) ).

% aset(8)
tff(fact_2236_ceiling__divide__lower,axiom,
    ! [Q3: rat,P2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),Q3)
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(minus_minus_rat(aa_int_rat(ring_1_of_int_rat,archim2889992004027027881ng_rat(aa_rat_rat(divide_divide_rat(P2),Q3)))),one_one_rat)),Q3)),P2) ) ).

% ceiling_divide_lower
tff(fact_2237_floor__divide__upper,axiom,
    ! [Q3: rat,P2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),Q3)
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,P2),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_int_rat(ring_1_of_int_rat,archim3151403230148437115or_rat(aa_rat_rat(divide_divide_rat(P2),Q3)))),one_one_rat)),Q3)) ) ).

% floor_divide_upper
tff(fact_2238_power__decreasing__iff,axiom,
    ! [B: code_integer,M: nat,N2: nat] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),B)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,B),one_one_Code_integer)
       => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,B),M)),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,B),N2))
        <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),M) ) ) ) ).

% power_decreasing_iff
tff(fact_2239_power__decreasing__iff,axiom,
    ! [B: rat,M: nat,N2: nat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),B)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,B),one_one_rat)
       => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,B),M)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,B),N2))
        <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),M) ) ) ) ).

% power_decreasing_iff
tff(fact_2240_power__decreasing__iff,axiom,
    ! [B: nat,M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),B)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,B),one_one_nat)
       => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,B),M)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,B),N2))
        <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),M) ) ) ) ).

% power_decreasing_iff
tff(fact_2241_power__decreasing__iff,axiom,
    ! [B: int,M: nat,N2: nat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),B)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,B),one_one_int)
       => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,B),M)),aa_nat_int(aa_int_fun_nat_int(power_power_int,B),N2))
        <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),M) ) ) ) ).

% power_decreasing_iff
tff(fact_2242_divmod__nat__def,axiom,
    ! [M: nat,N2: nat] : aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(divmod_nat,M),N2) = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,M),N2)),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,M),N2)) ).

% divmod_nat_def
tff(fact_2243_distrib__left__NO__MATCH,axiom,
    ! [X2: int,Y: int,A: rat,B: rat,C: rat] :
      ( aa_rat_o(aa_int_fun_rat_o(nO_MATCH_int_rat,aa_int_int(aa_int_fun_int_int(divide_divide_int,X2),Y)),A)
     => ( aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),C)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),B)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),C)) ) ) ).

% distrib_left_NO_MATCH
tff(fact_2244_distrib__left__NO__MATCH,axiom,
    ! [X2: int,Y: int,A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_int_fun_nat_o(nO_MATCH_int_nat,aa_int_int(aa_int_fun_int_int(divide_divide_int,X2),Y)),A)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),C)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),B)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),C)) ) ) ).

% distrib_left_NO_MATCH
tff(fact_2245_distrib__left__NO__MATCH,axiom,
    ! [X2: int,Y: int,A: int,B: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(nO_MATCH_int_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,X2),Y)),A)
     => ( aa_int_int(aa_int_fun_int_int(times_times_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),C)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),B)),aa_int_int(aa_int_fun_int_int(times_times_int,A),C)) ) ) ).

% distrib_left_NO_MATCH
tff(fact_2246_distrib__left__NO__MATCH,axiom,
    ! [X2: nat,Y: nat,A: rat,B: rat,C: rat] :
      ( aa_rat_o(aa_nat_fun_rat_o(nO_MATCH_nat_rat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,X2),Y)),A)
     => ( aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),C)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),B)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),C)) ) ) ).

% distrib_left_NO_MATCH
tff(fact_2247_distrib__left__NO__MATCH,axiom,
    ! [X2: nat,Y: nat,A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(nO_MATCH_nat_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,X2),Y)),A)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),C)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),B)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),C)) ) ) ).

% distrib_left_NO_MATCH
tff(fact_2248_distrib__left__NO__MATCH,axiom,
    ! [X2: nat,Y: nat,A: int,B: int,C: int] :
      ( aa_int_o(aa_nat_fun_int_o(nO_MATCH_nat_int,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,X2),Y)),A)
     => ( aa_int_int(aa_int_fun_int_int(times_times_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),C)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),B)),aa_int_int(aa_int_fun_int_int(times_times_int,A),C)) ) ) ).

% distrib_left_NO_MATCH
tff(fact_2249_distrib__left__NO__MATCH,axiom,
    ! [X2: code_integer,Y: code_integer,A: rat,B: rat,C: rat] :
      ( aa_rat_o(aa_Cod6561327387924323390_rat_o(nO_MAT7795273704451493282er_rat,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,X2),Y)),A)
     => ( aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),C)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),B)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),C)) ) ) ).

% distrib_left_NO_MATCH
tff(fact_2250_distrib__left__NO__MATCH,axiom,
    ! [X2: code_integer,Y: code_integer,A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_Cod1075288278386115654_nat_o(nO_MAT8430403764537989018er_nat,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,X2),Y)),A)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),C)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),B)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),C)) ) ) ).

% distrib_left_NO_MATCH
tff(fact_2251_distrib__left__NO__MATCH,axiom,
    ! [X2: code_integer,Y: code_integer,A: int,B: int,C: int] :
      ( aa_int_o(aa_Cod8477617969808203498_int_o(nO_MAT8427913294028938742er_int,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,X2),Y)),A)
     => ( aa_int_int(aa_int_fun_int_int(times_times_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),C)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),B)),aa_int_int(aa_int_fun_int_int(times_times_int,A),C)) ) ) ).

% distrib_left_NO_MATCH
tff(fact_2252_distrib__left__NO__MATCH,axiom,
    ! [X2: rat,Y: rat,A: rat,B: rat,C: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(nO_MATCH_rat_rat,aa_rat_rat(divide_divide_rat(X2),Y)),A)
     => ( aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),C)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),B)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),C)) ) ) ).

% distrib_left_NO_MATCH
tff(fact_2253_distrib__right__NO__MATCH,axiom,
    ! [X2: int,Y: int,C: rat,A: rat,B: rat] :
      ( aa_rat_o(aa_int_fun_rat_o(nO_MATCH_int_rat,aa_int_int(aa_int_fun_int_int(divide_divide_int,X2),Y)),C)
     => ( aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),C) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),C)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,B),C)) ) ) ).

% distrib_right_NO_MATCH
tff(fact_2254_distrib__right__NO__MATCH,axiom,
    ! [X2: int,Y: int,C: nat,A: nat,B: nat] :
      ( aa_nat_o(aa_int_fun_nat_o(nO_MATCH_int_nat,aa_int_int(aa_int_fun_int_int(divide_divide_int,X2),Y)),C)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),C) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),C)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),C)) ) ) ).

% distrib_right_NO_MATCH
tff(fact_2255_distrib__right__NO__MATCH,axiom,
    ! [X2: int,Y: int,C: int,A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(nO_MATCH_int_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,X2),Y)),C)
     => ( aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),C) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),C)),aa_int_int(aa_int_fun_int_int(times_times_int,B),C)) ) ) ).

% distrib_right_NO_MATCH
tff(fact_2256_distrib__right__NO__MATCH,axiom,
    ! [X2: nat,Y: nat,C: rat,A: rat,B: rat] :
      ( aa_rat_o(aa_nat_fun_rat_o(nO_MATCH_nat_rat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,X2),Y)),C)
     => ( aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),C) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),C)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,B),C)) ) ) ).

% distrib_right_NO_MATCH
tff(fact_2257_distrib__right__NO__MATCH,axiom,
    ! [X2: nat,Y: nat,C: nat,A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(nO_MATCH_nat_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,X2),Y)),C)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),C) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),C)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),C)) ) ) ).

% distrib_right_NO_MATCH
tff(fact_2258_distrib__right__NO__MATCH,axiom,
    ! [X2: nat,Y: nat,C: int,A: int,B: int] :
      ( aa_int_o(aa_nat_fun_int_o(nO_MATCH_nat_int,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,X2),Y)),C)
     => ( aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),C) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),C)),aa_int_int(aa_int_fun_int_int(times_times_int,B),C)) ) ) ).

% distrib_right_NO_MATCH
tff(fact_2259_distrib__right__NO__MATCH,axiom,
    ! [X2: code_integer,Y: code_integer,C: rat,A: rat,B: rat] :
      ( aa_rat_o(aa_Cod6561327387924323390_rat_o(nO_MAT7795273704451493282er_rat,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,X2),Y)),C)
     => ( aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),C) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),C)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,B),C)) ) ) ).

% distrib_right_NO_MATCH
tff(fact_2260_distrib__right__NO__MATCH,axiom,
    ! [X2: code_integer,Y: code_integer,C: nat,A: nat,B: nat] :
      ( aa_nat_o(aa_Cod1075288278386115654_nat_o(nO_MAT8430403764537989018er_nat,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,X2),Y)),C)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),C) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),C)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),C)) ) ) ).

% distrib_right_NO_MATCH
tff(fact_2261_distrib__right__NO__MATCH,axiom,
    ! [X2: code_integer,Y: code_integer,C: int,A: int,B: int] :
      ( aa_int_o(aa_Cod8477617969808203498_int_o(nO_MAT8427913294028938742er_int,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,X2),Y)),C)
     => ( aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),C) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),C)),aa_int_int(aa_int_fun_int_int(times_times_int,B),C)) ) ) ).

% distrib_right_NO_MATCH
tff(fact_2262_distrib__right__NO__MATCH,axiom,
    ! [X2: rat,Y: rat,C: rat,A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(nO_MATCH_rat_rat,aa_rat_rat(divide_divide_rat(X2),Y)),C)
     => ( aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),C) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),C)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,B),C)) ) ) ).

% distrib_right_NO_MATCH
tff(fact_2263_Suc__times__mod__eq,axiom,
    ! [M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(suc,zero_zero_nat)),M)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,M),N2))),M) = one_one_nat ) ) ).

% Suc_times_mod_eq
tff(fact_2264_power__one,axiom,
    ! [N2: nat] : aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,one_one_Code_integer),N2) = one_one_Code_integer ).

% power_one
tff(fact_2265_power__one,axiom,
    ! [N2: nat] : aa_nat_assn(aa_assn_fun_nat_assn(power_power_assn,one_one_assn),N2) = one_one_assn ).

% power_one
tff(fact_2266_power__one,axiom,
    ! [N2: nat] : aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,one_one_rat),N2) = one_one_rat ).

% power_one
tff(fact_2267_power__one,axiom,
    ! [N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,one_one_nat),N2) = one_one_nat ).

% power_one
tff(fact_2268_power__one,axiom,
    ! [N2: nat] : aa_nat_int(aa_int_fun_nat_int(power_power_int,one_one_int),N2) = one_one_int ).

% power_one
tff(fact_2269_add__Suc__right,axiom,
    ! [M: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),aa_nat_nat(suc,N2)) = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)) ).

% add_Suc_right
tff(fact_2270_power__one__right,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),one_one_nat) = A ).

% power_one_right
tff(fact_2271_power__one__right,axiom,
    ! [A: int] : aa_nat_int(aa_int_fun_nat_int(power_power_int,A),one_one_nat) = A ).

% power_one_right
tff(fact_2272_power__inject__exp,axiom,
    ! [A: code_integer,M: nat,N2: nat] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),A)
     => ( ( aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),M) = aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),N2) )
      <=> ( M = N2 ) ) ) ).

% power_inject_exp
tff(fact_2273_power__inject__exp,axiom,
    ! [A: rat,M: nat,N2: nat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),A)
     => ( ( aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),M) = aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),N2) )
      <=> ( M = N2 ) ) ) ).

% power_inject_exp
tff(fact_2274_power__inject__exp,axiom,
    ! [A: nat,M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,one_one_nat),A)
     => ( ( aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),M) = aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),N2) )
      <=> ( M = N2 ) ) ) ).

% power_inject_exp
tff(fact_2275_power__inject__exp,axiom,
    ! [A: int,M: nat,N2: nat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),A)
     => ( ( aa_nat_int(aa_int_fun_nat_int(power_power_int,A),M) = aa_nat_int(aa_int_fun_nat_int(power_power_int,A),N2) )
      <=> ( M = N2 ) ) ) ).

% power_inject_exp
tff(fact_2276_mult__Suc__right,axiom,
    ! [M: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,M),aa_nat_nat(suc,N2)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,M),N2)) ).

% mult_Suc_right
tff(fact_2277_diff__Suc__1,axiom,
    ! [N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(suc,N2)),one_one_nat) = N2 ).

% diff_Suc_1
tff(fact_2278_of__int__eq__1__iff,axiom,
    ! [Z: int] :
      ( ( aa_int_int(ring_1_of_int_int,Z) = one_one_int )
    <=> ( Z = one_one_int ) ) ).

% of_int_eq_1_iff
tff(fact_2279_of__int__eq__1__iff,axiom,
    ! [Z: int] :
      ( ( aa_int_Code_integer(ring_18347121197199848620nteger,Z) = one_one_Code_integer )
    <=> ( Z = one_one_int ) ) ).

% of_int_eq_1_iff
tff(fact_2280_of__int__eq__1__iff,axiom,
    ! [Z: int] :
      ( ( aa_int_rat(ring_1_of_int_rat,Z) = one_one_rat )
    <=> ( Z = one_one_int ) ) ).

% of_int_eq_1_iff
tff(fact_2281_of__int__1,axiom,
    aa_int_int(ring_1_of_int_int,one_one_int) = one_one_int ).

% of_int_1
tff(fact_2282_of__int__1,axiom,
    aa_int_Code_integer(ring_18347121197199848620nteger,one_one_int) = one_one_Code_integer ).

% of_int_1
tff(fact_2283_of__int__1,axiom,
    aa_int_rat(ring_1_of_int_rat,one_one_int) = one_one_rat ).

% of_int_1
tff(fact_2284_of__int__add,axiom,
    ! [W: int,Z: int] : aa_int_int(ring_1_of_int_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,W),Z)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(ring_1_of_int_int,W)),aa_int_int(ring_1_of_int_int,Z)) ).

% of_int_add
tff(fact_2285_of__int__add,axiom,
    ! [W: int,Z: int] : aa_int_Code_integer(ring_18347121197199848620nteger,aa_int_int(aa_int_fun_int_int(plus_plus_int,W),Z)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_int_Code_integer(ring_18347121197199848620nteger,W)),aa_int_Code_integer(ring_18347121197199848620nteger,Z)) ).

% of_int_add
tff(fact_2286_of__int__add,axiom,
    ! [W: int,Z: int] : aa_int_rat(ring_1_of_int_rat,aa_int_int(aa_int_fun_int_int(plus_plus_int,W),Z)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_int_rat(ring_1_of_int_rat,W)),aa_int_rat(ring_1_of_int_rat,Z)) ).

% of_int_add
tff(fact_2287_power__strict__increasing__iff,axiom,
    ! [B: code_integer,X2: nat,Y: nat] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),B)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,B),X2)),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,B),Y))
      <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,X2),Y) ) ) ).

% power_strict_increasing_iff
tff(fact_2288_power__strict__increasing__iff,axiom,
    ! [B: rat,X2: nat,Y: nat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),B)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,B),X2)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,B),Y))
      <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,X2),Y) ) ) ).

% power_strict_increasing_iff
tff(fact_2289_power__strict__increasing__iff,axiom,
    ! [B: nat,X2: nat,Y: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,one_one_nat),B)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,B),X2)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,B),Y))
      <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,X2),Y) ) ) ).

% power_strict_increasing_iff
tff(fact_2290_power__strict__increasing__iff,axiom,
    ! [B: int,X2: nat,Y: nat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),B)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,B),X2)),aa_nat_int(aa_int_fun_nat_int(power_power_int,B),Y))
      <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,X2),Y) ) ) ).

% power_strict_increasing_iff
tff(fact_2291_left__minus__one__mult__self,axiom,
    ! [N2: nat,A: int] : aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(uminus_uminus_int,one_one_int)),N2)),aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(uminus_uminus_int,one_one_int)),N2)),A)) = A ).

% left_minus_one_mult_self
tff(fact_2292_left__minus__one__mult__self,axiom,
    ! [N2: nat,A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),N2)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),N2)),A)) = A ).

% left_minus_one_mult_self
tff(fact_2293_left__minus__one__mult__self,axiom,
    ! [N2: nat,A: rat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),N2)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),N2)),A)) = A ).

% left_minus_one_mult_self
tff(fact_2294_minus__one__mult__self,axiom,
    ! [N2: nat] : aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(uminus_uminus_int,one_one_int)),N2)),aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(uminus_uminus_int,one_one_int)),N2)) = one_one_int ).

% minus_one_mult_self
tff(fact_2295_minus__one__mult__self,axiom,
    ! [N2: nat] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),N2)),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),N2)) = one_one_Code_integer ).

% minus_one_mult_self
tff(fact_2296_minus__one__mult__self,axiom,
    ! [N2: nat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),N2)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),N2)) = one_one_rat ).

% minus_one_mult_self
tff(fact_2297_diff__Suc__diff__eq2,axiom,
    ! [K: nat,J: nat,I: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),J)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,J),K))),I) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(suc,J)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,K),I)) ) ) ).

% diff_Suc_diff_eq2
tff(fact_2298_diff__Suc__diff__eq1,axiom,
    ! [K: nat,J: nat,I: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),J)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,I),aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,J),K))) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K)),aa_nat_nat(suc,J)) ) ) ).

% diff_Suc_diff_eq1
tff(fact_2299_Suc__diff,axiom,
    ! [M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),M)
       => ( aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),M)) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),one_one_nat)) ) ) ) ).

% Suc_diff
tff(fact_2300_Suc__mod__mult__self4,axiom,
    ! [N2: nat,K: nat,M: nat] : aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,N2),K)),M))),N2) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(suc,M)),N2) ).

% Suc_mod_mult_self4
tff(fact_2301_Suc__mod__mult__self3,axiom,
    ! [K: nat,N2: nat,M: nat] : aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,K),N2)),M))),N2) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(suc,M)),N2) ).

% Suc_mod_mult_self3
tff(fact_2302_Suc__mod__mult__self2,axiom,
    ! [M: nat,N2: nat,K: nat] : aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,N2),K)))),N2) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(suc,M)),N2) ).

% Suc_mod_mult_self2
tff(fact_2303_Suc__mod__mult__self1,axiom,
    ! [M: nat,K: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,K),N2)))),N2) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(suc,M)),N2) ).

% Suc_mod_mult_self1
tff(fact_2304_ceiling__add__of__int,axiom,
    ! [X2: rat,Z: int] : archim2889992004027027881ng_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),aa_int_rat(ring_1_of_int_rat,Z))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,archim2889992004027027881ng_rat(X2)),Z) ).

% ceiling_add_of_int
tff(fact_2305_power__strict__decreasing__iff,axiom,
    ! [B: code_integer,M: nat,N2: nat] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),B)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,B),one_one_Code_integer)
       => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,B),M)),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,B),N2))
        <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),M) ) ) ) ).

% power_strict_decreasing_iff
tff(fact_2306_power__strict__decreasing__iff,axiom,
    ! [B: rat,M: nat,N2: nat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),B)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,B),one_one_rat)
       => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,B),M)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,B),N2))
        <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),M) ) ) ) ).

% power_strict_decreasing_iff
tff(fact_2307_power__strict__decreasing__iff,axiom,
    ! [B: nat,M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),B)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,B),one_one_nat)
       => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,B),M)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,B),N2))
        <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),M) ) ) ) ).

% power_strict_decreasing_iff
tff(fact_2308_power__strict__decreasing__iff,axiom,
    ! [B: int,M: nat,N2: nat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),B)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,B),one_one_int)
       => ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,B),M)),aa_nat_int(aa_int_fun_nat_int(power_power_int,B),N2))
        <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),M) ) ) ) ).

% power_strict_decreasing_iff
tff(fact_2309_power__increasing__iff,axiom,
    ! [B: code_integer,X2: nat,Y: nat] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),B)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,B),X2)),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,B),Y))
      <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,X2),Y) ) ) ).

% power_increasing_iff
tff(fact_2310_power__increasing__iff,axiom,
    ! [B: rat,X2: nat,Y: nat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),B)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,B),X2)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,B),Y))
      <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,X2),Y) ) ) ).

% power_increasing_iff
tff(fact_2311_power__increasing__iff,axiom,
    ! [B: nat,X2: nat,Y: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,one_one_nat),B)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,B),X2)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,B),Y))
      <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,X2),Y) ) ) ).

% power_increasing_iff
tff(fact_2312_power__increasing__iff,axiom,
    ! [B: int,X2: nat,Y: nat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),B)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,B),X2)),aa_nat_int(aa_int_fun_nat_int(power_power_int,B),Y))
      <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,X2),Y) ) ) ).

% power_increasing_iff
tff(fact_2313_Suc__diff__1,axiom,
    ! [N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => ( aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)) = N2 ) ) ).

% Suc_diff_1
tff(fact_2314_of__int__1__le__iff,axiom,
    ! [Z: int] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),aa_int_Code_integer(ring_18347121197199848620nteger,Z))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,one_one_int),Z) ) ).

% of_int_1_le_iff
tff(fact_2315_of__int__1__le__iff,axiom,
    ! [Z: int] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),aa_int_rat(ring_1_of_int_rat,Z))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,one_one_int),Z) ) ).

% of_int_1_le_iff
tff(fact_2316_of__int__1__le__iff,axiom,
    ! [Z: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,one_one_int),aa_int_int(ring_1_of_int_int,Z))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,one_one_int),Z) ) ).

% of_int_1_le_iff
tff(fact_2317_of__int__le__1__iff,axiom,
    ! [Z: int] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_int_Code_integer(ring_18347121197199848620nteger,Z)),one_one_Code_integer)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,Z),one_one_int) ) ).

% of_int_le_1_iff
tff(fact_2318_of__int__le__1__iff,axiom,
    ! [Z: int] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_int_rat(ring_1_of_int_rat,Z)),one_one_rat)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,Z),one_one_int) ) ).

% of_int_le_1_iff
tff(fact_2319_of__int__le__1__iff,axiom,
    ! [Z: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(ring_1_of_int_int,Z)),one_one_int)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,Z),one_one_int) ) ).

% of_int_le_1_iff
tff(fact_2320_of__int__less__1__iff,axiom,
    ! [Z: int] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_int_Code_integer(ring_18347121197199848620nteger,Z)),one_one_Code_integer)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,Z),one_one_int) ) ).

% of_int_less_1_iff
tff(fact_2321_of__int__less__1__iff,axiom,
    ! [Z: int] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_int_rat(ring_1_of_int_rat,Z)),one_one_rat)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,Z),one_one_int) ) ).

% of_int_less_1_iff
tff(fact_2322_of__int__less__1__iff,axiom,
    ! [Z: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(ring_1_of_int_int,Z)),one_one_int)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,Z),one_one_int) ) ).

% of_int_less_1_iff
tff(fact_2323_of__int__1__less__iff,axiom,
    ! [Z: int] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),aa_int_Code_integer(ring_18347121197199848620nteger,Z))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),Z) ) ).

% of_int_1_less_iff
tff(fact_2324_of__int__1__less__iff,axiom,
    ! [Z: int] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),aa_int_rat(ring_1_of_int_rat,Z))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),Z) ) ).

% of_int_1_less_iff
tff(fact_2325_of__int__1__less__iff,axiom,
    ! [Z: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),aa_int_int(ring_1_of_int_int,Z))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),Z) ) ).

% of_int_1_less_iff
tff(fact_2326_power__gt1,axiom,
    ! [A: code_integer,N2: nat] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),A)
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),aa_nat_nat(suc,N2))) ) ).

% power_gt1
tff(fact_2327_power__gt1,axiom,
    ! [A: rat,N2: nat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),A)
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),aa_nat_nat(suc,N2))) ) ).

% power_gt1
tff(fact_2328_power__gt1,axiom,
    ! [A: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,one_one_nat),A)
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),aa_nat_nat(suc,N2))) ) ).

% power_gt1
tff(fact_2329_power__gt1,axiom,
    ! [A: int,N2: nat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),A)
     => aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),aa_nat_int(aa_int_fun_nat_int(power_power_int,A),aa_nat_nat(suc,N2))) ) ).

% power_gt1
tff(fact_2330_add__Suc__shift,axiom,
    ! [M: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(suc,M)),N2) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),aa_nat_nat(suc,N2)) ).

% add_Suc_shift
tff(fact_2331_add__Suc,axiom,
    ! [M: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(suc,M)),N2) = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)) ).

% add_Suc
tff(fact_2332_nat__arith_Osuc1,axiom,
    ! [A2: nat,K: nat,A: nat] :
      ( ( A2 = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,K),A) )
     => ( aa_nat_nat(suc,A2) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,K),aa_nat_nat(suc,A)) ) ) ).

% nat_arith.suc1
tff(fact_2333_power__Suc__le__self,axiom,
    ! [A: code_integer,N2: nat] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),A)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),one_one_Code_integer)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),aa_nat_nat(suc,N2))),A) ) ) ).

% power_Suc_le_self
tff(fact_2334_power__Suc__le__self,axiom,
    ! [A: rat,N2: nat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),A)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),one_one_rat)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),aa_nat_nat(suc,N2))),A) ) ) ).

% power_Suc_le_self
tff(fact_2335_power__Suc__le__self,axiom,
    ! [A: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),one_one_nat)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),aa_nat_nat(suc,N2))),A) ) ) ).

% power_Suc_le_self
tff(fact_2336_power__Suc__le__self,axiom,
    ! [A: int,N2: nat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),A)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),one_one_int)
       => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,A),aa_nat_nat(suc,N2))),A) ) ) ).

% power_Suc_le_self
tff(fact_2337_power__Suc__less__one,axiom,
    ! [A: code_integer,N2: nat] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),A)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),one_one_Code_integer)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),aa_nat_nat(suc,N2))),one_one_Code_integer) ) ) ).

% power_Suc_less_one
tff(fact_2338_power__Suc__less__one,axiom,
    ! [A: rat,N2: nat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),A)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),one_one_rat)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),aa_nat_nat(suc,N2))),one_one_rat) ) ) ).

% power_Suc_less_one
tff(fact_2339_power__Suc__less__one,axiom,
    ! [A: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),one_one_nat)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),aa_nat_nat(suc,N2))),one_one_nat) ) ) ).

% power_Suc_less_one
tff(fact_2340_power__Suc__less__one,axiom,
    ! [A: int,N2: nat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),A)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,A),one_one_int)
       => aa_int_o(aa_int_fun_int_o(ord_less_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,A),aa_nat_nat(suc,N2))),one_one_int) ) ) ).

% power_Suc_less_one
tff(fact_2341_power__minus_H,axiom,
    ! [X2: int,N2: nat] :
      ( aa_int_o(aa_int_fun_int_o(nO_MATCH_int_int,one_one_int),X2)
     => ( aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(uminus_uminus_int,X2)),N2) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(uminus_uminus_int,one_one_int)),N2)),aa_nat_int(aa_int_fun_nat_int(power_power_int,X2),N2)) ) ) ).

% power_minus'
tff(fact_2342_power__minus_H,axiom,
    ! [X2: code_integer,N2: nat] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(nO_MAT8252062027627875367nteger,one_one_Code_integer),X2)
     => ( aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,X2)),N2) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),N2)),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,X2),N2)) ) ) ).

% power_minus'
tff(fact_2343_power__minus_H,axiom,
    ! [X2: rat,N2: nat] :
      ( aa_rat_o(aa_rat_fun_rat_o(nO_MATCH_rat_rat,one_one_rat),X2)
     => ( aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(uminus_uminus_rat,X2)),N2) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),N2)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),N2)) ) ) ).

% power_minus'
tff(fact_2344_one__le__power,axiom,
    ! [A: code_integer,N2: nat] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),A)
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),N2)) ) ).

% one_le_power
tff(fact_2345_one__le__power,axiom,
    ! [A: rat,N2: nat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),A)
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),N2)) ) ).

% one_le_power
tff(fact_2346_one__le__power,axiom,
    ! [A: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),A)
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),N2)) ) ).

% one_le_power
tff(fact_2347_one__le__power,axiom,
    ! [A: int,N2: nat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,one_one_int),A)
     => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,one_one_int),aa_nat_int(aa_int_fun_nat_int(power_power_int,A),N2)) ) ).

% one_le_power
tff(fact_2348_left__right__inverse__power,axiom,
    ! [X2: code_integer,Y: code_integer,N2: nat] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,X2),Y) = one_one_Code_integer )
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,X2),N2)),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,Y),N2)) = one_one_Code_integer ) ) ).

% left_right_inverse_power
tff(fact_2349_left__right__inverse__power,axiom,
    ! [X2: assn,Y: assn,N2: nat] :
      ( ( aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,X2),Y) = one_one_assn )
     => ( aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_nat_assn(aa_assn_fun_nat_assn(power_power_assn,X2),N2)),aa_nat_assn(aa_assn_fun_nat_assn(power_power_assn,Y),N2)) = one_one_assn ) ) ).

% left_right_inverse_power
tff(fact_2350_left__right__inverse__power,axiom,
    ! [X2: rat,Y: rat,N2: nat] :
      ( ( aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,X2),Y) = one_one_rat )
     => ( aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),N2)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,Y),N2)) = one_one_rat ) ) ).

% left_right_inverse_power
tff(fact_2351_left__right__inverse__power,axiom,
    ! [X2: nat,Y: nat,N2: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X2),Y) = one_one_nat )
     => ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,X2),N2)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,Y),N2)) = one_one_nat ) ) ).

% left_right_inverse_power
tff(fact_2352_left__right__inverse__power,axiom,
    ! [X2: int,Y: int,N2: nat] :
      ( ( aa_int_int(aa_int_fun_int_int(times_times_int,X2),Y) = one_one_int )
     => ( aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,X2),N2)),aa_nat_int(aa_int_fun_nat_int(power_power_int,Y),N2)) = one_one_int ) ) ).

% left_right_inverse_power
tff(fact_2353_power__0,axiom,
    ! [A: code_integer] : aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),zero_zero_nat) = one_one_Code_integer ).

% power_0
tff(fact_2354_power__0,axiom,
    ! [A: assn] : aa_nat_assn(aa_assn_fun_nat_assn(power_power_assn,A),zero_zero_nat) = one_one_assn ).

% power_0
tff(fact_2355_power__0,axiom,
    ! [A: rat] : aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),zero_zero_nat) = one_one_rat ).

% power_0
tff(fact_2356_power__0,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),zero_zero_nat) = one_one_nat ).

% power_0
tff(fact_2357_power__0,axiom,
    ! [A: int] : aa_nat_int(aa_int_fun_nat_int(power_power_int,A),zero_zero_nat) = one_one_int ).

% power_0
tff(fact_2358_power__one__over,axiom,
    ! [A: rat,N2: nat] : aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(divide_divide_rat(one_one_rat),A)),N2) = aa_rat_rat(divide_divide_rat(one_one_rat),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),N2)) ).

% power_one_over
tff(fact_2359_power__add,axiom,
    ! [A: assn,M: nat,N2: nat] : aa_nat_assn(aa_assn_fun_nat_assn(power_power_assn,A),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_nat_assn(aa_assn_fun_nat_assn(power_power_assn,A),M)),aa_nat_assn(aa_assn_fun_nat_assn(power_power_assn,A),N2)) ).

% power_add
tff(fact_2360_power__add,axiom,
    ! [A: rat,M: nat,N2: nat] : aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),M)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),N2)) ).

% power_add
tff(fact_2361_power__add,axiom,
    ! [A: nat,M: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),M)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),N2)) ).

% power_add
tff(fact_2362_power__add,axiom,
    ! [A: int,M: nat,N2: nat] : aa_nat_int(aa_int_fun_nat_int(power_power_int,A),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,A),M)),aa_nat_int(aa_int_fun_nat_int(power_power_int,A),N2)) ).

% power_add
tff(fact_2363_nat__compl__induct_H,axiom,
    ! [P: fun_nat_o,N2: nat] :
      ( aa_nat_o(P,zero_zero_nat)
     => ( ! [N: nat] :
            ( ! [Nn: nat] :
                ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,Nn),N)
               => aa_nat_o(P,Nn) )
           => aa_nat_o(P,aa_nat_nat(suc,N)) )
       => aa_nat_o(P,N2) ) ) ).

% nat_compl_induct'
tff(fact_2364_nat__compl__induct,axiom,
    ! [P: fun_nat_o,N2: nat] :
      ( aa_nat_o(P,zero_zero_nat)
     => ( ! [N: nat] :
            ( ! [Nn: nat] :
                ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,Nn),N)
               => aa_nat_o(P,Nn) )
           => aa_nat_o(P,aa_nat_nat(suc,N)) )
       => aa_nat_o(P,N2) ) ) ).

% nat_compl_induct
tff(fact_2365_one__is__add,axiom,
    ! [M: nat,N2: nat] :
      ( ( aa_nat_nat(suc,zero_zero_nat) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2) )
    <=> ( ( ( M = aa_nat_nat(suc,zero_zero_nat) )
          & ( N2 = zero_zero_nat ) )
        | ( ( M = zero_zero_nat )
          & ( N2 = aa_nat_nat(suc,zero_zero_nat) ) ) ) ) ).

% one_is_add
tff(fact_2366_add__is__1,axiom,
    ! [M: nat,N2: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2) = aa_nat_nat(suc,zero_zero_nat) )
    <=> ( ( ( M = aa_nat_nat(suc,zero_zero_nat) )
          & ( N2 = zero_zero_nat ) )
        | ( ( M = zero_zero_nat )
          & ( N2 = aa_nat_nat(suc,zero_zero_nat) ) ) ) ) ).

% add_is_1
tff(fact_2367_nat__in__between__eq_I2_J,axiom,
    ! [A: nat,B: nat] :
      ( ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
        & aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,B),aa_nat_nat(suc,A)) )
    <=> ( B = A ) ) ).

% nat_in_between_eq(2)
tff(fact_2368_nat__in__between__eq_I1_J,axiom,
    ! [A: nat,B: nat] :
      ( ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),B)
        & aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,B),aa_nat_nat(suc,A)) )
    <=> ( B = aa_nat_nat(suc,A) ) ) ).

% nat_in_between_eq(1)
tff(fact_2369_less__imp__Suc__add,axiom,
    ! [M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M),N2)
     => ? [K3: nat] : N2 = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),K3)) ) ).

% less_imp_Suc_add
tff(fact_2370_less__iff__Suc__add,axiom,
    ! [M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M),N2)
    <=> ? [K4: nat] : N2 = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),K4)) ) ).

% less_iff_Suc_add
tff(fact_2371_less__add__Suc2,axiom,
    ! [I: nat,M: nat] : aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,I),aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),I))) ).

% less_add_Suc2
tff(fact_2372_less__add__Suc1,axiom,
    ! [I: nat,M: nat] : aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,I),aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),M))) ).

% less_add_Suc1
tff(fact_2373_less__natE,axiom,
    ! [M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M),N2)
     => ~ ! [Q2: nat] : N2 != aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),Q2)) ) ).

% less_natE
tff(fact_2374_Suc__to__right,axiom,
    ! [N2: nat,M: nat] :
      ( ( aa_nat_nat(suc,N2) = M )
     => ( N2 = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),aa_nat_nat(suc,zero_zero_nat)) ) ) ).

% Suc_to_right
tff(fact_2375_One__nat__def,axiom,
    one_one_nat = aa_nat_nat(suc,zero_zero_nat) ).

% One_nat_def
tff(fact_2376_mult__Suc,axiom,
    ! [M: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(suc,M)),N2) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,M),N2)) ).

% mult_Suc
tff(fact_2377_Suc__eq__plus1__left,axiom,
    ! [N2: nat] : aa_nat_nat(suc,N2) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N2) ).

% Suc_eq_plus1_left
tff(fact_2378_plus__1__eq__Suc,axiom,
    aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat) = suc ).

% plus_1_eq_Suc
tff(fact_2379_Suc__eq__plus1,axiom,
    ! [N2: nat] : aa_nat_nat(suc,N2) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),one_one_nat) ).

% Suc_eq_plus1
tff(fact_2380_diff__Suc__eq__diff__pred,axiom,
    ! [M: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),aa_nat_nat(suc,N2)) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),one_one_nat)),N2) ).

% diff_Suc_eq_diff_pred
tff(fact_2381_power__le__one,axiom,
    ! [A: code_integer,N2: nat] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),A)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),one_one_Code_integer)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),N2)),one_one_Code_integer) ) ) ).

% power_le_one
tff(fact_2382_power__le__one,axiom,
    ! [A: rat,N2: nat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),A)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),one_one_rat)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),N2)),one_one_rat) ) ) ).

% power_le_one
tff(fact_2383_power__le__one,axiom,
    ! [A: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),one_one_nat)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),N2)),one_one_nat) ) ) ).

% power_le_one
tff(fact_2384_power__le__one,axiom,
    ! [A: int,N2: nat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),A)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),one_one_int)
       => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,A),N2)),one_one_int) ) ) ).

% power_le_one
tff(fact_2385_power__less__power__Suc,axiom,
    ! [A: code_integer,N2: nat] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),A)
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),N2)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),N2))) ) ).

% power_less_power_Suc
tff(fact_2386_power__less__power__Suc,axiom,
    ! [A: rat,N2: nat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),A)
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),N2)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),N2))) ) ).

% power_less_power_Suc
tff(fact_2387_power__less__power__Suc,axiom,
    ! [A: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,one_one_nat),A)
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),N2)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),N2))) ) ).

% power_less_power_Suc
tff(fact_2388_power__less__power__Suc,axiom,
    ! [A: int,N2: nat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),A)
     => aa_int_o(aa_int_fun_int_o(ord_less_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,A),N2)),aa_int_int(aa_int_fun_int_int(times_times_int,A),aa_nat_int(aa_int_fun_nat_int(power_power_int,A),N2))) ) ).

% power_less_power_Suc
tff(fact_2389_power__gt1__lemma,axiom,
    ! [A: code_integer,N2: nat] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),A)
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),N2))) ) ).

% power_gt1_lemma
tff(fact_2390_power__gt1__lemma,axiom,
    ! [A: rat,N2: nat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),A)
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),N2))) ) ).

% power_gt1_lemma
tff(fact_2391_power__gt1__lemma,axiom,
    ! [A: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,one_one_nat),A)
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),N2))) ) ).

% power_gt1_lemma
tff(fact_2392_power__gt1__lemma,axiom,
    ! [A: int,N2: nat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),A)
     => aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),aa_int_int(aa_int_fun_int_int(times_times_int,A),aa_nat_int(aa_int_fun_nat_int(power_power_int,A),N2))) ) ).

% power_gt1_lemma
tff(fact_2393_power__0__left,axiom,
    ! [N2: nat] :
      aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,zero_z3403309356797280102nteger),N2) = $ite(N2 = zero_zero_nat,one_one_Code_integer,zero_z3403309356797280102nteger) ).

% power_0_left
tff(fact_2394_power__0__left,axiom,
    ! [N2: nat] :
      aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,zero_zero_rat),N2) = $ite(N2 = zero_zero_nat,one_one_rat,zero_zero_rat) ).

% power_0_left
tff(fact_2395_power__0__left,axiom,
    ! [N2: nat] :
      aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,zero_zero_nat),N2) = $ite(N2 = zero_zero_nat,one_one_nat,zero_zero_nat) ).

% power_0_left
tff(fact_2396_power__0__left,axiom,
    ! [N2: nat] :
      aa_nat_int(aa_int_fun_nat_int(power_power_int,zero_zero_int),N2) = $ite(N2 = zero_zero_nat,one_one_int,zero_zero_int) ).

% power_0_left
tff(fact_2397_power__strict__increasing,axiom,
    ! [N2: nat,N5: nat,A: code_integer] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),N5)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),A)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),N2)),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),N5)) ) ) ).

% power_strict_increasing
tff(fact_2398_power__strict__increasing,axiom,
    ! [N2: nat,N5: nat,A: rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),N5)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),A)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),N2)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),N5)) ) ) ).

% power_strict_increasing
tff(fact_2399_power__strict__increasing,axiom,
    ! [N2: nat,N5: nat,A: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),N5)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,one_one_nat),A)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),N2)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),N5)) ) ) ).

% power_strict_increasing
tff(fact_2400_power__strict__increasing,axiom,
    ! [N2: nat,N5: nat,A: int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),N5)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),A)
       => aa_int_o(aa_int_fun_int_o(ord_less_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,A),N2)),aa_nat_int(aa_int_fun_nat_int(power_power_int,A),N5)) ) ) ).

% power_strict_increasing
tff(fact_2401_power__less__imp__less__exp,axiom,
    ! [A: code_integer,M: nat,N2: nat] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),A)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),M)),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),N2))
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M),N2) ) ) ).

% power_less_imp_less_exp
tff(fact_2402_power__less__imp__less__exp,axiom,
    ! [A: rat,M: nat,N2: nat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),A)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),M)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),N2))
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M),N2) ) ) ).

% power_less_imp_less_exp
tff(fact_2403_power__less__imp__less__exp,axiom,
    ! [A: nat,M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,one_one_nat),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),M)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),N2))
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M),N2) ) ) ).

% power_less_imp_less_exp
tff(fact_2404_power__less__imp__less__exp,axiom,
    ! [A: int,M: nat,N2: nat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),A)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,A),M)),aa_nat_int(aa_int_fun_nat_int(power_power_int,A),N2))
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M),N2) ) ) ).

% power_less_imp_less_exp
tff(fact_2405_power__minus,axiom,
    ! [A: int,N2: nat] : aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(uminus_uminus_int,A)),N2) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(uminus_uminus_int,one_one_int)),N2)),aa_nat_int(aa_int_fun_nat_int(power_power_int,A),N2)) ).

% power_minus
tff(fact_2406_power__minus,axiom,
    ! [A: code_integer,N2: nat] : aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A)),N2) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),N2)),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),N2)) ).

% power_minus
tff(fact_2407_power__minus,axiom,
    ! [A: rat,N2: nat] : aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(uminus_uminus_rat,A)),N2) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),N2)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),N2)) ).

% power_minus
tff(fact_2408_power__increasing,axiom,
    ! [N2: nat,N5: nat,A: code_integer] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),N5)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),A)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),N2)),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),N5)) ) ) ).

% power_increasing
tff(fact_2409_power__increasing,axiom,
    ! [N2: nat,N5: nat,A: rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),N5)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),A)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),N2)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),N5)) ) ) ).

% power_increasing
tff(fact_2410_power__increasing,axiom,
    ! [N2: nat,N5: nat,A: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),N5)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),A)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),N2)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),N5)) ) ) ).

% power_increasing
tff(fact_2411_power__increasing,axiom,
    ! [N2: nat,N5: nat,A: int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),N5)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,one_one_int),A)
       => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,A),N2)),aa_nat_int(aa_int_fun_nat_int(power_power_int,A),N5)) ) ) ).

% power_increasing
tff(fact_2412_floor__add__int,axiom,
    ! [X2: rat,Z: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,archim3151403230148437115or_rat(X2)),Z) = archim3151403230148437115or_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),aa_int_rat(ring_1_of_int_rat,Z))) ).

% floor_add_int
tff(fact_2413_int__add__floor,axiom,
    ! [Z: int,X2: rat] : aa_int_int(aa_int_fun_int_int(plus_plus_int,Z),archim3151403230148437115or_rat(X2)) = archim3151403230148437115or_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_int_rat(ring_1_of_int_rat,Z)),X2)) ).

% int_add_floor
tff(fact_2414_nat__induct__non__zero,axiom,
    ! [N2: nat,P: fun_nat_o] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => ( aa_nat_o(P,one_one_nat)
       => ( ! [N: nat] :
              ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N)
             => ( aa_nat_o(P,N)
               => aa_nat_o(P,aa_nat_nat(suc,N)) ) )
         => aa_nat_o(P,N2) ) ) ) ).

% nat_induct_non_zero
tff(fact_2415_of__int__leD,axiom,
    ! [N2: int,X2: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_int_Code_integer(ring_18347121197199848620nteger,N2))),X2)
     => ( ( N2 = zero_zero_int )
        | aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),X2) ) ) ).

% of_int_leD
tff(fact_2416_of__int__leD,axiom,
    ! [N2: int,X2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(abs_abs_rat,aa_int_rat(ring_1_of_int_rat,N2))),X2)
     => ( ( N2 = zero_zero_int )
        | aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),X2) ) ) ).

% of_int_leD
tff(fact_2417_of__int__leD,axiom,
    ! [N2: int,X2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(abs_abs_int,aa_int_int(ring_1_of_int_int,N2))),X2)
     => ( ( N2 = zero_zero_int )
        | aa_int_o(aa_int_fun_int_o(ord_less_eq_int,one_one_int),X2) ) ) ).

% of_int_leD
tff(fact_2418_of__int__lessD,axiom,
    ! [N2: int,X2: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_int_Code_integer(ring_18347121197199848620nteger,N2))),X2)
     => ( ( N2 = zero_zero_int )
        | aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),X2) ) ) ).

% of_int_lessD
tff(fact_2419_of__int__lessD,axiom,
    ! [N2: int,X2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(abs_abs_rat,aa_int_rat(ring_1_of_int_rat,N2))),X2)
     => ( ( N2 = zero_zero_int )
        | aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),X2) ) ) ).

% of_int_lessD
tff(fact_2420_of__int__lessD,axiom,
    ! [N2: int,X2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(abs_abs_int,aa_int_int(ring_1_of_int_int,N2))),X2)
     => ( ( N2 = zero_zero_int )
        | aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),X2) ) ) ).

% of_int_lessD
tff(fact_2421_floor__exists,axiom,
    ! [X2: rat] :
    ? [Z2: int] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_int_rat(ring_1_of_int_rat,Z2)),X2)
      & aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,X2),aa_int_rat(ring_1_of_int_rat,aa_int_int(aa_int_fun_int_int(plus_plus_int,Z2),one_one_int))) ) ).

% floor_exists
tff(fact_2422_floor__exists1,axiom,
    ! [X2: rat] :
    ? [X3: int] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_int_rat(ring_1_of_int_rat,X3)),X2)
      & aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,X2),aa_int_rat(ring_1_of_int_rat,aa_int_int(aa_int_fun_int_int(plus_plus_int,X3),one_one_int)))
      & ! [Y5: int] :
          ( ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_int_rat(ring_1_of_int_rat,Y5)),X2)
            & aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,X2),aa_int_rat(ring_1_of_int_rat,aa_int_int(aa_int_fun_int_int(plus_plus_int,Y5),one_one_int))) )
         => ( Y5 = X3 ) ) ) ).

% floor_exists1
tff(fact_2423_power__Suc__less,axiom,
    ! [A: code_integer,N2: nat] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),A)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),one_one_Code_integer)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),N2))),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),N2)) ) ) ).

% power_Suc_less
tff(fact_2424_power__Suc__less,axiom,
    ! [A: rat,N2: nat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),A)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),one_one_rat)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),N2))),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),N2)) ) ) ).

% power_Suc_less
tff(fact_2425_power__Suc__less,axiom,
    ! [A: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),one_one_nat)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),N2))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),N2)) ) ) ).

% power_Suc_less
tff(fact_2426_power__Suc__less,axiom,
    ! [A: int,N2: nat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),A)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,A),one_one_int)
       => aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),aa_nat_int(aa_int_fun_nat_int(power_power_int,A),N2))),aa_nat_int(aa_int_fun_nat_int(power_power_int,A),N2)) ) ) ).

% power_Suc_less
tff(fact_2427_power__strict__decreasing,axiom,
    ! [N2: nat,N5: nat,A: code_integer] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),N5)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),A)
       => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),one_one_Code_integer)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),N5)),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),N2)) ) ) ) ).

% power_strict_decreasing
tff(fact_2428_power__strict__decreasing,axiom,
    ! [N2: nat,N5: nat,A: rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),N5)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),A)
       => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),one_one_rat)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),N5)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),N2)) ) ) ) ).

% power_strict_decreasing
tff(fact_2429_power__strict__decreasing,axiom,
    ! [N2: nat,N5: nat,A: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),N5)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),A)
       => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),one_one_nat)
         => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),N5)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),N2)) ) ) ) ).

% power_strict_decreasing
tff(fact_2430_power__strict__decreasing,axiom,
    ! [N2: nat,N5: nat,A: int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),N5)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),A)
       => ( aa_int_o(aa_int_fun_int_o(ord_less_int,A),one_one_int)
         => aa_int_o(aa_int_fun_int_o(ord_less_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,A),N5)),aa_nat_int(aa_int_fun_nat_int(power_power_int,A),N2)) ) ) ) ).

% power_strict_decreasing
tff(fact_2431_power__decreasing,axiom,
    ! [N2: nat,N5: nat,A: code_integer] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),N5)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),A)
       => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),one_one_Code_integer)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),N5)),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),N2)) ) ) ) ).

% power_decreasing
tff(fact_2432_power__decreasing,axiom,
    ! [N2: nat,N5: nat,A: rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),N5)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),A)
       => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),one_one_rat)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),N5)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),N2)) ) ) ) ).

% power_decreasing
tff(fact_2433_power__decreasing,axiom,
    ! [N2: nat,N5: nat,A: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),N5)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),A)
       => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),one_one_nat)
         => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),N5)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),N2)) ) ) ) ).

% power_decreasing
tff(fact_2434_power__decreasing,axiom,
    ! [N2: nat,N5: nat,A: int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),N5)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),A)
       => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),one_one_int)
         => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,A),N5)),aa_nat_int(aa_int_fun_nat_int(power_power_int,A),N2)) ) ) ) ).

% power_decreasing
tff(fact_2435_power__le__imp__le__exp,axiom,
    ! [A: code_integer,M: nat,N2: nat] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),A)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),M)),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),N2))
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2) ) ) ).

% power_le_imp_le_exp
tff(fact_2436_power__le__imp__le__exp,axiom,
    ! [A: rat,M: nat,N2: nat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),A)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),M)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),N2))
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2) ) ) ).

% power_le_imp_le_exp
tff(fact_2437_power__le__imp__le__exp,axiom,
    ! [A: nat,M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,one_one_nat),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),M)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),N2))
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2) ) ) ).

% power_le_imp_le_exp
tff(fact_2438_power__le__imp__le__exp,axiom,
    ! [A: int,M: nat,N2: nat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),A)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,A),M)),aa_nat_int(aa_int_fun_nat_int(power_power_int,A),N2))
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2) ) ) ).

% power_le_imp_le_exp
tff(fact_2439_self__le__power,axiom,
    ! [A: code_integer,N2: nat] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),N2)) ) ) ).

% self_le_power
tff(fact_2440_self__le__power,axiom,
    ! [A: rat,N2: nat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),N2)) ) ) ).

% self_le_power
tff(fact_2441_self__le__power,axiom,
    ! [A: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),N2)) ) ) ).

% self_le_power
tff(fact_2442_self__le__power,axiom,
    ! [A: int,N2: nat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,one_one_int),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
       => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),aa_nat_int(aa_int_fun_nat_int(power_power_int,A),N2)) ) ) ).

% self_le_power
tff(fact_2443_one__less__power,axiom,
    ! [A: code_integer,N2: nat] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),N2)) ) ) ).

% one_less_power
tff(fact_2444_one__less__power,axiom,
    ! [A: rat,N2: nat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),N2)) ) ) ).

% one_less_power
tff(fact_2445_one__less__power,axiom,
    ! [A: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,one_one_nat),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),N2)) ) ) ).

% one_less_power
tff(fact_2446_one__less__power,axiom,
    ! [A: int,N2: nat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
       => aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),aa_nat_int(aa_int_fun_nat_int(power_power_int,A),N2)) ) ) ).

% one_less_power
tff(fact_2447_nz__le__conv__less,axiom,
    ! [K: nat,M: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),K)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),M)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,K),aa_nat_nat(suc,zero_zero_nat))),M) ) ) ).

% nz_le_conv_less
tff(fact_2448_ceiling__altdef,axiom,
    ! [X2: rat] :
      archim2889992004027027881ng_rat(X2) = $ite(X2 = aa_int_rat(ring_1_of_int_rat,archim3151403230148437115or_rat(X2)),archim3151403230148437115or_rat(X2),aa_int_int(aa_int_fun_int_int(plus_plus_int,archim3151403230148437115or_rat(X2)),one_one_int)) ).

% ceiling_altdef
tff(fact_2449_Suc__diff__eq__diff__pred,axiom,
    ! [N2: nat,M: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(suc,M)),N2) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)) ) ) ).

% Suc_diff_eq_diff_pred
tff(fact_2450_Suc__pred_H,axiom,
    ! [N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => ( N2 = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)) ) ) ).

% Suc_pred'
tff(fact_2451_add__eq__if,axiom,
    ! [M: nat,N2: nat] :
      aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2) = $ite(M = zero_zero_nat,N2,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),one_one_nat)),N2))) ).

% add_eq_if
tff(fact_2452_Suc__n__minus__m__eq,axiom,
    ! [M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,one_one_nat),M)
       => ( aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),M)) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),one_one_nat)) ) ) ) ).

% Suc_n_minus_m_eq
tff(fact_2453_floor__unique,axiom,
    ! [Z: int,X2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_int_rat(ring_1_of_int_rat,Z)),X2)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,X2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_int_rat(ring_1_of_int_rat,Z)),one_one_rat))
       => ( archim3151403230148437115or_rat(X2) = Z ) ) ) ).

% floor_unique
tff(fact_2454_floor__eq__iff,axiom,
    ! [X2: rat,A: int] :
      ( ( archim3151403230148437115or_rat(X2) = A )
    <=> ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_int_rat(ring_1_of_int_rat,A)),X2)
        & aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,X2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_int_rat(ring_1_of_int_rat,A)),one_one_rat)) ) ) ).

% floor_eq_iff
tff(fact_2455_floor__split,axiom,
    ! [P: fun_int_o,T: rat] :
      ( aa_int_o(P,archim3151403230148437115or_rat(T))
    <=> ! [I3: int] :
          ( ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_int_rat(ring_1_of_int_rat,I3)),T)
            & aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,T),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_int_rat(ring_1_of_int_rat,I3)),one_one_rat)) )
         => aa_int_o(P,I3) ) ) ).

% floor_split
tff(fact_2456_ceiling__correct,axiom,
    ! [X2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(minus_minus_rat(aa_int_rat(ring_1_of_int_rat,archim2889992004027027881ng_rat(X2))),one_one_rat)),X2)
      & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,X2),aa_int_rat(ring_1_of_int_rat,archim2889992004027027881ng_rat(X2))) ) ).

% ceiling_correct
tff(fact_2457_ceiling__unique,axiom,
    ! [Z: int,X2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(minus_minus_rat(aa_int_rat(ring_1_of_int_rat,Z)),one_one_rat)),X2)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,X2),aa_int_rat(ring_1_of_int_rat,Z))
       => ( archim2889992004027027881ng_rat(X2) = Z ) ) ) ).

% ceiling_unique
tff(fact_2458_ceiling__eq__iff,axiom,
    ! [X2: rat,A: int] :
      ( ( archim2889992004027027881ng_rat(X2) = A )
    <=> ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(minus_minus_rat(aa_int_rat(ring_1_of_int_rat,A)),one_one_rat)),X2)
        & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,X2),aa_int_rat(ring_1_of_int_rat,A)) ) ) ).

% ceiling_eq_iff
tff(fact_2459_ceiling__split,axiom,
    ! [P: fun_int_o,T: rat] :
      ( aa_int_o(P,archim2889992004027027881ng_rat(T))
    <=> ! [I3: int] :
          ( ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(minus_minus_rat(aa_int_rat(ring_1_of_int_rat,I3)),one_one_rat)),T)
            & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,T),aa_int_rat(ring_1_of_int_rat,I3)) )
         => aa_int_o(P,I3) ) ) ).

% ceiling_split
tff(fact_2460_less__floor__iff,axiom,
    ! [Z: int,X2: rat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,Z),archim3151403230148437115or_rat(X2))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_int_rat(ring_1_of_int_rat,Z)),one_one_rat)),X2) ) ).

% less_floor_iff
tff(fact_2461_floor__le__iff,axiom,
    ! [X2: rat,Z: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,archim3151403230148437115or_rat(X2)),Z)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,X2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_int_rat(ring_1_of_int_rat,Z)),one_one_rat)) ) ).

% floor_le_iff
tff(fact_2462_ceiling__less__iff,axiom,
    ! [X2: rat,Z: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,archim2889992004027027881ng_rat(X2)),Z)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,X2),aa_rat_rat(minus_minus_rat(aa_int_rat(ring_1_of_int_rat,Z)),one_one_rat)) ) ).

% ceiling_less_iff
tff(fact_2463_le__ceiling__iff,axiom,
    ! [Z: int,X2: rat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,Z),archim2889992004027027881ng_rat(X2))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(minus_minus_rat(aa_int_rat(ring_1_of_int_rat,Z)),one_one_rat)),X2) ) ).

% le_ceiling_iff
tff(fact_2464_floor__correct,axiom,
    ! [X2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_int_rat(ring_1_of_int_rat,archim3151403230148437115or_rat(X2))),X2)
      & aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,X2),aa_int_rat(ring_1_of_int_rat,aa_int_int(aa_int_fun_int_int(plus_plus_int,archim3151403230148437115or_rat(X2)),one_one_int))) ) ).

% floor_correct
tff(fact_2465_power__diff__power__eq,axiom,
    ! [A: int,M: nat,N2: nat] :
      ( ( A != zero_zero_int )
     => ( aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,A),M)),aa_nat_int(aa_int_fun_nat_int(power_power_int,A),N2)) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),M),aa_nat_int(aa_int_fun_nat_int(power_power_int,A),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),N2)),aa_int_int(aa_int_fun_int_int(divide_divide_int,one_one_int),aa_nat_int(aa_int_fun_nat_int(power_power_int,A),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),M)))) ) ) ).

% power_diff_power_eq
tff(fact_2466_power__diff__power__eq,axiom,
    ! [A: nat,M: nat,N2: nat] :
      ( ( A != zero_zero_nat )
     => ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),M)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),N2)) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),M),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),N2)),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),M)))) ) ) ).

% power_diff_power_eq
tff(fact_2467_power__diff__power__eq,axiom,
    ! [A: code_integer,M: nat,N2: nat] :
      ( ( A != zero_z3403309356797280102nteger )
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),M)),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),N2)) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),M),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),N2)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,one_one_Code_integer),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),M)))) ) ) ).

% power_diff_power_eq
tff(fact_2468_power__diff__power__eq,axiom,
    ! [A: code_natural,M: nat,N2: nat] :
      ( ( A != zero_z2226904508553997617atural )
     => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_nat_Code_natural(power_7079662738309270450atural(A),M)),aa_nat_Code_natural(power_7079662738309270450atural(A),N2)) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),M),aa_nat_Code_natural(power_7079662738309270450atural(A),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),N2)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,one_one_Code_natural),aa_nat_Code_natural(power_7079662738309270450atural(A),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),M)))) ) ) ).

% power_diff_power_eq
tff(fact_2469_power__eq__if,axiom,
    ! [P2: code_integer,M: nat] :
      aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,P2),M) = $ite(M = zero_zero_nat,one_one_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,P2),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,P2),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),one_one_nat)))) ).

% power_eq_if
tff(fact_2470_power__eq__if,axiom,
    ! [P2: assn,M: nat] :
      aa_nat_assn(aa_assn_fun_nat_assn(power_power_assn,P2),M) = $ite(M = zero_zero_nat,one_one_assn,aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P2),aa_nat_assn(aa_assn_fun_nat_assn(power_power_assn,P2),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),one_one_nat)))) ).

% power_eq_if
tff(fact_2471_power__eq__if,axiom,
    ! [P2: rat,M: nat] :
      aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,P2),M) = $ite(M = zero_zero_nat,one_one_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,P2),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,P2),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),one_one_nat)))) ).

% power_eq_if
tff(fact_2472_power__eq__if,axiom,
    ! [P2: nat,M: nat] :
      aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,P2),M) = $ite(M = zero_zero_nat,one_one_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,P2),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,P2),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),one_one_nat)))) ).

% power_eq_if
tff(fact_2473_power__eq__if,axiom,
    ! [P2: int,M: nat] :
      aa_nat_int(aa_int_fun_nat_int(power_power_int,P2),M) = $ite(M = zero_zero_nat,one_one_int,aa_int_int(aa_int_fun_int_int(times_times_int,P2),aa_nat_int(aa_int_fun_nat_int(power_power_int,P2),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),one_one_nat)))) ).

% power_eq_if
tff(fact_2474_power__minus__mult,axiom,
    ! [N2: nat,A: assn] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => ( aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_nat_assn(aa_assn_fun_nat_assn(power_power_assn,A),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat))),A) = aa_nat_assn(aa_assn_fun_nat_assn(power_power_assn,A),N2) ) ) ).

% power_minus_mult
tff(fact_2475_power__minus__mult,axiom,
    ! [N2: nat,A: rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => ( aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat))),A) = aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),N2) ) ) ).

% power_minus_mult
tff(fact_2476_power__minus__mult,axiom,
    ! [N2: nat,A: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat))),A) = aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),N2) ) ) ).

% power_minus_mult
tff(fact_2477_power__minus__mult,axiom,
    ! [N2: nat,A: int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => ( aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,A),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat))),A) = aa_nat_int(aa_int_fun_nat_int(power_power_int,A),N2) ) ) ).

% power_minus_mult
tff(fact_2478_neg__one__power__add__eq__neg__one__power__diff,axiom,
    ! [K: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),N2)
     => ( aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(uminus_uminus_int,one_one_int)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),K)) = aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(uminus_uminus_int,one_one_int)),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),K)) ) ) ).

% neg_one_power_add_eq_neg_one_power_diff
tff(fact_2479_neg__one__power__add__eq__neg__one__power__diff,axiom,
    ! [K: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),N2)
     => ( aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),K)) = aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),K)) ) ) ).

% neg_one_power_add_eq_neg_one_power_diff
tff(fact_2480_neg__one__power__add__eq__neg__one__power__diff,axiom,
    ! [K: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),N2)
     => ( aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),K)) = aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),K)) ) ) ).

% neg_one_power_add_eq_neg_one_power_diff
tff(fact_2481_option_Osize__gen_I2_J,axiom,
    ! [X2: fun_num_nat,X22: num] : aa_option_num_nat(size_option_num(X2),aa_num_option_num(some_num,X22)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(X2,X22)),aa_nat_nat(suc,zero_zero_nat)) ).

% option.size_gen(2)
tff(fact_2482_option_Osize__gen_I2_J,axiom,
    ! [X2: fun_Pr367382672041210069at_nat,X22: produc8664842809031399944it_nat] : size_o29782932136985253it_nat(X2,aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X22)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_Pro5228051289423594006at_nat(X2,X22)),aa_nat_nat(suc,zero_zero_nat)) ).

% option.size_gen(2)
tff(fact_2483_Heap_Osize__gen,axiom,
    ! [Xa: fun_Product_unit_nat,X2: fun_he5234484606919320760it_nat] : heap_T4142866422068808505t_unit(Xa,heap_T6183433275982383450t_unit(X2)) = aa_nat_nat(suc,zero_zero_nat) ).

% Heap.size_gen
tff(fact_2484_num_Osize__gen_I2_J,axiom,
    ! [X22: num] : aa_num_nat(size_num,aa_num_num(bit0,X22)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(size_num,X22)),aa_nat_nat(suc,zero_zero_nat)) ).

% num.size_gen(2)
tff(fact_2485_normalize__negative,axiom,
    ! [Q3: int,P2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,Q3),zero_zero_int)
     => ( aa_Pro6970504127699319548nt_int(normalize,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,P2),Q3)) = aa_Pro6970504127699319548nt_int(normalize,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_int_int(uminus_uminus_int,P2)),aa_int_int(uminus_uminus_int,Q3))) ) ) ).

% normalize_negative
tff(fact_2486_option_Osize__gen_I1_J,axiom,
    ! [X2: fun_Pr515337093925520551at_nat] : size_o5312321843473198183it_nat(X2,none_P2587165478634041381it_nat) = aa_nat_nat(suc,zero_zero_nat) ).

% option.size_gen(1)
tff(fact_2487_option_Osize__gen_I1_J,axiom,
    ! [X2: fun_num_nat] : aa_option_num_nat(size_option_num(X2),none_num) = aa_nat_nat(suc,zero_zero_nat) ).

% option.size_gen(1)
tff(fact_2488_option_Osize__gen_I1_J,axiom,
    ! [X2: fun_Pr367382672041210069at_nat] : size_o29782932136985253it_nat(X2,none_P9117596204409417319it_nat) = aa_nat_nat(suc,zero_zero_nat) ).

% option.size_gen(1)
tff(fact_2489_Heap_Osize_I2_J,axiom,
    ! [X2: fun_he5234484606919320760it_nat] : size_s1564113455978345259t_unit(heap_T6183433275982383450t_unit(X2)) = aa_nat_nat(suc,zero_zero_nat) ).

% Heap.size(2)
tff(fact_2490_num_Osize_I5_J,axiom,
    ! [X22: num] : aa_num_nat(size_size_num,aa_num_num(bit0,X22)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(size_size_num,X22)),aa_nat_nat(suc,zero_zero_nat)) ).

% num.size(5)
tff(fact_2491_option_Osize_I3_J,axiom,
    size_s6797157356856800118it_nat(none_P2587165478634041381it_nat) = aa_nat_nat(suc,zero_zero_nat) ).

% option.size(3)
tff(fact_2492_option_Osize_I3_J,axiom,
    size_size_option_num(none_num) = aa_nat_nat(suc,zero_zero_nat) ).

% option.size(3)
tff(fact_2493_option_Osize_I3_J,axiom,
    size_s8766407808098229740it_nat(none_P9117596204409417319it_nat) = aa_nat_nat(suc,zero_zero_nat) ).

% option.size(3)
tff(fact_2494_normalize__denom__zero,axiom,
    ! [P2: int] : aa_Pro6970504127699319548nt_int(normalize,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,P2),zero_zero_int)) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,zero_zero_int),one_one_int) ).

% normalize_denom_zero
tff(fact_2495_option_Osize__gen__o__map,axiom,
    ! [F: fun_num_nat,G: fun_num_num] : comp_o6878144249584144265on_num(size_option_num(F),map_option_num_num(G)) = size_option_num(comp_num_nat_num(F,G)) ).

% option.size_gen_o_map
tff(fact_2496_normalize__denom__pos,axiom,
    ! [R2: product_prod_int_int,P2: int,Q3: int] :
      ( ( aa_Pro6970504127699319548nt_int(normalize,R2) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,P2),Q3) )
     => aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),Q3) ) ).

% normalize_denom_pos
tff(fact_2497_normalize__crossproduct,axiom,
    ! [Q3: int,S: int,P2: int,R2: int] :
      ( ( Q3 != zero_zero_int )
     => ( ( S != zero_zero_int )
       => ( ( aa_Pro6970504127699319548nt_int(normalize,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,P2),Q3)) = aa_Pro6970504127699319548nt_int(normalize,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,R2),S)) )
         => ( aa_int_int(aa_int_fun_int_int(times_times_int,P2),S) = aa_int_int(aa_int_fun_int_int(times_times_int,R2),Q3) ) ) ) ) ).

% normalize_crossproduct
tff(fact_2498_option_Osize_I4_J,axiom,
    ! [X22: num] : size_size_option_num(aa_num_option_num(some_num,X22)) = aa_nat_nat(suc,zero_zero_nat) ).

% option.size(4)
tff(fact_2499_option_Osize_I4_J,axiom,
    ! [X22: produc8664842809031399944it_nat] : size_s8766407808098229740it_nat(aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X22)) = aa_nat_nat(suc,zero_zero_nat) ).

% option.size(4)
tff(fact_2500_divmod__nat__if,axiom,
    ! [M: nat,N2: nat] :
      aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(divmod_nat,M),N2) = $ite(
        ( ( N2 = zero_zero_nat )
        | aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M),N2) ),
        aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,zero_zero_nat),M),
        aa_Pro262675715343573244at_nat(produc2626176000494625587at_nat(aTP_Lamm_cq),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(divmod_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),N2)),N2)) ) ).

% divmod_nat_if
tff(fact_2501_sum__gp__multiplied,axiom,
    ! [M: nat,N2: nat,X2: code_integer] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,one_one_Code_integer),X2)),groups7501900531339628137nteger(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,X2),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,X2),M)),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,X2),aa_nat_nat(suc,N2))) ) ) ).

% sum_gp_multiplied
tff(fact_2502_sum__gp__multiplied,axiom,
    ! [M: nat,N2: nat,X2: rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(minus_minus_rat(one_one_rat),X2)),groups2906978787729119204at_rat(aa_rat_fun_nat_rat(power_power_rat,X2),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))) = aa_rat_rat(minus_minus_rat(aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),M)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),aa_nat_nat(suc,N2))) ) ) ).

% sum_gp_multiplied
tff(fact_2503_sum__gp__multiplied,axiom,
    ! [M: nat,N2: nat,X2: int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,one_one_int),X2)),groups3539618377306564664at_int(aa_int_fun_nat_int(power_power_int,X2),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,X2),M)),aa_nat_int(aa_int_fun_nat_int(power_power_int,X2),aa_nat_nat(suc,N2))) ) ) ).

% sum_gp_multiplied
tff(fact_2504_pair__lessI2,axiom,
    ! [A: nat,B: nat,S: nat,T: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,S),T)
       => member8206827879206165904at_nat(produc6161850002892822231at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),S),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,B),T)),fun_pair_less) ) ) ).

% pair_lessI2
tff(fact_2505_pair__less__iff1,axiom,
    ! [X2: nat,Y: nat,Z: nat] :
      ( member8206827879206165904at_nat(produc6161850002892822231at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X2),Y),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X2),Z)),fun_pair_less)
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,Y),Z) ) ).

% pair_less_iff1
tff(fact_2506_Suc__times__numeral__mod__eq,axiom,
    ! [K: num,N2: nat] :
      ( ( aa_num_nat(numeral_numeral_nat,K) != one_one_nat )
     => ( aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,K)),N2))),aa_num_nat(numeral_numeral_nat,K)) = one_one_nat ) ) ).

% Suc_times_numeral_mod_eq
tff(fact_2507_one__int_Otransfer,axiom,
    aa_int_o(aa_Pro2912763917461432128_int_o(pcr_int,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,one_one_nat),zero_zero_nat)),one_one_int) ).

% one_int.transfer
tff(fact_2508_less__than__iff,axiom,
    ! [X2: nat,Y: nat] :
      ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X2),Y),less_than)
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,X2),Y) ) ).

% less_than_iff
tff(fact_2509_one__int__def,axiom,
    one_one_int = aa_Pro4240683299535347697at_int(abs_Integ,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,one_one_nat),zero_zero_nat)) ).

% one_int_def
tff(fact_2510_sum__telescope_H_H,axiom,
    ! [M: nat,N2: nat,F: fun_nat_Code_integer] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( groups7501900531339628137nteger(aTP_Lamm_cr(F),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,M)),N2)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_nat_Code_integer(F,N2)),aa_nat_Code_integer(F,M)) ) ) ).

% sum_telescope''
tff(fact_2511_sum__telescope_H_H,axiom,
    ! [M: nat,N2: nat,F: fun_nat_rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( groups2906978787729119204at_rat(aTP_Lamm_cs(F),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,M)),N2)) = aa_rat_rat(minus_minus_rat(aa_nat_rat(F,N2)),aa_nat_rat(F,M)) ) ) ).

% sum_telescope''
tff(fact_2512_sum__telescope_H_H,axiom,
    ! [M: nat,N2: nat,F: fun_nat_int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( groups3539618377306564664at_int(aTP_Lamm_ct(F),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,M)),N2)) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(F,N2)),aa_nat_int(F,M)) ) ) ).

% sum_telescope''
tff(fact_2513_case__prod__conv,axiom,
    ! [F: fun_nat_fun_nat_nat,A: nat,B: nat] : aa_Pro4243173770044397973at_nat(aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,F),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B)) = aa_nat_nat(aa_nat_fun_nat_nat(F,A),B) ).

% case_prod_conv
tff(fact_2514_case__prod__conv,axiom,
    ! [F: fun_na1668100129766719005at_nat,A: nat,B: nat] : aa_Pro8023792847356852296at_nat(aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,F),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B)) = aa_nat7997280740862404369at_nat(aa_nat5682243440470347102at_nat(F,A),B) ).

% case_prod_conv
tff(fact_2515_case__prod__conv,axiom,
    ! [F: fun_na5914473681949881652_nat_o,A: nat,B: nat] : aa_Pro989595756709598047_nat_o(aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,F),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B)) = aa_nat7695548938202568488_nat_o(aa_nat4259715169212259317_nat_o(F,A),B) ).

% case_prod_conv
tff(fact_2516_case__prod__conv,axiom,
    ! [F: fun_in1696471567231710611nt_int,A: int,B: int] : aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,F),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A),B)) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(F,A),B) ).

% case_prod_conv
tff(fact_2517_case__prod__conv,axiom,
    ! [F: fun_int_fun_int_int,A: int,B: int] : aa_Pro6799258434465214121nt_int(aa_fun914008879417524284nt_int(produc8211389475949308722nt_int,F),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A),B)) = aa_int_int(aa_int_fun_int_int(F,A),B) ).

% case_prod_conv
tff(fact_2518_case__prod__curry,axiom,
    ! [F: fun_Pr2602117396471556196at_nat] : aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,produc8871627978511607229at_nat(F)) = F ).

% case_prod_curry
tff(fact_2519_case__prod__curry,axiom,
    ! [F: fun_Pr2477239776880934807at_nat] : aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,produc4701859392678344816at_nat(F)) = F ).

% case_prod_curry
tff(fact_2520_case__prod__curry,axiom,
    ! [F: fun_Pr2028404973800837934_nat_o] : aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,produc2062876521443793799_nat_o(F)) = F ).

% case_prod_curry
tff(fact_2521_case__prod__curry,axiom,
    ! [F: fun_Pr2478283820680522243nt_int] : aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,produc8249235968001453780nt_int(F)) = F ).

% case_prod_curry
tff(fact_2522_case__prod__curry,axiom,
    ! [F: fun_Pr982841511892225912nt_int] : aa_fun914008879417524284nt_int(produc8211389475949308722nt_int,produc1016772743285680337nt_int(F)) = F ).

% case_prod_curry
tff(fact_2523_curry__case__prod,axiom,
    ! [F: fun_nat_fun_nat_nat] : produc8871627978511607229at_nat(aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,F)) = F ).

% curry_case_prod
tff(fact_2524_curry__case__prod,axiom,
    ! [F: fun_na1668100129766719005at_nat] : produc4701859392678344816at_nat(aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,F)) = F ).

% curry_case_prod
tff(fact_2525_curry__case__prod,axiom,
    ! [F: fun_na5914473681949881652_nat_o] : produc2062876521443793799_nat_o(aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,F)) = F ).

% curry_case_prod
tff(fact_2526_curry__case__prod,axiom,
    ! [F: fun_in1696471567231710611nt_int] : produc8249235968001453780nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,F)) = F ).

% curry_case_prod
tff(fact_2527_curry__case__prod,axiom,
    ! [F: fun_int_fun_int_int] : produc1016772743285680337nt_int(aa_fun914008879417524284nt_int(produc8211389475949308722nt_int,F)) = F ).

% curry_case_prod
tff(fact_2528_distrib__right__numeral,axiom,
    ! [A: nat,B: nat,V: num] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),aa_num_nat(numeral_numeral_nat,V)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),aa_num_nat(numeral_numeral_nat,V))),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),aa_num_nat(numeral_numeral_nat,V))) ).

% distrib_right_numeral
tff(fact_2529_distrib__right__numeral,axiom,
    ! [A: int,B: int,V: num] : aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),aa_num_int(numeral_numeral_int,V)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),aa_num_int(numeral_numeral_int,V))),aa_int_int(aa_int_fun_int_int(times_times_int,B),aa_num_int(numeral_numeral_int,V))) ).

% distrib_right_numeral
tff(fact_2530_distrib__right__numeral,axiom,
    ! [A: code_integer,B: code_integer,V: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)),aa_num_Code_integer(numera6620942414471956472nteger,V)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,V))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,B),aa_num_Code_integer(numera6620942414471956472nteger,V))) ).

% distrib_right_numeral
tff(fact_2531_distrib__right__numeral,axiom,
    ! [A: rat,B: rat,V: num] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),aa_num_rat(numeral_numeral_rat,V)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),aa_num_rat(numeral_numeral_rat,V))),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,B),aa_num_rat(numeral_numeral_rat,V))) ).

% distrib_right_numeral
tff(fact_2532_distrib__right__numeral,axiom,
    ! [A: code_natural,B: code_natural,V: num] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),B)),aa_num_Code_natural(numera5444537566228673987atural,V)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,A),aa_num_Code_natural(numera5444537566228673987atural,V))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,B),aa_num_Code_natural(numera5444537566228673987atural,V))) ).

% distrib_right_numeral
tff(fact_2533_distrib__left__numeral,axiom,
    ! [V: num,B: nat,C: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,V)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),C)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,V)),B)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,V)),C)) ).

% distrib_left_numeral
tff(fact_2534_distrib__left__numeral,axiom,
    ! [V: num,B: int,C: int] : aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,V)),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),C)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,V)),B)),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,V)),C)) ).

% distrib_left_numeral
tff(fact_2535_distrib__left__numeral,axiom,
    ! [V: num,B: code_integer,C: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,V)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,B),C)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,V)),B)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,V)),C)) ).

% distrib_left_numeral
tff(fact_2536_distrib__left__numeral,axiom,
    ! [V: num,B: rat,C: rat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_num_rat(numeral_numeral_rat,V)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),C)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_num_rat(numeral_numeral_rat,V)),B)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_num_rat(numeral_numeral_rat,V)),C)) ).

% distrib_left_numeral
tff(fact_2537_distrib__left__numeral,axiom,
    ! [V: num,B: code_natural,C: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,V)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,B),C)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,V)),B)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,V)),C)) ).

% distrib_left_numeral
tff(fact_2538_add__neg__numeral__simps_I3_J,axiom,
    ! [M: num,N2: num] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,M))),aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,N2))) = aa_int_int(uminus_uminus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_num_int(numeral_numeral_int,M)),aa_num_int(numeral_numeral_int,N2))) ).

% add_neg_numeral_simps(3)
tff(fact_2539_add__neg__numeral__simps_I3_J,axiom,
    ! [M: num,N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,M))),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,N2))) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_num_Code_integer(numera6620942414471956472nteger,M)),aa_num_Code_integer(numera6620942414471956472nteger,N2))) ).

% add_neg_numeral_simps(3)
tff(fact_2540_add__neg__numeral__simps_I3_J,axiom,
    ! [M: num,N2: num] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,M))),aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,N2))) = aa_rat_rat(uminus_uminus_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_num_rat(numeral_numeral_rat,M)),aa_num_rat(numeral_numeral_rat,N2))) ).

% add_neg_numeral_simps(3)
tff(fact_2541_add__numeral__left,axiom,
    ! [V: num,W: num,Z: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(numeral_numeral_nat,V)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(numeral_numeral_nat,W)),Z)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(aa_num_fun_num_num(plus_plus_num,V),W))),Z) ).

% add_numeral_left
tff(fact_2542_add__numeral__left,axiom,
    ! [V: num,W: num,Z: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_num_int(numeral_numeral_int,V)),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_num_int(numeral_numeral_int,W)),Z)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_num_int(numeral_numeral_int,aa_num_num(aa_num_fun_num_num(plus_plus_num,V),W))),Z) ).

% add_numeral_left
tff(fact_2543_add__numeral__left,axiom,
    ! [V: num,W: num,Z: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_num_Code_integer(numera6620942414471956472nteger,V)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_num_Code_integer(numera6620942414471956472nteger,W)),Z)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(aa_num_fun_num_num(plus_plus_num,V),W))),Z) ).

% add_numeral_left
tff(fact_2544_add__numeral__left,axiom,
    ! [V: num,W: num,Z: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_num_rat(numeral_numeral_rat,V)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_num_rat(numeral_numeral_rat,W)),Z)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(aa_num_fun_num_num(plus_plus_num,V),W))),Z) ).

% add_numeral_left
tff(fact_2545_add__numeral__left,axiom,
    ! [V: num,W: num,Z: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_num_Code_natural(numera5444537566228673987atural,V)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_num_Code_natural(numera5444537566228673987atural,W)),Z)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(aa_num_fun_num_num(plus_plus_num,V),W))),Z) ).

% add_numeral_left
tff(fact_2546_numeral__plus__numeral,axiom,
    ! [M: num,N2: num] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(numeral_numeral_nat,M)),aa_num_nat(numeral_numeral_nat,N2)) = aa_num_nat(numeral_numeral_nat,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2)) ).

% numeral_plus_numeral
tff(fact_2547_numeral__plus__numeral,axiom,
    ! [M: num,N2: num] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_num_int(numeral_numeral_int,M)),aa_num_int(numeral_numeral_int,N2)) = aa_num_int(numeral_numeral_int,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2)) ).

% numeral_plus_numeral
tff(fact_2548_numeral__plus__numeral,axiom,
    ! [M: num,N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_num_Code_integer(numera6620942414471956472nteger,M)),aa_num_Code_integer(numera6620942414471956472nteger,N2)) = aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2)) ).

% numeral_plus_numeral
tff(fact_2549_numeral__plus__numeral,axiom,
    ! [M: num,N2: num] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_num_rat(numeral_numeral_rat,M)),aa_num_rat(numeral_numeral_rat,N2)) = aa_num_rat(numeral_numeral_rat,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2)) ).

% numeral_plus_numeral
tff(fact_2550_numeral__plus__numeral,axiom,
    ! [M: num,N2: num] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_num_Code_natural(numera5444537566228673987atural,M)),aa_num_Code_natural(numera5444537566228673987atural,N2)) = aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2)) ).

% numeral_plus_numeral
tff(fact_2551_semiring__norm_I168_J,axiom,
    ! [V: num,W: num,Y: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,V))),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,W))),Y)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,aa_num_num(aa_num_fun_num_num(plus_plus_num,V),W)))),Y) ).

% semiring_norm(168)
tff(fact_2552_semiring__norm_I168_J,axiom,
    ! [V: num,W: num,Y: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,V))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,W))),Y)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(aa_num_fun_num_num(plus_plus_num,V),W)))),Y) ).

% semiring_norm(168)
tff(fact_2553_semiring__norm_I168_J,axiom,
    ! [V: num,W: num,Y: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,V))),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,W))),Y)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(aa_num_fun_num_num(plus_plus_num,V),W)))),Y) ).

% semiring_norm(168)
tff(fact_2554_diff__numeral__simps_I3_J,axiom,
    ! [M: num,N2: num] : aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,M))),aa_num_int(numeral_numeral_int,N2)) = aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2))) ).

% diff_numeral_simps(3)
tff(fact_2555_diff__numeral__simps_I3_J,axiom,
    ! [M: num,N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,M))),aa_num_Code_integer(numera6620942414471956472nteger,N2)) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2))) ).

% diff_numeral_simps(3)
tff(fact_2556_diff__numeral__simps_I3_J,axiom,
    ! [M: num,N2: num] : aa_rat_rat(minus_minus_rat(aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,M))),aa_num_rat(numeral_numeral_rat,N2)) = aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2))) ).

% diff_numeral_simps(3)
tff(fact_2557_diff__numeral__simps_I2_J,axiom,
    ! [M: num,N2: num] : aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_num_int(numeral_numeral_int,M)),aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,N2))) = aa_num_int(numeral_numeral_int,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2)) ).

% diff_numeral_simps(2)
tff(fact_2558_diff__numeral__simps_I2_J,axiom,
    ! [M: num,N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_num_Code_integer(numera6620942414471956472nteger,M)),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,N2))) = aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2)) ).

% diff_numeral_simps(2)
tff(fact_2559_diff__numeral__simps_I2_J,axiom,
    ! [M: num,N2: num] : aa_rat_rat(minus_minus_rat(aa_num_rat(numeral_numeral_rat,M)),aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,N2))) = aa_num_rat(numeral_numeral_rat,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2)) ).

% diff_numeral_simps(2)
tff(fact_2560_ceiling__add__numeral,axiom,
    ! [X2: rat,V: num] : archim2889992004027027881ng_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),aa_num_rat(numeral_numeral_rat,V))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,archim2889992004027027881ng_rat(X2)),aa_num_int(numeral_numeral_int,V)) ).

% ceiling_add_numeral
tff(fact_2561_power__add__numeral,axiom,
    ! [A: assn,M: num,N2: num] : aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_nat_assn(aa_assn_fun_nat_assn(power_power_assn,A),aa_num_nat(numeral_numeral_nat,M))),aa_nat_assn(aa_assn_fun_nat_assn(power_power_assn,A),aa_num_nat(numeral_numeral_nat,N2))) = aa_nat_assn(aa_assn_fun_nat_assn(power_power_assn,A),aa_num_nat(numeral_numeral_nat,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2))) ).

% power_add_numeral
tff(fact_2562_power__add__numeral,axiom,
    ! [A: rat,M: num,N2: num] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),aa_num_nat(numeral_numeral_nat,M))),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),aa_num_nat(numeral_numeral_nat,N2))) = aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2))) ).

% power_add_numeral
tff(fact_2563_power__add__numeral,axiom,
    ! [A: nat,M: num,N2: num] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),aa_num_nat(numeral_numeral_nat,M))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),aa_num_nat(numeral_numeral_nat,N2))) = aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2))) ).

% power_add_numeral
tff(fact_2564_power__add__numeral,axiom,
    ! [A: int,M: num,N2: num] : aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,A),aa_num_nat(numeral_numeral_nat,M))),aa_nat_int(aa_int_fun_nat_int(power_power_int,A),aa_num_nat(numeral_numeral_nat,N2))) = aa_nat_int(aa_int_fun_nat_int(power_power_int,A),aa_num_nat(numeral_numeral_nat,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2))) ).

% power_add_numeral
tff(fact_2565_power__add__numeral2,axiom,
    ! [A: assn,M: num,N2: num,B: assn] : aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_nat_assn(aa_assn_fun_nat_assn(power_power_assn,A),aa_num_nat(numeral_numeral_nat,M))),aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_nat_assn(aa_assn_fun_nat_assn(power_power_assn,A),aa_num_nat(numeral_numeral_nat,N2))),B)) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_nat_assn(aa_assn_fun_nat_assn(power_power_assn,A),aa_num_nat(numeral_numeral_nat,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2)))),B) ).

% power_add_numeral2
tff(fact_2566_power__add__numeral2,axiom,
    ! [A: rat,M: num,N2: num,B: rat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),aa_num_nat(numeral_numeral_nat,M))),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),aa_num_nat(numeral_numeral_nat,N2))),B)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2)))),B) ).

% power_add_numeral2
tff(fact_2567_power__add__numeral2,axiom,
    ! [A: nat,M: num,N2: num,B: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),aa_num_nat(numeral_numeral_nat,M))),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),aa_num_nat(numeral_numeral_nat,N2))),B)) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2)))),B) ).

% power_add_numeral2
tff(fact_2568_power__add__numeral2,axiom,
    ! [A: int,M: num,N2: num,B: int] : aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,A),aa_num_nat(numeral_numeral_nat,M))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,A),aa_num_nat(numeral_numeral_nat,N2))),B)) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,A),aa_num_nat(numeral_numeral_nat,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2)))),B) ).

% power_add_numeral2
tff(fact_2569_numeral__less__floor,axiom,
    ! [V: num,X2: rat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_num_int(numeral_numeral_int,V)),archim3151403230148437115or_rat(X2))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_num_rat(numeral_numeral_rat,V)),one_one_rat)),X2) ) ).

% numeral_less_floor
tff(fact_2570_floor__le__numeral,axiom,
    ! [X2: rat,V: num] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,archim3151403230148437115or_rat(X2)),aa_num_int(numeral_numeral_int,V))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,X2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_num_rat(numeral_numeral_rat,V)),one_one_rat)) ) ).

% floor_le_numeral
tff(fact_2571_sum_Ocl__ivl__Suc,axiom,
    ! [G: fun_nat_Code_integer,M: nat,N2: nat] :
      groups7501900531339628137nteger(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),aa_nat_nat(suc,N2))) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(suc,N2)),M),zero_z3403309356797280102nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,groups7501900531339628137nteger(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))),aa_nat_Code_integer(G,aa_nat_nat(suc,N2)))) ).

% sum.cl_ivl_Suc
tff(fact_2572_sum_Ocl__ivl__Suc,axiom,
    ! [G: fun_na2338080690716861136at_nat,M: nat,N2: nat] :
      groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),aa_nat_nat(suc,N2))) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(suc,N2)),M),zero_z1048942125864253310at_nat,aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))),aa_nat2240542744625857721at_nat(G,aa_nat_nat(suc,N2)))) ).

% sum.cl_ivl_Suc
tff(fact_2573_sum_Ocl__ivl__Suc,axiom,
    ! [G: fun_nat_rat,M: nat,N2: nat] :
      groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),aa_nat_nat(suc,N2))) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(suc,N2)),M),zero_zero_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))),aa_nat_rat(G,aa_nat_nat(suc,N2)))) ).

% sum.cl_ivl_Suc
tff(fact_2574_sum_Ocl__ivl__Suc,axiom,
    ! [G: fun_nat_int,M: nat,N2: nat] :
      groups3539618377306564664at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),aa_nat_nat(suc,N2))) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(suc,N2)),M),zero_zero_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,groups3539618377306564664at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))),aa_nat_int(G,aa_nat_nat(suc,N2)))) ).

% sum.cl_ivl_Suc
tff(fact_2575_sum_Ocl__ivl__Suc,axiom,
    ! [G: fun_nat_nat,M: nat,N2: nat] :
      aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),aa_nat_nat(suc,N2))) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(suc,N2)),M),zero_zero_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))),aa_nat_nat(G,aa_nat_nat(suc,N2)))) ).

% sum.cl_ivl_Suc
tff(fact_2576_ceiling__less__numeral,axiom,
    ! [X2: rat,V: num] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,archim2889992004027027881ng_rat(X2)),aa_num_int(numeral_numeral_int,V))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,X2),aa_rat_rat(minus_minus_rat(aa_num_rat(numeral_numeral_rat,V)),one_one_rat)) ) ).

% ceiling_less_numeral
tff(fact_2577_numeral__le__ceiling,axiom,
    ! [V: num,X2: rat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_num_int(numeral_numeral_int,V)),archim2889992004027027881ng_rat(X2))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(minus_minus_rat(aa_num_rat(numeral_numeral_rat,V)),one_one_rat)),X2) ) ).

% numeral_le_ceiling
tff(fact_2578_neg__numeral__less__floor,axiom,
    ! [V: num,X2: rat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,V))),archim3151403230148437115or_rat(X2))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,V))),one_one_rat)),X2) ) ).

% neg_numeral_less_floor
tff(fact_2579_floor__le__neg__numeral,axiom,
    ! [X2: rat,V: num] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,archim3151403230148437115or_rat(X2)),aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,V)))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,X2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,V))),one_one_rat)) ) ).

% floor_le_neg_numeral
tff(fact_2580_ceiling__less__neg__numeral,axiom,
    ! [X2: rat,V: num] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,archim2889992004027027881ng_rat(X2)),aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,V)))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,X2),aa_rat_rat(minus_minus_rat(aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,V))),one_one_rat)) ) ).

% ceiling_less_neg_numeral
tff(fact_2581_neg__numeral__le__ceiling,axiom,
    ! [V: num,X2: rat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,V))),archim2889992004027027881ng_rat(X2))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(minus_minus_rat(aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,V))),one_one_rat)),X2) ) ).

% neg_numeral_le_ceiling
tff(fact_2582_nested__case__prod__simp,axiom,
    ! [F: fun_na1668100129766719005at_nat,X2: product_prod_nat_nat,Y: product_prod_nat_nat] : aa_Pro262675715343573244at_nat(aa_Pro8023792847356852296at_nat(aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,F),X2),Y) = aa_Pro262675715343573244at_nat(produc2626176000494625587at_nat(aa_Pro6895555690143131534at_nat(aTP_Lamm_cu(F),Y)),X2) ).

% nested_case_prod_simp
tff(fact_2583_nested__case__prod__simp,axiom,
    ! [F: fun_na5914473681949881652_nat_o,X2: product_prod_nat_nat,Y: product_prod_nat_nat] :
      ( aa_Pro6150637604445964947_nat_o(aa_Pro989595756709598047_nat_o(aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,F),X2),Y)
    <=> aa_Pro6150637604445964947_nat_o(aa_fun7564604662015400456_nat_o(produc6081775807080527818_nat_o,aa_Pro1957341097241355813_nat_o(aTP_Lamm_cv(F),Y)),X2) ) ).

% nested_case_prod_simp
tff(fact_2584_prod_Ocase__distrib,axiom,
    ! [Ha: fun_nat_nat,F: fun_nat_fun_nat_nat,Prod: product_prod_nat_nat] : aa_nat_nat(Ha,aa_Pro4243173770044397973at_nat(aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,F),Prod)) = aa_Pro4243173770044397973at_nat(aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,aa_fun7716529229553496594at_nat(aTP_Lamm_cw(Ha),F)),Prod) ).

% prod.case_distrib
tff(fact_2585_prod_Ocase__distrib,axiom,
    ! [Ha: fun_int_int,F: fun_int_fun_int_int,Prod: product_prod_int_int] : aa_int_int(Ha,aa_Pro6799258434465214121nt_int(aa_fun914008879417524284nt_int(produc8211389475949308722nt_int,F),Prod)) = aa_Pro6799258434465214121nt_int(aa_fun914008879417524284nt_int(produc8211389475949308722nt_int,aa_fun6119123525526402106nt_int(aTP_Lamm_cx(Ha),F)),Prod) ).

% prod.case_distrib
tff(fact_2586_prod_Ocase__distrib,axiom,
    ! [Ha: fun_Pr982841511892225912nt_int,F: fun_in1696471567231710611nt_int,Prod: product_prod_int_int] : aa_Pro6799258434465214121nt_int(Ha,aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,F),Prod)) = aa_Pro6799258434465214121nt_int(aa_fun914008879417524284nt_int(produc8211389475949308722nt_int,aa_fun7461304428735181397nt_int(aTP_Lamm_cy(Ha),F)),Prod) ).

% prod.case_distrib
tff(fact_2587_prod_Ocase__distrib,axiom,
    ! [Ha: fun_in4211310926729683942nt_int,F: fun_int_fun_int_int,Prod: product_prod_int_int] : aa_int7462565939943104719nt_int(Ha,aa_Pro6799258434465214121nt_int(aa_fun914008879417524284nt_int(produc8211389475949308722nt_int,F),Prod)) = aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,aa_fun1034830265760468567nt_int(aTP_Lamm_cz(Ha),F)),Prod) ).

% prod.case_distrib
tff(fact_2588_prod_Ocase__distrib,axiom,
    ! [Ha: fun_na3970208099681795815_nat_o,F: fun_nat_fun_nat_nat,Prod: product_prod_nat_nat] : aa_nat7695548938202568488_nat_o(Ha,aa_Pro4243173770044397973at_nat(aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,F),Prod)) = aa_Pro989595756709598047_nat_o(aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,aa_fun2100511394839469148_nat_o(aTP_Lamm_da(Ha),F)),Prod) ).

% prod.case_distrib
tff(fact_2589_prod_Ocase__distrib,axiom,
    ! [Ha: fun_fu1115759055147092071_o_nat,F: fun_na5914473681949881652_nat_o,Prod: product_prod_nat_nat] : aa_fun1432809138467554728_o_nat(Ha,aa_Pro989595756709598047_nat_o(aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,F),Prod)) = aa_Pro4243173770044397973at_nat(aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,aa_fun3680403850923830236at_nat(aTP_Lamm_db(Ha),F)),Prod) ).

% prod.case_distrib
tff(fact_2590_prod_Ocase__distrib,axiom,
    ! [Ha: fun_Pr2478283820680522243nt_int,F: fun_in1696471567231710611nt_int,Prod: product_prod_int_int] : aa_Pro6970504127699319548nt_int(Ha,aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,F),Prod)) = aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,aa_fun4152872853588681340nt_int(aTP_Lamm_dc(Ha),F)),Prod) ).

% prod.case_distrib
tff(fact_2591_prod_Ocase__distrib,axiom,
    ! [Ha: fun_na8713714802964096592at_nat,F: fun_nat_fun_nat_nat,Prod: product_prod_nat_nat] : aa_nat7997280740862404369at_nat(Ha,aa_Pro4243173770044397973at_nat(aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,F),Prod)) = aa_Pro8023792847356852296at_nat(aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,aa_fun2484538639213223237at_nat(aTP_Lamm_dd(Ha),F)),Prod) ).

% prod.case_distrib
tff(fact_2592_prod_Ocase__distrib,axiom,
    ! [Ha: fun_fu1413608398870722896at_nat,F: fun_na1668100129766719005at_nat,Prod: product_prod_nat_nat] : aa_fun7582795104022253201at_nat(Ha,aa_Pro8023792847356852296at_nat(aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,F),Prod)) = aa_Pro4243173770044397973at_nat(aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,aa_fun8817627472026143685at_nat(aTP_Lamm_de(Ha),F)),Prod) ).

% prod.case_distrib
tff(fact_2593_prod_Ocase__distrib,axiom,
    ! [Ha: fun_fu3275390434952296369_nat_o,F: fun_na5914473681949881652_nat_o,Prod: product_prod_nat_nat] : aa_fun359341089595923442_nat_o(Ha,aa_Pro989595756709598047_nat_o(aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,F),Prod)) = aa_Pro989595756709598047_nat_o(aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,aa_fun824319262034445606_nat_o(aTP_Lamm_df(Ha),F)),Prod) ).

% prod.case_distrib
tff(fact_2594_sum_OatLeast__Suc__atMost__Suc__shift,axiom,
    ! [G: fun_nat_nat,M: nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,M)),aa_nat_nat(suc,N2))) = aa_set_nat_nat(groups3542108847815614940at_nat(comp_nat_nat_nat(G,suc)),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) ).

% sum.atLeast_Suc_atMost_Suc_shift
tff(fact_2595_sum_OatLeastAtMost__shift__bounds,axiom,
    ! [G: fun_nat_nat,M: nat,K: nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),K))) = aa_set_nat_nat(groups3542108847815614940at_nat(comp_nat_nat_nat(G,aa_nat_fun_nat_nat(plus_plus_nat,K))),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) ).

% sum.atLeastAtMost_shift_bounds
tff(fact_2596_split__cong,axiom,
    ! [Q3: product_prod_nat_nat,F: fun_nat_fun_nat_nat,G: fun_nat_fun_nat_nat,P2: product_prod_nat_nat] :
      ( ! [X3: nat,Y4: nat] :
          ( ( aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),Y4) = Q3 )
         => ( aa_nat_nat(aa_nat_fun_nat_nat(F,X3),Y4) = aa_nat_nat(aa_nat_fun_nat_nat(G,X3),Y4) ) )
     => ( ( P2 = Q3 )
       => ( aa_Pro4243173770044397973at_nat(aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,F),P2) = aa_Pro4243173770044397973at_nat(aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,G),Q3) ) ) ) ).

% split_cong
tff(fact_2597_split__cong,axiom,
    ! [Q3: product_prod_nat_nat,F: fun_na1668100129766719005at_nat,G: fun_na1668100129766719005at_nat,P2: product_prod_nat_nat] :
      ( ! [X3: nat,Y4: nat] :
          ( ( aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),Y4) = Q3 )
         => ( aa_nat7997280740862404369at_nat(aa_nat5682243440470347102at_nat(F,X3),Y4) = aa_nat7997280740862404369at_nat(aa_nat5682243440470347102at_nat(G,X3),Y4) ) )
     => ( ( P2 = Q3 )
       => ( aa_Pro8023792847356852296at_nat(aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,F),P2) = aa_Pro8023792847356852296at_nat(aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,G),Q3) ) ) ) ).

% split_cong
tff(fact_2598_split__cong,axiom,
    ! [Q3: product_prod_nat_nat,F: fun_na5914473681949881652_nat_o,G: fun_na5914473681949881652_nat_o,P2: product_prod_nat_nat] :
      ( ! [X3: nat,Y4: nat] :
          ( ( aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),Y4) = Q3 )
         => ( aa_nat7695548938202568488_nat_o(aa_nat4259715169212259317_nat_o(F,X3),Y4) = aa_nat7695548938202568488_nat_o(aa_nat4259715169212259317_nat_o(G,X3),Y4) ) )
     => ( ( P2 = Q3 )
       => ( aa_Pro989595756709598047_nat_o(aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,F),P2) = aa_Pro989595756709598047_nat_o(aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,G),Q3) ) ) ) ).

% split_cong
tff(fact_2599_split__cong,axiom,
    ! [Q3: product_prod_int_int,F: fun_in1696471567231710611nt_int,G: fun_in1696471567231710611nt_int,P2: product_prod_int_int] :
      ( ! [X3: int,Y4: int] :
          ( ( aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X3),Y4) = Q3 )
         => ( aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(F,X3),Y4) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(G,X3),Y4) ) )
     => ( ( P2 = Q3 )
       => ( aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,F),P2) = aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,G),Q3) ) ) ) ).

% split_cong
tff(fact_2600_split__cong,axiom,
    ! [Q3: product_prod_int_int,F: fun_int_fun_int_int,G: fun_int_fun_int_int,P2: product_prod_int_int] :
      ( ! [X3: int,Y4: int] :
          ( ( aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X3),Y4) = Q3 )
         => ( aa_int_int(aa_int_fun_int_int(F,X3),Y4) = aa_int_int(aa_int_fun_int_int(G,X3),Y4) ) )
     => ( ( P2 = Q3 )
       => ( aa_Pro6799258434465214121nt_int(aa_fun914008879417524284nt_int(produc8211389475949308722nt_int,F),P2) = aa_Pro6799258434465214121nt_int(aa_fun914008879417524284nt_int(produc8211389475949308722nt_int,G),Q3) ) ) ) ).

% split_cong
tff(fact_2601_old_Oprod_Ocase,axiom,
    ! [F: fun_nat_fun_nat_nat,X1: nat,X22: nat] : aa_Pro4243173770044397973at_nat(aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,F),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X1),X22)) = aa_nat_nat(aa_nat_fun_nat_nat(F,X1),X22) ).

% old.prod.case
tff(fact_2602_old_Oprod_Ocase,axiom,
    ! [F: fun_na1668100129766719005at_nat,X1: nat,X22: nat] : aa_Pro8023792847356852296at_nat(aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,F),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X1),X22)) = aa_nat7997280740862404369at_nat(aa_nat5682243440470347102at_nat(F,X1),X22) ).

% old.prod.case
tff(fact_2603_old_Oprod_Ocase,axiom,
    ! [F: fun_na5914473681949881652_nat_o,X1: nat,X22: nat] : aa_Pro989595756709598047_nat_o(aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,F),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X1),X22)) = aa_nat7695548938202568488_nat_o(aa_nat4259715169212259317_nat_o(F,X1),X22) ).

% old.prod.case
tff(fact_2604_old_Oprod_Ocase,axiom,
    ! [F: fun_in1696471567231710611nt_int,X1: int,X22: int] : aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,F),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X1),X22)) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(F,X1),X22) ).

% old.prod.case
tff(fact_2605_old_Oprod_Ocase,axiom,
    ! [F: fun_int_fun_int_int,X1: int,X22: int] : aa_Pro6799258434465214121nt_int(aa_fun914008879417524284nt_int(produc8211389475949308722nt_int,F),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X1),X22)) = aa_int_int(aa_int_fun_int_int(F,X1),X22) ).

% old.prod.case
tff(fact_2606_uminus__int_Oabs__eq,axiom,
    ! [X2: product_prod_nat_nat] : aa_int_int(uminus_uminus_int,aa_Pro4240683299535347697at_int(abs_Integ,X2)) = aa_Pro4240683299535347697at_int(abs_Integ,aa_Pro262675715343573244at_nat(produc2626176000494625587at_nat(aTP_Lamm_dg),X2)) ).

% uminus_int.abs_eq
tff(fact_2607_case__prod__Pair__iden,axiom,
    ! [P2: produc2453742332425399446nteger] : aa_Pro5909916214238876522nteger(produc697581972998607883nteger(produc565448451787809096nteger),P2) = P2 ).

% case_prod_Pair_iden
tff(fact_2608_case__prod__Pair__iden,axiom,
    ! [P2: produc8799533983703829792et_nat] : aa_Pro5931322043027775230et_nat(produc1949718844479134567et_nat(produc6017135503889078682et_nat),P2) = P2 ).

% case_prod_Pair_iden
tff(fact_2609_case__prod__Pair__iden,axiom,
    ! [P2: produc3112576180687729086et_nat] : aa_Pro5822770074865754298et_nat(produc2255458887868536227et_nat(produc7291855603632349880et_nat),P2) = P2 ).

% case_prod_Pair_iden
tff(fact_2610_case__prod__Pair__iden,axiom,
    ! [P2: produc3043004577601930755nt_int] : aa_Pro1064545558308985924nt_int(produc6823905543215200229nt_int(produc7320969046608631221nt_int),P2) = P2 ).

% case_prod_Pair_iden
tff(fact_2611_case__prod__Pair__iden,axiom,
    ! [P2: produc4788131091073775919nt_int] : aa_Pro356110846173809308nt_int(produc7102243260366339645nt_int(produc4729913460834754785nt_int),P2) = P2 ).

% case_prod_Pair_iden
tff(fact_2612_case__prod__Pair__iden,axiom,
    ! [P2: product_prod_int_int] : aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,product_Pair_int_int),P2) = P2 ).

% case_prod_Pair_iden
tff(fact_2613_sum_Oshift__bounds__cl__Suc__ivl,axiom,
    ! [G: fun_nat_nat,M: nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,M)),aa_nat_nat(suc,N2))) = aa_set_nat_nat(groups3542108847815614940at_nat(aTP_Lamm_dh(G)),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) ).

% sum.shift_bounds_cl_Suc_ivl
tff(fact_2614_sum_Oshift__bounds__cl__nat__ivl,axiom,
    ! [G: fun_nat_nat,M: nat,K: nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),K))) = aa_set_nat_nat(groups3542108847815614940at_nat(aa_nat_fun_nat_nat(aTP_Lamm_di(G),K)),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) ).

% sum.shift_bounds_cl_nat_ivl
tff(fact_2615_cond__case__prod__eta,axiom,
    ! [F: fun_nat_fun_nat_nat,G: fun_Pr2602117396471556196at_nat] :
      ( ! [X3: nat,Y4: nat] : aa_nat_nat(aa_nat_fun_nat_nat(F,X3),Y4) = aa_Pro4243173770044397973at_nat(G,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),Y4))
     => ( aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,F) = G ) ) ).

% cond_case_prod_eta
tff(fact_2616_cond__case__prod__eta,axiom,
    ! [F: fun_na1668100129766719005at_nat,G: fun_Pr2477239776880934807at_nat] :
      ( ! [X3: nat,Y4: nat] : aa_nat7997280740862404369at_nat(aa_nat5682243440470347102at_nat(F,X3),Y4) = aa_Pro8023792847356852296at_nat(G,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),Y4))
     => ( aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,F) = G ) ) ).

% cond_case_prod_eta
tff(fact_2617_cond__case__prod__eta,axiom,
    ! [F: fun_na5914473681949881652_nat_o,G: fun_Pr2028404973800837934_nat_o] :
      ( ! [X3: nat,Y4: nat] : aa_nat7695548938202568488_nat_o(aa_nat4259715169212259317_nat_o(F,X3),Y4) = aa_Pro989595756709598047_nat_o(G,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),Y4))
     => ( aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,F) = G ) ) ).

% cond_case_prod_eta
tff(fact_2618_cond__case__prod__eta,axiom,
    ! [F: fun_in1696471567231710611nt_int,G: fun_Pr2478283820680522243nt_int] :
      ( ! [X3: int,Y4: int] : aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(F,X3),Y4) = aa_Pro6970504127699319548nt_int(G,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X3),Y4))
     => ( aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,F) = G ) ) ).

% cond_case_prod_eta
tff(fact_2619_cond__case__prod__eta,axiom,
    ! [F: fun_int_fun_int_int,G: fun_Pr982841511892225912nt_int] :
      ( ! [X3: int,Y4: int] : aa_int_int(aa_int_fun_int_int(F,X3),Y4) = aa_Pro6799258434465214121nt_int(G,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X3),Y4))
     => ( aa_fun914008879417524284nt_int(produc8211389475949308722nt_int,F) = G ) ) ).

% cond_case_prod_eta
tff(fact_2620_case__prod__eta,axiom,
    ! [F: fun_Pr2602117396471556196at_nat] : aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,aTP_Lamm_dj(F)) = F ).

% case_prod_eta
tff(fact_2621_case__prod__eta,axiom,
    ! [F: fun_Pr2477239776880934807at_nat] : aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,aTP_Lamm_dk(F)) = F ).

% case_prod_eta
tff(fact_2622_case__prod__eta,axiom,
    ! [F: fun_Pr2028404973800837934_nat_o] : aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,aTP_Lamm_dl(F)) = F ).

% case_prod_eta
tff(fact_2623_case__prod__eta,axiom,
    ! [F: fun_Pr2478283820680522243nt_int] : aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,aTP_Lamm_dm(F)) = F ).

% case_prod_eta
tff(fact_2624_case__prod__eta,axiom,
    ! [F: fun_Pr982841511892225912nt_int] : aa_fun914008879417524284nt_int(produc8211389475949308722nt_int,aTP_Lamm_dn(F)) = F ).

% case_prod_eta
tff(fact_2625_case__prodE2,axiom,
    ! [Q: fun_nat_o,P: fun_nat_fun_nat_nat,Z: product_prod_nat_nat] :
      ( aa_nat_o(Q,aa_Pro4243173770044397973at_nat(aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,P),Z))
     => ~ ! [X3: nat,Y4: nat] :
            ( ( Z = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),Y4) )
           => ~ aa_nat_o(Q,aa_nat_nat(aa_nat_fun_nat_nat(P,X3),Y4)) ) ) ).

% case_prodE2
tff(fact_2626_case__prodE2,axiom,
    ! [Q: fun_fu8391177546919232046_nat_o,P: fun_na1668100129766719005at_nat,Z: product_prod_nat_nat] :
      ( aa_fun3538214411680374423_nat_o(Q,aa_Pro8023792847356852296at_nat(aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,P),Z))
     => ~ ! [X3: nat,Y4: nat] :
            ( ( Z = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),Y4) )
           => ~ aa_fun3538214411680374423_nat_o(Q,aa_nat7997280740862404369at_nat(aa_nat5682243440470347102at_nat(P,X3),Y4)) ) ) ).

% case_prodE2
tff(fact_2627_case__prodE2,axiom,
    ! [Q: fun_fu6891447142836604759at_o_o,P: fun_na5914473681949881652_nat_o,Z: product_prod_nat_nat] :
      ( aa_fun8408151826566693824at_o_o(Q,aa_Pro989595756709598047_nat_o(aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,P),Z))
     => ~ ! [X3: nat,Y4: nat] :
            ( ( Z = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),Y4) )
           => ~ aa_fun8408151826566693824at_o_o(Q,aa_nat7695548938202568488_nat_o(aa_nat4259715169212259317_nat_o(P,X3),Y4)) ) ) ).

% case_prodE2
tff(fact_2628_case__prodE2,axiom,
    ! [Q: fun_Pr3238374608701176162_int_o,P: fun_in1696471567231710611nt_int,Z: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(Q,aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,P),Z))
     => ~ ! [X3: int,Y4: int] :
            ( ( Z = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X3),Y4) )
           => ~ aa_Pro4592068669816069595_int_o(Q,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(P,X3),Y4)) ) ) ).

% case_prodE2
tff(fact_2629_case__prodE2,axiom,
    ! [Q: fun_int_o,P: fun_int_fun_int_int,Z: product_prod_int_int] :
      ( aa_int_o(Q,aa_Pro6799258434465214121nt_int(aa_fun914008879417524284nt_int(produc8211389475949308722nt_int,P),Z))
     => ~ ! [X3: int,Y4: int] :
            ( ( Z = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X3),Y4) )
           => ~ aa_int_o(Q,aa_int_int(aa_int_fun_int_int(P,X3),Y4)) ) ) ).

% case_prodE2
tff(fact_2630_eq__Abs__Integ,axiom,
    ! [Z: int] :
      ~ ! [X3: nat,Y4: nat] : Z != aa_Pro4240683299535347697at_int(abs_Integ,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),Y4)) ).

% eq_Abs_Integ
tff(fact_2631_one__le__numeral,axiom,
    ! [N2: num] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),aa_num_Code_integer(numera6620942414471956472nteger,N2)) ).

% one_le_numeral
tff(fact_2632_one__le__numeral,axiom,
    ! [N2: num] : aa_Code_natural_o(aa_Cod1485054954640246627ural_o(ord_le1926595141338095240atural,one_one_Code_natural),aa_num_Code_natural(numera5444537566228673987atural,N2)) ).

% one_le_numeral
tff(fact_2633_one__le__numeral,axiom,
    ! [N2: num] : aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),aa_num_rat(numeral_numeral_rat,N2)) ).

% one_le_numeral
tff(fact_2634_one__le__numeral,axiom,
    ! [N2: num] : aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),aa_num_nat(numeral_numeral_nat,N2)) ).

% one_le_numeral
tff(fact_2635_one__le__numeral,axiom,
    ! [N2: num] : aa_int_o(aa_int_fun_int_o(ord_less_eq_int,one_one_int),aa_num_int(numeral_numeral_int,N2)) ).

% one_le_numeral
tff(fact_2636_not__numeral__less__one,axiom,
    ! [N2: num] : ~ aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_num_nat(numeral_numeral_nat,N2)),one_one_nat) ).

% not_numeral_less_one
tff(fact_2637_not__numeral__less__one,axiom,
    ! [N2: num] : ~ aa_int_o(aa_int_fun_int_o(ord_less_int,aa_num_int(numeral_numeral_int,N2)),one_one_int) ).

% not_numeral_less_one
tff(fact_2638_not__numeral__less__one,axiom,
    ! [N2: num] : ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_num_Code_integer(numera6620942414471956472nteger,N2)),one_one_Code_integer) ).

% not_numeral_less_one
tff(fact_2639_not__numeral__less__one,axiom,
    ! [N2: num] : ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_num_rat(numeral_numeral_rat,N2)),one_one_rat) ).

% not_numeral_less_one
tff(fact_2640_not__numeral__less__one,axiom,
    ! [N2: num] : ~ aa_Code_natural_o(aa_Cod1485054954640246627ural_o(ord_le5570908160329646204atural,aa_num_Code_natural(numera5444537566228673987atural,N2)),one_one_Code_natural) ).

% not_numeral_less_one
tff(fact_2641_one__plus__numeral__commute,axiom,
    ! [X2: num] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_num_nat(numeral_numeral_nat,X2)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(numeral_numeral_nat,X2)),one_one_nat) ).

% one_plus_numeral_commute
tff(fact_2642_one__plus__numeral__commute,axiom,
    ! [X2: num] : aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_num_int(numeral_numeral_int,X2)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_num_int(numeral_numeral_int,X2)),one_one_int) ).

% one_plus_numeral_commute
tff(fact_2643_one__plus__numeral__commute,axiom,
    ! [X2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,one_one_Code_integer),aa_num_Code_integer(numera6620942414471956472nteger,X2)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_num_Code_integer(numera6620942414471956472nteger,X2)),one_one_Code_integer) ).

% one_plus_numeral_commute
tff(fact_2644_one__plus__numeral__commute,axiom,
    ! [X2: num] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,one_one_rat),aa_num_rat(numeral_numeral_rat,X2)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_num_rat(numeral_numeral_rat,X2)),one_one_rat) ).

% one_plus_numeral_commute
tff(fact_2645_one__plus__numeral__commute,axiom,
    ! [X2: num] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,one_one_Code_natural),aa_num_Code_natural(numera5444537566228673987atural,X2)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_num_Code_natural(numera5444537566228673987atural,X2)),one_one_Code_natural) ).

% one_plus_numeral_commute
tff(fact_2646_numeral__Bit0,axiom,
    ! [N2: num] : aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,N2)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(numeral_numeral_nat,N2)),aa_num_nat(numeral_numeral_nat,N2)) ).

% numeral_Bit0
tff(fact_2647_numeral__Bit0,axiom,
    ! [N2: num] : aa_num_int(numeral_numeral_int,aa_num_num(bit0,N2)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_num_int(numeral_numeral_int,N2)),aa_num_int(numeral_numeral_int,N2)) ).

% numeral_Bit0
tff(fact_2648_numeral__Bit0,axiom,
    ! [N2: num] : aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,N2)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_num_Code_integer(numera6620942414471956472nteger,N2)),aa_num_Code_integer(numera6620942414471956472nteger,N2)) ).

% numeral_Bit0
tff(fact_2649_numeral__Bit0,axiom,
    ! [N2: num] : aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,N2)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_num_rat(numeral_numeral_rat,N2)),aa_num_rat(numeral_numeral_rat,N2)) ).

% numeral_Bit0
tff(fact_2650_numeral__Bit0,axiom,
    ! [N2: num] : aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,N2)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_num_Code_natural(numera5444537566228673987atural,N2)),aa_num_Code_natural(numera5444537566228673987atural,N2)) ).

% numeral_Bit0
tff(fact_2651_one__neq__neg__numeral,axiom,
    ! [N2: num] : one_one_int != aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,N2)) ).

% one_neq_neg_numeral
tff(fact_2652_one__neq__neg__numeral,axiom,
    ! [N2: num] : one_one_Code_integer != aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,N2)) ).

% one_neq_neg_numeral
tff(fact_2653_one__neq__neg__numeral,axiom,
    ! [N2: num] : one_one_rat != aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,N2)) ).

% one_neq_neg_numeral
tff(fact_2654_numeral__neq__neg__one,axiom,
    ! [N2: num] : aa_num_int(numeral_numeral_int,N2) != aa_int_int(uminus_uminus_int,one_one_int) ).

% numeral_neq_neg_one
tff(fact_2655_numeral__neq__neg__one,axiom,
    ! [N2: num] : aa_num_Code_integer(numera6620942414471956472nteger,N2) != aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) ).

% numeral_neq_neg_one
tff(fact_2656_numeral__neq__neg__one,axiom,
    ! [N2: num] : aa_num_rat(numeral_numeral_rat,N2) != aa_rat_rat(uminus_uminus_rat,one_one_rat) ).

% numeral_neq_neg_one
tff(fact_2657_uncurry__def,axiom,
    ! [F: fun_nat_fun_nat_nat] : uncurry_nat_nat_nat(F) = aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,F) ).

% uncurry_def
tff(fact_2658_uncurry__def,axiom,
    ! [F: fun_na1668100129766719005at_nat] : uncurr9212869592684144700at_nat(F) = aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,F) ).

% uncurry_def
tff(fact_2659_uncurry__def,axiom,
    ! [F: fun_na5914473681949881652_nat_o] : uncurr8479020417594943315_nat_o(F) = aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,F) ).

% uncurry_def
tff(fact_2660_uncurry__def,axiom,
    ! [F: fun_in1696471567231710611nt_int] : uncurr7650761721940715016nt_int(F) = aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,F) ).

% uncurry_def
tff(fact_2661_uncurry__def,axiom,
    ! [F: fun_int_fun_int_int] : uncurry_int_int_int(F) = aa_fun914008879417524284nt_int(produc8211389475949308722nt_int,F) ).

% uncurry_def
tff(fact_2662_internal__case__prod__def,axiom,
    produc6557683772455589876at_nat = produc6842872674320459806at_nat ).

% internal_case_prod_def
tff(fact_2663_internal__case__prod__def,axiom,
    produc8104577556401574439at_nat = produc4528391901023682385at_nat ).

% internal_case_prod_def
tff(fact_2664_internal__case__prod__def,axiom,
    produc9189008374811844670_nat_o = produc6395135316500328296_nat_o ).

% internal_case_prod_def
tff(fact_2665_internal__case__prod__def,axiom,
    produc297006045350968285nt_int = produc4245557441103728435nt_int ).

% internal_case_prod_def
tff(fact_2666_internal__case__prod__def,axiom,
    produc7926200574084438792nt_int = produc8211389475949308722nt_int ).

% internal_case_prod_def
tff(fact_2667_sum_OatLeastAtMost__rev,axiom,
    ! [G: fun_nat_nat,N2: nat,M: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(N2),M)) = aa_set_nat_nat(groups3542108847815614940at_nat(aa_nat_fun_nat_nat(aa_nat3783148529270815480at_nat(aTP_Lamm_do(G),N2),M)),aa_nat_set_nat(set_or1269000886237332187st_nat(N2),M)) ).

% sum.atLeastAtMost_rev
tff(fact_2668_numeral__code_I2_J,axiom,
    ! [N2: num] :
      aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,N2)) = $let(
        m: nat,
        m:= aa_num_nat(numeral_numeral_nat,N2),
        aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,m),m) ) ).

% numeral_code(2)
tff(fact_2669_numeral__code_I2_J,axiom,
    ! [N2: num] :
      aa_num_int(numeral_numeral_int,aa_num_num(bit0,N2)) = $let(
        m: int,
        m:= aa_num_int(numeral_numeral_int,N2),
        aa_int_int(aa_int_fun_int_int(plus_plus_int,m),m) ) ).

% numeral_code(2)
tff(fact_2670_numeral__code_I2_J,axiom,
    ! [N2: num] :
      aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,N2)) = $let(
        m: code_integer,
        m:= aa_num_Code_integer(numera6620942414471956472nteger,N2),
        aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,m),m) ) ).

% numeral_code(2)
tff(fact_2671_numeral__code_I2_J,axiom,
    ! [N2: num] :
      aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,N2)) = $let(
        m: rat,
        m:= aa_num_rat(numeral_numeral_rat,N2),
        aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,m),m) ) ).

% numeral_code(2)
tff(fact_2672_numeral__code_I2_J,axiom,
    ! [N2: num] :
      aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,N2)) = $let(
        m: code_natural,
        m:= aa_num_Code_natural(numera5444537566228673987atural,N2),
        aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,m),m) ) ).

% numeral_code(2)
tff(fact_2673_sum__shift__lb__Suc0__0,axiom,
    ! [F: fun_nat_Code_integer,K: nat] :
      ( ( aa_nat_Code_integer(F,zero_zero_nat) = zero_z3403309356797280102nteger )
     => ( groups7501900531339628137nteger(F,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,zero_zero_nat)),K)) = groups7501900531339628137nteger(F,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),K)) ) ) ).

% sum_shift_lb_Suc0_0
tff(fact_2674_sum__shift__lb__Suc0__0,axiom,
    ! [F: fun_na2338080690716861136at_nat,K: nat] :
      ( ( aa_nat2240542744625857721at_nat(F,zero_zero_nat) = zero_z1048942125864253310at_nat )
     => ( groups6857163185585827899at_nat(F,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,zero_zero_nat)),K)) = groups6857163185585827899at_nat(F,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),K)) ) ) ).

% sum_shift_lb_Suc0_0
tff(fact_2675_sum__shift__lb__Suc0__0,axiom,
    ! [F: fun_nat_rat,K: nat] :
      ( ( aa_nat_rat(F,zero_zero_nat) = zero_zero_rat )
     => ( groups2906978787729119204at_rat(F,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,zero_zero_nat)),K)) = groups2906978787729119204at_rat(F,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),K)) ) ) ).

% sum_shift_lb_Suc0_0
tff(fact_2676_sum__shift__lb__Suc0__0,axiom,
    ! [F: fun_nat_int,K: nat] :
      ( ( aa_nat_int(F,zero_zero_nat) = zero_zero_int )
     => ( groups3539618377306564664at_int(F,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,zero_zero_nat)),K)) = groups3539618377306564664at_int(F,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),K)) ) ) ).

% sum_shift_lb_Suc0_0
tff(fact_2677_sum__shift__lb__Suc0__0,axiom,
    ! [F: fun_nat_nat,K: nat] :
      ( ( aa_nat_nat(F,zero_zero_nat) = zero_zero_nat )
     => ( aa_set_nat_nat(groups3542108847815614940at_nat(F),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,zero_zero_nat)),K)) = aa_set_nat_nat(groups3542108847815614940at_nat(F),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),K)) ) ) ).

% sum_shift_lb_Suc0_0
tff(fact_2678_sum_OatLeast0__atMost__Suc,axiom,
    ! [G: fun_na2338080690716861136at_nat,N2: nat] : groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2))),aa_nat2240542744625857721at_nat(G,aa_nat_nat(suc,N2))) ).

% sum.atLeast0_atMost_Suc
tff(fact_2679_sum_OatLeast0__atMost__Suc,axiom,
    ! [G: fun_nat_rat,N2: nat] : groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2))),aa_nat_rat(G,aa_nat_nat(suc,N2))) ).

% sum.atLeast0_atMost_Suc
tff(fact_2680_sum_OatLeast0__atMost__Suc,axiom,
    ! [G: fun_nat_int,N2: nat] : groups3539618377306564664at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,groups3539618377306564664at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2))),aa_nat_int(G,aa_nat_nat(suc,N2))) ).

% sum.atLeast0_atMost_Suc
tff(fact_2681_sum_OatLeast0__atMost__Suc,axiom,
    ! [G: fun_nat_nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2))),aa_nat_nat(G,aa_nat_nat(suc,N2))) ).

% sum.atLeast0_atMost_Suc
tff(fact_2682_sum_OatLeast0__atMost__Suc__shift,axiom,
    ! [G: fun_na2338080690716861136at_nat,N2: nat] : groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(aa_nat2240542744625857721at_nat(G,zero_zero_nat)),groups6857163185585827899at_nat(comp_n8698576032424989604at_nat(G,suc),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2))) ).

% sum.atLeast0_atMost_Suc_shift
tff(fact_2683_sum_OatLeast0__atMost__Suc__shift,axiom,
    ! [G: fun_nat_rat,N2: nat] : groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(G,zero_zero_nat)),groups2906978787729119204at_rat(comp_nat_rat_nat(G,suc),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2))) ).

% sum.atLeast0_atMost_Suc_shift
tff(fact_2684_sum_OatLeast0__atMost__Suc__shift,axiom,
    ! [G: fun_nat_int,N2: nat] : groups3539618377306564664at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(G,zero_zero_nat)),groups3539618377306564664at_int(comp_nat_int_nat(G,suc),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2))) ).

% sum.atLeast0_atMost_Suc_shift
tff(fact_2685_sum_OatLeast0__atMost__Suc__shift,axiom,
    ! [G: fun_nat_nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(G,zero_zero_nat)),aa_set_nat_nat(groups3542108847815614940at_nat(comp_nat_nat_nat(G,suc)),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2))) ).

% sum.atLeast0_atMost_Suc_shift
tff(fact_2686_sum_OatLeast__Suc__atMost,axiom,
    ! [M: nat,N2: nat,G: fun_na2338080690716861136at_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(aa_nat2240542744625857721at_nat(G,M)),groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,M)),N2))) ) ) ).

% sum.atLeast_Suc_atMost
tff(fact_2687_sum_OatLeast__Suc__atMost,axiom,
    ! [M: nat,N2: nat,G: fun_nat_rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(G,M)),groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,M)),N2))) ) ) ).

% sum.atLeast_Suc_atMost
tff(fact_2688_sum_OatLeast__Suc__atMost,axiom,
    ! [M: nat,N2: nat,G: fun_nat_int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( groups3539618377306564664at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(G,M)),groups3539618377306564664at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,M)),N2))) ) ) ).

% sum.atLeast_Suc_atMost
tff(fact_2689_sum_OatLeast__Suc__atMost,axiom,
    ! [M: nat,N2: nat,G: fun_nat_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(G,M)),aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,M)),N2))) ) ) ).

% sum.atLeast_Suc_atMost
tff(fact_2690_sum_Onat__ivl__Suc_H,axiom,
    ! [M: nat,N2: nat,G: fun_na2338080690716861136at_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),aa_nat_nat(suc,N2))
     => ( groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),aa_nat_nat(suc,N2))) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(aa_nat2240542744625857721at_nat(G,aa_nat_nat(suc,N2))),groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))) ) ) ).

% sum.nat_ivl_Suc'
tff(fact_2691_sum_Onat__ivl__Suc_H,axiom,
    ! [M: nat,N2: nat,G: fun_nat_rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),aa_nat_nat(suc,N2))
     => ( groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),aa_nat_nat(suc,N2))) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(G,aa_nat_nat(suc,N2))),groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))) ) ) ).

% sum.nat_ivl_Suc'
tff(fact_2692_sum_Onat__ivl__Suc_H,axiom,
    ! [M: nat,N2: nat,G: fun_nat_int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),aa_nat_nat(suc,N2))
     => ( groups3539618377306564664at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),aa_nat_nat(suc,N2))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(G,aa_nat_nat(suc,N2))),groups3539618377306564664at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))) ) ) ).

% sum.nat_ivl_Suc'
tff(fact_2693_sum_Onat__ivl__Suc_H,axiom,
    ! [M: nat,N2: nat,G: fun_nat_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),aa_nat_nat(suc,N2))
     => ( aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),aa_nat_nat(suc,N2))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(G,aa_nat_nat(suc,N2))),aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))) ) ) ).

% sum.nat_ivl_Suc'
tff(fact_2694_neg__numeral__le__one,axiom,
    ! [M: num] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,M))),one_one_Code_integer) ).

% neg_numeral_le_one
tff(fact_2695_neg__numeral__le__one,axiom,
    ! [M: num] : aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,M))),one_one_rat) ).

% neg_numeral_le_one
tff(fact_2696_neg__numeral__le__one,axiom,
    ! [M: num] : aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,M))),one_one_int) ).

% neg_numeral_le_one
tff(fact_2697_neg__one__le__numeral,axiom,
    ! [M: num] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),aa_num_Code_integer(numera6620942414471956472nteger,M)) ).

% neg_one_le_numeral
tff(fact_2698_neg__one__le__numeral,axiom,
    ! [M: num] : aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),aa_num_rat(numeral_numeral_rat,M)) ).

% neg_one_le_numeral
tff(fact_2699_neg__one__le__numeral,axiom,
    ! [M: num] : aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(uminus_uminus_int,one_one_int)),aa_num_int(numeral_numeral_int,M)) ).

% neg_one_le_numeral
tff(fact_2700_neg__numeral__le__neg__one,axiom,
    ! [M: num] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,M))),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) ).

% neg_numeral_le_neg_one
tff(fact_2701_neg__numeral__le__neg__one,axiom,
    ! [M: num] : aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,M))),aa_rat_rat(uminus_uminus_rat,one_one_rat)) ).

% neg_numeral_le_neg_one
tff(fact_2702_neg__numeral__le__neg__one,axiom,
    ! [M: num] : aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,M))),aa_int_int(uminus_uminus_int,one_one_int)) ).

% neg_numeral_le_neg_one
tff(fact_2703_not__numeral__le__neg__one,axiom,
    ! [M: num] : ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_num_Code_integer(numera6620942414471956472nteger,M)),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) ).

% not_numeral_le_neg_one
tff(fact_2704_not__numeral__le__neg__one,axiom,
    ! [M: num] : ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_num_rat(numeral_numeral_rat,M)),aa_rat_rat(uminus_uminus_rat,one_one_rat)) ).

% not_numeral_le_neg_one
tff(fact_2705_not__numeral__le__neg__one,axiom,
    ! [M: num] : ~ aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_num_int(numeral_numeral_int,M)),aa_int_int(uminus_uminus_int,one_one_int)) ).

% not_numeral_le_neg_one
tff(fact_2706_not__one__le__neg__numeral,axiom,
    ! [M: num] : ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,M))) ).

% not_one_le_neg_numeral
tff(fact_2707_not__one__le__neg__numeral,axiom,
    ! [M: num] : ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,M))) ).

% not_one_le_neg_numeral
tff(fact_2708_not__one__le__neg__numeral,axiom,
    ! [M: num] : ~ aa_int_o(aa_int_fun_int_o(ord_less_eq_int,one_one_int),aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,M))) ).

% not_one_le_neg_numeral
tff(fact_2709_not__neg__one__less__neg__numeral,axiom,
    ! [M: num] : ~ aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(uminus_uminus_int,one_one_int)),aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,M))) ).

% not_neg_one_less_neg_numeral
tff(fact_2710_not__neg__one__less__neg__numeral,axiom,
    ! [M: num] : ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,M))) ).

% not_neg_one_less_neg_numeral
tff(fact_2711_not__neg__one__less__neg__numeral,axiom,
    ! [M: num] : ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,M))) ).

% not_neg_one_less_neg_numeral
tff(fact_2712_not__one__less__neg__numeral,axiom,
    ! [M: num] : ~ aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,M))) ).

% not_one_less_neg_numeral
tff(fact_2713_not__one__less__neg__numeral,axiom,
    ! [M: num] : ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,M))) ).

% not_one_less_neg_numeral
tff(fact_2714_not__one__less__neg__numeral,axiom,
    ! [M: num] : ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,M))) ).

% not_one_less_neg_numeral
tff(fact_2715_not__numeral__less__neg__one,axiom,
    ! [M: num] : ~ aa_int_o(aa_int_fun_int_o(ord_less_int,aa_num_int(numeral_numeral_int,M)),aa_int_int(uminus_uminus_int,one_one_int)) ).

% not_numeral_less_neg_one
tff(fact_2716_not__numeral__less__neg__one,axiom,
    ! [M: num] : ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_num_Code_integer(numera6620942414471956472nteger,M)),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) ).

% not_numeral_less_neg_one
tff(fact_2717_not__numeral__less__neg__one,axiom,
    ! [M: num] : ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_num_rat(numeral_numeral_rat,M)),aa_rat_rat(uminus_uminus_rat,one_one_rat)) ).

% not_numeral_less_neg_one
tff(fact_2718_neg__one__less__numeral,axiom,
    ! [M: num] : aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(uminus_uminus_int,one_one_int)),aa_num_int(numeral_numeral_int,M)) ).

% neg_one_less_numeral
tff(fact_2719_neg__one__less__numeral,axiom,
    ! [M: num] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),aa_num_Code_integer(numera6620942414471956472nteger,M)) ).

% neg_one_less_numeral
tff(fact_2720_neg__one__less__numeral,axiom,
    ! [M: num] : aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),aa_num_rat(numeral_numeral_rat,M)) ).

% neg_one_less_numeral
tff(fact_2721_neg__numeral__less__one,axiom,
    ! [M: num] : aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,M))),one_one_int) ).

% neg_numeral_less_one
tff(fact_2722_neg__numeral__less__one,axiom,
    ! [M: num] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,M))),one_one_Code_integer) ).

% neg_numeral_less_one
tff(fact_2723_neg__numeral__less__one,axiom,
    ! [M: num] : aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,M))),one_one_rat) ).

% neg_numeral_less_one
tff(fact_2724_sum_OSuc__reindex__ivl,axiom,
    ! [M: nat,N2: nat,G: fun_na2338080690716861136at_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))),aa_nat2240542744625857721at_nat(G,aa_nat_nat(suc,N2))) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(aa_nat2240542744625857721at_nat(G,M)),groups6857163185585827899at_nat(aTP_Lamm_dp(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))) ) ) ).

% sum.Suc_reindex_ivl
tff(fact_2725_sum_OSuc__reindex__ivl,axiom,
    ! [M: nat,N2: nat,G: fun_nat_rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))),aa_nat_rat(G,aa_nat_nat(suc,N2))) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(G,M)),groups2906978787729119204at_rat(aTP_Lamm_dq(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))) ) ) ).

% sum.Suc_reindex_ivl
tff(fact_2726_sum_OSuc__reindex__ivl,axiom,
    ! [M: nat,N2: nat,G: fun_nat_int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_int_int(aa_int_fun_int_int(plus_plus_int,groups3539618377306564664at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))),aa_nat_int(G,aa_nat_nat(suc,N2))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(G,M)),groups3539618377306564664at_int(aTP_Lamm_dr(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))) ) ) ).

% sum.Suc_reindex_ivl
tff(fact_2727_sum_OSuc__reindex__ivl,axiom,
    ! [M: nat,N2: nat,G: fun_nat_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))),aa_nat_nat(G,aa_nat_nat(suc,N2))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(G,M)),aa_set_nat_nat(groups3542108847815614940at_nat(aTP_Lamm_dh(G)),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))) ) ) ).

% sum.Suc_reindex_ivl
tff(fact_2728_sum__Suc__diff,axiom,
    ! [M: nat,N2: nat,F: fun_nat_Code_integer] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),aa_nat_nat(suc,N2))
     => ( groups7501900531339628137nteger(aTP_Lamm_ds(F),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_nat_Code_integer(F,aa_nat_nat(suc,N2))),aa_nat_Code_integer(F,M)) ) ) ).

% sum_Suc_diff
tff(fact_2729_sum__Suc__diff,axiom,
    ! [M: nat,N2: nat,F: fun_nat_rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),aa_nat_nat(suc,N2))
     => ( groups2906978787729119204at_rat(aTP_Lamm_dt(F),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = aa_rat_rat(minus_minus_rat(aa_nat_rat(F,aa_nat_nat(suc,N2))),aa_nat_rat(F,M)) ) ) ).

% sum_Suc_diff
tff(fact_2730_sum__Suc__diff,axiom,
    ! [M: nat,N2: nat,F: fun_nat_int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),aa_nat_nat(suc,N2))
     => ( groups3539618377306564664at_int(aTP_Lamm_du(F),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(F,aa_nat_nat(suc,N2))),aa_nat_int(F,M)) ) ) ).

% sum_Suc_diff
tff(fact_2731_sum__power__add,axiom,
    ! [X2: rat,M: nat,I4: set_nat] : groups2906978787729119204at_rat(aa_nat_fun_nat_rat(aTP_Lamm_dv(X2),M),I4) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),M)),groups2906978787729119204at_rat(aa_rat_fun_nat_rat(power_power_rat,X2),I4)) ).

% sum_power_add
tff(fact_2732_sum__power__add,axiom,
    ! [X2: int,M: nat,I4: set_nat] : groups3539618377306564664at_int(aa_nat_fun_nat_int(aTP_Lamm_dw(X2),M),I4) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,X2),M)),groups3539618377306564664at_int(aa_int_fun_nat_int(power_power_int,X2),I4)) ).

% sum_power_add
tff(fact_2733_sum_OatLeast__atMost__pred__shift,axiom,
    ! [G: fun_nat_nat,M: nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(comp_nat_nat_nat(G,aTP_Lamm_dx)),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,M)),aa_nat_nat(suc,N2))) = aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) ).

% sum.atLeast_atMost_pred_shift
tff(fact_2734_sum__atLeastAtMost__code,axiom,
    ! [F: fun_nat_Code_integer,A: nat,B: nat] : groups7501900531339628137nteger(F,aa_nat_set_nat(set_or1269000886237332187st_nat(A),B)) = aa_Cod1783974652533396728nteger(set_fo1084959871951514735nteger(aTP_Lamm_dy(F),A,B),zero_z3403309356797280102nteger) ).

% sum_atLeastAtMost_code
tff(fact_2735_sum__atLeastAtMost__code,axiom,
    ! [F: fun_na2338080690716861136at_nat,A: nat,B: nat] : groups6857163185585827899at_nat(F,aa_nat_set_nat(set_or1269000886237332187st_nat(A),B)) = set_fo4497565046347964853at_nat(aTP_Lamm_dz(F),A,B,zero_z1048942125864253310at_nat) ).

% sum_atLeastAtMost_code
tff(fact_2736_sum__atLeastAtMost__code,axiom,
    ! [F: fun_nat_rat,A: nat,B: nat] : groups2906978787729119204at_rat(F,aa_nat_set_nat(set_or1269000886237332187st_nat(A),B)) = aa_rat_rat(set_fo1949268297981939178at_rat(aTP_Lamm_ea(F),A,B),zero_zero_rat) ).

% sum_atLeastAtMost_code
tff(fact_2737_sum__atLeastAtMost__code,axiom,
    ! [F: fun_nat_int,A: nat,B: nat] : groups3539618377306564664at_int(F,aa_nat_set_nat(set_or1269000886237332187st_nat(A),B)) = aa_int_int(set_fo2581907887559384638at_int(aTP_Lamm_eb(F),A,B),zero_zero_int) ).

% sum_atLeastAtMost_code
tff(fact_2738_sum__atLeastAtMost__code,axiom,
    ! [F: fun_nat_nat,A: nat,B: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(F),aa_nat_set_nat(set_or1269000886237332187st_nat(A),B)) = aa_nat_nat(aa_nat_fun_nat_nat(set_fo2584398358068434914at_nat(aTP_Lamm_ec(F),A),B),zero_zero_nat) ).

% sum_atLeastAtMost_code
tff(fact_2739_sum_Oub__add__nat,axiom,
    ! [M: nat,N2: nat,G: fun_na2338080690716861136at_nat,P2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),one_one_nat))
     => ( groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),P2))) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))),groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),one_one_nat)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),P2)))) ) ) ).

% sum.ub_add_nat
tff(fact_2740_sum_Oub__add__nat,axiom,
    ! [M: nat,N2: nat,G: fun_nat_rat,P2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),one_one_nat))
     => ( groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),P2))) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))),groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),one_one_nat)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),P2)))) ) ) ).

% sum.ub_add_nat
tff(fact_2741_sum_Oub__add__nat,axiom,
    ! [M: nat,N2: nat,G: fun_nat_int,P2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),one_one_nat))
     => ( groups3539618377306564664at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),P2))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,groups3539618377306564664at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))),groups3539618377306564664at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),one_one_nat)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),P2)))) ) ) ).

% sum.ub_add_nat
tff(fact_2742_sum_Oub__add__nat,axiom,
    ! [M: nat,N2: nat,G: fun_nat_nat,P2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),one_one_nat))
     => ( aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),P2))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))),aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),one_one_nat)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),P2)))) ) ) ).

% sum.ub_add_nat
tff(fact_2743_sum_OatLeastAtMost__shift__0,axiom,
    ! [M: nat,N2: nat,G: fun_nat_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = aa_set_nat_nat(groups3542108847815614940at_nat(comp_nat_nat_nat(G,aa_nat_fun_nat_nat(plus_plus_nat,M))),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),M))) ) ) ).

% sum.atLeastAtMost_shift_0
tff(fact_2744_zero__int__def,axiom,
    zero_zero_int = aa_Pro4240683299535347697at_int(abs_Integ,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,zero_zero_nat),zero_zero_nat)) ).

% zero_int_def
tff(fact_2745_pair__lessI1,axiom,
    ! [A: nat,B: nat,S: nat,T: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),B)
     => member8206827879206165904at_nat(produc6161850002892822231at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),S),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,B),T)),fun_pair_less) ) ).

% pair_lessI1
tff(fact_2746_zero__int_Otransfer,axiom,
    aa_int_o(aa_Pro2912763917461432128_int_o(pcr_int,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,zero_zero_nat),zero_zero_nat)),zero_zero_int) ).

% zero_int.transfer
tff(fact_2747_sum__natinterval__diff,axiom,
    ! [F: fun_nat_Code_integer,M: nat,N2: nat] :
      groups7501900531339628137nteger(aTP_Lamm_ed(F),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_nat_Code_integer(F,M)),aa_nat_Code_integer(F,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),one_one_nat))),zero_z3403309356797280102nteger) ).

% sum_natinterval_diff
tff(fact_2748_sum__natinterval__diff,axiom,
    ! [F: fun_nat_rat,M: nat,N2: nat] :
      groups2906978787729119204at_rat(aTP_Lamm_ee(F),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2),aa_rat_rat(minus_minus_rat(aa_nat_rat(F,M)),aa_nat_rat(F,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),one_one_nat))),zero_zero_rat) ).

% sum_natinterval_diff
tff(fact_2749_sum__natinterval__diff,axiom,
    ! [F: fun_nat_int,M: nat,N2: nat] :
      groups3539618377306564664at_int(aTP_Lamm_ef(F),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2),aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(F,M)),aa_nat_int(F,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),one_one_nat))),zero_zero_int) ).

% sum_natinterval_diff
tff(fact_2750_convex__sum__bound__le,axiom,
    ! [I4: set_o,X2: fun_o_Code_integer,A: fun_o_Code_integer,B: code_integer,Delta: code_integer] :
      ( ! [I2: $o] :
          ( member_o((I2),I4)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_o_Code_integer(X2,(I2))) )
     => ( ( groups4406642042086082107nteger(X2,I4) = one_one_Code_integer )
       => ( ! [I2: $o] :
              ( member_o((I2),I4)
             => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_o_Code_integer(A,(I2))),B))),Delta) )
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,groups4406642042086082107nteger(aa_fun8520278569782659900nteger(aTP_Lamm_eg(X2),A),I4)),B))),Delta) ) ) ) ).

% convex_sum_bound_le
tff(fact_2751_convex__sum__bound__le,axiom,
    ! [I4: set_nat,X2: fun_nat_Code_integer,A: fun_nat_Code_integer,B: code_integer,Delta: code_integer] :
      ( ! [I2: nat] :
          ( member_nat(I2,I4)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_nat_Code_integer(X2,I2)) )
     => ( ( groups7501900531339628137nteger(X2,I4) = one_one_Code_integer )
       => ( ! [I2: nat] :
              ( member_nat(I2,I4)
             => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_nat_Code_integer(A,I2)),B))),Delta) )
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,groups7501900531339628137nteger(aa_fun589076786913273746nteger(aTP_Lamm_eh(X2),A),I4)),B))),Delta) ) ) ) ).

% convex_sum_bound_le
tff(fact_2752_convex__sum__bound__le,axiom,
    ! [I4: set_int,X2: fun_int_Code_integer,A: fun_int_Code_integer,B: code_integer,Delta: code_integer] :
      ( ! [I2: int] :
          ( member_int(I2,I4)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_int_Code_integer(X2,I2)) )
     => ( ( groups7873554091576472773nteger(X2,I4) = one_one_Code_integer )
       => ( ! [I2: int] :
              ( member_int(I2,I4)
             => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_int_Code_integer(A,I2)),B))),Delta) )
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,groups7873554091576472773nteger(aa_fun5304498221708291146nteger(aTP_Lamm_ei(X2),A),I4)),B))),Delta) ) ) ) ).

% convex_sum_bound_le
tff(fact_2753_convex__sum__bound__le,axiom,
    ! [I4: set_o,X2: fun_o_rat,A: fun_o_rat,B: rat,Delta: rat] :
      ( ! [I2: $o] :
          ( member_o((I2),I4)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),aa_o_rat(X2,(I2))) )
     => ( ( groups7872700643590313910_o_rat(X2,I4) = one_one_rat )
       => ( ! [I2: $o] :
              ( member_o((I2),I4)
             => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(abs_abs_rat,aa_rat_rat(minus_minus_rat(aa_o_rat(A,(I2))),B))),Delta) )
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(abs_abs_rat,aa_rat_rat(minus_minus_rat(groups7872700643590313910_o_rat(aa_fun4336163974892599420_o_rat(aTP_Lamm_ej(X2),A),I4)),B))),Delta) ) ) ) ).

% convex_sum_bound_le
tff(fact_2754_convex__sum__bound__le,axiom,
    ! [I4: set_nat,X2: fun_nat_rat,A: fun_nat_rat,B: rat,Delta: rat] :
      ( ! [I2: nat] :
          ( member_nat(I2,I4)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),aa_nat_rat(X2,I2)) )
     => ( ( groups2906978787729119204at_rat(X2,I4) = one_one_rat )
       => ( ! [I2: nat] :
              ( member_nat(I2,I4)
             => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(abs_abs_rat,aa_rat_rat(minus_minus_rat(aa_nat_rat(A,I2)),B))),Delta) )
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(abs_abs_rat,aa_rat_rat(minus_minus_rat(groups2906978787729119204at_rat(aa_fun765758790203053448at_rat(aTP_Lamm_ek(X2),A),I4)),B))),Delta) ) ) ) ).

% convex_sum_bound_le
tff(fact_2755_convex__sum__bound__le,axiom,
    ! [I4: set_int,X2: fun_int_rat,A: fun_int_rat,B: rat,Delta: rat] :
      ( ! [I2: int] :
          ( member_int(I2,I4)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),aa_int_rat(X2,I2)) )
     => ( ( groups3906332499630173760nt_rat(X2,I4) = one_one_rat )
       => ( ! [I2: int] :
              ( member_int(I2,I4)
             => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(abs_abs_rat,aa_rat_rat(minus_minus_rat(aa_int_rat(A,I2)),B))),Delta) )
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(abs_abs_rat,aa_rat_rat(minus_minus_rat(groups3906332499630173760nt_rat(aa_fun1481061427733998144nt_rat(aTP_Lamm_el(X2),A),I4)),B))),Delta) ) ) ) ).

% convex_sum_bound_le
tff(fact_2756_convex__sum__bound__le,axiom,
    ! [I4: set_o,X2: fun_o_int,A: fun_o_int,B: int,Delta: int] :
      ( ! [I2: $o] :
          ( member_o((I2),I4)
         => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),aa_o_int(X2,(I2))) )
     => ( ( groups8505340233167759370_o_int(X2,I4) = one_one_int )
       => ( ! [I2: $o] :
              ( member_o((I2),I4)
             => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(abs_abs_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_o_int(A,(I2))),B))),Delta) )
         => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(abs_abs_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,groups8505340233167759370_o_int(aa_fun4727766026823762812_o_int(aTP_Lamm_em(X2),A),I4)),B))),Delta) ) ) ) ).

% convex_sum_bound_le
tff(fact_2757_convex__sum__bound__le,axiom,
    ! [I4: set_nat,X2: fun_nat_int,A: fun_nat_int,B: int,Delta: int] :
      ( ! [I2: nat] :
          ( member_nat(I2,I4)
         => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),aa_nat_int(X2,I2)) )
     => ( ( groups3539618377306564664at_int(X2,I4) = one_one_int )
       => ( ! [I2: nat] :
              ( member_nat(I2,I4)
             => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(abs_abs_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(A,I2)),B))),Delta) )
         => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(abs_abs_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,groups3539618377306564664at_int(aa_fun5565043122120104496at_int(aTP_Lamm_en(X2),A),I4)),B))),Delta) ) ) ) ).

% convex_sum_bound_le
tff(fact_2758_convex__sum__bound__le,axiom,
    ! [I4: set_int,X2: fun_int_int,A: fun_int_int,B: int,Delta: int] :
      ( ! [I2: int] :
          ( member_int(I2,I4)
         => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),aa_int_int(X2,I2)) )
     => ( ( aa_set_int_int(groups4538972089207619220nt_int(X2),I4) = one_one_int )
       => ( ! [I2: int] :
              ( member_int(I2,I4)
             => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(abs_abs_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(A,I2)),B))),Delta) )
         => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(abs_abs_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_set_int_int(groups4538972089207619220nt_int(aa_fun6280345759651049192nt_int(aTP_Lamm_eo(X2),A)),I4)),B))),Delta) ) ) ) ).

% convex_sum_bound_le
tff(fact_2759_convex__sum__bound__le,axiom,
    ! [I4: set_Pr1261947904930325089at_nat,X2: fun_Pr6026251430685297nteger,A: fun_Pr6026251430685297nteger,B: code_integer,Delta: code_integer] :
      ( ! [I2: product_prod_nat_nat] :
          ( member8440522571783428010at_nat(I2,I4)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_Pro4764841431850000930nteger(X2,I2)) )
     => ( ( groups196832835297161892nteger(X2,I4) = one_one_Code_integer )
       => ( ! [I2: product_prod_nat_nat] :
              ( member8440522571783428010at_nat(I2,I4)
             => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Pro4764841431850000930nteger(A,I2)),B))),Delta) )
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,groups196832835297161892nteger(aa_fun1555571767557915900nteger(aTP_Lamm_ep(X2),A),I4)),B))),Delta) ) ) ) ).

% convex_sum_bound_le
tff(fact_2760_sum__comp__morphism,axiom,
    ! [Ha: fun_Co8499238673658658103nteger,G: fun_num_Code_integer,A2: set_num] :
      ( ( aa_Cod1783974652533396728nteger(Ha,zero_z3403309356797280102nteger) = zero_z3403309356797280102nteger )
     => ( ! [X3: code_integer,Y4: code_integer] : aa_Cod1783974652533396728nteger(Ha,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X3),Y4)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(Ha,X3)),aa_Cod1783974652533396728nteger(Ha,Y4))
       => ( groups5442708359310287027nteger(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,Ha),G),A2) = aa_Cod1783974652533396728nteger(Ha,groups5442708359310287027nteger(G,A2)) ) ) ) ).

% sum_comp_morphism
tff(fact_2761_sum__comp__morphism,axiom,
    ! [Ha: fun_nat_Code_integer,G: fun_nat_nat,A2: set_nat] :
      ( ( aa_nat_Code_integer(Ha,zero_zero_nat) = zero_z3403309356797280102nteger )
     => ( ! [X3: nat,Y4: nat] : aa_nat_Code_integer(Ha,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X3),Y4)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_nat_Code_integer(Ha,X3)),aa_nat_Code_integer(Ha,Y4))
       => ( groups7501900531339628137nteger(comp_n3898172953802868194er_nat(Ha,G),A2) = aa_nat_Code_integer(Ha,aa_set_nat_nat(groups3542108847815614940at_nat(G),A2)) ) ) ) ).

% sum_comp_morphism
tff(fact_2762_sum__comp__morphism,axiom,
    ! [Ha: fun_nat_rat,G: fun_nat_nat,A2: set_nat] :
      ( ( aa_nat_rat(Ha,zero_zero_nat) = zero_zero_rat )
     => ( ! [X3: nat,Y4: nat] : aa_nat_rat(Ha,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X3),Y4)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(Ha,X3)),aa_nat_rat(Ha,Y4))
       => ( groups2906978787729119204at_rat(comp_nat_rat_nat(Ha,G),A2) = aa_nat_rat(Ha,aa_set_nat_nat(groups3542108847815614940at_nat(G),A2)) ) ) ) ).

% sum_comp_morphism
tff(fact_2763_sum__comp__morphism,axiom,
    ! [Ha: fun_nat_int,G: fun_nat_nat,A2: set_nat] :
      ( ( aa_nat_int(Ha,zero_zero_nat) = zero_zero_int )
     => ( ! [X3: nat,Y4: nat] : aa_nat_int(Ha,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X3),Y4)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(Ha,X3)),aa_nat_int(Ha,Y4))
       => ( groups3539618377306564664at_int(comp_nat_int_nat(Ha,G),A2) = aa_nat_int(Ha,aa_set_nat_nat(groups3542108847815614940at_nat(G),A2)) ) ) ) ).

% sum_comp_morphism
tff(fact_2764_sum__comp__morphism,axiom,
    ! [Ha: fun_int_Code_integer,G: fun_int_int,A2: set_int] :
      ( ( aa_int_Code_integer(Ha,zero_zero_int) = zero_z3403309356797280102nteger )
     => ( ! [X3: int,Y4: int] : aa_int_Code_integer(Ha,aa_int_int(aa_int_fun_int_int(plus_plus_int,X3),Y4)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_int_Code_integer(Ha,X3)),aa_int_Code_integer(Ha,Y4))
       => ( groups7873554091576472773nteger(comp_i1585864551200866970er_int(Ha,G),A2) = aa_int_Code_integer(Ha,aa_set_int_int(groups4538972089207619220nt_int(G),A2)) ) ) ) ).

% sum_comp_morphism
tff(fact_2765_sum__comp__morphism,axiom,
    ! [Ha: fun_int_rat,G: fun_int_int,A2: set_int] :
      ( ( aa_int_rat(Ha,zero_zero_int) = zero_zero_rat )
     => ( ! [X3: int,Y4: int] : aa_int_rat(Ha,aa_int_int(aa_int_fun_int_int(plus_plus_int,X3),Y4)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_int_rat(Ha,X3)),aa_int_rat(Ha,Y4))
       => ( groups3906332499630173760nt_rat(comp_int_rat_int(Ha,G),A2) = aa_int_rat(Ha,aa_set_int_int(groups4538972089207619220nt_int(G),A2)) ) ) ) ).

% sum_comp_morphism
tff(fact_2766_sum__comp__morphism,axiom,
    ! [Ha: fun_int_nat,G: fun_int_int,A2: set_int] :
      ( ( aa_int_nat(Ha,zero_zero_int) = zero_zero_nat )
     => ( ! [X3: int,Y4: int] : aa_int_nat(Ha,aa_int_int(aa_int_fun_int_int(plus_plus_int,X3),Y4)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_int_nat(Ha,X3)),aa_int_nat(Ha,Y4))
       => ( groups4541462559716669496nt_nat(comp_int_nat_int(Ha,G),A2) = aa_int_nat(Ha,aa_set_int_int(groups4538972089207619220nt_int(G),A2)) ) ) ) ).

% sum_comp_morphism
tff(fact_2767_sum__comp__morphism,axiom,
    ! [Ha: fun_Code_integer_nat,G: fun_nat_Code_integer,A2: set_nat] :
      ( ( aa_Code_integer_nat(Ha,zero_z3403309356797280102nteger) = zero_zero_nat )
     => ( ! [X3: code_integer,Y4: code_integer] : aa_Code_integer_nat(Ha,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X3),Y4)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_Code_integer_nat(Ha,X3)),aa_Code_integer_nat(Ha,Y4))
       => ( aa_set_nat_nat(groups3542108847815614940at_nat(comp_C4049556595663050210at_nat(Ha,G)),A2) = aa_Code_integer_nat(Ha,groups7501900531339628137nteger(G,A2)) ) ) ) ).

% sum_comp_morphism
tff(fact_2768_sum__comp__morphism,axiom,
    ! [Ha: fun_rat_nat,G: fun_nat_rat,A2: set_nat] :
      ( ( aa_rat_nat(Ha,zero_zero_rat) = zero_zero_nat )
     => ( ! [X3: rat,Y4: rat] : aa_rat_nat(Ha,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X3),Y4)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_rat_nat(Ha,X3)),aa_rat_nat(Ha,Y4))
       => ( aa_set_nat_nat(groups3542108847815614940at_nat(comp_rat_nat_nat(Ha,G)),A2) = aa_rat_nat(Ha,groups2906978787729119204at_rat(G,A2)) ) ) ) ).

% sum_comp_morphism
tff(fact_2769_sum__comp__morphism,axiom,
    ! [Ha: fun_int_nat,G: fun_nat_int,A2: set_nat] :
      ( ( aa_int_nat(Ha,zero_zero_int) = zero_zero_nat )
     => ( ! [X3: int,Y4: int] : aa_int_nat(Ha,aa_int_int(aa_int_fun_int_int(plus_plus_int,X3),Y4)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_int_nat(Ha,X3)),aa_int_nat(Ha,Y4))
       => ( aa_set_nat_nat(groups3542108847815614940at_nat(comp_int_nat_nat(Ha,G)),A2) = aa_int_nat(Ha,groups3539618377306564664at_int(G,A2)) ) ) ) ).

% sum_comp_morphism
tff(fact_2770_sum__gp,axiom,
    ! [X2: rat,M: nat,N2: nat] :
      groups2906978787729119204at_rat(aa_rat_fun_nat_rat(power_power_rat,X2),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = $ite(
        aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),M),
        zero_zero_rat,
        $ite(X2 = one_one_rat,aa_nat_rat(semiri681578069525770553at_rat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),one_one_nat)),M)),aa_rat_rat(divide_divide_rat(aa_rat_rat(minus_minus_rat(aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),M)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),aa_nat_nat(suc,N2)))),aa_rat_rat(minus_minus_rat(one_one_rat),X2))) ) ).

% sum_gp
tff(fact_2771_divmod__digit__1_I1_J,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),A)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),B)
       => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,B),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),B)))
         => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),B)))),one_one_Code_integer) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),B) ) ) ) ) ).

% divmod_digit_1(1)
tff(fact_2772_divmod__digit__1_I1_J,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),B)
       => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,B),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),B)))
         => ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),B)))),one_one_nat) = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),B) ) ) ) ) ).

% divmod_digit_1(1)
tff(fact_2773_divmod__digit__1_I1_J,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),A)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),B)
       => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,B),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),B)))
         => ( aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),B)))),one_one_int) = aa_int_int(aa_int_fun_int_int(divide_divide_int,A),B) ) ) ) ) ).

% divmod_digit_1(1)
tff(fact_2774_sum__gp__offset,axiom,
    ! [X2: rat,M: nat,N2: nat] :
      groups2906978787729119204at_rat(aa_rat_fun_nat_rat(power_power_rat,X2),aa_nat_set_nat(set_or1269000886237332187st_nat(M),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2))) = $ite(X2 = one_one_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(semiri681578069525770553at_rat,N2)),one_one_rat),aa_rat_rat(divide_divide_rat(aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),M)),aa_rat_rat(minus_minus_rat(one_one_rat),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),aa_nat_nat(suc,N2))))),aa_rat_rat(minus_minus_rat(one_one_rat),X2))) ).

% sum_gp_offset
tff(fact_2775_Sum__Icc__nat,axiom,
    ! [M: nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(aTP_Lamm_co),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),one_one_nat))),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),one_one_nat)))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) ).

% Sum_Icc_nat
tff(fact_2776_arith__series__nat,axiom,
    ! [A: nat,D2: nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(aa_nat_fun_nat_nat(aTP_Lamm_eq(A),D2)),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2)) = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(suc,N2)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,N2),D2)))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) ).

% arith_series_nat
tff(fact_2777_mod__double__modulus,axiom,
    ! [M: code_integer,X2: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),M)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),X2)
       => ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,X2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),M)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,X2),M) )
          | ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,X2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),M)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,X2),M)),M) ) ) ) ) ).

% mod_double_modulus
tff(fact_2778_mod__double__modulus,axiom,
    ! [M: nat,X2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),M)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),X2)
       => ( ( aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X2),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),M)) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X2),M) )
          | ( aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X2),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),M)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X2),M)),M) ) ) ) ) ).

% mod_double_modulus
tff(fact_2779_mod__double__modulus,axiom,
    ! [M: int,X2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),M)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),X2)
       => ( ( aa_int_int(aa_int_fun_int_int(modulo_modulo_int,X2),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),M)) = aa_int_int(aa_int_fun_int_int(modulo_modulo_int,X2),M) )
          | ( aa_int_int(aa_int_fun_int_int(modulo_modulo_int,X2),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),M)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(modulo_modulo_int,X2),M)),M) ) ) ) ) ).

% mod_double_modulus
tff(fact_2780_sum_Odistrib,axiom,
    ! [G: fun_nat_nat,Ha: fun_nat_nat,A2: set_nat] : aa_set_nat_nat(groups3542108847815614940at_nat(aa_fun5791449513213591928at_nat(aTP_Lamm_er(G),Ha)),A2) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_set_nat_nat(groups3542108847815614940at_nat(G),A2)),aa_set_nat_nat(groups3542108847815614940at_nat(Ha),A2)) ).

% sum.distrib
tff(fact_2781_sum_Odistrib,axiom,
    ! [G: fun_int_int,Ha: fun_int_int,A2: set_int] : aa_set_int_int(groups4538972089207619220nt_int(aa_fun6280345759651049192nt_int(aTP_Lamm_es(G),Ha)),A2) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_set_int_int(groups4538972089207619220nt_int(G),A2)),aa_set_int_int(groups4538972089207619220nt_int(Ha),A2)) ).

% sum.distrib
tff(fact_2782_case__prodI,axiom,
    ! [F: fun_fu7695273699059480439eger_o,A: fun_Pr5098669352780829690e_term,B: produc8923325533196201883nteger] :
      ( aa_Pro4926521453222654329eger_o(aa_fun4505422719058378424eger_o(F,A),B)
     => aa_Pro4148064003102580676eger_o(aa_fun7761728421758185830eger_o(produc7373287791920631523eger_o,F),aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A),B)) ) ).

% case_prodI
tff(fact_2783_case__prodI,axiom,
    ! [F: fun_fu8419763957888848259_nat_o,A: fun_Pr6460944699146269935_nat_o,B: produc3658429121746597890et_nat] :
      ( aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(F,A),B)
     => aa_Pro5643009357358181178_nat_o(aa_fun6593097867094858448_nat_o(produc2915205735004773393_nat_o,F),aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A),B)) ) ).

% case_prodI
tff(fact_2784_case__prodI,axiom,
    ! [F: fun_fu2611741329380808165_nat_o,A: fun_Pr6460944699146269935_nat_o,B: produc8799533983703829792et_nat] :
      ( aa_Pro5643009357358181178_nat_o(aa_fun912680268133416158_nat_o(F,A),B)
     => aa_Pro2671238023309943196_nat_o(aa_fun4447940216497214800_nat_o(produc4465912260561112435_nat_o,F),aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A),B)) ) ).

% case_prodI
tff(fact_2785_case__prodI,axiom,
    ! [F: fun_fu6865642474282033866_int_o,A: fun_Pr7763680713840462443e_term,B: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(aa_fun3538162476766722827_int_o(F,A),B)
     => aa_Pro2601676399929874711_int_o(aa_fun6978165455603620006_int_o(produc2207054017359051062_int_o,F),aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,A),B)) ) ).

% case_prodI
tff(fact_2786_case__prodI,axiom,
    ! [F: fun_fu2978539155105838238_int_o,A: fun_in5730379987311621695e_term,B: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(aa_fun586359091965693151_int_o(F,A),B)
     => aa_Pro5451197003417746155_int_o(aa_fun1749673562058638246_int_o(produc7271678899836001034_int_o,F),aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A),B)) ) ).

% case_prodI
tff(fact_2787_case__prodI2,axiom,
    ! [P2: produc2453742332425399446nteger,C: fun_fu7695273699059480439eger_o] :
      ( ! [A3: fun_Pr5098669352780829690e_term,B2: produc8923325533196201883nteger] :
          ( ( P2 = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A3),B2) )
         => aa_Pro4926521453222654329eger_o(aa_fun4505422719058378424eger_o(C,A3),B2) )
     => aa_Pro4148064003102580676eger_o(aa_fun7761728421758185830eger_o(produc7373287791920631523eger_o,C),P2) ) ).

% case_prodI2
tff(fact_2788_case__prodI2,axiom,
    ! [P2: produc8799533983703829792et_nat,C: fun_fu8419763957888848259_nat_o] :
      ( ! [A3: fun_Pr6460944699146269935_nat_o,B2: produc3658429121746597890et_nat] :
          ( ( P2 = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A3),B2) )
         => aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(C,A3),B2) )
     => aa_Pro5643009357358181178_nat_o(aa_fun6593097867094858448_nat_o(produc2915205735004773393_nat_o,C),P2) ) ).

% case_prodI2
tff(fact_2789_case__prodI2,axiom,
    ! [P2: produc3112576180687729086et_nat,C: fun_fu2611741329380808165_nat_o] :
      ( ! [A3: fun_Pr6460944699146269935_nat_o,B2: produc8799533983703829792et_nat] :
          ( ( P2 = aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A3),B2) )
         => aa_Pro5643009357358181178_nat_o(aa_fun912680268133416158_nat_o(C,A3),B2) )
     => aa_Pro2671238023309943196_nat_o(aa_fun4447940216497214800_nat_o(produc4465912260561112435_nat_o,C),P2) ) ).

% case_prodI2
tff(fact_2790_case__prodI2,axiom,
    ! [P2: produc3043004577601930755nt_int,C: fun_fu6865642474282033866_int_o] :
      ( ! [A3: fun_Pr7763680713840462443e_term,B2: product_prod_int_int] :
          ( ( P2 = aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,A3),B2) )
         => aa_Pro4592068669816069595_int_o(aa_fun3538162476766722827_int_o(C,A3),B2) )
     => aa_Pro2601676399929874711_int_o(aa_fun6978165455603620006_int_o(produc2207054017359051062_int_o,C),P2) ) ).

% case_prodI2
tff(fact_2791_case__prodI2,axiom,
    ! [P2: produc4788131091073775919nt_int,C: fun_fu2978539155105838238_int_o] :
      ( ! [A3: fun_in5730379987311621695e_term,B2: product_prod_int_int] :
          ( ( P2 = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A3),B2) )
         => aa_Pro4592068669816069595_int_o(aa_fun586359091965693151_int_o(C,A3),B2) )
     => aa_Pro5451197003417746155_int_o(aa_fun1749673562058638246_int_o(produc7271678899836001034_int_o,C),P2) ) ).

% case_prodI2
tff(fact_2792_mem__case__prodI,axiom,
    ! [Z: $o,C: fun_fu4618385802829667198_set_o,A: fun_in5730379987311621695e_term,B: product_prod_int_int] :
      ( member_o((Z),aa_Pro2653658648327035067_set_o(aa_fun8934358842864497599_set_o(C,A),B))
     => member_o((Z),produc8509172437693241834_set_o(C,aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A),B))) ) ).

% mem_case_prodI
tff(fact_2793_mem__case__prodI,axiom,
    ! [Z: nat,C: fun_fu9079770784915425324et_nat,A: fun_in5730379987311621695e_term,B: product_prod_int_int] :
      ( member_nat(Z,aa_Pro3599192995643711491et_nat(aa_fun8409204002232819093et_nat(C,A),B))
     => member_nat(Z,produc5011043943518292116et_nat(C,aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A),B))) ) ).

% mem_case_prodI
tff(fact_2794_mem__case__prodI,axiom,
    ! [Z: int,C: fun_fu4266222366127506568et_int,A: fun_in5730379987311621695e_term,B: product_prod_int_int] :
      ( member_int(Z,aa_Pro8644714012989290591et_int(aa_fun5919120857301092337et_int(C,A),B))
     => member_int(Z,produc833192924009095408et_int(C,aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A),B))) ) ).

% mem_case_prodI
tff(fact_2795_mem__case__prodI,axiom,
    ! [Z: $o,C: fun_fu4934440599869564003_set_o,A: fun_Pr6460944699146269935_nat_o,B: produc3658429121746597890et_nat] :
      ( member_o((Z),aa_Pro3581020192872483896_set_o(aa_fun1634346356166085724_set_o(C,A),B))
     => member_o((Z),produc330442800291577585_set_o(C,aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A),B))) ) ).

% mem_case_prodI
tff(fact_2796_mem__case__prodI,axiom,
    ! [Z: nat,C: fun_fu86038545275896455et_nat,A: fun_Pr6460944699146269935_nat_o,B: produc3658429121746597890et_nat] :
      ( member_nat(Z,aa_Pro3416150927818442182et_nat(aa_fun6477889762090788408et_nat(C,A),B))
     => member_nat(Z,produc6247649352436904781et_nat(C,aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A),B))) ) ).

% mem_case_prodI
tff(fact_2797_mem__case__prodI,axiom,
    ! [Z: int,C: fun_fu4495862163342753507et_int,A: fun_Pr6460944699146269935_nat_o,B: produc3658429121746597890et_nat] :
      ( member_int(Z,aa_Pro8461671945164021282et_int(aa_fun3987806617159061652et_int(C,A),B))
     => member_int(Z,produc2069798332927708073et_int(C,aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A),B))) ) ).

% mem_case_prodI
tff(fact_2798_mem__case__prodI,axiom,
    ! [Z: product_prod_nat_nat,C: fun_fu6029601804184707687at_nat,A: fun_in5730379987311621695e_term,B: product_prod_int_int] :
      ( member8440522571783428010at_nat(Z,aa_Pro6675321895958450596at_nat(aa_fun712031703178175272at_nat(C,A),B))
     => member8440522571783428010at_nat(Z,produc8603558621761785811at_nat(C,aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A),B))) ) ).

% mem_case_prodI
tff(fact_2799_mem__case__prodI,axiom,
    ! [Z: $o,C: fun_fu6788480576040630871_set_o,A: fun_Pr5098669352780829690e_term,B: produc8923325533196201883nteger] :
      ( member_o((Z),aa_Pro3874180734779831385_set_o(aa_fun6611983550656184728_set_o(C,A),B))
     => member_o((Z),produc8770320508000790979_set_o(C,aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A),B))) ) ).

% mem_case_prodI
tff(fact_2800_mem__case__prodI,axiom,
    ! [Z: nat,C: fun_fu2531416508075921811et_nat,A: fun_Pr5098669352780829690e_term,B: produc8923325533196201883nteger] :
      ( member_nat(Z,aa_Pro381016180347496421et_nat(aa_fun4088370000251959292et_nat(C,A),B))
     => member_nat(Z,produc6164657169593426171et_nat(C,aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A),B))) ) ).

% mem_case_prodI
tff(fact_2801_mem__case__prodI,axiom,
    ! [Z: int,C: fun_fu6941240126142778863et_int,A: fun_Pr5098669352780829690e_term,B: produc8923325533196201883nteger] :
      ( member_int(Z,aa_Pro5426537197693075521et_int(aa_fun1598286855320232536et_int(C,A),B))
     => member_int(Z,produc1986806150084229463et_int(C,aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A),B))) ) ).

% mem_case_prodI
tff(fact_2802_mem__case__prodI2,axiom,
    ! [P2: produc4788131091073775919nt_int,Z: $o,C: fun_fu4618385802829667198_set_o] :
      ( ! [A3: fun_in5730379987311621695e_term,B2: product_prod_int_int] :
          ( ( P2 = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A3),B2) )
         => member_o((Z),aa_Pro2653658648327035067_set_o(aa_fun8934358842864497599_set_o(C,A3),B2)) )
     => member_o((Z),produc8509172437693241834_set_o(C,P2)) ) ).

% mem_case_prodI2
tff(fact_2803_mem__case__prodI2,axiom,
    ! [P2: produc4788131091073775919nt_int,Z: nat,C: fun_fu9079770784915425324et_nat] :
      ( ! [A3: fun_in5730379987311621695e_term,B2: product_prod_int_int] :
          ( ( P2 = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A3),B2) )
         => member_nat(Z,aa_Pro3599192995643711491et_nat(aa_fun8409204002232819093et_nat(C,A3),B2)) )
     => member_nat(Z,produc5011043943518292116et_nat(C,P2)) ) ).

% mem_case_prodI2
tff(fact_2804_mem__case__prodI2,axiom,
    ! [P2: produc4788131091073775919nt_int,Z: int,C: fun_fu4266222366127506568et_int] :
      ( ! [A3: fun_in5730379987311621695e_term,B2: product_prod_int_int] :
          ( ( P2 = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A3),B2) )
         => member_int(Z,aa_Pro8644714012989290591et_int(aa_fun5919120857301092337et_int(C,A3),B2)) )
     => member_int(Z,produc833192924009095408et_int(C,P2)) ) ).

% mem_case_prodI2
tff(fact_2805_mem__case__prodI2,axiom,
    ! [P2: produc8799533983703829792et_nat,Z: $o,C: fun_fu4934440599869564003_set_o] :
      ( ! [A3: fun_Pr6460944699146269935_nat_o,B2: produc3658429121746597890et_nat] :
          ( ( P2 = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A3),B2) )
         => member_o((Z),aa_Pro3581020192872483896_set_o(aa_fun1634346356166085724_set_o(C,A3),B2)) )
     => member_o((Z),produc330442800291577585_set_o(C,P2)) ) ).

% mem_case_prodI2
tff(fact_2806_mem__case__prodI2,axiom,
    ! [P2: produc8799533983703829792et_nat,Z: nat,C: fun_fu86038545275896455et_nat] :
      ( ! [A3: fun_Pr6460944699146269935_nat_o,B2: produc3658429121746597890et_nat] :
          ( ( P2 = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A3),B2) )
         => member_nat(Z,aa_Pro3416150927818442182et_nat(aa_fun6477889762090788408et_nat(C,A3),B2)) )
     => member_nat(Z,produc6247649352436904781et_nat(C,P2)) ) ).

% mem_case_prodI2
tff(fact_2807_mem__case__prodI2,axiom,
    ! [P2: produc8799533983703829792et_nat,Z: int,C: fun_fu4495862163342753507et_int] :
      ( ! [A3: fun_Pr6460944699146269935_nat_o,B2: produc3658429121746597890et_nat] :
          ( ( P2 = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A3),B2) )
         => member_int(Z,aa_Pro8461671945164021282et_int(aa_fun3987806617159061652et_int(C,A3),B2)) )
     => member_int(Z,produc2069798332927708073et_int(C,P2)) ) ).

% mem_case_prodI2
tff(fact_2808_mem__case__prodI2,axiom,
    ! [P2: produc4788131091073775919nt_int,Z: product_prod_nat_nat,C: fun_fu6029601804184707687at_nat] :
      ( ! [A3: fun_in5730379987311621695e_term,B2: product_prod_int_int] :
          ( ( P2 = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A3),B2) )
         => member8440522571783428010at_nat(Z,aa_Pro6675321895958450596at_nat(aa_fun712031703178175272at_nat(C,A3),B2)) )
     => member8440522571783428010at_nat(Z,produc8603558621761785811at_nat(C,P2)) ) ).

% mem_case_prodI2
tff(fact_2809_mem__case__prodI2,axiom,
    ! [P2: produc2453742332425399446nteger,Z: $o,C: fun_fu6788480576040630871_set_o] :
      ( ! [A3: fun_Pr5098669352780829690e_term,B2: produc8923325533196201883nteger] :
          ( ( P2 = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A3),B2) )
         => member_o((Z),aa_Pro3874180734779831385_set_o(aa_fun6611983550656184728_set_o(C,A3),B2)) )
     => member_o((Z),produc8770320508000790979_set_o(C,P2)) ) ).

% mem_case_prodI2
tff(fact_2810_mem__case__prodI2,axiom,
    ! [P2: produc2453742332425399446nteger,Z: nat,C: fun_fu2531416508075921811et_nat] :
      ( ! [A3: fun_Pr5098669352780829690e_term,B2: produc8923325533196201883nteger] :
          ( ( P2 = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A3),B2) )
         => member_nat(Z,aa_Pro381016180347496421et_nat(aa_fun4088370000251959292et_nat(C,A3),B2)) )
     => member_nat(Z,produc6164657169593426171et_nat(C,P2)) ) ).

% mem_case_prodI2
tff(fact_2811_mem__case__prodI2,axiom,
    ! [P2: produc2453742332425399446nteger,Z: int,C: fun_fu6941240126142778863et_int] :
      ( ! [A3: fun_Pr5098669352780829690e_term,B2: produc8923325533196201883nteger] :
          ( ( P2 = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A3),B2) )
         => member_int(Z,aa_Pro5426537197693075521et_int(aa_fun1598286855320232536et_int(C,A3),B2)) )
     => member_int(Z,produc1986806150084229463et_int(C,P2)) ) ).

% mem_case_prodI2
tff(fact_2812_case__prodI2_H,axiom,
    ! [P2: product_prod_nat_nat,C: fun_na5914473681949881652_nat_o,X2: product_prod_nat_nat] :
      ( ! [A3: nat,B2: nat] :
          ( ( aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A3),B2) = P2 )
         => aa_Pro6150637604445964947_nat_o(aa_nat7695548938202568488_nat_o(aa_nat4259715169212259317_nat_o(C,A3),B2),X2) )
     => aa_Pro6150637604445964947_nat_o(aa_Pro989595756709598047_nat_o(aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,C),P2),X2) ) ).

% case_prodI2'
tff(fact_2813_one__eq__numeral__iff,axiom,
    ! [N2: num] :
      ( ( one_one_nat = aa_num_nat(numeral_numeral_nat,N2) )
    <=> ( one = N2 ) ) ).

% one_eq_numeral_iff
tff(fact_2814_one__eq__numeral__iff,axiom,
    ! [N2: num] :
      ( ( one_one_int = aa_num_int(numeral_numeral_int,N2) )
    <=> ( one = N2 ) ) ).

% one_eq_numeral_iff
tff(fact_2815_one__eq__numeral__iff,axiom,
    ! [N2: num] :
      ( ( one_one_Code_integer = aa_num_Code_integer(numera6620942414471956472nteger,N2) )
    <=> ( one = N2 ) ) ).

% one_eq_numeral_iff
tff(fact_2816_one__eq__numeral__iff,axiom,
    ! [N2: num] :
      ( ( one_one_rat = aa_num_rat(numeral_numeral_rat,N2) )
    <=> ( one = N2 ) ) ).

% one_eq_numeral_iff
tff(fact_2817_one__eq__numeral__iff,axiom,
    ! [N2: num] :
      ( ( one_one_Code_natural = aa_num_Code_natural(numera5444537566228673987atural,N2) )
    <=> ( one = N2 ) ) ).

% one_eq_numeral_iff
tff(fact_2818_numeral__eq__one__iff,axiom,
    ! [N2: num] :
      ( ( aa_num_nat(numeral_numeral_nat,N2) = one_one_nat )
    <=> ( N2 = one ) ) ).

% numeral_eq_one_iff
tff(fact_2819_numeral__eq__one__iff,axiom,
    ! [N2: num] :
      ( ( aa_num_int(numeral_numeral_int,N2) = one_one_int )
    <=> ( N2 = one ) ) ).

% numeral_eq_one_iff
tff(fact_2820_numeral__eq__one__iff,axiom,
    ! [N2: num] :
      ( ( aa_num_Code_integer(numera6620942414471956472nteger,N2) = one_one_Code_integer )
    <=> ( N2 = one ) ) ).

% numeral_eq_one_iff
tff(fact_2821_numeral__eq__one__iff,axiom,
    ! [N2: num] :
      ( ( aa_num_rat(numeral_numeral_rat,N2) = one_one_rat )
    <=> ( N2 = one ) ) ).

% numeral_eq_one_iff
tff(fact_2822_numeral__eq__one__iff,axiom,
    ! [N2: num] :
      ( ( aa_num_Code_natural(numera5444537566228673987atural,N2) = one_one_Code_natural )
    <=> ( N2 = one ) ) ).

% numeral_eq_one_iff
tff(fact_2823_of__nat__add,axiom,
    ! [M: nat,N2: nat] : aa_nat_rat(semiri681578069525770553at_rat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(semiri681578069525770553at_rat,M)),aa_nat_rat(semiri681578069525770553at_rat,N2)) ).

% of_nat_add
tff(fact_2824_of__nat__add,axiom,
    ! [M: nat,N2: nat] : aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(semiri1314217659103216013at_int,M)),aa_nat_int(semiri1314217659103216013at_int,N2)) ).

% of_nat_add
tff(fact_2825_of__nat__add,axiom,
    ! [M: nat,N2: nat] : aa_nat_nat(semiri1316708129612266289at_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(semiri1316708129612266289at_nat,M)),aa_nat_nat(semiri1316708129612266289at_nat,N2)) ).

% of_nat_add
tff(fact_2826_of__nat__add,axiom,
    ! [M: nat,N2: nat] : aa_nat_Code_integer(semiri4939895301339042750nteger,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_nat_Code_integer(semiri4939895301339042750nteger,M)),aa_nat_Code_integer(semiri4939895301339042750nteger,N2)) ).

% of_nat_add
tff(fact_2827_of__nat__add,axiom,
    ! [M: nat,N2: nat] : aa_nat_Code_natural(semiri3763490453095760265atural,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_nat_Code_natural(semiri3763490453095760265atural,M)),aa_nat_Code_natural(semiri3763490453095760265atural,N2)) ).

% of_nat_add
tff(fact_2828_of__nat__1,axiom,
    aa_nat_rat(semiri681578069525770553at_rat,one_one_nat) = one_one_rat ).

% of_nat_1
tff(fact_2829_of__nat__1,axiom,
    aa_nat_int(semiri1314217659103216013at_int,one_one_nat) = one_one_int ).

% of_nat_1
tff(fact_2830_of__nat__1,axiom,
    aa_nat_nat(semiri1316708129612266289at_nat,one_one_nat) = one_one_nat ).

% of_nat_1
tff(fact_2831_of__nat__1,axiom,
    aa_nat_Code_integer(semiri4939895301339042750nteger,one_one_nat) = one_one_Code_integer ).

% of_nat_1
tff(fact_2832_of__nat__1,axiom,
    aa_nat_Code_natural(semiri3763490453095760265atural,one_one_nat) = one_one_Code_natural ).

% of_nat_1
tff(fact_2833_of__nat__1__eq__iff,axiom,
    ! [N2: nat] :
      ( ( one_one_rat = aa_nat_rat(semiri681578069525770553at_rat,N2) )
    <=> ( N2 = one_one_nat ) ) ).

% of_nat_1_eq_iff
tff(fact_2834_of__nat__1__eq__iff,axiom,
    ! [N2: nat] :
      ( ( one_one_int = aa_nat_int(semiri1314217659103216013at_int,N2) )
    <=> ( N2 = one_one_nat ) ) ).

% of_nat_1_eq_iff
tff(fact_2835_of__nat__1__eq__iff,axiom,
    ! [N2: nat] :
      ( ( one_one_nat = aa_nat_nat(semiri1316708129612266289at_nat,N2) )
    <=> ( N2 = one_one_nat ) ) ).

% of_nat_1_eq_iff
tff(fact_2836_of__nat__1__eq__iff,axiom,
    ! [N2: nat] :
      ( ( one_one_Code_integer = aa_nat_Code_integer(semiri4939895301339042750nteger,N2) )
    <=> ( N2 = one_one_nat ) ) ).

% of_nat_1_eq_iff
tff(fact_2837_of__nat__1__eq__iff,axiom,
    ! [N2: nat] :
      ( ( one_one_Code_natural = aa_nat_Code_natural(semiri3763490453095760265atural,N2) )
    <=> ( N2 = one_one_nat ) ) ).

% of_nat_1_eq_iff
tff(fact_2838_of__nat__eq__1__iff,axiom,
    ! [N2: nat] :
      ( ( aa_nat_rat(semiri681578069525770553at_rat,N2) = one_one_rat )
    <=> ( N2 = one_one_nat ) ) ).

% of_nat_eq_1_iff
tff(fact_2839_of__nat__eq__1__iff,axiom,
    ! [N2: nat] :
      ( ( aa_nat_int(semiri1314217659103216013at_int,N2) = one_one_int )
    <=> ( N2 = one_one_nat ) ) ).

% of_nat_eq_1_iff
tff(fact_2840_of__nat__eq__1__iff,axiom,
    ! [N2: nat] :
      ( ( aa_nat_nat(semiri1316708129612266289at_nat,N2) = one_one_nat )
    <=> ( N2 = one_one_nat ) ) ).

% of_nat_eq_1_iff
tff(fact_2841_of__nat__eq__1__iff,axiom,
    ! [N2: nat] :
      ( ( aa_nat_Code_integer(semiri4939895301339042750nteger,N2) = one_one_Code_integer )
    <=> ( N2 = one_one_nat ) ) ).

% of_nat_eq_1_iff
tff(fact_2842_of__nat__eq__1__iff,axiom,
    ! [N2: nat] :
      ( ( aa_nat_Code_natural(semiri3763490453095760265atural,N2) = one_one_Code_natural )
    <=> ( N2 = one_one_nat ) ) ).

% of_nat_eq_1_iff
tff(fact_2843_semiring__norm_I2_J,axiom,
    aa_num_num(aa_num_fun_num_num(plus_plus_num,one),one) = aa_num_num(bit0,one) ).

% semiring_norm(2)
tff(fact_2844_numeral__le__one__iff,axiom,
    ! [N2: num] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_num_Code_integer(numera6620942414471956472nteger,N2)),one_one_Code_integer)
    <=> aa_num_o(aa_num_fun_num_o(ord_less_eq_num,N2),one) ) ).

% numeral_le_one_iff
tff(fact_2845_numeral__le__one__iff,axiom,
    ! [N2: num] :
      ( aa_Code_natural_o(aa_Cod1485054954640246627ural_o(ord_le1926595141338095240atural,aa_num_Code_natural(numera5444537566228673987atural,N2)),one_one_Code_natural)
    <=> aa_num_o(aa_num_fun_num_o(ord_less_eq_num,N2),one) ) ).

% numeral_le_one_iff
tff(fact_2846_numeral__le__one__iff,axiom,
    ! [N2: num] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_num_rat(numeral_numeral_rat,N2)),one_one_rat)
    <=> aa_num_o(aa_num_fun_num_o(ord_less_eq_num,N2),one) ) ).

% numeral_le_one_iff
tff(fact_2847_numeral__le__one__iff,axiom,
    ! [N2: num] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_num_nat(numeral_numeral_nat,N2)),one_one_nat)
    <=> aa_num_o(aa_num_fun_num_o(ord_less_eq_num,N2),one) ) ).

% numeral_le_one_iff
tff(fact_2848_numeral__le__one__iff,axiom,
    ! [N2: num] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_num_int(numeral_numeral_int,N2)),one_one_int)
    <=> aa_num_o(aa_num_fun_num_o(ord_less_eq_num,N2),one) ) ).

% numeral_le_one_iff
tff(fact_2849_one__less__numeral__iff,axiom,
    ! [N2: num] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,one_one_nat),aa_num_nat(numeral_numeral_nat,N2))
    <=> aa_num_o(aa_num_fun_num_o(ord_less_num,one),N2) ) ).

% one_less_numeral_iff
tff(fact_2850_one__less__numeral__iff,axiom,
    ! [N2: num] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),aa_num_int(numeral_numeral_int,N2))
    <=> aa_num_o(aa_num_fun_num_o(ord_less_num,one),N2) ) ).

% one_less_numeral_iff
tff(fact_2851_one__less__numeral__iff,axiom,
    ! [N2: num] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),aa_num_Code_integer(numera6620942414471956472nteger,N2))
    <=> aa_num_o(aa_num_fun_num_o(ord_less_num,one),N2) ) ).

% one_less_numeral_iff
tff(fact_2852_one__less__numeral__iff,axiom,
    ! [N2: num] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),aa_num_rat(numeral_numeral_rat,N2))
    <=> aa_num_o(aa_num_fun_num_o(ord_less_num,one),N2) ) ).

% one_less_numeral_iff
tff(fact_2853_one__less__numeral__iff,axiom,
    ! [N2: num] :
      ( aa_Code_natural_o(aa_Cod1485054954640246627ural_o(ord_le5570908160329646204atural,one_one_Code_natural),aa_num_Code_natural(numera5444537566228673987atural,N2))
    <=> aa_num_o(aa_num_fun_num_o(ord_less_num,one),N2) ) ).

% one_less_numeral_iff
tff(fact_2854_numeral__eq__neg__one__iff,axiom,
    ! [N2: num] :
      ( ( aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,N2)) = aa_int_int(uminus_uminus_int,one_one_int) )
    <=> ( N2 = one ) ) ).

% numeral_eq_neg_one_iff
tff(fact_2855_numeral__eq__neg__one__iff,axiom,
    ! [N2: num] :
      ( ( aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,N2)) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) )
    <=> ( N2 = one ) ) ).

% numeral_eq_neg_one_iff
tff(fact_2856_numeral__eq__neg__one__iff,axiom,
    ! [N2: num] :
      ( ( aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,N2)) = aa_rat_rat(uminus_uminus_rat,one_one_rat) )
    <=> ( N2 = one ) ) ).

% numeral_eq_neg_one_iff
tff(fact_2857_neg__one__eq__numeral__iff,axiom,
    ! [N2: num] :
      ( ( aa_int_int(uminus_uminus_int,one_one_int) = aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,N2)) )
    <=> ( N2 = one ) ) ).

% neg_one_eq_numeral_iff
tff(fact_2858_neg__one__eq__numeral__iff,axiom,
    ! [N2: num] :
      ( ( aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,N2)) )
    <=> ( N2 = one ) ) ).

% neg_one_eq_numeral_iff
tff(fact_2859_neg__one__eq__numeral__iff,axiom,
    ! [N2: num] :
      ( ( aa_rat_rat(uminus_uminus_rat,one_one_rat) = aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,N2)) )
    <=> ( N2 = one ) ) ).

% neg_one_eq_numeral_iff
tff(fact_2860_of__nat__Suc,axiom,
    ! [M: nat] : aa_nat_rat(semiri681578069525770553at_rat,aa_nat_nat(suc,M)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,one_one_rat),aa_nat_rat(semiri681578069525770553at_rat,M)) ).

% of_nat_Suc
tff(fact_2861_of__nat__Suc,axiom,
    ! [M: nat] : aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(suc,M)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_nat_int(semiri1314217659103216013at_int,M)) ).

% of_nat_Suc
tff(fact_2862_of__nat__Suc,axiom,
    ! [M: nat] : aa_nat_nat(semiri1316708129612266289at_nat,aa_nat_nat(suc,M)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_nat_nat(semiri1316708129612266289at_nat,M)) ).

% of_nat_Suc
tff(fact_2863_of__nat__Suc,axiom,
    ! [M: nat] : aa_nat_Code_integer(semiri4939895301339042750nteger,aa_nat_nat(suc,M)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,one_one_Code_integer),aa_nat_Code_integer(semiri4939895301339042750nteger,M)) ).

% of_nat_Suc
tff(fact_2864_of__nat__Suc,axiom,
    ! [M: nat] : aa_nat_Code_natural(semiri3763490453095760265atural,aa_nat_nat(suc,M)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,one_one_Code_natural),aa_nat_Code_natural(semiri3763490453095760265atural,M)) ).

% of_nat_Suc
tff(fact_2865_Suc__numeral,axiom,
    ! [N2: num] : aa_nat_nat(suc,aa_num_nat(numeral_numeral_nat,N2)) = aa_num_nat(numeral_numeral_nat,aa_num_num(aa_num_fun_num_num(plus_plus_num,N2),one)) ).

% Suc_numeral
tff(fact_2866_not__neg__one__le__neg__numeral__iff,axiom,
    ! [M: num] :
      ( ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,M)))
    <=> ( M != one ) ) ).

% not_neg_one_le_neg_numeral_iff
tff(fact_2867_not__neg__one__le__neg__numeral__iff,axiom,
    ! [M: num] :
      ( ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,M)))
    <=> ( M != one ) ) ).

% not_neg_one_le_neg_numeral_iff
tff(fact_2868_not__neg__one__le__neg__numeral__iff,axiom,
    ! [M: num] :
      ( ~ aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(uminus_uminus_int,one_one_int)),aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,M)))
    <=> ( M != one ) ) ).

% not_neg_one_le_neg_numeral_iff
tff(fact_2869_one__add__one,axiom,
    aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)) ).

% one_add_one
tff(fact_2870_one__add__one,axiom,
    aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),one_one_int) = aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)) ).

% one_add_one
tff(fact_2871_one__add__one,axiom,
    aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,one_one_Code_integer),one_one_Code_integer) = aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)) ).

% one_add_one
tff(fact_2872_one__add__one,axiom,
    aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,one_one_rat),one_one_rat) = aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one)) ).

% one_add_one
tff(fact_2873_one__add__one,axiom,
    aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,one_one_Code_natural),one_one_Code_natural) = aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one)) ).

% one_add_one
tff(fact_2874_neg__numeral__less__neg__one__iff,axiom,
    ! [M: num] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,M))),aa_int_int(uminus_uminus_int,one_one_int))
    <=> ( M != one ) ) ).

% neg_numeral_less_neg_one_iff
tff(fact_2875_neg__numeral__less__neg__one__iff,axiom,
    ! [M: num] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,M))),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer))
    <=> ( M != one ) ) ).

% neg_numeral_less_neg_one_iff
tff(fact_2876_neg__numeral__less__neg__one__iff,axiom,
    ! [M: num] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,M))),aa_rat_rat(uminus_uminus_rat,one_one_rat))
    <=> ( M != one ) ) ).

% neg_numeral_less_neg_one_iff
tff(fact_2877_bits__one__mod__two__eq__one,axiom,
    aa_int_int(aa_int_fun_int_int(modulo_modulo_int,one_one_int),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) = one_one_int ).

% bits_one_mod_two_eq_one
tff(fact_2878_bits__one__mod__two__eq__one,axiom,
    aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,one_one_nat),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = one_one_nat ).

% bits_one_mod_two_eq_one
tff(fact_2879_bits__one__mod__two__eq__one,axiom,
    aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,one_one_Code_integer),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) = one_one_Code_integer ).

% bits_one_mod_two_eq_one
tff(fact_2880_bits__one__mod__two__eq__one,axiom,
    aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,one_one_Code_natural),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))) = one_one_Code_natural ).

% bits_one_mod_two_eq_one
tff(fact_2881_one__mod__two__eq__one,axiom,
    aa_int_int(aa_int_fun_int_int(modulo_modulo_int,one_one_int),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) = one_one_int ).

% one_mod_two_eq_one
tff(fact_2882_one__mod__two__eq__one,axiom,
    aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,one_one_nat),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = one_one_nat ).

% one_mod_two_eq_one
tff(fact_2883_one__mod__two__eq__one,axiom,
    aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,one_one_Code_integer),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) = one_one_Code_integer ).

% one_mod_two_eq_one
tff(fact_2884_one__mod__two__eq__one,axiom,
    aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,one_one_Code_natural),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))) = one_one_Code_natural ).

% one_mod_two_eq_one
tff(fact_2885_add__2__eq__Suc,axiom,
    ! [N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2) = aa_nat_nat(suc,aa_nat_nat(suc,N2)) ).

% add_2_eq_Suc
tff(fact_2886_add__2__eq__Suc_H,axiom,
    ! [N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(suc,aa_nat_nat(suc,N2)) ).

% add_2_eq_Suc'
tff(fact_2887_Suc__1,axiom,
    aa_nat_nat(suc,one_one_nat) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)) ).

% Suc_1
tff(fact_2888_numeral__plus__one,axiom,
    ! [N2: num] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(numeral_numeral_nat,N2)),one_one_nat) = aa_num_nat(numeral_numeral_nat,aa_num_num(aa_num_fun_num_num(plus_plus_num,N2),one)) ).

% numeral_plus_one
tff(fact_2889_numeral__plus__one,axiom,
    ! [N2: num] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_num_int(numeral_numeral_int,N2)),one_one_int) = aa_num_int(numeral_numeral_int,aa_num_num(aa_num_fun_num_num(plus_plus_num,N2),one)) ).

% numeral_plus_one
tff(fact_2890_numeral__plus__one,axiom,
    ! [N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_num_Code_integer(numera6620942414471956472nteger,N2)),one_one_Code_integer) = aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(aa_num_fun_num_num(plus_plus_num,N2),one)) ).

% numeral_plus_one
tff(fact_2891_numeral__plus__one,axiom,
    ! [N2: num] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_num_rat(numeral_numeral_rat,N2)),one_one_rat) = aa_num_rat(numeral_numeral_rat,aa_num_num(aa_num_fun_num_num(plus_plus_num,N2),one)) ).

% numeral_plus_one
tff(fact_2892_numeral__plus__one,axiom,
    ! [N2: num] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_num_Code_natural(numera5444537566228673987atural,N2)),one_one_Code_natural) = aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(aa_num_fun_num_num(plus_plus_num,N2),one)) ).

% numeral_plus_one
tff(fact_2893_one__plus__numeral,axiom,
    ! [N2: num] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_num_nat(numeral_numeral_nat,N2)) = aa_num_nat(numeral_numeral_nat,aa_num_num(aa_num_fun_num_num(plus_plus_num,one),N2)) ).

% one_plus_numeral
tff(fact_2894_one__plus__numeral,axiom,
    ! [N2: num] : aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_num_int(numeral_numeral_int,N2)) = aa_num_int(numeral_numeral_int,aa_num_num(aa_num_fun_num_num(plus_plus_num,one),N2)) ).

% one_plus_numeral
tff(fact_2895_one__plus__numeral,axiom,
    ! [N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,one_one_Code_integer),aa_num_Code_integer(numera6620942414471956472nteger,N2)) = aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(aa_num_fun_num_num(plus_plus_num,one),N2)) ).

% one_plus_numeral
tff(fact_2896_one__plus__numeral,axiom,
    ! [N2: num] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,one_one_rat),aa_num_rat(numeral_numeral_rat,N2)) = aa_num_rat(numeral_numeral_rat,aa_num_num(aa_num_fun_num_num(plus_plus_num,one),N2)) ).

% one_plus_numeral
tff(fact_2897_one__plus__numeral,axiom,
    ! [N2: num] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,one_one_Code_natural),aa_num_Code_natural(numera5444537566228673987atural,N2)) = aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(aa_num_fun_num_num(plus_plus_num,one),N2)) ).

% one_plus_numeral
tff(fact_2898_add__self__div__2,axiom,
    ! [M: nat] : aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),M)),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = M ).

% add_self_div_2
tff(fact_2899_bits__1__div__2,axiom,
    aa_int_int(aa_int_fun_int_int(divide_divide_int,one_one_int),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) = zero_zero_int ).

% bits_1_div_2
tff(fact_2900_bits__1__div__2,axiom,
    aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,one_one_nat),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = zero_zero_nat ).

% bits_1_div_2
tff(fact_2901_bits__1__div__2,axiom,
    aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,one_one_Code_integer),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) = zero_z3403309356797280102nteger ).

% bits_1_div_2
tff(fact_2902_bits__1__div__2,axiom,
    aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,one_one_Code_natural),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))) = zero_z2226904508553997617atural ).

% bits_1_div_2
tff(fact_2903_one__div__two__eq__zero,axiom,
    aa_int_int(aa_int_fun_int_int(divide_divide_int,one_one_int),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) = zero_zero_int ).

% one_div_two_eq_zero
tff(fact_2904_one__div__two__eq__zero,axiom,
    aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,one_one_nat),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = zero_zero_nat ).

% one_div_two_eq_zero
tff(fact_2905_one__div__two__eq__zero,axiom,
    aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,one_one_Code_integer),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) = zero_z3403309356797280102nteger ).

% one_div_two_eq_zero
tff(fact_2906_one__div__two__eq__zero,axiom,
    aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,one_one_Code_natural),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))) = zero_z2226904508553997617atural ).

% one_div_two_eq_zero
tff(fact_2907_add__neg__numeral__special_I9_J,axiom,
    aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(uminus_uminus_int,one_one_int)),aa_int_int(uminus_uminus_int,one_one_int)) = aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) ).

% add_neg_numeral_special(9)
tff(fact_2908_add__neg__numeral__special_I9_J,axiom,
    aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) ).

% add_neg_numeral_special(9)
tff(fact_2909_add__neg__numeral__special_I9_J,axiom,
    aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),aa_rat_rat(uminus_uminus_rat,one_one_rat)) = aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one))) ).

% add_neg_numeral_special(9)
tff(fact_2910_diff__numeral__special_I11_J,axiom,
    aa_int_int(aa_int_fun_int_int(minus_minus_int,one_one_int),aa_int_int(uminus_uminus_int,one_one_int)) = aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)) ).

% diff_numeral_special(11)
tff(fact_2911_diff__numeral__special_I11_J,axiom,
    aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,one_one_Code_integer),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) = aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)) ).

% diff_numeral_special(11)
tff(fact_2912_diff__numeral__special_I11_J,axiom,
    aa_rat_rat(minus_minus_rat(one_one_rat),aa_rat_rat(uminus_uminus_rat,one_one_rat)) = aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one)) ).

% diff_numeral_special(11)
tff(fact_2913_diff__numeral__special_I10_J,axiom,
    aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(uminus_uminus_int,one_one_int)),one_one_int) = aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) ).

% diff_numeral_special(10)
tff(fact_2914_diff__numeral__special_I10_J,axiom,
    aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),one_one_Code_integer) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) ).

% diff_numeral_special(10)
tff(fact_2915_diff__numeral__special_I10_J,axiom,
    aa_rat_rat(minus_minus_rat(aa_rat_rat(uminus_uminus_rat,one_one_rat)),one_one_rat) = aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one))) ).

% diff_numeral_special(10)
tff(fact_2916_not__mod__2__eq__0__eq__1,axiom,
    ! [A: int] :
      ( ( aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) != zero_zero_int )
    <=> ( aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) = one_one_int ) ) ).

% not_mod_2_eq_0_eq_1
tff(fact_2917_not__mod__2__eq__0__eq__1,axiom,
    ! [A: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) != zero_zero_nat )
    <=> ( aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = one_one_nat ) ) ).

% not_mod_2_eq_0_eq_1
tff(fact_2918_not__mod__2__eq__0__eq__1,axiom,
    ! [A: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) != zero_z3403309356797280102nteger )
    <=> ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) = one_one_Code_integer ) ) ).

% not_mod_2_eq_0_eq_1
tff(fact_2919_not__mod__2__eq__0__eq__1,axiom,
    ! [A: code_natural] :
      ( ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))) != zero_z2226904508553997617atural )
    <=> ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))) = one_one_Code_natural ) ) ).

% not_mod_2_eq_0_eq_1
tff(fact_2920_not__mod__2__eq__1__eq__0,axiom,
    ! [A: int] :
      ( ( aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) != one_one_int )
    <=> ( aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) = zero_zero_int ) ) ).

% not_mod_2_eq_1_eq_0
tff(fact_2921_not__mod__2__eq__1__eq__0,axiom,
    ! [A: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) != one_one_nat )
    <=> ( aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = zero_zero_nat ) ) ).

% not_mod_2_eq_1_eq_0
tff(fact_2922_not__mod__2__eq__1__eq__0,axiom,
    ! [A: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) != one_one_Code_integer )
    <=> ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) = zero_z3403309356797280102nteger ) ) ).

% not_mod_2_eq_1_eq_0
tff(fact_2923_not__mod__2__eq__1__eq__0,axiom,
    ! [A: code_natural] :
      ( ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))) != one_one_Code_natural )
    <=> ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))) = zero_z2226904508553997617atural ) ) ).

% not_mod_2_eq_1_eq_0
tff(fact_2924_minus__1__div__2__eq,axiom,
    aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(uminus_uminus_int,one_one_int)),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) = aa_int_int(uminus_uminus_int,one_one_int) ).

% minus_1_div_2_eq
tff(fact_2925_minus__1__div__2__eq,axiom,
    aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) ).

% minus_1_div_2_eq
tff(fact_2926_bits__minus__1__mod__2__eq,axiom,
    aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_int_int(uminus_uminus_int,one_one_int)),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) = one_one_int ).

% bits_minus_1_mod_2_eq
tff(fact_2927_bits__minus__1__mod__2__eq,axiom,
    aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) = one_one_Code_integer ).

% bits_minus_1_mod_2_eq
tff(fact_2928_minus__1__mod__2__eq,axiom,
    aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_int_int(uminus_uminus_int,one_one_int)),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) = one_one_int ).

% minus_1_mod_2_eq
tff(fact_2929_minus__1__mod__2__eq,axiom,
    aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) = one_one_Code_integer ).

% minus_1_mod_2_eq
tff(fact_2930_diff__numeral__special_I3_J,axiom,
    ! [N2: num] : aa_int_int(aa_int_fun_int_int(minus_minus_int,one_one_int),aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,N2))) = aa_num_int(numeral_numeral_int,aa_num_num(aa_num_fun_num_num(plus_plus_num,one),N2)) ).

% diff_numeral_special(3)
tff(fact_2931_diff__numeral__special_I3_J,axiom,
    ! [N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,one_one_Code_integer),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,N2))) = aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(aa_num_fun_num_num(plus_plus_num,one),N2)) ).

% diff_numeral_special(3)
tff(fact_2932_diff__numeral__special_I3_J,axiom,
    ! [N2: num] : aa_rat_rat(minus_minus_rat(one_one_rat),aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,N2))) = aa_num_rat(numeral_numeral_rat,aa_num_num(aa_num_fun_num_num(plus_plus_num,one),N2)) ).

% diff_numeral_special(3)
tff(fact_2933_diff__numeral__special_I4_J,axiom,
    ! [M: num] : aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,M))),one_one_int) = aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),one))) ).

% diff_numeral_special(4)
tff(fact_2934_diff__numeral__special_I4_J,axiom,
    ! [M: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,M))),one_one_Code_integer) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),one))) ).

% diff_numeral_special(4)
tff(fact_2935_diff__numeral__special_I4_J,axiom,
    ! [M: num] : aa_rat_rat(minus_minus_rat(aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,M))),one_one_rat) = aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),one))) ).

% diff_numeral_special(4)
tff(fact_2936_add__self__mod__2,axiom,
    ! [M: nat] : aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),M)),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = zero_zero_nat ).

% add_self_mod_2
tff(fact_2937_power__minus1__even,axiom,
    ! [N2: nat] : aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(uminus_uminus_int,one_one_int)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)) = one_one_int ).

% power_minus1_even
tff(fact_2938_power__minus1__even,axiom,
    ! [N2: nat] : aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)) = one_one_Code_integer ).

% power_minus1_even
tff(fact_2939_power__minus1__even,axiom,
    ! [N2: nat] : aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)) = one_one_rat ).

% power_minus1_even
tff(fact_2940_mod2__gr__0,axiom,
    ! [M: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,M),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))
    <=> ( aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,M),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = one_one_nat ) ) ).

% mod2_gr_0
tff(fact_2941_lex__prod__def,axiom,
    ! [Ra: set_Pr4329608150637261639at_nat,Rb: set_Pr4329608150637261639at_nat] : lex_pr8000699672184251119at_nat(Ra,Rb) = collec223960383693904210at_nat(produc1561160019221259564_nat_o(produc7150000874791569568_nat_o(aa_set2810100084588730581_nat_o(aTP_Lamm_eu(Ra),Rb)))) ).

% lex_prod_def
tff(fact_2942_lex__prod__def,axiom,
    ! [Ra: set_Pr4329608150637261639at_nat,Rb: set_Pr1261947904930325089at_nat] : lex_pr1951919194703979714at_nat(Ra,Rb) = collec1461227866750739596at_nat(produc8701595406162815018_nat_o(produc6627902574045077578_nat_o(aa_set5873268817925218273_nat_o(aTP_Lamm_ew(Ra),Rb)))) ).

% lex_prod_def
tff(fact_2943_lex__prod__def,axiom,
    ! [Ra: set_Pr1261947904930325089at_nat,Rb: set_Pr4329608150637261639at_nat] : lex_pr4265550801952275104at_nat(Ra,Rb) = collec2088441199205367000at_nat(produc7830147906768200158_nat_o(produc5481773914224270406_nat_o(aa_set2321460896359935973_nat_o(aTP_Lamm_ey(Ra),Rb)))) ).

% lex_prod_def
tff(fact_2944_lex__prod__def,axiom,
    ! [Ra: set_Pr1261947904930325089at_nat,Rb: set_Pr1261947904930325089at_nat] : lex_prod_nat_nat(Ra,Rb) = collec7088162979684241874at_nat(produc6590410687421337004_nat_o(aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,aa_set1501693898512841689_nat_o(aTP_Lamm_fa(Ra),Rb)))) ).

% lex_prod_def
tff(fact_2945_same__fst__def,axiom,
    ! [P: fun_nat_o,R3: fun_na7044673412300895210at_nat] : same_fst_nat_nat(P,R3) = collec7088162979684241874at_nat(produc6590410687421337004_nat_o(aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,aa_fun1888629816020924642_nat_o(aTP_Lamm_fc(P),R3)))) ).

% same_fst_def
tff(fact_2946_mem__case__prodE,axiom,
    ! [Z: $o,C: fun_fu4618385802829667198_set_o,P2: produc4788131091073775919nt_int] :
      ( member_o((Z),produc8509172437693241834_set_o(C,P2))
     => ~ ! [X3: fun_in5730379987311621695e_term,Y4: product_prod_int_int] :
            ( ( P2 = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X3),Y4) )
           => ~ member_o((Z),aa_Pro2653658648327035067_set_o(aa_fun8934358842864497599_set_o(C,X3),Y4)) ) ) ).

% mem_case_prodE
tff(fact_2947_mem__case__prodE,axiom,
    ! [Z: nat,C: fun_fu9079770784915425324et_nat,P2: produc4788131091073775919nt_int] :
      ( member_nat(Z,produc5011043943518292116et_nat(C,P2))
     => ~ ! [X3: fun_in5730379987311621695e_term,Y4: product_prod_int_int] :
            ( ( P2 = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X3),Y4) )
           => ~ member_nat(Z,aa_Pro3599192995643711491et_nat(aa_fun8409204002232819093et_nat(C,X3),Y4)) ) ) ).

% mem_case_prodE
tff(fact_2948_mem__case__prodE,axiom,
    ! [Z: int,C: fun_fu4266222366127506568et_int,P2: produc4788131091073775919nt_int] :
      ( member_int(Z,produc833192924009095408et_int(C,P2))
     => ~ ! [X3: fun_in5730379987311621695e_term,Y4: product_prod_int_int] :
            ( ( P2 = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X3),Y4) )
           => ~ member_int(Z,aa_Pro8644714012989290591et_int(aa_fun5919120857301092337et_int(C,X3),Y4)) ) ) ).

% mem_case_prodE
tff(fact_2949_mem__case__prodE,axiom,
    ! [Z: $o,C: fun_fu4934440599869564003_set_o,P2: produc8799533983703829792et_nat] :
      ( member_o((Z),produc330442800291577585_set_o(C,P2))
     => ~ ! [X3: fun_Pr6460944699146269935_nat_o,Y4: produc3658429121746597890et_nat] :
            ( ( P2 = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X3),Y4) )
           => ~ member_o((Z),aa_Pro3581020192872483896_set_o(aa_fun1634346356166085724_set_o(C,X3),Y4)) ) ) ).

% mem_case_prodE
tff(fact_2950_mem__case__prodE,axiom,
    ! [Z: nat,C: fun_fu86038545275896455et_nat,P2: produc8799533983703829792et_nat] :
      ( member_nat(Z,produc6247649352436904781et_nat(C,P2))
     => ~ ! [X3: fun_Pr6460944699146269935_nat_o,Y4: produc3658429121746597890et_nat] :
            ( ( P2 = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X3),Y4) )
           => ~ member_nat(Z,aa_Pro3416150927818442182et_nat(aa_fun6477889762090788408et_nat(C,X3),Y4)) ) ) ).

% mem_case_prodE
tff(fact_2951_mem__case__prodE,axiom,
    ! [Z: int,C: fun_fu4495862163342753507et_int,P2: produc8799533983703829792et_nat] :
      ( member_int(Z,produc2069798332927708073et_int(C,P2))
     => ~ ! [X3: fun_Pr6460944699146269935_nat_o,Y4: produc3658429121746597890et_nat] :
            ( ( P2 = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X3),Y4) )
           => ~ member_int(Z,aa_Pro8461671945164021282et_int(aa_fun3987806617159061652et_int(C,X3),Y4)) ) ) ).

% mem_case_prodE
tff(fact_2952_mem__case__prodE,axiom,
    ! [Z: product_prod_nat_nat,C: fun_fu6029601804184707687at_nat,P2: produc4788131091073775919nt_int] :
      ( member8440522571783428010at_nat(Z,produc8603558621761785811at_nat(C,P2))
     => ~ ! [X3: fun_in5730379987311621695e_term,Y4: product_prod_int_int] :
            ( ( P2 = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X3),Y4) )
           => ~ member8440522571783428010at_nat(Z,aa_Pro6675321895958450596at_nat(aa_fun712031703178175272at_nat(C,X3),Y4)) ) ) ).

% mem_case_prodE
tff(fact_2953_mem__case__prodE,axiom,
    ! [Z: $o,C: fun_fu6788480576040630871_set_o,P2: produc2453742332425399446nteger] :
      ( member_o((Z),produc8770320508000790979_set_o(C,P2))
     => ~ ! [X3: fun_Pr5098669352780829690e_term,Y4: produc8923325533196201883nteger] :
            ( ( P2 = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X3),Y4) )
           => ~ member_o((Z),aa_Pro3874180734779831385_set_o(aa_fun6611983550656184728_set_o(C,X3),Y4)) ) ) ).

% mem_case_prodE
tff(fact_2954_mem__case__prodE,axiom,
    ! [Z: nat,C: fun_fu2531416508075921811et_nat,P2: produc2453742332425399446nteger] :
      ( member_nat(Z,produc6164657169593426171et_nat(C,P2))
     => ~ ! [X3: fun_Pr5098669352780829690e_term,Y4: produc8923325533196201883nteger] :
            ( ( P2 = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X3),Y4) )
           => ~ member_nat(Z,aa_Pro381016180347496421et_nat(aa_fun4088370000251959292et_nat(C,X3),Y4)) ) ) ).

% mem_case_prodE
tff(fact_2955_mem__case__prodE,axiom,
    ! [Z: int,C: fun_fu6941240126142778863et_int,P2: produc2453742332425399446nteger] :
      ( member_int(Z,produc1986806150084229463et_int(C,P2))
     => ~ ! [X3: fun_Pr5098669352780829690e_term,Y4: produc8923325533196201883nteger] :
            ( ( P2 = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X3),Y4) )
           => ~ member_int(Z,aa_Pro5426537197693075521et_int(aa_fun1598286855320232536et_int(C,X3),Y4)) ) ) ).

% mem_case_prodE
tff(fact_2956_case__prodD,axiom,
    ! [F: fun_fu7695273699059480439eger_o,A: fun_Pr5098669352780829690e_term,B: produc8923325533196201883nteger] :
      ( aa_Pro4148064003102580676eger_o(aa_fun7761728421758185830eger_o(produc7373287791920631523eger_o,F),aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A),B))
     => aa_Pro4926521453222654329eger_o(aa_fun4505422719058378424eger_o(F,A),B) ) ).

% case_prodD
tff(fact_2957_case__prodD,axiom,
    ! [F: fun_fu8419763957888848259_nat_o,A: fun_Pr6460944699146269935_nat_o,B: produc3658429121746597890et_nat] :
      ( aa_Pro5643009357358181178_nat_o(aa_fun6593097867094858448_nat_o(produc2915205735004773393_nat_o,F),aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A),B))
     => aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(F,A),B) ) ).

% case_prodD
tff(fact_2958_case__prodD,axiom,
    ! [F: fun_fu2611741329380808165_nat_o,A: fun_Pr6460944699146269935_nat_o,B: produc8799533983703829792et_nat] :
      ( aa_Pro2671238023309943196_nat_o(aa_fun4447940216497214800_nat_o(produc4465912260561112435_nat_o,F),aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A),B))
     => aa_Pro5643009357358181178_nat_o(aa_fun912680268133416158_nat_o(F,A),B) ) ).

% case_prodD
tff(fact_2959_case__prodD,axiom,
    ! [F: fun_fu6865642474282033866_int_o,A: fun_Pr7763680713840462443e_term,B: product_prod_int_int] :
      ( aa_Pro2601676399929874711_int_o(aa_fun6978165455603620006_int_o(produc2207054017359051062_int_o,F),aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,A),B))
     => aa_Pro4592068669816069595_int_o(aa_fun3538162476766722827_int_o(F,A),B) ) ).

% case_prodD
tff(fact_2960_case__prodD,axiom,
    ! [F: fun_fu2978539155105838238_int_o,A: fun_in5730379987311621695e_term,B: product_prod_int_int] :
      ( aa_Pro5451197003417746155_int_o(aa_fun1749673562058638246_int_o(produc7271678899836001034_int_o,F),aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A),B))
     => aa_Pro4592068669816069595_int_o(aa_fun586359091965693151_int_o(F,A),B) ) ).

% case_prodD
tff(fact_2961_case__prodE,axiom,
    ! [C: fun_fu7695273699059480439eger_o,P2: produc2453742332425399446nteger] :
      ( aa_Pro4148064003102580676eger_o(aa_fun7761728421758185830eger_o(produc7373287791920631523eger_o,C),P2)
     => ~ ! [X3: fun_Pr5098669352780829690e_term,Y4: produc8923325533196201883nteger] :
            ( ( P2 = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X3),Y4) )
           => ~ aa_Pro4926521453222654329eger_o(aa_fun4505422719058378424eger_o(C,X3),Y4) ) ) ).

% case_prodE
tff(fact_2962_case__prodE,axiom,
    ! [C: fun_fu8419763957888848259_nat_o,P2: produc8799533983703829792et_nat] :
      ( aa_Pro5643009357358181178_nat_o(aa_fun6593097867094858448_nat_o(produc2915205735004773393_nat_o,C),P2)
     => ~ ! [X3: fun_Pr6460944699146269935_nat_o,Y4: produc3658429121746597890et_nat] :
            ( ( P2 = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X3),Y4) )
           => ~ aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(C,X3),Y4) ) ) ).

% case_prodE
tff(fact_2963_case__prodE,axiom,
    ! [C: fun_fu2611741329380808165_nat_o,P2: produc3112576180687729086et_nat] :
      ( aa_Pro2671238023309943196_nat_o(aa_fun4447940216497214800_nat_o(produc4465912260561112435_nat_o,C),P2)
     => ~ ! [X3: fun_Pr6460944699146269935_nat_o,Y4: produc8799533983703829792et_nat] :
            ( ( P2 = aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X3),Y4) )
           => ~ aa_Pro5643009357358181178_nat_o(aa_fun912680268133416158_nat_o(C,X3),Y4) ) ) ).

% case_prodE
tff(fact_2964_case__prodE,axiom,
    ! [C: fun_fu6865642474282033866_int_o,P2: produc3043004577601930755nt_int] :
      ( aa_Pro2601676399929874711_int_o(aa_fun6978165455603620006_int_o(produc2207054017359051062_int_o,C),P2)
     => ~ ! [X3: fun_Pr7763680713840462443e_term,Y4: product_prod_int_int] :
            ( ( P2 = aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X3),Y4) )
           => ~ aa_Pro4592068669816069595_int_o(aa_fun3538162476766722827_int_o(C,X3),Y4) ) ) ).

% case_prodE
tff(fact_2965_case__prodE,axiom,
    ! [C: fun_fu2978539155105838238_int_o,P2: produc4788131091073775919nt_int] :
      ( aa_Pro5451197003417746155_int_o(aa_fun1749673562058638246_int_o(produc7271678899836001034_int_o,C),P2)
     => ~ ! [X3: fun_in5730379987311621695e_term,Y4: product_prod_int_int] :
            ( ( P2 = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X3),Y4) )
           => ~ aa_Pro4592068669816069595_int_o(aa_fun586359091965693151_int_o(C,X3),Y4) ) ) ).

% case_prodE
tff(fact_2966_add__One__commute,axiom,
    ! [N2: num] : aa_num_num(aa_num_fun_num_num(plus_plus_num,one),N2) = aa_num_num(aa_num_fun_num_num(plus_plus_num,N2),one) ).

% add_One_commute
tff(fact_2967_case__prodD_H,axiom,
    ! [R3: fun_na5914473681949881652_nat_o,A: nat,B: nat,C: product_prod_nat_nat] :
      ( aa_Pro6150637604445964947_nat_o(aa_Pro989595756709598047_nat_o(aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,R3),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B)),C)
     => aa_Pro6150637604445964947_nat_o(aa_nat7695548938202568488_nat_o(aa_nat4259715169212259317_nat_o(R3,A),B),C) ) ).

% case_prodD'
tff(fact_2968_case__prodE_H,axiom,
    ! [C: fun_na5914473681949881652_nat_o,P2: product_prod_nat_nat,Z: product_prod_nat_nat] :
      ( aa_Pro6150637604445964947_nat_o(aa_Pro989595756709598047_nat_o(aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,C),P2),Z)
     => ~ ! [X3: nat,Y4: nat] :
            ( ( P2 = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),Y4) )
           => ~ aa_Pro6150637604445964947_nat_o(aa_nat7695548938202568488_nat_o(aa_nat4259715169212259317_nat_o(C,X3),Y4),Z) ) ) ).

% case_prodE'
tff(fact_2969_sum_OatLeast__int__atMost__int__shift,axiom,
    ! [G: fun_int_nat,M: nat,N2: nat] : groups4541462559716669496nt_nat(G,aa_int_set_int(set_or1266510415728281911st_int(aa_nat_int(semiri1314217659103216013at_int,M)),aa_nat_int(semiri1314217659103216013at_int,N2))) = aa_set_nat_nat(groups3542108847815614940at_nat(comp_int_nat_nat(G,semiri1314217659103216013at_int)),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) ).

% sum.atLeast_int_atMost_int_shift
tff(fact_2970_sum_OatLeast__int__atMost__int__shift,axiom,
    ! [G: fun_int_int,M: nat,N2: nat] : aa_set_int_int(groups4538972089207619220nt_int(G),aa_int_set_int(set_or1266510415728281911st_int(aa_nat_int(semiri1314217659103216013at_int,M)),aa_nat_int(semiri1314217659103216013at_int,N2))) = groups3539618377306564664at_int(comp_int_int_nat(G,semiri1314217659103216013at_int),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) ).

% sum.atLeast_int_atMost_int_shift
tff(fact_2971_less__int_Oabs__eq,axiom,
    ! [Xa: product_prod_nat_nat,X2: product_prod_nat_nat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_Pro4240683299535347697at_int(abs_Integ,Xa)),aa_Pro4240683299535347697at_int(abs_Integ,X2))
    <=> aa_Pro6150637604445964947_nat_o(aa_Pro989595756709598047_nat_o(aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,aTP_Lamm_fe),Xa),X2) ) ).

% less_int.abs_eq
tff(fact_2972_less__eq__int_Oabs__eq,axiom,
    ! [Xa: product_prod_nat_nat,X2: product_prod_nat_nat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_Pro4240683299535347697at_int(abs_Integ,Xa)),aa_Pro4240683299535347697at_int(abs_Integ,X2))
    <=> aa_Pro6150637604445964947_nat_o(aa_Pro989595756709598047_nat_o(aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,aTP_Lamm_fg),Xa),X2) ) ).

% less_eq_int.abs_eq
tff(fact_2973_zadd__int__left,axiom,
    ! [M: nat,N2: nat,Z: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(semiri1314217659103216013at_int,M)),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(semiri1314217659103216013at_int,N2)),Z)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2))),Z) ).

% zadd_int_left
tff(fact_2974_int__plus,axiom,
    ! [N2: nat,M: nat] : aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),M)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(semiri1314217659103216013at_int,N2)),aa_nat_int(semiri1314217659103216013at_int,M)) ).

% int_plus
tff(fact_2975_int__ops_I5_J,axiom,
    ! [A: nat,B: nat] : aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(semiri1314217659103216013at_int,A)),aa_nat_int(semiri1314217659103216013at_int,B)) ).

% int_ops(5)
tff(fact_2976_int__ops_I2_J,axiom,
    aa_nat_int(semiri1314217659103216013at_int,one_one_nat) = one_one_int ).

% int_ops(2)
tff(fact_2977_zle__iff__zadd,axiom,
    ! [W: int,Z: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,W),Z)
    <=> ? [N7: nat] : Z = aa_int_int(aa_int_fun_int_int(plus_plus_int,W),aa_nat_int(semiri1314217659103216013at_int,N7)) ) ).

% zle_iff_zadd
tff(fact_2978_numeral__One,axiom,
    aa_num_nat(numeral_numeral_nat,one) = one_one_nat ).

% numeral_One
tff(fact_2979_numeral__One,axiom,
    aa_num_int(numeral_numeral_int,one) = one_one_int ).

% numeral_One
tff(fact_2980_numeral__One,axiom,
    aa_num_Code_integer(numera6620942414471956472nteger,one) = one_one_Code_integer ).

% numeral_One
tff(fact_2981_numeral__One,axiom,
    aa_num_rat(numeral_numeral_rat,one) = one_one_rat ).

% numeral_One
tff(fact_2982_numeral__One,axiom,
    aa_num_Code_natural(numera5444537566228673987atural,one) = one_one_Code_natural ).

% numeral_One
tff(fact_2983_numerals_I1_J,axiom,
    aa_num_nat(numeral_numeral_nat,one) = one_one_nat ).

% numerals(1)
tff(fact_2984_execute__bind__case,axiom,
    ! [F: heap_T6362127782908069795rray_a,G: fun_ar3891948820113774757rray_a,Ha: heap_e7401611519738050253t_unit] : aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(heap_T2407400398799471159rray_a(F,G)),Ha) = case_o8555119740594961093it_nat(none_P2587165478634041381it_nat,produc8915672860170107321it_nat(aTP_Lamm_fi(G)),aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(F),Ha)) ).

% execute_bind_case
tff(fact_2985_execute__bind__case,axiom,
    ! [F: heap_T5738788834812785303t_unit,G: fun_Pr5924905948197006361rray_a,Ha: heap_e7401611519738050253t_unit] : aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(heap_T7158140910958840029rray_a(F,G)),Ha) = case_o5699750240967658439it_nat(none_P2587165478634041381it_nat,produc875294279294635931it_nat(aTP_Lamm_fk(G)),aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(F),Ha)) ).

% execute_bind_case
tff(fact_2986_execute__bind__case,axiom,
    ! [F: heap_T6362127782908069795rray_a,G: fun_ar1074044450438384043t_unit,Ha: heap_e7401611519738050253t_unit] : aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(heap_T7324619625323989613t_unit(F,G)),Ha) = case_o3886096569520666655it_nat(none_P9117596204409417319it_nat,produc3495058329975564393it_nat(aTP_Lamm_fm(G)),aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(F),Ha)) ).

% execute_bind_case
tff(fact_2987_execute__bind__case,axiom,
    ! [F: heap_T5738788834812785303t_unit,G: fun_Pr292408699144966967t_unit,Ha: heap_e7401611519738050253t_unit] : aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(heap_T2633723481742716231t_unit(F,G)),Ha) = case_o2963978774867076333it_nat(none_P9117596204409417319it_nat,produc1230459020282432263it_nat(aTP_Lamm_fo(G)),aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(F),Ha)) ).

% execute_bind_case
tff(fact_2988_Sum__Icc__int,axiom,
    ! [M: int,N2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,M),N2)
     => ( aa_set_int_int(groups4538972089207619220nt_int(aTP_Lamm_cp),aa_int_set_int(set_or1266510415728281911st_int(M),N2)) = aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(aa_int_fun_int_int(times_times_int,N2),aa_int_int(aa_int_fun_int_int(plus_plus_int,N2),one_one_int))),aa_int_int(aa_int_fun_int_int(times_times_int,M),aa_int_int(aa_int_fun_int_int(minus_minus_int,M),one_one_int)))),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) ) ) ).

% Sum_Icc_int
tff(fact_2989_Heap__Time__Monad_Obind__def,axiom,
    ! [F: heap_T6362127782908069795rray_a,G: fun_ar3891948820113774757rray_a] : heap_T2407400398799471159rray_a(F,G) = heap_T1488828001306802186rray_a(aa_fun8757595186270888873it_nat(aTP_Lamm_fp(F),G)) ).

% Heap_Time_Monad.bind_def
tff(fact_2990_Heap__Time__Monad_Obind__def,axiom,
    ! [F: heap_T5738788834812785303t_unit,G: fun_Pr5924905948197006361rray_a] : heap_T7158140910958840029rray_a(F,G) = heap_T1488828001306802186rray_a(aa_fun6304779250881220759it_nat(aTP_Lamm_fq(F),G)) ).

% Heap_Time_Monad.bind_def
tff(fact_2991_Heap__Time__Monad_Obind__def,axiom,
    ! [F: heap_T6362127782908069795rray_a,G: fun_ar1074044450438384043t_unit] : heap_T7324619625323989613t_unit(F,G) = heap_T6183433275982383450t_unit(aa_fun3741944862212262031it_nat(aTP_Lamm_fr(F),G)) ).

% Heap_Time_Monad.bind_def
tff(fact_2992_Heap__Time__Monad_Obind__def,axiom,
    ! [F: heap_T5738788834812785303t_unit,G: fun_Pr292408699144966967t_unit] : heap_T2633723481742716231t_unit(F,G) = heap_T6183433275982383450t_unit(aa_fun3883837016763096701it_nat(aTP_Lamm_fs(F),G)) ).

% Heap_Time_Monad.bind_def
tff(fact_2993_zless__iff__Suc__zadd,axiom,
    ! [W: int,Z: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,W),Z)
    <=> ? [N7: nat] : Z = aa_int_int(aa_int_fun_int_int(plus_plus_int,W),aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(suc,N7))) ) ).

% zless_iff_Suc_zadd
tff(fact_2994_int__ops_I4_J,axiom,
    ! [A: nat] : aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(suc,A)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(semiri1314217659103216013at_int,A)),one_one_int) ).

% int_ops(4)
tff(fact_2995_int__Suc,axiom,
    ! [N2: nat] : aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(suc,N2)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(semiri1314217659103216013at_int,N2)),one_one_int) ).

% int_Suc
tff(fact_2996_int__bit__induct,axiom,
    ! [P: fun_int_o,K: int] :
      ( aa_int_o(P,zero_zero_int)
     => ( aa_int_o(P,aa_int_int(uminus_uminus_int,one_one_int))
       => ( ! [K3: int] :
              ( aa_int_o(P,K3)
             => ( ( K3 != zero_zero_int )
               => aa_int_o(P,aa_int_int(aa_int_fun_int_int(times_times_int,K3),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))) ) )
         => ( ! [K3: int] :
                ( aa_int_o(P,K3)
               => ( ( K3 != aa_int_int(uminus_uminus_int,one_one_int) )
                 => aa_int_o(P,aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_int_int(aa_int_fun_int_int(times_times_int,K3),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))))) ) )
           => aa_int_o(P,K) ) ) ) ) ).

% int_bit_induct
tff(fact_2997_uminus__numeral__One,axiom,
    aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,one)) = aa_int_int(uminus_uminus_int,one_one_int) ).

% uminus_numeral_One
tff(fact_2998_uminus__numeral__One,axiom,
    aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,one)) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) ).

% uminus_numeral_One
tff(fact_2999_uminus__numeral__One,axiom,
    aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,one)) = aa_rat_rat(uminus_uminus_rat,one_one_rat) ).

% uminus_numeral_One
tff(fact_3000_int__def,axiom,
    ! [N2: nat] : aa_nat_int(semiri1314217659103216013at_int,N2) = aa_Pro4240683299535347697at_int(abs_Integ,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,N2),zero_zero_nat)) ).

% int_def
tff(fact_3001_num__of__nat__One,axiom,
    ! [N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),one_one_nat)
     => ( aa_nat_num(num_of_nat,N2) = one ) ) ).

% num_of_nat_One
tff(fact_3002_neg__zdiv__mult__2,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),zero_zero_int)
     => ( aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),B))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A)) = aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,B),one_one_int)),A) ) ) ).

% neg_zdiv_mult_2
tff(fact_3003_pos__zdiv__mult__2,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),A)
     => ( aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),B))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A)) = aa_int_int(aa_int_fun_int_int(divide_divide_int,B),A) ) ) ).

% pos_zdiv_mult_2
tff(fact_3004_pos__zmod__mult__2,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),A)
     => ( aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),B))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,B),A))) ) ) ).

% pos_zmod_mult_2
tff(fact_3005_mod__mult2__eq_H,axiom,
    ! [A: int,M: nat,N2: nat] : aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(semiri1314217659103216013at_int,M)),aa_nat_int(semiri1314217659103216013at_int,N2))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(semiri1314217659103216013at_int,M)),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_nat_int(semiri1314217659103216013at_int,M))),aa_nat_int(semiri1314217659103216013at_int,N2)))),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),aa_nat_int(semiri1314217659103216013at_int,M))) ).

% mod_mult2_eq'
tff(fact_3006_mod__mult2__eq_H,axiom,
    ! [A: nat,M: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(semiri1316708129612266289at_nat,M)),aa_nat_nat(semiri1316708129612266289at_nat,N2))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(semiri1316708129612266289at_nat,M)),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),aa_nat_nat(semiri1316708129612266289at_nat,M))),aa_nat_nat(semiri1316708129612266289at_nat,N2)))),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),aa_nat_nat(semiri1316708129612266289at_nat,M))) ).

% mod_mult2_eq'
tff(fact_3007_mod__mult2__eq_H,axiom,
    ! [A: code_integer,M: nat,N2: nat] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(semiri4939895301339042750nteger,M)),aa_nat_Code_integer(semiri4939895301339042750nteger,N2))) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(semiri4939895301339042750nteger,M)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_nat_Code_integer(semiri4939895301339042750nteger,M))),aa_nat_Code_integer(semiri4939895301339042750nteger,N2)))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),aa_nat_Code_integer(semiri4939895301339042750nteger,M))) ).

% mod_mult2_eq'
tff(fact_3008_mod__mult2__eq_H,axiom,
    ! [A: code_natural,M: nat,N2: nat] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_nat_Code_natural(semiri3763490453095760265atural,M)),aa_nat_Code_natural(semiri3763490453095760265atural,N2))) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_nat_Code_natural(semiri3763490453095760265atural,M)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),aa_nat_Code_natural(semiri3763490453095760265atural,M))),aa_nat_Code_natural(semiri3763490453095760265atural,N2)))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),aa_nat_Code_natural(semiri3763490453095760265atural,M))) ).

% mod_mult2_eq'
tff(fact_3009_numeral__num__of__nat__unfold,axiom,
    ! [N2: nat] :
      aa_num_rat(numeral_numeral_rat,aa_nat_num(num_of_nat,N2)) = $ite(N2 = zero_zero_nat,one_one_rat,aa_nat_rat(semiri681578069525770553at_rat,N2)) ).

% numeral_num_of_nat_unfold
tff(fact_3010_numeral__num__of__nat__unfold,axiom,
    ! [N2: nat] :
      aa_num_int(numeral_numeral_int,aa_nat_num(num_of_nat,N2)) = $ite(N2 = zero_zero_nat,one_one_int,aa_nat_int(semiri1314217659103216013at_int,N2)) ).

% numeral_num_of_nat_unfold
tff(fact_3011_numeral__num__of__nat__unfold,axiom,
    ! [N2: nat] :
      aa_num_nat(numeral_numeral_nat,aa_nat_num(num_of_nat,N2)) = $ite(N2 = zero_zero_nat,one_one_nat,aa_nat_nat(semiri1316708129612266289at_nat,N2)) ).

% numeral_num_of_nat_unfold
tff(fact_3012_numeral__num__of__nat__unfold,axiom,
    ! [N2: nat] :
      aa_num_Code_integer(numera6620942414471956472nteger,aa_nat_num(num_of_nat,N2)) = $ite(N2 = zero_zero_nat,one_one_Code_integer,aa_nat_Code_integer(semiri4939895301339042750nteger,N2)) ).

% numeral_num_of_nat_unfold
tff(fact_3013_numeral__num__of__nat__unfold,axiom,
    ! [N2: nat] :
      aa_num_Code_natural(numera5444537566228673987atural,aa_nat_num(num_of_nat,N2)) = $ite(N2 = zero_zero_nat,one_one_Code_natural,aa_nat_Code_natural(semiri3763490453095760265atural,N2)) ).

% numeral_num_of_nat_unfold
tff(fact_3014_double__arith__series,axiom,
    ! [A: rat,D2: rat,N2: nat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one))),groups2906978787729119204at_rat(aa_rat_fun_nat_rat(aTP_Lamm_ft(A),D2),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2))) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(semiri681578069525770553at_rat,N2)),one_one_rat)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one))),A)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(semiri681578069525770553at_rat,N2)),D2))) ).

% double_arith_series
tff(fact_3015_double__arith__series,axiom,
    ! [A: int,D2: int,N2: nat] : aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),groups3539618377306564664at_int(aa_int_fun_nat_int(aTP_Lamm_fu(A),D2),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2))) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(semiri1314217659103216013at_int,N2)),one_one_int)),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A)),aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(semiri1314217659103216013at_int,N2)),D2))) ).

% double_arith_series
tff(fact_3016_double__arith__series,axiom,
    ! [A: code_integer,D2: code_integer,N2: nat] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),groups7501900531339628137nteger(aa_Cod1578151519121547077nteger(aTP_Lamm_fv(A),D2),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2))) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_nat_Code_integer(semiri4939895301339042750nteger,N2)),one_one_Code_integer)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(semiri4939895301339042750nteger,N2)),D2))) ).

% double_arith_series
tff(fact_3017_double__arith__series,axiom,
    ! [A: code_natural,D2: code_natural,N2: nat] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),groups6325495683096345652atural(aa_Cod5320533616963873627atural(aTP_Lamm_fw(A),D2),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2))) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_nat_Code_natural(semiri3763490453095760265atural,N2)),one_one_Code_natural)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_nat_Code_natural(semiri3763490453095760265atural,N2)),D2))) ).

% double_arith_series
tff(fact_3018_double__arith__series,axiom,
    ! [A: nat,D2: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_set_nat_nat(groups3542108847815614940at_nat(aa_nat_fun_nat_nat(aTP_Lamm_fx(A),D2)),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2))) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(semiri1316708129612266289at_nat,N2)),one_one_nat)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(semiri1316708129612266289at_nat,N2)),D2))) ).

% double_arith_series
tff(fact_3019_double__gauss__sum,axiom,
    ! [N2: nat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one))),groups2906978787729119204at_rat(semiri681578069525770553at_rat,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2))) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(semiri681578069525770553at_rat,N2)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(semiri681578069525770553at_rat,N2)),one_one_rat)) ).

% double_gauss_sum
tff(fact_3020_double__gauss__sum,axiom,
    ! [N2: nat] : aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),groups3539618377306564664at_int(semiri1314217659103216013at_int,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2))) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(semiri1314217659103216013at_int,N2)),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(semiri1314217659103216013at_int,N2)),one_one_int)) ).

% double_gauss_sum
tff(fact_3021_double__gauss__sum,axiom,
    ! [N2: nat] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),groups7501900531339628137nteger(semiri4939895301339042750nteger,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2))) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(semiri4939895301339042750nteger,N2)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_nat_Code_integer(semiri4939895301339042750nteger,N2)),one_one_Code_integer)) ).

% double_gauss_sum
tff(fact_3022_double__gauss__sum,axiom,
    ! [N2: nat] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),groups6325495683096345652atural(semiri3763490453095760265atural,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2))) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_nat_Code_natural(semiri3763490453095760265atural,N2)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_nat_Code_natural(semiri3763490453095760265atural,N2)),one_one_Code_natural)) ).

% double_gauss_sum
tff(fact_3023_double__gauss__sum,axiom,
    ! [N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_set_nat_nat(groups3542108847815614940at_nat(semiri1316708129612266289at_nat),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2))) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(semiri1316708129612266289at_nat,N2)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(semiri1316708129612266289at_nat,N2)),one_one_nat)) ).

% double_gauss_sum
tff(fact_3024_neg__zmod__mult__2,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),zero_zero_int)
     => ( aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),B))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A)) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,B),one_one_int)),A))),one_one_int) ) ) ).

% neg_zmod_mult_2
tff(fact_3025_mult__2,axiom,
    ! [Z: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),Z) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Z),Z) ).

% mult_2
tff(fact_3026_mult__2,axiom,
    ! [Z: int] : aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),Z) = aa_int_int(aa_int_fun_int_int(plus_plus_int,Z),Z) ).

% mult_2
tff(fact_3027_mult__2,axiom,
    ! [Z: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),Z) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,Z),Z) ).

% mult_2
tff(fact_3028_mult__2,axiom,
    ! [Z: rat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one))),Z) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,Z),Z) ).

% mult_2
tff(fact_3029_mult__2,axiom,
    ! [Z: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),Z) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,Z),Z) ).

% mult_2
tff(fact_3030_mult__2__right,axiom,
    ! [Z: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,Z),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Z),Z) ).

% mult_2_right
tff(fact_3031_mult__2__right,axiom,
    ! [Z: int] : aa_int_int(aa_int_fun_int_int(times_times_int,Z),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,Z),Z) ).

% mult_2_right
tff(fact_3032_mult__2__right,axiom,
    ! [Z: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,Z),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,Z),Z) ).

% mult_2_right
tff(fact_3033_mult__2__right,axiom,
    ! [Z: rat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,Z),aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one))) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,Z),Z) ).

% mult_2_right
tff(fact_3034_mult__2__right,axiom,
    ! [Z: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,Z),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,Z),Z) ).

% mult_2_right
tff(fact_3035_left__add__twice,axiom,
    ! [A: nat,B: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A)),B) ).

% left_add_twice
tff(fact_3036_left__add__twice,axiom,
    ! [A: int,B: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A)),B) ).

% left_add_twice
tff(fact_3037_left__add__twice,axiom,
    ! [A: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A)),B) ).

% left_add_twice
tff(fact_3038_left__add__twice,axiom,
    ! [A: rat,B: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one))),A)),B) ).

% left_add_twice
tff(fact_3039_left__add__twice,axiom,
    ! [A: code_natural,B: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),B)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A)),B) ).

% left_add_twice
tff(fact_3040_pos__eucl__rel__int__mult__2,axiom,
    ! [B: int,A: int,Q3: int,R2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),B)
     => ( aa_Pro4592068669816069595_int_o(eucl_rel_int(A,B),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Q3),R2))
       => aa_Pro4592068669816069595_int_o(eucl_rel_int(aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A)),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),B)),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Q3),aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),R2)))) ) ) ).

% pos_eucl_rel_int_mult_2
tff(fact_3041_one__power2,axiom,
    aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,one_one_Code_integer),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = one_one_Code_integer ).

% one_power2
tff(fact_3042_one__power2,axiom,
    aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,one_one_rat),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = one_one_rat ).

% one_power2
tff(fact_3043_one__power2,axiom,
    aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,one_one_nat),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = one_one_nat ).

% one_power2
tff(fact_3044_one__power2,axiom,
    aa_nat_int(aa_int_fun_nat_int(power_power_int,one_one_int),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = one_one_int ).

% one_power2
tff(fact_3045_nat__1__add__1,axiom,
    aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)) ).

% nat_1_add_1
tff(fact_3046_Suc__nat__number__of__add,axiom,
    ! [V: num,N2: nat] : aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(numeral_numeral_nat,V)),N2)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(aa_num_fun_num_num(plus_plus_num,V),one))),N2) ).

% Suc_nat_number_of_add
tff(fact_3047_double__gauss__sum__from__Suc__0,axiom,
    ! [N2: nat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one))),groups2906978787729119204at_rat(semiri681578069525770553at_rat,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,zero_zero_nat)),N2))) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(semiri681578069525770553at_rat,N2)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(semiri681578069525770553at_rat,N2)),one_one_rat)) ).

% double_gauss_sum_from_Suc_0
tff(fact_3048_double__gauss__sum__from__Suc__0,axiom,
    ! [N2: nat] : aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),groups3539618377306564664at_int(semiri1314217659103216013at_int,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,zero_zero_nat)),N2))) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(semiri1314217659103216013at_int,N2)),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(semiri1314217659103216013at_int,N2)),one_one_int)) ).

% double_gauss_sum_from_Suc_0
tff(fact_3049_double__gauss__sum__from__Suc__0,axiom,
    ! [N2: nat] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),groups7501900531339628137nteger(semiri4939895301339042750nteger,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,zero_zero_nat)),N2))) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(semiri4939895301339042750nteger,N2)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_nat_Code_integer(semiri4939895301339042750nteger,N2)),one_one_Code_integer)) ).

% double_gauss_sum_from_Suc_0
tff(fact_3050_double__gauss__sum__from__Suc__0,axiom,
    ! [N2: nat] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),groups6325495683096345652atural(semiri3763490453095760265atural,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,zero_zero_nat)),N2))) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_nat_Code_natural(semiri3763490453095760265atural,N2)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_nat_Code_natural(semiri3763490453095760265atural,N2)),one_one_Code_natural)) ).

% double_gauss_sum_from_Suc_0
tff(fact_3051_double__gauss__sum__from__Suc__0,axiom,
    ! [N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_set_nat_nat(groups3542108847815614940at_nat(semiri1316708129612266289at_nat),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,zero_zero_nat)),N2))) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(semiri1316708129612266289at_nat,N2)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(semiri1316708129612266289at_nat,N2)),one_one_nat)) ).

% double_gauss_sum_from_Suc_0
tff(fact_3052_arith__series,axiom,
    ! [A: int,D2: int,N2: nat] : groups3539618377306564664at_int(aa_int_fun_nat_int(aTP_Lamm_fu(A),D2),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2)) = aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(semiri1314217659103216013at_int,N2)),one_one_int)),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A)),aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(semiri1314217659103216013at_int,N2)),D2)))),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) ).

% arith_series
tff(fact_3053_arith__series,axiom,
    ! [A: code_integer,D2: code_integer,N2: nat] : groups7501900531339628137nteger(aa_Cod1578151519121547077nteger(aTP_Lamm_fv(A),D2),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_nat_Code_integer(semiri4939895301339042750nteger,N2)),one_one_Code_integer)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(semiri4939895301339042750nteger,N2)),D2)))),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) ).

% arith_series
tff(fact_3054_arith__series,axiom,
    ! [A: code_natural,D2: code_natural,N2: nat] : groups6325495683096345652atural(aa_Cod5320533616963873627atural(aTP_Lamm_fw(A),D2),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_nat_Code_natural(semiri3763490453095760265atural,N2)),one_one_Code_natural)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_nat_Code_natural(semiri3763490453095760265atural,N2)),D2)))),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))) ).

% arith_series
tff(fact_3055_arith__series,axiom,
    ! [A: nat,D2: nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(aa_nat_fun_nat_nat(aTP_Lamm_fx(A),D2)),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2)) = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(semiri1316708129612266289at_nat,N2)),one_one_nat)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(semiri1316708129612266289at_nat,N2)),D2)))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) ).

% arith_series
tff(fact_3056_gauss__sum,axiom,
    ! [N2: nat] : groups3539618377306564664at_int(semiri1314217659103216013at_int,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2)) = aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(semiri1314217659103216013at_int,N2)),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(semiri1314217659103216013at_int,N2)),one_one_int))),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) ).

% gauss_sum
tff(fact_3057_gauss__sum,axiom,
    ! [N2: nat] : groups7501900531339628137nteger(semiri4939895301339042750nteger,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(semiri4939895301339042750nteger,N2)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_nat_Code_integer(semiri4939895301339042750nteger,N2)),one_one_Code_integer))),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) ).

% gauss_sum
tff(fact_3058_gauss__sum,axiom,
    ! [N2: nat] : groups6325495683096345652atural(semiri3763490453095760265atural,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_nat_Code_natural(semiri3763490453095760265atural,N2)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_nat_Code_natural(semiri3763490453095760265atural,N2)),one_one_Code_natural))),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))) ).

% gauss_sum
tff(fact_3059_gauss__sum,axiom,
    ! [N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(semiri1316708129612266289at_nat),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2)) = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(semiri1316708129612266289at_nat,N2)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(semiri1316708129612266289at_nat,N2)),one_one_nat))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) ).

% gauss_sum
tff(fact_3060_nat__approx__posE,axiom,
    ! [E: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),E)
     => ~ ! [N: nat] : ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(divide_divide_rat(one_one_rat),aa_nat_rat(semiri681578069525770553at_rat,aa_nat_nat(suc,N)))),E) ) ).

% nat_approx_posE
tff(fact_3061_neg__eucl__rel__int__mult__2,axiom,
    ! [B: int,A: int,Q3: int,R2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,B),zero_zero_int)
     => ( aa_Pro4592068669816069595_int_o(eucl_rel_int(aa_int_int(aa_int_fun_int_int(plus_plus_int,A),one_one_int),B),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Q3),R2))
       => aa_Pro4592068669816069595_int_o(eucl_rel_int(aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A)),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),B)),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Q3),aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),R2)),one_one_int))) ) ) ).

% neg_eucl_rel_int_mult_2
tff(fact_3062_gauss__sum__from__Suc__0,axiom,
    ! [N2: nat] : groups3539618377306564664at_int(semiri1314217659103216013at_int,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,zero_zero_nat)),N2)) = aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(semiri1314217659103216013at_int,N2)),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(semiri1314217659103216013at_int,N2)),one_one_int))),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) ).

% gauss_sum_from_Suc_0
tff(fact_3063_gauss__sum__from__Suc__0,axiom,
    ! [N2: nat] : groups7501900531339628137nteger(semiri4939895301339042750nteger,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,zero_zero_nat)),N2)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(semiri4939895301339042750nteger,N2)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_nat_Code_integer(semiri4939895301339042750nteger,N2)),one_one_Code_integer))),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) ).

% gauss_sum_from_Suc_0
tff(fact_3064_gauss__sum__from__Suc__0,axiom,
    ! [N2: nat] : groups6325495683096345652atural(semiri3763490453095760265atural,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,zero_zero_nat)),N2)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_nat_Code_natural(semiri3763490453095760265atural,N2)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_nat_Code_natural(semiri3763490453095760265atural,N2)),one_one_Code_natural))),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))) ).

% gauss_sum_from_Suc_0
tff(fact_3065_gauss__sum__from__Suc__0,axiom,
    ! [N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(semiri1316708129612266289at_nat),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,zero_zero_nat)),N2)) = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(semiri1316708129612266289at_nat,N2)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(semiri1316708129612266289at_nat,N2)),one_one_nat))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) ).

% gauss_sum_from_Suc_0
tff(fact_3066_exp__add__not__zero__imp__right,axiom,
    ! [M: nat,N2: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)) != zero_zero_nat )
     => ( aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2) != zero_zero_nat ) ) ).

% exp_add_not_zero_imp_right
tff(fact_3067_exp__add__not__zero__imp__right,axiom,
    ! [M: nat,N2: nat] :
      ( ( aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)) != zero_zero_int )
     => ( aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),N2) != zero_zero_int ) ) ).

% exp_add_not_zero_imp_right
tff(fact_3068_exp__add__not__zero__imp__right,axiom,
    ! [M: nat,N2: nat] :
      ( ( aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)) != zero_z3403309356797280102nteger )
     => ( aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),N2) != zero_z3403309356797280102nteger ) ) ).

% exp_add_not_zero_imp_right
tff(fact_3069_exp__add__not__zero__imp__right,axiom,
    ! [M: nat,N2: nat] :
      ( ( aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)) != zero_z2226904508553997617atural )
     => ( aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),N2) != zero_z2226904508553997617atural ) ) ).

% exp_add_not_zero_imp_right
tff(fact_3070_exp__add__not__zero__imp__left,axiom,
    ! [M: nat,N2: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)) != zero_zero_nat )
     => ( aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),M) != zero_zero_nat ) ) ).

% exp_add_not_zero_imp_left
tff(fact_3071_exp__add__not__zero__imp__left,axiom,
    ! [M: nat,N2: nat] :
      ( ( aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)) != zero_zero_int )
     => ( aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),M) != zero_zero_int ) ) ).

% exp_add_not_zero_imp_left
tff(fact_3072_exp__add__not__zero__imp__left,axiom,
    ! [M: nat,N2: nat] :
      ( ( aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)) != zero_z3403309356797280102nteger )
     => ( aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),M) != zero_z3403309356797280102nteger ) ) ).

% exp_add_not_zero_imp_left
tff(fact_3073_exp__add__not__zero__imp__left,axiom,
    ! [M: nat,N2: nat] :
      ( ( aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)) != zero_z2226904508553997617atural )
     => ( aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),M) != zero_z2226904508553997617atural ) ) ).

% exp_add_not_zero_imp_left
tff(fact_3074_sum__power2__eq__zero__iff,axiom,
    ! [X2: code_integer,Y: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,Y),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) = zero_z3403309356797280102nteger )
    <=> ( ( X2 = zero_z3403309356797280102nteger )
        & ( Y = zero_z3403309356797280102nteger ) ) ) ).

% sum_power2_eq_zero_iff
tff(fact_3075_sum__power2__eq__zero__iff,axiom,
    ! [X2: rat,Y: rat] :
      ( ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,Y),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) = zero_zero_rat )
    <=> ( ( X2 = zero_zero_rat )
        & ( Y = zero_zero_rat ) ) ) ).

% sum_power2_eq_zero_iff
tff(fact_3076_sum__power2__eq__zero__iff,axiom,
    ! [X2: int,Y: int] :
      ( ( aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_int(aa_int_fun_nat_int(power_power_int,Y),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) = zero_zero_int )
    <=> ( ( X2 = zero_zero_int )
        & ( Y = zero_zero_int ) ) ) ).

% sum_power2_eq_zero_iff
tff(fact_3077_div__exp__eq,axiom,
    ! [A: int,M: nat,N2: nat] : aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),M))),aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),N2)) = aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2))) ).

% div_exp_eq
tff(fact_3078_div__exp__eq,axiom,
    ! [A: nat,M: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),M))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)) = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2))) ).

% div_exp_eq
tff(fact_3079_div__exp__eq,axiom,
    ! [A: code_integer,M: nat,N2: nat] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),M))),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),N2)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2))) ).

% div_exp_eq
tff(fact_3080_div__exp__eq,axiom,
    ! [A: code_natural,M: nat,N2: nat] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),M))),aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),N2)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2))) ).

% div_exp_eq
tff(fact_3081_power2__eq__1__iff,axiom,
    ! [A: int] :
      ( ( aa_nat_int(aa_int_fun_nat_int(power_power_int,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = one_one_int )
    <=> ( ( A = one_one_int )
        | ( A = aa_int_int(uminus_uminus_int,one_one_int) ) ) ) ).

% power2_eq_1_iff
tff(fact_3082_power2__eq__1__iff,axiom,
    ! [A: code_integer] :
      ( ( aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = one_one_Code_integer )
    <=> ( ( A = one_one_Code_integer )
        | ( A = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) ) ) ) ).

% power2_eq_1_iff
tff(fact_3083_power2__eq__1__iff,axiom,
    ! [A: rat] :
      ( ( aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = one_one_rat )
    <=> ( ( A = one_one_rat )
        | ( A = aa_rat_rat(uminus_uminus_rat,one_one_rat) ) ) ) ).

% power2_eq_1_iff
tff(fact_3084_plus__int_Oabs__eq,axiom,
    ! [Xa: product_prod_nat_nat,X2: product_prod_nat_nat] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_Pro4240683299535347697at_int(abs_Integ,Xa)),aa_Pro4240683299535347697at_int(abs_Integ,X2)) = aa_Pro4240683299535347697at_int(abs_Integ,aa_Pro262675715343573244at_nat(aa_Pro8023792847356852296at_nat(aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,aTP_Lamm_fz),Xa),X2)) ).

% plus_int.abs_eq
tff(fact_3085_abs__square__eq__1,axiom,
    ! [X2: code_integer] :
      ( ( aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = one_one_Code_integer )
    <=> ( aa_Cod1783974652533396728nteger(abs_abs_Code_integer,X2) = one_one_Code_integer ) ) ).

% abs_square_eq_1
tff(fact_3086_abs__square__eq__1,axiom,
    ! [X2: rat] :
      ( ( aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = one_one_rat )
    <=> ( aa_rat_rat(abs_abs_rat,X2) = one_one_rat ) ) ).

% abs_square_eq_1
tff(fact_3087_abs__square__eq__1,axiom,
    ! [X2: int] :
      ( ( aa_nat_int(aa_int_fun_nat_int(power_power_int,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = one_one_int )
    <=> ( aa_int_int(abs_abs_int,X2) = one_one_int ) ) ).

% abs_square_eq_1
tff(fact_3088_minus__int_Oabs__eq,axiom,
    ! [Xa: product_prod_nat_nat,X2: product_prod_nat_nat] : aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_Pro4240683299535347697at_int(abs_Integ,Xa)),aa_Pro4240683299535347697at_int(abs_Integ,X2)) = aa_Pro4240683299535347697at_int(abs_Integ,aa_Pro262675715343573244at_nat(aa_Pro8023792847356852296at_nat(aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,aTP_Lamm_gb),Xa),X2)) ).

% minus_int.abs_eq
tff(fact_3089_nat__induct2,axiom,
    ! [P: fun_nat_o,N2: nat] :
      ( aa_nat_o(P,zero_zero_nat)
     => ( aa_nat_o(P,one_one_nat)
       => ( ! [N: nat] :
              ( aa_nat_o(P,N)
             => aa_nat_o(P,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) )
         => aa_nat_o(P,N2) ) ) ) ).

% nat_induct2
tff(fact_3090_times__int_Oabs__eq,axiom,
    ! [Xa: product_prod_nat_nat,X2: product_prod_nat_nat] : aa_int_int(aa_int_fun_int_int(times_times_int,aa_Pro4240683299535347697at_int(abs_Integ,Xa)),aa_Pro4240683299535347697at_int(abs_Integ,X2)) = aa_Pro4240683299535347697at_int(abs_Integ,aa_Pro262675715343573244at_nat(aa_Pro8023792847356852296at_nat(aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,aTP_Lamm_gd),Xa),X2)) ).

% times_int.abs_eq
tff(fact_3091_sum__power2__le__zero__iff,axiom,
    ! [X2: code_integer,Y: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,Y),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),zero_z3403309356797280102nteger)
    <=> ( ( X2 = zero_z3403309356797280102nteger )
        & ( Y = zero_z3403309356797280102nteger ) ) ) ).

% sum_power2_le_zero_iff
tff(fact_3092_sum__power2__le__zero__iff,axiom,
    ! [X2: rat,Y: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,Y),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),zero_zero_rat)
    <=> ( ( X2 = zero_zero_rat )
        & ( Y = zero_zero_rat ) ) ) ).

% sum_power2_le_zero_iff
tff(fact_3093_sum__power2__le__zero__iff,axiom,
    ! [X2: int,Y: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_int(aa_int_fun_nat_int(power_power_int,Y),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),zero_zero_int)
    <=> ( ( X2 = zero_zero_int )
        & ( Y = zero_zero_int ) ) ) ).

% sum_power2_le_zero_iff
tff(fact_3094_sum__power2__ge__zero,axiom,
    ! [X2: code_integer,Y: code_integer] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,Y),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))) ).

% sum_power2_ge_zero
tff(fact_3095_sum__power2__ge__zero,axiom,
    ! [X2: rat,Y: rat] : aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,Y),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))) ).

% sum_power2_ge_zero
tff(fact_3096_sum__power2__ge__zero,axiom,
    ! [X2: int,Y: int] : aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_int(aa_int_fun_nat_int(power_power_int,Y),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))) ).

% sum_power2_ge_zero
tff(fact_3097_bits__stable__imp__add__self,axiom,
    ! [A: int] :
      ( ( aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) = A )
     => ( aa_int_int(aa_int_fun_int_int(plus_plus_int,A),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))) = zero_zero_int ) ) ).

% bits_stable_imp_add_self
tff(fact_3098_bits__stable__imp__add__self,axiom,
    ! [A: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = A )
     => ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) = zero_zero_nat ) ) ).

% bits_stable_imp_add_self
tff(fact_3099_bits__stable__imp__add__self,axiom,
    ! [A: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) = A )
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)))) = zero_z3403309356797280102nteger ) ) ).

% bits_stable_imp_add_self
tff(fact_3100_bits__stable__imp__add__self,axiom,
    ! [A: code_natural] :
      ( ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))) = A )
     => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one)))) = zero_z2226904508553997617atural ) ) ).

% bits_stable_imp_add_self
tff(fact_3101_not__sum__power2__lt__zero,axiom,
    ! [X2: code_integer,Y: code_integer] : ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,Y),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),zero_z3403309356797280102nteger) ).

% not_sum_power2_lt_zero
tff(fact_3102_not__sum__power2__lt__zero,axiom,
    ! [X2: rat,Y: rat] : ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,Y),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),zero_zero_rat) ).

% not_sum_power2_lt_zero
tff(fact_3103_not__sum__power2__lt__zero,axiom,
    ! [X2: int,Y: int] : ~ aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_int(aa_int_fun_nat_int(power_power_int,Y),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),zero_zero_int) ).

% not_sum_power2_lt_zero
tff(fact_3104_sum__power2__gt__zero__iff,axiom,
    ! [X2: code_integer,Y: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,Y),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))
    <=> ( ( X2 != zero_z3403309356797280102nteger )
        | ( Y != zero_z3403309356797280102nteger ) ) ) ).

% sum_power2_gt_zero_iff
tff(fact_3105_sum__power2__gt__zero__iff,axiom,
    ! [X2: rat,Y: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,Y),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))
    <=> ( ( X2 != zero_zero_rat )
        | ( Y != zero_zero_rat ) ) ) ).

% sum_power2_gt_zero_iff
tff(fact_3106_sum__power2__gt__zero__iff,axiom,
    ! [X2: int,Y: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_int(aa_int_fun_nat_int(power_power_int,Y),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))
    <=> ( ( X2 != zero_zero_int )
        | ( Y != zero_zero_int ) ) ) ).

% sum_power2_gt_zero_iff
tff(fact_3107_power2__sum,axiom,
    ! [X2: nat,Y: nat] : aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X2),Y)),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,Y),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),X2)),Y)) ).

% power2_sum
tff(fact_3108_power2__sum,axiom,
    ! [X2: int,Y: int] : aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),Y)),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_int(aa_int_fun_nat_int(power_power_int,Y),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),X2)),Y)) ).

% power2_sum
tff(fact_3109_power2__sum,axiom,
    ! [X2: code_integer,Y: code_integer] : aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X2),Y)),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,Y),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),X2)),Y)) ).

% power2_sum
tff(fact_3110_power2__sum,axiom,
    ! [X2: rat,Y: rat] : aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),Y)),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,Y),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one))),X2)),Y)) ).

% power2_sum
tff(fact_3111_power2__sum,axiom,
    ! [X2: code_natural,Y: code_natural] : aa_nat_Code_natural(power_7079662738309270450atural(aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,X2),Y)),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_nat_Code_natural(power_7079662738309270450atural(X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_Code_natural(power_7079662738309270450atural(Y),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),X2)),Y)) ).

% power2_sum
tff(fact_3112_square__le__1,axiom,
    ! [X2: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),X2)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,X2),one_one_Code_integer)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),one_one_Code_integer) ) ) ).

% square_le_1
tff(fact_3113_square__le__1,axiom,
    ! [X2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),X2)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,X2),one_one_rat)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),one_one_rat) ) ) ).

% square_le_1
tff(fact_3114_square__le__1,axiom,
    ! [X2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(uminus_uminus_int,one_one_int)),X2)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,X2),one_one_int)
       => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),one_one_int) ) ) ).

% square_le_1
tff(fact_3115_abs__square__le__1,axiom,
    ! [X2: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),one_one_Code_integer)
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,X2)),one_one_Code_integer) ) ).

% abs_square_le_1
tff(fact_3116_abs__square__le__1,axiom,
    ! [X2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),one_one_rat)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(abs_abs_rat,X2)),one_one_rat) ) ).

% abs_square_le_1
tff(fact_3117_abs__square__le__1,axiom,
    ! [X2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),one_one_int)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(abs_abs_int,X2)),one_one_int) ) ).

% abs_square_le_1
tff(fact_3118_abs__square__less__1,axiom,
    ! [X2: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),one_one_Code_integer)
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,X2)),one_one_Code_integer) ) ).

% abs_square_less_1
tff(fact_3119_abs__square__less__1,axiom,
    ! [X2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),one_one_rat)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(abs_abs_rat,X2)),one_one_rat) ) ).

% abs_square_less_1
tff(fact_3120_abs__square__less__1,axiom,
    ! [X2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),one_one_int)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(abs_abs_int,X2)),one_one_int) ) ).

% abs_square_less_1
tff(fact_3121_div__exp__mod__exp__eq,axiom,
    ! [A: int,N2: nat,M: nat] : aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),N2))),aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),M)) = aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),M)))),aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),N2)) ).

% div_exp_mod_exp_eq
tff(fact_3122_div__exp__mod__exp__eq,axiom,
    ! [A: nat,N2: nat,M: nat] : aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),M)) = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),M)))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)) ).

% div_exp_mod_exp_eq
tff(fact_3123_div__exp__mod__exp__eq,axiom,
    ! [A: code_integer,N2: nat,M: nat] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),N2))),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),M)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),M)))),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),N2)) ).

% div_exp_mod_exp_eq
tff(fact_3124_div__exp__mod__exp__eq,axiom,
    ! [A: code_natural,N2: nat,M: nat] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),N2))),aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),M)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),M)))),aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),N2)) ).

% div_exp_mod_exp_eq
tff(fact_3125_ex__power__ivl2,axiom,
    ! [B: nat,K: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),B)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),K)
       => ? [N: nat] :
            ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,B),N)),K)
            & aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,B),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat))) ) ) ) ).

% ex_power_ivl2
tff(fact_3126_ex__power__ivl1,axiom,
    ! [B: nat,K: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),B)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),K)
       => ? [N: nat] :
            ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,B),N)),K)
            & aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,K),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,B),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat))) ) ) ) ).

% ex_power_ivl1
tff(fact_3127_power2__diff,axiom,
    ! [X2: int,Y: int] : aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,X2),Y)),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_int(aa_int_fun_nat_int(power_power_int,Y),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),X2)),Y)) ).

% power2_diff
tff(fact_3128_power2__diff,axiom,
    ! [X2: code_integer,Y: code_integer] : aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,X2),Y)),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,Y),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),X2)),Y)) ).

% power2_diff
tff(fact_3129_power2__diff,axiom,
    ! [X2: rat,Y: rat] : aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(minus_minus_rat(X2),Y)),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_rat_rat(minus_minus_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,Y),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one))),X2)),Y)) ).

% power2_diff
tff(fact_3130_power__minus1__odd,axiom,
    ! [N2: nat] : aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(uminus_uminus_int,one_one_int)),aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2))) = aa_int_int(uminus_uminus_int,one_one_int) ).

% power_minus1_odd
tff(fact_3131_power__minus1__odd,axiom,
    ! [N2: nat] : aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2))) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) ).

% power_minus1_odd
tff(fact_3132_power__minus1__odd,axiom,
    ! [N2: nat] : aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2))) = aa_rat_rat(uminus_uminus_rat,one_one_rat) ).

% power_minus1_odd
tff(fact_3133_mask__eq__sum__exp,axiom,
    ! [N2: nat] : aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),N2)),one_one_int) = groups3539618377306564664at_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),collect_nat(aa_nat_fun_nat_o(aTP_Lamm_bj,N2))) ).

% mask_eq_sum_exp
tff(fact_3134_mask__eq__sum__exp,axiom,
    ! [N2: nat] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),N2)),one_one_Code_integer) = groups7501900531339628137nteger(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),collect_nat(aa_nat_fun_nat_o(aTP_Lamm_bj,N2))) ).

% mask_eq_sum_exp
tff(fact_3135_mask__eq__sum__exp,axiom,
    ! [N2: nat] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(minus_7197305767214868737atural,aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),N2)),one_one_Code_natural) = groups6325495683096345652atural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),collect_nat(aa_nat_fun_nat_o(aTP_Lamm_bj,N2))) ).

% mask_eq_sum_exp
tff(fact_3136_mask__eq__sum__exp,axiom,
    ! [N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)),one_one_nat) = aa_set_nat_nat(groups3542108847815614940at_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),collect_nat(aa_nat_fun_nat_o(aTP_Lamm_bj,N2))) ).

% mask_eq_sum_exp
tff(fact_3137_sum_Oin__pairs,axiom,
    ! [G: fun_na2338080690716861136at_nat,M: nat,N2: nat] : groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),M)),aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)))) = groups6857163185585827899at_nat(aTP_Lamm_ge(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) ).

% sum.in_pairs
tff(fact_3138_sum_Oin__pairs,axiom,
    ! [G: fun_nat_rat,M: nat,N2: nat] : groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),M)),aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)))) = groups2906978787729119204at_rat(aTP_Lamm_gf(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) ).

% sum.in_pairs
tff(fact_3139_sum_Oin__pairs,axiom,
    ! [G: fun_nat_int,M: nat,N2: nat] : groups3539618377306564664at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),M)),aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)))) = groups3539618377306564664at_int(aTP_Lamm_gg(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) ).

% sum.in_pairs
tff(fact_3140_sum_Oin__pairs,axiom,
    ! [G: fun_nat_nat,M: nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),M)),aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)))) = aa_set_nat_nat(groups3542108847815614940at_nat(aTP_Lamm_gh(G)),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) ).

% sum.in_pairs
tff(fact_3141_gauss__sum__nat,axiom,
    ! [N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(aTP_Lamm_co),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2)) = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,N2),aa_nat_nat(suc,N2))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) ).

% gauss_sum_nat
tff(fact_3142_divmod__step__eq,axiom,
    ! [L: num,Q3: nat,R2: nat] :
      aa_Pro262675715343573244at_nat(unique5026877609467782581ep_nat(L),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Q3),R2)) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_num_nat(numeral_numeral_nat,L)),R2),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),Q3)),one_one_nat)),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,R2),aa_num_nat(numeral_numeral_nat,L))),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),Q3)),R2)) ).

% divmod_step_eq
tff(fact_3143_divmod__step__eq,axiom,
    ! [L: num,Q3: int,R2: int] :
      aa_Pro6970504127699319548nt_int(unique5024387138958732305ep_int(L),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Q3),R2)) = $ite(aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_num_int(numeral_numeral_int,L)),R2),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),Q3)),one_one_int)),aa_int_int(aa_int_fun_int_int(minus_minus_int,R2),aa_num_int(numeral_numeral_int,L))),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),Q3)),R2)) ).

% divmod_step_eq
tff(fact_3144_divmod__step__eq,axiom,
    ! [L: num,Q3: code_integer,R2: code_integer] :
      aa_Pro4693618923521437820nteger(unique4921790084139445826nteger(L),aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(Q3),R2)) = $ite(aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_num_Code_integer(numera6620942414471956472nteger,L)),R2),aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),Q3)),one_one_Code_integer)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,R2),aa_num_Code_integer(numera6620942414471956472nteger,L))),aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),Q3)),R2)) ).

% divmod_step_eq
tff(fact_3145_divmod__step__def,axiom,
    ! [L: num,Qr: product_prod_nat_nat] : aa_Pro262675715343573244at_nat(unique5026877609467782581ep_nat(L),Qr) = aa_Pro262675715343573244at_nat(produc2626176000494625587at_nat(aTP_Lamm_gi(L)),Qr) ).

% divmod_step_def
tff(fact_3146_divmod__step__def,axiom,
    ! [L: num,Qr: product_prod_int_int] : aa_Pro6970504127699319548nt_int(unique5024387138958732305ep_int(L),Qr) = aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,aTP_Lamm_gj(L)),Qr) ).

% divmod_step_def
tff(fact_3147_divmod__step__def,axiom,
    ! [L: num,Qr: produc8923325533196201883nteger] : aa_Pro4693618923521437820nteger(unique4921790084139445826nteger(L),Qr) = aa_Pro4693618923521437820nteger(produc6916734918728496179nteger(aTP_Lamm_gk(L)),Qr) ).

% divmod_step_def
tff(fact_3148_divmod__step__nat__def,axiom,
    ! [L: num,Qr: product_prod_nat_nat] : aa_Pro262675715343573244at_nat(unique5026877609467782581ep_nat(L),Qr) = aa_Pro262675715343573244at_nat(produc2626176000494625587at_nat(aTP_Lamm_gi(L)),Qr) ).

% divmod_step_nat_def
tff(fact_3149_divmod__step__int__def,axiom,
    ! [L: num,Qr: product_prod_int_int] : aa_Pro6970504127699319548nt_int(unique5024387138958732305ep_int(L),Qr) = aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,aTP_Lamm_gj(L)),Qr) ).

% divmod_step_int_def
tff(fact_3150_set__bit__0,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se2793503036327961859nteger,zero_zero_nat),A) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,one_one_Code_integer),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))))) ).

% set_bit_0
tff(fact_3151_set__bit__0,axiom,
    ! [A: int] : aa_int_int(aa_nat_fun_int_int(bit_se7879613467334960850it_int,zero_zero_nat),A) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))))) ).

% set_bit_0
tff(fact_3152_set__bit__0,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se7882103937844011126it_nat,zero_zero_nat),A) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))) ).

% set_bit_0
tff(fact_3153_set__bit__0,axiom,
    ! [A: code_natural] : aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se1617098188084679374atural,zero_zero_nat),A) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,one_one_Code_natural),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))))) ).

% set_bit_0
tff(fact_3154_mlex__eq,axiom,
    ! [F: fun_se4097146774670233028at_nat,R3: set_Pr4329608150637261639at_nat] : mlex_p3502713205431853936at_nat(F,R3) = aa_fun1965866159956205013at_nat(collec6321179662152712658at_nat,aa_fun762164075915671590_nat_o(produc410239310623530412_nat_o,aa_set5605188905385065315_nat_o(aTP_Lamm_gl(F),R3))) ).

% mlex_eq
tff(fact_3155_mlex__eq,axiom,
    ! [F: fun_nat_nat,R3: set_Pr1261947904930325089at_nat] : aa_set8868280134176360700at_nat(mlex_prod_nat(F),R3) = aa_fun7046812543386002057at_nat(collec3392354462482085612at_nat,aa_fun7564604662015400456_nat_o(produc6081775807080527818_nat_o,aa_set2634951030311766213_nat_o(aTP_Lamm_gm(F),R3))) ).

% mlex_eq
tff(fact_3156_unset__bit__Suc,axiom,
    ! [N2: nat,A: code_integer] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se8260200283734997820nteger,aa_nat_nat(suc,N2)),A) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se8260200283734997820nteger,N2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)))))) ).

% unset_bit_Suc
tff(fact_3157_unset__bit__Suc,axiom,
    ! [N2: nat,A: int] : aa_int_int(aa_nat_fun_int_int(bit_se4203085406695923979it_int,aa_nat_nat(suc,N2)),A) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_nat_fun_int_int(bit_se4203085406695923979it_int,N2),aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))))) ).

% unset_bit_Suc
tff(fact_3158_unset__bit__Suc,axiom,
    ! [N2: nat,A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se4205575877204974255it_nat,aa_nat_nat(suc,N2)),A) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(bit_se4205575877204974255it_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) ).

% unset_bit_Suc
tff(fact_3159_unset__bit__Suc,axiom,
    ! [N2: nat,A: code_natural] : aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se7083795435491715335atural,aa_nat_nat(suc,N2)),A) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one)))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se7083795435491715335atural,N2),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one)))))) ).

% unset_bit_Suc
tff(fact_3160_flip__bit__Suc,axiom,
    ! [N2: nat,A: code_integer] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1345352211410354436nteger,aa_nat_nat(suc,N2)),A) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1345352211410354436nteger,N2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)))))) ).

% flip_bit_Suc
tff(fact_3161_flip__bit__Suc,axiom,
    ! [N2: nat,A: int] : aa_int_int(aa_nat_fun_int_int(bit_se2159334234014336723it_int,aa_nat_nat(suc,N2)),A) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_nat_fun_int_int(bit_se2159334234014336723it_int,N2),aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))))) ).

% flip_bit_Suc
tff(fact_3162_flip__bit__Suc,axiom,
    ! [N2: nat,A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se2161824704523386999it_nat,aa_nat_nat(suc,N2)),A) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(bit_se2161824704523386999it_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) ).

% flip_bit_Suc
tff(fact_3163_flip__bit__Suc,axiom,
    ! [N2: nat,A: code_natural] : aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se168947363167071951atural,aa_nat_nat(suc,N2)),A) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one)))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se168947363167071951atural,N2),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one)))))) ).

% flip_bit_Suc
tff(fact_3164_set__bit__Suc,axiom,
    ! [N2: nat,A: code_integer] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se2793503036327961859nteger,aa_nat_nat(suc,N2)),A) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se2793503036327961859nteger,N2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)))))) ).

% set_bit_Suc
tff(fact_3165_set__bit__Suc,axiom,
    ! [N2: nat,A: int] : aa_int_int(aa_nat_fun_int_int(bit_se7879613467334960850it_int,aa_nat_nat(suc,N2)),A) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_nat_fun_int_int(bit_se7879613467334960850it_int,N2),aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))))) ).

% set_bit_Suc
tff(fact_3166_set__bit__Suc,axiom,
    ! [N2: nat,A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se7882103937844011126it_nat,aa_nat_nat(suc,N2)),A) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(bit_se7882103937844011126it_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) ).

% set_bit_Suc
tff(fact_3167_set__bit__Suc,axiom,
    ! [N2: nat,A: code_natural] : aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se1617098188084679374atural,aa_nat_nat(suc,N2)),A) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one)))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se1617098188084679374atural,N2),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one)))))) ).

% set_bit_Suc
tff(fact_3168_divmod__step__integer__def,axiom,
    ! [L: num,Qr: produc8923325533196201883nteger] : aa_Pro4693618923521437820nteger(unique4921790084139445826nteger(L),Qr) = aa_Pro4693618923521437820nteger(produc6916734918728496179nteger(aTP_Lamm_gk(L)),Qr) ).

% divmod_step_integer_def
tff(fact_3169_signed__take__bit__rec,axiom,
    ! [N2: nat,A: code_integer] :
      aa_Cod1783974652533396728nteger(bit_ri6519982836138164636nteger(N2),A) = $ite(N2 = zero_zero_nat,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_Cod1783974652533396728nteger(bit_ri6519982836138164636nteger(aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))))))) ).

% signed_take_bit_rec
tff(fact_3170_signed__take__bit__rec,axiom,
    ! [N2: nat,A: int] :
      aa_int_int(bit_ri631733984087533419it_int(N2),A) = $ite(N2 = zero_zero_nat,aa_int_int(uminus_uminus_int,aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(bit_ri631733984087533419it_int(aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)),aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))))))) ).

% signed_take_bit_rec
tff(fact_3171_round__unique,axiom,
    ! [X2: rat,Y: int] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(minus_minus_rat(X2),aa_rat_rat(divide_divide_rat(one_one_rat),aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one))))),aa_int_rat(ring_1_of_int_rat,Y))
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_int_rat(ring_1_of_int_rat,Y)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),aa_rat_rat(divide_divide_rat(one_one_rat),aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one)))))
       => ( archim7778729529865785530nd_rat(X2) = Y ) ) ) ).

% round_unique
tff(fact_3172_rel__of__def,axiom,
    ! [M: fun_fu4810197545401214784nteger,P: fun_Pr7015759342434529115eger_o] : rel_of3240586176920340263nteger(M,P) = aa_fun1565836460712643691nteger(collec2950617477150063211nteger,aa_fun7761728421758185830eger_o(produc7373287791920631523eger_o,aa_fun5185621348090534806eger_o(aTP_Lamm_gn(M),P))) ).

% rel_of_def
tff(fact_3173_rel__of__def,axiom,
    ! [M: fun_fu2352890940381120596et_nat,P: fun_Pr2620521676128474833_nat_o] : rel_of7233497478102412281et_nat(M,P) = aa_fun4278629577996002795et_nat(collec6193113176214168693et_nat,aa_fun6593097867094858448_nat_o(produc2915205735004773393_nat_o,aa_fun1045796833200626456_nat_o(aTP_Lamm_go(M),P))) ).

% rel_of_def
tff(fact_3174_rel__of__def,axiom,
    ! [M: fun_fu1905361174868762994et_nat,P: fun_Pr1227177680593602867_nat_o] : rel_of4573248530116435351et_nat(M,P) = aa_fun766325623412317803et_nat(collec5916191906451531411et_nat,aa_fun4447940216497214800_nat_o(produc4465912260561112435_nat_o,aa_fun4422562838209026524_nat_o(aTP_Lamm_gp(M),P))) ).

% rel_of_def
tff(fact_3175_rel__of__def,axiom,
    ! [M: fun_fu4253467608928286509nt_int,P: fun_Pr3540825087398332590_int_o] : rel_of9206080981073604500nt_int(M,P) = aa_fun4710078337987813035nt_int(collec2586211367037964248nt_int,aa_fun6978165455603620006_int_o(produc2207054017359051062_int_o,aa_fun1054583131507368252_int_o(aTP_Lamm_gq(M),P))) ).

% rel_of_def
tff(fact_3176_rel__of__def,axiom,
    ! [M: fun_fu5631754973857388633nt_int,P: fun_Pr1196100989263358594_int_o] : rel_of6825086619541906112nt_int(M,P) = aa_fun3799641615823574443nt_int(collec8113046454796679940nt_int,aa_fun1749673562058638246_int_o(produc7271678899836001034_int_o,aa_fun8601777901039773924_int_o(aTP_Lamm_gr(M),P))) ).

% rel_of_def
tff(fact_3177_dbl__simps_I4_J,axiom,
    aa_int_int(neg_numeral_dbl_int,aa_int_int(uminus_uminus_int,one_one_int)) = aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) ).

% dbl_simps(4)
tff(fact_3178_dbl__simps_I4_J,axiom,
    aa_Cod1783974652533396728nteger(neg_nu8804712462038260780nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) ).

% dbl_simps(4)
tff(fact_3179_dbl__simps_I4_J,axiom,
    aa_rat_rat(neg_numeral_dbl_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)) = aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one))) ).

% dbl_simps(4)
tff(fact_3180_round__altdef,axiom,
    ! [X2: rat] :
      archim7778729529865785530nd_rat(X2) = $ite(aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(divide_divide_rat(one_one_rat),aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one)))),aa_rat_rat(archimedean_frac_rat,X2)),archim2889992004027027881ng_rat(X2),archim3151403230148437115or_rat(X2)) ).

% round_altdef
tff(fact_3181_round__unique_H,axiom,
    ! [X2: rat,N2: int] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(abs_abs_rat,aa_rat_rat(minus_minus_rat(X2),aa_int_rat(ring_1_of_int_rat,N2)))),aa_rat_rat(divide_divide_rat(one_one_rat),aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one))))
     => ( archim7778729529865785530nd_rat(X2) = N2 ) ) ).

% round_unique'
tff(fact_3182_of__int__round__abs__le,axiom,
    ! [X2: rat] : aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(abs_abs_rat,aa_rat_rat(minus_minus_rat(aa_int_rat(ring_1_of_int_rat,archim7778729529865785530nd_rat(X2))),X2))),aa_rat_rat(divide_divide_rat(one_one_rat),aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one)))) ).

% of_int_round_abs_le
tff(fact_3183_divmod__algorithm__code_I5_J,axiom,
    ! [M: num,N2: num] : unique3479559517661332726nteger(aa_num_num(bit0,M),aa_num_num(bit0,N2)) = aa_Pro4693618923521437820nteger(produc6916734918728496179nteger(aTP_Lamm_gs),unique3479559517661332726nteger(M,N2)) ).

% divmod_algorithm_code(5)
tff(fact_3184_divmod__algorithm__code_I5_J,axiom,
    ! [M: num,N2: num] : unique5052692396658037445od_int(aa_num_num(bit0,M),aa_num_num(bit0,N2)) = aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,aTP_Lamm_gt),unique5052692396658037445od_int(M,N2)) ).

% divmod_algorithm_code(5)
tff(fact_3185_divmod__algorithm__code_I5_J,axiom,
    ! [M: num,N2: num] : unique5055182867167087721od_nat(aa_num_num(bit0,M),aa_num_num(bit0,N2)) = aa_Pro262675715343573244at_nat(produc2626176000494625587at_nat(aTP_Lamm_gu),unique5055182867167087721od_nat(M,N2)) ).

% divmod_algorithm_code(5)
tff(fact_3186_signed__take__bit__of__minus__1,axiom,
    ! [N2: nat] : aa_Cod1783974652533396728nteger(bit_ri6519982836138164636nteger(N2),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) ).

% signed_take_bit_of_minus_1
tff(fact_3187_signed__take__bit__of__minus__1,axiom,
    ! [N2: nat] : aa_int_int(bit_ri631733984087533419it_int(N2),aa_int_int(uminus_uminus_int,one_one_int)) = aa_int_int(uminus_uminus_int,one_one_int) ).

% signed_take_bit_of_minus_1
tff(fact_3188_signed__take__bit__Suc__1,axiom,
    ! [N2: nat] : aa_Cod1783974652533396728nteger(bit_ri6519982836138164636nteger(aa_nat_nat(suc,N2)),one_one_Code_integer) = one_one_Code_integer ).

% signed_take_bit_Suc_1
tff(fact_3189_signed__take__bit__Suc__1,axiom,
    ! [N2: nat] : aa_int_int(bit_ri631733984087533419it_int(aa_nat_nat(suc,N2)),one_one_int) = one_one_int ).

% signed_take_bit_Suc_1
tff(fact_3190_signed__take__bit__numeral__of__1,axiom,
    ! [K: num] : aa_Cod1783974652533396728nteger(bit_ri6519982836138164636nteger(aa_num_nat(numeral_numeral_nat,K)),one_one_Code_integer) = one_one_Code_integer ).

% signed_take_bit_numeral_of_1
tff(fact_3191_signed__take__bit__numeral__of__1,axiom,
    ! [K: num] : aa_int_int(bit_ri631733984087533419it_int(aa_num_nat(numeral_numeral_nat,K)),one_one_int) = one_one_int ).

% signed_take_bit_numeral_of_1
tff(fact_3192_round__1,axiom,
    archim7778729529865785530nd_rat(one_one_rat) = one_one_int ).

% round_1
tff(fact_3193_divmod__algorithm__code_I2_J,axiom,
    ! [M: num] : unique3479559517661332726nteger(M,one) = aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(aa_num_Code_integer(numera6620942414471956472nteger,M)),zero_z3403309356797280102nteger) ).

% divmod_algorithm_code(2)
tff(fact_3194_divmod__algorithm__code_I2_J,axiom,
    ! [M: num] : unique5052692396658037445od_int(M,one) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_num_int(numeral_numeral_int,M)),zero_zero_int) ).

% divmod_algorithm_code(2)
tff(fact_3195_divmod__algorithm__code_I2_J,axiom,
    ! [M: num] : unique5055182867167087721od_nat(M,one) = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_num_nat(numeral_numeral_nat,M)),zero_zero_nat) ).

% divmod_algorithm_code(2)
tff(fact_3196_dbl__simps_I3_J,axiom,
    aa_int_int(neg_numeral_dbl_int,one_one_int) = aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)) ).

% dbl_simps(3)
tff(fact_3197_dbl__simps_I3_J,axiom,
    aa_Cod1783974652533396728nteger(neg_nu8804712462038260780nteger,one_one_Code_integer) = aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)) ).

% dbl_simps(3)
tff(fact_3198_dbl__simps_I3_J,axiom,
    aa_rat_rat(neg_numeral_dbl_rat,one_one_rat) = aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one)) ).

% dbl_simps(3)
tff(fact_3199_divmod__algorithm__code_I3_J,axiom,
    ! [N2: num] : unique3479559517661332726nteger(one,aa_num_num(bit0,N2)) = aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(zero_z3403309356797280102nteger),aa_num_Code_integer(numera6620942414471956472nteger,one)) ).

% divmod_algorithm_code(3)
tff(fact_3200_divmod__algorithm__code_I3_J,axiom,
    ! [N2: num] : unique5052692396658037445od_int(one,aa_num_num(bit0,N2)) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,zero_zero_int),aa_num_int(numeral_numeral_int,one)) ).

% divmod_algorithm_code(3)
tff(fact_3201_divmod__algorithm__code_I3_J,axiom,
    ! [N2: num] : unique5055182867167087721od_nat(one,aa_num_num(bit0,N2)) = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,zero_zero_nat),aa_num_nat(numeral_numeral_nat,one)) ).

% divmod_algorithm_code(3)
tff(fact_3202_less__eq__integer__code_I1_J,axiom,
    aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),zero_z3403309356797280102nteger) ).

% less_eq_integer_code(1)
tff(fact_3203_sgn__integer__code,axiom,
    ! [K: code_integer] :
      aa_Cod1783974652533396728nteger(sgn_sgn_Code_integer,K) = $ite(
        K = zero_z3403309356797280102nteger,
        zero_z3403309356797280102nteger,
        $ite(aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,K),zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer),one_one_Code_integer) ) ).

% sgn_integer_code
tff(fact_3204_exhaustive__integer_H_Ocases,axiom,
    ! [X2: produc7509114972854644512nteger] :
      ~ ! [F2: fun_Co3460408610320954864e_term,D: code_integer,I2: code_integer] : X2 != produc7264323995540650962nteger(F2,aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(D),I2)) ).

% exhaustive_integer'.cases
tff(fact_3205_full__exhaustive__integer_H_Ocases,axiom,
    ! [X2: produc2453742332425399446nteger] :
      ~ ! [F2: fun_Pr5098669352780829690e_term,D: code_integer,I2: code_integer] : X2 != aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,F2),aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(D),I2)) ).

% full_exhaustive_integer'.cases
tff(fact_3206_times__integer__code_I1_J,axiom,
    ! [K: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,K),zero_z3403309356797280102nteger) = zero_z3403309356797280102nteger ).

% times_integer_code(1)
tff(fact_3207_times__integer__code_I2_J,axiom,
    ! [L: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,zero_z3403309356797280102nteger),L) = zero_z3403309356797280102nteger ).

% times_integer_code(2)
tff(fact_3208_minus__integer__code_I1_J,axiom,
    ! [K: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,K),zero_z3403309356797280102nteger) = K ).

% minus_integer_code(1)
tff(fact_3209_plus__integer__code_I2_J,axiom,
    ! [L: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,zero_z3403309356797280102nteger),L) = L ).

% plus_integer_code(2)
tff(fact_3210_plus__integer__code_I1_J,axiom,
    ! [K: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,K),zero_z3403309356797280102nteger) = K ).

% plus_integer_code(1)
tff(fact_3211_minus__integer__code_I2_J,axiom,
    ! [L: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,zero_z3403309356797280102nteger),L) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,L) ).

% minus_integer_code(2)
tff(fact_3212_divmod__integer_H__def,axiom,
    ! [M: num,N2: num] : unique3479559517661332726nteger(M,N2) = aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_num_Code_integer(numera6620942414471956472nteger,M)),aa_num_Code_integer(numera6620942414471956472nteger,N2))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,aa_num_Code_integer(numera6620942414471956472nteger,M)),aa_num_Code_integer(numera6620942414471956472nteger,N2))) ).

% divmod_integer'_def
tff(fact_3213_signed__take__bit__add,axiom,
    ! [N2: nat,K: int,L: int] : aa_int_int(bit_ri631733984087533419it_int(N2),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(bit_ri631733984087533419it_int(N2),K)),aa_int_int(bit_ri631733984087533419it_int(N2),L))) = aa_int_int(bit_ri631733984087533419it_int(N2),aa_int_int(aa_int_fun_int_int(plus_plus_int,K),L)) ).

% signed_take_bit_add
tff(fact_3214_dbl__def,axiom,
    ! [X2: rat] : aa_rat_rat(neg_numeral_dbl_rat,X2) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),X2) ).

% dbl_def
tff(fact_3215_dbl__def,axiom,
    ! [X2: int] : aa_int_int(neg_numeral_dbl_int,X2) = aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),X2) ).

% dbl_def
tff(fact_3216_divmod__int__def,axiom,
    ! [M: num,N2: num] : unique5052692396658037445od_int(M,N2) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_num_int(numeral_numeral_int,M)),aa_num_int(numeral_numeral_int,N2))),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_num_int(numeral_numeral_int,M)),aa_num_int(numeral_numeral_int,N2))) ).

% divmod_int_def
tff(fact_3217_divmod__def,axiom,
    ! [M: num,N2: num] : unique3479559517661332726nteger(M,N2) = aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_num_Code_integer(numera6620942414471956472nteger,M)),aa_num_Code_integer(numera6620942414471956472nteger,N2))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,aa_num_Code_integer(numera6620942414471956472nteger,M)),aa_num_Code_integer(numera6620942414471956472nteger,N2))) ).

% divmod_def
tff(fact_3218_divmod__def,axiom,
    ! [M: num,N2: num] : unique5052692396658037445od_int(M,N2) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_num_int(numeral_numeral_int,M)),aa_num_int(numeral_numeral_int,N2))),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_num_int(numeral_numeral_int,M)),aa_num_int(numeral_numeral_int,N2))) ).

% divmod_def
tff(fact_3219_divmod__def,axiom,
    ! [M: num,N2: num] : unique5055182867167087721od_nat(M,N2) = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_num_nat(numeral_numeral_nat,M)),aa_num_nat(numeral_numeral_nat,N2))),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_num_nat(numeral_numeral_nat,M)),aa_num_nat(numeral_numeral_nat,N2))) ).

% divmod_def
tff(fact_3220_divmod_H__nat__def,axiom,
    ! [M: num,N2: num] : unique5055182867167087721od_nat(M,N2) = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_num_nat(numeral_numeral_nat,M)),aa_num_nat(numeral_numeral_nat,N2))),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_num_nat(numeral_numeral_nat,M)),aa_num_nat(numeral_numeral_nat,N2))) ).

% divmod'_nat_def
tff(fact_3221_signed__take__bit__int__greater__eq,axiom,
    ! [K: int,N2: nat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,K),aa_int_int(uminus_uminus_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),N2)))
     => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,K),aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_nat_nat(suc,N2)))),aa_int_int(bit_ri631733984087533419it_int(N2),K)) ) ).

% signed_take_bit_int_greater_eq
tff(fact_3222_divmod__divmod__step,axiom,
    ! [M: num,N2: num] :
      unique5055182867167087721od_nat(M,N2) = $ite(aa_num_o(aa_num_fun_num_o(ord_less_num,M),N2),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,zero_zero_nat),aa_num_nat(numeral_numeral_nat,M)),aa_Pro262675715343573244at_nat(unique5026877609467782581ep_nat(N2),unique5055182867167087721od_nat(M,aa_num_num(bit0,N2)))) ).

% divmod_divmod_step
tff(fact_3223_divmod__divmod__step,axiom,
    ! [M: num,N2: num] :
      unique5052692396658037445od_int(M,N2) = $ite(aa_num_o(aa_num_fun_num_o(ord_less_num,M),N2),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,zero_zero_int),aa_num_int(numeral_numeral_int,M)),aa_Pro6970504127699319548nt_int(unique5024387138958732305ep_int(N2),unique5052692396658037445od_int(M,aa_num_num(bit0,N2)))) ).

% divmod_divmod_step
tff(fact_3224_divmod__divmod__step,axiom,
    ! [M: num,N2: num] :
      unique3479559517661332726nteger(M,N2) = $ite(aa_num_o(aa_num_fun_num_o(ord_less_num,M),N2),aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(zero_z3403309356797280102nteger),aa_num_Code_integer(numera6620942414471956472nteger,M)),aa_Pro4693618923521437820nteger(unique4921790084139445826nteger(N2),unique3479559517661332726nteger(M,aa_num_num(bit0,N2)))) ).

% divmod_divmod_step
tff(fact_3225_round__def,axiom,
    ! [X2: rat] : archim7778729529865785530nd_rat(X2) = archim3151403230148437115or_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),aa_rat_rat(divide_divide_rat(one_one_rat),aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one))))) ).

% round_def
tff(fact_3226_signed__take__bit__Suc,axiom,
    ! [N2: nat,A: code_integer] : aa_Cod1783974652533396728nteger(bit_ri6519982836138164636nteger(aa_nat_nat(suc,N2)),A) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_Cod1783974652533396728nteger(bit_ri6519982836138164636nteger(N2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)))))) ).

% signed_take_bit_Suc
tff(fact_3227_signed__take__bit__Suc,axiom,
    ! [N2: nat,A: int] : aa_int_int(bit_ri631733984087533419it_int(aa_nat_nat(suc,N2)),A) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(bit_ri631733984087533419it_int(N2),aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))))) ).

% signed_take_bit_Suc
tff(fact_3228_of__int__round__le,axiom,
    ! [X2: rat] : aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_int_rat(ring_1_of_int_rat,archim7778729529865785530nd_rat(X2))),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),aa_rat_rat(divide_divide_rat(one_one_rat),aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one))))) ).

% of_int_round_le
tff(fact_3229_of__int__round__ge,axiom,
    ! [X2: rat] : aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(minus_minus_rat(X2),aa_rat_rat(divide_divide_rat(one_one_rat),aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one))))),aa_int_rat(ring_1_of_int_rat,archim7778729529865785530nd_rat(X2))) ).

% of_int_round_ge
tff(fact_3230_of__int__round__gt,axiom,
    ! [X2: rat] : aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(minus_minus_rat(X2),aa_rat_rat(divide_divide_rat(one_one_rat),aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one))))),aa_int_rat(ring_1_of_int_rat,archim7778729529865785530nd_rat(X2))) ).

% of_int_round_gt
tff(fact_3231_integer__of__int__code,axiom,
    ! [K: int] :
      aa_int_Code_integer(code_integer_of_int,K) = $ite(
        aa_int_o(aa_int_fun_int_o(ord_less_int,K),zero_zero_int),
        aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_int_Code_integer(code_integer_of_int,aa_int_int(uminus_uminus_int,K))),
        $ite(
          K = zero_zero_int,
          zero_z3403309356797280102nteger,
          $let(
            l: code_integer,
            l:= aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_int_Code_integer(code_integer_of_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,K),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))))),
            $ite(aa_int_int(aa_int_fun_int_int(modulo_modulo_int,K),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) = zero_zero_int,l,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,l),one_one_Code_integer)) ) ) ) ).

% integer_of_int_code
tff(fact_3232_divmod__algorithm__code_I6_J,axiom,
    ! [M: num,N2: num] : unique3479559517661332726nteger(aa_num_num(bit1,M),aa_num_num(bit0,N2)) = aa_Pro4693618923521437820nteger(produc6916734918728496179nteger(aTP_Lamm_gv),unique3479559517661332726nteger(M,N2)) ).

% divmod_algorithm_code(6)
tff(fact_3233_divmod__algorithm__code_I6_J,axiom,
    ! [M: num,N2: num] : unique5052692396658037445od_int(aa_num_num(bit1,M),aa_num_num(bit0,N2)) = aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,aTP_Lamm_gw),unique5052692396658037445od_int(M,N2)) ).

% divmod_algorithm_code(6)
tff(fact_3234_divmod__algorithm__code_I6_J,axiom,
    ! [M: num,N2: num] : unique5055182867167087721od_nat(aa_num_num(bit1,M),aa_num_num(bit0,N2)) = aa_Pro262675715343573244at_nat(produc2626176000494625587at_nat(aTP_Lamm_gx),unique5055182867167087721od_nat(M,N2)) ).

% divmod_algorithm_code(6)
tff(fact_3235_of__nat__code,axiom,
    ! [N2: nat] : aa_nat_rat(semiri681578069525770553at_rat,N2) = aa_rat_rat(semiri7787848453975740701ux_rat(aTP_Lamm_gy,N2),zero_zero_rat) ).

% of_nat_code
tff(fact_3236_of__nat__code,axiom,
    ! [N2: nat] : aa_nat_int(semiri1314217659103216013at_int,N2) = aa_int_int(semiri8420488043553186161ux_int(aTP_Lamm_gz,N2),zero_zero_int) ).

% of_nat_code
tff(fact_3237_of__nat__code,axiom,
    ! [N2: nat] : aa_nat_nat(semiri1316708129612266289at_nat,N2) = aa_nat_nat(aa_nat_fun_nat_nat(semiri8422978514062236437ux_nat(aTP_Lamm_ha),N2),zero_zero_nat) ).

% of_nat_code
tff(fact_3238_of__nat__code,axiom,
    ! [N2: nat] : aa_nat_Code_integer(semiri4939895301339042750nteger,N2) = aa_Cod1783974652533396728nteger(semiri4055485073559036834nteger(aTP_Lamm_hb,N2),zero_z3403309356797280102nteger) ).

% of_nat_code
tff(fact_3239_of__nat__code,axiom,
    ! [N2: nat] : aa_nat_Code_natural(semiri3763490453095760265atural,N2) = aa_Cod4272041906116450446atural(semiri2879080225315754349atural(aTP_Lamm_hc,N2),zero_z2226904508553997617atural) ).

% of_nat_code
tff(fact_3240_signed__take__bit__Suc__minus__bit1,axiom,
    ! [N2: nat,K: num] : aa_int_int(bit_ri631733984087533419it_int(aa_nat_nat(suc,N2)),aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,aa_num_num(bit1,K)))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(bit_ri631733984087533419it_int(N2),aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,K))),one_one_int))),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),one_one_int) ).

% signed_take_bit_Suc_minus_bit1
tff(fact_3241_concat__bit__Suc,axiom,
    ! [N2: nat,K: int,L: int] : aa_int_int(aa_int_fun_int_int(bit_concat_bit(aa_nat_nat(suc,N2)),K),L) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(modulo_modulo_int,K),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(bit_concat_bit(N2),aa_int_int(aa_int_fun_int_int(divide_divide_int,K),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),L))) ).

% concat_bit_Suc
tff(fact_3242_even__succ__mod__exp,axiom,
    ! [A: int,N2: nat] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
       => ( aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),A)),aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),N2)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),N2))) ) ) ) ).

% even_succ_mod_exp
tff(fact_3243_even__succ__mod__exp,axiom,
    ! [A: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
       => ( aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),A)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2))) ) ) ) ).

% even_succ_mod_exp
tff(fact_3244_even__succ__mod__exp,axiom,
    ! [A: code_integer,N2: nat] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
       => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,one_one_Code_integer),A)),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),N2)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,one_one_Code_integer),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),N2))) ) ) ) ).

% even_succ_mod_exp
tff(fact_3245_even__succ__mod__exp,axiom,
    ! [A: code_natural,N2: nat] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
       => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,one_one_Code_natural),A)),aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),N2)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,one_one_Code_natural),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),N2))) ) ) ) ).

% even_succ_mod_exp
tff(fact_3246_even__succ__div__exp,axiom,
    ! [A: int,N2: nat] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
       => ( aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),A)),aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),N2)) = aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),N2)) ) ) ) ).

% even_succ_div_exp
tff(fact_3247_even__succ__div__exp,axiom,
    ! [A: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
       => ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),A)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)) = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)) ) ) ) ).

% even_succ_div_exp
tff(fact_3248_even__succ__div__exp,axiom,
    ! [A: code_integer,N2: nat] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
       => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,one_one_Code_integer),A)),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),N2)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),N2)) ) ) ) ).

% even_succ_div_exp
tff(fact_3249_even__succ__div__exp,axiom,
    ! [A: code_natural,N2: nat] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
       => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,one_one_Code_natural),A)),aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),N2)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),N2)) ) ) ) ).

% even_succ_div_exp
tff(fact_3250_take__bit__rec,axiom,
    ! [N2: nat,A: code_integer] :
      aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,N2),A) = $ite(N2 = zero_zero_nat,zero_z3403309356797280102nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))))),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))))) ).

% take_bit_rec
tff(fact_3251_take__bit__rec,axiom,
    ! [N2: nat,A: int] :
      aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,N2),A) = $ite(N2 = zero_zero_nat,zero_zero_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)),aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))))),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))))) ).

% take_bit_rec
tff(fact_3252_take__bit__rec,axiom,
    ! [N2: nat,A: nat] :
      aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,N2),A) = $ite(N2 = zero_zero_nat,zero_zero_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))) ).

% take_bit_rec
tff(fact_3253_take__bit__rec,axiom,
    ! [N2: nat,A: code_natural] :
      aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se569199155075624693atural,N2),A) = $ite(N2 = zero_zero_nat,zero_z2226904508553997617atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se569199155075624693atural,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))))),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one)))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))))) ).

% take_bit_rec
tff(fact_3254_nat__dvd__1__iff__1,axiom,
    ! [M: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,M),one_one_nat)
    <=> ( M = one_one_nat ) ) ).

% nat_dvd_1_iff_1
tff(fact_3255_integer__of__int__eq__of__int,axiom,
    code_integer_of_int = ring_18347121197199848620nteger ).

% integer_of_int_eq_of_int
tff(fact_3256_dvd__add__triv__right__iff,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,B),A))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),B) ) ).

% dvd_add_triv_right_iff
tff(fact_3257_dvd__add__triv__right__iff,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),A))
    <=> aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,A),B) ) ).

% dvd_add_triv_right_iff
tff(fact_3258_dvd__add__triv__right__iff,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),A))
    <=> aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),B) ) ).

% dvd_add_triv_right_iff
tff(fact_3259_dvd__add__triv__right__iff,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),A))
    <=> aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),B) ) ).

% dvd_add_triv_right_iff
tff(fact_3260_dvd__add__triv__left__iff,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),B) ) ).

% dvd_add_triv_left_iff
tff(fact_3261_dvd__add__triv__left__iff,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B))
    <=> aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,A),B) ) ).

% dvd_add_triv_left_iff
tff(fact_3262_dvd__add__triv__left__iff,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B))
    <=> aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),B) ) ).

% dvd_add_triv_left_iff
tff(fact_3263_dvd__add__triv__left__iff,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B))
    <=> aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),B) ) ).

% dvd_add_triv_left_iff
tff(fact_3264_dvd__add__times__triv__right__iff,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,B),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,C),A)))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),B) ) ).

% dvd_add_times_triv_right_iff
tff(fact_3265_dvd__add__times__triv__right__iff,axiom,
    ! [A: rat,B: rat,C: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,C),A)))
    <=> aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,A),B) ) ).

% dvd_add_times_triv_right_iff
tff(fact_3266_dvd__add__times__triv__right__iff,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,C),A)))
    <=> aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),B) ) ).

% dvd_add_times_triv_right_iff
tff(fact_3267_dvd__add__times__triv__right__iff,axiom,
    ! [A: int,B: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),aa_int_int(aa_int_fun_int_int(times_times_int,C),A)))
    <=> aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),B) ) ).

% dvd_add_times_triv_right_iff
tff(fact_3268_dvd__add__times__triv__left__iff,axiom,
    ! [A: code_integer,C: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,C),A)),B))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),B) ) ).

% dvd_add_times_triv_left_iff
tff(fact_3269_dvd__add__times__triv__left__iff,axiom,
    ! [A: rat,C: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,C),A)),B))
    <=> aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,A),B) ) ).

% dvd_add_times_triv_left_iff
tff(fact_3270_dvd__add__times__triv__left__iff,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,C),A)),B))
    <=> aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),B) ) ).

% dvd_add_times_triv_left_iff
tff(fact_3271_dvd__add__times__triv__left__iff,axiom,
    ! [A: int,C: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,C),A)),B))
    <=> aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),B) ) ).

% dvd_add_times_triv_left_iff
tff(fact_3272_unit__prod,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),one_one_Code_integer)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,B),one_one_Code_integer)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),B)),one_one_Code_integer) ) ) ).

% unit_prod
tff(fact_3273_unit__prod,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),one_one_nat)
     => ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,B),one_one_nat)
       => aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),B)),one_one_nat) ) ) ).

% unit_prod
tff(fact_3274_unit__prod,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),one_one_int)
     => ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,B),one_one_int)
       => aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),B)),one_one_int) ) ) ).

% unit_prod
tff(fact_3275_div__add,axiom,
    ! [C: int,A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,C),A)
     => ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,C),B)
       => ( aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),C) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,A),C)),aa_int_int(aa_int_fun_int_int(divide_divide_int,B),C)) ) ) ) ).

% div_add
tff(fact_3276_div__add,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,C),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,C),B)
       => ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),C) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),C)),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,B),C)) ) ) ) ).

% div_add
tff(fact_3277_div__add,axiom,
    ! [C: code_integer,A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,C),A)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,C),B)
       => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)),C) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),C)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,B),C)) ) ) ) ).

% div_add
tff(fact_3278_div__add,axiom,
    ! [C: code_natural,A: code_natural,B: code_natural] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(C),A)
     => ( aa_Code_natural_o(dvd_dvd_Code_natural(C),B)
       => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),B)),C) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),C)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,B),C)) ) ) ) ).

% div_add
tff(fact_3279_unit__div__1__div__1,axiom,
    ! [A: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),one_one_int)
     => ( aa_int_int(aa_int_fun_int_int(divide_divide_int,one_one_int),aa_int_int(aa_int_fun_int_int(divide_divide_int,one_one_int),A)) = A ) ) ).

% unit_div_1_div_1
tff(fact_3280_unit__div__1__div__1,axiom,
    ! [A: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),one_one_nat)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,one_one_nat),A)) = A ) ) ).

% unit_div_1_div_1
tff(fact_3281_unit__div__1__div__1,axiom,
    ! [A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),one_one_Code_integer)
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,one_one_Code_integer),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,one_one_Code_integer),A)) = A ) ) ).

% unit_div_1_div_1
tff(fact_3282_unit__div__1__div__1,axiom,
    ! [A: code_natural] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(A),one_one_Code_natural)
     => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,one_one_Code_natural),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,one_one_Code_natural),A)) = A ) ) ).

% unit_div_1_div_1
tff(fact_3283_unit__div__1__unit,axiom,
    ! [A: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),one_one_int)
     => aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,one_one_int),A)),one_one_int) ) ).

% unit_div_1_unit
tff(fact_3284_unit__div__1__unit,axiom,
    ! [A: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),one_one_nat)
     => aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,one_one_nat),A)),one_one_nat) ) ).

% unit_div_1_unit
tff(fact_3285_unit__div__1__unit,axiom,
    ! [A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),one_one_Code_integer)
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,one_one_Code_integer),A)),one_one_Code_integer) ) ).

% unit_div_1_unit
tff(fact_3286_unit__div__1__unit,axiom,
    ! [A: code_natural] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(A),one_one_Code_natural)
     => aa_Code_natural_o(dvd_dvd_Code_natural(aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,one_one_Code_natural),A)),one_one_Code_natural) ) ).

% unit_div_1_unit
tff(fact_3287_unit__div,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),one_one_int)
     => ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,B),one_one_int)
       => aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,A),B)),one_one_int) ) ) ).

% unit_div
tff(fact_3288_unit__div,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),one_one_nat)
     => ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,B),one_one_nat)
       => aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),B)),one_one_nat) ) ) ).

% unit_div
tff(fact_3289_unit__div,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),one_one_Code_integer)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,B),one_one_Code_integer)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),B)),one_one_Code_integer) ) ) ).

% unit_div
tff(fact_3290_unit__div,axiom,
    ! [A: code_natural,B: code_natural] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(A),one_one_Code_natural)
     => ( aa_Code_natural_o(dvd_dvd_Code_natural(B),one_one_Code_natural)
       => aa_Code_natural_o(dvd_dvd_Code_natural(aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),B)),one_one_Code_natural) ) ) ).

% unit_div
tff(fact_3291_take__bit__Suc__1,axiom,
    ! [N2: nat] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,aa_nat_nat(suc,N2)),one_one_Code_integer) = one_one_Code_integer ).

% take_bit_Suc_1
tff(fact_3292_take__bit__Suc__1,axiom,
    ! [N2: nat] : aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,aa_nat_nat(suc,N2)),one_one_int) = one_one_int ).

% take_bit_Suc_1
tff(fact_3293_take__bit__Suc__1,axiom,
    ! [N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,aa_nat_nat(suc,N2)),one_one_nat) = one_one_nat ).

% take_bit_Suc_1
tff(fact_3294_take__bit__Suc__1,axiom,
    ! [N2: nat] : aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se569199155075624693atural,aa_nat_nat(suc,N2)),one_one_Code_natural) = one_one_Code_natural ).

% take_bit_Suc_1
tff(fact_3295_take__bit__numeral__1,axiom,
    ! [L: num] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,aa_num_nat(numeral_numeral_nat,L)),one_one_Code_integer) = one_one_Code_integer ).

% take_bit_numeral_1
tff(fact_3296_take__bit__numeral__1,axiom,
    ! [L: num] : aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,aa_num_nat(numeral_numeral_nat,L)),one_one_int) = one_one_int ).

% take_bit_numeral_1
tff(fact_3297_take__bit__numeral__1,axiom,
    ! [L: num] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,aa_num_nat(numeral_numeral_nat,L)),one_one_nat) = one_one_nat ).

% take_bit_numeral_1
tff(fact_3298_take__bit__numeral__1,axiom,
    ! [L: num] : aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se569199155075624693atural,aa_num_nat(numeral_numeral_nat,L)),one_one_Code_natural) = one_one_Code_natural ).

% take_bit_numeral_1
tff(fact_3299_semiring__norm_I9_J,axiom,
    ! [M: num,N2: num] : aa_num_num(aa_num_fun_num_num(plus_plus_num,aa_num_num(bit1,M)),aa_num_num(bit0,N2)) = aa_num_num(bit1,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2)) ).

% semiring_norm(9)
tff(fact_3300_semiring__norm_I7_J,axiom,
    ! [M: num,N2: num] : aa_num_num(aa_num_fun_num_num(plus_plus_num,aa_num_num(bit0,M)),aa_num_num(bit1,N2)) = aa_num_num(bit1,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2)) ).

% semiring_norm(7)
tff(fact_3301_semiring__norm_I16_J,axiom,
    ! [M: num,N2: num] : aa_num_num(aa_num_fun_num_num(times_times_num,aa_num_num(bit1,M)),aa_num_num(bit1,N2)) = aa_num_num(bit1,aa_num_num(aa_num_fun_num_num(plus_plus_num,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2)),aa_num_num(bit0,aa_num_num(aa_num_fun_num_num(times_times_num,M),N2)))) ).

% semiring_norm(16)
tff(fact_3302_unit__mult__div__div,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),one_one_int)
     => ( aa_int_int(aa_int_fun_int_int(times_times_int,B),aa_int_int(aa_int_fun_int_int(divide_divide_int,one_one_int),A)) = aa_int_int(aa_int_fun_int_int(divide_divide_int,B),A) ) ) ).

% unit_mult_div_div
tff(fact_3303_unit__mult__div__div,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),one_one_nat)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,one_one_nat),A)) = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,B),A) ) ) ).

% unit_mult_div_div
tff(fact_3304_unit__mult__div__div,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),one_one_Code_integer)
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,B),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,one_one_Code_integer),A)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,B),A) ) ) ).

% unit_mult_div_div
tff(fact_3305_unit__mult__div__div,axiom,
    ! [A: code_natural,B: code_natural] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(A),one_one_Code_natural)
     => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,B),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,one_one_Code_natural),A)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,B),A) ) ) ).

% unit_mult_div_div
tff(fact_3306_unit__div__mult__self,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),one_one_int)
     => ( aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,B),A)),A) = B ) ) ).

% unit_div_mult_self
tff(fact_3307_unit__div__mult__self,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),one_one_nat)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,B),A)),A) = B ) ) ).

% unit_div_mult_self
tff(fact_3308_unit__div__mult__self,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),one_one_Code_integer)
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,B),A)),A) = B ) ) ).

% unit_div_mult_self
tff(fact_3309_unit__div__mult__self,axiom,
    ! [A: code_natural,B: code_natural] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(A),one_one_Code_natural)
     => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,B),A)),A) = B ) ) ).

% unit_div_mult_self
tff(fact_3310_take__bit__of__1__eq__0__iff,axiom,
    ! [N2: nat] :
      ( ( aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,N2),one_one_Code_integer) = zero_z3403309356797280102nteger )
    <=> ( N2 = zero_zero_nat ) ) ).

% take_bit_of_1_eq_0_iff
tff(fact_3311_take__bit__of__1__eq__0__iff,axiom,
    ! [N2: nat] :
      ( ( aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,N2),one_one_int) = zero_zero_int )
    <=> ( N2 = zero_zero_nat ) ) ).

% take_bit_of_1_eq_0_iff
tff(fact_3312_take__bit__of__1__eq__0__iff,axiom,
    ! [N2: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,N2),one_one_nat) = zero_zero_nat )
    <=> ( N2 = zero_zero_nat ) ) ).

% take_bit_of_1_eq_0_iff
tff(fact_3313_take__bit__of__1__eq__0__iff,axiom,
    ! [N2: nat] :
      ( ( aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se569199155075624693atural,N2),one_one_Code_natural) = zero_z2226904508553997617atural )
    <=> ( N2 = zero_zero_nat ) ) ).

% take_bit_of_1_eq_0_iff
tff(fact_3314_semiring__norm_I10_J,axiom,
    ! [M: num,N2: num] : aa_num_num(aa_num_fun_num_num(plus_plus_num,aa_num_num(bit1,M)),aa_num_num(bit1,N2)) = aa_num_num(bit0,aa_num_num(aa_num_fun_num_num(plus_plus_num,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2)),one)) ).

% semiring_norm(10)
tff(fact_3315_semiring__norm_I8_J,axiom,
    ! [M: num] : aa_num_num(aa_num_fun_num_num(plus_plus_num,aa_num_num(bit1,M)),one) = aa_num_num(bit0,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),one)) ).

% semiring_norm(8)
tff(fact_3316_semiring__norm_I5_J,axiom,
    ! [M: num] : aa_num_num(aa_num_fun_num_num(plus_plus_num,aa_num_num(bit0,M)),one) = aa_num_num(bit1,M) ).

% semiring_norm(5)
tff(fact_3317_semiring__norm_I4_J,axiom,
    ! [N2: num] : aa_num_num(aa_num_fun_num_num(plus_plus_num,one),aa_num_num(bit1,N2)) = aa_num_num(bit0,aa_num_num(aa_num_fun_num_num(plus_plus_num,N2),one)) ).

% semiring_norm(4)
tff(fact_3318_semiring__norm_I3_J,axiom,
    ! [N2: num] : aa_num_num(aa_num_fun_num_num(plus_plus_num,one),aa_num_num(bit0,N2)) = aa_num_num(bit1,N2) ).

% semiring_norm(3)
tff(fact_3319_odd__add,axiom,
    ! [A: nat,B: nat] :
      ( ~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B))
    <=> ~ ( ~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A)
        <=> ~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),B) ) ) ).

% odd_add
tff(fact_3320_odd__add,axiom,
    ! [A: int,B: int] :
      ( ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B))
    <=> ~ ( ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A)
        <=> ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),B) ) ) ).

% odd_add
tff(fact_3321_odd__add,axiom,
    ! [A: code_integer,B: code_integer] :
      ( ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B))
    <=> ~ ( ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A)
        <=> ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),B) ) ) ).

% odd_add
tff(fact_3322_odd__add,axiom,
    ! [A: code_natural,B: code_natural] :
      ( ~ aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),B))
    <=> ~ ( ~ aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A)
        <=> ~ aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),B) ) ) ).

% odd_add
tff(fact_3323_even__add,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B))
    <=> ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A)
      <=> aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),B) ) ) ).

% even_add
tff(fact_3324_even__add,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B))
    <=> ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A)
      <=> aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),B) ) ) ).

% even_add
tff(fact_3325_even__add,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B))
    <=> ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A)
      <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),B) ) ) ).

% even_add
tff(fact_3326_even__add,axiom,
    ! [A: code_natural,B: code_natural] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),B))
    <=> ( aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A)
      <=> aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),B) ) ) ).

% even_add
tff(fact_3327_dbl__inc__simps_I3_J,axiom,
    aa_int_int(neg_nu5851722552734809277nc_int,one_one_int) = aa_num_int(numeral_numeral_int,aa_num_num(bit1,one)) ).

% dbl_inc_simps(3)
tff(fact_3328_dbl__inc__simps_I3_J,axiom,
    aa_Cod1783974652533396728nteger(neg_nu5831290666863070958nteger,one_one_Code_integer) = aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit1,one)) ).

% dbl_inc_simps(3)
tff(fact_3329_dbl__inc__simps_I3_J,axiom,
    aa_rat_rat(neg_nu5219082963157363817nc_rat,one_one_rat) = aa_num_rat(numeral_numeral_rat,aa_num_num(bit1,one)) ).

% dbl_inc_simps(3)
tff(fact_3330_even__plus__one__iff,axiom,
    ! [A: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),one_one_nat))
    <=> ~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A) ) ).

% even_plus_one_iff
tff(fact_3331_even__plus__one__iff,axiom,
    ! [A: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),one_one_int))
    <=> ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A) ) ).

% even_plus_one_iff
tff(fact_3332_even__plus__one__iff,axiom,
    ! [A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),one_one_Code_integer))
    <=> ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A) ) ).

% even_plus_one_iff
tff(fact_3333_even__plus__one__iff,axiom,
    ! [A: code_natural] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),one_one_Code_natural))
    <=> ~ aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A) ) ).

% even_plus_one_iff
tff(fact_3334_even__diff,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B))
    <=> aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)) ) ).

% even_diff
tff(fact_3335_even__diff,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)) ) ).

% even_diff
tff(fact_3336_neg__one__even__power,axiom,
    ! [N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)
     => ( aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(uminus_uminus_int,one_one_int)),N2) = one_one_int ) ) ).

% neg_one_even_power
tff(fact_3337_neg__one__even__power,axiom,
    ! [N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)
     => ( aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),N2) = one_one_Code_integer ) ) ).

% neg_one_even_power
tff(fact_3338_neg__one__even__power,axiom,
    ! [N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)
     => ( aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),N2) = one_one_rat ) ) ).

% neg_one_even_power
tff(fact_3339_neg__one__odd__power,axiom,
    ! [N2: nat] :
      ( ~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)
     => ( aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(uminus_uminus_int,one_one_int)),N2) = aa_int_int(uminus_uminus_int,one_one_int) ) ) ).

% neg_one_odd_power
tff(fact_3340_neg__one__odd__power,axiom,
    ! [N2: nat] :
      ( ~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)
     => ( aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),N2) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) ) ) ).

% neg_one_odd_power
tff(fact_3341_neg__one__odd__power,axiom,
    ! [N2: nat] :
      ( ~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)
     => ( aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),N2) = aa_rat_rat(uminus_uminus_rat,one_one_rat) ) ) ).

% neg_one_odd_power
tff(fact_3342_even__diff__nat,axiom,
    ! [M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),N2))
    <=> ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M),N2)
        | aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)) ) ) ).

% even_diff_nat
tff(fact_3343_divmod__algorithm__code_I4_J,axiom,
    ! [N2: num] : unique3479559517661332726nteger(one,aa_num_num(bit1,N2)) = aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(zero_z3403309356797280102nteger),aa_num_Code_integer(numera6620942414471956472nteger,one)) ).

% divmod_algorithm_code(4)
tff(fact_3344_divmod__algorithm__code_I4_J,axiom,
    ! [N2: num] : unique5052692396658037445od_int(one,aa_num_num(bit1,N2)) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,zero_zero_int),aa_num_int(numeral_numeral_int,one)) ).

% divmod_algorithm_code(4)
tff(fact_3345_divmod__algorithm__code_I4_J,axiom,
    ! [N2: num] : unique5055182867167087721od_nat(one,aa_num_num(bit1,N2)) = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,zero_zero_nat),aa_num_nat(numeral_numeral_nat,one)) ).

% divmod_algorithm_code(4)
tff(fact_3346_mod__Suc__eq__mod__add3,axiom,
    ! [M: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,M),aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(suc,N2)))) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,one))),N2)) ).

% mod_Suc_eq_mod_add3
tff(fact_3347_Suc__mod__eq__add3__mod__numeral,axiom,
    ! [M: nat,V: num] : aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(suc,M)))),aa_num_nat(numeral_numeral_nat,V)) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,one))),M)),aa_num_nat(numeral_numeral_nat,V)) ).

% Suc_mod_eq_add3_mod_numeral
tff(fact_3348_div__Suc__eq__div__add3,axiom,
    ! [M: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,M),aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(suc,N2)))) = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,one))),N2)) ).

% div_Suc_eq_div_add3
tff(fact_3349_Suc__div__eq__add3__div__numeral,axiom,
    ! [M: nat,V: num] : aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(suc,M)))),aa_num_nat(numeral_numeral_nat,V)) = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,one))),M)),aa_num_nat(numeral_numeral_nat,V)) ).

% Suc_div_eq_add3_div_numeral
tff(fact_3350_dbl__dec__simps_I4_J,axiom,
    aa_int_int(neg_nu3811975205180677377ec_int,aa_int_int(uminus_uminus_int,one_one_int)) = aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,aa_num_num(bit1,one))) ).

% dbl_dec_simps(4)
tff(fact_3351_dbl__dec__simps_I4_J,axiom,
    aa_Cod1783974652533396728nteger(neg_nu7757733837767384882nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit1,one))) ).

% dbl_dec_simps(4)
tff(fact_3352_dbl__dec__simps_I4_J,axiom,
    aa_rat_rat(neg_nu3179335615603231917ec_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)) = aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(bit1,one))) ).

% dbl_dec_simps(4)
tff(fact_3353_even__succ__div__2,axiom,
    ! [A: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A)
     => ( aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),A)),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) = aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) ) ) ).

% even_succ_div_2
tff(fact_3354_even__succ__div__2,axiom,
    ! [A: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),A)),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) ) ) ).

% even_succ_div_2
tff(fact_3355_even__succ__div__2,axiom,
    ! [A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A)
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,one_one_Code_integer),A)),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) ) ) ).

% even_succ_div_2
tff(fact_3356_even__succ__div__2,axiom,
    ! [A: code_natural] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A)
     => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,one_one_Code_natural),A)),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))) ) ) ).

% even_succ_div_2
tff(fact_3357_odd__succ__div__two,axiom,
    ! [A: int] :
      ( ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A)
     => ( aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),one_one_int)),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),one_one_int) ) ) ).

% odd_succ_div_two
tff(fact_3358_odd__succ__div__two,axiom,
    ! [A: nat] :
      ( ~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),one_one_nat)),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),one_one_nat) ) ) ).

% odd_succ_div_two
tff(fact_3359_odd__succ__div__two,axiom,
    ! [A: code_integer] :
      ( ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A)
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),one_one_Code_integer)),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)))),one_one_Code_integer) ) ) ).

% odd_succ_div_two
tff(fact_3360_odd__succ__div__two,axiom,
    ! [A: code_natural] :
      ( ~ aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A)
     => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),one_one_Code_natural)),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one)))),one_one_Code_natural) ) ) ).

% odd_succ_div_two
tff(fact_3361_even__succ__div__two,axiom,
    ! [A: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A)
     => ( aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),one_one_int)),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) = aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) ) ) ).

% even_succ_div_two
tff(fact_3362_even__succ__div__two,axiom,
    ! [A: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),one_one_nat)),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) ) ) ).

% even_succ_div_two
tff(fact_3363_even__succ__div__two,axiom,
    ! [A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A)
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),one_one_Code_integer)),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) ) ) ).

% even_succ_div_two
tff(fact_3364_even__succ__div__two,axiom,
    ! [A: code_natural] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A)
     => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),one_one_Code_natural)),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))) ) ) ).

% even_succ_div_two
tff(fact_3365_odd__two__times__div__two__nat,axiom,
    ! [N2: nat] :
      ( ~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,N2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat) ) ) ).

% odd_two_times_div_two_nat
tff(fact_3366_odd__two__times__div__two__succ,axiom,
    ! [A: int] :
      ( ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A)
     => ( aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))))),one_one_int) = A ) ) ).

% odd_two_times_div_two_succ
tff(fact_3367_odd__two__times__div__two__succ,axiom,
    ! [A: nat] :
      ( ~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),one_one_nat) = A ) ) ).

% odd_two_times_div_two_succ
tff(fact_3368_odd__two__times__div__two__succ,axiom,
    ! [A: code_integer] :
      ( ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A)
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))))),one_one_Code_integer) = A ) ) ).

% odd_two_times_div_two_succ
tff(fact_3369_odd__two__times__div__two__succ,axiom,
    ! [A: code_natural] :
      ( ~ aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A)
     => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))))),one_one_Code_natural) = A ) ) ).

% odd_two_times_div_two_succ
tff(fact_3370_semiring__parity__class_Oeven__mask__iff,axiom,
    ! [N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)),one_one_nat))
    <=> ( N2 = zero_zero_nat ) ) ).

% semiring_parity_class.even_mask_iff
tff(fact_3371_semiring__parity__class_Oeven__mask__iff,axiom,
    ! [N2: nat] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),N2)),one_one_int))
    <=> ( N2 = zero_zero_nat ) ) ).

% semiring_parity_class.even_mask_iff
tff(fact_3372_semiring__parity__class_Oeven__mask__iff,axiom,
    ! [N2: nat] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),N2)),one_one_Code_integer))
    <=> ( N2 = zero_zero_nat ) ) ).

% semiring_parity_class.even_mask_iff
tff(fact_3373_semiring__parity__class_Oeven__mask__iff,axiom,
    ! [N2: nat] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(minus_7197305767214868737atural,aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),N2)),one_one_Code_natural))
    <=> ( N2 = zero_zero_nat ) ) ).

% semiring_parity_class.even_mask_iff
tff(fact_3374_zmod__numeral__Bit1,axiom,
    ! [V: num,W: num] : aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_num_int(numeral_numeral_int,aa_num_num(bit1,V))),aa_num_int(numeral_numeral_int,aa_num_num(bit0,W))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_num_int(numeral_numeral_int,V)),aa_num_int(numeral_numeral_int,W)))),one_one_int) ).

% zmod_numeral_Bit1
tff(fact_3375_divmod__algorithm__code_I8_J,axiom,
    ! [M: num,N2: num] :
      unique5055182867167087721od_nat(aa_num_num(bit1,M),aa_num_num(bit1,N2)) = $ite(aa_num_o(aa_num_fun_num_o(ord_less_num,M),N2),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,zero_zero_nat),aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,M))),aa_Pro262675715343573244at_nat(unique5026877609467782581ep_nat(aa_num_num(bit1,N2)),unique5055182867167087721od_nat(aa_num_num(bit1,M),aa_num_num(bit0,aa_num_num(bit1,N2))))) ).

% divmod_algorithm_code(8)
tff(fact_3376_divmod__algorithm__code_I8_J,axiom,
    ! [M: num,N2: num] :
      unique5052692396658037445od_int(aa_num_num(bit1,M),aa_num_num(bit1,N2)) = $ite(aa_num_o(aa_num_fun_num_o(ord_less_num,M),N2),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,zero_zero_int),aa_num_int(numeral_numeral_int,aa_num_num(bit1,M))),aa_Pro6970504127699319548nt_int(unique5024387138958732305ep_int(aa_num_num(bit1,N2)),unique5052692396658037445od_int(aa_num_num(bit1,M),aa_num_num(bit0,aa_num_num(bit1,N2))))) ).

% divmod_algorithm_code(8)
tff(fact_3377_divmod__algorithm__code_I8_J,axiom,
    ! [M: num,N2: num] :
      unique3479559517661332726nteger(aa_num_num(bit1,M),aa_num_num(bit1,N2)) = $ite(aa_num_o(aa_num_fun_num_o(ord_less_num,M),N2),aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(zero_z3403309356797280102nteger),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit1,M))),aa_Pro4693618923521437820nteger(unique4921790084139445826nteger(aa_num_num(bit1,N2)),unique3479559517661332726nteger(aa_num_num(bit1,M),aa_num_num(bit0,aa_num_num(bit1,N2))))) ).

% divmod_algorithm_code(8)
tff(fact_3378_divmod__algorithm__code_I7_J,axiom,
    ! [M: num,N2: num] :
      unique5055182867167087721od_nat(aa_num_num(bit0,M),aa_num_num(bit1,N2)) = $ite(aa_num_o(aa_num_fun_num_o(ord_less_eq_num,M),N2),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,zero_zero_nat),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,M))),aa_Pro262675715343573244at_nat(unique5026877609467782581ep_nat(aa_num_num(bit1,N2)),unique5055182867167087721od_nat(aa_num_num(bit0,M),aa_num_num(bit0,aa_num_num(bit1,N2))))) ).

% divmod_algorithm_code(7)
tff(fact_3379_divmod__algorithm__code_I7_J,axiom,
    ! [M: num,N2: num] :
      unique5052692396658037445od_int(aa_num_num(bit0,M),aa_num_num(bit1,N2)) = $ite(aa_num_o(aa_num_fun_num_o(ord_less_eq_num,M),N2),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,zero_zero_int),aa_num_int(numeral_numeral_int,aa_num_num(bit0,M))),aa_Pro6970504127699319548nt_int(unique5024387138958732305ep_int(aa_num_num(bit1,N2)),unique5052692396658037445od_int(aa_num_num(bit0,M),aa_num_num(bit0,aa_num_num(bit1,N2))))) ).

% divmod_algorithm_code(7)
tff(fact_3380_divmod__algorithm__code_I7_J,axiom,
    ! [M: num,N2: num] :
      unique3479559517661332726nteger(aa_num_num(bit0,M),aa_num_num(bit1,N2)) = $ite(aa_num_o(aa_num_fun_num_o(ord_less_eq_num,M),N2),aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(zero_z3403309356797280102nteger),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,M))),aa_Pro4693618923521437820nteger(unique4921790084139445826nteger(aa_num_num(bit1,N2)),unique3479559517661332726nteger(aa_num_num(bit0,M),aa_num_num(bit0,aa_num_num(bit1,N2))))) ).

% divmod_algorithm_code(7)
tff(fact_3381_signed__take__bit__Suc__bit1,axiom,
    ! [N2: nat,K: num] : aa_int_int(bit_ri631733984087533419it_int(aa_nat_nat(suc,N2)),aa_num_int(numeral_numeral_int,aa_num_num(bit1,K))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(bit_ri631733984087533419it_int(N2),aa_num_int(numeral_numeral_int,K))),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),one_one_int) ).

% signed_take_bit_Suc_bit1
tff(fact_3382_uminus__integer__code_I1_J,axiom,
    aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,zero_z3403309356797280102nteger) = zero_z3403309356797280102nteger ).

% uminus_integer_code(1)
tff(fact_3383_take__bit__integer_Oabs__eq,axiom,
    ! [Xa: nat,X2: int] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,Xa),aa_int_Code_integer(code_integer_of_int,X2)) = aa_int_Code_integer(code_integer_of_int,aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,Xa),X2)) ).

% take_bit_integer.abs_eq
tff(fact_3384_abs__integer__code,axiom,
    ! [K: code_integer] :
      aa_Cod1783974652533396728nteger(abs_abs_Code_integer,K) = $ite(aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,K),zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,K),K) ).

% abs_integer_code
tff(fact_3385_less__integer__code_I1_J,axiom,
    ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),zero_z3403309356797280102nteger) ).

% less_integer_code(1)
tff(fact_3386_unset__bit__integer_Oabs__eq,axiom,
    ! [Xa: nat,X2: int] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se8260200283734997820nteger,Xa),aa_int_Code_integer(code_integer_of_int,X2)) = aa_int_Code_integer(code_integer_of_int,aa_int_int(aa_nat_fun_int_int(bit_se4203085406695923979it_int,Xa),X2)) ).

% unset_bit_integer.abs_eq
tff(fact_3387_flip__bit__integer_Oabs__eq,axiom,
    ! [Xa: nat,X2: int] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1345352211410354436nteger,Xa),aa_int_Code_integer(code_integer_of_int,X2)) = aa_int_Code_integer(code_integer_of_int,aa_int_int(aa_nat_fun_int_int(bit_se2159334234014336723it_int,Xa),X2)) ).

% flip_bit_integer.abs_eq
tff(fact_3388_set__bit__integer_Oabs__eq,axiom,
    ! [Xa: nat,X2: int] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se2793503036327961859nteger,Xa),aa_int_Code_integer(code_integer_of_int,X2)) = aa_int_Code_integer(code_integer_of_int,aa_int_int(aa_nat_fun_int_int(bit_se7879613467334960850it_int,Xa),X2)) ).

% set_bit_integer.abs_eq
tff(fact_3389_take__bit__add,axiom,
    ! [N2: nat,A: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,N2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,N2),A)),aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,N2),B))) = aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,N2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)) ).

% take_bit_add
tff(fact_3390_take__bit__add,axiom,
    ! [N2: nat,A: int,B: int] : aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,N2),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,N2),A)),aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,N2),B))) = aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,N2),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)) ).

% take_bit_add
tff(fact_3391_take__bit__add,axiom,
    ! [N2: nat,A: nat,B: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,N2),A)),aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,N2),B))) = aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)) ).

% take_bit_add
tff(fact_3392_take__bit__add,axiom,
    ! [N2: nat,A: code_natural,B: code_natural] : aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se569199155075624693atural,N2),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se569199155075624693atural,N2),A)),aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se569199155075624693atural,N2),B))) = aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se569199155075624693atural,N2),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),B)) ).

% take_bit_add
tff(fact_3393_zero__integer__def,axiom,
    zero_z3403309356797280102nteger = aa_int_Code_integer(code_integer_of_int,zero_zero_int) ).

% zero_integer_def
tff(fact_3394_less__integer_Oabs__eq,axiom,
    ! [Xa: int,X2: int] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_int_Code_integer(code_integer_of_int,Xa)),aa_int_Code_integer(code_integer_of_int,X2))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,Xa),X2) ) ).

% less_integer.abs_eq
tff(fact_3395_uminus__integer_Oabs__eq,axiom,
    ! [X2: int] : aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_int_Code_integer(code_integer_of_int,X2)) = aa_int_Code_integer(code_integer_of_int,aa_int_int(uminus_uminus_int,X2)) ).

% uminus_integer.abs_eq
tff(fact_3396_abs__integer_Oabs__eq,axiom,
    ! [X2: int] : aa_Cod1783974652533396728nteger(abs_abs_Code_integer,aa_int_Code_integer(code_integer_of_int,X2)) = aa_int_Code_integer(code_integer_of_int,aa_int_int(abs_abs_int,X2)) ).

% abs_integer.abs_eq
tff(fact_3397_dvd__add__right__iff,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),B)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,B),C))
      <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),C) ) ) ).

% dvd_add_right_iff
tff(fact_3398_dvd__add__right__iff,axiom,
    ! [A: rat,B: rat,C: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,A),B)
     => ( aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),C))
      <=> aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,A),C) ) ) ).

% dvd_add_right_iff
tff(fact_3399_dvd__add__right__iff,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),B)
     => ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),C))
      <=> aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),C) ) ) ).

% dvd_add_right_iff
tff(fact_3400_dvd__add__right__iff,axiom,
    ! [A: int,B: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),B)
     => ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),C))
      <=> aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),C) ) ) ).

% dvd_add_right_iff
tff(fact_3401_dvd__add__left__iff,axiom,
    ! [A: code_integer,C: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),C)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,B),C))
      <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),B) ) ) ).

% dvd_add_left_iff
tff(fact_3402_dvd__add__left__iff,axiom,
    ! [A: rat,C: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,A),C)
     => ( aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),C))
      <=> aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,A),B) ) ) ).

% dvd_add_left_iff
tff(fact_3403_dvd__add__left__iff,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),C)
     => ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),C))
      <=> aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),B) ) ) ).

% dvd_add_left_iff
tff(fact_3404_dvd__add__left__iff,axiom,
    ! [A: int,C: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),C)
     => ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),C))
      <=> aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),B) ) ) ).

% dvd_add_left_iff
tff(fact_3405_dvd__add,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),B)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),C)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,B),C)) ) ) ).

% dvd_add
tff(fact_3406_dvd__add,axiom,
    ! [A: rat,B: rat,C: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,A),B)
     => ( aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,A),C)
       => aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,A),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,B),C)) ) ) ).

% dvd_add
tff(fact_3407_dvd__add,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),B)
     => ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),C)
       => aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),C)) ) ) ).

% dvd_add
tff(fact_3408_dvd__add,axiom,
    ! [A: int,B: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),B)
     => ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),C)
       => aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,B),C)) ) ) ).

% dvd_add
tff(fact_3409_divide__integer_Oabs__eq,axiom,
    ! [Xa: int,X2: int] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_int_Code_integer(code_integer_of_int,Xa)),aa_int_Code_integer(code_integer_of_int,X2)) = aa_int_Code_integer(code_integer_of_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,Xa),X2)) ).

% divide_integer.abs_eq
tff(fact_3410_dvd__unit__imp__unit,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),B)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,B),one_one_Code_integer)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),one_one_Code_integer) ) ) ).

% dvd_unit_imp_unit
tff(fact_3411_dvd__unit__imp__unit,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),B)
     => ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,B),one_one_nat)
       => aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),one_one_nat) ) ) ).

% dvd_unit_imp_unit
tff(fact_3412_dvd__unit__imp__unit,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),B)
     => ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,B),one_one_int)
       => aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),one_one_int) ) ) ).

% dvd_unit_imp_unit
tff(fact_3413_unit__imp__dvd,axiom,
    ! [B: code_integer,A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,B),one_one_Code_integer)
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,B),A) ) ).

% unit_imp_dvd
tff(fact_3414_unit__imp__dvd,axiom,
    ! [B: nat,A: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,B),one_one_nat)
     => aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,B),A) ) ).

% unit_imp_dvd
tff(fact_3415_unit__imp__dvd,axiom,
    ! [B: int,A: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,B),one_one_int)
     => aa_int_o(aa_int_fun_int_o(dvd_dvd_int,B),A) ) ).

% unit_imp_dvd
tff(fact_3416_one__dvd,axiom,
    ! [A: code_integer] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,one_one_Code_integer),A) ).

% one_dvd
tff(fact_3417_one__dvd,axiom,
    ! [A: assn] : aa_assn_o(aa_assn_fun_assn_o(dvd_dvd_assn,one_one_assn),A) ).

% one_dvd
tff(fact_3418_one__dvd,axiom,
    ! [A: rat] : aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,one_one_rat),A) ).

% one_dvd
tff(fact_3419_one__dvd,axiom,
    ! [A: nat] : aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,one_one_nat),A) ).

% one_dvd
tff(fact_3420_one__dvd,axiom,
    ! [A: int] : aa_int_o(aa_int_fun_int_o(dvd_dvd_int,one_one_int),A) ).

% one_dvd
tff(fact_3421_modulo__integer_Oabs__eq,axiom,
    ! [Xa: int,X2: int] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,aa_int_Code_integer(code_integer_of_int,Xa)),aa_int_Code_integer(code_integer_of_int,X2)) = aa_int_Code_integer(code_integer_of_int,aa_int_int(aa_int_fun_int_int(modulo_modulo_int,Xa),X2)) ).

% modulo_integer.abs_eq
tff(fact_3422_sgn__integer_Oabs__eq,axiom,
    ! [X2: int] : aa_Cod1783974652533396728nteger(sgn_sgn_Code_integer,aa_int_Code_integer(code_integer_of_int,X2)) = aa_int_Code_integer(code_integer_of_int,aa_int_int(sgn_sgn_int,X2)) ).

% sgn_integer.abs_eq
tff(fact_3423_concat__bit__assoc,axiom,
    ! [N2: nat,K: int,M: nat,L: int,R2: int] : aa_int_int(aa_int_fun_int_int(bit_concat_bit(N2),K),aa_int_int(aa_int_fun_int_int(bit_concat_bit(M),L),R2)) = aa_int_int(aa_int_fun_int_int(bit_concat_bit(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)),aa_int_int(aa_int_fun_int_int(bit_concat_bit(N2),K),L)),R2) ).

% concat_bit_assoc
tff(fact_3424_not__is__unit__0,axiom,
    ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,zero_z3403309356797280102nteger),one_one_Code_integer) ).

% not_is_unit_0
tff(fact_3425_not__is__unit__0,axiom,
    ~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,zero_zero_nat),one_one_nat) ).

% not_is_unit_0
tff(fact_3426_not__is__unit__0,axiom,
    ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,zero_zero_int),one_one_int) ).

% not_is_unit_0
tff(fact_3427_pinf_I9_J,axiom,
    ! [D2: code_integer,S: code_integer] :
    ? [Z2: code_integer] :
    ! [X: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,Z2),X)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,D2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X),S))
      <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,D2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X),S)) ) ) ).

% pinf(9)
tff(fact_3428_pinf_I9_J,axiom,
    ! [D2: rat,S: rat] :
    ? [Z2: rat] :
    ! [X: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,Z2),X)
     => ( aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,D2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X),S))
      <=> aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,D2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X),S)) ) ) ).

% pinf(9)
tff(fact_3429_pinf_I9_J,axiom,
    ! [D2: nat,S: nat] :
    ? [Z2: nat] :
    ! [X: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,Z2),X)
     => ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,D2),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X),S))
      <=> aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,D2),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X),S)) ) ) ).

% pinf(9)
tff(fact_3430_pinf_I9_J,axiom,
    ! [D2: int,S: int] :
    ? [Z2: int] :
    ! [X: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,Z2),X)
     => ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,D2),aa_int_int(aa_int_fun_int_int(plus_plus_int,X),S))
      <=> aa_int_o(aa_int_fun_int_o(dvd_dvd_int,D2),aa_int_int(aa_int_fun_int_int(plus_plus_int,X),S)) ) ) ).

% pinf(9)
tff(fact_3431_pinf_I10_J,axiom,
    ! [D2: code_integer,S: code_integer] :
    ? [Z2: code_integer] :
    ! [X: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,Z2),X)
     => ( ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,D2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X),S))
      <=> ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,D2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X),S)) ) ) ).

% pinf(10)
tff(fact_3432_pinf_I10_J,axiom,
    ! [D2: rat,S: rat] :
    ? [Z2: rat] :
    ! [X: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,Z2),X)
     => ( ~ aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,D2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X),S))
      <=> ~ aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,D2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X),S)) ) ) ).

% pinf(10)
tff(fact_3433_pinf_I10_J,axiom,
    ! [D2: nat,S: nat] :
    ? [Z2: nat] :
    ! [X: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,Z2),X)
     => ( ~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,D2),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X),S))
      <=> ~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,D2),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X),S)) ) ) ).

% pinf(10)
tff(fact_3434_pinf_I10_J,axiom,
    ! [D2: int,S: int] :
    ? [Z2: int] :
    ! [X: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,Z2),X)
     => ( ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,D2),aa_int_int(aa_int_fun_int_int(plus_plus_int,X),S))
      <=> ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,D2),aa_int_int(aa_int_fun_int_int(plus_plus_int,X),S)) ) ) ).

% pinf(10)
tff(fact_3435_minf_I9_J,axiom,
    ! [D2: code_integer,S: code_integer] :
    ? [Z2: code_integer] :
    ! [X: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,X),Z2)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,D2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X),S))
      <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,D2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X),S)) ) ) ).

% minf(9)
tff(fact_3436_minf_I9_J,axiom,
    ! [D2: rat,S: rat] :
    ? [Z2: rat] :
    ! [X: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,X),Z2)
     => ( aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,D2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X),S))
      <=> aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,D2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X),S)) ) ) ).

% minf(9)
tff(fact_3437_minf_I9_J,axiom,
    ! [D2: nat,S: nat] :
    ? [Z2: nat] :
    ! [X: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,X),Z2)
     => ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,D2),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X),S))
      <=> aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,D2),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X),S)) ) ) ).

% minf(9)
tff(fact_3438_minf_I9_J,axiom,
    ! [D2: int,S: int] :
    ? [Z2: int] :
    ! [X: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,X),Z2)
     => ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,D2),aa_int_int(aa_int_fun_int_int(plus_plus_int,X),S))
      <=> aa_int_o(aa_int_fun_int_o(dvd_dvd_int,D2),aa_int_int(aa_int_fun_int_int(plus_plus_int,X),S)) ) ) ).

% minf(9)
tff(fact_3439_minf_I10_J,axiom,
    ! [D2: code_integer,S: code_integer] :
    ? [Z2: code_integer] :
    ! [X: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,X),Z2)
     => ( ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,D2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X),S))
      <=> ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,D2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X),S)) ) ) ).

% minf(10)
tff(fact_3440_minf_I10_J,axiom,
    ! [D2: rat,S: rat] :
    ? [Z2: rat] :
    ! [X: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,X),Z2)
     => ( ~ aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,D2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X),S))
      <=> ~ aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,D2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X),S)) ) ) ).

% minf(10)
tff(fact_3441_minf_I10_J,axiom,
    ! [D2: nat,S: nat] :
    ? [Z2: nat] :
    ! [X: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,X),Z2)
     => ( ~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,D2),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X),S))
      <=> ~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,D2),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X),S)) ) ) ).

% minf(10)
tff(fact_3442_minf_I10_J,axiom,
    ! [D2: int,S: int] :
    ? [Z2: int] :
    ! [X: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,X),Z2)
     => ( ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,D2),aa_int_int(aa_int_fun_int_int(plus_plus_int,X),S))
      <=> ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,D2),aa_int_int(aa_int_fun_int_int(plus_plus_int,X),S)) ) ) ).

% minf(10)
tff(fact_3443_unit__mult__right__cancel,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),one_one_Code_integer)
     => ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,B),A) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,C),A) )
      <=> ( B = C ) ) ) ).

% unit_mult_right_cancel
tff(fact_3444_unit__mult__right__cancel,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),one_one_nat)
     => ( ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),A) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,C),A) )
      <=> ( B = C ) ) ) ).

% unit_mult_right_cancel
tff(fact_3445_unit__mult__right__cancel,axiom,
    ! [A: int,B: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),one_one_int)
     => ( ( aa_int_int(aa_int_fun_int_int(times_times_int,B),A) = aa_int_int(aa_int_fun_int_int(times_times_int,C),A) )
      <=> ( B = C ) ) ) ).

% unit_mult_right_cancel
tff(fact_3446_unit__mult__left__cancel,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),one_one_Code_integer)
     => ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),B) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),C) )
      <=> ( B = C ) ) ) ).

% unit_mult_left_cancel
tff(fact_3447_unit__mult__left__cancel,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),one_one_nat)
     => ( ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),C) )
      <=> ( B = C ) ) ) ).

% unit_mult_left_cancel
tff(fact_3448_unit__mult__left__cancel,axiom,
    ! [A: int,B: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),one_one_int)
     => ( ( aa_int_int(aa_int_fun_int_int(times_times_int,A),B) = aa_int_int(aa_int_fun_int_int(times_times_int,A),C) )
      <=> ( B = C ) ) ) ).

% unit_mult_left_cancel
tff(fact_3449_mult__unit__dvd__iff_H,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),one_one_Code_integer)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),B)),C)
      <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,B),C) ) ) ).

% mult_unit_dvd_iff'
tff(fact_3450_mult__unit__dvd__iff_H,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),one_one_nat)
     => ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),B)),C)
      <=> aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,B),C) ) ) ).

% mult_unit_dvd_iff'
tff(fact_3451_mult__unit__dvd__iff_H,axiom,
    ! [A: int,B: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),one_one_int)
     => ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),B)),C)
      <=> aa_int_o(aa_int_fun_int_o(dvd_dvd_int,B),C) ) ) ).

% mult_unit_dvd_iff'
tff(fact_3452_dvd__mult__unit__iff_H,axiom,
    ! [B: code_integer,A: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,B),one_one_Code_integer)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,B),C))
      <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),C) ) ) ).

% dvd_mult_unit_iff'
tff(fact_3453_dvd__mult__unit__iff_H,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,B),one_one_nat)
     => ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),C))
      <=> aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),C) ) ) ).

% dvd_mult_unit_iff'
tff(fact_3454_dvd__mult__unit__iff_H,axiom,
    ! [B: int,A: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,B),one_one_int)
     => ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),aa_int_int(aa_int_fun_int_int(times_times_int,B),C))
      <=> aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),C) ) ) ).

% dvd_mult_unit_iff'
tff(fact_3455_mult__unit__dvd__iff,axiom,
    ! [B: code_integer,A: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,B),one_one_Code_integer)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),B)),C)
      <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),C) ) ) ).

% mult_unit_dvd_iff
tff(fact_3456_mult__unit__dvd__iff,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,B),one_one_nat)
     => ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),B)),C)
      <=> aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),C) ) ) ).

% mult_unit_dvd_iff
tff(fact_3457_mult__unit__dvd__iff,axiom,
    ! [B: int,A: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,B),one_one_int)
     => ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),B)),C)
      <=> aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),C) ) ) ).

% mult_unit_dvd_iff
tff(fact_3458_dvd__mult__unit__iff,axiom,
    ! [B: code_integer,A: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,B),one_one_Code_integer)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,C),B))
      <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),C) ) ) ).

% dvd_mult_unit_iff
tff(fact_3459_dvd__mult__unit__iff,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,B),one_one_nat)
     => ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,C),B))
      <=> aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),C) ) ) ).

% dvd_mult_unit_iff
tff(fact_3460_dvd__mult__unit__iff,axiom,
    ! [B: int,A: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,B),one_one_int)
     => ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),aa_int_int(aa_int_fun_int_int(times_times_int,C),B))
      <=> aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),C) ) ) ).

% dvd_mult_unit_iff
tff(fact_3461_is__unit__mult__iff,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),B)),one_one_Code_integer)
    <=> ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),one_one_Code_integer)
        & aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,B),one_one_Code_integer) ) ) ).

% is_unit_mult_iff
tff(fact_3462_is__unit__mult__iff,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),B)),one_one_nat)
    <=> ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),one_one_nat)
        & aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,B),one_one_nat) ) ) ).

% is_unit_mult_iff
tff(fact_3463_is__unit__mult__iff,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),B)),one_one_int)
    <=> ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),one_one_int)
        & aa_int_o(aa_int_fun_int_o(dvd_dvd_int,B),one_one_int) ) ) ).

% is_unit_mult_iff
tff(fact_3464_div__plus__div__distrib__dvd__left,axiom,
    ! [C: int,A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,C),A)
     => ( aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),C) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,A),C)),aa_int_int(aa_int_fun_int_int(divide_divide_int,B),C)) ) ) ).

% div_plus_div_distrib_dvd_left
tff(fact_3465_div__plus__div__distrib__dvd__left,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,C),A)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),C) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),C)),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,B),C)) ) ) ).

% div_plus_div_distrib_dvd_left
tff(fact_3466_div__plus__div__distrib__dvd__left,axiom,
    ! [C: code_integer,A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,C),A)
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)),C) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),C)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,B),C)) ) ) ).

% div_plus_div_distrib_dvd_left
tff(fact_3467_div__plus__div__distrib__dvd__left,axiom,
    ! [C: code_natural,A: code_natural,B: code_natural] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(C),A)
     => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),B)),C) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),C)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,B),C)) ) ) ).

% div_plus_div_distrib_dvd_left
tff(fact_3468_div__plus__div__distrib__dvd__right,axiom,
    ! [C: int,B: int,A: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,C),B)
     => ( aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),C) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,A),C)),aa_int_int(aa_int_fun_int_int(divide_divide_int,B),C)) ) ) ).

% div_plus_div_distrib_dvd_right
tff(fact_3469_div__plus__div__distrib__dvd__right,axiom,
    ! [C: nat,B: nat,A: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,C),B)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),C) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),C)),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,B),C)) ) ) ).

% div_plus_div_distrib_dvd_right
tff(fact_3470_div__plus__div__distrib__dvd__right,axiom,
    ! [C: code_integer,B: code_integer,A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,C),B)
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)),C) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),C)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,B),C)) ) ) ).

% div_plus_div_distrib_dvd_right
tff(fact_3471_div__plus__div__distrib__dvd__right,axiom,
    ! [C: code_natural,B: code_natural,A: code_natural] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(C),B)
     => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),B)),C) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),C)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,B),C)) ) ) ).

% div_plus_div_distrib_dvd_right
tff(fact_3472_unit__div__cancel,axiom,
    ! [A: int,B: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),one_one_int)
     => ( ( aa_int_int(aa_int_fun_int_int(divide_divide_int,B),A) = aa_int_int(aa_int_fun_int_int(divide_divide_int,C),A) )
      <=> ( B = C ) ) ) ).

% unit_div_cancel
tff(fact_3473_unit__div__cancel,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),one_one_nat)
     => ( ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,B),A) = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,C),A) )
      <=> ( B = C ) ) ) ).

% unit_div_cancel
tff(fact_3474_unit__div__cancel,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),one_one_Code_integer)
     => ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,B),A) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,C),A) )
      <=> ( B = C ) ) ) ).

% unit_div_cancel
tff(fact_3475_unit__div__cancel,axiom,
    ! [A: code_natural,B: code_natural,C: code_natural] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(A),one_one_Code_natural)
     => ( ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,B),A) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,C),A) )
      <=> ( B = C ) ) ) ).

% unit_div_cancel
tff(fact_3476_div__unit__dvd__iff,axiom,
    ! [B: int,A: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,B),one_one_int)
     => ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,A),B)),C)
      <=> aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),C) ) ) ).

% div_unit_dvd_iff
tff(fact_3477_div__unit__dvd__iff,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,B),one_one_nat)
     => ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),B)),C)
      <=> aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),C) ) ) ).

% div_unit_dvd_iff
tff(fact_3478_div__unit__dvd__iff,axiom,
    ! [B: code_integer,A: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,B),one_one_Code_integer)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),B)),C)
      <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),C) ) ) ).

% div_unit_dvd_iff
tff(fact_3479_div__unit__dvd__iff,axiom,
    ! [B: code_natural,A: code_natural,C: code_natural] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(B),one_one_Code_natural)
     => ( aa_Code_natural_o(dvd_dvd_Code_natural(aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),B)),C)
      <=> aa_Code_natural_o(dvd_dvd_Code_natural(A),C) ) ) ).

% div_unit_dvd_iff
tff(fact_3480_dvd__div__unit__iff,axiom,
    ! [B: int,A: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,B),one_one_int)
     => ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),aa_int_int(aa_int_fun_int_int(divide_divide_int,C),B))
      <=> aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),C) ) ) ).

% dvd_div_unit_iff
tff(fact_3481_dvd__div__unit__iff,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,B),one_one_nat)
     => ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,C),B))
      <=> aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),C) ) ) ).

% dvd_div_unit_iff
tff(fact_3482_dvd__div__unit__iff,axiom,
    ! [B: code_integer,A: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,B),one_one_Code_integer)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,C),B))
      <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),C) ) ) ).

% dvd_div_unit_iff
tff(fact_3483_dvd__div__unit__iff,axiom,
    ! [B: code_natural,A: code_natural,C: code_natural] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(B),one_one_Code_natural)
     => ( aa_Code_natural_o(dvd_dvd_Code_natural(A),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,C),B))
      <=> aa_Code_natural_o(dvd_dvd_Code_natural(A),C) ) ) ).

% dvd_div_unit_iff
tff(fact_3484_xor__num_Ocases,axiom,
    ! [X2: product_prod_num_num] :
      ( ( X2 != product_Pair_num_num(one,one) )
     => ( ! [N: num] : X2 != product_Pair_num_num(one,aa_num_num(bit0,N))
       => ( ! [N: num] : X2 != product_Pair_num_num(one,aa_num_num(bit1,N))
         => ( ! [M4: num] : X2 != product_Pair_num_num(aa_num_num(bit0,M4),one)
           => ( ! [M4: num,N: num] : X2 != product_Pair_num_num(aa_num_num(bit0,M4),aa_num_num(bit0,N))
             => ( ! [M4: num,N: num] : X2 != product_Pair_num_num(aa_num_num(bit0,M4),aa_num_num(bit1,N))
               => ( ! [M4: num] : X2 != product_Pair_num_num(aa_num_num(bit1,M4),one)
                 => ( ! [M4: num,N: num] : X2 != product_Pair_num_num(aa_num_num(bit1,M4),aa_num_num(bit0,N))
                   => ~ ! [M4: num,N: num] : X2 != product_Pair_num_num(aa_num_num(bit1,M4),aa_num_num(bit1,N)) ) ) ) ) ) ) ) ) ).

% xor_num.cases
tff(fact_3485_plus__integer_Oabs__eq,axiom,
    ! [Xa: int,X2: int] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_int_Code_integer(code_integer_of_int,Xa)),aa_int_Code_integer(code_integer_of_int,X2)) = aa_int_Code_integer(code_integer_of_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,Xa),X2)) ).

% plus_integer.abs_eq
tff(fact_3486_bezout__lemma__nat,axiom,
    ! [D2: nat,A: nat,B: nat,X2: nat,Y: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,D2),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,D2),B)
       => ( ( ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),X2) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),Y)),D2) )
            | ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),X2) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),Y)),D2) ) )
         => ? [X3: nat,Y4: nat] :
              ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,D2),A)
              & aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,D2),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B))
              & ( ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),X3) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),Y4)),D2) )
                | ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),X3) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),Y4)),D2) ) ) ) ) ) ) ).

% bezout_lemma_nat
tff(fact_3487_bezout__add__nat,axiom,
    ! [A: nat,B: nat] :
    ? [D: nat,X3: nat,Y4: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,D),A)
      & aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,D),B)
      & ( ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),X3) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),Y4)),D) )
        | ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),X3) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),Y4)),D) ) ) ) ).

% bezout_add_nat
tff(fact_3488_one__integer__def,axiom,
    one_one_Code_integer = aa_int_Code_integer(code_integer_of_int,one_one_int) ).

% one_integer_def
tff(fact_3489_less__eq__integer_Oabs__eq,axiom,
    ! [Xa: int,X2: int] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_int_Code_integer(code_integer_of_int,Xa)),aa_int_Code_integer(code_integer_of_int,X2))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,Xa),X2) ) ).

% less_eq_integer.abs_eq
tff(fact_3490_times__integer_Oabs__eq,axiom,
    ! [Xa: int,X2: int] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_int_Code_integer(code_integer_of_int,Xa)),aa_int_Code_integer(code_integer_of_int,X2)) = aa_int_Code_integer(code_integer_of_int,aa_int_int(aa_int_fun_int_int(times_times_int,Xa),X2)) ).

% times_integer.abs_eq
tff(fact_3491_zdvd__period,axiom,
    ! [A: int,D2: int,X2: int,T: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),D2)
     => ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),T))
      <=> aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),aa_int_int(aa_int_fun_int_int(times_times_int,C),D2))),T)) ) ) ).

% zdvd_period
tff(fact_3492_zdvd__reduce,axiom,
    ! [K: int,N2: int,M: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,K),aa_int_int(aa_int_fun_int_int(plus_plus_int,N2),aa_int_int(aa_int_fun_int_int(times_times_int,K),M)))
    <=> aa_int_o(aa_int_fun_int_o(dvd_dvd_int,K),N2) ) ).

% zdvd_reduce
tff(fact_3493_minus__integer_Oabs__eq,axiom,
    ! [Xa: int,X2: int] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_int_Code_integer(code_integer_of_int,Xa)),aa_int_Code_integer(code_integer_of_int,X2)) = aa_int_Code_integer(code_integer_of_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,Xa),X2)) ).

% minus_integer.abs_eq
tff(fact_3494_unity__coeff__ex,axiom,
    ! [P: fun_Code_integer_o,L: code_integer] :
      ( ? [X4: code_integer] : aa_Code_integer_o(P,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,L),X4))
    <=> ? [X4: code_integer] :
          ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,L),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X4),zero_z3403309356797280102nteger))
          & aa_Code_integer_o(P,X4) ) ) ).

% unity_coeff_ex
tff(fact_3495_unity__coeff__ex,axiom,
    ! [P: fun_rat_o,L: rat] :
      ( ? [X4: rat] : aa_rat_o(P,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,L),X4))
    <=> ? [X4: rat] :
          ( aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,L),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X4),zero_zero_rat))
          & aa_rat_o(P,X4) ) ) ).

% unity_coeff_ex
tff(fact_3496_unity__coeff__ex,axiom,
    ! [P: fun_nat_o,L: nat] :
      ( ? [X4: nat] : aa_nat_o(P,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,L),X4))
    <=> ? [X4: nat] :
          ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,L),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X4),zero_zero_nat))
          & aa_nat_o(P,X4) ) ) ).

% unity_coeff_ex
tff(fact_3497_unity__coeff__ex,axiom,
    ! [P: fun_int_o,L: int] :
      ( ? [X4: int] : aa_int_o(P,aa_int_int(aa_int_fun_int_int(times_times_int,L),X4))
    <=> ? [X4: int] :
          ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,L),aa_int_int(aa_int_fun_int_int(plus_plus_int,X4),zero_zero_int))
          & aa_int_o(P,X4) ) ) ).

% unity_coeff_ex
tff(fact_3498_unit__dvdE,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),one_one_Code_integer)
     => ~ ( ( A != zero_z3403309356797280102nteger )
         => ! [C2: code_integer] : B != aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),C2) ) ) ).

% unit_dvdE
tff(fact_3499_unit__dvdE,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),one_one_nat)
     => ~ ( ( A != zero_zero_nat )
         => ! [C2: nat] : B != aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),C2) ) ) ).

% unit_dvdE
tff(fact_3500_unit__dvdE,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),one_one_int)
     => ~ ( ( A != zero_zero_int )
         => ! [C2: int] : B != aa_int_int(aa_int_fun_int_int(times_times_int,A),C2) ) ) ).

% unit_dvdE
tff(fact_3501_inf__period_I4_J,axiom,
    ! [D2: code_integer,D3: code_integer,T: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,D2),D3)
     => ! [X: code_integer,K5: code_integer] :
          ( ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,D2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X),T))
        <=> ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,D2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,X),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,K5),D3))),T)) ) ) ).

% inf_period(4)
tff(fact_3502_inf__period_I4_J,axiom,
    ! [D2: rat,D3: rat,T: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,D2),D3)
     => ! [X: rat,K5: rat] :
          ( ~ aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,D2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X),T))
        <=> ~ aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,D2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(minus_minus_rat(X),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,K5),D3))),T)) ) ) ).

% inf_period(4)
tff(fact_3503_inf__period_I4_J,axiom,
    ! [D2: int,D3: int,T: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,D2),D3)
     => ! [X: int,K5: int] :
          ( ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,D2),aa_int_int(aa_int_fun_int_int(plus_plus_int,X),T))
        <=> ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,D2),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,X),aa_int_int(aa_int_fun_int_int(times_times_int,K5),D3))),T)) ) ) ).

% inf_period(4)
tff(fact_3504_inf__period_I3_J,axiom,
    ! [D2: code_integer,D3: code_integer,T: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,D2),D3)
     => ! [X: code_integer,K5: code_integer] :
          ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,D2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X),T))
        <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,D2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,X),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,K5),D3))),T)) ) ) ).

% inf_period(3)
tff(fact_3505_inf__period_I3_J,axiom,
    ! [D2: rat,D3: rat,T: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,D2),D3)
     => ! [X: rat,K5: rat] :
          ( aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,D2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X),T))
        <=> aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,D2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(minus_minus_rat(X),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,K5),D3))),T)) ) ) ).

% inf_period(3)
tff(fact_3506_inf__period_I3_J,axiom,
    ! [D2: int,D3: int,T: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,D2),D3)
     => ! [X: int,K5: int] :
          ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,D2),aa_int_int(aa_int_fun_int_int(plus_plus_int,X),T))
        <=> aa_int_o(aa_int_fun_int_o(dvd_dvd_int,D2),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,X),aa_int_int(aa_int_fun_int_int(times_times_int,K5),D3))),T)) ) ) ).

% inf_period(3)
tff(fact_3507_unit__div__eq__0__iff,axiom,
    ! [B: int,A: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,B),one_one_int)
     => ( ( aa_int_int(aa_int_fun_int_int(divide_divide_int,A),B) = zero_zero_int )
      <=> ( A = zero_zero_int ) ) ) ).

% unit_div_eq_0_iff
tff(fact_3508_unit__div__eq__0__iff,axiom,
    ! [B: nat,A: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,B),one_one_nat)
     => ( ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),B) = zero_zero_nat )
      <=> ( A = zero_zero_nat ) ) ) ).

% unit_div_eq_0_iff
tff(fact_3509_unit__div__eq__0__iff,axiom,
    ! [B: code_integer,A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,B),one_one_Code_integer)
     => ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),B) = zero_z3403309356797280102nteger )
      <=> ( A = zero_z3403309356797280102nteger ) ) ) ).

% unit_div_eq_0_iff
tff(fact_3510_unit__div__eq__0__iff,axiom,
    ! [B: code_natural,A: code_natural] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(B),one_one_Code_natural)
     => ( ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),B) = zero_z2226904508553997617atural )
      <=> ( A = zero_z2226904508553997617atural ) ) ) ).

% unit_div_eq_0_iff
tff(fact_3511_numeral__Bit1,axiom,
    ! [N2: num] : aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,N2)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(numeral_numeral_nat,N2)),aa_num_nat(numeral_numeral_nat,N2))),one_one_nat) ).

% numeral_Bit1
tff(fact_3512_numeral__Bit1,axiom,
    ! [N2: num] : aa_num_int(numeral_numeral_int,aa_num_num(bit1,N2)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_num_int(numeral_numeral_int,N2)),aa_num_int(numeral_numeral_int,N2))),one_one_int) ).

% numeral_Bit1
tff(fact_3513_numeral__Bit1,axiom,
    ! [N2: num] : aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit1,N2)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_num_Code_integer(numera6620942414471956472nteger,N2)),aa_num_Code_integer(numera6620942414471956472nteger,N2))),one_one_Code_integer) ).

% numeral_Bit1
tff(fact_3514_numeral__Bit1,axiom,
    ! [N2: num] : aa_num_rat(numeral_numeral_rat,aa_num_num(bit1,N2)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_num_rat(numeral_numeral_rat,N2)),aa_num_rat(numeral_numeral_rat,N2))),one_one_rat) ).

% numeral_Bit1
tff(fact_3515_numeral__Bit1,axiom,
    ! [N2: num] : aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,N2)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_num_Code_natural(numera5444537566228673987atural,N2)),aa_num_Code_natural(numera5444537566228673987atural,N2))),one_one_Code_natural) ).

% numeral_Bit1
tff(fact_3516_unit__eq__div1,axiom,
    ! [B: int,A: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,B),one_one_int)
     => ( ( aa_int_int(aa_int_fun_int_int(divide_divide_int,A),B) = C )
      <=> ( A = aa_int_int(aa_int_fun_int_int(times_times_int,C),B) ) ) ) ).

% unit_eq_div1
tff(fact_3517_unit__eq__div1,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,B),one_one_nat)
     => ( ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),B) = C )
      <=> ( A = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,C),B) ) ) ) ).

% unit_eq_div1
tff(fact_3518_unit__eq__div1,axiom,
    ! [B: code_integer,A: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,B),one_one_Code_integer)
     => ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),B) = C )
      <=> ( A = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,C),B) ) ) ) ).

% unit_eq_div1
tff(fact_3519_unit__eq__div1,axiom,
    ! [B: code_natural,A: code_natural,C: code_natural] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(B),one_one_Code_natural)
     => ( ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),B) = C )
      <=> ( A = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,C),B) ) ) ) ).

% unit_eq_div1
tff(fact_3520_unit__eq__div2,axiom,
    ! [B: int,A: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,B),one_one_int)
     => ( ( A = aa_int_int(aa_int_fun_int_int(divide_divide_int,C),B) )
      <=> ( aa_int_int(aa_int_fun_int_int(times_times_int,A),B) = C ) ) ) ).

% unit_eq_div2
tff(fact_3521_unit__eq__div2,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,B),one_one_nat)
     => ( ( A = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,C),B) )
      <=> ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),B) = C ) ) ) ).

% unit_eq_div2
tff(fact_3522_unit__eq__div2,axiom,
    ! [B: code_integer,A: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,B),one_one_Code_integer)
     => ( ( A = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,C),B) )
      <=> ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),B) = C ) ) ) ).

% unit_eq_div2
tff(fact_3523_unit__eq__div2,axiom,
    ! [B: code_natural,A: code_natural,C: code_natural] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(B),one_one_Code_natural)
     => ( ( A = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,C),B) )
      <=> ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,A),B) = C ) ) ) ).

% unit_eq_div2
tff(fact_3524_div__mult__unit2,axiom,
    ! [C: int,B: int,A: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,C),one_one_int)
     => ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,B),A)
       => ( aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_int_int(aa_int_fun_int_int(times_times_int,B),C)) = aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,A),B)),C) ) ) ) ).

% div_mult_unit2
tff(fact_3525_div__mult__unit2,axiom,
    ! [C: nat,B: nat,A: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,C),one_one_nat)
     => ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,B),A)
       => ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),C)) = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),B)),C) ) ) ) ).

% div_mult_unit2
tff(fact_3526_div__mult__unit2,axiom,
    ! [C: code_integer,B: code_integer,A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,C),one_one_Code_integer)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,B),A)
       => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,B),C)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),B)),C) ) ) ) ).

% div_mult_unit2
tff(fact_3527_div__mult__unit2,axiom,
    ! [C: code_natural,B: code_natural,A: code_natural] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(C),one_one_Code_natural)
     => ( aa_Code_natural_o(dvd_dvd_Code_natural(B),A)
       => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,B),C)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),B)),C) ) ) ) ).

% div_mult_unit2
tff(fact_3528_unit__div__commute,axiom,
    ! [B: int,A: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,B),one_one_int)
     => ( aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,A),B)),C) = aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),C)),B) ) ) ).

% unit_div_commute
tff(fact_3529_unit__div__commute,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,B),one_one_nat)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),B)),C) = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),C)),B) ) ) ).

% unit_div_commute
tff(fact_3530_unit__div__commute,axiom,
    ! [B: code_integer,A: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,B),one_one_Code_integer)
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),B)),C) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),C)),B) ) ) ).

% unit_div_commute
tff(fact_3531_unit__div__commute,axiom,
    ! [B: code_natural,A: code_natural,C: code_natural] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(B),one_one_Code_natural)
     => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),B)),C) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,A),C)),B) ) ) ).

% unit_div_commute
tff(fact_3532_unit__div__mult__swap,axiom,
    ! [C: int,A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,C),one_one_int)
     => ( aa_int_int(aa_int_fun_int_int(times_times_int,A),aa_int_int(aa_int_fun_int_int(divide_divide_int,B),C)) = aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),B)),C) ) ) ).

% unit_div_mult_swap
tff(fact_3533_unit__div__mult__swap,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,C),one_one_nat)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,B),C)) = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),B)),C) ) ) ).

% unit_div_mult_swap
tff(fact_3534_unit__div__mult__swap,axiom,
    ! [C: code_integer,A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,C),one_one_Code_integer)
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,B),C)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),B)),C) ) ) ).

% unit_div_mult_swap
tff(fact_3535_unit__div__mult__swap,axiom,
    ! [C: code_natural,A: code_natural,B: code_natural] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(C),one_one_Code_natural)
     => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,A),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,B),C)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,A),B)),C) ) ) ).

% unit_div_mult_swap
tff(fact_3536_is__unit__div__mult2__eq,axiom,
    ! [B: int,C: int,A: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,B),one_one_int)
     => ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,C),one_one_int)
       => ( aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_int_int(aa_int_fun_int_int(times_times_int,B),C)) = aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,A),B)),C) ) ) ) ).

% is_unit_div_mult2_eq
tff(fact_3537_is__unit__div__mult2__eq,axiom,
    ! [B: nat,C: nat,A: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,B),one_one_nat)
     => ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,C),one_one_nat)
       => ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),C)) = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),B)),C) ) ) ) ).

% is_unit_div_mult2_eq
tff(fact_3538_is__unit__div__mult2__eq,axiom,
    ! [B: code_integer,C: code_integer,A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,B),one_one_Code_integer)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,C),one_one_Code_integer)
       => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,B),C)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),B)),C) ) ) ) ).

% is_unit_div_mult2_eq
tff(fact_3539_is__unit__div__mult2__eq,axiom,
    ! [B: code_natural,C: code_natural,A: code_natural] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(B),one_one_Code_natural)
     => ( aa_Code_natural_o(dvd_dvd_Code_natural(C),one_one_Code_natural)
       => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,B),C)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),B)),C) ) ) ) ).

% is_unit_div_mult2_eq
tff(fact_3540_unit__imp__mod__eq__0,axiom,
    ! [B: int,A: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,B),one_one_int)
     => ( aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),B) = zero_zero_int ) ) ).

% unit_imp_mod_eq_0
tff(fact_3541_unit__imp__mod__eq__0,axiom,
    ! [B: nat,A: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,B),one_one_nat)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),B) = zero_zero_nat ) ) ).

% unit_imp_mod_eq_0
tff(fact_3542_unit__imp__mod__eq__0,axiom,
    ! [B: code_integer,A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,B),one_one_Code_integer)
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),B) = zero_z3403309356797280102nteger ) ) ).

% unit_imp_mod_eq_0
tff(fact_3543_unit__imp__mod__eq__0,axiom,
    ! [B: code_natural,A: code_natural] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(B),one_one_Code_natural)
     => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),B) = zero_z2226904508553997617atural ) ) ).

% unit_imp_mod_eq_0
tff(fact_3544_is__unit__power__iff,axiom,
    ! [A: code_integer,N2: nat] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,A),N2)),one_one_Code_integer)
    <=> ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),one_one_Code_integer)
        | ( N2 = zero_zero_nat ) ) ) ).

% is_unit_power_iff
tff(fact_3545_is__unit__power__iff,axiom,
    ! [A: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,A),N2)),one_one_nat)
    <=> ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),one_one_nat)
        | ( N2 = zero_zero_nat ) ) ) ).

% is_unit_power_iff
tff(fact_3546_is__unit__power__iff,axiom,
    ! [A: int,N2: nat] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,A),N2)),one_one_int)
    <=> ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),one_one_int)
        | ( N2 = zero_zero_nat ) ) ) ).

% is_unit_power_iff
tff(fact_3547_bezout__add__strong__nat,axiom,
    ! [A: nat,B: nat] :
      ( ( A != zero_zero_nat )
     => ? [D: nat,X3: nat,Y4: nat] :
          ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,D),A)
          & aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,D),B)
          & ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),X3) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),Y4)),D) ) ) ) ).

% bezout_add_strong_nat
tff(fact_3548_take__bit__Suc__bit1,axiom,
    ! [N2: nat,K: num] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,aa_nat_nat(suc,N2)),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit1,K))) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,N2),aa_num_Code_integer(numera6620942414471956472nteger,K))),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)))),one_one_Code_integer) ).

% take_bit_Suc_bit1
tff(fact_3549_take__bit__Suc__bit1,axiom,
    ! [N2: nat,K: num] : aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,aa_nat_nat(suc,N2)),aa_num_int(numeral_numeral_int,aa_num_num(bit1,K))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,N2),aa_num_int(numeral_numeral_int,K))),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),one_one_int) ).

% take_bit_Suc_bit1
tff(fact_3550_take__bit__Suc__bit1,axiom,
    ! [N2: nat,K: num] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,aa_nat_nat(suc,N2)),aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,K))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,N2),aa_num_nat(numeral_numeral_nat,K))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),one_one_nat) ).

% take_bit_Suc_bit1
tff(fact_3551_take__bit__Suc__bit1,axiom,
    ! [N2: nat,K: num] : aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se569199155075624693atural,aa_nat_nat(suc,N2)),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,K))) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se569199155075624693atural,N2),aa_num_Code_natural(numera5444537566228673987atural,K))),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one)))),one_one_Code_natural) ).

% take_bit_Suc_bit1
tff(fact_3552_numeral__code_I3_J,axiom,
    ! [N2: num] :
      aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,N2)) = $let(
        m: nat,
        m:= aa_num_nat(numeral_numeral_nat,N2),
        aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,m),m)),one_one_nat) ) ).

% numeral_code(3)
tff(fact_3553_numeral__code_I3_J,axiom,
    ! [N2: num] :
      aa_num_int(numeral_numeral_int,aa_num_num(bit1,N2)) = $let(
        m: int,
        m:= aa_num_int(numeral_numeral_int,N2),
        aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,m),m)),one_one_int) ) ).

% numeral_code(3)
tff(fact_3554_numeral__code_I3_J,axiom,
    ! [N2: num] :
      aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit1,N2)) = $let(
        m: code_integer,
        m:= aa_num_Code_integer(numera6620942414471956472nteger,N2),
        aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,m),m)),one_one_Code_integer) ) ).

% numeral_code(3)
tff(fact_3555_numeral__code_I3_J,axiom,
    ! [N2: num] :
      aa_num_rat(numeral_numeral_rat,aa_num_num(bit1,N2)) = $let(
        m: rat,
        m:= aa_num_rat(numeral_numeral_rat,N2),
        aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,m),m)),one_one_rat) ) ).

% numeral_code(3)
tff(fact_3556_numeral__code_I3_J,axiom,
    ! [N2: num] :
      aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,N2)) = $let(
        m: code_natural,
        m:= aa_num_Code_natural(numera5444537566228673987atural,N2),
        aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,m),m)),one_one_Code_natural) ) ).

% numeral_code(3)
tff(fact_3557_stable__imp__take__bit__eq,axiom,
    ! [A: code_integer,N2: nat] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) = A )
     => ( aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,N2),A) = $ite(aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A),zero_z3403309356797280102nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),N2)),one_one_Code_integer)) ) ) ).

% stable_imp_take_bit_eq
tff(fact_3558_stable__imp__take__bit__eq,axiom,
    ! [A: int,N2: nat] :
      ( ( aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) = A )
     => ( aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,N2),A) = $ite(aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A),zero_zero_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),N2)),one_one_int)) ) ) ).

% stable_imp_take_bit_eq
tff(fact_3559_stable__imp__take__bit__eq,axiom,
    ! [A: nat,N2: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = A )
     => ( aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,N2),A) = $ite(aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A),zero_zero_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)),one_one_nat)) ) ) ).

% stable_imp_take_bit_eq
tff(fact_3560_stable__imp__take__bit__eq,axiom,
    ! [A: code_natural,N2: nat] :
      ( ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))) = A )
     => ( aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se569199155075624693atural,N2),A) = $ite(aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A),zero_z2226904508553997617atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(minus_7197305767214868737atural,aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),N2)),one_one_Code_natural)) ) ) ).

% stable_imp_take_bit_eq
tff(fact_3561_is__unitE,axiom,
    ! [A: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),one_one_int)
     => ~ ( ( A != zero_zero_int )
         => ! [B2: int] :
              ( ( B2 != zero_zero_int )
             => ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,B2),one_one_int)
               => ( ( aa_int_int(aa_int_fun_int_int(divide_divide_int,one_one_int),A) = B2 )
                 => ( ( aa_int_int(aa_int_fun_int_int(divide_divide_int,one_one_int),B2) = A )
                   => ( ( aa_int_int(aa_int_fun_int_int(times_times_int,A),B2) = one_one_int )
                     => ( aa_int_int(aa_int_fun_int_int(divide_divide_int,C),A) != aa_int_int(aa_int_fun_int_int(times_times_int,C),B2) ) ) ) ) ) ) ) ) ).

% is_unitE
tff(fact_3562_is__unitE,axiom,
    ! [A: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),one_one_nat)
     => ~ ( ( A != zero_zero_nat )
         => ! [B2: nat] :
              ( ( B2 != zero_zero_nat )
             => ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,B2),one_one_nat)
               => ( ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,one_one_nat),A) = B2 )
                 => ( ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,one_one_nat),B2) = A )
                   => ( ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),B2) = one_one_nat )
                     => ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,C),A) != aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,C),B2) ) ) ) ) ) ) ) ) ).

% is_unitE
tff(fact_3563_is__unitE,axiom,
    ! [A: code_integer,C: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,A),one_one_Code_integer)
     => ~ ( ( A != zero_z3403309356797280102nteger )
         => ! [B2: code_integer] :
              ( ( B2 != zero_z3403309356797280102nteger )
             => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,B2),one_one_Code_integer)
               => ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,one_one_Code_integer),A) = B2 )
                 => ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,one_one_Code_integer),B2) = A )
                   => ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),B2) = one_one_Code_integer )
                     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,C),A) != aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,C),B2) ) ) ) ) ) ) ) ) ).

% is_unitE
tff(fact_3564_is__unitE,axiom,
    ! [A: code_natural,C: code_natural] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(A),one_one_Code_natural)
     => ~ ( ( A != zero_z2226904508553997617atural )
         => ! [B2: code_natural] :
              ( ( B2 != zero_z2226904508553997617atural )
             => ( aa_Code_natural_o(dvd_dvd_Code_natural(B2),one_one_Code_natural)
               => ( ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,one_one_Code_natural),A) = B2 )
                 => ( ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,one_one_Code_natural),B2) = A )
                   => ( ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,A),B2) = one_one_Code_natural )
                     => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,C),A) != aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,C),B2) ) ) ) ) ) ) ) ) ).

% is_unitE
tff(fact_3565_is__unit__div__mult__cancel__left,axiom,
    ! [A: int,B: int] :
      ( ( A != zero_zero_int )
     => ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,B),one_one_int)
       => ( aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_int_int(aa_int_fun_int_int(times_times_int,A),B)) = aa_int_int(aa_int_fun_int_int(divide_divide_int,one_one_int),B) ) ) ) ).

% is_unit_div_mult_cancel_left
tff(fact_3566_is__unit__div__mult__cancel__left,axiom,
    ! [A: nat,B: nat] :
      ( ( A != zero_zero_nat )
     => ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,B),one_one_nat)
       => ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),B)) = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,one_one_nat),B) ) ) ) ).

% is_unit_div_mult_cancel_left
tff(fact_3567_is__unit__div__mult__cancel__left,axiom,
    ! [A: code_integer,B: code_integer] :
      ( ( A != zero_z3403309356797280102nteger )
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,B),one_one_Code_integer)
       => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),B)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,one_one_Code_integer),B) ) ) ) ).

% is_unit_div_mult_cancel_left
tff(fact_3568_is__unit__div__mult__cancel__left,axiom,
    ! [A: code_natural,B: code_natural] :
      ( ( A != zero_z2226904508553997617atural )
     => ( aa_Code_natural_o(dvd_dvd_Code_natural(B),one_one_Code_natural)
       => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,A),B)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,one_one_Code_natural),B) ) ) ) ).

% is_unit_div_mult_cancel_left
tff(fact_3569_is__unit__div__mult__cancel__right,axiom,
    ! [A: int,B: int] :
      ( ( A != zero_zero_int )
     => ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,B),one_one_int)
       => ( aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_int_int(aa_int_fun_int_int(times_times_int,B),A)) = aa_int_int(aa_int_fun_int_int(divide_divide_int,one_one_int),B) ) ) ) ).

% is_unit_div_mult_cancel_right
tff(fact_3570_is__unit__div__mult__cancel__right,axiom,
    ! [A: nat,B: nat] :
      ( ( A != zero_zero_nat )
     => ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,B),one_one_nat)
       => ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),A)) = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,one_one_nat),B) ) ) ) ).

% is_unit_div_mult_cancel_right
tff(fact_3571_is__unit__div__mult__cancel__right,axiom,
    ! [A: code_integer,B: code_integer] :
      ( ( A != zero_z3403309356797280102nteger )
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,B),one_one_Code_integer)
       => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,B),A)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,one_one_Code_integer),B) ) ) ) ).

% is_unit_div_mult_cancel_right
tff(fact_3572_is__unit__div__mult__cancel__right,axiom,
    ! [A: code_natural,B: code_natural] :
      ( ( A != zero_z2226904508553997617atural )
     => ( aa_Code_natural_o(dvd_dvd_Code_natural(B),one_one_Code_natural)
       => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,B),A)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,one_one_Code_natural),B) ) ) ) ).

% is_unit_div_mult_cancel_right
tff(fact_3573_odd__even__add,axiom,
    ! [A: nat,B: nat] :
      ( ~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A)
     => ( ~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),B)
       => aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)) ) ) ).

% odd_even_add
tff(fact_3574_odd__even__add,axiom,
    ! [A: int,B: int] :
      ( ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A)
     => ( ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),B)
       => aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)) ) ) ).

% odd_even_add
tff(fact_3575_odd__even__add,axiom,
    ! [A: code_integer,B: code_integer] :
      ( ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A)
     => ( ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),B)
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)) ) ) ).

% odd_even_add
tff(fact_3576_odd__even__add,axiom,
    ! [A: code_natural,B: code_natural] :
      ( ~ aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A)
     => ( ~ aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),B)
       => aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),B)) ) ) ).

% odd_even_add
tff(fact_3577_odd__one,axiom,
    ~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),one_one_nat) ).

% odd_one
tff(fact_3578_odd__one,axiom,
    ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),one_one_int) ).

% odd_one
tff(fact_3579_odd__one,axiom,
    ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),one_one_Code_integer) ).

% odd_one
tff(fact_3580_odd__one,axiom,
    ~ aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),one_one_Code_natural) ).

% odd_one
tff(fact_3581_dvd__power__iff,axiom,
    ! [X2: code_integer,M: nat,N2: nat] :
      ( ( X2 != zero_z3403309356797280102nteger )
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,X2),M)),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,X2),N2))
      <=> ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,X2),one_one_Code_integer)
          | aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2) ) ) ) ).

% dvd_power_iff
tff(fact_3582_dvd__power__iff,axiom,
    ! [X2: nat,M: nat,N2: nat] :
      ( ( X2 != zero_zero_nat )
     => ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,X2),M)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,X2),N2))
      <=> ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,X2),one_one_nat)
          | aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2) ) ) ) ).

% dvd_power_iff
tff(fact_3583_dvd__power__iff,axiom,
    ! [X2: int,M: nat,N2: nat] :
      ( ( X2 != zero_zero_int )
     => ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,X2),M)),aa_nat_int(aa_int_fun_nat_int(power_power_int,X2),N2))
      <=> ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,X2),one_one_int)
          | aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2) ) ) ) ).

% dvd_power_iff
tff(fact_3584_dvd__power,axiom,
    ! [N2: nat,X2: code_integer] :
      ( ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
        | ( X2 = one_one_Code_integer ) )
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,X2),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,X2),N2)) ) ).

% dvd_power
tff(fact_3585_dvd__power,axiom,
    ! [N2: nat,X2: rat] :
      ( ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
        | ( X2 = one_one_rat ) )
     => aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,X2),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),N2)) ) ).

% dvd_power
tff(fact_3586_dvd__power,axiom,
    ! [N2: nat,X2: nat] :
      ( ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
        | ( X2 = one_one_nat ) )
     => aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,X2),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,X2),N2)) ) ).

% dvd_power
tff(fact_3587_dvd__power,axiom,
    ! [N2: nat,X2: int] :
      ( ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
        | ( X2 = one_one_int ) )
     => aa_int_o(aa_int_fun_int_o(dvd_dvd_int,X2),aa_nat_int(aa_int_fun_nat_int(power_power_int,X2),N2)) ) ).

% dvd_power
tff(fact_3588_Suc3__eq__add__3,axiom,
    ! [N2: nat] : aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(suc,N2))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,one))),N2) ).

% Suc3_eq_add_3
tff(fact_3589_dvd__mult__cancel2,axiom,
    ! [M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),M)
     => ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,N2),M)),M)
      <=> ( N2 = one_one_nat ) ) ) ).

% dvd_mult_cancel2
tff(fact_3590_dvd__mult__cancel1,axiom,
    ! [M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),M)
     => ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,M),N2)),M)
      <=> ( N2 = one_one_nat ) ) ) ).

% dvd_mult_cancel1
tff(fact_3591_dvd__minus__add,axiom,
    ! [Q3: nat,N2: nat,R2: nat,M: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,Q3),N2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,Q3),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,R2),M))
       => ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),Q3))
        <=> aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,R2),M)),Q3))) ) ) ) ).

% dvd_minus_add
tff(fact_3592_power__dvd__imp__le,axiom,
    ! [I: nat,M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,I),M)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,I),N2))
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,one_one_nat),I)
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2) ) ) ).

% power_dvd_imp_le
tff(fact_3593_aset_I10_J,axiom,
    ! [D2: int,D3: int,A2: set_int,T: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,D2),D3)
     => ! [X: int] :
          ( ! [Xa4: int] :
              ( member_int(Xa4,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
             => ! [Xb3: int] :
                  ( member_int(Xb3,A2)
                 => ( X != aa_int_int(aa_int_fun_int_int(minus_minus_int,Xb3),Xa4) ) ) )
         => ( ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,D2),aa_int_int(aa_int_fun_int_int(plus_plus_int,X),T))
           => ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,D2),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,X),D3)),T)) ) ) ) ).

% aset(10)
tff(fact_3594_aset_I9_J,axiom,
    ! [D2: int,D3: int,A2: set_int,T: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,D2),D3)
     => ! [X: int] :
          ( ! [Xa4: int] :
              ( member_int(Xa4,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
             => ! [Xb3: int] :
                  ( member_int(Xb3,A2)
                 => ( X != aa_int_int(aa_int_fun_int_int(minus_minus_int,Xb3),Xa4) ) ) )
         => ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,D2),aa_int_int(aa_int_fun_int_int(plus_plus_int,X),T))
           => aa_int_o(aa_int_fun_int_o(dvd_dvd_int,D2),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,X),D3)),T)) ) ) ) ).

% aset(9)
tff(fact_3595_bset_I10_J,axiom,
    ! [D2: int,D3: int,B4: set_int,T: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,D2),D3)
     => ! [X: int] :
          ( ! [Xa4: int] :
              ( member_int(Xa4,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
             => ! [Xb3: int] :
                  ( member_int(Xb3,B4)
                 => ( X != aa_int_int(aa_int_fun_int_int(plus_plus_int,Xb3),Xa4) ) ) )
         => ( ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,D2),aa_int_int(aa_int_fun_int_int(plus_plus_int,X),T))
           => ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,D2),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,X),D3)),T)) ) ) ) ).

% bset(10)
tff(fact_3596_bset_I9_J,axiom,
    ! [D2: int,D3: int,B4: set_int,T: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,D2),D3)
     => ! [X: int] :
          ( ! [Xa4: int] :
              ( member_int(Xa4,aa_int_set_int(set_or1266510415728281911st_int(one_one_int),D3))
             => ! [Xb3: int] :
                  ( member_int(Xb3,B4)
                 => ( X != aa_int_int(aa_int_fun_int_int(plus_plus_int,Xb3),Xa4) ) ) )
         => ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,D2),aa_int_int(aa_int_fun_int_int(plus_plus_int,X),T))
           => aa_int_o(aa_int_fun_int_o(dvd_dvd_int,D2),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,X),D3)),T)) ) ) ) ).

% bset(9)
tff(fact_3597_num_Osize__gen_I3_J,axiom,
    ! [X32: num] : aa_num_nat(size_num,aa_num_num(bit1,X32)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(size_num,X32)),aa_nat_nat(suc,zero_zero_nat)) ).

% num.size_gen(3)
tff(fact_3598_num_Osize_I6_J,axiom,
    ! [X32: num] : aa_num_nat(size_size_num,aa_num_num(bit1,X32)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(size_size_num,X32)),aa_nat_nat(suc,zero_zero_nat)) ).

% num.size(6)
tff(fact_3599_odd__iff__mod__2__eq__one,axiom,
    ! [A: int] :
      ( ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A)
    <=> ( aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) = one_one_int ) ) ).

% odd_iff_mod_2_eq_one
tff(fact_3600_odd__iff__mod__2__eq__one,axiom,
    ! [A: nat] :
      ( ~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A)
    <=> ( aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = one_one_nat ) ) ).

% odd_iff_mod_2_eq_one
tff(fact_3601_odd__iff__mod__2__eq__one,axiom,
    ! [A: code_integer] :
      ( ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A)
    <=> ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) = one_one_Code_integer ) ) ).

% odd_iff_mod_2_eq_one
tff(fact_3602_odd__iff__mod__2__eq__one,axiom,
    ! [A: code_natural] :
      ( ~ aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A)
    <=> ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))) = one_one_Code_natural ) ) ).

% odd_iff_mod_2_eq_one
tff(fact_3603_Suc__mod__eq__add3__mod,axiom,
    ! [M: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(suc,M)))),N2) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,one))),M)),N2) ).

% Suc_mod_eq_add3_mod
tff(fact_3604_Suc__div__eq__add3__div,axiom,
    ! [M: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(suc,aa_nat_nat(suc,aa_nat_nat(suc,M)))),N2) = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,one))),M)),N2) ).

% Suc_div_eq_add3_div
tff(fact_3605_even__diff__iff,axiom,
    ! [K: int,L: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(minus_minus_int,K),L))
    <=> aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(plus_plus_int,K),L)) ) ).

% even_diff_iff
tff(fact_3606_even__abs__add__iff,axiom,
    ! [K: int,L: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(abs_abs_int,K)),L))
    <=> aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(plus_plus_int,K),L)) ) ).

% even_abs_add_iff
tff(fact_3607_even__add__abs__iff,axiom,
    ! [K: int,L: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(plus_plus_int,K),aa_int_int(abs_abs_int,L)))
    <=> aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(plus_plus_int,K),L)) ) ).

% even_add_abs_iff
tff(fact_3608_signed__take__bit__eq__take__bit__shift,axiom,
    ! [N2: nat,K: int] : aa_int_int(bit_ri631733984087533419it_int(N2),K) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,aa_nat_nat(suc,N2)),aa_int_int(aa_int_fun_int_int(plus_plus_int,K),aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),N2)))),aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),N2)) ).

% signed_take_bit_eq_take_bit_shift
tff(fact_3609_take__bit__incr__eq,axiom,
    ! [N2: nat,K: int] :
      ( ( aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,N2),K) != aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),N2)),one_one_int) )
     => ( aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,N2),aa_int_int(aa_int_fun_int_int(plus_plus_int,K),one_one_int)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,N2),K)) ) ) ).

% take_bit_incr_eq
tff(fact_3610_oddE,axiom,
    ! [A: nat] :
      ( ~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A)
     => ~ ! [B2: nat] : A != aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),B2)),one_one_nat) ) ).

% oddE
tff(fact_3611_oddE,axiom,
    ! [A: int] :
      ( ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A)
     => ~ ! [B2: int] : A != aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),B2)),one_one_int) ) ).

% oddE
tff(fact_3612_oddE,axiom,
    ! [A: code_integer] :
      ( ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A)
     => ~ ! [B2: code_integer] : A != aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),B2)),one_one_Code_integer) ) ).

% oddE
tff(fact_3613_oddE,axiom,
    ! [A: code_natural] :
      ( ~ aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A)
     => ~ ! [B2: code_natural] : A != aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),B2)),one_one_Code_natural) ) ).

% oddE
tff(fact_3614_parity__cases,axiom,
    ! [A: int] :
      ( ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A)
       => ( aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) != zero_zero_int ) )
     => ~ ( ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A)
         => ( aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) != one_one_int ) ) ) ).

% parity_cases
tff(fact_3615_parity__cases,axiom,
    ! [A: nat] :
      ( ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A)
       => ( aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) != zero_zero_nat ) )
     => ~ ( ~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A)
         => ( aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) != one_one_nat ) ) ) ).

% parity_cases
tff(fact_3616_parity__cases,axiom,
    ! [A: code_integer] :
      ( ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A)
       => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) != zero_z3403309356797280102nteger ) )
     => ~ ( ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A)
         => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) != one_one_Code_integer ) ) ) ).

% parity_cases
tff(fact_3617_parity__cases,axiom,
    ! [A: code_natural] :
      ( ( aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A)
       => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))) != zero_z2226904508553997617atural ) )
     => ~ ( ~ aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A)
         => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))) != one_one_Code_natural ) ) ) ).

% parity_cases
tff(fact_3618_mod2__eq__if,axiom,
    ! [A: int] :
      aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) = $ite(aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A),zero_zero_int,one_one_int) ).

% mod2_eq_if
tff(fact_3619_mod2__eq__if,axiom,
    ! [A: nat] :
      aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = $ite(aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A),zero_zero_nat,one_one_nat) ).

% mod2_eq_if
tff(fact_3620_mod2__eq__if,axiom,
    ! [A: code_integer] :
      aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) = $ite(aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A),zero_z3403309356797280102nteger,one_one_Code_integer) ).

% mod2_eq_if
tff(fact_3621_mod2__eq__if,axiom,
    ! [A: code_natural] :
      aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))) = $ite(aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A),zero_z2226904508553997617atural,one_one_Code_natural) ).

% mod2_eq_if
tff(fact_3622_minus__one__power__iff,axiom,
    ! [N2: nat] :
      aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(uminus_uminus_int,one_one_int)),N2) = $ite(aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2),one_one_int,aa_int_int(uminus_uminus_int,one_one_int)) ).

% minus_one_power_iff
tff(fact_3623_minus__one__power__iff,axiom,
    ! [N2: nat] :
      aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),N2) = $ite(aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2),one_one_Code_integer,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) ).

% minus_one_power_iff
tff(fact_3624_minus__one__power__iff,axiom,
    ! [N2: nat] :
      aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),N2) = $ite(aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2),one_one_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)) ).

% minus_one_power_iff
tff(fact_3625_take__bit__int__greater__eq,axiom,
    ! [K: int,N2: nat] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,K),zero_zero_int)
     => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,K),aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),N2))),aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,N2),K)) ) ).

% take_bit_int_greater_eq
tff(fact_3626_take__bit__Suc__minus__1__eq,axiom,
    ! [N2: nat] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,aa_nat_nat(suc,N2)),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_nat_nat(suc,N2))),one_one_Code_integer) ).

% take_bit_Suc_minus_1_eq
tff(fact_3627_take__bit__Suc__minus__1__eq,axiom,
    ! [N2: nat] : aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,aa_nat_nat(suc,N2)),aa_int_int(uminus_uminus_int,one_one_int)) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_nat_nat(suc,N2))),one_one_int) ).

% take_bit_Suc_minus_1_eq
tff(fact_3628_take__bit__Suc,axiom,
    ! [N2: nat,A: code_integer] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,aa_nat_nat(suc,N2)),A) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,N2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))))),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)))) ).

% take_bit_Suc
tff(fact_3629_take__bit__Suc,axiom,
    ! [N2: nat,A: int] : aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,aa_nat_nat(suc,N2)),A) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,N2),aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))))),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))) ).

% take_bit_Suc
tff(fact_3630_take__bit__Suc,axiom,
    ! [N2: nat,A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,aa_nat_nat(suc,N2)),A) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))) ).

% take_bit_Suc
tff(fact_3631_take__bit__Suc,axiom,
    ! [N2: nat,A: code_natural] : aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se569199155075624693atural,aa_nat_nat(suc,N2)),A) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se569199155075624693atural,N2),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))))),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one)))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one)))) ).

% take_bit_Suc
tff(fact_3632_take__bit__numeral__minus__1__eq,axiom,
    ! [K: num] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,aa_num_nat(numeral_numeral_nat,K)),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_num_nat(numeral_numeral_nat,K))),one_one_Code_integer) ).

% take_bit_numeral_minus_1_eq
tff(fact_3633_take__bit__numeral__minus__1__eq,axiom,
    ! [K: num] : aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,aa_num_nat(numeral_numeral_nat,K)),aa_int_int(uminus_uminus_int,one_one_int)) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_num_nat(numeral_numeral_nat,K))),one_one_int) ).

% take_bit_numeral_minus_1_eq
tff(fact_3634_even__mask__div__iff_H,axiom,
    ! [M: nat,N2: nat] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),M)),one_one_int)),aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),N2)))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2) ) ).

% even_mask_div_iff'
tff(fact_3635_even__mask__div__iff_H,axiom,
    ! [M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),M)),one_one_nat)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2) ) ).

% even_mask_div_iff'
tff(fact_3636_even__mask__div__iff_H,axiom,
    ! [M: nat,N2: nat] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),M)),one_one_Code_integer)),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),N2)))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2) ) ).

% even_mask_div_iff'
tff(fact_3637_even__mask__div__iff_H,axiom,
    ! [M: nat,N2: nat] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(minus_7197305767214868737atural,aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),M)),one_one_Code_natural)),aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),N2)))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2) ) ).

% even_mask_div_iff'
tff(fact_3638_even__mask__div__iff,axiom,
    ! [M: nat,N2: nat] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),M)),one_one_int)),aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),N2)))
    <=> ( ( aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),N2) = zero_zero_int )
        | aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2) ) ) ).

% even_mask_div_iff
tff(fact_3639_even__mask__div__iff,axiom,
    ! [M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),M)),one_one_nat)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)))
    <=> ( ( aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2) = zero_zero_nat )
        | aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2) ) ) ).

% even_mask_div_iff
tff(fact_3640_even__mask__div__iff,axiom,
    ! [M: nat,N2: nat] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),M)),one_one_Code_integer)),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),N2)))
    <=> ( ( aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),N2) = zero_z3403309356797280102nteger )
        | aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2) ) ) ).

% even_mask_div_iff
tff(fact_3641_even__mask__div__iff,axiom,
    ! [M: nat,N2: nat] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(minus_7197305767214868737atural,aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),M)),one_one_Code_natural)),aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),N2)))
    <=> ( ( aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),N2) = zero_z2226904508553997617atural )
        | aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2) ) ) ).

% even_mask_div_iff
tff(fact_3642_Code__Numeral_Onegative__def,axiom,
    code_negative = aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,uminus1351360451143612070nteger),numera6620942414471956472nteger) ).

% Code_Numeral.negative_def
tff(fact_3643_take__bit__numeral__minus__numeral__int,axiom,
    ! [M: num,N2: num] : aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,aa_num_nat(numeral_numeral_nat,M)),aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,N2))) = aa_option_num_int(case_option_int_num(zero_zero_int,aTP_Lamm_hd(M)),aa_num_option_num(bit_take_bit_num(aa_num_nat(numeral_numeral_nat,M)),N2)) ).

% take_bit_numeral_minus_numeral_int
tff(fact_3644_signed__take__bit__numeral__minus__bit1,axiom,
    ! [L: num,K: num] : aa_int_int(bit_ri631733984087533419it_int(aa_num_nat(numeral_numeral_nat,L)),aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,aa_num_num(bit1,K)))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(bit_ri631733984087533419it_int(aa_num_nat(pred_numeral,L)),aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,K))),one_one_int))),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),one_one_int) ).

% signed_take_bit_numeral_minus_bit1
tff(fact_3645_execute__change,axiom,
    ! [F: fun_array_a_array_a,R2: ref_array_a,Ha: heap_e7401611519738050253t_unit] : aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(ref_change_array_a(F,R2)),Ha) = aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,produc1733996804261680252it_nat(aa_array_a_array_a(F,ref_get_array_a(Ha,R2)),produc584006145561248582it_nat(ref_set_array_a(R2,aa_array_a_array_a(F,ref_get_array_a(Ha,R2)),Ha),aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,one))))) ).

% execute_change
tff(fact_3646_execute__change,axiom,
    ! [F: fun_Pr2191293291710260995t_unit,R2: ref_Product_unit,Ha: heap_e7401611519738050253t_unit] : aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(ref_ch7259622376331601608t_unit(F,R2)),Ha) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(aa_Pro8294289767544744956t_unit(F,ref_get_Product_unit(Ha,R2)),produc584006145561248582it_nat(ref_set_Product_unit(R2,aa_Pro8294289767544744956t_unit(F,ref_get_Product_unit(Ha,R2)),Ha),aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,one))))) ).

% execute_change
tff(fact_3647_signed__take__bit__numeral__bit1,axiom,
    ! [L: num,K: num] : aa_int_int(bit_ri631733984087533419it_int(aa_num_nat(numeral_numeral_nat,L)),aa_num_int(numeral_numeral_int,aa_num_num(bit1,K))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(bit_ri631733984087533419it_int(aa_num_nat(pred_numeral,L)),aa_num_int(numeral_numeral_int,K))),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),one_one_int) ).

% signed_take_bit_numeral_bit1
tff(fact_3648_take__bit__Suc__minus__bit1,axiom,
    ! [N2: nat,K: num] : aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,aa_nat_nat(suc,N2)),aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,aa_num_num(bit1,K)))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,N2),aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,aa_num_num(inc,K))))),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),one_one_int) ).

% take_bit_Suc_minus_bit1
tff(fact_3649_divmod__BitM__2__eq,axiom,
    ! [M: num] : unique5052692396658037445od_int(aa_num_num(bitM,M),aa_num_num(bit0,one)) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_num_int(numeral_numeral_int,M)),one_one_int)),one_one_int) ).

% divmod_BitM_2_eq
tff(fact_3650_flip__bit__0,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1345352211410354436nteger,zero_zero_nat),A) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_o_Code_integer(zero_n356916108424825756nteger,aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))))) ).

% flip_bit_0
tff(fact_3651_flip__bit__0,axiom,
    ! [A: int] : aa_int_int(aa_nat_fun_int_int(bit_se2159334234014336723it_int,zero_zero_nat),A) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_o_int(zero_n2684676970156552555ol_int,aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))))) ).

% flip_bit_0
tff(fact_3652_flip__bit__0,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se2161824704523386999it_nat,zero_zero_nat),A) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_o_nat(zero_n2687167440665602831ol_nat,aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A))),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))) ).

% flip_bit_0
tff(fact_3653_flip__bit__0,axiom,
    ! [A: code_natural] : aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se168947363167071951atural,zero_zero_nat),A) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,zero_n8403883297036319079atural(aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))))) ).

% flip_bit_0
tff(fact_3654_of__bool__eq_I2_J,axiom,
    aa_o_rat(zero_n2052037380579107095ol_rat,$true) = one_one_rat ).

% of_bool_eq(2)
tff(fact_3655_of__bool__eq_I2_J,axiom,
    aa_o_nat(zero_n2687167440665602831ol_nat,$true) = one_one_nat ).

% of_bool_eq(2)
tff(fact_3656_of__bool__eq_I2_J,axiom,
    aa_o_int(zero_n2684676970156552555ol_int,$true) = one_one_int ).

% of_bool_eq(2)
tff(fact_3657_of__bool__eq_I2_J,axiom,
    aa_o_Code_integer(zero_n356916108424825756nteger,$true) = one_one_Code_integer ).

% of_bool_eq(2)
tff(fact_3658_of__bool__eq__1__iff,axiom,
    ! [P: $o] :
      ( ( aa_o_rat(zero_n2052037380579107095ol_rat,(P)) = one_one_rat )
    <=> (P) ) ).

% of_bool_eq_1_iff
tff(fact_3659_of__bool__eq__1__iff,axiom,
    ! [P: $o] :
      ( ( aa_o_nat(zero_n2687167440665602831ol_nat,(P)) = one_one_nat )
    <=> (P) ) ).

% of_bool_eq_1_iff
tff(fact_3660_of__bool__eq__1__iff,axiom,
    ! [P: $o] :
      ( ( aa_o_int(zero_n2684676970156552555ol_int,(P)) = one_one_int )
    <=> (P) ) ).

% of_bool_eq_1_iff
tff(fact_3661_of__bool__eq__1__iff,axiom,
    ! [P: $o] :
      ( ( aa_o_Code_integer(zero_n356916108424825756nteger,(P)) = one_one_Code_integer )
    <=> (P) ) ).

% of_bool_eq_1_iff
tff(fact_3662_of__bool__less__one__iff,axiom,
    ! [P: $o] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_o_rat(zero_n2052037380579107095ol_rat,(P))),one_one_rat)
    <=> ~ (P) ) ).

% of_bool_less_one_iff
tff(fact_3663_of__bool__less__one__iff,axiom,
    ! [P: $o] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_o_nat(zero_n2687167440665602831ol_nat,(P))),one_one_nat)
    <=> ~ (P) ) ).

% of_bool_less_one_iff
tff(fact_3664_of__bool__less__one__iff,axiom,
    ! [P: $o] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_o_int(zero_n2684676970156552555ol_int,(P))),one_one_int)
    <=> ~ (P) ) ).

% of_bool_less_one_iff
tff(fact_3665_of__bool__less__one__iff,axiom,
    ! [P: $o] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_o_Code_integer(zero_n356916108424825756nteger,(P))),one_one_Code_integer)
    <=> ~ (P) ) ).

% of_bool_less_one_iff
tff(fact_3666_of__bool__not__iff,axiom,
    ! [P: $o] : aa_o_rat(zero_n2052037380579107095ol_rat,~ (P)) = aa_rat_rat(minus_minus_rat(one_one_rat),aa_o_rat(zero_n2052037380579107095ol_rat,(P))) ).

% of_bool_not_iff
tff(fact_3667_of__bool__not__iff,axiom,
    ! [P: $o] : aa_o_int(zero_n2684676970156552555ol_int,~ (P)) = aa_int_int(aa_int_fun_int_int(minus_minus_int,one_one_int),aa_o_int(zero_n2684676970156552555ol_int,(P))) ).

% of_bool_not_iff
tff(fact_3668_of__bool__not__iff,axiom,
    ! [P: $o] : aa_o_Code_integer(zero_n356916108424825756nteger,~ (P)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,one_one_Code_integer),aa_o_Code_integer(zero_n356916108424825756nteger,(P))) ).

% of_bool_not_iff
tff(fact_3669_take__bit__num__simps_I3_J,axiom,
    ! [N2: nat,M: num] : aa_num_option_num(bit_take_bit_num(aa_nat_nat(suc,N2)),aa_num_num(bit0,M)) = aa_opt5369159329878751634on_num(case_o6005452278849405969um_num(none_num,aTP_Lamm_he),aa_num_option_num(bit_take_bit_num(N2),M)) ).

% take_bit_num_simps(3)
tff(fact_3670_take__bit__num__simps_I4_J,axiom,
    ! [N2: nat,M: num] : aa_num_option_num(bit_take_bit_num(aa_nat_nat(suc,N2)),aa_num_num(bit1,M)) = aa_num_option_num(some_num,aa_option_num_num(case_option_num_num(one,bit1),aa_num_option_num(bit_take_bit_num(N2),M))) ).

% take_bit_num_simps(4)
tff(fact_3671_take__bit__num__simps_I6_J,axiom,
    ! [R2: num,M: num] : aa_num_option_num(bit_take_bit_num(aa_num_nat(numeral_numeral_nat,R2)),aa_num_num(bit0,M)) = aa_opt5369159329878751634on_num(case_o6005452278849405969um_num(none_num,aTP_Lamm_he),aa_num_option_num(bit_take_bit_num(aa_num_nat(pred_numeral,R2)),M)) ).

% take_bit_num_simps(6)
tff(fact_3672_take__bit__of__1,axiom,
    ! [N2: nat] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,N2),one_one_Code_integer) = aa_o_Code_integer(zero_n356916108424825756nteger,aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)) ).

% take_bit_of_1
tff(fact_3673_take__bit__of__1,axiom,
    ! [N2: nat] : aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,N2),one_one_int) = aa_o_int(zero_n2684676970156552555ol_int,aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)) ).

% take_bit_of_1
tff(fact_3674_take__bit__of__1,axiom,
    ! [N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,N2),one_one_nat) = aa_o_nat(zero_n2687167440665602831ol_nat,aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)) ).

% take_bit_of_1
tff(fact_3675_take__bit__of__1,axiom,
    ! [N2: nat] : aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se569199155075624693atural,N2),one_one_Code_natural) = zero_n8403883297036319079atural(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)) ).

% take_bit_of_1
tff(fact_3676_add__neg__numeral__special_I6_J,axiom,
    ! [M: num] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,M))),aa_int_int(uminus_uminus_int,one_one_int)) = aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,aa_num_num(inc,M))) ).

% add_neg_numeral_special(6)
tff(fact_3677_add__neg__numeral__special_I6_J,axiom,
    ! [M: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,M))),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(inc,M))) ).

% add_neg_numeral_special(6)
tff(fact_3678_add__neg__numeral__special_I6_J,axiom,
    ! [M: num] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,M))),aa_rat_rat(uminus_uminus_rat,one_one_rat)) = aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(inc,M))) ).

% add_neg_numeral_special(6)
tff(fact_3679_add__neg__numeral__special_I5_J,axiom,
    ! [N2: num] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(uminus_uminus_int,one_one_int)),aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,N2))) = aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,aa_num_num(inc,N2))) ).

% add_neg_numeral_special(5)
tff(fact_3680_add__neg__numeral__special_I5_J,axiom,
    ! [N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,N2))) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(inc,N2))) ).

% add_neg_numeral_special(5)
tff(fact_3681_add__neg__numeral__special_I5_J,axiom,
    ! [N2: num] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,N2))) = aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(inc,N2))) ).

% add_neg_numeral_special(5)
tff(fact_3682_diff__numeral__special_I5_J,axiom,
    ! [N2: num] : aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(uminus_uminus_int,one_one_int)),aa_num_int(numeral_numeral_int,N2)) = aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,aa_num_num(inc,N2))) ).

% diff_numeral_special(5)
tff(fact_3683_diff__numeral__special_I5_J,axiom,
    ! [N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),aa_num_Code_integer(numera6620942414471956472nteger,N2)) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(inc,N2))) ).

% diff_numeral_special(5)
tff(fact_3684_diff__numeral__special_I5_J,axiom,
    ! [N2: num] : aa_rat_rat(minus_minus_rat(aa_rat_rat(uminus_uminus_rat,one_one_rat)),aa_num_rat(numeral_numeral_rat,N2)) = aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(inc,N2))) ).

% diff_numeral_special(5)
tff(fact_3685_diff__numeral__special_I6_J,axiom,
    ! [M: num] : aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_num_int(numeral_numeral_int,M)),aa_int_int(uminus_uminus_int,one_one_int)) = aa_num_int(numeral_numeral_int,aa_num_num(inc,M)) ).

% diff_numeral_special(6)
tff(fact_3686_diff__numeral__special_I6_J,axiom,
    ! [M: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_num_Code_integer(numera6620942414471956472nteger,M)),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) = aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(inc,M)) ).

% diff_numeral_special(6)
tff(fact_3687_diff__numeral__special_I6_J,axiom,
    ! [M: num] : aa_rat_rat(minus_minus_rat(aa_num_rat(numeral_numeral_rat,M)),aa_rat_rat(uminus_uminus_rat,one_one_rat)) = aa_num_rat(numeral_numeral_rat,aa_num_num(inc,M)) ).

% diff_numeral_special(6)
tff(fact_3688_take__bit__num__simps_I7_J,axiom,
    ! [R2: num,M: num] : aa_num_option_num(bit_take_bit_num(aa_num_nat(numeral_numeral_nat,R2)),aa_num_num(bit1,M)) = aa_num_option_num(some_num,aa_option_num_num(case_option_num_num(one,bit1),aa_num_option_num(bit_take_bit_num(aa_num_nat(pred_numeral,R2)),M))) ).

% take_bit_num_simps(7)
tff(fact_3689_take__bit__numeral__numeral,axiom,
    ! [M: num,N2: num] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,aa_num_nat(numeral_numeral_nat,M)),aa_num_Code_integer(numera6620942414471956472nteger,N2)) = case_o356765784539232260er_num(zero_z3403309356797280102nteger,numera6620942414471956472nteger,aa_num_option_num(bit_take_bit_num(aa_num_nat(numeral_numeral_nat,M)),N2)) ).

% take_bit_numeral_numeral
tff(fact_3690_take__bit__numeral__numeral,axiom,
    ! [M: num,N2: num] : aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,aa_num_nat(numeral_numeral_nat,M)),aa_num_int(numeral_numeral_int,N2)) = aa_option_num_int(case_option_int_num(zero_zero_int,numeral_numeral_int),aa_num_option_num(bit_take_bit_num(aa_num_nat(numeral_numeral_nat,M)),N2)) ).

% take_bit_numeral_numeral
tff(fact_3691_take__bit__numeral__numeral,axiom,
    ! [M: num,N2: num] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,aa_num_nat(numeral_numeral_nat,M)),aa_num_nat(numeral_numeral_nat,N2)) = case_option_nat_num(zero_zero_nat,numeral_numeral_nat,aa_num_option_num(bit_take_bit_num(aa_num_nat(numeral_numeral_nat,M)),N2)) ).

% take_bit_numeral_numeral
tff(fact_3692_take__bit__numeral__numeral,axiom,
    ! [M: num,N2: num] : aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se569199155075624693atural,aa_num_nat(numeral_numeral_nat,M)),aa_num_Code_natural(numera5444537566228673987atural,N2)) = case_o5621594795226839503al_num(zero_z2226904508553997617atural,numera5444537566228673987atural,aa_num_option_num(bit_take_bit_num(aa_num_nat(numeral_numeral_nat,M)),N2)) ).

% take_bit_numeral_numeral
tff(fact_3693_bits__1__div__exp,axiom,
    ! [N2: nat] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,one_one_Code_natural),aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),N2)) = zero_n8403883297036319079atural(N2 = zero_zero_nat) ).

% bits_1_div_exp
tff(fact_3694_bits__1__div__exp,axiom,
    ! [N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)) = aa_o_nat(zero_n2687167440665602831ol_nat,N2 = zero_zero_nat) ).

% bits_1_div_exp
tff(fact_3695_bits__1__div__exp,axiom,
    ! [N2: nat] : aa_int_int(aa_int_fun_int_int(divide_divide_int,one_one_int),aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),N2)) = aa_o_int(zero_n2684676970156552555ol_int,N2 = zero_zero_nat) ).

% bits_1_div_exp
tff(fact_3696_bits__1__div__exp,axiom,
    ! [N2: nat] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,one_one_Code_integer),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),N2)) = aa_o_Code_integer(zero_n356916108424825756nteger,N2 = zero_zero_nat) ).

% bits_1_div_exp
tff(fact_3697_one__div__2__pow__eq,axiom,
    ! [N2: nat] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,one_one_Code_natural),aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),N2)) = zero_n8403883297036319079atural(N2 = zero_zero_nat) ).

% one_div_2_pow_eq
tff(fact_3698_one__div__2__pow__eq,axiom,
    ! [N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)) = aa_o_nat(zero_n2687167440665602831ol_nat,N2 = zero_zero_nat) ).

% one_div_2_pow_eq
tff(fact_3699_one__div__2__pow__eq,axiom,
    ! [N2: nat] : aa_int_int(aa_int_fun_int_int(divide_divide_int,one_one_int),aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),N2)) = aa_o_int(zero_n2684676970156552555ol_int,N2 = zero_zero_nat) ).

% one_div_2_pow_eq
tff(fact_3700_one__div__2__pow__eq,axiom,
    ! [N2: nat] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,one_one_Code_integer),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),N2)) = aa_o_Code_integer(zero_n356916108424825756nteger,N2 = zero_zero_nat) ).

% one_div_2_pow_eq
tff(fact_3701_one__mod__2__pow__eq,axiom,
    ! [N2: nat] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,one_one_Code_natural),aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),N2)) = zero_n8403883297036319079atural(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)) ).

% one_mod_2_pow_eq
tff(fact_3702_one__mod__2__pow__eq,axiom,
    ! [N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)) = aa_o_nat(zero_n2687167440665602831ol_nat,aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)) ).

% one_mod_2_pow_eq
tff(fact_3703_one__mod__2__pow__eq,axiom,
    ! [N2: nat] : aa_int_int(aa_int_fun_int_int(modulo_modulo_int,one_one_int),aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),N2)) = aa_o_int(zero_n2684676970156552555ol_int,aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)) ).

% one_mod_2_pow_eq
tff(fact_3704_one__mod__2__pow__eq,axiom,
    ! [N2: nat] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,one_one_Code_integer),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),N2)) = aa_o_Code_integer(zero_n356916108424825756nteger,aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)) ).

% one_mod_2_pow_eq
tff(fact_3705_mult__inc,axiom,
    ! [X2: num,Y: num] : aa_num_num(aa_num_fun_num_num(times_times_num,X2),aa_num_num(inc,Y)) = aa_num_num(aa_num_fun_num_num(plus_plus_num,aa_num_num(aa_num_fun_num_num(times_times_num,X2),Y)),X2) ).

% mult_inc
tff(fact_3706_add__inc,axiom,
    ! [X2: num,Y: num] : aa_num_num(aa_num_fun_num_num(plus_plus_num,X2),aa_num_num(inc,Y)) = aa_num_num(inc,aa_num_num(aa_num_fun_num_num(plus_plus_num,X2),Y)) ).

% add_inc
tff(fact_3707_of__bool__less__eq__one,axiom,
    ! [P: $o] : aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_o_rat(zero_n2052037380579107095ol_rat,(P))),one_one_rat) ).

% of_bool_less_eq_one
tff(fact_3708_of__bool__less__eq__one,axiom,
    ! [P: $o] : aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_o_nat(zero_n2687167440665602831ol_nat,(P))),one_one_nat) ).

% of_bool_less_eq_one
tff(fact_3709_of__bool__less__eq__one,axiom,
    ! [P: $o] : aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_o_int(zero_n2684676970156552555ol_int,(P))),one_one_int) ).

% of_bool_less_eq_one
tff(fact_3710_of__bool__less__eq__one,axiom,
    ! [P: $o] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_o_Code_integer(zero_n356916108424825756nteger,(P))),one_one_Code_integer) ).

% of_bool_less_eq_one
tff(fact_3711_of__bool__def,axiom,
    ! [P2: $o] :
      aa_o_rat(zero_n2052037380579107095ol_rat,(P2)) = $ite((P2),one_one_rat,zero_zero_rat) ).

% of_bool_def
tff(fact_3712_of__bool__def,axiom,
    ! [P2: $o] :
      aa_o_nat(zero_n2687167440665602831ol_nat,(P2)) = $ite((P2),one_one_nat,zero_zero_nat) ).

% of_bool_def
tff(fact_3713_of__bool__def,axiom,
    ! [P2: $o] :
      aa_o_int(zero_n2684676970156552555ol_int,(P2)) = $ite((P2),one_one_int,zero_zero_int) ).

% of_bool_def
tff(fact_3714_of__bool__def,axiom,
    ! [P2: $o] :
      aa_o_Code_integer(zero_n356916108424825756nteger,(P2)) = $ite((P2),one_one_Code_integer,zero_z3403309356797280102nteger) ).

% of_bool_def
tff(fact_3715_split__of__bool,axiom,
    ! [P: fun_rat_o,P2: $o] :
      ( aa_rat_o(P,aa_o_rat(zero_n2052037380579107095ol_rat,(P2)))
    <=> ( ( (P2)
         => aa_rat_o(P,one_one_rat) )
        & ( ~ (P2)
         => aa_rat_o(P,zero_zero_rat) ) ) ) ).

% split_of_bool
tff(fact_3716_split__of__bool,axiom,
    ! [P: fun_nat_o,P2: $o] :
      ( aa_nat_o(P,aa_o_nat(zero_n2687167440665602831ol_nat,(P2)))
    <=> ( ( (P2)
         => aa_nat_o(P,one_one_nat) )
        & ( ~ (P2)
         => aa_nat_o(P,zero_zero_nat) ) ) ) ).

% split_of_bool
tff(fact_3717_split__of__bool,axiom,
    ! [P: fun_int_o,P2: $o] :
      ( aa_int_o(P,aa_o_int(zero_n2684676970156552555ol_int,(P2)))
    <=> ( ( (P2)
         => aa_int_o(P,one_one_int) )
        & ( ~ (P2)
         => aa_int_o(P,zero_zero_int) ) ) ) ).

% split_of_bool
tff(fact_3718_split__of__bool,axiom,
    ! [P: fun_Code_integer_o,P2: $o] :
      ( aa_Code_integer_o(P,aa_o_Code_integer(zero_n356916108424825756nteger,(P2)))
    <=> ( ( (P2)
         => aa_Code_integer_o(P,one_one_Code_integer) )
        & ( ~ (P2)
         => aa_Code_integer_o(P,zero_z3403309356797280102nteger) ) ) ) ).

% split_of_bool
tff(fact_3719_split__of__bool__asm,axiom,
    ! [P: fun_rat_o,P2: $o] :
      ( aa_rat_o(P,aa_o_rat(zero_n2052037380579107095ol_rat,(P2)))
    <=> ~ ( ( (P2)
            & ~ aa_rat_o(P,one_one_rat) )
          | ( ~ (P2)
            & ~ aa_rat_o(P,zero_zero_rat) ) ) ) ).

% split_of_bool_asm
tff(fact_3720_split__of__bool__asm,axiom,
    ! [P: fun_nat_o,P2: $o] :
      ( aa_nat_o(P,aa_o_nat(zero_n2687167440665602831ol_nat,(P2)))
    <=> ~ ( ( (P2)
            & ~ aa_nat_o(P,one_one_nat) )
          | ( ~ (P2)
            & ~ aa_nat_o(P,zero_zero_nat) ) ) ) ).

% split_of_bool_asm
tff(fact_3721_split__of__bool__asm,axiom,
    ! [P: fun_int_o,P2: $o] :
      ( aa_int_o(P,aa_o_int(zero_n2684676970156552555ol_int,(P2)))
    <=> ~ ( ( (P2)
            & ~ aa_int_o(P,one_one_int) )
          | ( ~ (P2)
            & ~ aa_int_o(P,zero_zero_int) ) ) ) ).

% split_of_bool_asm
tff(fact_3722_split__of__bool__asm,axiom,
    ! [P: fun_Code_integer_o,P2: $o] :
      ( aa_Code_integer_o(P,aa_o_Code_integer(zero_n356916108424825756nteger,(P2)))
    <=> ~ ( ( (P2)
            & ~ aa_Code_integer_o(P,one_one_Code_integer) )
          | ( ~ (P2)
            & ~ aa_Code_integer_o(P,zero_z3403309356797280102nteger) ) ) ) ).

% split_of_bool_asm
tff(fact_3723_add__One,axiom,
    ! [X2: num] : aa_num_num(aa_num_fun_num_num(plus_plus_num,X2),one) = aa_num_num(inc,X2) ).

% add_One
tff(fact_3724_pred__numeral__def,axiom,
    ! [K: num] : aa_num_nat(pred_numeral,K) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_num_nat(numeral_numeral_nat,K)),one_one_nat) ).

% pred_numeral_def
tff(fact_3725_BitM__plus__one,axiom,
    ! [N2: num] : aa_num_num(aa_num_fun_num_num(plus_plus_num,aa_num_num(bitM,N2)),one) = aa_num_num(bit0,N2) ).

% BitM_plus_one
tff(fact_3726_one__plus__BitM,axiom,
    ! [N2: num] : aa_num_num(aa_num_fun_num_num(plus_plus_num,one),aa_num_num(bitM,N2)) = aa_num_num(bit0,N2) ).

% one_plus_BitM
tff(fact_3727_numeral__inc,axiom,
    ! [X2: num] : aa_num_nat(numeral_numeral_nat,aa_num_num(inc,X2)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(numeral_numeral_nat,X2)),one_one_nat) ).

% numeral_inc
tff(fact_3728_numeral__inc,axiom,
    ! [X2: num] : aa_num_int(numeral_numeral_int,aa_num_num(inc,X2)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_num_int(numeral_numeral_int,X2)),one_one_int) ).

% numeral_inc
tff(fact_3729_numeral__inc,axiom,
    ! [X2: num] : aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(inc,X2)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_num_Code_integer(numera6620942414471956472nteger,X2)),one_one_Code_integer) ).

% numeral_inc
tff(fact_3730_numeral__inc,axiom,
    ! [X2: num] : aa_num_rat(numeral_numeral_rat,aa_num_num(inc,X2)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_num_rat(numeral_numeral_rat,X2)),one_one_rat) ).

% numeral_inc
tff(fact_3731_numeral__inc,axiom,
    ! [X2: num] : aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(inc,X2)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_num_Code_natural(numera5444537566228673987atural,X2)),one_one_Code_natural) ).

% numeral_inc
tff(fact_3732_numeral__BitM,axiom,
    ! [N2: num] : aa_num_int(numeral_numeral_int,aa_num_num(bitM,N2)) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,N2))),one_one_int) ).

% numeral_BitM
tff(fact_3733_numeral__BitM,axiom,
    ! [N2: num] : aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bitM,N2)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,N2))),one_one_Code_integer) ).

% numeral_BitM
tff(fact_3734_numeral__BitM,axiom,
    ! [N2: num] : aa_num_rat(numeral_numeral_rat,aa_num_num(bitM,N2)) = aa_rat_rat(minus_minus_rat(aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,N2))),one_one_rat) ).

% numeral_BitM
tff(fact_3735_take__bit__numeral__minus__bit1,axiom,
    ! [L: num,K: num] : aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,aa_num_nat(numeral_numeral_nat,L)),aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,aa_num_num(bit1,K)))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,aa_num_nat(pred_numeral,L)),aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,aa_num_num(inc,K))))),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),one_one_int) ).

% take_bit_numeral_minus_bit1
tff(fact_3736_bits__induct,axiom,
    ! [P: fun_Code_natural_o,A: code_natural] :
      ( ! [A3: code_natural] :
          ( ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A3),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))) = A3 )
         => aa_Code_natural_o(P,A3) )
     => ( ! [A3: code_natural,B2: $o] :
            ( aa_Code_natural_o(P,A3)
           => ( ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,zero_n8403883297036319079atural((B2))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A3))),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))) = A3 )
             => aa_Code_natural_o(P,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,zero_n8403883297036319079atural((B2))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A3))) ) )
       => aa_Code_natural_o(P,A) ) ) ).

% bits_induct
tff(fact_3737_bits__induct,axiom,
    ! [P: fun_nat_o,A: nat] :
      ( ! [A3: nat] :
          ( ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A3),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = A3 )
         => aa_nat_o(P,A3) )
     => ( ! [A3: nat,B2: $o] :
            ( aa_nat_o(P,A3)
           => ( ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_o_nat(zero_n2687167440665602831ol_nat,(B2))),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A3))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = A3 )
             => aa_nat_o(P,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_o_nat(zero_n2687167440665602831ol_nat,(B2))),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A3))) ) )
       => aa_nat_o(P,A) ) ) ).

% bits_induct
tff(fact_3738_bits__induct,axiom,
    ! [P: fun_int_o,A: int] :
      ( ! [A3: int] :
          ( ( aa_int_int(aa_int_fun_int_int(divide_divide_int,A3),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) = A3 )
         => aa_int_o(P,A3) )
     => ( ! [A3: int,B2: $o] :
            ( aa_int_o(P,A3)
           => ( ( aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_o_int(zero_n2684676970156552555ol_int,(B2))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A3))),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) = A3 )
             => aa_int_o(P,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_o_int(zero_n2684676970156552555ol_int,(B2))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A3))) ) )
       => aa_int_o(P,A) ) ) ).

% bits_induct
tff(fact_3739_bits__induct,axiom,
    ! [P: fun_Code_integer_o,A: code_integer] :
      ( ! [A3: code_integer] :
          ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A3),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) = A3 )
         => aa_Code_integer_o(P,A3) )
     => ( ! [A3: code_integer,B2: $o] :
            ( aa_Code_integer_o(P,A3)
           => ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_o_Code_integer(zero_n356916108424825756nteger,(B2))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A3))),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) = A3 )
             => aa_Code_integer_o(P,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_o_Code_integer(zero_n356916108424825756nteger,(B2))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A3))) ) )
       => aa_Code_integer_o(P,A) ) ) ).

% bits_induct
tff(fact_3740_divide__int__unfold,axiom,
    ! [K: int,M: nat,L: int,N2: nat] :
      aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(sgn_sgn_int,K)),aa_nat_int(semiri1314217659103216013at_int,M))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(sgn_sgn_int,L)),aa_nat_int(semiri1314217659103216013at_int,N2))) = $ite(
        ( ( aa_int_int(sgn_sgn_int,L) = zero_zero_int )
        | ( aa_int_int(sgn_sgn_int,K) = zero_zero_int )
        | ( N2 = zero_zero_nat ) ),
        zero_zero_int,
        $ite(aa_int_int(sgn_sgn_int,K) = aa_int_int(sgn_sgn_int,L),aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,M),N2)),aa_int_int(uminus_uminus_int,aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,M),N2)),aa_o_nat(zero_n2687167440665602831ol_nat,~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,N2),M)))))) ) ).

% divide_int_unfold
tff(fact_3741_take__bit__numeral__bit1,axiom,
    ! [L: num,K: num] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,aa_num_nat(numeral_numeral_nat,L)),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit1,K))) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,aa_num_nat(pred_numeral,L)),aa_num_Code_integer(numera6620942414471956472nteger,K))),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)))),one_one_Code_integer) ).

% take_bit_numeral_bit1
tff(fact_3742_take__bit__numeral__bit1,axiom,
    ! [L: num,K: num] : aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,aa_num_nat(numeral_numeral_nat,L)),aa_num_int(numeral_numeral_int,aa_num_num(bit1,K))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,aa_num_nat(pred_numeral,L)),aa_num_int(numeral_numeral_int,K))),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),one_one_int) ).

% take_bit_numeral_bit1
tff(fact_3743_take__bit__numeral__bit1,axiom,
    ! [L: num,K: num] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,aa_num_nat(numeral_numeral_nat,L)),aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,K))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,aa_num_nat(pred_numeral,L)),aa_num_nat(numeral_numeral_nat,K))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),one_one_nat) ).

% take_bit_numeral_bit1
tff(fact_3744_take__bit__numeral__bit1,axiom,
    ! [L: num,K: num] : aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se569199155075624693atural,aa_num_nat(numeral_numeral_nat,L)),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,K))) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se569199155075624693atural,aa_num_nat(pred_numeral,L)),aa_num_Code_natural(numera5444537566228673987atural,K))),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one)))),one_one_Code_natural) ).

% take_bit_numeral_bit1
tff(fact_3745_Divides_Oadjust__div__eq,axiom,
    ! [Q3: int,R2: int] : aa_Pro6799258434465214121nt_int(adjust_div,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Q3),R2)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,Q3),aa_o_int(zero_n2684676970156552555ol_int,R2 != zero_zero_int)) ).

% Divides.adjust_div_eq
tff(fact_3746_mask__numeral,axiom,
    ! [N2: num] : aa_nat_int(bit_se2000444600071755411sk_int,aa_num_nat(numeral_numeral_nat,N2)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_nat_int(bit_se2000444600071755411sk_int,aa_num_nat(pred_numeral,N2)))) ).

% mask_numeral
tff(fact_3747_mask__numeral,axiom,
    ! [N2: num] : aa_nat_Code_integer(bit_se2119862282449309892nteger,aa_num_nat(numeral_numeral_nat,N2)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,one_one_Code_integer),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_nat_Code_integer(bit_se2119862282449309892nteger,aa_num_nat(pred_numeral,N2)))) ).

% mask_numeral
tff(fact_3748_mask__numeral,axiom,
    ! [N2: num] : aa_nat_nat(bit_se2002935070580805687sk_nat,aa_num_nat(numeral_numeral_nat,N2)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(bit_se2002935070580805687sk_nat,aa_num_nat(pred_numeral,N2)))) ).

% mask_numeral
tff(fact_3749_mask__numeral,axiom,
    ! [N2: num] : aa_nat_Code_natural(bit_se943457434206027407atural,aa_num_nat(numeral_numeral_nat,N2)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,one_one_Code_natural),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),aa_nat_Code_natural(bit_se943457434206027407atural,aa_num_nat(pred_numeral,N2)))) ).

% mask_numeral
tff(fact_3750_and__int__unfold,axiom,
    ! [K: int,L: int] :
      aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,K),L) = $ite(
        ( ( K = zero_zero_int )
        | ( L = zero_zero_int ) ),
        zero_zero_int,
        $ite(
          K = aa_int_int(uminus_uminus_int,one_one_int),
          L,
          $ite(L = aa_int_int(uminus_uminus_int,one_one_int),K,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(modulo_modulo_int,K),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,L),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,K),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),aa_int_int(aa_int_fun_int_int(divide_divide_int,L),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))))))) ) ) ).

% and_int_unfold
tff(fact_3751_the__res__def,axiom,
    ! [M: heap_T6362127782908069795rray_a,Ha: heap_e7401611519738050253t_unit] : aa_hea3268681801748734376rray_a(time_the_res_array_a(M),Ha) = case_o8314599424437789472it_nat(undefined_array_a,produc8767961711439910440rray_a(aTP_Lamm_hg),aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(M),Ha)) ).

% the_res_def
tff(fact_3752_the__res__def,axiom,
    ! [M: heap_T5738788834812785303t_unit,Ha: heap_e7401611519738050253t_unit] : aa_hea4146273921685161788t_unit(time_t2745601220510131320t_unit(M),Ha) = case_o9196786658626276042it_nat(undefi2974082611360736373t_unit,produc5075907435489727646t_unit(aTP_Lamm_hi),aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(M),Ha)) ).

% the_res_def
tff(fact_3753_take__bit__eq__mask__iff__exp__dvd,axiom,
    ! [N2: nat,K: int] :
      ( ( aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,N2),K) = aa_nat_int(bit_se2000444600071755411sk_int,N2) )
    <=> aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),N2)),aa_int_int(aa_int_fun_int_int(plus_plus_int,K),one_one_int)) ) ).

% take_bit_eq_mask_iff_exp_dvd
tff(fact_3754_Code__Numeral_Opositive__def,axiom,
    code_positive = numera6620942414471956472nteger ).

% Code_Numeral.positive_def
tff(fact_3755_divide__int__def,axiom,
    ! [K: int,L: int] :
      aa_int_int(aa_int_fun_int_int(divide_divide_int,K),L) = $ite(
        L = zero_zero_int,
        zero_zero_int,
        $ite(aa_int_int(sgn_sgn_int,K) = aa_int_int(sgn_sgn_int,L),aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_int_nat(nat2,aa_int_int(abs_abs_int,K))),aa_int_nat(nat2,aa_int_int(abs_abs_int,L)))),aa_int_int(uminus_uminus_int,aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_int_nat(nat2,aa_int_int(abs_abs_int,K))),aa_int_nat(nat2,aa_int_int(abs_abs_int,L)))),aa_o_nat(zero_n2687167440665602831ol_nat,~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,L),K)))))) ) ).

% divide_int_def
tff(fact_3756_sum__gp0,axiom,
    ! [X2: rat,N2: nat] :
      groups2906978787729119204at_rat(aa_rat_fun_nat_rat(power_power_rat,X2),aa_nat_set_nat(set_ord_atMost_nat,N2)) = $ite(X2 = one_one_rat,aa_nat_rat(semiri681578069525770553at_rat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),one_one_nat)),aa_rat_rat(divide_divide_rat(aa_rat_rat(minus_minus_rat(one_one_rat),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),aa_nat_nat(suc,N2)))),aa_rat_rat(minus_minus_rat(one_one_rat),X2))) ).

% sum_gp0
tff(fact_3757_atMost__eq__iff,axiom,
    ! [X2: nat,Y: nat] :
      ( ( aa_nat_set_nat(set_ord_atMost_nat,X2) = aa_nat_set_nat(set_ord_atMost_nat,Y) )
    <=> ( X2 = Y ) ) ).

% atMost_eq_iff
tff(fact_3758_atMost__iff,axiom,
    ! [I: $o,K: $o] :
      ( member_o((I),aa_o_set_o(set_ord_atMost_o,(K)))
    <=> aa_o_o(aa_o_fun_o_o(ord_less_eq_o,(I)),(K)) ) ).

% atMost_iff
tff(fact_3759_atMost__iff,axiom,
    ! [I: set_nat,K: set_nat] :
      ( member_set_nat(I,set_or4236626031148496127et_nat(K))
    <=> aa_set_nat_o(ord_less_eq_set_nat(I),K) ) ).

% atMost_iff
tff(fact_3760_atMost__iff,axiom,
    ! [I: rat,K: rat] :
      ( member_rat(I,set_ord_atMost_rat(K))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,I),K) ) ).

% atMost_iff
tff(fact_3761_atMost__iff,axiom,
    ! [I: num,K: num] :
      ( member_num(I,set_ord_atMost_num(K))
    <=> aa_num_o(aa_num_fun_num_o(ord_less_eq_num,I),K) ) ).

% atMost_iff
tff(fact_3762_atMost__iff,axiom,
    ! [I: int,K: int] :
      ( member_int(I,aa_int_set_int(set_ord_atMost_int,K))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,I),K) ) ).

% atMost_iff
tff(fact_3763_atMost__iff,axiom,
    ! [I: nat,K: nat] :
      ( member_nat(I,aa_nat_set_nat(set_ord_atMost_nat,K))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,I),K) ) ).

% atMost_iff
tff(fact_3764_atMost__subset__iff,axiom,
    ! [X2: set_nat,Y: set_nat] :
      ( ord_le6893508408891458716et_nat(set_or4236626031148496127et_nat(X2),set_or4236626031148496127et_nat(Y))
    <=> aa_set_nat_o(ord_less_eq_set_nat(X2),Y) ) ).

% atMost_subset_iff
tff(fact_3765_atMost__subset__iff,axiom,
    ! [X2: rat,Y: rat] :
      ( ord_less_eq_set_rat(set_ord_atMost_rat(X2),set_ord_atMost_rat(Y))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,X2),Y) ) ).

% atMost_subset_iff
tff(fact_3766_atMost__subset__iff,axiom,
    ! [X2: num,Y: num] :
      ( ord_less_eq_set_num(set_ord_atMost_num(X2),set_ord_atMost_num(Y))
    <=> aa_num_o(aa_num_fun_num_o(ord_less_eq_num,X2),Y) ) ).

% atMost_subset_iff
tff(fact_3767_atMost__subset__iff,axiom,
    ! [X2: int,Y: int] :
      ( ord_less_eq_set_int(aa_int_set_int(set_ord_atMost_int,X2),aa_int_set_int(set_ord_atMost_int,Y))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,X2),Y) ) ).

% atMost_subset_iff
tff(fact_3768_atMost__subset__iff,axiom,
    ! [X2: nat,Y: nat] :
      ( aa_set_nat_o(ord_less_eq_set_nat(aa_nat_set_nat(set_ord_atMost_nat,X2)),aa_nat_set_nat(set_ord_atMost_nat,Y))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,X2),Y) ) ).

% atMost_subset_iff
tff(fact_3769_bit_Oconj__one__right,axiom,
    ! [X2: int] : aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,X2),aa_int_int(uminus_uminus_int,one_one_int)) = X2 ).

% bit.conj_one_right
tff(fact_3770_bit_Oconj__one__right,axiom,
    ! [X2: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3949692690581998587nteger,X2),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) = X2 ).

% bit.conj_one_right
tff(fact_3771_and_Oright__neutral,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,A),aa_int_int(uminus_uminus_int,one_one_int)) = A ).

% and.right_neutral
tff(fact_3772_and_Oright__neutral,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3949692690581998587nteger,A),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) = A ).

% and.right_neutral
tff(fact_3773_and_Oleft__neutral,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,aa_int_int(uminus_uminus_int,one_one_int)),A) = A ).

% and.left_neutral
tff(fact_3774_and_Oleft__neutral,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3949692690581998587nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),A) = A ).

% and.left_neutral
tff(fact_3775_and__numerals_I2_J,axiom,
    ! [Y: num] : aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,one_one_int),aa_num_int(numeral_numeral_int,aa_num_num(bit1,Y))) = one_one_int ).

% and_numerals(2)
tff(fact_3776_and__numerals_I2_J,axiom,
    ! [Y: num] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se727722235901077358nd_nat,one_one_nat),aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,Y))) = one_one_nat ).

% and_numerals(2)
tff(fact_3777_and__numerals_I2_J,axiom,
    ! [Y: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3949692690581998587nteger,one_one_Code_integer),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit1,Y))) = one_one_Code_integer ).

% and_numerals(2)
tff(fact_3778_and__numerals_I2_J,axiom,
    ! [Y: num] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se2773287842338716102atural,one_one_Code_natural),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,Y))) = one_one_Code_natural ).

% and_numerals(2)
tff(fact_3779_and__numerals_I8_J,axiom,
    ! [X2: num] : aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit1,X2))),one_one_int) = one_one_int ).

% and_numerals(8)
tff(fact_3780_and__numerals_I8_J,axiom,
    ! [X2: num] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se727722235901077358nd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,X2))),one_one_nat) = one_one_nat ).

% and_numerals(8)
tff(fact_3781_and__numerals_I8_J,axiom,
    ! [X2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3949692690581998587nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit1,X2))),one_one_Code_integer) = one_one_Code_integer ).

% and_numerals(8)
tff(fact_3782_and__numerals_I8_J,axiom,
    ! [X2: num] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se2773287842338716102atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,X2))),one_one_Code_natural) = one_one_Code_natural ).

% and_numerals(8)
tff(fact_3783_Icc__subset__Iic__iff,axiom,
    ! [L: set_nat,Ha: set_nat,H3: set_nat] :
      ( ord_le6893508408891458716et_nat(set_or4548717258645045905et_nat(L,Ha),set_or4236626031148496127et_nat(H3))
    <=> ( ~ aa_set_nat_o(ord_less_eq_set_nat(L),Ha)
        | aa_set_nat_o(ord_less_eq_set_nat(Ha),H3) ) ) ).

% Icc_subset_Iic_iff
tff(fact_3784_Icc__subset__Iic__iff,axiom,
    ! [L: rat,Ha: rat,H3: rat] :
      ( ord_less_eq_set_rat(set_or633870826150836451st_rat(L,Ha),set_ord_atMost_rat(H3))
    <=> ( ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,L),Ha)
        | aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,Ha),H3) ) ) ).

% Icc_subset_Iic_iff
tff(fact_3785_Icc__subset__Iic__iff,axiom,
    ! [L: num,Ha: num,H3: num] :
      ( ord_less_eq_set_num(set_or7049704709247886629st_num(L,Ha),set_ord_atMost_num(H3))
    <=> ( ~ aa_num_o(aa_num_fun_num_o(ord_less_eq_num,L),Ha)
        | aa_num_o(aa_num_fun_num_o(ord_less_eq_num,Ha),H3) ) ) ).

% Icc_subset_Iic_iff
tff(fact_3786_Icc__subset__Iic__iff,axiom,
    ! [L: int,Ha: int,H3: int] :
      ( ord_less_eq_set_int(aa_int_set_int(set_or1266510415728281911st_int(L),Ha),aa_int_set_int(set_ord_atMost_int,H3))
    <=> ( ~ aa_int_o(aa_int_fun_int_o(ord_less_eq_int,L),Ha)
        | aa_int_o(aa_int_fun_int_o(ord_less_eq_int,Ha),H3) ) ) ).

% Icc_subset_Iic_iff
tff(fact_3787_Icc__subset__Iic__iff,axiom,
    ! [L: nat,Ha: nat,H3: nat] :
      ( aa_set_nat_o(ord_less_eq_set_nat(aa_nat_set_nat(set_or1269000886237332187st_nat(L),Ha)),aa_nat_set_nat(set_ord_atMost_nat,H3))
    <=> ( ~ aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,L),Ha)
        | aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,Ha),H3) ) ) ).

% Icc_subset_Iic_iff
tff(fact_3788_Icc__subset__Iic__iff,axiom,
    ! [L: code_integer,Ha: code_integer,H3: code_integer] :
      ( ord_le7084787975880047091nteger(aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(L),Ha),aa_Cod2813182003028390446nteger(set_or9101266186257409494nteger,H3))
    <=> ( ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,L),Ha)
        | aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,Ha),H3) ) ) ).

% Icc_subset_Iic_iff
tff(fact_3789_mask__Suc__0,axiom,
    aa_nat_int(bit_se2000444600071755411sk_int,aa_nat_nat(suc,zero_zero_nat)) = one_one_int ).

% mask_Suc_0
tff(fact_3790_mask__Suc__0,axiom,
    aa_nat_Code_integer(bit_se2119862282449309892nteger,aa_nat_nat(suc,zero_zero_nat)) = one_one_Code_integer ).

% mask_Suc_0
tff(fact_3791_mask__Suc__0,axiom,
    aa_nat_nat(bit_se2002935070580805687sk_nat,aa_nat_nat(suc,zero_zero_nat)) = one_one_nat ).

% mask_Suc_0
tff(fact_3792_mask__Suc__0,axiom,
    aa_nat_Code_natural(bit_se943457434206027407atural,aa_nat_nat(suc,zero_zero_nat)) = one_one_Code_natural ).

% mask_Suc_0
tff(fact_3793_sum_OatMost__Suc,axiom,
    ! [G: fun_na2338080690716861136at_nat,N2: nat] : groups6857163185585827899at_nat(G,aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(suc,N2))) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(groups6857163185585827899at_nat(G,aa_nat_set_nat(set_ord_atMost_nat,N2))),aa_nat2240542744625857721at_nat(G,aa_nat_nat(suc,N2))) ).

% sum.atMost_Suc
tff(fact_3794_sum_OatMost__Suc,axiom,
    ! [G: fun_nat_rat,N2: nat] : groups2906978787729119204at_rat(G,aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(suc,N2))) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,groups2906978787729119204at_rat(G,aa_nat_set_nat(set_ord_atMost_nat,N2))),aa_nat_rat(G,aa_nat_nat(suc,N2))) ).

% sum.atMost_Suc
tff(fact_3795_sum_OatMost__Suc,axiom,
    ! [G: fun_nat_int,N2: nat] : groups3539618377306564664at_int(G,aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(suc,N2))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,groups3539618377306564664at_int(G,aa_nat_set_nat(set_ord_atMost_nat,N2))),aa_nat_int(G,aa_nat_nat(suc,N2))) ).

% sum.atMost_Suc
tff(fact_3796_sum_OatMost__Suc,axiom,
    ! [G: fun_nat_nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(suc,N2))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_ord_atMost_nat,N2))),aa_nat_nat(G,aa_nat_nat(suc,N2))) ).

% sum.atMost_Suc
tff(fact_3797_take__bit__minus__one__eq__mask,axiom,
    ! [N2: nat] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,N2),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) = aa_nat_Code_integer(bit_se2119862282449309892nteger,N2) ).

% take_bit_minus_one_eq_mask
tff(fact_3798_take__bit__minus__one__eq__mask,axiom,
    ! [N2: nat] : aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,N2),aa_int_int(uminus_uminus_int,one_one_int)) = aa_nat_int(bit_se2000444600071755411sk_int,N2) ).

% take_bit_minus_one_eq_mask
tff(fact_3799_and__numerals_I1_J,axiom,
    ! [Y: num] : aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,one_one_int),aa_num_int(numeral_numeral_int,aa_num_num(bit0,Y))) = zero_zero_int ).

% and_numerals(1)
tff(fact_3800_and__numerals_I1_J,axiom,
    ! [Y: num] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se727722235901077358nd_nat,one_one_nat),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,Y))) = zero_zero_nat ).

% and_numerals(1)
tff(fact_3801_and__numerals_I1_J,axiom,
    ! [Y: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3949692690581998587nteger,one_one_Code_integer),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,Y))) = zero_z3403309356797280102nteger ).

% and_numerals(1)
tff(fact_3802_and__numerals_I1_J,axiom,
    ! [Y: num] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se2773287842338716102atural,one_one_Code_natural),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,Y))) = zero_z2226904508553997617atural ).

% and_numerals(1)
tff(fact_3803_and__numerals_I5_J,axiom,
    ! [X2: num] : aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,X2))),one_one_int) = zero_zero_int ).

% and_numerals(5)
tff(fact_3804_and__numerals_I5_J,axiom,
    ! [X2: num] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se727722235901077358nd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,X2))),one_one_nat) = zero_zero_nat ).

% and_numerals(5)
tff(fact_3805_and__numerals_I5_J,axiom,
    ! [X2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3949692690581998587nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,X2))),one_one_Code_integer) = zero_z3403309356797280102nteger ).

% and_numerals(5)
tff(fact_3806_and__numerals_I5_J,axiom,
    ! [X2: num] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se2773287842338716102atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,X2))),one_one_Code_natural) = zero_z2226904508553997617atural ).

% and_numerals(5)
tff(fact_3807_nat__numeral__diff__1,axiom,
    ! [V: num] : aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_num_nat(numeral_numeral_nat,V)),one_one_nat) = aa_int_nat(nat2,aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_num_int(numeral_numeral_int,V)),one_one_int)) ).

% nat_numeral_diff_1
tff(fact_3808_and__numerals_I7_J,axiom,
    ! [X2: num,Y: num] : aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit1,X2))),aa_num_int(numeral_numeral_int,aa_num_num(bit1,Y))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,aa_num_int(numeral_numeral_int,X2)),aa_num_int(numeral_numeral_int,Y)))) ).

% and_numerals(7)
tff(fact_3809_and__numerals_I7_J,axiom,
    ! [X2: num,Y: num] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se727722235901077358nd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,X2))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,Y))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(bit_se727722235901077358nd_nat,aa_num_nat(numeral_numeral_nat,X2)),aa_num_nat(numeral_numeral_nat,Y)))) ).

% and_numerals(7)
tff(fact_3810_and__numerals_I7_J,axiom,
    ! [X2: num,Y: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3949692690581998587nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit1,X2))),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit1,Y))) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,one_one_Code_integer),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3949692690581998587nteger,aa_num_Code_integer(numera6620942414471956472nteger,X2)),aa_num_Code_integer(numera6620942414471956472nteger,Y)))) ).

% and_numerals(7)
tff(fact_3811_and__numerals_I7_J,axiom,
    ! [X2: num,Y: num] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se2773287842338716102atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,X2))),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,Y))) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,one_one_Code_natural),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se2773287842338716102atural,aa_num_Code_natural(numera5444537566228673987atural,X2)),aa_num_Code_natural(numera5444537566228673987atural,Y)))) ).

% and_numerals(7)
tff(fact_3812_mask__integer_Oabs__eq,axiom,
    ! [X2: nat] : aa_nat_Code_integer(bit_se2119862282449309892nteger,X2) = aa_int_Code_integer(code_integer_of_int,aa_nat_int(bit_se2000444600071755411sk_int,X2)) ).

% mask_integer.abs_eq
tff(fact_3813_not__Iic__eq__Icc,axiom,
    ! [H3: int,L: int,Ha: int] : aa_int_set_int(set_ord_atMost_int,H3) != aa_int_set_int(set_or1266510415728281911st_int(L),Ha) ).

% not_Iic_eq_Icc
tff(fact_3814_atMost__def,axiom,
    ! [U: set_nat] : set_or4236626031148496127et_nat(U) = collect_set_nat(aTP_Lamm_hj(U)) ).

% atMost_def
tff(fact_3815_atMost__def,axiom,
    ! [U: rat] : set_ord_atMost_rat(U) = collect_rat(aa_rat_fun_rat_o(aTP_Lamm_hk,U)) ).

% atMost_def
tff(fact_3816_atMost__def,axiom,
    ! [U: num] : set_ord_atMost_num(U) = collect_num(aa_num_fun_num_o(aTP_Lamm_hl,U)) ).

% atMost_def
tff(fact_3817_atMost__def,axiom,
    ! [U: int] : aa_int_set_int(set_ord_atMost_int,U) = collect_int(aa_int_fun_int_o(aTP_Lamm_hm,U)) ).

% atMost_def
tff(fact_3818_atMost__def,axiom,
    ! [U: nat] : aa_nat_set_nat(set_ord_atMost_nat,U) = collect_nat(aa_nat_fun_nat_o(aTP_Lamm_hn,U)) ).

% atMost_def
tff(fact_3819_and__eq__minus__1__iff,axiom,
    ! [A: int,B: int] :
      ( ( aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,A),B) = aa_int_int(uminus_uminus_int,one_one_int) )
    <=> ( ( A = aa_int_int(uminus_uminus_int,one_one_int) )
        & ( B = aa_int_int(uminus_uminus_int,one_one_int) ) ) ) ).

% and_eq_minus_1_iff
tff(fact_3820_and__eq__minus__1__iff,axiom,
    ! [A: code_integer,B: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3949692690581998587nteger,A),B) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) )
    <=> ( ( A = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) )
        & ( B = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) ) ) ) ).

% and_eq_minus_1_iff
tff(fact_3821_atMost__atLeast0,axiom,
    ! [N2: nat] : aa_nat_set_nat(set_ord_atMost_nat,N2) = aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2) ).

% atMost_atLeast0
tff(fact_3822_nat__one__as__int,axiom,
    one_one_nat = aa_int_nat(nat2,one_one_int) ).

% nat_one_as_int
tff(fact_3823_not__Iic__le__Icc,axiom,
    ! [Ha: int,L4: int,H3: int] : ~ ord_less_eq_set_int(aa_int_set_int(set_ord_atMost_int,Ha),aa_int_set_int(set_or1266510415728281911st_int(L4),H3)) ).

% not_Iic_le_Icc
tff(fact_3824_nat__int__add,axiom,
    ! [A: nat,B: nat] : aa_int_nat(nat2,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(semiri1314217659103216013at_int,A)),aa_nat_int(semiri1314217659103216013at_int,B))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) ).

% nat_int_add
tff(fact_3825_option_Othe__def,axiom,
    ! [Option: option_num] : aa_option_num_num(the_num,Option) = aa_option_num_num(case_option_num_num(undefined_num,aTP_Lamm_cg),Option) ).

% option.the_def
tff(fact_3826_nat__plus__as__int,axiom,
    ! [X: nat,Xa3: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X),Xa3) = aa_int_nat(nat2,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(semiri1314217659103216013at_int,X)),aa_nat_int(semiri1314217659103216013at_int,Xa3))) ).

% nat_plus_as_int
tff(fact_3827_nat__add__distrib,axiom,
    ! [Z: int,Z5: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),Z)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),Z5)
       => ( aa_int_nat(nat2,aa_int_int(aa_int_fun_int_int(plus_plus_int,Z),Z5)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_int_nat(nat2,Z)),aa_int_nat(nat2,Z5)) ) ) ) ).

% nat_add_distrib
tff(fact_3828_Suc__as__int,axiom,
    ! [X: nat] : aa_nat_nat(suc,X) = aa_int_nat(nat2,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(semiri1314217659103216013at_int,X)),one_one_int)) ).

% Suc_as_int
tff(fact_3829_nat__abs__triangle__ineq,axiom,
    ! [K: int,L: int] : aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_int_nat(nat2,aa_int_int(abs_abs_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,K),L)))),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_int_nat(nat2,aa_int_int(abs_abs_int,K))),aa_int_nat(nat2,aa_int_int(abs_abs_int,L)))) ).

% nat_abs_triangle_ineq
tff(fact_3830_sum_OatMost__Suc__shift,axiom,
    ! [G: fun_na2338080690716861136at_nat,N2: nat] : groups6857163185585827899at_nat(G,aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(suc,N2))) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(aa_nat2240542744625857721at_nat(G,zero_zero_nat)),groups6857163185585827899at_nat(aTP_Lamm_dp(G),aa_nat_set_nat(set_ord_atMost_nat,N2))) ).

% sum.atMost_Suc_shift
tff(fact_3831_sum_OatMost__Suc__shift,axiom,
    ! [G: fun_nat_rat,N2: nat] : groups2906978787729119204at_rat(G,aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(suc,N2))) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(G,zero_zero_nat)),groups2906978787729119204at_rat(aTP_Lamm_dq(G),aa_nat_set_nat(set_ord_atMost_nat,N2))) ).

% sum.atMost_Suc_shift
tff(fact_3832_sum_OatMost__Suc__shift,axiom,
    ! [G: fun_nat_int,N2: nat] : groups3539618377306564664at_int(G,aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(suc,N2))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(G,zero_zero_nat)),groups3539618377306564664at_int(aTP_Lamm_dr(G),aa_nat_set_nat(set_ord_atMost_nat,N2))) ).

% sum.atMost_Suc_shift
tff(fact_3833_sum_OatMost__Suc__shift,axiom,
    ! [G: fun_nat_nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(suc,N2))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(G,zero_zero_nat)),aa_set_nat_nat(groups3542108847815614940at_nat(aTP_Lamm_dh(G)),aa_nat_set_nat(set_ord_atMost_nat,N2))) ).

% sum.atMost_Suc_shift
tff(fact_3834_sum__telescope,axiom,
    ! [F: fun_nat_Code_integer,I: nat] : groups7501900531339628137nteger(aTP_Lamm_ho(F),aa_nat_set_nat(set_ord_atMost_nat,I)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_nat_Code_integer(F,zero_zero_nat)),aa_nat_Code_integer(F,aa_nat_nat(suc,I))) ).

% sum_telescope
tff(fact_3835_sum__telescope,axiom,
    ! [F: fun_nat_rat,I: nat] : groups2906978787729119204at_rat(aTP_Lamm_hp(F),aa_nat_set_nat(set_ord_atMost_nat,I)) = aa_rat_rat(minus_minus_rat(aa_nat_rat(F,zero_zero_nat)),aa_nat_rat(F,aa_nat_nat(suc,I))) ).

% sum_telescope
tff(fact_3836_sum__telescope,axiom,
    ! [F: fun_nat_int,I: nat] : groups3539618377306564664at_int(aTP_Lamm_hq(F),aa_nat_set_nat(set_ord_atMost_nat,I)) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(F,zero_zero_nat)),aa_nat_int(F,aa_nat_nat(suc,I))) ).

% sum_telescope
tff(fact_3837_the__heap__def,axiom,
    ! [M: heap_T6362127782908069795rray_a,Ha: heap_e7401611519738050253t_unit] : time_t490086488869527696rray_a(M,Ha) = case_o8180226181140434498it_nat(undefi8805113437130903861t_unit,produc7016084256669755260t_unit(aTP_Lamm_hs),aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(M),Ha)) ).

% the_heap_def
tff(fact_3838_the__heap__def,axiom,
    ! [M: heap_T5738788834812785303t_unit,Ha: heap_e7401611519738050253t_unit] : time_t3350536682685678164t_unit(M,Ha) = case_o2566993838309857162it_nat(undefi8805113437130903861t_unit,produc6568152436032731486t_unit(aTP_Lamm_ht),aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(M),Ha)) ).

% the_heap_def
tff(fact_3839_and__one__eq,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,A),one_one_int) = aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) ).

% and_one_eq
tff(fact_3840_and__one__eq,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se727722235901077358nd_nat,A),one_one_nat) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) ).

% and_one_eq
tff(fact_3841_and__one__eq,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3949692690581998587nteger,A),one_one_Code_integer) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) ).

% and_one_eq
tff(fact_3842_and__one__eq,axiom,
    ! [A: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se2773287842338716102atural,A),one_one_Code_natural) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))) ).

% and_one_eq
tff(fact_3843_one__and__eq,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,one_one_int),A) = aa_int_int(aa_int_fun_int_int(modulo_modulo_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) ).

% one_and_eq
tff(fact_3844_one__and__eq,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se727722235901077358nd_nat,one_one_nat),A) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) ).

% one_and_eq
tff(fact_3845_one__and__eq,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3949692690581998587nteger,one_one_Code_integer),A) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) ).

% one_and_eq
tff(fact_3846_one__and__eq,axiom,
    ! [A: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se2773287842338716102atural,one_one_Code_natural),A) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))) ).

% one_and_eq
tff(fact_3847_take__bit__eq__mask__iff,axiom,
    ! [N2: nat,K: int] :
      ( ( aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,N2),K) = aa_nat_int(bit_se2000444600071755411sk_int,N2) )
    <=> ( aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,N2),aa_int_int(aa_int_fun_int_int(plus_plus_int,K),one_one_int)) = zero_zero_int ) ) ).

% take_bit_eq_mask_iff
tff(fact_3848_Suc__nat__eq__nat__zadd1,axiom,
    ! [Z: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),Z)
     => ( aa_nat_nat(suc,aa_int_nat(nat2,Z)) = aa_int_nat(nat2,aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),Z)) ) ) ).

% Suc_nat_eq_nat_zadd1
tff(fact_3849_Divides_Oadjust__div__def,axiom,
    ! [Qr: product_prod_int_int] : aa_Pro6799258434465214121nt_int(adjust_div,Qr) = aa_Pro6799258434465214121nt_int(aa_fun914008879417524284nt_int(produc8211389475949308722nt_int,aTP_Lamm_hu),Qr) ).

% Divides.adjust_div_def
tff(fact_3850_sum__gp__basic,axiom,
    ! [X2: code_integer,N2: nat] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,one_one_Code_integer),X2)),groups7501900531339628137nteger(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,X2),aa_nat_set_nat(set_ord_atMost_nat,N2))) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,one_one_Code_integer),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,X2),aa_nat_nat(suc,N2))) ).

% sum_gp_basic
tff(fact_3851_sum__gp__basic,axiom,
    ! [X2: rat,N2: nat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(minus_minus_rat(one_one_rat),X2)),groups2906978787729119204at_rat(aa_rat_fun_nat_rat(power_power_rat,X2),aa_nat_set_nat(set_ord_atMost_nat,N2))) = aa_rat_rat(minus_minus_rat(one_one_rat),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),aa_nat_nat(suc,N2))) ).

% sum_gp_basic
tff(fact_3852_sum__gp__basic,axiom,
    ! [X2: int,N2: nat] : aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,one_one_int),X2)),groups3539618377306564664at_int(aa_int_fun_nat_int(power_power_int,X2),aa_nat_set_nat(set_ord_atMost_nat,N2))) = aa_int_int(aa_int_fun_int_int(minus_minus_int,one_one_int),aa_nat_int(aa_int_fun_nat_int(power_power_int,X2),aa_nat_nat(suc,N2))) ).

% sum_gp_basic
tff(fact_3853_sum__power__shift,axiom,
    ! [M: nat,N2: nat,X2: rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( groups2906978787729119204at_rat(aa_rat_fun_nat_rat(power_power_rat,X2),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),M)),groups2906978787729119204at_rat(aa_rat_fun_nat_rat(power_power_rat,X2),aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),M)))) ) ) ).

% sum_power_shift
tff(fact_3854_sum__power__shift,axiom,
    ! [M: nat,N2: nat,X2: int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( groups3539618377306564664at_int(aa_int_fun_nat_int(power_power_int,X2),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,X2),M)),groups3539618377306564664at_int(aa_int_fun_nat_int(power_power_int,X2),aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),M)))) ) ) ).

% sum_power_shift
tff(fact_3855_sum_Otriangle__reindex__eq,axiom,
    ! [G: fun_nat_fun_nat_nat,N2: nat] : aa_set4749074711808745205at_nat(groups977919841031483927at_nat(aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,G)),aa_fun7046812543386002057at_nat(collec3392354462482085612at_nat,aa_fun7564604662015400456_nat_o(produc6081775807080527818_nat_o,aTP_Lamm_hv(N2)))) = aa_set_nat_nat(groups3542108847815614940at_nat(aTP_Lamm_hx(G)),aa_nat_set_nat(set_ord_atMost_nat,N2)) ).

% sum.triangle_reindex_eq
tff(fact_3856_and__int__rec,axiom,
    ! [K: int,L: int] :
      aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,K),L) = aa_int_int(aa_int_fun_int_int(plus_plus_int,
          aa_o_int(zero_n2684676970156552555ol_int,
            ( ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),K)
            & ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),L) ))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,K),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),aa_int_int(aa_int_fun_int_int(divide_divide_int,L),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))))) ).

% and_int_rec
tff(fact_3857_mask__half__int,axiom,
    ! [N2: nat] : aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_nat_int(bit_se2000444600071755411sk_int,N2)),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) = aa_nat_int(bit_se2000444600071755411sk_int,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)) ).

% mask_half_int
tff(fact_3858_sum_Oin__pairs__0,axiom,
    ! [G: fun_na2338080690716861136at_nat,N2: nat] : groups6857163185585827899at_nat(G,aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)))) = groups6857163185585827899at_nat(aTP_Lamm_ge(G),aa_nat_set_nat(set_ord_atMost_nat,N2)) ).

% sum.in_pairs_0
tff(fact_3859_sum_Oin__pairs__0,axiom,
    ! [G: fun_nat_rat,N2: nat] : groups2906978787729119204at_rat(G,aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)))) = groups2906978787729119204at_rat(aTP_Lamm_gf(G),aa_nat_set_nat(set_ord_atMost_nat,N2)) ).

% sum.in_pairs_0
tff(fact_3860_sum_Oin__pairs__0,axiom,
    ! [G: fun_nat_int,N2: nat] : groups3539618377306564664at_int(G,aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)))) = groups3539618377306564664at_int(aTP_Lamm_gg(G),aa_nat_set_nat(set_ord_atMost_nat,N2)) ).

% sum.in_pairs_0
tff(fact_3861_sum_Oin__pairs__0,axiom,
    ! [G: fun_nat_nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)))) = aa_set_nat_nat(groups3542108847815614940at_nat(aTP_Lamm_gh(G)),aa_nat_set_nat(set_ord_atMost_nat,N2)) ).

% sum.in_pairs_0
tff(fact_3862_mask__nat__def,axiom,
    ! [N2: nat] : aa_nat_nat(bit_se2002935070580805687sk_nat,N2) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)),one_one_nat) ).

% mask_nat_def
tff(fact_3863_mask__eq__exp__minus__1,axiom,
    ! [N2: nat] : aa_nat_int(bit_se2000444600071755411sk_int,N2) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),N2)),one_one_int) ).

% mask_eq_exp_minus_1
tff(fact_3864_mask__eq__exp__minus__1,axiom,
    ! [N2: nat] : aa_nat_Code_integer(bit_se2119862282449309892nteger,N2) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),N2)),one_one_Code_integer) ).

% mask_eq_exp_minus_1
tff(fact_3865_mask__eq__exp__minus__1,axiom,
    ! [N2: nat] : aa_nat_nat(bit_se2002935070580805687sk_nat,N2) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)),one_one_nat) ).

% mask_eq_exp_minus_1
tff(fact_3866_mask__eq__exp__minus__1,axiom,
    ! [N2: nat] : aa_nat_Code_natural(bit_se943457434206027407atural,N2) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(minus_7197305767214868737atural,aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),N2)),one_one_Code_natural) ).

% mask_eq_exp_minus_1
tff(fact_3867_sum_Ozero__middle,axiom,
    ! [P2: nat,K: nat,G: fun_nat_Code_integer,Ha: fun_nat_Code_integer] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),P2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),P2)
       => ( groups7501900531339628137nteger(aa_fun589076786913273746nteger(aa_fun3918145391673965625nteger(aTP_Lamm_hy(K),G),Ha),aa_nat_set_nat(set_ord_atMost_nat,P2)) = groups7501900531339628137nteger(aa_fun589076786913273746nteger(aa_fun3918145391673965625nteger(aTP_Lamm_hz(K),G),Ha),aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,P2),aa_nat_nat(suc,zero_zero_nat)))) ) ) ) ).

% sum.zero_middle
tff(fact_3868_sum_Ozero__middle,axiom,
    ! [P2: nat,K: nat,G: fun_na2338080690716861136at_nat,Ha: fun_na2338080690716861136at_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),P2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),P2)
       => ( groups6857163185585827899at_nat(aa_fun4141531684813184444at_nat(aa_fun8230936523094545239at_nat(aTP_Lamm_ia(K),G),Ha),aa_nat_set_nat(set_ord_atMost_nat,P2)) = groups6857163185585827899at_nat(aa_fun4141531684813184444at_nat(aa_fun8230936523094545239at_nat(aTP_Lamm_ib(K),G),Ha),aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,P2),aa_nat_nat(suc,zero_zero_nat)))) ) ) ) ).

% sum.zero_middle
tff(fact_3869_sum_Ozero__middle,axiom,
    ! [P2: nat,K: nat,G: fun_nat_rat,Ha: fun_nat_rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),P2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),P2)
       => ( groups2906978787729119204at_rat(aa_fun765758790203053448at_rat(aa_fun3638354034882855594at_rat(aTP_Lamm_ic(K),G),Ha),aa_nat_set_nat(set_ord_atMost_nat,P2)) = groups2906978787729119204at_rat(aa_fun765758790203053448at_rat(aa_fun3638354034882855594at_rat(aTP_Lamm_id(K),G),Ha),aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,P2),aa_nat_nat(suc,zero_zero_nat)))) ) ) ) ).

% sum.zero_middle
tff(fact_3870_sum_Ozero__middle,axiom,
    ! [P2: nat,K: nat,G: fun_nat_int,Ha: fun_nat_int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),P2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),P2)
       => ( groups3539618377306564664at_int(aa_fun5565043122120104496at_int(aa_fun5140708168904641446at_int(aTP_Lamm_ie(K),G),Ha),aa_nat_set_nat(set_ord_atMost_nat,P2)) = groups3539618377306564664at_int(aa_fun5565043122120104496at_int(aa_fun5140708168904641446at_int(aTP_Lamm_if(K),G),Ha),aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,P2),aa_nat_nat(suc,zero_zero_nat)))) ) ) ) ).

% sum.zero_middle
tff(fact_3871_sum_Ozero__middle,axiom,
    ! [P2: nat,K: nat,G: fun_nat_nat,Ha: fun_nat_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),P2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),P2)
       => ( aa_set_nat_nat(groups3542108847815614940at_nat(aa_fun5791449513213591928at_nat(aa_fun6854695580826382482at_nat(aTP_Lamm_ig(K),G),Ha)),aa_nat_set_nat(set_ord_atMost_nat,P2)) = aa_set_nat_nat(groups3542108847815614940at_nat(aa_fun5791449513213591928at_nat(aa_fun6854695580826382482at_nat(aTP_Lamm_ih(K),G),Ha)),aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,P2),aa_nat_nat(suc,zero_zero_nat)))) ) ) ) ).

% sum.zero_middle
tff(fact_3872_and__minus__numerals_I3_J,axiom,
    ! [M: num,N2: num] : aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,aa_num_int(numeral_numeral_int,M)),aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,N2)))) = aa_option_num_int(case_option_int_num(zero_zero_int,numeral_numeral_int),aa_num_option_num(bit_and_not_num(M),aa_num_num(bitM,N2))) ).

% and_minus_numerals(3)
tff(fact_3873_and__minus__numerals_I7_J,axiom,
    ! [N2: num,M: num] : aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,N2)))),aa_num_int(numeral_numeral_int,M)) = aa_option_num_int(case_option_int_num(zero_zero_int,numeral_numeral_int),aa_num_option_num(bit_and_not_num(M),aa_num_num(bitM,N2))) ).

% and_minus_numerals(7)
tff(fact_3874_and__minus__numerals_I4_J,axiom,
    ! [M: num,N2: num] : aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,aa_num_int(numeral_numeral_int,M)),aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,aa_num_num(bit1,N2)))) = aa_option_num_int(case_option_int_num(zero_zero_int,numeral_numeral_int),aa_num_option_num(bit_and_not_num(M),aa_num_num(bit0,N2))) ).

% and_minus_numerals(4)
tff(fact_3875_and__minus__numerals_I8_J,axiom,
    ! [N2: num,M: num] : aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,aa_num_num(bit1,N2)))),aa_num_int(numeral_numeral_int,M)) = aa_option_num_int(case_option_int_num(zero_zero_int,numeral_numeral_int),aa_num_option_num(bit_and_not_num(M),aa_num_num(bit0,N2))) ).

% and_minus_numerals(8)
tff(fact_3876_gbinomial__partial__row__sum,axiom,
    ! [A: rat,M: nat] : groups2906978787729119204at_rat(aTP_Lamm_ii(A),aa_nat_set_nat(set_ord_atMost_nat,M)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(divide_divide_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(semiri681578069525770553at_rat,M)),one_one_rat)),aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one)))),aa_nat_rat(gbinomial_rat(A),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),one_one_nat))) ).

% gbinomial_partial_row_sum
tff(fact_3877_gbinomial__r__part__sum,axiom,
    ! [M: nat] : groups2906978787729119204at_rat(gbinomial_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one))),aa_nat_rat(semiri681578069525770553at_rat,M))),one_one_rat)),aa_nat_set_nat(set_ord_atMost_nat,M)) = aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),M)) ).

% gbinomial_r_part_sum
tff(fact_3878_and__num_Oelims,axiom,
    ! [X2: num,Xa: num,Y: option_num] :
      ( ( aa_num_option_num(bit_un7362597486090784418nd_num(X2),Xa) = Y )
     => ( ( ( X2 = one )
         => ( ( Xa = one )
           => ( Y != aa_num_option_num(some_num,one) ) ) )
       => ( ( ( X2 = one )
           => ( ? [N: num] : Xa = aa_num_num(bit0,N)
             => ( Y != none_num ) ) )
         => ( ( ( X2 = one )
             => ( ? [N: num] : Xa = aa_num_num(bit1,N)
               => ( Y != aa_num_option_num(some_num,one) ) ) )
           => ( ( ? [M4: num] : X2 = aa_num_num(bit0,M4)
               => ( ( Xa = one )
                 => ( Y != none_num ) ) )
             => ( ! [M4: num] :
                    ( ( X2 = aa_num_num(bit0,M4) )
                   => ! [N: num] :
                        ( ( Xa = aa_num_num(bit0,N) )
                       => ( Y != aa_opt5369159329878751634on_num(map_option_num_num(bit0),aa_num_option_num(bit_un7362597486090784418nd_num(M4),N)) ) ) )
               => ( ! [M4: num] :
                      ( ( X2 = aa_num_num(bit0,M4) )
                     => ! [N: num] :
                          ( ( Xa = aa_num_num(bit1,N) )
                         => ( Y != aa_opt5369159329878751634on_num(map_option_num_num(bit0),aa_num_option_num(bit_un7362597486090784418nd_num(M4),N)) ) ) )
                 => ( ( ? [M4: num] : X2 = aa_num_num(bit1,M4)
                     => ( ( Xa = one )
                       => ( Y != aa_num_option_num(some_num,one) ) ) )
                   => ( ! [M4: num] :
                          ( ( X2 = aa_num_num(bit1,M4) )
                         => ! [N: num] :
                              ( ( Xa = aa_num_num(bit0,N) )
                             => ( Y != aa_opt5369159329878751634on_num(map_option_num_num(bit0),aa_num_option_num(bit_un7362597486090784418nd_num(M4),N)) ) ) )
                     => ~ ! [M4: num] :
                            ( ( X2 = aa_num_num(bit1,M4) )
                           => ! [N: num] :
                                ( ( Xa = aa_num_num(bit1,N) )
                               => ( Y != aa_opt5369159329878751634on_num(case_o6005452278849405969um_num(aa_num_option_num(some_num,one),aTP_Lamm_ij),aa_num_option_num(bit_un7362597486090784418nd_num(M4),N)) ) ) ) ) ) ) ) ) ) ) ) ) ).

% and_num.elims
tff(fact_3879_take__bit__Suc__from__most,axiom,
    ! [N2: nat,K: int] : aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,aa_nat_nat(suc,N2)),K) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),N2)),aa_o_int(zero_n2684676970156552555ol_int,aa_nat_o(aa_int_fun_nat_o(bit_se1146084159140164899it_int,K),N2)))),aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,N2),K)) ).

% take_bit_Suc_from_most
tff(fact_3880_gbinomial__0_I1_J,axiom,
    ! [A: code_integer] : aa_nat_Code_integer(gbinom8545251970709558553nteger(A),zero_zero_nat) = one_one_Code_integer ).

% gbinomial_0(1)
tff(fact_3881_gbinomial__0_I1_J,axiom,
    ! [A: rat] : aa_nat_rat(gbinomial_rat(A),zero_zero_nat) = one_one_rat ).

% gbinomial_0(1)
tff(fact_3882_gbinomial__0_I1_J,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(gbinomial_nat,A),zero_zero_nat) = one_one_nat ).

% gbinomial_0(1)
tff(fact_3883_gbinomial__0_I1_J,axiom,
    ! [A: int] : aa_nat_int(gbinomial_int(A),zero_zero_nat) = one_one_int ).

% gbinomial_0(1)
tff(fact_3884_and__nat__numerals_I2_J,axiom,
    ! [Y: num] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se727722235901077358nd_nat,aa_nat_nat(suc,zero_zero_nat)),aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,Y))) = one_one_nat ).

% and_nat_numerals(2)
tff(fact_3885_and__nat__numerals_I4_J,axiom,
    ! [X2: num] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se727722235901077358nd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,X2))),aa_nat_nat(suc,zero_zero_nat)) = one_one_nat ).

% and_nat_numerals(4)
tff(fact_3886_bit__disjunctive__add__iff,axiom,
    ! [A: int,B: int,N2: nat] :
      ( ! [N: nat] :
          ( ~ aa_nat_o(aa_int_fun_nat_o(bit_se1146084159140164899it_int,A),N)
          | ~ aa_nat_o(aa_int_fun_nat_o(bit_se1146084159140164899it_int,B),N) )
     => ( aa_nat_o(aa_int_fun_nat_o(bit_se1146084159140164899it_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),N2)
      <=> ( aa_nat_o(aa_int_fun_nat_o(bit_se1146084159140164899it_int,A),N2)
          | aa_nat_o(aa_int_fun_nat_o(bit_se1146084159140164899it_int,B),N2) ) ) ) ).

% bit_disjunctive_add_iff
tff(fact_3887_bit__disjunctive__add__iff,axiom,
    ! [A: code_integer,B: code_integer,N2: nat] :
      ( ! [N: nat] :
          ( ~ aa_nat_o(aa_Cod1075288278386115654_nat_o(bit_se9216721137139052372nteger,A),N)
          | ~ aa_nat_o(aa_Cod1075288278386115654_nat_o(bit_se9216721137139052372nteger,B),N) )
     => ( aa_nat_o(aa_Cod1075288278386115654_nat_o(bit_se9216721137139052372nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)),N2)
      <=> ( aa_nat_o(aa_Cod1075288278386115654_nat_o(bit_se9216721137139052372nteger,A),N2)
          | aa_nat_o(aa_Cod1075288278386115654_nat_o(bit_se9216721137139052372nteger,B),N2) ) ) ) ).

% bit_disjunctive_add_iff
tff(fact_3888_bit__disjunctive__add__iff,axiom,
    ! [A: nat,B: nat,N2: nat] :
      ( ! [N: nat] :
          ( ~ aa_nat_o(aa_nat_fun_nat_o(bit_se1148574629649215175it_nat,A),N)
          | ~ aa_nat_o(aa_nat_fun_nat_o(bit_se1148574629649215175it_nat,B),N) )
     => ( aa_nat_o(aa_nat_fun_nat_o(bit_se1148574629649215175it_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),N2)
      <=> ( aa_nat_o(aa_nat_fun_nat_o(bit_se1148574629649215175it_nat,A),N2)
          | aa_nat_o(aa_nat_fun_nat_o(bit_se1148574629649215175it_nat,B),N2) ) ) ) ).

% bit_disjunctive_add_iff
tff(fact_3889_bit__disjunctive__add__iff,axiom,
    ! [A: code_natural,B: code_natural,N2: nat] :
      ( ! [N: nat] :
          ( ~ aa_nat_o(aa_Cod9120328075896114107_nat_o(bit_se8040316288895769887atural,A),N)
          | ~ aa_nat_o(aa_Cod9120328075896114107_nat_o(bit_se8040316288895769887atural,B),N) )
     => ( aa_nat_o(aa_Cod9120328075896114107_nat_o(bit_se8040316288895769887atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),B)),N2)
      <=> ( aa_nat_o(aa_Cod9120328075896114107_nat_o(bit_se8040316288895769887atural,A),N2)
          | aa_nat_o(aa_Cod9120328075896114107_nat_o(bit_se8040316288895769887atural,B),N2) ) ) ) ).

% bit_disjunctive_add_iff
tff(fact_3890_bit__1__iff,axiom,
    ! [N2: nat] :
      ( aa_nat_o(aa_int_fun_nat_o(bit_se1146084159140164899it_int,one_one_int),N2)
    <=> ( N2 = zero_zero_nat ) ) ).

% bit_1_iff
tff(fact_3891_bit__1__iff,axiom,
    ! [N2: nat] :
      ( aa_nat_o(aa_Cod1075288278386115654_nat_o(bit_se9216721137139052372nteger,one_one_Code_integer),N2)
    <=> ( N2 = zero_zero_nat ) ) ).

% bit_1_iff
tff(fact_3892_bit__1__iff,axiom,
    ! [N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(bit_se1148574629649215175it_nat,one_one_nat),N2)
    <=> ( N2 = zero_zero_nat ) ) ).

% bit_1_iff
tff(fact_3893_bit__1__iff,axiom,
    ! [N2: nat] :
      ( aa_nat_o(aa_Cod9120328075896114107_nat_o(bit_se8040316288895769887atural,one_one_Code_natural),N2)
    <=> ( N2 = zero_zero_nat ) ) ).

% bit_1_iff
tff(fact_3894_not__bit__1__Suc,axiom,
    ! [N2: nat] : ~ aa_nat_o(aa_int_fun_nat_o(bit_se1146084159140164899it_int,one_one_int),aa_nat_nat(suc,N2)) ).

% not_bit_1_Suc
tff(fact_3895_not__bit__1__Suc,axiom,
    ! [N2: nat] : ~ aa_nat_o(aa_Cod1075288278386115654_nat_o(bit_se9216721137139052372nteger,one_one_Code_integer),aa_nat_nat(suc,N2)) ).

% not_bit_1_Suc
tff(fact_3896_not__bit__1__Suc,axiom,
    ! [N2: nat] : ~ aa_nat_o(aa_nat_fun_nat_o(bit_se1148574629649215175it_nat,one_one_nat),aa_nat_nat(suc,N2)) ).

% not_bit_1_Suc
tff(fact_3897_not__bit__1__Suc,axiom,
    ! [N2: nat] : ~ aa_nat_o(aa_Cod9120328075896114107_nat_o(bit_se8040316288895769887atural,one_one_Code_natural),aa_nat_nat(suc,N2)) ).

% not_bit_1_Suc
tff(fact_3898_bit__numeral__simps_I1_J,axiom,
    ! [N2: num] : ~ aa_nat_o(aa_int_fun_nat_o(bit_se1146084159140164899it_int,one_one_int),aa_num_nat(numeral_numeral_nat,N2)) ).

% bit_numeral_simps(1)
tff(fact_3899_bit__numeral__simps_I1_J,axiom,
    ! [N2: num] : ~ aa_nat_o(aa_Cod1075288278386115654_nat_o(bit_se9216721137139052372nteger,one_one_Code_integer),aa_num_nat(numeral_numeral_nat,N2)) ).

% bit_numeral_simps(1)
tff(fact_3900_bit__numeral__simps_I1_J,axiom,
    ! [N2: num] : ~ aa_nat_o(aa_nat_fun_nat_o(bit_se1148574629649215175it_nat,one_one_nat),aa_num_nat(numeral_numeral_nat,N2)) ).

% bit_numeral_simps(1)
tff(fact_3901_bit__numeral__simps_I1_J,axiom,
    ! [N2: num] : ~ aa_nat_o(aa_Cod9120328075896114107_nat_o(bit_se8040316288895769887atural,one_one_Code_natural),aa_num_nat(numeral_numeral_nat,N2)) ).

% bit_numeral_simps(1)
tff(fact_3902_gbinomial__Suc__Suc,axiom,
    ! [A: rat,K: nat] : aa_nat_rat(gbinomial_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),one_one_rat)),aa_nat_nat(suc,K)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(gbinomial_rat(A),K)),aa_nat_rat(gbinomial_rat(A),aa_nat_nat(suc,K))) ).

% gbinomial_Suc_Suc
tff(fact_3903_and__integer_Oabs__eq,axiom,
    ! [Xa: int,X2: int] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3949692690581998587nteger,aa_int_Code_integer(code_integer_of_int,Xa)),aa_int_Code_integer(code_integer_of_int,X2)) = aa_int_Code_integer(code_integer_of_int,aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,Xa),X2)) ).

% and_integer.abs_eq
tff(fact_3904_gbinomial__addition__formula,axiom,
    ! [A: rat,K: nat] : aa_nat_rat(gbinomial_rat(A),aa_nat_nat(suc,K)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(gbinomial_rat(aa_rat_rat(minus_minus_rat(A),one_one_rat)),aa_nat_nat(suc,K))),aa_nat_rat(gbinomial_rat(aa_rat_rat(minus_minus_rat(A),one_one_rat)),K)) ).

% gbinomial_addition_formula
tff(fact_3905_gbinomial__absorb__comp,axiom,
    ! [A: rat,K: nat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(minus_minus_rat(A),aa_nat_rat(semiri681578069525770553at_rat,K))),aa_nat_rat(gbinomial_rat(A),K)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),aa_nat_rat(gbinomial_rat(aa_rat_rat(minus_minus_rat(A),one_one_rat)),K)) ).

% gbinomial_absorb_comp
tff(fact_3906_gbinomial__mult__1_H,axiom,
    ! [A: rat,K: nat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(gbinomial_rat(A),K)),A) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(semiri681578069525770553at_rat,K)),aa_nat_rat(gbinomial_rat(A),K))),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(semiri681578069525770553at_rat,aa_nat_nat(suc,K))),aa_nat_rat(gbinomial_rat(A),aa_nat_nat(suc,K)))) ).

% gbinomial_mult_1'
tff(fact_3907_gbinomial__mult__1,axiom,
    ! [A: rat,K: nat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),aa_nat_rat(gbinomial_rat(A),K)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(semiri681578069525770553at_rat,K)),aa_nat_rat(gbinomial_rat(A),K))),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(semiri681578069525770553at_rat,aa_nat_nat(suc,K))),aa_nat_rat(gbinomial_rat(A),aa_nat_nat(suc,K)))) ).

% gbinomial_mult_1
tff(fact_3908_Suc__times__gbinomial,axiom,
    ! [K: nat,A: rat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(semiri681578069525770553at_rat,aa_nat_nat(suc,K))),aa_nat_rat(gbinomial_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),one_one_rat)),aa_nat_nat(suc,K))) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),one_one_rat)),aa_nat_rat(gbinomial_rat(A),K)) ).

% Suc_times_gbinomial
tff(fact_3909_gbinomial__absorption,axiom,
    ! [K: nat,A: rat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(semiri681578069525770553at_rat,aa_nat_nat(suc,K))),aa_nat_rat(gbinomial_rat(A),aa_nat_nat(suc,K))) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),aa_nat_rat(gbinomial_rat(aa_rat_rat(minus_minus_rat(A),one_one_rat)),K)) ).

% gbinomial_absorption
tff(fact_3910_gbinomial__parallel__sum,axiom,
    ! [A: rat,N2: nat] : groups2906978787729119204at_rat(aTP_Lamm_ik(A),aa_nat_set_nat(set_ord_atMost_nat,N2)) = aa_nat_rat(gbinomial_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),aa_nat_rat(semiri681578069525770553at_rat,N2))),one_one_rat)),N2) ).

% gbinomial_parallel_sum
tff(fact_3911_gbinomial__rec,axiom,
    ! [A: rat,K: nat] : aa_nat_rat(gbinomial_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),one_one_rat)),aa_nat_nat(suc,K)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(gbinomial_rat(A),K)),aa_rat_rat(divide_divide_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),one_one_rat)),aa_nat_rat(semiri681578069525770553at_rat,aa_nat_nat(suc,K)))) ).

% gbinomial_rec
tff(fact_3912_gbinomial__factors,axiom,
    ! [A: rat,K: nat] : aa_nat_rat(gbinomial_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),one_one_rat)),aa_nat_nat(suc,K)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(divide_divide_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),one_one_rat)),aa_nat_rat(semiri681578069525770553at_rat,aa_nat_nat(suc,K)))),aa_nat_rat(gbinomial_rat(A),K)) ).

% gbinomial_factors
tff(fact_3913_gbinomial__negated__upper,axiom,
    ! [A: rat,K: nat] : aa_nat_rat(gbinomial_rat(A),K) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),K)),aa_nat_rat(gbinomial_rat(aa_rat_rat(minus_minus_rat(aa_rat_rat(minus_minus_rat(aa_nat_rat(semiri681578069525770553at_rat,K)),A)),one_one_rat)),K)) ).

% gbinomial_negated_upper
tff(fact_3914_gbinomial__index__swap,axiom,
    ! [K: nat,N2: nat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),K)),aa_nat_rat(gbinomial_rat(aa_rat_rat(minus_minus_rat(aa_rat_rat(uminus_uminus_rat,aa_nat_rat(semiri681578069525770553at_rat,N2))),one_one_rat)),K)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),N2)),aa_nat_rat(gbinomial_rat(aa_rat_rat(minus_minus_rat(aa_rat_rat(uminus_uminus_rat,aa_nat_rat(semiri681578069525770553at_rat,K))),one_one_rat)),N2)) ).

% gbinomial_index_swap
tff(fact_3915_int__bit__bound,axiom,
    ! [K: int] :
      ~ ! [N: nat] :
          ( ! [M5: nat] :
              ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N),M5)
             => ( aa_nat_o(aa_int_fun_nat_o(bit_se1146084159140164899it_int,K),M5)
              <=> aa_nat_o(aa_int_fun_nat_o(bit_se1146084159140164899it_int,K),N) ) )
         => ~ ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N)
             => ( aa_nat_o(aa_int_fun_nat_o(bit_se1146084159140164899it_int,K),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N),one_one_nat))
              <=> ~ aa_nat_o(aa_int_fun_nat_o(bit_se1146084159140164899it_int,K),N) ) ) ) ).

% int_bit_bound
tff(fact_3916_gbinomial__minus,axiom,
    ! [A: rat,K: nat] : aa_nat_rat(gbinomial_rat(aa_rat_rat(uminus_uminus_rat,A)),K) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),K)),aa_nat_rat(gbinomial_rat(aa_rat_rat(minus_minus_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),aa_nat_rat(semiri681578069525770553at_rat,K))),one_one_rat)),K)) ).

% gbinomial_minus
tff(fact_3917_gbinomial__reduce__nat,axiom,
    ! [K: nat,A: rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),K)
     => ( aa_nat_rat(gbinomial_rat(A),K) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(gbinomial_rat(aa_rat_rat(minus_minus_rat(A),one_one_rat)),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,K),one_one_nat))),aa_nat_rat(gbinomial_rat(aa_rat_rat(minus_minus_rat(A),one_one_rat)),K)) ) ) ).

% gbinomial_reduce_nat
tff(fact_3918_gbinomial__sum__lower__neg,axiom,
    ! [A: rat,M: nat] : groups2906978787729119204at_rat(aTP_Lamm_il(A),aa_nat_set_nat(set_ord_atMost_nat,M)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),M)),aa_nat_rat(gbinomial_rat(aa_rat_rat(minus_minus_rat(A),one_one_rat)),M)) ).

% gbinomial_sum_lower_neg
tff(fact_3919_numeral__and__num,axiom,
    ! [M: num,N2: num] : aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,aa_num_int(numeral_numeral_int,M)),aa_num_int(numeral_numeral_int,N2)) = aa_option_num_int(case_option_int_num(zero_zero_int,numeral_numeral_int),aa_num_option_num(bit_un7362597486090784418nd_num(M),N2)) ).

% numeral_and_num
tff(fact_3920_numeral__and__num,axiom,
    ! [M: num,N2: num] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se727722235901077358nd_nat,aa_num_nat(numeral_numeral_nat,M)),aa_num_nat(numeral_numeral_nat,N2)) = case_option_nat_num(zero_zero_nat,numeral_numeral_nat,aa_num_option_num(bit_un7362597486090784418nd_num(M),N2)) ).

% numeral_and_num
tff(fact_3921_numeral__and__num,axiom,
    ! [M: num,N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3949692690581998587nteger,aa_num_Code_integer(numera6620942414471956472nteger,M)),aa_num_Code_integer(numera6620942414471956472nteger,N2)) = case_o356765784539232260er_num(zero_z3403309356797280102nteger,numera6620942414471956472nteger,aa_num_option_num(bit_un7362597486090784418nd_num(M),N2)) ).

% numeral_and_num
tff(fact_3922_numeral__and__num,axiom,
    ! [M: num,N2: num] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se2773287842338716102atural,aa_num_Code_natural(numera5444537566228673987atural,M)),aa_num_Code_natural(numera5444537566228673987atural,N2)) = case_o5621594795226839503al_num(zero_z2226904508553997617atural,numera5444537566228673987atural,aa_num_option_num(bit_un7362597486090784418nd_num(M),N2)) ).

% numeral_and_num
tff(fact_3923_gbinomial__sum__up__index,axiom,
    ! [K: nat,N2: nat] : groups2906978787729119204at_rat(aTP_Lamm_im(K),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2)) = aa_nat_rat(gbinomial_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(semiri681578069525770553at_rat,N2)),one_one_rat)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,K),one_one_nat)) ).

% gbinomial_sum_up_index
tff(fact_3924_gbinomial__partial__sum__poly,axiom,
    ! [M: nat,A: rat,X2: rat,Y: rat] : groups2906978787729119204at_rat(aa_rat_fun_nat_rat(aa_rat3146053865535587600at_rat(aa_rat7467449789483521253at_rat(aTP_Lamm_in(M),A),X2),Y),aa_nat_set_nat(set_ord_atMost_nat,M)) = groups2906978787729119204at_rat(aa_rat_fun_nat_rat(aa_rat3146053865535587600at_rat(aa_rat7467449789483521253at_rat(aTP_Lamm_io(M),A),X2),Y),aa_nat_set_nat(set_ord_atMost_nat,M)) ).

% gbinomial_partial_sum_poly
tff(fact_3925_even__bit__succ__iff,axiom,
    ! [A: int,N2: nat] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A)
     => ( aa_nat_o(aa_int_fun_nat_o(bit_se1146084159140164899it_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),A)),N2)
      <=> ( aa_nat_o(aa_int_fun_nat_o(bit_se1146084159140164899it_int,A),N2)
          | ( N2 = zero_zero_nat ) ) ) ) ).

% even_bit_succ_iff
tff(fact_3926_even__bit__succ__iff,axiom,
    ! [A: code_integer,N2: nat] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A)
     => ( aa_nat_o(aa_Cod1075288278386115654_nat_o(bit_se9216721137139052372nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,one_one_Code_integer),A)),N2)
      <=> ( aa_nat_o(aa_Cod1075288278386115654_nat_o(bit_se9216721137139052372nteger,A),N2)
          | ( N2 = zero_zero_nat ) ) ) ) ).

% even_bit_succ_iff
tff(fact_3927_even__bit__succ__iff,axiom,
    ! [A: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(bit_se1148574629649215175it_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),A)),N2)
      <=> ( aa_nat_o(aa_nat_fun_nat_o(bit_se1148574629649215175it_nat,A),N2)
          | ( N2 = zero_zero_nat ) ) ) ) ).

% even_bit_succ_iff
tff(fact_3928_even__bit__succ__iff,axiom,
    ! [A: code_natural,N2: nat] :
      ( aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A)
     => ( aa_nat_o(aa_Cod9120328075896114107_nat_o(bit_se8040316288895769887atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,one_one_Code_natural),A)),N2)
      <=> ( aa_nat_o(aa_Cod9120328075896114107_nat_o(bit_se8040316288895769887atural,A),N2)
          | ( N2 = zero_zero_nat ) ) ) ) ).

% even_bit_succ_iff
tff(fact_3929_odd__bit__iff__bit__pred,axiom,
    ! [A: int,N2: nat] :
      ( ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A)
     => ( aa_nat_o(aa_int_fun_nat_o(bit_se1146084159140164899it_int,A),N2)
      <=> ( aa_nat_o(aa_int_fun_nat_o(bit_se1146084159140164899it_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),one_one_int)),N2)
          | ( N2 = zero_zero_nat ) ) ) ) ).

% odd_bit_iff_bit_pred
tff(fact_3930_odd__bit__iff__bit__pred,axiom,
    ! [A: code_integer,N2: nat] :
      ( ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A)
     => ( aa_nat_o(aa_Cod1075288278386115654_nat_o(bit_se9216721137139052372nteger,A),N2)
      <=> ( aa_nat_o(aa_Cod1075288278386115654_nat_o(bit_se9216721137139052372nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),one_one_Code_integer)),N2)
          | ( N2 = zero_zero_nat ) ) ) ) ).

% odd_bit_iff_bit_pred
tff(fact_3931_odd__bit__iff__bit__pred,axiom,
    ! [A: nat,N2: nat] :
      ( ~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A)
     => ( aa_nat_o(aa_nat_fun_nat_o(bit_se1148574629649215175it_nat,A),N2)
      <=> ( aa_nat_o(aa_nat_fun_nat_o(bit_se1148574629649215175it_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,A),one_one_nat)),N2)
          | ( N2 = zero_zero_nat ) ) ) ) ).

% odd_bit_iff_bit_pred
tff(fact_3932_odd__bit__iff__bit__pred,axiom,
    ! [A: code_natural,N2: nat] :
      ( ~ aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A)
     => ( aa_nat_o(aa_Cod9120328075896114107_nat_o(bit_se8040316288895769887atural,A),N2)
      <=> ( aa_nat_o(aa_Cod9120328075896114107_nat_o(bit_se8040316288895769887atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(minus_7197305767214868737atural,A),one_one_Code_natural)),N2)
          | ( N2 = zero_zero_nat ) ) ) ) ).

% odd_bit_iff_bit_pred
tff(fact_3933_and__num_Osimps_I9_J,axiom,
    ! [M: num,N2: num] : aa_num_option_num(bit_un7362597486090784418nd_num(aa_num_num(bit1,M)),aa_num_num(bit1,N2)) = aa_opt5369159329878751634on_num(case_o6005452278849405969um_num(aa_num_option_num(some_num,one),aTP_Lamm_ij),aa_num_option_num(bit_un7362597486090784418nd_num(M),N2)) ).

% and_num.simps(9)
tff(fact_3934_gbinomial__absorption_H,axiom,
    ! [K: nat,A: rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),K)
     => ( aa_nat_rat(gbinomial_rat(A),K) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(divide_divide_rat(A),aa_nat_rat(semiri681578069525770553at_rat,K))),aa_nat_rat(gbinomial_rat(aa_rat_rat(minus_minus_rat(A),one_one_rat)),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,K),one_one_nat))) ) ) ).

% gbinomial_absorption'
tff(fact_3935_gbinomial__partial__sum__poly__xpos,axiom,
    ! [M: nat,A: rat,X2: rat,Y: rat] : groups2906978787729119204at_rat(aa_rat_fun_nat_rat(aa_rat3146053865535587600at_rat(aa_rat7467449789483521253at_rat(aTP_Lamm_in(M),A),X2),Y),aa_nat_set_nat(set_ord_atMost_nat,M)) = groups2906978787729119204at_rat(aa_rat_fun_nat_rat(aa_rat3146053865535587600at_rat(aa_rat7467449789483521253at_rat(aTP_Lamm_ip(M),A),X2),Y),aa_nat_set_nat(set_ord_atMost_nat,M)) ).

% gbinomial_partial_sum_poly_xpos
tff(fact_3936_gbinomial__sum__nat__pow2,axiom,
    ! [M: nat] : groups2906978787729119204at_rat(aTP_Lamm_iq(M),aa_nat_set_nat(set_ord_atMost_nat,M)) = aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one))),M) ).

% gbinomial_sum_nat_pow2
tff(fact_3937_bit__sum__mult__2__cases,axiom,
    ! [A: int,B: int,N2: nat] :
      ( ! [J3: nat] : ~ aa_nat_o(aa_int_fun_nat_o(bit_se1146084159140164899it_int,A),aa_nat_nat(suc,J3))
     => ( aa_nat_o(aa_int_fun_nat_o(bit_se1146084159140164899it_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),B))),N2)
      <=> $ite(N2 = zero_zero_nat,~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A),aa_nat_o(aa_int_fun_nat_o(bit_se1146084159140164899it_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),B)),N2)) ) ) ).

% bit_sum_mult_2_cases
tff(fact_3938_bit__sum__mult__2__cases,axiom,
    ! [A: code_integer,B: code_integer,N2: nat] :
      ( ! [J3: nat] : ~ aa_nat_o(aa_Cod1075288278386115654_nat_o(bit_se9216721137139052372nteger,A),aa_nat_nat(suc,J3))
     => ( aa_nat_o(aa_Cod1075288278386115654_nat_o(bit_se9216721137139052372nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),B))),N2)
      <=> $ite(N2 = zero_zero_nat,~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A),aa_nat_o(aa_Cod1075288278386115654_nat_o(bit_se9216721137139052372nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),B)),N2)) ) ) ).

% bit_sum_mult_2_cases
tff(fact_3939_bit__sum__mult__2__cases,axiom,
    ! [A: nat,B: nat,N2: nat] :
      ( ! [J3: nat] : ~ aa_nat_o(aa_nat_fun_nat_o(bit_se1148574629649215175it_nat,A),aa_nat_nat(suc,J3))
     => ( aa_nat_o(aa_nat_fun_nat_o(bit_se1148574629649215175it_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),B))),N2)
      <=> $ite(N2 = zero_zero_nat,~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A),aa_nat_o(aa_nat_fun_nat_o(bit_se1148574629649215175it_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),B)),N2)) ) ) ).

% bit_sum_mult_2_cases
tff(fact_3940_bit__sum__mult__2__cases,axiom,
    ! [A: code_natural,B: code_natural,N2: nat] :
      ( ! [J3: nat] : ~ aa_nat_o(aa_Cod9120328075896114107_nat_o(bit_se8040316288895769887atural,A),aa_nat_nat(suc,J3))
     => ( aa_nat_o(aa_Cod9120328075896114107_nat_o(bit_se8040316288895769887atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),B))),N2)
      <=> $ite(N2 = zero_zero_nat,~ aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A),aa_nat_o(aa_Cod9120328075896114107_nat_o(bit_se8040316288895769887atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),B)),N2)) ) ) ).

% bit_sum_mult_2_cases
tff(fact_3941_and__not__num_Osimps_I8_J,axiom,
    ! [M: num,N2: num] : aa_num_option_num(bit_and_not_num(aa_num_num(bit1,M)),aa_num_num(bit0,N2)) = aa_opt5369159329878751634on_num(case_o6005452278849405969um_num(aa_num_option_num(some_num,one),aTP_Lamm_ij),aa_num_option_num(bit_and_not_num(M),N2)) ).

% and_not_num.simps(8)
tff(fact_3942_bit__rec,axiom,
    ! [A: int,N2: nat] :
      ( aa_nat_o(aa_int_fun_nat_o(bit_se1146084159140164899it_int,A),N2)
    <=> $ite(N2 = zero_zero_nat,~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A),aa_nat_o(aa_int_fun_nat_o(bit_se1146084159140164899it_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat))) ) ).

% bit_rec
tff(fact_3943_bit__rec,axiom,
    ! [A: code_integer,N2: nat] :
      ( aa_nat_o(aa_Cod1075288278386115654_nat_o(bit_se9216721137139052372nteger,A),N2)
    <=> $ite(N2 = zero_zero_nat,~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A),aa_nat_o(aa_Cod1075288278386115654_nat_o(bit_se9216721137139052372nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)))),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat))) ) ).

% bit_rec
tff(fact_3944_bit__rec,axiom,
    ! [A: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(bit_se1148574629649215175it_nat,A),N2)
    <=> $ite(N2 = zero_zero_nat,~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A),aa_nat_o(aa_nat_fun_nat_o(bit_se1148574629649215175it_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat))) ) ).

% bit_rec
tff(fact_3945_bit__rec,axiom,
    ! [A: code_natural,N2: nat] :
      ( aa_nat_o(aa_Cod9120328075896114107_nat_o(bit_se8040316288895769887atural,A),N2)
    <=> $ite(N2 = zero_zero_nat,~ aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A),aa_nat_o(aa_Cod9120328075896114107_nat_o(bit_se8040316288895769887atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one)))),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat))) ) ).

% bit_rec
tff(fact_3946_and__nat__unfold,axiom,
    ! [M: nat,N2: nat] :
      aa_nat_nat(aa_nat_fun_nat_nat(bit_se727722235901077358nd_nat,M),N2) = $ite(
        ( ( M = zero_zero_nat )
        | ( N2 = zero_zero_nat ) ),
        zero_zero_nat,
        aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,M),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,N2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(bit_se727722235901077358nd_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,M),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,N2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) ) ).

% and_nat_unfold
tff(fact_3947_and__nat__rec,axiom,
    ! [M: nat,N2: nat] :
      aa_nat_nat(aa_nat_fun_nat_nat(bit_se727722235901077358nd_nat,M),N2) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,
          aa_o_nat(zero_n2687167440665602831ol_nat,
            ( ~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),M)
            & ~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2) ))),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(bit_se727722235901077358nd_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,M),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,N2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) ).

% and_nat_rec
tff(fact_3948_set__bit__eq,axiom,
    ! [N2: nat,K: int] : aa_int_int(aa_nat_fun_int_int(bit_se7879613467334960850it_int,N2),K) = aa_int_int(aa_int_fun_int_int(plus_plus_int,K),aa_int_int(aa_int_fun_int_int(times_times_int,aa_o_int(zero_n2684676970156552555ol_int,~ aa_nat_o(aa_int_fun_nat_o(bit_se1146084159140164899it_int,K),N2))),aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),N2))) ).

% set_bit_eq
tff(fact_3949_and__not__num_Oelims,axiom,
    ! [X2: num,Xa: num,Y: option_num] :
      ( ( aa_num_option_num(bit_and_not_num(X2),Xa) = Y )
     => ( ( ( X2 = one )
         => ( ( Xa = one )
           => ( Y != none_num ) ) )
       => ( ( ( X2 = one )
           => ( ? [N: num] : Xa = aa_num_num(bit0,N)
             => ( Y != aa_num_option_num(some_num,one) ) ) )
         => ( ( ( X2 = one )
             => ( ? [N: num] : Xa = aa_num_num(bit1,N)
               => ( Y != none_num ) ) )
           => ( ! [M4: num] :
                  ( ( X2 = aa_num_num(bit0,M4) )
                 => ( ( Xa = one )
                   => ( Y != aa_num_option_num(some_num,aa_num_num(bit0,M4)) ) ) )
             => ( ! [M4: num] :
                    ( ( X2 = aa_num_num(bit0,M4) )
                   => ! [N: num] :
                        ( ( Xa = aa_num_num(bit0,N) )
                       => ( Y != aa_opt5369159329878751634on_num(map_option_num_num(bit0),aa_num_option_num(bit_and_not_num(M4),N)) ) ) )
               => ( ! [M4: num] :
                      ( ( X2 = aa_num_num(bit0,M4) )
                     => ! [N: num] :
                          ( ( Xa = aa_num_num(bit1,N) )
                         => ( Y != aa_opt5369159329878751634on_num(map_option_num_num(bit0),aa_num_option_num(bit_and_not_num(M4),N)) ) ) )
                 => ( ! [M4: num] :
                        ( ( X2 = aa_num_num(bit1,M4) )
                       => ( ( Xa = one )
                         => ( Y != aa_num_option_num(some_num,aa_num_num(bit0,M4)) ) ) )
                   => ( ! [M4: num] :
                          ( ( X2 = aa_num_num(bit1,M4) )
                         => ! [N: num] :
                              ( ( Xa = aa_num_num(bit0,N) )
                             => ( Y != aa_opt5369159329878751634on_num(case_o6005452278849405969um_num(aa_num_option_num(some_num,one),aTP_Lamm_ij),aa_num_option_num(bit_and_not_num(M4),N)) ) ) )
                     => ~ ! [M4: num] :
                            ( ( X2 = aa_num_num(bit1,M4) )
                           => ! [N: num] :
                                ( ( Xa = aa_num_num(bit1,N) )
                               => ( Y != aa_opt5369159329878751634on_num(map_option_num_num(bit0),aa_num_option_num(bit_and_not_num(M4),N)) ) ) ) ) ) ) ) ) ) ) ) ) ).

% and_not_num.elims
tff(fact_3950_and__not__num_Opelims,axiom,
    ! [X2: num,Xa: num,Y: option_num] :
      ( ( aa_num_option_num(bit_and_not_num(X2),Xa) = Y )
     => ( accp_P3113834385874906142um_num(bit_and_not_num_rel,product_Pair_num_num(X2,Xa))
       => ( ( ( X2 = one )
           => ( ( Xa = one )
             => ( ( Y = none_num )
               => ~ accp_P3113834385874906142um_num(bit_and_not_num_rel,product_Pair_num_num(one,one)) ) ) )
         => ( ( ( X2 = one )
             => ! [N: num] :
                  ( ( Xa = aa_num_num(bit0,N) )
                 => ( ( Y = aa_num_option_num(some_num,one) )
                   => ~ accp_P3113834385874906142um_num(bit_and_not_num_rel,product_Pair_num_num(one,aa_num_num(bit0,N))) ) ) )
           => ( ( ( X2 = one )
               => ! [N: num] :
                    ( ( Xa = aa_num_num(bit1,N) )
                   => ( ( Y = none_num )
                     => ~ accp_P3113834385874906142um_num(bit_and_not_num_rel,product_Pair_num_num(one,aa_num_num(bit1,N))) ) ) )
             => ( ! [M4: num] :
                    ( ( X2 = aa_num_num(bit0,M4) )
                   => ( ( Xa = one )
                     => ( ( Y = aa_num_option_num(some_num,aa_num_num(bit0,M4)) )
                       => ~ accp_P3113834385874906142um_num(bit_and_not_num_rel,product_Pair_num_num(aa_num_num(bit0,M4),one)) ) ) )
               => ( ! [M4: num] :
                      ( ( X2 = aa_num_num(bit0,M4) )
                     => ! [N: num] :
                          ( ( Xa = aa_num_num(bit0,N) )
                         => ( ( Y = aa_opt5369159329878751634on_num(map_option_num_num(bit0),aa_num_option_num(bit_and_not_num(M4),N)) )
                           => ~ accp_P3113834385874906142um_num(bit_and_not_num_rel,product_Pair_num_num(aa_num_num(bit0,M4),aa_num_num(bit0,N))) ) ) )
                 => ( ! [M4: num] :
                        ( ( X2 = aa_num_num(bit0,M4) )
                       => ! [N: num] :
                            ( ( Xa = aa_num_num(bit1,N) )
                           => ( ( Y = aa_opt5369159329878751634on_num(map_option_num_num(bit0),aa_num_option_num(bit_and_not_num(M4),N)) )
                             => ~ accp_P3113834385874906142um_num(bit_and_not_num_rel,product_Pair_num_num(aa_num_num(bit0,M4),aa_num_num(bit1,N))) ) ) )
                   => ( ! [M4: num] :
                          ( ( X2 = aa_num_num(bit1,M4) )
                         => ( ( Xa = one )
                           => ( ( Y = aa_num_option_num(some_num,aa_num_num(bit0,M4)) )
                             => ~ accp_P3113834385874906142um_num(bit_and_not_num_rel,product_Pair_num_num(aa_num_num(bit1,M4),one)) ) ) )
                     => ( ! [M4: num] :
                            ( ( X2 = aa_num_num(bit1,M4) )
                           => ! [N: num] :
                                ( ( Xa = aa_num_num(bit0,N) )
                               => ( ( Y = aa_opt5369159329878751634on_num(case_o6005452278849405969um_num(aa_num_option_num(some_num,one),aTP_Lamm_ij),aa_num_option_num(bit_and_not_num(M4),N)) )
                                 => ~ accp_P3113834385874906142um_num(bit_and_not_num_rel,product_Pair_num_num(aa_num_num(bit1,M4),aa_num_num(bit0,N))) ) ) )
                       => ~ ! [M4: num] :
                              ( ( X2 = aa_num_num(bit1,M4) )
                             => ! [N: num] :
                                  ( ( Xa = aa_num_num(bit1,N) )
                                 => ( ( Y = aa_opt5369159329878751634on_num(map_option_num_num(bit0),aa_num_option_num(bit_and_not_num(M4),N)) )
                                   => ~ accp_P3113834385874906142um_num(bit_and_not_num_rel,product_Pair_num_num(aa_num_num(bit1,M4),aa_num_num(bit1,N))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% and_not_num.pelims
tff(fact_3951_and__num_Opelims,axiom,
    ! [X2: num,Xa: num,Y: option_num] :
      ( ( aa_num_option_num(bit_un7362597486090784418nd_num(X2),Xa) = Y )
     => ( accp_P3113834385874906142um_num(bit_un4731106466462545111um_rel,product_Pair_num_num(X2,Xa))
       => ( ( ( X2 = one )
           => ( ( Xa = one )
             => ( ( Y = aa_num_option_num(some_num,one) )
               => ~ accp_P3113834385874906142um_num(bit_un4731106466462545111um_rel,product_Pair_num_num(one,one)) ) ) )
         => ( ( ( X2 = one )
             => ! [N: num] :
                  ( ( Xa = aa_num_num(bit0,N) )
                 => ( ( Y = none_num )
                   => ~ accp_P3113834385874906142um_num(bit_un4731106466462545111um_rel,product_Pair_num_num(one,aa_num_num(bit0,N))) ) ) )
           => ( ( ( X2 = one )
               => ! [N: num] :
                    ( ( Xa = aa_num_num(bit1,N) )
                   => ( ( Y = aa_num_option_num(some_num,one) )
                     => ~ accp_P3113834385874906142um_num(bit_un4731106466462545111um_rel,product_Pair_num_num(one,aa_num_num(bit1,N))) ) ) )
             => ( ! [M4: num] :
                    ( ( X2 = aa_num_num(bit0,M4) )
                   => ( ( Xa = one )
                     => ( ( Y = none_num )
                       => ~ accp_P3113834385874906142um_num(bit_un4731106466462545111um_rel,product_Pair_num_num(aa_num_num(bit0,M4),one)) ) ) )
               => ( ! [M4: num] :
                      ( ( X2 = aa_num_num(bit0,M4) )
                     => ! [N: num] :
                          ( ( Xa = aa_num_num(bit0,N) )
                         => ( ( Y = aa_opt5369159329878751634on_num(map_option_num_num(bit0),aa_num_option_num(bit_un7362597486090784418nd_num(M4),N)) )
                           => ~ accp_P3113834385874906142um_num(bit_un4731106466462545111um_rel,product_Pair_num_num(aa_num_num(bit0,M4),aa_num_num(bit0,N))) ) ) )
                 => ( ! [M4: num] :
                        ( ( X2 = aa_num_num(bit0,M4) )
                       => ! [N: num] :
                            ( ( Xa = aa_num_num(bit1,N) )
                           => ( ( Y = aa_opt5369159329878751634on_num(map_option_num_num(bit0),aa_num_option_num(bit_un7362597486090784418nd_num(M4),N)) )
                             => ~ accp_P3113834385874906142um_num(bit_un4731106466462545111um_rel,product_Pair_num_num(aa_num_num(bit0,M4),aa_num_num(bit1,N))) ) ) )
                   => ( ! [M4: num] :
                          ( ( X2 = aa_num_num(bit1,M4) )
                         => ( ( Xa = one )
                           => ( ( Y = aa_num_option_num(some_num,one) )
                             => ~ accp_P3113834385874906142um_num(bit_un4731106466462545111um_rel,product_Pair_num_num(aa_num_num(bit1,M4),one)) ) ) )
                     => ( ! [M4: num] :
                            ( ( X2 = aa_num_num(bit1,M4) )
                           => ! [N: num] :
                                ( ( Xa = aa_num_num(bit0,N) )
                               => ( ( Y = aa_opt5369159329878751634on_num(map_option_num_num(bit0),aa_num_option_num(bit_un7362597486090784418nd_num(M4),N)) )
                                 => ~ accp_P3113834385874906142um_num(bit_un4731106466462545111um_rel,product_Pair_num_num(aa_num_num(bit1,M4),aa_num_num(bit0,N))) ) ) )
                       => ~ ! [M4: num] :
                              ( ( X2 = aa_num_num(bit1,M4) )
                             => ! [N: num] :
                                  ( ( Xa = aa_num_num(bit1,N) )
                                 => ( ( Y = aa_opt5369159329878751634on_num(case_o6005452278849405969um_num(aa_num_option_num(some_num,one),aTP_Lamm_ij),aa_num_option_num(bit_un7362597486090784418nd_num(M4),N)) )
                                   => ~ accp_P3113834385874906142um_num(bit_un4731106466462545111um_rel,product_Pair_num_num(aa_num_num(bit1,M4),aa_num_num(bit1,N))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% and_num.pelims
tff(fact_3952_gbinomial__code,axiom,
    ! [A: rat,K: nat] :
      aa_nat_rat(gbinomial_rat(A),K) = $ite(K = zero_zero_nat,one_one_rat,aa_rat_rat(divide_divide_rat(aa_rat_rat(set_fo1949268297981939178at_rat(aTP_Lamm_ir(A),zero_zero_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,K),one_one_nat)),one_one_rat)),aa_nat_rat(semiri773545260158071498ct_rat,K))) ).

% gbinomial_code
tff(fact_3953_xor__num_Oelims,axiom,
    ! [X2: num,Xa: num,Y: option_num] :
      ( ( aa_num_option_num(bit_un2480387367778600638or_num(X2),Xa) = Y )
     => ( ( ( X2 = one )
         => ( ( Xa = one )
           => ( Y != none_num ) ) )
       => ( ( ( X2 = one )
           => ! [N: num] :
                ( ( Xa = aa_num_num(bit0,N) )
               => ( Y != aa_num_option_num(some_num,aa_num_num(bit1,N)) ) ) )
         => ( ( ( X2 = one )
             => ! [N: num] :
                  ( ( Xa = aa_num_num(bit1,N) )
                 => ( Y != aa_num_option_num(some_num,aa_num_num(bit0,N)) ) ) )
           => ( ! [M4: num] :
                  ( ( X2 = aa_num_num(bit0,M4) )
                 => ( ( Xa = one )
                   => ( Y != aa_num_option_num(some_num,aa_num_num(bit1,M4)) ) ) )
             => ( ! [M4: num] :
                    ( ( X2 = aa_num_num(bit0,M4) )
                   => ! [N: num] :
                        ( ( Xa = aa_num_num(bit0,N) )
                       => ( Y != aa_opt5369159329878751634on_num(map_option_num_num(bit0),aa_num_option_num(bit_un2480387367778600638or_num(M4),N)) ) ) )
               => ( ! [M4: num] :
                      ( ( X2 = aa_num_num(bit0,M4) )
                     => ! [N: num] :
                          ( ( Xa = aa_num_num(bit1,N) )
                         => ( Y != aa_num_option_num(some_num,aa_option_num_num(case_option_num_num(one,bit1),aa_num_option_num(bit_un2480387367778600638or_num(M4),N))) ) ) )
                 => ( ! [M4: num] :
                        ( ( X2 = aa_num_num(bit1,M4) )
                       => ( ( Xa = one )
                         => ( Y != aa_num_option_num(some_num,aa_num_num(bit0,M4)) ) ) )
                   => ( ! [M4: num] :
                          ( ( X2 = aa_num_num(bit1,M4) )
                         => ! [N: num] :
                              ( ( Xa = aa_num_num(bit0,N) )
                             => ( Y != aa_num_option_num(some_num,aa_option_num_num(case_option_num_num(one,bit1),aa_num_option_num(bit_un2480387367778600638or_num(M4),N))) ) ) )
                     => ~ ! [M4: num] :
                            ( ( X2 = aa_num_num(bit1,M4) )
                           => ! [N: num] :
                                ( ( Xa = aa_num_num(bit1,N) )
                               => ( Y != aa_opt5369159329878751634on_num(map_option_num_num(bit0),aa_num_option_num(bit_un2480387367778600638or_num(M4),N)) ) ) ) ) ) ) ) ) ) ) ) ) ).

% xor_num.elims
tff(fact_3954_choose__alternating__sum,axiom,
    ! [N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => ( groups2906978787729119204at_rat(aTP_Lamm_is(N2),aa_nat_set_nat(set_ord_atMost_nat,N2)) = zero_zero_rat ) ) ).

% choose_alternating_sum
tff(fact_3955_choose__alternating__sum,axiom,
    ! [N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => ( groups3539618377306564664at_int(aa_nat_fun_nat_int(aTP_Lamm_it,N2),aa_nat_set_nat(set_ord_atMost_nat,N2)) = zero_zero_int ) ) ).

% choose_alternating_sum
tff(fact_3956_choose__alternating__sum,axiom,
    ! [N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => ( groups7501900531339628137nteger(aTP_Lamm_iu(N2),aa_nat_set_nat(set_ord_atMost_nat,N2)) = zero_z3403309356797280102nteger ) ) ).

% choose_alternating_sum
tff(fact_3957_choose__linear__sum,axiom,
    ! [N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(aa_nat_fun_nat_nat(aTP_Lamm_iv,N2)),aa_nat_set_nat(set_ord_atMost_nat,N2)) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat))) ).

% choose_linear_sum
tff(fact_3958_binomial__r__part__sum,axiom,
    ! [M: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(aa_nat_fun_nat_nat(binomial,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),M)),one_one_nat))),aa_nat_set_nat(set_ord_atMost_nat,M)) = aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),M)) ).

% binomial_r_part_sum
tff(fact_3959_sum_Otriangle__reindex,axiom,
    ! [G: fun_nat_fun_nat_nat,N2: nat] : aa_set4749074711808745205at_nat(groups977919841031483927at_nat(aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,G)),aa_fun7046812543386002057at_nat(collec3392354462482085612at_nat,aa_fun7564604662015400456_nat_o(produc6081775807080527818_nat_o,aTP_Lamm_iw(N2)))) = aa_set_nat_nat(groups3542108847815614940at_nat(aTP_Lamm_hx(G)),aa_nat_set_nat(set_ord_lessThan_nat,N2)) ).

% sum.triangle_reindex
tff(fact_3960_lessThan__eq__iff,axiom,
    ! [X2: nat,Y: nat] :
      ( ( aa_nat_set_nat(set_ord_lessThan_nat,X2) = aa_nat_set_nat(set_ord_lessThan_nat,Y) )
    <=> ( X2 = Y ) ) ).

% lessThan_eq_iff
tff(fact_3961_lessThan__iff,axiom,
    ! [I: $o,K: $o] :
      ( member_o((I),aa_o_set_o(set_ord_lessThan_o,(K)))
    <=> aa_o_o(aa_o_fun_o_o(ord_less_o,(I)),(K)) ) ).

% lessThan_iff
tff(fact_3962_lessThan__iff,axiom,
    ! [I: code_integer,K: code_integer] :
      ( member_Code_integer(I,aa_Cod2813182003028390446nteger(set_or5754767410780653050nteger,K))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,I),K) ) ).

% lessThan_iff
tff(fact_3963_lessThan__iff,axiom,
    ! [I: rat,K: rat] :
      ( member_rat(I,set_ord_lessThan_rat(K))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,I),K) ) ).

% lessThan_iff
tff(fact_3964_lessThan__iff,axiom,
    ! [I: num,K: num] :
      ( member_num(I,set_ord_lessThan_num(K))
    <=> aa_num_o(aa_num_fun_num_o(ord_less_num,I),K) ) ).

% lessThan_iff
tff(fact_3965_lessThan__iff,axiom,
    ! [I: int,K: int] :
      ( member_int(I,aa_int_set_int(set_ord_lessThan_int,K))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,I),K) ) ).

% lessThan_iff
tff(fact_3966_lessThan__iff,axiom,
    ! [I: nat,K: nat] :
      ( member_nat(I,aa_nat_set_nat(set_ord_lessThan_nat,K))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,I),K) ) ).

% lessThan_iff
tff(fact_3967_binomial__n__n,axiom,
    ! [N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(binomial,N2),N2) = one_one_nat ).

% binomial_n_n
tff(fact_3968_lessThan__subset__iff,axiom,
    ! [X2: rat,Y: rat] :
      ( ord_less_eq_set_rat(set_ord_lessThan_rat(X2),set_ord_lessThan_rat(Y))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,X2),Y) ) ).

% lessThan_subset_iff
tff(fact_3969_lessThan__subset__iff,axiom,
    ! [X2: num,Y: num] :
      ( ord_less_eq_set_num(set_ord_lessThan_num(X2),set_ord_lessThan_num(Y))
    <=> aa_num_o(aa_num_fun_num_o(ord_less_eq_num,X2),Y) ) ).

% lessThan_subset_iff
tff(fact_3970_lessThan__subset__iff,axiom,
    ! [X2: int,Y: int] :
      ( ord_less_eq_set_int(aa_int_set_int(set_ord_lessThan_int,X2),aa_int_set_int(set_ord_lessThan_int,Y))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,X2),Y) ) ).

% lessThan_subset_iff
tff(fact_3971_lessThan__subset__iff,axiom,
    ! [X2: nat,Y: nat] :
      ( aa_set_nat_o(ord_less_eq_set_nat(aa_nat_set_nat(set_ord_lessThan_nat,X2)),aa_nat_set_nat(set_ord_lessThan_nat,Y))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,X2),Y) ) ).

% lessThan_subset_iff
tff(fact_3972_binomial__Suc__Suc,axiom,
    ! [N2: nat,K: nat] : aa_nat_nat(aa_nat_fun_nat_nat(binomial,aa_nat_nat(suc,N2)),aa_nat_nat(suc,K)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(binomial,N2),K)),aa_nat_nat(aa_nat_fun_nat_nat(binomial,N2),aa_nat_nat(suc,K))) ).

% binomial_Suc_Suc
tff(fact_3973_binomial__n__0,axiom,
    ! [N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(binomial,N2),zero_zero_nat) = one_one_nat ).

% binomial_n_0
tff(fact_3974_sum_OlessThan__Suc,axiom,
    ! [G: fun_na2338080690716861136at_nat,N2: nat] : groups6857163185585827899at_nat(G,aa_nat_set_nat(set_ord_lessThan_nat,aa_nat_nat(suc,N2))) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(groups6857163185585827899at_nat(G,aa_nat_set_nat(set_ord_lessThan_nat,N2))),aa_nat2240542744625857721at_nat(G,N2)) ).

% sum.lessThan_Suc
tff(fact_3975_sum_OlessThan__Suc,axiom,
    ! [G: fun_nat_rat,N2: nat] : groups2906978787729119204at_rat(G,aa_nat_set_nat(set_ord_lessThan_nat,aa_nat_nat(suc,N2))) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,groups2906978787729119204at_rat(G,aa_nat_set_nat(set_ord_lessThan_nat,N2))),aa_nat_rat(G,N2)) ).

% sum.lessThan_Suc
tff(fact_3976_sum_OlessThan__Suc,axiom,
    ! [G: fun_nat_int,N2: nat] : groups3539618377306564664at_int(G,aa_nat_set_nat(set_ord_lessThan_nat,aa_nat_nat(suc,N2))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,groups3539618377306564664at_int(G,aa_nat_set_nat(set_ord_lessThan_nat,N2))),aa_nat_int(G,N2)) ).

% sum.lessThan_Suc
tff(fact_3977_sum_OlessThan__Suc,axiom,
    ! [G: fun_nat_nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_ord_lessThan_nat,aa_nat_nat(suc,N2))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_ord_lessThan_nat,N2))),aa_nat_nat(G,N2)) ).

% sum.lessThan_Suc
tff(fact_3978_choose__one,axiom,
    ! [N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(binomial,N2),one_one_nat) = N2 ).

% choose_one
tff(fact_3979_lessThan__def,axiom,
    ! [U: code_integer] : aa_Cod2813182003028390446nteger(set_or5754767410780653050nteger,U) = collect_Code_integer(aa_Cod326357343816142457eger_o(aTP_Lamm_bd,U)) ).

% lessThan_def
tff(fact_3980_lessThan__def,axiom,
    ! [U: rat] : set_ord_lessThan_rat(U) = collect_rat(aa_rat_fun_rat_o(aTP_Lamm_bf,U)) ).

% lessThan_def
tff(fact_3981_lessThan__def,axiom,
    ! [U: num] : set_ord_lessThan_num(U) = collect_num(aa_num_fun_num_o(aTP_Lamm_bh,U)) ).

% lessThan_def
tff(fact_3982_lessThan__def,axiom,
    ! [U: int] : aa_int_set_int(set_ord_lessThan_int,U) = collect_int(aa_int_fun_int_o(aTP_Lamm_bl,U)) ).

% lessThan_def
tff(fact_3983_lessThan__def,axiom,
    ! [U: nat] : aa_nat_set_nat(set_ord_lessThan_nat,U) = collect_nat(aa_nat_fun_nat_o(aTP_Lamm_bj,U)) ).

% lessThan_def
tff(fact_3984_choose__mult__lemma,axiom,
    ! [M: nat,R2: nat,K: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(binomial,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),R2)),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),K))),aa_nat_nat(aa_nat_fun_nat_nat(binomial,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),K)),K)) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(binomial,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),R2)),K)),K)),aa_nat_nat(aa_nat_fun_nat_nat(binomial,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),R2)),M)) ).

% choose_mult_lemma
tff(fact_3985_lessThan__Suc__atMost,axiom,
    ! [K: nat] : aa_nat_set_nat(set_ord_lessThan_nat,aa_nat_nat(suc,K)) = aa_nat_set_nat(set_ord_atMost_nat,K) ).

% lessThan_Suc_atMost
tff(fact_3986_bit__integer_Oabs__eq,axiom,
    ! [X2: int] : aa_Cod1075288278386115654_nat_o(bit_se9216721137139052372nteger,aa_int_Code_integer(code_integer_of_int,X2)) = aa_int_fun_nat_o(bit_se1146084159140164899it_int,X2) ).

% bit_integer.abs_eq
tff(fact_3987_lessThan__strict__subset__iff,axiom,
    ! [M: code_integer,N2: code_integer] :
      ( ord_le1307284697595431911nteger(aa_Cod2813182003028390446nteger(set_or5754767410780653050nteger,M),aa_Cod2813182003028390446nteger(set_or5754767410780653050nteger,N2))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,M),N2) ) ).

% lessThan_strict_subset_iff
tff(fact_3988_lessThan__strict__subset__iff,axiom,
    ! [M: rat,N2: rat] :
      ( ord_less_set_rat(set_ord_lessThan_rat(M),set_ord_lessThan_rat(N2))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,M),N2) ) ).

% lessThan_strict_subset_iff
tff(fact_3989_lessThan__strict__subset__iff,axiom,
    ! [M: num,N2: num] :
      ( ord_less_set_num(set_ord_lessThan_num(M),set_ord_lessThan_num(N2))
    <=> aa_num_o(aa_num_fun_num_o(ord_less_num,M),N2) ) ).

% lessThan_strict_subset_iff
tff(fact_3990_lessThan__strict__subset__iff,axiom,
    ! [M: int,N2: int] :
      ( ord_less_set_int(aa_int_set_int(set_ord_lessThan_int,M),aa_int_set_int(set_ord_lessThan_int,N2))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,M),N2) ) ).

% lessThan_strict_subset_iff
tff(fact_3991_lessThan__strict__subset__iff,axiom,
    ! [M: nat,N2: nat] :
      ( ord_less_set_nat(aa_nat_set_nat(set_ord_lessThan_nat,M),aa_nat_set_nat(set_ord_lessThan_nat,N2))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M),N2) ) ).

% lessThan_strict_subset_iff
tff(fact_3992_Suc__times__binomial__add,axiom,
    ! [A: nat,B: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(suc,A)),aa_nat_nat(aa_nat_fun_nat_nat(binomial,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B))),aa_nat_nat(suc,A))) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(suc,B)),aa_nat_nat(aa_nat_fun_nat_nat(binomial,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B))),A)) ).

% Suc_times_binomial_add
tff(fact_3993_binomial__absorb__comp,axiom,
    ! [N2: nat,K: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),K)),aa_nat_nat(aa_nat_fun_nat_nat(binomial,N2),K)) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(binomial,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)),K)) ).

% binomial_absorb_comp
tff(fact_3994_fact__fact__dvd__fact,axiom,
    ! [K: nat,N2: nat] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(semiri3624122377584611663nteger,K)),aa_nat_Code_integer(semiri3624122377584611663nteger,N2))),aa_nat_Code_integer(semiri3624122377584611663nteger,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,K),N2))) ).

% fact_fact_dvd_fact
tff(fact_3995_fact__fact__dvd__fact,axiom,
    ! [K: nat,N2: nat] : aa_rat_o(aa_rat_fun_rat_o(dvd_dvd_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(semiri773545260158071498ct_rat,K)),aa_nat_rat(semiri773545260158071498ct_rat,N2))),aa_nat_rat(semiri773545260158071498ct_rat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,K),N2))) ).

% fact_fact_dvd_fact
tff(fact_3996_fact__fact__dvd__fact,axiom,
    ! [K: nat,N2: nat] : aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(semiri1406184849735516958ct_int,K)),aa_nat_int(semiri1406184849735516958ct_int,N2))),aa_nat_int(semiri1406184849735516958ct_int,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,K),N2))) ).

% fact_fact_dvd_fact
tff(fact_3997_fact__fact__dvd__fact,axiom,
    ! [K: nat,N2: nat] : aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(semiri1408675320244567234ct_nat,K)),aa_nat_nat(semiri1408675320244567234ct_nat,N2))),aa_nat_nat(semiri1408675320244567234ct_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,K),N2))) ).

% fact_fact_dvd_fact
tff(fact_3998_sum_Onat__diff__reindex,axiom,
    ! [G: fun_nat_nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(aa_nat_fun_nat_nat(aTP_Lamm_ix(G),N2)),aa_nat_set_nat(set_ord_lessThan_nat,N2)) = aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_ord_lessThan_nat,N2)) ).

% sum.nat_diff_reindex
tff(fact_3999_Iic__subset__Iio__iff,axiom,
    ! [A: code_integer,B: code_integer] :
      ( ord_le7084787975880047091nteger(aa_Cod2813182003028390446nteger(set_or9101266186257409494nteger,A),aa_Cod2813182003028390446nteger(set_or5754767410780653050nteger,B))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),B) ) ).

% Iic_subset_Iio_iff
tff(fact_4000_Iic__subset__Iio__iff,axiom,
    ! [A: rat,B: rat] :
      ( ord_less_eq_set_rat(set_ord_atMost_rat(A),set_ord_lessThan_rat(B))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B) ) ).

% Iic_subset_Iio_iff
tff(fact_4001_Iic__subset__Iio__iff,axiom,
    ! [A: num,B: num] :
      ( ord_less_eq_set_num(set_ord_atMost_num(A),set_ord_lessThan_num(B))
    <=> aa_num_o(aa_num_fun_num_o(ord_less_num,A),B) ) ).

% Iic_subset_Iio_iff
tff(fact_4002_Iic__subset__Iio__iff,axiom,
    ! [A: int,B: int] :
      ( ord_less_eq_set_int(aa_int_set_int(set_ord_atMost_int,A),aa_int_set_int(set_ord_lessThan_int,B))
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,A),B) ) ).

% Iic_subset_Iio_iff
tff(fact_4003_Iic__subset__Iio__iff,axiom,
    ! [A: nat,B: nat] :
      ( aa_set_nat_o(ord_less_eq_set_nat(aa_nat_set_nat(set_ord_atMost_nat,A)),aa_nat_set_nat(set_ord_lessThan_nat,B))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),B) ) ).

% Iic_subset_Iio_iff
tff(fact_4004_binomial__absorption,axiom,
    ! [K: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(suc,K)),aa_nat_nat(aa_nat_fun_nat_nat(binomial,N2),aa_nat_nat(suc,K))) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(binomial,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)),K)) ).

% binomial_absorption
tff(fact_4005_sum__diff__distrib,axiom,
    ! [Q: fun_nat_nat,P: fun_nat_nat,N2: nat] :
      ( ! [X3: nat] : aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(Q,X3)),aa_nat_nat(P,X3))
     => ( aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_set_nat_nat(groups3542108847815614940at_nat(P),aa_nat_set_nat(set_ord_lessThan_nat,N2))),aa_set_nat_nat(groups3542108847815614940at_nat(Q),aa_nat_set_nat(set_ord_lessThan_nat,N2))) = aa_set_nat_nat(groups3542108847815614940at_nat(aa_fun5791449513213591928at_nat(aTP_Lamm_iy(Q),P)),aa_nat_set_nat(set_ord_lessThan_nat,N2)) ) ) ).

% sum_diff_distrib
tff(fact_4006_sum_OlessThan__Suc__shift,axiom,
    ! [G: fun_na2338080690716861136at_nat,N2: nat] : groups6857163185585827899at_nat(G,aa_nat_set_nat(set_ord_lessThan_nat,aa_nat_nat(suc,N2))) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(aa_nat2240542744625857721at_nat(G,zero_zero_nat)),groups6857163185585827899at_nat(aTP_Lamm_dp(G),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% sum.lessThan_Suc_shift
tff(fact_4007_sum_OlessThan__Suc__shift,axiom,
    ! [G: fun_nat_rat,N2: nat] : groups2906978787729119204at_rat(G,aa_nat_set_nat(set_ord_lessThan_nat,aa_nat_nat(suc,N2))) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(G,zero_zero_nat)),groups2906978787729119204at_rat(aTP_Lamm_dq(G),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% sum.lessThan_Suc_shift
tff(fact_4008_sum_OlessThan__Suc__shift,axiom,
    ! [G: fun_nat_int,N2: nat] : groups3539618377306564664at_int(G,aa_nat_set_nat(set_ord_lessThan_nat,aa_nat_nat(suc,N2))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(G,zero_zero_nat)),groups3539618377306564664at_int(aTP_Lamm_dr(G),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% sum.lessThan_Suc_shift
tff(fact_4009_sum_OlessThan__Suc__shift,axiom,
    ! [G: fun_nat_nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_ord_lessThan_nat,aa_nat_nat(suc,N2))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(G,zero_zero_nat)),aa_set_nat_nat(groups3542108847815614940at_nat(aTP_Lamm_dh(G)),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% sum.lessThan_Suc_shift
tff(fact_4010_sum__lessThan__telescope,axiom,
    ! [F: fun_nat_Code_integer,M: nat] : groups7501900531339628137nteger(aTP_Lamm_ds(F),aa_nat_set_nat(set_ord_lessThan_nat,M)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_nat_Code_integer(F,M)),aa_nat_Code_integer(F,zero_zero_nat)) ).

% sum_lessThan_telescope
tff(fact_4011_sum__lessThan__telescope,axiom,
    ! [F: fun_nat_rat,M: nat] : groups2906978787729119204at_rat(aTP_Lamm_dt(F),aa_nat_set_nat(set_ord_lessThan_nat,M)) = aa_rat_rat(minus_minus_rat(aa_nat_rat(F,M)),aa_nat_rat(F,zero_zero_nat)) ).

% sum_lessThan_telescope
tff(fact_4012_sum__lessThan__telescope,axiom,
    ! [F: fun_nat_int,M: nat] : groups3539618377306564664at_int(aTP_Lamm_du(F),aa_nat_set_nat(set_ord_lessThan_nat,M)) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(F,M)),aa_nat_int(F,zero_zero_nat)) ).

% sum_lessThan_telescope
tff(fact_4013_sum__lessThan__telescope_H,axiom,
    ! [F: fun_nat_Code_integer,M: nat] : groups7501900531339628137nteger(aTP_Lamm_ho(F),aa_nat_set_nat(set_ord_lessThan_nat,M)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_nat_Code_integer(F,zero_zero_nat)),aa_nat_Code_integer(F,M)) ).

% sum_lessThan_telescope'
tff(fact_4014_sum__lessThan__telescope_H,axiom,
    ! [F: fun_nat_rat,M: nat] : groups2906978787729119204at_rat(aTP_Lamm_hp(F),aa_nat_set_nat(set_ord_lessThan_nat,M)) = aa_rat_rat(minus_minus_rat(aa_nat_rat(F,zero_zero_nat)),aa_nat_rat(F,M)) ).

% sum_lessThan_telescope'
tff(fact_4015_sum__lessThan__telescope_H,axiom,
    ! [F: fun_nat_int,M: nat] : groups3539618377306564664at_int(aTP_Lamm_hq(F),aa_nat_set_nat(set_ord_lessThan_nat,M)) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(F,zero_zero_nat)),aa_nat_int(F,M)) ).

% sum_lessThan_telescope'
tff(fact_4016_sum_OatLeast1__atMost__eq,axiom,
    ! [G: fun_nat_nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,zero_zero_nat)),N2)) = aa_set_nat_nat(groups3542108847815614940at_nat(aTP_Lamm_dh(G)),aa_nat_set_nat(set_ord_lessThan_nat,N2)) ).

% sum.atLeast1_atMost_eq
tff(fact_4017_sum__bounds__lt__plus1,axiom,
    ! [F: fun_nat_nat,Mm: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(aTP_Lamm_dh(F)),aa_nat_set_nat(set_ord_lessThan_nat,Mm)) = aa_set_nat_nat(groups3542108847815614940at_nat(F),aa_nat_set_nat(set_or1269000886237332187st_nat(one_one_nat),Mm)) ).

% sum_bounds_lt_plus1
tff(fact_4018_sum_Onested__swap_H,axiom,
    ! [A: fun_nat_fun_nat_nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(aTP_Lamm_iz(A)),aa_nat_set_nat(set_ord_atMost_nat,N2)) = aa_set_nat_nat(groups3542108847815614940at_nat(aa_nat_fun_nat_nat(aTP_Lamm_jb(A),N2)),aa_nat_set_nat(set_ord_lessThan_nat,N2)) ).

% sum.nested_swap'
tff(fact_4019_sum__choose__lower,axiom,
    ! [R2: nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(aa_nat_fun_nat_nat(aTP_Lamm_jc,R2)),aa_nat_set_nat(set_ord_atMost_nat,N2)) = aa_nat_nat(aa_nat_fun_nat_nat(binomial,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,R2),N2))),N2) ).

% sum_choose_lower
tff(fact_4020_choose__rising__sum_I2_J,axiom,
    ! [N2: nat,M: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(aa_nat_fun_nat_nat(aTP_Lamm_jd,N2)),aa_nat_set_nat(set_ord_atMost_nat,M)) = aa_nat_nat(aa_nat_fun_nat_nat(binomial,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),M)),one_one_nat)),M) ).

% choose_rising_sum(2)
tff(fact_4021_choose__rising__sum_I1_J,axiom,
    ! [N2: nat,M: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(aa_nat_fun_nat_nat(aTP_Lamm_jd,N2)),aa_nat_set_nat(set_ord_atMost_nat,M)) = aa_nat_nat(aa_nat_fun_nat_nat(binomial,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),M)),one_one_nat)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),one_one_nat)) ).

% choose_rising_sum(1)
tff(fact_4022_binomial__code,axiom,
    ! [N2: nat,K: nat] :
      aa_nat_nat(aa_nat_fun_nat_nat(binomial,N2),K) = $ite(
        aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),K),
        zero_zero_nat,
        $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),K)),aa_nat_nat(aa_nat_fun_nat_nat(binomial,N2),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),K)),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(set_fo2584398358068434914at_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),K)),one_one_nat)),N2),one_one_nat)),aa_nat_nat(semiri1408675320244567234ct_nat,K))) ) ).

% binomial_code
tff(fact_4023_choose__reduce__nat,axiom,
    ! [N2: nat,K: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),K)
       => ( aa_nat_nat(aa_nat_fun_nat_nat(binomial,N2),K) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(binomial,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,K),one_one_nat))),aa_nat_nat(aa_nat_fun_nat_nat(binomial,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)),K)) ) ) ) ).

% choose_reduce_nat
tff(fact_4024_times__binomial__minus1__eq,axiom,
    ! [K: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),K)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,K),aa_nat_nat(aa_nat_fun_nat_nat(binomial,N2),K)) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(binomial,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,K),one_one_nat))) ) ) ).

% times_binomial_minus1_eq
tff(fact_4025_one__diff__power__eq,axiom,
    ! [X2: code_integer,N2: nat] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,one_one_Code_integer),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,X2),N2)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,one_one_Code_integer),X2)),groups7501900531339628137nteger(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,X2),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% one_diff_power_eq
tff(fact_4026_one__diff__power__eq,axiom,
    ! [X2: rat,N2: nat] : aa_rat_rat(minus_minus_rat(one_one_rat),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),N2)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(minus_minus_rat(one_one_rat),X2)),groups2906978787729119204at_rat(aa_rat_fun_nat_rat(power_power_rat,X2),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% one_diff_power_eq
tff(fact_4027_one__diff__power__eq,axiom,
    ! [X2: int,N2: nat] : aa_int_int(aa_int_fun_int_int(minus_minus_int,one_one_int),aa_nat_int(aa_int_fun_nat_int(power_power_int,X2),N2)) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,one_one_int),X2)),groups3539618377306564664at_int(aa_int_fun_nat_int(power_power_int,X2),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% one_diff_power_eq
tff(fact_4028_power__diff__1__eq,axiom,
    ! [X2: code_integer,N2: nat] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,X2),N2)),one_one_Code_integer) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,X2),one_one_Code_integer)),groups7501900531339628137nteger(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,X2),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% power_diff_1_eq
tff(fact_4029_power__diff__1__eq,axiom,
    ! [X2: rat,N2: nat] : aa_rat_rat(minus_minus_rat(aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),N2)),one_one_rat) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(minus_minus_rat(X2),one_one_rat)),groups2906978787729119204at_rat(aa_rat_fun_nat_rat(power_power_rat,X2),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% power_diff_1_eq
tff(fact_4030_power__diff__1__eq,axiom,
    ! [X2: int,N2: nat] : aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,X2),N2)),one_one_int) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,X2),one_one_int)),groups3539618377306564664at_int(aa_int_fun_nat_int(power_power_int,X2),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% power_diff_1_eq
tff(fact_4031_geometric__sum,axiom,
    ! [X2: rat,N2: nat] :
      ( ( X2 != one_one_rat )
     => ( groups2906978787729119204at_rat(aa_rat_fun_nat_rat(power_power_rat,X2),aa_nat_set_nat(set_ord_lessThan_nat,N2)) = aa_rat_rat(divide_divide_rat(aa_rat_rat(minus_minus_rat(aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),N2)),one_one_rat)),aa_rat_rat(minus_minus_rat(X2),one_one_rat)) ) ) ).

% geometric_sum
tff(fact_4032_sum_OatMost__shift,axiom,
    ! [G: fun_na2338080690716861136at_nat,N2: nat] : groups6857163185585827899at_nat(G,aa_nat_set_nat(set_ord_atMost_nat,N2)) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(aa_nat2240542744625857721at_nat(G,zero_zero_nat)),groups6857163185585827899at_nat(aTP_Lamm_dp(G),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% sum.atMost_shift
tff(fact_4033_sum_OatMost__shift,axiom,
    ! [G: fun_nat_rat,N2: nat] : groups2906978787729119204at_rat(G,aa_nat_set_nat(set_ord_atMost_nat,N2)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(G,zero_zero_nat)),groups2906978787729119204at_rat(aTP_Lamm_dq(G),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% sum.atMost_shift
tff(fact_4034_sum_OatMost__shift,axiom,
    ! [G: fun_nat_int,N2: nat] : groups3539618377306564664at_int(G,aa_nat_set_nat(set_ord_atMost_nat,N2)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(G,zero_zero_nat)),groups3539618377306564664at_int(aTP_Lamm_dr(G),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% sum.atMost_shift
tff(fact_4035_sum_OatMost__shift,axiom,
    ! [G: fun_nat_nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_ord_atMost_nat,N2)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(G,zero_zero_nat)),aa_set_nat_nat(groups3542108847815614940at_nat(aTP_Lamm_dh(G)),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% sum.atMost_shift
tff(fact_4036_vandermonde,axiom,
    ! [M: nat,N2: nat,R2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(aa_nat_fun_nat_nat(aa_nat3783148529270815480at_nat(aTP_Lamm_je(M),N2),R2)),aa_nat_set_nat(set_ord_atMost_nat,R2)) = aa_nat_nat(aa_nat_fun_nat_nat(binomial,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)),R2) ).

% vandermonde
tff(fact_4037_binomial__addition__formula,axiom,
    ! [N2: nat,K: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(binomial,N2),aa_nat_nat(suc,K)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(binomial,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)),aa_nat_nat(suc,K))),aa_nat_nat(aa_nat_fun_nat_nat(binomial,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)),K)) ) ) ).

% binomial_addition_formula
tff(fact_4038_power__diff__sumr2,axiom,
    ! [X2: code_integer,N2: nat,Y: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,X2),N2)),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,Y),N2)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,X2),Y)),groups7501900531339628137nteger(aa_Cod1578151519121547077nteger(aa_nat2351529209232473362nteger(aTP_Lamm_jf(X2),N2),Y),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% power_diff_sumr2
tff(fact_4039_power__diff__sumr2,axiom,
    ! [X2: rat,N2: nat,Y: rat] : aa_rat_rat(minus_minus_rat(aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),N2)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,Y),N2)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(minus_minus_rat(X2),Y)),groups2906978787729119204at_rat(aa_rat_fun_nat_rat(aa_nat298952458717073160at_rat(aTP_Lamm_jg(X2),N2),Y),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% power_diff_sumr2
tff(fact_4040_power__diff__sumr2,axiom,
    ! [X2: int,N2: nat,Y: int] : aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,X2),N2)),aa_nat_int(aa_int_fun_nat_int(power_power_int,Y),N2)) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,X2),Y)),groups3539618377306564664at_int(aa_int_fun_nat_int(aa_nat6704147566042551216at_int(aTP_Lamm_jh(X2),N2),Y),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% power_diff_sumr2
tff(fact_4041_diff__power__eq__sum,axiom,
    ! [X2: code_integer,N2: nat,Y: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,X2),aa_nat_nat(suc,N2))),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,Y),aa_nat_nat(suc,N2))) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,X2),Y)),groups7501900531339628137nteger(aa_Cod1578151519121547077nteger(aa_nat2351529209232473362nteger(aTP_Lamm_ji(X2),N2),Y),aa_nat_set_nat(set_ord_lessThan_nat,aa_nat_nat(suc,N2)))) ).

% diff_power_eq_sum
tff(fact_4042_diff__power__eq__sum,axiom,
    ! [X2: rat,N2: nat,Y: rat] : aa_rat_rat(minus_minus_rat(aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),aa_nat_nat(suc,N2))),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,Y),aa_nat_nat(suc,N2))) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(minus_minus_rat(X2),Y)),groups2906978787729119204at_rat(aa_rat_fun_nat_rat(aa_nat298952458717073160at_rat(aTP_Lamm_jj(X2),N2),Y),aa_nat_set_nat(set_ord_lessThan_nat,aa_nat_nat(suc,N2)))) ).

% diff_power_eq_sum
tff(fact_4043_diff__power__eq__sum,axiom,
    ! [X2: int,N2: nat,Y: int] : aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,X2),aa_nat_nat(suc,N2))),aa_nat_int(aa_int_fun_nat_int(power_power_int,Y),aa_nat_nat(suc,N2))) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,X2),Y)),groups3539618377306564664at_int(aa_int_fun_nat_int(aa_nat6704147566042551216at_int(aTP_Lamm_jk(X2),N2),Y),aa_nat_set_nat(set_ord_lessThan_nat,aa_nat_nat(suc,N2)))) ).

% diff_power_eq_sum
tff(fact_4044_sum__gp__strict,axiom,
    ! [X2: rat,N2: nat] :
      groups2906978787729119204at_rat(aa_rat_fun_nat_rat(power_power_rat,X2),aa_nat_set_nat(set_ord_lessThan_nat,N2)) = $ite(X2 = one_one_rat,aa_nat_rat(semiri681578069525770553at_rat,N2),aa_rat_rat(divide_divide_rat(aa_rat_rat(minus_minus_rat(one_one_rat),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),N2))),aa_rat_rat(minus_minus_rat(one_one_rat),X2))) ).

% sum_gp_strict
tff(fact_4045_binomial,axiom,
    ! [A: nat,B: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),N2) = aa_set_nat_nat(groups3542108847815614940at_nat(aa_nat_fun_nat_nat(aa_nat3783148529270815480at_nat(aTP_Lamm_jl(A),B),N2)),aa_nat_set_nat(set_ord_atMost_nat,N2)) ).

% binomial
tff(fact_4046_choose__two,axiom,
    ! [N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(binomial,N2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) ).

% choose_two
tff(fact_4047_one__diff__power__eq_H,axiom,
    ! [X2: code_integer,N2: nat] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,one_one_Code_integer),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,X2),N2)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,one_one_Code_integer),X2)),groups7501900531339628137nteger(aa_nat2010205248571845816nteger(aTP_Lamm_jm(X2),N2),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% one_diff_power_eq'
tff(fact_4048_one__diff__power__eq_H,axiom,
    ! [X2: rat,N2: nat] : aa_rat_rat(minus_minus_rat(one_one_rat),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,X2),N2)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(minus_minus_rat(one_one_rat),X2)),groups2906978787729119204at_rat(aa_nat_fun_nat_rat(aTP_Lamm_jn(X2),N2),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% one_diff_power_eq'
tff(fact_4049_one__diff__power__eq_H,axiom,
    ! [X2: int,N2: nat] : aa_int_int(aa_int_fun_int_int(minus_minus_int,one_one_int),aa_nat_int(aa_int_fun_nat_int(power_power_int,X2),N2)) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,one_one_int),X2)),groups3539618377306564664at_int(aa_nat_fun_nat_int(aTP_Lamm_jo(X2),N2),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% one_diff_power_eq'
tff(fact_4050_binomial__ring,axiom,
    ! [A: rat,B: rat,N2: nat] : aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),N2) = groups2906978787729119204at_rat(aa_nat_fun_nat_rat(aa_rat250263598611652360at_rat(aTP_Lamm_jp(A),B),N2),aa_nat_set_nat(set_ord_atMost_nat,N2)) ).

% binomial_ring
tff(fact_4051_binomial__ring,axiom,
    ! [A: int,B: int,N2: nat] : aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),N2) = groups3539618377306564664at_int(aa_nat_fun_nat_int(aa_int431785320988601264at_int(aTP_Lamm_jq(A),B),N2),aa_nat_set_nat(set_ord_atMost_nat,N2)) ).

% binomial_ring
tff(fact_4052_binomial__ring,axiom,
    ! [A: code_integer,B: code_integer,N2: nat] : aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)),N2) = groups7501900531339628137nteger(aa_nat2010205248571845816nteger(aa_Cod3140087502949435154nteger(aTP_Lamm_jr(A),B),N2),aa_nat_set_nat(set_ord_atMost_nat,N2)) ).

% binomial_ring
tff(fact_4053_binomial__ring,axiom,
    ! [A: code_natural,B: code_natural,N2: nat] : aa_nat_Code_natural(power_7079662738309270450atural(aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),B)),N2) = groups6325495683096345652atural(aa_nat6468655069083034883atural(aa_Cod217761371205376936atural(aTP_Lamm_js(A),B),N2),aa_nat_set_nat(set_ord_atMost_nat,N2)) ).

% binomial_ring
tff(fact_4054_binomial__ring,axiom,
    ! [A: nat,B: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)),N2) = aa_set_nat_nat(groups3542108847815614940at_nat(aa_nat_fun_nat_nat(aa_nat3783148529270815480at_nat(aTP_Lamm_jl(A),B),N2)),aa_nat_set_nat(set_ord_atMost_nat,N2)) ).

% binomial_ring
tff(fact_4055_xor__num_Osimps_I6_J,axiom,
    ! [M: num,N2: num] : aa_num_option_num(bit_un2480387367778600638or_num(aa_num_num(bit0,M)),aa_num_num(bit1,N2)) = aa_num_option_num(some_num,aa_option_num_num(case_option_num_num(one,bit1),aa_num_option_num(bit_un2480387367778600638or_num(M),N2))) ).

% xor_num.simps(6)
tff(fact_4056_xor__num_Osimps_I8_J,axiom,
    ! [M: num,N2: num] : aa_num_option_num(bit_un2480387367778600638or_num(aa_num_num(bit1,M)),aa_num_num(bit0,N2)) = aa_num_option_num(some_num,aa_option_num_num(case_option_num_num(one,bit1),aa_num_option_num(bit_un2480387367778600638or_num(M),N2))) ).

% xor_num.simps(8)
tff(fact_4057_choose__alternating__linear__sum,axiom,
    ! [N2: nat] :
      ( ( N2 != one_one_nat )
     => ( groups2906978787729119204at_rat(aTP_Lamm_jt(N2),aa_nat_set_nat(set_ord_atMost_nat,N2)) = zero_zero_rat ) ) ).

% choose_alternating_linear_sum
tff(fact_4058_choose__alternating__linear__sum,axiom,
    ! [N2: nat] :
      ( ( N2 != one_one_nat )
     => ( groups3539618377306564664at_int(aa_nat_fun_nat_int(aTP_Lamm_ju,N2),aa_nat_set_nat(set_ord_atMost_nat,N2)) = zero_zero_int ) ) ).

% choose_alternating_linear_sum
tff(fact_4059_choose__alternating__linear__sum,axiom,
    ! [N2: nat] :
      ( ( N2 != one_one_nat )
     => ( groups7501900531339628137nteger(aTP_Lamm_jv(N2),aa_nat_set_nat(set_ord_atMost_nat,N2)) = zero_z3403309356797280102nteger ) ) ).

% choose_alternating_linear_sum
tff(fact_4060_fact__Suc__0,axiom,
    aa_nat_Code_integer(semiri3624122377584611663nteger,aa_nat_nat(suc,zero_zero_nat)) = one_one_Code_integer ).

% fact_Suc_0
tff(fact_4061_fact__Suc__0,axiom,
    aa_nat_rat(semiri773545260158071498ct_rat,aa_nat_nat(suc,zero_zero_nat)) = one_one_rat ).

% fact_Suc_0
tff(fact_4062_fact__Suc__0,axiom,
    aa_nat_int(semiri1406184849735516958ct_int,aa_nat_nat(suc,zero_zero_nat)) = one_one_int ).

% fact_Suc_0
tff(fact_4063_fact__Suc__0,axiom,
    aa_nat_nat(semiri1408675320244567234ct_nat,aa_nat_nat(suc,zero_zero_nat)) = one_one_nat ).

% fact_Suc_0
tff(fact_4064_fact__1,axiom,
    aa_nat_Code_integer(semiri3624122377584611663nteger,one_one_nat) = one_one_Code_integer ).

% fact_1
tff(fact_4065_fact__1,axiom,
    aa_nat_rat(semiri773545260158071498ct_rat,one_one_nat) = one_one_rat ).

% fact_1
tff(fact_4066_fact__1,axiom,
    aa_nat_int(semiri1406184849735516958ct_int,one_one_nat) = one_one_int ).

% fact_1
tff(fact_4067_fact__1,axiom,
    aa_nat_nat(semiri1408675320244567234ct_nat,one_one_nat) = one_one_nat ).

% fact_1
tff(fact_4068_fact__0,axiom,
    aa_nat_Code_integer(semiri3624122377584611663nteger,zero_zero_nat) = one_one_Code_integer ).

% fact_0
tff(fact_4069_fact__0,axiom,
    aa_nat_rat(semiri773545260158071498ct_rat,zero_zero_nat) = one_one_rat ).

% fact_0
tff(fact_4070_fact__0,axiom,
    aa_nat_int(semiri1406184849735516958ct_int,zero_zero_nat) = one_one_int ).

% fact_0
tff(fact_4071_fact__0,axiom,
    aa_nat_nat(semiri1408675320244567234ct_nat,zero_zero_nat) = one_one_nat ).

% fact_0
tff(fact_4072_fact__code,axiom,
    ! [N2: nat] : aa_nat_int(semiri1406184849735516958ct_int,N2) = aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(aa_nat_fun_nat_nat(set_fo2584398358068434914at_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2),one_one_nat)) ).

% fact_code
tff(fact_4073_fact__code,axiom,
    ! [N2: nat] : aa_nat_Code_integer(semiri3624122377584611663nteger,N2) = aa_nat_Code_integer(semiri4939895301339042750nteger,aa_nat_nat(aa_nat_fun_nat_nat(set_fo2584398358068434914at_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2),one_one_nat)) ).

% fact_code
tff(fact_4074_fact__code,axiom,
    ! [N2: nat] : aa_nat_Code_natural(semiri2447717529341329178atural,N2) = aa_nat_Code_natural(semiri3763490453095760265atural,aa_nat_nat(aa_nat_fun_nat_nat(set_fo2584398358068434914at_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2),one_one_nat)) ).

% fact_code
tff(fact_4075_fact__code,axiom,
    ! [N2: nat] : aa_nat_nat(semiri1408675320244567234ct_nat,N2) = aa_nat_nat(semiri1316708129612266289at_nat,aa_nat_nat(aa_nat_fun_nat_nat(set_fo2584398358068434914at_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2),one_one_nat)) ).

% fact_code
tff(fact_4076_fact__reduce,axiom,
    ! [N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => ( aa_nat_rat(semiri773545260158071498ct_rat,N2) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(semiri681578069525770553at_rat,N2)),aa_nat_rat(semiri773545260158071498ct_rat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat))) ) ) ).

% fact_reduce
tff(fact_4077_fact__reduce,axiom,
    ! [N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => ( aa_nat_int(semiri1406184849735516958ct_int,N2) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(semiri1314217659103216013at_int,N2)),aa_nat_int(semiri1406184849735516958ct_int,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat))) ) ) ).

% fact_reduce
tff(fact_4078_fact__reduce,axiom,
    ! [N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => ( aa_nat_Code_integer(semiri3624122377584611663nteger,N2) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(semiri4939895301339042750nteger,N2)),aa_nat_Code_integer(semiri3624122377584611663nteger,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat))) ) ) ).

% fact_reduce
tff(fact_4079_fact__reduce,axiom,
    ! [N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => ( aa_nat_Code_natural(semiri2447717529341329178atural,N2) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_nat_Code_natural(semiri3763490453095760265atural,N2)),aa_nat_Code_natural(semiri2447717529341329178atural,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat))) ) ) ).

% fact_reduce
tff(fact_4080_fact__reduce,axiom,
    ! [N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => ( aa_nat_nat(semiri1408675320244567234ct_nat,N2) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(semiri1316708129612266289at_nat,N2)),aa_nat_nat(semiri1408675320244567234ct_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat))) ) ) ).

% fact_reduce
tff(fact_4081_fact__num__eq__if,axiom,
    ! [M: nat] :
      aa_nat_rat(semiri773545260158071498ct_rat,M) = $ite(M = zero_zero_nat,one_one_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(semiri681578069525770553at_rat,M)),aa_nat_rat(semiri773545260158071498ct_rat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),one_one_nat)))) ).

% fact_num_eq_if
tff(fact_4082_fact__num__eq__if,axiom,
    ! [M: nat] :
      aa_nat_int(semiri1406184849735516958ct_int,M) = $ite(M = zero_zero_nat,one_one_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(semiri1314217659103216013at_int,M)),aa_nat_int(semiri1406184849735516958ct_int,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),one_one_nat)))) ).

% fact_num_eq_if
tff(fact_4083_fact__num__eq__if,axiom,
    ! [M: nat] :
      aa_nat_Code_integer(semiri3624122377584611663nteger,M) = $ite(M = zero_zero_nat,one_one_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(semiri4939895301339042750nteger,M)),aa_nat_Code_integer(semiri3624122377584611663nteger,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),one_one_nat)))) ).

% fact_num_eq_if
tff(fact_4084_fact__num__eq__if,axiom,
    ! [M: nat] :
      aa_nat_Code_natural(semiri2447717529341329178atural,M) = $ite(M = zero_zero_nat,one_one_Code_natural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_nat_Code_natural(semiri3763490453095760265atural,M)),aa_nat_Code_natural(semiri2447717529341329178atural,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),one_one_nat)))) ).

% fact_num_eq_if
tff(fact_4085_fact__num__eq__if,axiom,
    ! [M: nat] :
      aa_nat_nat(semiri1408675320244567234ct_nat,M) = $ite(M = zero_zero_nat,one_one_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(semiri1316708129612266289at_nat,M)),aa_nat_nat(semiri1408675320244567234ct_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),one_one_nat)))) ).

% fact_num_eq_if
tff(fact_4086_xor__num_Opelims,axiom,
    ! [X2: num,Xa: num,Y: option_num] :
      ( ( aa_num_option_num(bit_un2480387367778600638or_num(X2),Xa) = Y )
     => ( accp_P3113834385874906142um_num(bit_un2901131394128224187um_rel,product_Pair_num_num(X2,Xa))
       => ( ( ( X2 = one )
           => ( ( Xa = one )
             => ( ( Y = none_num )
               => ~ accp_P3113834385874906142um_num(bit_un2901131394128224187um_rel,product_Pair_num_num(one,one)) ) ) )
         => ( ( ( X2 = one )
             => ! [N: num] :
                  ( ( Xa = aa_num_num(bit0,N) )
                 => ( ( Y = aa_num_option_num(some_num,aa_num_num(bit1,N)) )
                   => ~ accp_P3113834385874906142um_num(bit_un2901131394128224187um_rel,product_Pair_num_num(one,aa_num_num(bit0,N))) ) ) )
           => ( ( ( X2 = one )
               => ! [N: num] :
                    ( ( Xa = aa_num_num(bit1,N) )
                   => ( ( Y = aa_num_option_num(some_num,aa_num_num(bit0,N)) )
                     => ~ accp_P3113834385874906142um_num(bit_un2901131394128224187um_rel,product_Pair_num_num(one,aa_num_num(bit1,N))) ) ) )
             => ( ! [M4: num] :
                    ( ( X2 = aa_num_num(bit0,M4) )
                   => ( ( Xa = one )
                     => ( ( Y = aa_num_option_num(some_num,aa_num_num(bit1,M4)) )
                       => ~ accp_P3113834385874906142um_num(bit_un2901131394128224187um_rel,product_Pair_num_num(aa_num_num(bit0,M4),one)) ) ) )
               => ( ! [M4: num] :
                      ( ( X2 = aa_num_num(bit0,M4) )
                     => ! [N: num] :
                          ( ( Xa = aa_num_num(bit0,N) )
                         => ( ( Y = aa_opt5369159329878751634on_num(map_option_num_num(bit0),aa_num_option_num(bit_un2480387367778600638or_num(M4),N)) )
                           => ~ accp_P3113834385874906142um_num(bit_un2901131394128224187um_rel,product_Pair_num_num(aa_num_num(bit0,M4),aa_num_num(bit0,N))) ) ) )
                 => ( ! [M4: num] :
                        ( ( X2 = aa_num_num(bit0,M4) )
                       => ! [N: num] :
                            ( ( Xa = aa_num_num(bit1,N) )
                           => ( ( Y = aa_num_option_num(some_num,aa_option_num_num(case_option_num_num(one,bit1),aa_num_option_num(bit_un2480387367778600638or_num(M4),N))) )
                             => ~ accp_P3113834385874906142um_num(bit_un2901131394128224187um_rel,product_Pair_num_num(aa_num_num(bit0,M4),aa_num_num(bit1,N))) ) ) )
                   => ( ! [M4: num] :
                          ( ( X2 = aa_num_num(bit1,M4) )
                         => ( ( Xa = one )
                           => ( ( Y = aa_num_option_num(some_num,aa_num_num(bit0,M4)) )
                             => ~ accp_P3113834385874906142um_num(bit_un2901131394128224187um_rel,product_Pair_num_num(aa_num_num(bit1,M4),one)) ) ) )
                     => ( ! [M4: num] :
                            ( ( X2 = aa_num_num(bit1,M4) )
                           => ! [N: num] :
                                ( ( Xa = aa_num_num(bit0,N) )
                               => ( ( Y = aa_num_option_num(some_num,aa_option_num_num(case_option_num_num(one,bit1),aa_num_option_num(bit_un2480387367778600638or_num(M4),N))) )
                                 => ~ accp_P3113834385874906142um_num(bit_un2901131394128224187um_rel,product_Pair_num_num(aa_num_num(bit1,M4),aa_num_num(bit0,N))) ) ) )
                       => ~ ! [M4: num] :
                              ( ( X2 = aa_num_num(bit1,M4) )
                             => ! [N: num] :
                                  ( ( Xa = aa_num_num(bit1,N) )
                                 => ( ( Y = aa_opt5369159329878751634on_num(map_option_num_num(bit0),aa_num_option_num(bit_un2480387367778600638or_num(M4),N)) )
                                   => ~ accp_P3113834385874906142um_num(bit_un2901131394128224187um_rel,product_Pair_num_num(aa_num_num(bit1,M4),aa_num_num(bit1,N))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% xor_num.pelims
tff(fact_4087_dvd__fact,axiom,
    ! [M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),M)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
       => aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,M),aa_nat_nat(semiri1408675320244567234ct_nat,N2)) ) ) ).

% dvd_fact
tff(fact_4088_fact__ge__1,axiom,
    ! [N2: nat] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),aa_nat_Code_integer(semiri3624122377584611663nteger,N2)) ).

% fact_ge_1
tff(fact_4089_fact__ge__1,axiom,
    ! [N2: nat] : aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),aa_nat_rat(semiri773545260158071498ct_rat,N2)) ).

% fact_ge_1
tff(fact_4090_fact__ge__1,axiom,
    ! [N2: nat] : aa_int_o(aa_int_fun_int_o(ord_less_eq_int,one_one_int),aa_nat_int(semiri1406184849735516958ct_int,N2)) ).

% fact_ge_1
tff(fact_4091_fact__ge__1,axiom,
    ! [N2: nat] : aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),aa_nat_nat(semiri1408675320244567234ct_nat,N2)) ).

% fact_ge_1
tff(fact_4092_pochhammer__double,axiom,
    ! [Z: rat,N2: nat] : aa_nat_rat(comm_s4028243227959126397er_rat(aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one))),Z)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(semiri681578069525770553at_rat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)))),aa_nat_rat(comm_s4028243227959126397er_rat(Z),N2))),aa_nat_rat(comm_s4028243227959126397er_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,Z),aa_rat_rat(divide_divide_rat(one_one_rat),aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one))))),N2)) ).

% pochhammer_double
tff(fact_4093_fact__double,axiom,
    ! [N2: nat] : aa_nat_rat(semiri773545260158071498ct_rat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2))),aa_nat_rat(comm_s4028243227959126397er_rat(aa_rat_rat(divide_divide_rat(one_one_rat),aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one)))),N2))),aa_nat_rat(semiri773545260158071498ct_rat,N2)) ).

% fact_double
tff(fact_4094_pochhammer__code,axiom,
    ! [A: rat,N2: nat] :
      aa_nat_rat(comm_s4028243227959126397er_rat(A),N2) = $ite(N2 = zero_zero_nat,one_one_rat,aa_rat_rat(set_fo1949268297981939178at_rat(aTP_Lamm_jw(A),zero_zero_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)),one_one_rat)) ).

% pochhammer_code
tff(fact_4095_pochhammer__code,axiom,
    ! [A: int,N2: nat] :
      aa_nat_int(comm_s4660882817536571857er_int(A),N2) = $ite(N2 = zero_zero_nat,one_one_int,aa_int_int(set_fo2581907887559384638at_int(aTP_Lamm_jx(A),zero_zero_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)),one_one_int)) ).

% pochhammer_code
tff(fact_4096_pochhammer__code,axiom,
    ! [A: code_integer,N2: nat] :
      aa_nat_Code_integer(comm_s8582702949713902594nteger(A),N2) = $ite(N2 = zero_zero_nat,one_one_Code_integer,aa_Cod1783974652533396728nteger(set_fo1084959871951514735nteger(aTP_Lamm_jy(A),zero_zero_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)),one_one_Code_integer)) ).

% pochhammer_code
tff(fact_4097_pochhammer__code,axiom,
    ! [A: code_natural,N2: nat] :
      aa_nat_Code_natural(comm_s7406298101470620109atural(A),N2) = $ite(N2 = zero_zero_nat,one_one_Code_natural,aa_Cod4272041906116450446atural(set_fo9131927060563008058atural(aTP_Lamm_jz(A),zero_zero_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)),one_one_Code_natural)) ).

% pochhammer_code
tff(fact_4098_pochhammer__code,axiom,
    ! [A: nat,N2: nat] :
      aa_nat_nat(aa_nat_fun_nat_nat(comm_s4663373288045622133er_nat,A),N2) = $ite(N2 = zero_zero_nat,one_one_nat,aa_nat_nat(aa_nat_fun_nat_nat(set_fo2584398358068434914at_nat(aTP_Lamm_ka(A),zero_zero_nat),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)),one_one_nat)) ).

% pochhammer_code
tff(fact_4099_xor__Suc__0__eq,axiom,
    ! [N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se6528837805403552850or_nat,N2),aa_nat_nat(suc,zero_zero_nat)) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),aa_o_nat(zero_n2687167440665602831ol_nat,aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)))),aa_o_nat(zero_n2687167440665602831ol_nat,~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2))) ).

% xor_Suc_0_eq
tff(fact_4100_Suc__0__xor__eq,axiom,
    ! [N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se6528837805403552850or_nat,aa_nat_nat(suc,zero_zero_nat)),N2) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),aa_o_nat(zero_n2687167440665602831ol_nat,aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)))),aa_o_nat(zero_n2687167440665602831ol_nat,~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2))) ).

% Suc_0_xor_eq
tff(fact_4101_push__bit__numeral__minus__1,axiom,
    ! [N2: num] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se7788150548672797655nteger,aa_num_nat(numeral_numeral_nat,N2)),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_num_nat(numeral_numeral_nat,N2))) ).

% push_bit_numeral_minus_1
tff(fact_4102_push__bit__numeral__minus__1,axiom,
    ! [N2: num] : aa_int_int(aa_nat_fun_int_int(bit_se545348938243370406it_int,aa_num_nat(numeral_numeral_nat,N2)),aa_int_int(uminus_uminus_int,one_one_int)) = aa_int_int(uminus_uminus_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_num_nat(numeral_numeral_nat,N2))) ).

% push_bit_numeral_minus_1
tff(fact_4103_num__of__integer__code,axiom,
    ! [K: code_integer] :
      aa_Code_integer_num(code_num_of_integer,K) = $ite(aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,K),one_one_Code_integer),one,produc7336495610019696514er_num(aTP_Lamm_kb,aa_Cod6977894654539884864nteger(code_divmod_integer(K),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))))) ).

% num_of_integer_code
tff(fact_4104_Sum__Ico__nat,axiom,
    ! [M: nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(aTP_Lamm_co),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat))),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),one_one_nat)))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))) ).

% Sum_Ico_nat
tff(fact_4105_ivl__diff,axiom,
    ! [I: rat,N2: rat,M: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,I),N2)
     => ( minus_minus_set_rat(set_or4029947393144176647an_rat(I,M),set_or4029947393144176647an_rat(I,N2)) = set_or4029947393144176647an_rat(N2,M) ) ) ).

% ivl_diff
tff(fact_4106_ivl__diff,axiom,
    ! [I: num,N2: num,M: num] :
      ( aa_num_o(aa_num_fun_num_o(ord_less_eq_num,I),N2)
     => ( minus_minus_set_num(set_or1222409239386451017an_num(I,M),set_or1222409239386451017an_num(I,N2)) = set_or1222409239386451017an_num(N2,M) ) ) ).

% ivl_diff
tff(fact_4107_ivl__diff,axiom,
    ! [I: nat,N2: nat,M: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,I),N2)
     => ( minus_minus_set_nat(aa_nat_set_nat(set_or4665077453230672383an_nat(I),M),aa_nat_set_nat(set_or4665077453230672383an_nat(I),N2)) = aa_nat_set_nat(set_or4665077453230672383an_nat(N2),M) ) ) ).

% ivl_diff
tff(fact_4108_ivl__diff,axiom,
    ! [I: code_integer,N2: code_integer,M: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,I),N2)
     => ( minus_2355218937544613996nteger(aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(I),M),aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(I),N2)) = aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(N2),M) ) ) ).

% ivl_diff
tff(fact_4109_ivl__diff,axiom,
    ! [I: int,N2: int,M: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,I),N2)
     => ( minus_minus_set_int(aa_int_set_int(set_or4662586982721622107an_int(I),M),aa_int_set_int(set_or4662586982721622107an_int(I),N2)) = aa_int_set_int(set_or4662586982721622107an_int(N2),M) ) ) ).

% ivl_diff
tff(fact_4110_push__bit__push__bit,axiom,
    ! [M: nat,N2: nat,A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se547839408752420682it_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(bit_se547839408752420682it_nat,N2),A)) = aa_nat_nat(aa_nat_fun_nat_nat(bit_se547839408752420682it_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)),A) ).

% push_bit_push_bit
tff(fact_4111_push__bit__push__bit,axiom,
    ! [M: nat,N2: nat,A: code_integer] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se7788150548672797655nteger,M),aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se7788150548672797655nteger,N2),A)) = aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se7788150548672797655nteger,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)),A) ).

% push_bit_push_bit
tff(fact_4112_push__bit__push__bit,axiom,
    ! [M: nat,N2: nat,A: int] : aa_int_int(aa_nat_fun_int_int(bit_se545348938243370406it_int,M),aa_int_int(aa_nat_fun_int_int(bit_se545348938243370406it_int,N2),A)) = aa_int_int(aa_nat_fun_int_int(bit_se545348938243370406it_int,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)),A) ).

% push_bit_push_bit
tff(fact_4113_push__bit__push__bit,axiom,
    ! [M: nat,N2: nat,A: code_natural] : aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se6611745700429515170atural,M),aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se6611745700429515170atural,N2),A)) = aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se6611745700429515170atural,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)),A) ).

% push_bit_push_bit
tff(fact_4114_lessThan__minus__lessThan,axiom,
    ! [N2: nat,M: nat] : minus_minus_set_nat(aa_nat_set_nat(set_ord_lessThan_nat,N2),aa_nat_set_nat(set_ord_lessThan_nat,M)) = aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2) ).

% lessThan_minus_lessThan
tff(fact_4115_lessThan__minus__lessThan,axiom,
    ! [N2: code_integer,M: code_integer] : minus_2355218937544613996nteger(aa_Cod2813182003028390446nteger(set_or5754767410780653050nteger,N2),aa_Cod2813182003028390446nteger(set_or5754767410780653050nteger,M)) = aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(M),N2) ).

% lessThan_minus_lessThan
tff(fact_4116_lessThan__minus__lessThan,axiom,
    ! [N2: int,M: int] : minus_minus_set_int(aa_int_set_int(set_ord_lessThan_int,N2),aa_int_set_int(set_ord_lessThan_int,M)) = aa_int_set_int(set_or4662586982721622107an_int(M),N2) ).

% lessThan_minus_lessThan
tff(fact_4117_atLeastLessThan__iff,axiom,
    ! [I: $o,L: $o,U: $o] :
      ( member_o((I),aa_o_set_o(set_or7139685690850216873Than_o((L)),(U)))
    <=> ( aa_o_o(aa_o_fun_o_o(ord_less_eq_o,(L)),(I))
        & aa_o_o(aa_o_fun_o_o(ord_less_o,(I)),(U)) ) ) ).

% atLeastLessThan_iff
tff(fact_4118_atLeastLessThan__iff,axiom,
    ! [I: set_nat,L: set_nat,U: set_nat] :
      ( member_set_nat(I,set_or3540276404033026485et_nat(L,U))
    <=> ( aa_set_nat_o(ord_less_eq_set_nat(L),I)
        & ord_less_set_nat(I,U) ) ) ).

% atLeastLessThan_iff
tff(fact_4119_atLeastLessThan__iff,axiom,
    ! [I: rat,L: rat,U: rat] :
      ( member_rat(I,set_or4029947393144176647an_rat(L,U))
    <=> ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,L),I)
        & aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,I),U) ) ) ).

% atLeastLessThan_iff
tff(fact_4120_atLeastLessThan__iff,axiom,
    ! [I: num,L: num,U: num] :
      ( member_num(I,set_or1222409239386451017an_num(L,U))
    <=> ( aa_num_o(aa_num_fun_num_o(ord_less_eq_num,L),I)
        & aa_num_o(aa_num_fun_num_o(ord_less_num,I),U) ) ) ).

% atLeastLessThan_iff
tff(fact_4121_atLeastLessThan__iff,axiom,
    ! [I: nat,L: nat,U: nat] :
      ( member_nat(I,aa_nat_set_nat(set_or4665077453230672383an_nat(L),U))
    <=> ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,L),I)
        & aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,I),U) ) ) ).

% atLeastLessThan_iff
tff(fact_4122_atLeastLessThan__iff,axiom,
    ! [I: code_integer,L: code_integer,U: code_integer] :
      ( member_Code_integer(I,aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(L),U))
    <=> ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,L),I)
        & aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,I),U) ) ) ).

% atLeastLessThan_iff
tff(fact_4123_atLeastLessThan__iff,axiom,
    ! [I: int,L: int,U: int] :
      ( member_int(I,aa_int_set_int(set_or4662586982721622107an_int(L),U))
    <=> ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,L),I)
        & aa_int_o(aa_int_fun_int_o(ord_less_int,I),U) ) ) ).

% atLeastLessThan_iff
tff(fact_4124_ivl__subset,axiom,
    ! [I: rat,J: rat,M: rat,N2: rat] :
      ( ord_less_eq_set_rat(set_or4029947393144176647an_rat(I,J),set_or4029947393144176647an_rat(M,N2))
    <=> ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,J),I)
        | ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,M),I)
          & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,J),N2) ) ) ) ).

% ivl_subset
tff(fact_4125_ivl__subset,axiom,
    ! [I: num,J: num,M: num,N2: num] :
      ( ord_less_eq_set_num(set_or1222409239386451017an_num(I,J),set_or1222409239386451017an_num(M,N2))
    <=> ( aa_num_o(aa_num_fun_num_o(ord_less_eq_num,J),I)
        | ( aa_num_o(aa_num_fun_num_o(ord_less_eq_num,M),I)
          & aa_num_o(aa_num_fun_num_o(ord_less_eq_num,J),N2) ) ) ) ).

% ivl_subset
tff(fact_4126_ivl__subset,axiom,
    ! [I: nat,J: nat,M: nat,N2: nat] :
      ( aa_set_nat_o(ord_less_eq_set_nat(aa_nat_set_nat(set_or4665077453230672383an_nat(I),J)),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))
    <=> ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,J),I)
        | ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),I)
          & aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,J),N2) ) ) ) ).

% ivl_subset
tff(fact_4127_ivl__subset,axiom,
    ! [I: code_integer,J: code_integer,M: code_integer,N2: code_integer] :
      ( ord_le7084787975880047091nteger(aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(I),J),aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(M),N2))
    <=> ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,J),I)
        | ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,M),I)
          & aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,J),N2) ) ) ) ).

% ivl_subset
tff(fact_4128_ivl__subset,axiom,
    ! [I: int,J: int,M: int,N2: int] :
      ( ord_less_eq_set_int(aa_int_set_int(set_or4662586982721622107an_int(I),J),aa_int_set_int(set_or4662586982721622107an_int(M),N2))
    <=> ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,J),I)
        | ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,M),I)
          & aa_int_o(aa_int_fun_int_o(ord_less_eq_int,J),N2) ) ) ) ).

% ivl_subset
tff(fact_4129_pochhammer__0,axiom,
    ! [A: code_integer] : aa_nat_Code_integer(comm_s8582702949713902594nteger(A),zero_zero_nat) = one_one_Code_integer ).

% pochhammer_0
tff(fact_4130_pochhammer__0,axiom,
    ! [A: rat] : aa_nat_rat(comm_s4028243227959126397er_rat(A),zero_zero_nat) = one_one_rat ).

% pochhammer_0
tff(fact_4131_pochhammer__0,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(comm_s4663373288045622133er_nat,A),zero_zero_nat) = one_one_nat ).

% pochhammer_0
tff(fact_4132_pochhammer__0,axiom,
    ! [A: int] : aa_nat_int(comm_s4660882817536571857er_int(A),zero_zero_nat) = one_one_int ).

% pochhammer_0
tff(fact_4133_xor__numerals_I1_J,axiom,
    ! [Y: num] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se6528837805403552850or_nat,one_one_nat),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,Y))) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,Y)) ).

% xor_numerals(1)
tff(fact_4134_xor__numerals_I1_J,axiom,
    ! [Y: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3222712562003087583nteger,one_one_Code_integer),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,Y))) = aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit1,Y)) ).

% xor_numerals(1)
tff(fact_4135_xor__numerals_I1_J,axiom,
    ! [Y: num] : aa_int_int(aa_int_fun_int_int(bit_se6526347334894502574or_int,one_one_int),aa_num_int(numeral_numeral_int,aa_num_num(bit0,Y))) = aa_num_int(numeral_numeral_int,aa_num_num(bit1,Y)) ).

% xor_numerals(1)
tff(fact_4136_xor__numerals_I1_J,axiom,
    ! [Y: num] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se2046307713759805098atural,one_one_Code_natural),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,Y))) = aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,Y)) ).

% xor_numerals(1)
tff(fact_4137_xor__numerals_I2_J,axiom,
    ! [Y: num] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se6528837805403552850or_nat,one_one_nat),aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,Y))) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,Y)) ).

% xor_numerals(2)
tff(fact_4138_xor__numerals_I2_J,axiom,
    ! [Y: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3222712562003087583nteger,one_one_Code_integer),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit1,Y))) = aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,Y)) ).

% xor_numerals(2)
tff(fact_4139_xor__numerals_I2_J,axiom,
    ! [Y: num] : aa_int_int(aa_int_fun_int_int(bit_se6526347334894502574or_int,one_one_int),aa_num_int(numeral_numeral_int,aa_num_num(bit1,Y))) = aa_num_int(numeral_numeral_int,aa_num_num(bit0,Y)) ).

% xor_numerals(2)
tff(fact_4140_xor__numerals_I2_J,axiom,
    ! [Y: num] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se2046307713759805098atural,one_one_Code_natural),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,Y))) = aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,Y)) ).

% xor_numerals(2)
tff(fact_4141_xor__numerals_I5_J,axiom,
    ! [X2: num] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se6528837805403552850or_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,X2))),one_one_nat) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,X2)) ).

% xor_numerals(5)
tff(fact_4142_xor__numerals_I5_J,axiom,
    ! [X2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3222712562003087583nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,X2))),one_one_Code_integer) = aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit1,X2)) ).

% xor_numerals(5)
tff(fact_4143_xor__numerals_I5_J,axiom,
    ! [X2: num] : aa_int_int(aa_int_fun_int_int(bit_se6526347334894502574or_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,X2))),one_one_int) = aa_num_int(numeral_numeral_int,aa_num_num(bit1,X2)) ).

% xor_numerals(5)
tff(fact_4144_xor__numerals_I5_J,axiom,
    ! [X2: num] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se2046307713759805098atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,X2))),one_one_Code_natural) = aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,X2)) ).

% xor_numerals(5)
tff(fact_4145_xor__numerals_I8_J,axiom,
    ! [X2: num] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se6528837805403552850or_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,X2))),one_one_nat) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,X2)) ).

% xor_numerals(8)
tff(fact_4146_xor__numerals_I8_J,axiom,
    ! [X2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3222712562003087583nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit1,X2))),one_one_Code_integer) = aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,X2)) ).

% xor_numerals(8)
tff(fact_4147_xor__numerals_I8_J,axiom,
    ! [X2: num] : aa_int_int(aa_int_fun_int_int(bit_se6526347334894502574or_int,aa_num_int(numeral_numeral_int,aa_num_num(bit1,X2))),one_one_int) = aa_num_int(numeral_numeral_int,aa_num_num(bit0,X2)) ).

% xor_numerals(8)
tff(fact_4148_xor__numerals_I8_J,axiom,
    ! [X2: num] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se2046307713759805098atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,X2))),one_one_Code_natural) = aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,X2)) ).

% xor_numerals(8)
tff(fact_4149_push__bit__of__1,axiom,
    ! [N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se547839408752420682it_nat,N2),one_one_nat) = aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2) ).

% push_bit_of_1
tff(fact_4150_push__bit__of__1,axiom,
    ! [N2: nat] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se7788150548672797655nteger,N2),one_one_Code_integer) = aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),N2) ).

% push_bit_of_1
tff(fact_4151_push__bit__of__1,axiom,
    ! [N2: nat] : aa_int_int(aa_nat_fun_int_int(bit_se545348938243370406it_int,N2),one_one_int) = aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),N2) ).

% push_bit_of_1
tff(fact_4152_push__bit__of__1,axiom,
    ! [N2: nat] : aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se6611745700429515170atural,N2),one_one_Code_natural) = aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),N2) ).

% push_bit_of_1
tff(fact_4153_sum_Oop__ivl__Suc,axiom,
    ! [G: fun_nat_Code_integer,M: nat,N2: nat] :
      groups7501900531339628137nteger(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),aa_nat_nat(suc,N2))) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),M),zero_z3403309356797280102nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,groups7501900531339628137nteger(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))),aa_nat_Code_integer(G,N2))) ).

% sum.op_ivl_Suc
tff(fact_4154_sum_Oop__ivl__Suc,axiom,
    ! [G: fun_na2338080690716861136at_nat,M: nat,N2: nat] :
      groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),aa_nat_nat(suc,N2))) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),M),zero_z1048942125864253310at_nat,aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))),aa_nat2240542744625857721at_nat(G,N2))) ).

% sum.op_ivl_Suc
tff(fact_4155_sum_Oop__ivl__Suc,axiom,
    ! [G: fun_nat_rat,M: nat,N2: nat] :
      groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),aa_nat_nat(suc,N2))) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),M),zero_zero_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))),aa_nat_rat(G,N2))) ).

% sum.op_ivl_Suc
tff(fact_4156_sum_Oop__ivl__Suc,axiom,
    ! [G: fun_nat_int,M: nat,N2: nat] :
      groups3539618377306564664at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),aa_nat_nat(suc,N2))) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),M),zero_zero_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,groups3539618377306564664at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))),aa_nat_int(G,N2))) ).

% sum.op_ivl_Suc
tff(fact_4157_sum_Oop__ivl__Suc,axiom,
    ! [G: fun_nat_nat,M: nat,N2: nat] :
      aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(M),aa_nat_nat(suc,N2))) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),M),zero_zero_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))),aa_nat_nat(G,N2))) ).

% sum.op_ivl_Suc
tff(fact_4158_xor__numerals_I4_J,axiom,
    ! [X2: num,Y: num] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se6528837805403552850or_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,X2))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,Y))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(bit_se6528837805403552850or_nat,aa_num_nat(numeral_numeral_nat,X2)),aa_num_nat(numeral_numeral_nat,Y)))) ).

% xor_numerals(4)
tff(fact_4159_xor__numerals_I4_J,axiom,
    ! [X2: num,Y: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3222712562003087583nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,X2))),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit1,Y))) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,one_one_Code_integer),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3222712562003087583nteger,aa_num_Code_integer(numera6620942414471956472nteger,X2)),aa_num_Code_integer(numera6620942414471956472nteger,Y)))) ).

% xor_numerals(4)
tff(fact_4160_xor__numerals_I4_J,axiom,
    ! [X2: num,Y: num] : aa_int_int(aa_int_fun_int_int(bit_se6526347334894502574or_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,X2))),aa_num_int(numeral_numeral_int,aa_num_num(bit1,Y))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(bit_se6526347334894502574or_int,aa_num_int(numeral_numeral_int,X2)),aa_num_int(numeral_numeral_int,Y)))) ).

% xor_numerals(4)
tff(fact_4161_xor__numerals_I4_J,axiom,
    ! [X2: num,Y: num] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se2046307713759805098atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,X2))),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,Y))) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,one_one_Code_natural),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se2046307713759805098atural,aa_num_Code_natural(numera5444537566228673987atural,X2)),aa_num_Code_natural(numera5444537566228673987atural,Y)))) ).

% xor_numerals(4)
tff(fact_4162_xor__numerals_I6_J,axiom,
    ! [X2: num,Y: num] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se6528837805403552850or_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,X2))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,Y))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(bit_se6528837805403552850or_nat,aa_num_nat(numeral_numeral_nat,X2)),aa_num_nat(numeral_numeral_nat,Y)))) ).

% xor_numerals(6)
tff(fact_4163_xor__numerals_I6_J,axiom,
    ! [X2: num,Y: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3222712562003087583nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit1,X2))),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,Y))) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,one_one_Code_integer),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3222712562003087583nteger,aa_num_Code_integer(numera6620942414471956472nteger,X2)),aa_num_Code_integer(numera6620942414471956472nteger,Y)))) ).

% xor_numerals(6)
tff(fact_4164_xor__numerals_I6_J,axiom,
    ! [X2: num,Y: num] : aa_int_int(aa_int_fun_int_int(bit_se6526347334894502574or_int,aa_num_int(numeral_numeral_int,aa_num_num(bit1,X2))),aa_num_int(numeral_numeral_int,aa_num_num(bit0,Y))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(bit_se6526347334894502574or_int,aa_num_int(numeral_numeral_int,X2)),aa_num_int(numeral_numeral_int,Y)))) ).

% xor_numerals(6)
tff(fact_4165_xor__numerals_I6_J,axiom,
    ! [X2: num,Y: num] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se2046307713759805098atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,X2))),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,Y))) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,one_one_Code_natural),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se2046307713759805098atural,aa_num_Code_natural(numera5444537566228673987atural,X2)),aa_num_Code_natural(numera5444537566228673987atural,Y)))) ).

% xor_numerals(6)
tff(fact_4166_flip__bit__nat__def,axiom,
    ! [M: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se2161824704523386999it_nat,M),N2) = aa_nat_nat(aa_nat_fun_nat_nat(bit_se6528837805403552850or_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(bit_se547839408752420682it_nat,M),one_one_nat)) ).

% flip_bit_nat_def
tff(fact_4167_push__bit__integer_Oabs__eq,axiom,
    ! [Xa: nat,X2: int] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se7788150548672797655nteger,Xa),aa_int_Code_integer(code_integer_of_int,X2)) = aa_int_Code_integer(code_integer_of_int,aa_int_int(aa_nat_fun_int_int(bit_se545348938243370406it_int,Xa),X2)) ).

% push_bit_integer.abs_eq
tff(fact_4168_atLeastLessThan__inj_I2_J,axiom,
    ! [A: rat,B: rat,C: rat,D2: rat] :
      ( ( set_or4029947393144176647an_rat(A,B) = set_or4029947393144176647an_rat(C,D2) )
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B)
       => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,C),D2)
         => ( B = D2 ) ) ) ) ).

% atLeastLessThan_inj(2)
tff(fact_4169_atLeastLessThan__inj_I2_J,axiom,
    ! [A: num,B: num,C: num,D2: num] :
      ( ( set_or1222409239386451017an_num(A,B) = set_or1222409239386451017an_num(C,D2) )
     => ( aa_num_o(aa_num_fun_num_o(ord_less_num,A),B)
       => ( aa_num_o(aa_num_fun_num_o(ord_less_num,C),D2)
         => ( B = D2 ) ) ) ) ).

% atLeastLessThan_inj(2)
tff(fact_4170_atLeastLessThan__inj_I2_J,axiom,
    ! [A: nat,B: nat,C: nat,D2: nat] :
      ( ( aa_nat_set_nat(set_or4665077453230672383an_nat(A),B) = aa_nat_set_nat(set_or4665077453230672383an_nat(C),D2) )
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),B)
       => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,C),D2)
         => ( B = D2 ) ) ) ) ).

% atLeastLessThan_inj(2)
tff(fact_4171_atLeastLessThan__inj_I2_J,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
      ( ( aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(A),B) = aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(C),D2) )
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),B)
       => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,C),D2)
         => ( B = D2 ) ) ) ) ).

% atLeastLessThan_inj(2)
tff(fact_4172_atLeastLessThan__inj_I2_J,axiom,
    ! [A: int,B: int,C: int,D2: int] :
      ( ( aa_int_set_int(set_or4662586982721622107an_int(A),B) = aa_int_set_int(set_or4662586982721622107an_int(C),D2) )
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,A),B)
       => ( aa_int_o(aa_int_fun_int_o(ord_less_int,C),D2)
         => ( B = D2 ) ) ) ) ).

% atLeastLessThan_inj(2)
tff(fact_4173_atLeastLessThan__inj_I1_J,axiom,
    ! [A: rat,B: rat,C: rat,D2: rat] :
      ( ( set_or4029947393144176647an_rat(A,B) = set_or4029947393144176647an_rat(C,D2) )
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B)
       => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,C),D2)
         => ( A = C ) ) ) ) ).

% atLeastLessThan_inj(1)
tff(fact_4174_atLeastLessThan__inj_I1_J,axiom,
    ! [A: num,B: num,C: num,D2: num] :
      ( ( set_or1222409239386451017an_num(A,B) = set_or1222409239386451017an_num(C,D2) )
     => ( aa_num_o(aa_num_fun_num_o(ord_less_num,A),B)
       => ( aa_num_o(aa_num_fun_num_o(ord_less_num,C),D2)
         => ( A = C ) ) ) ) ).

% atLeastLessThan_inj(1)
tff(fact_4175_atLeastLessThan__inj_I1_J,axiom,
    ! [A: nat,B: nat,C: nat,D2: nat] :
      ( ( aa_nat_set_nat(set_or4665077453230672383an_nat(A),B) = aa_nat_set_nat(set_or4665077453230672383an_nat(C),D2) )
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),B)
       => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,C),D2)
         => ( A = C ) ) ) ) ).

% atLeastLessThan_inj(1)
tff(fact_4176_atLeastLessThan__inj_I1_J,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
      ( ( aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(A),B) = aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(C),D2) )
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),B)
       => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,C),D2)
         => ( A = C ) ) ) ) ).

% atLeastLessThan_inj(1)
tff(fact_4177_atLeastLessThan__inj_I1_J,axiom,
    ! [A: int,B: int,C: int,D2: int] :
      ( ( aa_int_set_int(set_or4662586982721622107an_int(A),B) = aa_int_set_int(set_or4662586982721622107an_int(C),D2) )
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,A),B)
       => ( aa_int_o(aa_int_fun_int_o(ord_less_int,C),D2)
         => ( A = C ) ) ) ) ).

% atLeastLessThan_inj(1)
tff(fact_4178_atLeastLessThan__eq__iff,axiom,
    ! [A: rat,B: rat,C: rat,D2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,C),D2)
       => ( ( set_or4029947393144176647an_rat(A,B) = set_or4029947393144176647an_rat(C,D2) )
        <=> ( ( A = C )
            & ( B = D2 ) ) ) ) ) ).

% atLeastLessThan_eq_iff
tff(fact_4179_atLeastLessThan__eq__iff,axiom,
    ! [A: num,B: num,C: num,D2: num] :
      ( aa_num_o(aa_num_fun_num_o(ord_less_num,A),B)
     => ( aa_num_o(aa_num_fun_num_o(ord_less_num,C),D2)
       => ( ( set_or1222409239386451017an_num(A,B) = set_or1222409239386451017an_num(C,D2) )
        <=> ( ( A = C )
            & ( B = D2 ) ) ) ) ) ).

% atLeastLessThan_eq_iff
tff(fact_4180_atLeastLessThan__eq__iff,axiom,
    ! [A: nat,B: nat,C: nat,D2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),B)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,C),D2)
       => ( ( aa_nat_set_nat(set_or4665077453230672383an_nat(A),B) = aa_nat_set_nat(set_or4665077453230672383an_nat(C),D2) )
        <=> ( ( A = C )
            & ( B = D2 ) ) ) ) ) ).

% atLeastLessThan_eq_iff
tff(fact_4181_atLeastLessThan__eq__iff,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),B)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,C),D2)
       => ( ( aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(A),B) = aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(C),D2) )
        <=> ( ( A = C )
            & ( B = D2 ) ) ) ) ) ).

% atLeastLessThan_eq_iff
tff(fact_4182_atLeastLessThan__eq__iff,axiom,
    ! [A: int,B: int,C: int,D2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,A),B)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,C),D2)
       => ( ( aa_int_set_int(set_or4662586982721622107an_int(A),B) = aa_int_set_int(set_or4662586982721622107an_int(C),D2) )
        <=> ( ( A = C )
            & ( B = D2 ) ) ) ) ) ).

% atLeastLessThan_eq_iff
tff(fact_4183_flip__bit__eq__xor,axiom,
    ! [N2: nat,A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se2161824704523386999it_nat,N2),A) = aa_nat_nat(aa_nat_fun_nat_nat(bit_se6528837805403552850or_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(bit_se547839408752420682it_nat,N2),one_one_nat)) ).

% flip_bit_eq_xor
tff(fact_4184_flip__bit__eq__xor,axiom,
    ! [N2: nat,A: code_integer] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1345352211410354436nteger,N2),A) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3222712562003087583nteger,A),aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se7788150548672797655nteger,N2),one_one_Code_integer)) ).

% flip_bit_eq_xor
tff(fact_4185_flip__bit__eq__xor,axiom,
    ! [N2: nat,A: int] : aa_int_int(aa_nat_fun_int_int(bit_se2159334234014336723it_int,N2),A) = aa_int_int(aa_int_fun_int_int(bit_se6526347334894502574or_int,A),aa_int_int(aa_nat_fun_int_int(bit_se545348938243370406it_int,N2),one_one_int)) ).

% flip_bit_eq_xor
tff(fact_4186_flip__bit__eq__xor,axiom,
    ! [N2: nat,A: code_natural] : aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se168947363167071951atural,N2),A) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se2046307713759805098atural,A),aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se6611745700429515170atural,N2),one_one_Code_natural)) ).

% flip_bit_eq_xor
tff(fact_4187_push__bit__add,axiom,
    ! [N2: nat,A: nat,B: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se547839408752420682it_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(bit_se547839408752420682it_nat,N2),A)),aa_nat_nat(aa_nat_fun_nat_nat(bit_se547839408752420682it_nat,N2),B)) ).

% push_bit_add
tff(fact_4188_push__bit__add,axiom,
    ! [N2: nat,A: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se7788150548672797655nteger,N2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se7788150548672797655nteger,N2),A)),aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se7788150548672797655nteger,N2),B)) ).

% push_bit_add
tff(fact_4189_push__bit__add,axiom,
    ! [N2: nat,A: int,B: int] : aa_int_int(aa_nat_fun_int_int(bit_se545348938243370406it_int,N2),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_nat_fun_int_int(bit_se545348938243370406it_int,N2),A)),aa_int_int(aa_nat_fun_int_int(bit_se545348938243370406it_int,N2),B)) ).

% push_bit_add
tff(fact_4190_push__bit__add,axiom,
    ! [N2: nat,A: code_natural,B: code_natural] : aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se6611745700429515170atural,N2),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),B)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se6611745700429515170atural,N2),A)),aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se6611745700429515170atural,N2),B)) ).

% push_bit_add
tff(fact_4191_atLeastLessThan__subset__iff,axiom,
    ! [A: rat,B: rat,C: rat,D2: rat] :
      ( ord_less_eq_set_rat(set_or4029947393144176647an_rat(A,B),set_or4029947393144176647an_rat(C,D2))
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),A)
        | ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,C),A)
          & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),D2) ) ) ) ).

% atLeastLessThan_subset_iff
tff(fact_4192_atLeastLessThan__subset__iff,axiom,
    ! [A: num,B: num,C: num,D2: num] :
      ( ord_less_eq_set_num(set_or1222409239386451017an_num(A,B),set_or1222409239386451017an_num(C,D2))
     => ( aa_num_o(aa_num_fun_num_o(ord_less_eq_num,B),A)
        | ( aa_num_o(aa_num_fun_num_o(ord_less_eq_num,C),A)
          & aa_num_o(aa_num_fun_num_o(ord_less_eq_num,B),D2) ) ) ) ).

% atLeastLessThan_subset_iff
tff(fact_4193_atLeastLessThan__subset__iff,axiom,
    ! [A: nat,B: nat,C: nat,D2: nat] :
      ( aa_set_nat_o(ord_less_eq_set_nat(aa_nat_set_nat(set_or4665077453230672383an_nat(A),B)),aa_nat_set_nat(set_or4665077453230672383an_nat(C),D2))
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,B),A)
        | ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,C),A)
          & aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,B),D2) ) ) ) ).

% atLeastLessThan_subset_iff
tff(fact_4194_atLeastLessThan__subset__iff,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
      ( ord_le7084787975880047091nteger(aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(A),B),aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(C),D2))
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,B),A)
        | ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,C),A)
          & aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,B),D2) ) ) ) ).

% atLeastLessThan_subset_iff
tff(fact_4195_atLeastLessThan__subset__iff,axiom,
    ! [A: int,B: int,C: int,D2: int] :
      ( ord_less_eq_set_int(aa_int_set_int(set_or4662586982721622107an_int(A),B),aa_int_set_int(set_or4662586982721622107an_int(C),D2))
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,B),A)
        | ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,C),A)
          & aa_int_o(aa_int_fun_int_o(ord_less_eq_int,B),D2) ) ) ) ).

% atLeastLessThan_subset_iff
tff(fact_4196_atLeastLessThanSuc__atLeastAtMost,axiom,
    ! [L: nat,U: nat] : aa_nat_set_nat(set_or4665077453230672383an_nat(L),aa_nat_nat(suc,U)) = aa_nat_set_nat(set_or1269000886237332187st_nat(L),U) ).

% atLeastLessThanSuc_atLeastAtMost
tff(fact_4197_lessThan__atLeast0,axiom,
    ! [N2: nat] : aa_nat_set_nat(set_ord_lessThan_nat,N2) = aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2) ).

% lessThan_atLeast0
tff(fact_4198_push__bit__take__bit,axiom,
    ! [M: nat,N2: nat,A: code_integer] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se7788150548672797655nteger,M),aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,N2),A)) = aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)),aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se7788150548672797655nteger,M),A)) ).

% push_bit_take_bit
tff(fact_4199_push__bit__take__bit,axiom,
    ! [M: nat,N2: nat,A: int] : aa_int_int(aa_nat_fun_int_int(bit_se545348938243370406it_int,M),aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,N2),A)) = aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)),aa_int_int(aa_nat_fun_int_int(bit_se545348938243370406it_int,M),A)) ).

% push_bit_take_bit
tff(fact_4200_push__bit__take__bit,axiom,
    ! [M: nat,N2: nat,A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se547839408752420682it_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,N2),A)) = aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)),aa_nat_nat(aa_nat_fun_nat_nat(bit_se547839408752420682it_nat,M),A)) ).

% push_bit_take_bit
tff(fact_4201_push__bit__take__bit,axiom,
    ! [M: nat,N2: nat,A: code_natural] : aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se6611745700429515170atural,M),aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se569199155075624693atural,N2),A)) = aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se569199155075624693atural,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)),aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se6611745700429515170atural,M),A)) ).

% push_bit_take_bit
tff(fact_4202_pochhammer__fact,axiom,
    ! [N2: nat] : aa_nat_Code_integer(semiri3624122377584611663nteger,N2) = aa_nat_Code_integer(comm_s8582702949713902594nteger(one_one_Code_integer),N2) ).

% pochhammer_fact
tff(fact_4203_pochhammer__fact,axiom,
    ! [N2: nat] : aa_nat_rat(semiri773545260158071498ct_rat,N2) = aa_nat_rat(comm_s4028243227959126397er_rat(one_one_rat),N2) ).

% pochhammer_fact
tff(fact_4204_pochhammer__fact,axiom,
    ! [N2: nat] : aa_nat_int(semiri1406184849735516958ct_int,N2) = aa_nat_int(comm_s4660882817536571857er_int(one_one_int),N2) ).

% pochhammer_fact
tff(fact_4205_pochhammer__fact,axiom,
    ! [N2: nat] : aa_nat_nat(semiri1408675320244567234ct_nat,N2) = aa_nat_nat(aa_nat_fun_nat_nat(comm_s4663373288045622133er_nat,one_one_nat),N2) ).

% pochhammer_fact
tff(fact_4206_sum_Oshift__bounds__Suc__ivl,axiom,
    ! [G: fun_nat_nat,M: nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(suc,M)),aa_nat_nat(suc,N2))) = aa_set_nat_nat(groups3542108847815614940at_nat(aTP_Lamm_dh(G)),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) ).

% sum.shift_bounds_Suc_ivl
tff(fact_4207_sum_Oshift__bounds__nat__ivl,axiom,
    ! [G: fun_nat_nat,M: nat,K: nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),K))) = aa_set_nat_nat(groups3542108847815614940at_nat(aa_nat_fun_nat_nat(aTP_Lamm_di(G),K)),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) ).

% sum.shift_bounds_nat_ivl
tff(fact_4208_sum_Oivl__cong,axiom,
    ! [A: nat,C: nat,B: nat,D2: nat,G: fun_nat_nat,Ha: fun_nat_nat] :
      ( ( A = C )
     => ( ( B = D2 )
       => ( ! [X3: nat] :
              ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,C),X3)
             => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,X3),D2)
               => ( aa_nat_nat(G,X3) = aa_nat_nat(Ha,X3) ) ) )
         => ( aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(A),B)) = aa_set_nat_nat(groups3542108847815614940at_nat(Ha),aa_nat_set_nat(set_or4665077453230672383an_nat(C),D2)) ) ) ) ) ).

% sum.ivl_cong
tff(fact_4209_sum_Oivl__cong,axiom,
    ! [A: int,C: int,B: int,D2: int,G: fun_int_int,Ha: fun_int_int] :
      ( ( A = C )
     => ( ( B = D2 )
       => ( ! [X3: int] :
              ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,C),X3)
             => ( aa_int_o(aa_int_fun_int_o(ord_less_int,X3),D2)
               => ( aa_int_int(G,X3) = aa_int_int(Ha,X3) ) ) )
         => ( aa_set_int_int(groups4538972089207619220nt_int(G),aa_int_set_int(set_or4662586982721622107an_int(A),B)) = aa_set_int_int(groups4538972089207619220nt_int(Ha),aa_int_set_int(set_or4662586982721622107an_int(C),D2)) ) ) ) ) ).

% sum.ivl_cong
tff(fact_4210_sum_OatLeastLessThan__concat,axiom,
    ! [M: nat,N2: nat,P2: nat,G: fun_na2338080690716861136at_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),P2)
       => ( aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))),groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(N2),P2))) = groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),P2)) ) ) ) ).

% sum.atLeastLessThan_concat
tff(fact_4211_sum_OatLeastLessThan__concat,axiom,
    ! [M: nat,N2: nat,P2: nat,G: fun_nat_rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),P2)
       => ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))),groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(N2),P2))) = groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),P2)) ) ) ) ).

% sum.atLeastLessThan_concat
tff(fact_4212_sum_OatLeastLessThan__concat,axiom,
    ! [M: nat,N2: nat,P2: nat,G: fun_nat_int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),P2)
       => ( aa_int_int(aa_int_fun_int_int(plus_plus_int,groups3539618377306564664at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))),groups3539618377306564664at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(N2),P2))) = groups3539618377306564664at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),P2)) ) ) ) ).

% sum.atLeastLessThan_concat
tff(fact_4213_sum_OatLeastLessThan__concat,axiom,
    ! [M: nat,N2: nat,P2: nat,G: fun_nat_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),P2)
       => ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))),aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(N2),P2))) = aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(M),P2)) ) ) ) ).

% sum.atLeastLessThan_concat
tff(fact_4214_sum__diff__nat__ivl,axiom,
    ! [M: nat,N2: nat,P2: nat,F: fun_nat_Code_integer] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),P2)
       => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,groups7501900531339628137nteger(F,aa_nat_set_nat(set_or4665077453230672383an_nat(M),P2))),groups7501900531339628137nteger(F,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))) = groups7501900531339628137nteger(F,aa_nat_set_nat(set_or4665077453230672383an_nat(N2),P2)) ) ) ) ).

% sum_diff_nat_ivl
tff(fact_4215_sum__diff__nat__ivl,axiom,
    ! [M: nat,N2: nat,P2: nat,F: fun_nat_rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),P2)
       => ( aa_rat_rat(minus_minus_rat(groups2906978787729119204at_rat(F,aa_nat_set_nat(set_or4665077453230672383an_nat(M),P2))),groups2906978787729119204at_rat(F,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))) = groups2906978787729119204at_rat(F,aa_nat_set_nat(set_or4665077453230672383an_nat(N2),P2)) ) ) ) ).

% sum_diff_nat_ivl
tff(fact_4216_sum__diff__nat__ivl,axiom,
    ! [M: nat,N2: nat,P2: nat,F: fun_nat_int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),P2)
       => ( aa_int_int(aa_int_fun_int_int(minus_minus_int,groups3539618377306564664at_int(F,aa_nat_set_nat(set_or4665077453230672383an_nat(M),P2))),groups3539618377306564664at_int(F,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))) = groups3539618377306564664at_int(F,aa_nat_set_nat(set_or4665077453230672383an_nat(N2),P2)) ) ) ) ).

% sum_diff_nat_ivl
tff(fact_4217_pochhammer__0__left,axiom,
    ! [N2: nat] :
      aa_nat_Code_integer(comm_s8582702949713902594nteger(zero_z3403309356797280102nteger),N2) = $ite(N2 = zero_zero_nat,one_one_Code_integer,zero_z3403309356797280102nteger) ).

% pochhammer_0_left
tff(fact_4218_pochhammer__0__left,axiom,
    ! [N2: nat] :
      aa_nat_rat(comm_s4028243227959126397er_rat(zero_zero_rat),N2) = $ite(N2 = zero_zero_nat,one_one_rat,zero_zero_rat) ).

% pochhammer_0_left
tff(fact_4219_pochhammer__0__left,axiom,
    ! [N2: nat] :
      aa_nat_nat(aa_nat_fun_nat_nat(comm_s4663373288045622133er_nat,zero_zero_nat),N2) = $ite(N2 = zero_zero_nat,one_one_nat,zero_zero_nat) ).

% pochhammer_0_left
tff(fact_4220_pochhammer__0__left,axiom,
    ! [N2: nat] :
      aa_nat_int(comm_s4660882817536571857er_int(zero_zero_int),N2) = $ite(N2 = zero_zero_nat,one_one_int,zero_zero_int) ).

% pochhammer_0_left
tff(fact_4221_sum_OatLeast__Suc__lessThan__Suc__shift,axiom,
    ! [G: fun_nat_nat,M: nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(suc,M)),aa_nat_nat(suc,N2))) = aa_set_nat_nat(groups3542108847815614940at_nat(comp_nat_nat_nat(G,suc)),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) ).

% sum.atLeast_Suc_lessThan_Suc_shift
tff(fact_4222_sum_OatLeastLessThan__shift__bounds,axiom,
    ! [G: fun_nat_nat,M: nat,K: nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),K))) = aa_set_nat_nat(groups3542108847815614940at_nat(comp_nat_nat_nat(G,aa_nat_fun_nat_nat(plus_plus_nat,K))),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) ).

% sum.atLeastLessThan_shift_bounds
tff(fact_4223_concat__bit__eq,axiom,
    ! [N2: nat,K: int,L: int] : aa_int_int(aa_int_fun_int_int(bit_concat_bit(N2),K),L) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,N2),K)),aa_int_int(aa_nat_fun_int_int(bit_se545348938243370406it_int,N2),L)) ).

% concat_bit_eq
tff(fact_4224_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
    ! [A: set_nat,B: set_nat,C: set_nat,D2: set_nat] :
      ( ord_le6893508408891458716et_nat(set_or4548717258645045905et_nat(A,B),set_or3540276404033026485et_nat(C,D2))
    <=> ( aa_set_nat_o(ord_less_eq_set_nat(A),B)
       => ( aa_set_nat_o(ord_less_eq_set_nat(C),A)
          & ord_less_set_nat(B,D2) ) ) ) ).

% atLeastAtMost_subseteq_atLeastLessThan_iff
tff(fact_4225_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
    ! [A: rat,B: rat,C: rat,D2: rat] :
      ( ord_less_eq_set_rat(set_or633870826150836451st_rat(A,B),set_or4029947393144176647an_rat(C,D2))
    <=> ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),B)
       => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,C),A)
          & aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,B),D2) ) ) ) ).

% atLeastAtMost_subseteq_atLeastLessThan_iff
tff(fact_4226_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
    ! [A: num,B: num,C: num,D2: num] :
      ( ord_less_eq_set_num(set_or7049704709247886629st_num(A,B),set_or1222409239386451017an_num(C,D2))
    <=> ( aa_num_o(aa_num_fun_num_o(ord_less_eq_num,A),B)
       => ( aa_num_o(aa_num_fun_num_o(ord_less_eq_num,C),A)
          & aa_num_o(aa_num_fun_num_o(ord_less_num,B),D2) ) ) ) ).

% atLeastAtMost_subseteq_atLeastLessThan_iff
tff(fact_4227_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
    ! [A: nat,B: nat,C: nat,D2: nat] :
      ( aa_set_nat_o(ord_less_eq_set_nat(aa_nat_set_nat(set_or1269000886237332187st_nat(A),B)),aa_nat_set_nat(set_or4665077453230672383an_nat(C),D2))
    <=> ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
       => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,C),A)
          & aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,B),D2) ) ) ) ).

% atLeastAtMost_subseteq_atLeastLessThan_iff
tff(fact_4228_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
      ( ord_le7084787975880047091nteger(aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(A),B),aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(C),D2))
    <=> ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),B)
       => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,C),A)
          & aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,B),D2) ) ) ) ).

% atLeastAtMost_subseteq_atLeastLessThan_iff
tff(fact_4229_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
    ! [A: int,B: int,C: int,D2: int] :
      ( ord_less_eq_set_int(aa_int_set_int(set_or1266510415728281911st_int(A),B),aa_int_set_int(set_or4662586982721622107an_int(C),D2))
    <=> ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),B)
       => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,C),A)
          & aa_int_o(aa_int_fun_int_o(ord_less_int,B),D2) ) ) ) ).

% atLeastAtMost_subseteq_atLeastLessThan_iff
tff(fact_4230_atLeastLessThan__subseteq__atLeastAtMost__iff,axiom,
    ! [A: rat,B: rat,C: rat,D2: rat] :
      ( ord_less_eq_set_rat(set_or4029947393144176647an_rat(A,B),set_or633870826150836451st_rat(C,D2))
    <=> ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B)
       => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,C),A)
          & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),D2) ) ) ) ).

% atLeastLessThan_subseteq_atLeastAtMost_iff
tff(fact_4231_sum__shift__lb__Suc0__0__upt,axiom,
    ! [F: fun_nat_Code_integer,K: nat] :
      ( ( aa_nat_Code_integer(F,zero_zero_nat) = zero_z3403309356797280102nteger )
     => ( groups7501900531339628137nteger(F,aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(suc,zero_zero_nat)),K)) = groups7501900531339628137nteger(F,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),K)) ) ) ).

% sum_shift_lb_Suc0_0_upt
tff(fact_4232_sum__shift__lb__Suc0__0__upt,axiom,
    ! [F: fun_na2338080690716861136at_nat,K: nat] :
      ( ( aa_nat2240542744625857721at_nat(F,zero_zero_nat) = zero_z1048942125864253310at_nat )
     => ( groups6857163185585827899at_nat(F,aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(suc,zero_zero_nat)),K)) = groups6857163185585827899at_nat(F,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),K)) ) ) ).

% sum_shift_lb_Suc0_0_upt
tff(fact_4233_sum__shift__lb__Suc0__0__upt,axiom,
    ! [F: fun_nat_rat,K: nat] :
      ( ( aa_nat_rat(F,zero_zero_nat) = zero_zero_rat )
     => ( groups2906978787729119204at_rat(F,aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(suc,zero_zero_nat)),K)) = groups2906978787729119204at_rat(F,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),K)) ) ) ).

% sum_shift_lb_Suc0_0_upt
tff(fact_4234_sum__shift__lb__Suc0__0__upt,axiom,
    ! [F: fun_nat_int,K: nat] :
      ( ( aa_nat_int(F,zero_zero_nat) = zero_zero_int )
     => ( groups3539618377306564664at_int(F,aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(suc,zero_zero_nat)),K)) = groups3539618377306564664at_int(F,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),K)) ) ) ).

% sum_shift_lb_Suc0_0_upt
tff(fact_4235_sum__shift__lb__Suc0__0__upt,axiom,
    ! [F: fun_nat_nat,K: nat] :
      ( ( aa_nat_nat(F,zero_zero_nat) = zero_zero_nat )
     => ( aa_set_nat_nat(groups3542108847815614940at_nat(F),aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(suc,zero_zero_nat)),K)) = aa_set_nat_nat(groups3542108847815614940at_nat(F),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),K)) ) ) ).

% sum_shift_lb_Suc0_0_upt
tff(fact_4236_sum_OatLeast0__lessThan__Suc,axiom,
    ! [G: fun_na2338080690716861136at_nat,N2: nat] : groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2))),aa_nat2240542744625857721at_nat(G,N2)) ).

% sum.atLeast0_lessThan_Suc
tff(fact_4237_sum_OatLeast0__lessThan__Suc,axiom,
    ! [G: fun_nat_rat,N2: nat] : groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2))),aa_nat_rat(G,N2)) ).

% sum.atLeast0_lessThan_Suc
tff(fact_4238_sum_OatLeast0__lessThan__Suc,axiom,
    ! [G: fun_nat_int,N2: nat] : groups3539618377306564664at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,groups3539618377306564664at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2))),aa_nat_int(G,N2)) ).

% sum.atLeast0_lessThan_Suc
tff(fact_4239_sum_OatLeast0__lessThan__Suc,axiom,
    ! [G: fun_nat_nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2))),aa_nat_nat(G,N2)) ).

% sum.atLeast0_lessThan_Suc
tff(fact_4240_sum_OatLeast__Suc__lessThan,axiom,
    ! [M: nat,N2: nat,G: fun_na2338080690716861136at_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M),N2)
     => ( groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(aa_nat2240542744625857721at_nat(G,M)),groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(suc,M)),N2))) ) ) ).

% sum.atLeast_Suc_lessThan
tff(fact_4241_sum_OatLeast__Suc__lessThan,axiom,
    ! [M: nat,N2: nat,G: fun_nat_rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M),N2)
     => ( groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(G,M)),groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(suc,M)),N2))) ) ) ).

% sum.atLeast_Suc_lessThan
tff(fact_4242_sum_OatLeast__Suc__lessThan,axiom,
    ! [M: nat,N2: nat,G: fun_nat_int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M),N2)
     => ( groups3539618377306564664at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(G,M)),groups3539618377306564664at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(suc,M)),N2))) ) ) ).

% sum.atLeast_Suc_lessThan
tff(fact_4243_sum_OatLeast__Suc__lessThan,axiom,
    ! [M: nat,N2: nat,G: fun_nat_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M),N2)
     => ( aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(G,M)),aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(suc,M)),N2))) ) ) ).

% sum.atLeast_Suc_lessThan
tff(fact_4244_sum_OatLeastLessThan__Suc,axiom,
    ! [A: nat,B: nat,G: fun_na2338080690716861136at_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
     => ( groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(A),aa_nat_nat(suc,B))) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(A),B))),aa_nat2240542744625857721at_nat(G,B)) ) ) ).

% sum.atLeastLessThan_Suc
tff(fact_4245_sum_OatLeastLessThan__Suc,axiom,
    ! [A: nat,B: nat,G: fun_nat_rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
     => ( groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(A),aa_nat_nat(suc,B))) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(A),B))),aa_nat_rat(G,B)) ) ) ).

% sum.atLeastLessThan_Suc
tff(fact_4246_sum_OatLeastLessThan__Suc,axiom,
    ! [A: nat,B: nat,G: fun_nat_int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
     => ( groups3539618377306564664at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(A),aa_nat_nat(suc,B))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,groups3539618377306564664at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(A),B))),aa_nat_int(G,B)) ) ) ).

% sum.atLeastLessThan_Suc
tff(fact_4247_sum_OatLeastLessThan__Suc,axiom,
    ! [A: nat,B: nat,G: fun_nat_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
     => ( aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(A),aa_nat_nat(suc,B))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(A),B))),aa_nat_nat(G,B)) ) ) ).

% sum.atLeastLessThan_Suc
tff(fact_4248_sum_Olast__plus,axiom,
    ! [M: nat,N2: nat,G: fun_na2338080690716861136at_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(aa_nat2240542744625857721at_nat(G,N2)),groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))) ) ) ).

% sum.last_plus
tff(fact_4249_sum_Olast__plus,axiom,
    ! [M: nat,N2: nat,G: fun_nat_rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(G,N2)),groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))) ) ) ).

% sum.last_plus
tff(fact_4250_sum_Olast__plus,axiom,
    ! [M: nat,N2: nat,G: fun_nat_int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( groups3539618377306564664at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(G,N2)),groups3539618377306564664at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))) ) ) ).

% sum.last_plus
tff(fact_4251_sum_Olast__plus,axiom,
    ! [M: nat,N2: nat,G: fun_nat_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(G,N2)),aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))) ) ) ).

% sum.last_plus
tff(fact_4252_pochhammer__rec,axiom,
    ! [A: code_integer,N2: nat] : aa_nat_Code_integer(comm_s8582702949713902594nteger(A),aa_nat_nat(suc,N2)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,A),aa_nat_Code_integer(comm_s8582702949713902594nteger(aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),one_one_Code_integer)),N2)) ).

% pochhammer_rec
tff(fact_4253_pochhammer__rec,axiom,
    ! [A: rat,N2: nat] : aa_nat_rat(comm_s4028243227959126397er_rat(A),aa_nat_nat(suc,N2)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),aa_nat_rat(comm_s4028243227959126397er_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),one_one_rat)),N2)) ).

% pochhammer_rec
tff(fact_4254_pochhammer__rec,axiom,
    ! [A: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(comm_s4663373288045622133er_nat,A),aa_nat_nat(suc,N2)) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(comm_s4663373288045622133er_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),one_one_nat)),N2)) ).

% pochhammer_rec
tff(fact_4255_pochhammer__rec,axiom,
    ! [A: int,N2: nat] : aa_nat_int(comm_s4660882817536571857er_int(A),aa_nat_nat(suc,N2)) = aa_int_int(aa_int_fun_int_int(times_times_int,A),aa_nat_int(comm_s4660882817536571857er_int(aa_int_int(aa_int_fun_int_int(plus_plus_int,A),one_one_int)),N2)) ).

% pochhammer_rec
tff(fact_4256_pochhammer__Suc,axiom,
    ! [A: rat,N2: nat] : aa_nat_rat(comm_s4028243227959126397er_rat(A),aa_nat_nat(suc,N2)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(comm_s4028243227959126397er_rat(A),N2)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),aa_nat_rat(semiri681578069525770553at_rat,N2))) ).

% pochhammer_Suc
tff(fact_4257_pochhammer__Suc,axiom,
    ! [A: int,N2: nat] : aa_nat_int(comm_s4660882817536571857er_int(A),aa_nat_nat(suc,N2)) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(comm_s4660882817536571857er_int(A),N2)),aa_int_int(aa_int_fun_int_int(plus_plus_int,A),aa_nat_int(semiri1314217659103216013at_int,N2))) ).

% pochhammer_Suc
tff(fact_4258_pochhammer__Suc,axiom,
    ! [A: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(comm_s4663373288045622133er_nat,A),aa_nat_nat(suc,N2)) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(comm_s4663373288045622133er_nat,A),N2)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),aa_nat_nat(semiri1316708129612266289at_nat,N2))) ).

% pochhammer_Suc
tff(fact_4259_pochhammer__Suc,axiom,
    ! [A: code_integer,N2: nat] : aa_nat_Code_integer(comm_s8582702949713902594nteger(A),aa_nat_nat(suc,N2)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(comm_s8582702949713902594nteger(A),N2)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),aa_nat_Code_integer(semiri4939895301339042750nteger,N2))) ).

% pochhammer_Suc
tff(fact_4260_pochhammer__Suc,axiom,
    ! [A: code_natural,N2: nat] : aa_nat_Code_natural(comm_s7406298101470620109atural(A),aa_nat_nat(suc,N2)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_nat_Code_natural(comm_s7406298101470620109atural(A),N2)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),aa_nat_Code_natural(semiri3763490453095760265atural,N2))) ).

% pochhammer_Suc
tff(fact_4261_pochhammer__rec_H,axiom,
    ! [Z: rat,N2: nat] : aa_nat_rat(comm_s4028243227959126397er_rat(Z),aa_nat_nat(suc,N2)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,Z),aa_nat_rat(semiri681578069525770553at_rat,N2))),aa_nat_rat(comm_s4028243227959126397er_rat(Z),N2)) ).

% pochhammer_rec'
tff(fact_4262_pochhammer__rec_H,axiom,
    ! [Z: int,N2: nat] : aa_nat_int(comm_s4660882817536571857er_int(Z),aa_nat_nat(suc,N2)) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,Z),aa_nat_int(semiri1314217659103216013at_int,N2))),aa_nat_int(comm_s4660882817536571857er_int(Z),N2)) ).

% pochhammer_rec'
tff(fact_4263_pochhammer__rec_H,axiom,
    ! [Z: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(comm_s4663373288045622133er_nat,Z),aa_nat_nat(suc,N2)) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Z),aa_nat_nat(semiri1316708129612266289at_nat,N2))),aa_nat_nat(aa_nat_fun_nat_nat(comm_s4663373288045622133er_nat,Z),N2)) ).

% pochhammer_rec'
tff(fact_4264_pochhammer__rec_H,axiom,
    ! [Z: code_integer,N2: nat] : aa_nat_Code_integer(comm_s8582702949713902594nteger(Z),aa_nat_nat(suc,N2)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,Z),aa_nat_Code_integer(semiri4939895301339042750nteger,N2))),aa_nat_Code_integer(comm_s8582702949713902594nteger(Z),N2)) ).

% pochhammer_rec'
tff(fact_4265_pochhammer__rec_H,axiom,
    ! [Z: code_natural,N2: nat] : aa_nat_Code_natural(comm_s7406298101470620109atural(Z),aa_nat_nat(suc,N2)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,Z),aa_nat_Code_natural(semiri3763490453095760265atural,N2))),aa_nat_Code_natural(comm_s7406298101470620109atural(Z),N2)) ).

% pochhammer_rec'
tff(fact_4266_pochhammer__product_H,axiom,
    ! [Z: rat,N2: nat,M: nat] : aa_nat_rat(comm_s4028243227959126397er_rat(Z),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),M)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(comm_s4028243227959126397er_rat(Z),N2)),aa_nat_rat(comm_s4028243227959126397er_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,Z),aa_nat_rat(semiri681578069525770553at_rat,N2))),M)) ).

% pochhammer_product'
tff(fact_4267_pochhammer__product_H,axiom,
    ! [Z: int,N2: nat,M: nat] : aa_nat_int(comm_s4660882817536571857er_int(Z),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),M)) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(comm_s4660882817536571857er_int(Z),N2)),aa_nat_int(comm_s4660882817536571857er_int(aa_int_int(aa_int_fun_int_int(plus_plus_int,Z),aa_nat_int(semiri1314217659103216013at_int,N2))),M)) ).

% pochhammer_product'
tff(fact_4268_pochhammer__product_H,axiom,
    ! [Z: nat,N2: nat,M: nat] : aa_nat_nat(aa_nat_fun_nat_nat(comm_s4663373288045622133er_nat,Z),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),M)) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(comm_s4663373288045622133er_nat,Z),N2)),aa_nat_nat(aa_nat_fun_nat_nat(comm_s4663373288045622133er_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Z),aa_nat_nat(semiri1316708129612266289at_nat,N2))),M)) ).

% pochhammer_product'
tff(fact_4269_pochhammer__product_H,axiom,
    ! [Z: code_integer,N2: nat,M: nat] : aa_nat_Code_integer(comm_s8582702949713902594nteger(Z),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),M)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(comm_s8582702949713902594nteger(Z),N2)),aa_nat_Code_integer(comm_s8582702949713902594nteger(aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,Z),aa_nat_Code_integer(semiri4939895301339042750nteger,N2))),M)) ).

% pochhammer_product'
tff(fact_4270_pochhammer__product_H,axiom,
    ! [Z: code_natural,N2: nat,M: nat] : aa_nat_Code_natural(comm_s7406298101470620109atural(Z),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),M)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_nat_Code_natural(comm_s7406298101470620109atural(Z),N2)),aa_nat_Code_natural(comm_s7406298101470620109atural(aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,Z),aa_nat_Code_natural(semiri3763490453095760265atural,N2))),M)) ).

% pochhammer_product'
tff(fact_4271_bit__iff__and__push__bit__not__eq__0,axiom,
    ! [A: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(bit_se1148574629649215175it_nat,A),N2)
    <=> ( aa_nat_nat(aa_nat_fun_nat_nat(bit_se727722235901077358nd_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(bit_se547839408752420682it_nat,N2),one_one_nat)) != zero_zero_nat ) ) ).

% bit_iff_and_push_bit_not_eq_0
tff(fact_4272_bit__iff__and__push__bit__not__eq__0,axiom,
    ! [A: code_integer,N2: nat] :
      ( aa_nat_o(aa_Cod1075288278386115654_nat_o(bit_se9216721137139052372nteger,A),N2)
    <=> ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3949692690581998587nteger,A),aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se7788150548672797655nteger,N2),one_one_Code_integer)) != zero_z3403309356797280102nteger ) ) ).

% bit_iff_and_push_bit_not_eq_0
tff(fact_4273_bit__iff__and__push__bit__not__eq__0,axiom,
    ! [A: int,N2: nat] :
      ( aa_nat_o(aa_int_fun_nat_o(bit_se1146084159140164899it_int,A),N2)
    <=> ( aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,A),aa_int_int(aa_nat_fun_int_int(bit_se545348938243370406it_int,N2),one_one_int)) != zero_zero_int ) ) ).

% bit_iff_and_push_bit_not_eq_0
tff(fact_4274_bit__iff__and__push__bit__not__eq__0,axiom,
    ! [A: code_natural,N2: nat] :
      ( aa_nat_o(aa_Cod9120328075896114107_nat_o(bit_se8040316288895769887atural,A),N2)
    <=> ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se2773287842338716102atural,A),aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se6611745700429515170atural,N2),one_one_Code_natural)) != zero_z2226904508553997617atural ) ) ).

% bit_iff_and_push_bit_not_eq_0
tff(fact_4275_sum__Suc__diff_H,axiom,
    ! [M: nat,N2: nat,F: fun_nat_Code_integer] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( groups7501900531339628137nteger(aTP_Lamm_ds(F),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_nat_Code_integer(F,N2)),aa_nat_Code_integer(F,M)) ) ) ).

% sum_Suc_diff'
tff(fact_4276_sum__Suc__diff_H,axiom,
    ! [M: nat,N2: nat,F: fun_nat_rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( groups2906978787729119204at_rat(aTP_Lamm_dt(F),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) = aa_rat_rat(minus_minus_rat(aa_nat_rat(F,N2)),aa_nat_rat(F,M)) ) ) ).

% sum_Suc_diff'
tff(fact_4277_sum__Suc__diff_H,axiom,
    ! [M: nat,N2: nat,F: fun_nat_int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( groups3539618377306564664at_int(aTP_Lamm_du(F),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(F,N2)),aa_nat_int(F,M)) ) ) ).

% sum_Suc_diff'
tff(fact_4278_sum_OatLeastLessThan__rev,axiom,
    ! [G: fun_nat_nat,N2: nat,M: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(N2),M)) = aa_set_nat_nat(groups3542108847815614940at_nat(aa_nat_fun_nat_nat(aa_nat3783148529270815480at_nat(aTP_Lamm_kc(G),N2),M)),aa_nat_set_nat(set_or4665077453230672383an_nat(N2),M)) ).

% sum.atLeastLessThan_rev
tff(fact_4279_sum_Onested__swap,axiom,
    ! [A: fun_nat_fun_nat_nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(aTP_Lamm_kd(A)),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2)) = aa_set_nat_nat(groups3542108847815614940at_nat(aa_nat_fun_nat_nat(aTP_Lamm_jb(A),N2)),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2)) ).

% sum.nested_swap
tff(fact_4280_sum_Onat__group,axiom,
    ! [G: fun_nat_nat,K: nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(aa_nat_fun_nat_nat(aTP_Lamm_ke(G),K)),aa_nat_set_nat(set_ord_lessThan_nat,N2)) = aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_ord_lessThan_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,N2),K))) ).

% sum.nat_group
tff(fact_4281_numeral__xor__num,axiom,
    ! [M: num,N2: num] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se6528837805403552850or_nat,aa_num_nat(numeral_numeral_nat,M)),aa_num_nat(numeral_numeral_nat,N2)) = case_option_nat_num(zero_zero_nat,numeral_numeral_nat,aa_num_option_num(bit_un2480387367778600638or_num(M),N2)) ).

% numeral_xor_num
tff(fact_4282_numeral__xor__num,axiom,
    ! [M: num,N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3222712562003087583nteger,aa_num_Code_integer(numera6620942414471956472nteger,M)),aa_num_Code_integer(numera6620942414471956472nteger,N2)) = case_o356765784539232260er_num(zero_z3403309356797280102nteger,numera6620942414471956472nteger,aa_num_option_num(bit_un2480387367778600638or_num(M),N2)) ).

% numeral_xor_num
tff(fact_4283_numeral__xor__num,axiom,
    ! [M: num,N2: num] : aa_int_int(aa_int_fun_int_int(bit_se6526347334894502574or_int,aa_num_int(numeral_numeral_int,M)),aa_num_int(numeral_numeral_int,N2)) = aa_option_num_int(case_option_int_num(zero_zero_int,numeral_numeral_int),aa_num_option_num(bit_un2480387367778600638or_num(M),N2)) ).

% numeral_xor_num
tff(fact_4284_numeral__xor__num,axiom,
    ! [M: num,N2: num] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se2046307713759805098atural,aa_num_Code_natural(numera5444537566228673987atural,M)),aa_num_Code_natural(numera5444537566228673987atural,N2)) = case_o5621594795226839503al_num(zero_z2226904508553997617atural,numera5444537566228673987atural,aa_num_option_num(bit_un2480387367778600638or_num(M),N2)) ).

% numeral_xor_num
tff(fact_4285_sum_Ohead__if,axiom,
    ! [G: fun_nat_Code_integer,M: nat,N2: nat] :
      groups7501900531339628137nteger(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),M),zero_z3403309356797280102nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,groups7501900531339628137nteger(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))),aa_nat_Code_integer(G,N2))) ).

% sum.head_if
tff(fact_4286_sum_Ohead__if,axiom,
    ! [G: fun_na2338080690716861136at_nat,M: nat,N2: nat] :
      groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),M),zero_z1048942125864253310at_nat,aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))),aa_nat2240542744625857721at_nat(G,N2))) ).

% sum.head_if
tff(fact_4287_sum_Ohead__if,axiom,
    ! [G: fun_nat_rat,M: nat,N2: nat] :
      groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),M),zero_zero_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))),aa_nat_rat(G,N2))) ).

% sum.head_if
tff(fact_4288_sum_Ohead__if,axiom,
    ! [G: fun_nat_int,M: nat,N2: nat] :
      groups3539618377306564664at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),M),zero_zero_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,groups3539618377306564664at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))),aa_nat_int(G,N2))) ).

% sum.head_if
tff(fact_4289_sum_Ohead__if,axiom,
    ! [G: fun_nat_nat,M: nat,N2: nat] :
      aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),M),zero_zero_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))),aa_nat_nat(G,N2))) ).

% sum.head_if
tff(fact_4290_sum_OatLeast0__lessThan__Suc__shift,axiom,
    ! [G: fun_na2338080690716861136at_nat,N2: nat] : groups6857163185585827899at_nat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(aa_nat2240542744625857721at_nat(G,zero_zero_nat)),groups6857163185585827899at_nat(comp_n8698576032424989604at_nat(G,suc),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2))) ).

% sum.atLeast0_lessThan_Suc_shift
tff(fact_4291_sum_OatLeast0__lessThan__Suc__shift,axiom,
    ! [G: fun_nat_rat,N2: nat] : groups2906978787729119204at_rat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(G,zero_zero_nat)),groups2906978787729119204at_rat(comp_nat_rat_nat(G,suc),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2))) ).

% sum.atLeast0_lessThan_Suc_shift
tff(fact_4292_sum_OatLeast0__lessThan__Suc__shift,axiom,
    ! [G: fun_nat_int,N2: nat] : groups3539618377306564664at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(G,zero_zero_nat)),groups3539618377306564664at_int(comp_nat_int_nat(G,suc),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2))) ).

% sum.atLeast0_lessThan_Suc_shift
tff(fact_4293_sum_OatLeast0__lessThan__Suc__shift,axiom,
    ! [G: fun_nat_nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(G,zero_zero_nat)),aa_set_nat_nat(groups3542108847815614940at_nat(comp_nat_nat_nat(G,suc)),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2))) ).

% sum.atLeast0_lessThan_Suc_shift
tff(fact_4294_sum_OatLeastLessThan__shift__0,axiom,
    ! [G: fun_nat_nat,M: nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) = aa_set_nat_nat(groups3542108847815614940at_nat(comp_nat_nat_nat(G,aa_nat_fun_nat_nat(plus_plus_nat,M))),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),M))) ).

% sum.atLeastLessThan_shift_0
tff(fact_4295_pochhammer__product,axiom,
    ! [M: nat,N2: nat,Z: rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_nat_rat(comm_s4028243227959126397er_rat(Z),N2) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(comm_s4028243227959126397er_rat(Z),M)),aa_nat_rat(comm_s4028243227959126397er_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,Z),aa_nat_rat(semiri681578069525770553at_rat,M))),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),M))) ) ) ).

% pochhammer_product
tff(fact_4296_pochhammer__product,axiom,
    ! [M: nat,N2: nat,Z: int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_nat_int(comm_s4660882817536571857er_int(Z),N2) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(comm_s4660882817536571857er_int(Z),M)),aa_nat_int(comm_s4660882817536571857er_int(aa_int_int(aa_int_fun_int_int(plus_plus_int,Z),aa_nat_int(semiri1314217659103216013at_int,M))),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),M))) ) ) ).

% pochhammer_product
tff(fact_4297_pochhammer__product,axiom,
    ! [M: nat,N2: nat,Z: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(comm_s4663373288045622133er_nat,Z),N2) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(comm_s4663373288045622133er_nat,Z),M)),aa_nat_nat(aa_nat_fun_nat_nat(comm_s4663373288045622133er_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Z),aa_nat_nat(semiri1316708129612266289at_nat,M))),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),M))) ) ) ).

% pochhammer_product
tff(fact_4298_pochhammer__product,axiom,
    ! [M: nat,N2: nat,Z: code_integer] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_nat_Code_integer(comm_s8582702949713902594nteger(Z),N2) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(comm_s8582702949713902594nteger(Z),M)),aa_nat_Code_integer(comm_s8582702949713902594nteger(aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,Z),aa_nat_Code_integer(semiri4939895301339042750nteger,M))),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),M))) ) ) ).

% pochhammer_product
tff(fact_4299_pochhammer__product,axiom,
    ! [M: nat,N2: nat,Z: code_natural] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_nat_Code_natural(comm_s7406298101470620109atural(Z),N2) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_nat_Code_natural(comm_s7406298101470620109atural(Z),M)),aa_nat_Code_natural(comm_s7406298101470620109atural(aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,Z),aa_nat_Code_natural(semiri3763490453095760265atural,M))),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),M))) ) ) ).

% pochhammer_product
tff(fact_4300_sum_OatLeastLessThan__rev__at__least__Suc__atMost,axiom,
    ! [G: fun_nat_nat,N2: nat,M: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(N2),M)) = aa_set_nat_nat(groups3542108847815614940at_nat(aa_nat_fun_nat_nat(aa_nat3783148529270815480at_nat(aTP_Lamm_do(G),N2),M)),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,N2)),M)) ).

% sum.atLeastLessThan_rev_at_least_Suc_atMost
tff(fact_4301_sum_OatLeast__lessThan__pred__shift,axiom,
    ! [G: fun_nat_nat,M: nat,N2: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(comp_nat_nat_nat(G,aTP_Lamm_dx)),aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(suc,M)),aa_nat_nat(suc,N2))) = aa_set_nat_nat(groups3542108847815614940at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) ).

% sum.atLeast_lessThan_pred_shift
tff(fact_4302_pochhammer__absorb__comp,axiom,
    ! [R2: rat,K: nat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(minus_minus_rat(R2),aa_nat_rat(semiri681578069525770553at_rat,K))),aa_nat_rat(comm_s4028243227959126397er_rat(aa_rat_rat(uminus_uminus_rat,R2)),K)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,R2),aa_nat_rat(comm_s4028243227959126397er_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,R2)),one_one_rat)),K)) ).

% pochhammer_absorb_comp
tff(fact_4303_pochhammer__absorb__comp,axiom,
    ! [R2: int,K: nat] : aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,R2),aa_nat_int(semiri1314217659103216013at_int,K))),aa_nat_int(comm_s4660882817536571857er_int(aa_int_int(uminus_uminus_int,R2)),K)) = aa_int_int(aa_int_fun_int_int(times_times_int,R2),aa_nat_int(comm_s4660882817536571857er_int(aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(uminus_uminus_int,R2)),one_one_int)),K)) ).

% pochhammer_absorb_comp
tff(fact_4304_pochhammer__absorb__comp,axiom,
    ! [R2: code_integer,K: nat] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,R2),aa_nat_Code_integer(semiri4939895301339042750nteger,K))),aa_nat_Code_integer(comm_s8582702949713902594nteger(aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,R2)),K)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,R2),aa_nat_Code_integer(comm_s8582702949713902594nteger(aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,R2)),one_one_Code_integer)),K)) ).

% pochhammer_absorb_comp
tff(fact_4305_pochhammer__same,axiom,
    ! [N2: nat] : aa_nat_rat(comm_s4028243227959126397er_rat(aa_rat_rat(uminus_uminus_rat,aa_nat_rat(semiri681578069525770553at_rat,N2))),N2) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),N2)),aa_nat_rat(semiri773545260158071498ct_rat,N2)) ).

% pochhammer_same
tff(fact_4306_pochhammer__same,axiom,
    ! [N2: nat] : aa_nat_int(comm_s4660882817536571857er_int(aa_int_int(uminus_uminus_int,aa_nat_int(semiri1314217659103216013at_int,N2))),N2) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(uminus_uminus_int,one_one_int)),N2)),aa_nat_int(semiri1406184849735516958ct_int,N2)) ).

% pochhammer_same
tff(fact_4307_pochhammer__same,axiom,
    ! [N2: nat] : aa_nat_Code_integer(comm_s8582702949713902594nteger(aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_nat_Code_integer(semiri4939895301339042750nteger,N2))),N2) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),N2)),aa_nat_Code_integer(semiri3624122377584611663nteger,N2)) ).

% pochhammer_same
tff(fact_4308_pochhammer__minus,axiom,
    ! [B: rat,K: nat] : aa_nat_rat(comm_s4028243227959126397er_rat(aa_rat_rat(uminus_uminus_rat,B)),K) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),K)),aa_nat_rat(comm_s4028243227959126397er_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(minus_minus_rat(B),aa_nat_rat(semiri681578069525770553at_rat,K))),one_one_rat)),K)) ).

% pochhammer_minus
tff(fact_4309_pochhammer__minus,axiom,
    ! [B: int,K: nat] : aa_nat_int(comm_s4660882817536571857er_int(aa_int_int(uminus_uminus_int,B)),K) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(uminus_uminus_int,one_one_int)),K)),aa_nat_int(comm_s4660882817536571857er_int(aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,B),aa_nat_int(semiri1314217659103216013at_int,K))),one_one_int)),K)) ).

% pochhammer_minus
tff(fact_4310_pochhammer__minus,axiom,
    ! [B: code_integer,K: nat] : aa_nat_Code_integer(comm_s8582702949713902594nteger(aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,B)),K) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),K)),aa_nat_Code_integer(comm_s8582702949713902594nteger(aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,B),aa_nat_Code_integer(semiri4939895301339042750nteger,K))),one_one_Code_integer)),K)) ).

% pochhammer_minus
tff(fact_4311_pochhammer__minus_H,axiom,
    ! [B: rat,K: nat] : aa_nat_rat(comm_s4028243227959126397er_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(minus_minus_rat(B),aa_nat_rat(semiri681578069525770553at_rat,K))),one_one_rat)),K) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),K)),aa_nat_rat(comm_s4028243227959126397er_rat(aa_rat_rat(uminus_uminus_rat,B)),K)) ).

% pochhammer_minus'
tff(fact_4312_pochhammer__minus_H,axiom,
    ! [B: int,K: nat] : aa_nat_int(comm_s4660882817536571857er_int(aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,B),aa_nat_int(semiri1314217659103216013at_int,K))),one_one_int)),K) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(uminus_uminus_int,one_one_int)),K)),aa_nat_int(comm_s4660882817536571857er_int(aa_int_int(uminus_uminus_int,B)),K)) ).

% pochhammer_minus'
tff(fact_4313_pochhammer__minus_H,axiom,
    ! [B: code_integer,K: nat] : aa_nat_Code_integer(comm_s8582702949713902594nteger(aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,B),aa_nat_Code_integer(semiri4939895301339042750nteger,K))),one_one_Code_integer)),K) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),K)),aa_nat_Code_integer(comm_s8582702949713902594nteger(aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,B)),K)) ).

% pochhammer_minus'
tff(fact_4314_gbinomial__pochhammer_H,axiom,
    ! [A: rat,K: nat] : aa_nat_rat(gbinomial_rat(A),K) = aa_rat_rat(divide_divide_rat(aa_nat_rat(comm_s4028243227959126397er_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(minus_minus_rat(A),aa_nat_rat(semiri681578069525770553at_rat,K))),one_one_rat)),K)),aa_nat_rat(semiri773545260158071498ct_rat,K)) ).

% gbinomial_pochhammer'
tff(fact_4315_gbinomial__pochhammer,axiom,
    ! [A: rat,K: nat] : aa_nat_rat(gbinomial_rat(A),K) = aa_rat_rat(divide_divide_rat(aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),K)),aa_nat_rat(comm_s4028243227959126397er_rat(aa_rat_rat(uminus_uminus_rat,A)),K))),aa_nat_rat(semiri773545260158071498ct_rat,K)) ).

% gbinomial_pochhammer
tff(fact_4316_xor__nat__unfold,axiom,
    ! [M: nat,N2: nat] :
      aa_nat_nat(aa_nat_fun_nat_nat(bit_se6528837805403552850or_nat,M),N2) = $ite(
        M = zero_zero_nat,
        N2,
        $ite(N2 = zero_zero_nat,M,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,M),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,N2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(bit_se6528837805403552850or_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,M),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,N2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) ) ).

% xor_nat_unfold
tff(fact_4317_num__of__integer_Oabs__eq,axiom,
    ! [X2: int] : aa_Code_integer_num(code_num_of_integer,aa_int_Code_integer(code_integer_of_int,X2)) = aa_nat_num(num_of_nat,aa_int_nat(nat2,X2)) ).

% num_of_integer.abs_eq
tff(fact_4318_signed__take__bit__code,axiom,
    ! [N2: nat,A: code_integer] :
      aa_Cod1783974652533396728nteger(bit_ri6519982836138164636nteger(N2),A) = $let(
        l: code_integer,
        l:= aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,aa_nat_nat(suc,N2)),A),
        $ite(aa_nat_o(aa_Cod1075288278386115654_nat_o(bit_se9216721137139052372nteger,l),N2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,l),aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se7788150548672797655nteger,aa_nat_nat(suc,N2)),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer))),l) ) ).

% signed_take_bit_code
tff(fact_4319_signed__take__bit__code,axiom,
    ! [N2: nat,A: int] :
      aa_int_int(bit_ri631733984087533419it_int(N2),A) = $let(
        l: int,
        l:= aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,aa_nat_nat(suc,N2)),A),
        $ite(aa_nat_o(aa_int_fun_nat_o(bit_se1146084159140164899it_int,l),N2),aa_int_int(aa_int_fun_int_int(plus_plus_int,l),aa_int_int(aa_nat_fun_int_int(bit_se545348938243370406it_int,aa_nat_nat(suc,N2)),aa_int_int(uminus_uminus_int,one_one_int))),l) ) ).

% signed_take_bit_code
tff(fact_4320_xor__nat__rec,axiom,
    ! [M: nat,N2: nat] :
      aa_nat_nat(aa_nat_fun_nat_nat(bit_se6528837805403552850or_nat,M),N2) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,
          aa_o_nat(zero_n2687167440665602831ol_nat,
            ~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),M) != ~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2))),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(bit_se6528837805403552850or_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,M),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,N2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) ).

% xor_nat_rec
tff(fact_4321_xor__one__eq,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se6528837805403552850or_nat,A),one_one_nat) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),aa_o_nat(zero_n2687167440665602831ol_nat,aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A)))),aa_o_nat(zero_n2687167440665602831ol_nat,~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A))) ).

% xor_one_eq
tff(fact_4322_xor__one__eq,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3222712562003087583nteger,A),one_one_Code_integer) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),aa_o_Code_integer(zero_n356916108424825756nteger,aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A)))),aa_o_Code_integer(zero_n356916108424825756nteger,~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A))) ).

% xor_one_eq
tff(fact_4323_xor__one__eq,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(bit_se6526347334894502574or_int,A),one_one_int) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),aa_o_int(zero_n2684676970156552555ol_int,aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A)))),aa_o_int(zero_n2684676970156552555ol_int,~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A))) ).

% xor_one_eq
tff(fact_4324_xor__one__eq,axiom,
    ! [A: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se2046307713759805098atural,A),one_one_Code_natural) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(minus_7197305767214868737atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),zero_n8403883297036319079atural(aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A)))),zero_n8403883297036319079atural(~ aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A))) ).

% xor_one_eq
tff(fact_4325_one__xor__eq,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se6528837805403552850or_nat,one_one_nat),A) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),aa_o_nat(zero_n2687167440665602831ol_nat,aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A)))),aa_o_nat(zero_n2687167440665602831ol_nat,~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A))) ).

% one_xor_eq
tff(fact_4326_one__xor__eq,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3222712562003087583nteger,one_one_Code_integer),A) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),aa_o_Code_integer(zero_n356916108424825756nteger,aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A)))),aa_o_Code_integer(zero_n356916108424825756nteger,~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A))) ).

% one_xor_eq
tff(fact_4327_one__xor__eq,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(bit_se6526347334894502574or_int,one_one_int),A) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),aa_o_int(zero_n2684676970156552555ol_int,aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A)))),aa_o_int(zero_n2684676970156552555ol_int,~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A))) ).

% one_xor_eq
tff(fact_4328_one__xor__eq,axiom,
    ! [A: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se2046307713759805098atural,one_one_Code_natural),A) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(minus_7197305767214868737atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),zero_n8403883297036319079atural(aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A)))),zero_n8403883297036319079atural(~ aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A))) ).

% one_xor_eq
tff(fact_4329_pochhammer__binomial__sum,axiom,
    ! [A: rat,B: rat,N2: nat] : aa_nat_rat(comm_s4028243227959126397er_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),N2) = groups2906978787729119204at_rat(aa_nat_fun_nat_rat(aa_rat250263598611652360at_rat(aTP_Lamm_kf(A),B),N2),aa_nat_set_nat(set_ord_atMost_nat,N2)) ).

% pochhammer_binomial_sum
tff(fact_4330_pochhammer__binomial__sum,axiom,
    ! [A: int,B: int,N2: nat] : aa_nat_int(comm_s4660882817536571857er_int(aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)),N2) = groups3539618377306564664at_int(aa_nat_fun_nat_int(aa_int431785320988601264at_int(aTP_Lamm_kg(A),B),N2),aa_nat_set_nat(set_ord_atMost_nat,N2)) ).

% pochhammer_binomial_sum
tff(fact_4331_pochhammer__binomial__sum,axiom,
    ! [A: code_integer,B: code_integer,N2: nat] : aa_nat_Code_integer(comm_s8582702949713902594nteger(aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)),N2) = groups7501900531339628137nteger(aa_nat2010205248571845816nteger(aa_Cod3140087502949435154nteger(aTP_Lamm_kh(A),B),N2),aa_nat_set_nat(set_ord_atMost_nat,N2)) ).

% pochhammer_binomial_sum
tff(fact_4332_divmod__integer__def,axiom,
    ! [K: code_integer,L: code_integer] : aa_Cod6977894654539884864nteger(code_divmod_integer(K),L) = aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,K),L)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,K),L)) ).

% divmod_integer_def
tff(fact_4333_sum__power2,axiom,
    ! [K: nat] : aa_set_nat_nat(groups3542108847815614940at_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),K)) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),K)),one_one_nat) ).

% sum_power2
tff(fact_4334_nat__of__integer__code,axiom,
    ! [K: code_integer] :
      aa_Code_integer_nat(code_nat_of_integer,K) = $ite(aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,K),zero_z3403309356797280102nteger),zero_zero_nat,produc1555791787009142072er_nat(aTP_Lamm_ki,aa_Cod6977894654539884864nteger(code_divmod_integer(K),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))))) ).

% nat_of_integer_code
tff(fact_4335_pochhammer__times__pochhammer__half,axiom,
    ! [Z: rat,N2: nat] : aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(comm_s4028243227959126397er_rat(Z),aa_nat_nat(suc,N2))),aa_nat_rat(comm_s4028243227959126397er_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,Z),aa_rat_rat(divide_divide_rat(one_one_rat),aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one))))),aa_nat_nat(suc,N2))) = groups73079841787564623at_rat(aTP_Lamm_kj(Z),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)),one_one_nat))) ).

% pochhammer_times_pochhammer_half
tff(fact_4336_int__of__integer__code,axiom,
    ! [K: code_integer] :
      aa_Code_integer_int(code_int_of_integer,K) = $ite(
        aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,K),zero_z3403309356797280102nteger),
        aa_int_int(uminus_uminus_int,aa_Code_integer_int(code_int_of_integer,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,K))),
        $ite(K = zero_z3403309356797280102nteger,zero_zero_int,produc1553301316500091796er_int(aTP_Lamm_kk,aa_Cod6977894654539884864nteger(code_divmod_integer(K),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))))) ) ).

% int_of_integer_code
tff(fact_4337_divmod__integer__eq__cases,axiom,
    ! [K: code_integer,L: code_integer] :
      aa_Cod6977894654539884864nteger(code_divmod_integer(K),L) = $ite(
        K = zero_z3403309356797280102nteger,
        aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(zero_z3403309356797280102nteger),zero_z3403309356797280102nteger),
        $ite(
          L = zero_z3403309356797280102nteger,
          aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(zero_z3403309356797280102nteger),K),
          aa_Pro4693618923521437820nteger(aa_Cod1978467581589928094nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,comp_f6739083541385432444nteger(produc6499014454317279255nteger,times_3573771949741848930nteger)),sgn_sgn_Code_integer),L),
            $ite(aa_Cod1783974652533396728nteger(sgn_sgn_Code_integer,K) = aa_Cod1783974652533396728nteger(sgn_sgn_Code_integer,L),aa_Cod6977894654539884864nteger(code_divmod_abs(K),L),aa_Pro4693618923521437820nteger(produc6916734918728496179nteger(aTP_Lamm_kl(L)),aa_Cod6977894654539884864nteger(code_divmod_abs(K),L)))) ) ) ).

% divmod_integer_eq_cases
tff(fact_4338_time__def,axiom,
    ! [C: heap_T6362127782908069795rray_a,Ha: heap_e7401611519738050253t_unit] : time_time_array_a(C,Ha) = case_o1134687144775446439it_nat(zero_zero_nat,produc6028340861379781217at_nat(aTP_Lamm_kn),aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(C),Ha)) ).

% time_def
tff(fact_4339_time__def,axiom,
    ! [C: heap_T5738788834812785303t_unit,Ha: heap_e7401611519738050253t_unit] : time_t4224138285095624986t_unit(C,Ha) = case_o5424514124273913701it_nat(zero_zero_nat,produc5629734405777326591at_nat(aTP_Lamm_ko),aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(C),Ha)) ).

% time_def
tff(fact_4340_bit__cut__integer__def,axiom,
    ! [K: code_integer] : code_bit_cut_integer(K) = produc6677183202524767010eger_o(aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,K),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),K)) ).

% bit_cut_integer_def
tff(fact_4341_integer__of__num_I3_J,axiom,
    ! [N2: num] :
      aa_num_Code_integer(code_integer_of_num,aa_num_num(bit1,N2)) = $let(
        k: code_integer,
        k:= aa_num_Code_integer(code_integer_of_num,N2),
        aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,k),k)),one_one_Code_integer) ) ).

% integer_of_num(3)
tff(fact_4342_less__eq__int_Orep__eq,axiom,
    ! [X2: int,Xa: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,X2),Xa)
    <=> aa_Pro6150637604445964947_nat_o(aa_Pro989595756709598047_nat_o(aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,aTP_Lamm_fg),aa_int1417691210696471063at_nat(rep_Integ,X2)),aa_int1417691210696471063at_nat(rep_Integ,Xa)) ) ).

% less_eq_int.rep_eq
tff(fact_4343_nat__of__integer__of__nat,axiom,
    ! [N2: nat] : aa_Code_integer_nat(code_nat_of_integer,aa_nat_Code_integer(semiri4939895301339042750nteger,N2)) = N2 ).

% nat_of_integer_of_nat
tff(fact_4344_int__of__integer__of__nat,axiom,
    ! [N2: nat] : aa_Code_integer_int(code_int_of_integer,aa_nat_Code_integer(semiri4939895301339042750nteger,N2)) = aa_nat_int(semiri1314217659103216013at_int,N2) ).

% int_of_integer_of_nat
tff(fact_4345_integer__of__int__int__of__integer,axiom,
    ! [K: code_integer] : aa_int_Code_integer(code_integer_of_int,aa_Code_integer_int(code_int_of_integer,K)) = K ).

% integer_of_int_int_of_integer
tff(fact_4346_int__of__integer__integer__of__int,axiom,
    ! [K: int] : aa_Code_integer_int(code_int_of_integer,aa_int_Code_integer(code_integer_of_int,K)) = K ).

% int_of_integer_integer_of_int
tff(fact_4347_int__of__integer__inverse,axiom,
    ! [X2: code_integer] : aa_int_Code_integer(code_integer_of_int,aa_Code_integer_int(code_int_of_integer,X2)) = X2 ).

% int_of_integer_inverse
tff(fact_4348_apsnd__conv,axiom,
    ! [F: fun_Pr5876161306168176259nteger,X2: fun_Pr5098669352780829690e_term,Y: produc8923325533196201883nteger] : produc2265439103302406840e_term(F,aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X2),Y)) = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X2),aa_Pro4693618923521437820nteger(F,Y)) ).

% apsnd_conv
tff(fact_4349_apsnd__conv,axiom,
    ! [F: fun_Pr7091840695141096449et_nat,X2: fun_Pr6460944699146269935_nat_o,Y: produc3658429121746597890et_nat] : aa_Pro5931322043027775230et_nat(produc1991759244683392747_nat_o(F),aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X2),Y)) = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X2),aa_Pro3679490825741336130et_nat(F,Y)) ).

% apsnd_conv
tff(fact_4350_apsnd__conv,axiom,
    ! [F: fun_Pr4885567672785483807et_nat,X2: fun_Pr6460944699146269935_nat_o,Y: produc3658429121746597890et_nat] : produc4622684310891945677_nat_o(F,aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X2),Y)) = aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X2),aa_Pro434340453207536480et_nat(F,Y)) ).

% apsnd_conv
tff(fact_4351_apsnd__conv,axiom,
    ! [F: fun_Pr2813956079162534559et_nat,X2: fun_Pr6460944699146269935_nat_o,Y: produc8799533983703829792et_nat] : produc174852792182663501_nat_o(F,aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X2),Y)) = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X2),aa_Pro5541488491759012064et_nat(F,Y)) ).

% apsnd_conv
tff(fact_4352_apsnd__conv,axiom,
    ! [F: fun_Pr836988951548913597et_nat,X2: fun_Pr6460944699146269935_nat_o,Y: produc8799533983703829792et_nat] : produc2056317742435807279_nat_o(F,aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X2),Y)) = aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X2),aa_Pro5931322043027775230et_nat(F,Y)) ).

% apsnd_conv
tff(fact_4353_apsnd__conv,axiom,
    ! [F: fun_Pr2478283820680522243nt_int,X2: fun_Pr7763680713840462443e_term,Y: product_prod_int_int] : produc8061333830752525225e_term(F,aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X2),Y)) = aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X2),aa_Pro6970504127699319548nt_int(F,Y)) ).

% apsnd_conv
tff(fact_4354_apsnd__conv,axiom,
    ! [F: fun_Pr2478283820680522243nt_int,X2: fun_in5730379987311621695e_term,Y: product_prod_int_int] : produc2254893824690362237e_term(F,aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X2),Y)) = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X2),aa_Pro6970504127699319548nt_int(F,Y)) ).

% apsnd_conv
tff(fact_4355_apsnd__conv,axiom,
    ! [F: fun_Co8499238673658658103nteger,X2: code_integer,Y: code_integer] : aa_Pro4693618923521437820nteger(aa_fun2509385170507305080nteger(produc6499014454317279255nteger,F),aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(X2),Y)) = aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(X2),aa_Cod1783974652533396728nteger(F,Y)) ).

% apsnd_conv
tff(fact_4356_prod_Oneutral__const,axiom,
    ! [A2: set_nat] : aa_set_nat_nat(groups708209901874060359at_nat(aTP_Lamm_kp),A2) = one_one_nat ).

% prod.neutral_const
tff(fact_4357_prod_Oneutral__const,axiom,
    ! [A2: set_nat] : groups705719431365010083at_int(aTP_Lamm_kq,A2) = one_one_int ).

% prod.neutral_const
tff(fact_4358_prod_Oneutral__const,axiom,
    ! [A2: set_int] : aa_set_int_int(groups1705073143266064639nt_int(aTP_Lamm_kr),A2) = one_one_int ).

% prod.neutral_const
tff(fact_4359_of__int__integer__of,axiom,
    ! [K: code_integer] : aa_int_Code_integer(ring_18347121197199848620nteger,aa_Code_integer_int(code_int_of_integer,K)) = K ).

% of_int_integer_of
tff(fact_4360_int__of__integer__of__int,axiom,
    ! [K: int] : aa_Code_integer_int(code_int_of_integer,aa_int_Code_integer(ring_18347121197199848620nteger,K)) = K ).

% int_of_integer_of_int
tff(fact_4361_zero__integer_Orep__eq,axiom,
    aa_Code_integer_int(code_int_of_integer,zero_z3403309356797280102nteger) = zero_zero_int ).

% zero_integer.rep_eq
tff(fact_4362_int__of__integer__numeral,axiom,
    ! [K: num] : aa_Code_integer_int(code_int_of_integer,aa_num_Code_integer(numera6620942414471956472nteger,K)) = aa_num_int(numeral_numeral_int,K) ).

% int_of_integer_numeral
tff(fact_4363_plus__integer_Orep__eq,axiom,
    ! [X2: code_integer,Xa: code_integer] : aa_Code_integer_int(code_int_of_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X2),Xa)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_Code_integer_int(code_int_of_integer,X2)),aa_Code_integer_int(code_int_of_integer,Xa)) ).

% plus_integer.rep_eq
tff(fact_4364_one__integer_Orep__eq,axiom,
    aa_Code_integer_int(code_int_of_integer,one_one_Code_integer) = one_one_int ).

% one_integer.rep_eq
tff(fact_4365_uminus__integer_Orep__eq,axiom,
    ! [X2: code_integer] : aa_Code_integer_int(code_int_of_integer,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,X2)) = aa_int_int(uminus_uminus_int,aa_Code_integer_int(code_int_of_integer,X2)) ).

% uminus_integer.rep_eq
tff(fact_4366_times__integer_Orep__eq,axiom,
    ! [X2: code_integer,Xa: code_integer] : aa_Code_integer_int(code_int_of_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,X2),Xa)) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_Code_integer_int(code_int_of_integer,X2)),aa_Code_integer_int(code_int_of_integer,Xa)) ).

% times_integer.rep_eq
tff(fact_4367_minus__integer_Orep__eq,axiom,
    ! [X2: code_integer,Xa: code_integer] : aa_Code_integer_int(code_int_of_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,X2),Xa)) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_Code_integer_int(code_int_of_integer,X2)),aa_Code_integer_int(code_int_of_integer,Xa)) ).

% minus_integer.rep_eq
tff(fact_4368_abs__integer_Orep__eq,axiom,
    ! [X2: code_integer] : aa_Code_integer_int(code_int_of_integer,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,X2)) = aa_int_int(abs_abs_int,aa_Code_integer_int(code_int_of_integer,X2)) ).

% abs_integer.rep_eq
tff(fact_4369_divide__integer_Orep__eq,axiom,
    ! [X2: code_integer,Xa: code_integer] : aa_Code_integer_int(code_int_of_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,X2),Xa)) = aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_Code_integer_int(code_int_of_integer,X2)),aa_Code_integer_int(code_int_of_integer,Xa)) ).

% divide_integer.rep_eq
tff(fact_4370_modulo__integer_Orep__eq,axiom,
    ! [X2: code_integer,Xa: code_integer] : aa_Code_integer_int(code_int_of_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,X2),Xa)) = aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_Code_integer_int(code_int_of_integer,X2)),aa_Code_integer_int(code_int_of_integer,Xa)) ).

% modulo_integer.rep_eq
tff(fact_4371_sgn__integer_Orep__eq,axiom,
    ! [X2: code_integer] : aa_Code_integer_int(code_int_of_integer,aa_Cod1783974652533396728nteger(sgn_sgn_Code_integer,X2)) = aa_int_int(sgn_sgn_int,aa_Code_integer_int(code_int_of_integer,X2)) ).

% sgn_integer.rep_eq
tff(fact_4372_prod_OatMost__Suc,axiom,
    ! [G: fun_nat_assn,N2: nat] : groups6906906614972039071t_assn(G,aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(suc,N2))) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,groups6906906614972039071t_assn(G,aa_nat_set_nat(set_ord_atMost_nat,N2))),aa_nat_assn(G,aa_nat_nat(suc,N2))) ).

% prod.atMost_Suc
tff(fact_4373_prod_OatMost__Suc,axiom,
    ! [G: fun_nat_rat,N2: nat] : groups73079841787564623at_rat(G,aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(suc,N2))) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,groups73079841787564623at_rat(G,aa_nat_set_nat(set_ord_atMost_nat,N2))),aa_nat_rat(G,aa_nat_nat(suc,N2))) ).

% prod.atMost_Suc
tff(fact_4374_prod_OatMost__Suc,axiom,
    ! [G: fun_nat_nat,N2: nat] : aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(suc,N2))) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_ord_atMost_nat,N2))),aa_nat_nat(G,aa_nat_nat(suc,N2))) ).

% prod.atMost_Suc
tff(fact_4375_prod_OatMost__Suc,axiom,
    ! [G: fun_nat_int,N2: nat] : groups705719431365010083at_int(G,aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(suc,N2))) = aa_int_int(aa_int_fun_int_int(times_times_int,groups705719431365010083at_int(G,aa_nat_set_nat(set_ord_atMost_nat,N2))),aa_nat_int(G,aa_nat_nat(suc,N2))) ).

% prod.atMost_Suc
tff(fact_4376_prod_OlessThan__Suc,axiom,
    ! [G: fun_nat_assn,N2: nat] : groups6906906614972039071t_assn(G,aa_nat_set_nat(set_ord_lessThan_nat,aa_nat_nat(suc,N2))) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,groups6906906614972039071t_assn(G,aa_nat_set_nat(set_ord_lessThan_nat,N2))),aa_nat_assn(G,N2)) ).

% prod.lessThan_Suc
tff(fact_4377_prod_OlessThan__Suc,axiom,
    ! [G: fun_nat_rat,N2: nat] : groups73079841787564623at_rat(G,aa_nat_set_nat(set_ord_lessThan_nat,aa_nat_nat(suc,N2))) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,groups73079841787564623at_rat(G,aa_nat_set_nat(set_ord_lessThan_nat,N2))),aa_nat_rat(G,N2)) ).

% prod.lessThan_Suc
tff(fact_4378_prod_OlessThan__Suc,axiom,
    ! [G: fun_nat_nat,N2: nat] : aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_ord_lessThan_nat,aa_nat_nat(suc,N2))) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_ord_lessThan_nat,N2))),aa_nat_nat(G,N2)) ).

% prod.lessThan_Suc
tff(fact_4379_prod_OlessThan__Suc,axiom,
    ! [G: fun_nat_int,N2: nat] : groups705719431365010083at_int(G,aa_nat_set_nat(set_ord_lessThan_nat,aa_nat_nat(suc,N2))) = aa_int_int(aa_int_fun_int_int(times_times_int,groups705719431365010083at_int(G,aa_nat_set_nat(set_ord_lessThan_nat,N2))),aa_nat_int(G,N2)) ).

% prod.lessThan_Suc
tff(fact_4380_nat__of__integer__non__positive,axiom,
    ! [K: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,K),zero_z3403309356797280102nteger)
     => ( aa_Code_integer_nat(code_nat_of_integer,K) = zero_zero_nat ) ) ).

% nat_of_integer_non_positive
tff(fact_4381_prod_Ocl__ivl__Suc,axiom,
    ! [G: fun_nat_Code_integer,M: nat,N2: nat] :
      groups3455450783089532116nteger(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),aa_nat_nat(suc,N2))) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(suc,N2)),M),one_one_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,groups3455450783089532116nteger(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))),aa_nat_Code_integer(G,aa_nat_nat(suc,N2)))) ).

% prod.cl_ivl_Suc
tff(fact_4382_prod_Ocl__ivl__Suc,axiom,
    ! [G: fun_nat_assn,M: nat,N2: nat] :
      groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),aa_nat_nat(suc,N2))) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(suc,N2)),M),one_one_assn,aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))),aa_nat_assn(G,aa_nat_nat(suc,N2)))) ).

% prod.cl_ivl_Suc
tff(fact_4383_prod_Ocl__ivl__Suc,axiom,
    ! [G: fun_nat_rat,M: nat,N2: nat] :
      groups73079841787564623at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),aa_nat_nat(suc,N2))) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(suc,N2)),M),one_one_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,groups73079841787564623at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))),aa_nat_rat(G,aa_nat_nat(suc,N2)))) ).

% prod.cl_ivl_Suc
tff(fact_4384_prod_Ocl__ivl__Suc,axiom,
    ! [G: fun_nat_nat,M: nat,N2: nat] :
      aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),aa_nat_nat(suc,N2))) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(suc,N2)),M),one_one_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))),aa_nat_nat(G,aa_nat_nat(suc,N2)))) ).

% prod.cl_ivl_Suc
tff(fact_4385_prod_Ocl__ivl__Suc,axiom,
    ! [G: fun_nat_int,M: nat,N2: nat] :
      groups705719431365010083at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),aa_nat_nat(suc,N2))) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(suc,N2)),M),one_one_int,aa_int_int(aa_int_fun_int_int(times_times_int,groups705719431365010083at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))),aa_nat_int(G,aa_nat_nat(suc,N2)))) ).

% prod.cl_ivl_Suc
tff(fact_4386_prod_Oop__ivl__Suc,axiom,
    ! [G: fun_nat_Code_integer,M: nat,N2: nat] :
      groups3455450783089532116nteger(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),aa_nat_nat(suc,N2))) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),M),one_one_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,groups3455450783089532116nteger(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))),aa_nat_Code_integer(G,N2))) ).

% prod.op_ivl_Suc
tff(fact_4387_prod_Oop__ivl__Suc,axiom,
    ! [G: fun_nat_assn,M: nat,N2: nat] :
      groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),aa_nat_nat(suc,N2))) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),M),one_one_assn,aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))),aa_nat_assn(G,N2))) ).

% prod.op_ivl_Suc
tff(fact_4388_prod_Oop__ivl__Suc,axiom,
    ! [G: fun_nat_rat,M: nat,N2: nat] :
      groups73079841787564623at_rat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),aa_nat_nat(suc,N2))) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),M),one_one_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,groups73079841787564623at_rat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))),aa_nat_rat(G,N2))) ).

% prod.op_ivl_Suc
tff(fact_4389_prod_Oop__ivl__Suc,axiom,
    ! [G: fun_nat_nat,M: nat,N2: nat] :
      aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(M),aa_nat_nat(suc,N2))) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),M),one_one_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))),aa_nat_nat(G,N2))) ).

% prod.op_ivl_Suc
tff(fact_4390_prod_Oop__ivl__Suc,axiom,
    ! [G: fun_nat_int,M: nat,N2: nat] :
      groups705719431365010083at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),aa_nat_nat(suc,N2))) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),M),one_one_int,aa_int_int(aa_int_fun_int_int(times_times_int,groups705719431365010083at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))),aa_nat_int(G,N2))) ).

% prod.op_ivl_Suc
tff(fact_4391_xor__integer_Orep__eq,axiom,
    ! [X2: code_integer,Xa: code_integer] : aa_Code_integer_int(code_int_of_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3222712562003087583nteger,X2),Xa)) = aa_int_int(aa_int_fun_int_int(bit_se6526347334894502574or_int,aa_Code_integer_int(code_int_of_integer,X2)),aa_Code_integer_int(code_int_of_integer,Xa)) ).

% xor_integer.rep_eq
tff(fact_4392_push__bit__integer_Orep__eq,axiom,
    ! [X2: nat,Xa: code_integer] : aa_Code_integer_int(code_int_of_integer,aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se7788150548672797655nteger,X2),Xa)) = aa_int_int(aa_nat_fun_int_int(bit_se545348938243370406it_int,X2),aa_Code_integer_int(code_int_of_integer,Xa)) ).

% push_bit_integer.rep_eq
tff(fact_4393_xor__integer_Oabs__eq,axiom,
    ! [Xa: int,X2: int] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3222712562003087583nteger,aa_int_Code_integer(code_integer_of_int,Xa)),aa_int_Code_integer(code_integer_of_int,X2)) = aa_int_Code_integer(code_integer_of_int,aa_int_int(aa_int_fun_int_int(bit_se6526347334894502574or_int,Xa),X2)) ).

% xor_integer.abs_eq
tff(fact_4394_nat__of__integer_Orep__eq,axiom,
    ! [X2: code_integer] : aa_Code_integer_nat(code_nat_of_integer,X2) = aa_int_nat(nat2,aa_Code_integer_int(code_int_of_integer,X2)) ).

% nat_of_integer.rep_eq
tff(fact_4395_integer__eq__iff,axiom,
    ! [K: code_integer,L: code_integer] :
      ( ( K = L )
    <=> ( aa_Code_integer_int(code_int_of_integer,K) = aa_Code_integer_int(code_int_of_integer,L) ) ) ).

% integer_eq_iff
tff(fact_4396_integer__eqI,axiom,
    ! [K: code_integer,L: code_integer] :
      ( ( aa_Code_integer_int(code_int_of_integer,K) = aa_Code_integer_int(code_int_of_integer,L) )
     => ( K = L ) ) ).

% integer_eqI
tff(fact_4397_int__of__integer__inject,axiom,
    ! [X2: code_integer,Y: code_integer] :
      ( ( aa_Code_integer_int(code_int_of_integer,X2) = aa_Code_integer_int(code_int_of_integer,Y) )
    <=> ( X2 = Y ) ) ).

% int_of_integer_inject
tff(fact_4398_prod_Onot__neutral__contains__not__neutral,axiom,
    ! [G: fun_o_Code_integer,A2: set_o] :
      ( ( aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,G),A2) != one_one_Code_integer )
     => ~ ! [A3: $o] :
            ( member_o((A3),A2)
           => ( aa_o_Code_integer(G,(A3)) = one_one_Code_integer ) ) ) ).

% prod.not_neutral_contains_not_neutral
tff(fact_4399_prod_Onot__neutral__contains__not__neutral,axiom,
    ! [G: fun_nat_Code_integer,A2: set_nat] :
      ( ( groups3455450783089532116nteger(G,A2) != one_one_Code_integer )
     => ~ ! [A3: nat] :
            ( member_nat(A3,A2)
           => ( aa_nat_Code_integer(G,A3) = one_one_Code_integer ) ) ) ).

% prod.not_neutral_contains_not_neutral
tff(fact_4400_prod_Onot__neutral__contains__not__neutral,axiom,
    ! [G: fun_int_Code_integer,A2: set_int] :
      ( ( aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,G),A2) != one_one_Code_integer )
     => ~ ! [A3: int] :
            ( member_int(A3,A2)
           => ( aa_int_Code_integer(G,A3) = one_one_Code_integer ) ) ) ).

% prod.not_neutral_contains_not_neutral
tff(fact_4401_prod_Onot__neutral__contains__not__neutral,axiom,
    ! [G: fun_o_assn,A2: set_o] :
      ( ( aa_set_o_assn(aa_fun1914167119812169564o_assn(groups5301882518646026715o_assn,G),A2) != one_one_assn )
     => ~ ! [A3: $o] :
            ( member_o((A3),A2)
           => ( aa_o_assn(G,(A3)) = one_one_assn ) ) ) ).

% prod.not_neutral_contains_not_neutral
tff(fact_4402_prod_Onot__neutral__contains__not__neutral,axiom,
    ! [G: fun_nat_assn,A2: set_nat] :
      ( ( groups6906906614972039071t_assn(G,A2) != one_one_assn )
     => ~ ! [A3: nat] :
            ( member_nat(A3,A2)
           => ( aa_nat_assn(G,A3) = one_one_assn ) ) ) ).

% prod.not_neutral_contains_not_neutral
tff(fact_4403_prod_Onot__neutral__contains__not__neutral,axiom,
    ! [G: fun_int_assn,A2: set_int] :
      ( ( aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,G),A2) != one_one_assn )
     => ~ ! [A3: int] :
            ( member_int(A3,A2)
           => ( aa_int_assn(G,A3) = one_one_assn ) ) ) ).

% prod.not_neutral_contains_not_neutral
tff(fact_4404_prod_Onot__neutral__contains__not__neutral,axiom,
    ! [G: fun_o_rat,A2: set_o] :
      ( ( aa_set_o_rat(aa_fun7302669049306738524_o_rat(groups2869687844427037835_o_rat,G),A2) != one_one_rat )
     => ~ ! [A3: $o] :
            ( member_o((A3),A2)
           => ( aa_o_rat(G,(A3)) = one_one_rat ) ) ) ).

% prod.not_neutral_contains_not_neutral
tff(fact_4405_prod_Onot__neutral__contains__not__neutral,axiom,
    ! [G: fun_nat_rat,A2: set_nat] :
      ( ( groups73079841787564623at_rat(G,A2) != one_one_rat )
     => ~ ! [A3: nat] :
            ( member_nat(A3,A2)
           => ( aa_nat_rat(G,A3) = one_one_rat ) ) ) ).

% prod.not_neutral_contains_not_neutral
tff(fact_4406_prod_Onot__neutral__contains__not__neutral,axiom,
    ! [G: fun_int_rat,A2: set_int] :
      ( ( aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,G),A2) != one_one_rat )
     => ~ ! [A3: int] :
            ( member_int(A3,A2)
           => ( aa_int_rat(G,A3) = one_one_rat ) ) ) ).

% prod.not_neutral_contains_not_neutral
tff(fact_4407_prod_Onot__neutral__contains__not__neutral,axiom,
    ! [G: fun_o_nat,A2: set_o] :
      ( ( aa_set_o_nat(aa_fun8470299178418016604_o_nat(groups3504817904513533571_o_nat,G),A2) != one_one_nat )
     => ~ ! [A3: $o] :
            ( member_o((A3),A2)
           => ( aa_o_nat(G,(A3)) = one_one_nat ) ) ) ).

% prod.not_neutral_contains_not_neutral
tff(fact_4408_prod_Oneutral,axiom,
    ! [A2: set_nat,G: fun_nat_nat] :
      ( ! [X3: nat] :
          ( member_nat(X3,A2)
         => ( aa_nat_nat(G,X3) = one_one_nat ) )
     => ( aa_set_nat_nat(groups708209901874060359at_nat(G),A2) = one_one_nat ) ) ).

% prod.neutral
tff(fact_4409_prod_Oneutral,axiom,
    ! [A2: set_nat,G: fun_nat_int] :
      ( ! [X3: nat] :
          ( member_nat(X3,A2)
         => ( aa_nat_int(G,X3) = one_one_int ) )
     => ( groups705719431365010083at_int(G,A2) = one_one_int ) ) ).

% prod.neutral
tff(fact_4410_prod_Oneutral,axiom,
    ! [A2: set_int,G: fun_int_int] :
      ( ! [X3: int] :
          ( member_int(X3,A2)
         => ( aa_int_int(G,X3) = one_one_int ) )
     => ( aa_set_int_int(groups1705073143266064639nt_int(G),A2) = one_one_int ) ) ).

% prod.neutral
tff(fact_4411_apsnd__compose,axiom,
    ! [F: fun_Co1561183069634336733nteger,G: fun_Co8499238673658658103nteger,X2: produc8923325533196201883nteger] : produc5043883716779652157nteger(F,aa_Pro4693618923521437820nteger(aa_fun2509385170507305080nteger(produc6499014454317279255nteger,G),X2)) = produc5043883716779652157nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),G),X2) ).

% apsnd_compose
tff(fact_4412_apsnd__compose,axiom,
    ! [F: fun_Co8499238673658658103nteger,G: fun_num_Code_integer,X2: produc7142191362829087448er_num] : aa_Pro4693618923521437820nteger(aa_fun2509385170507305080nteger(produc6499014454317279255nteger,F),produc7418200839687411156nteger(G,X2)) = produc7418200839687411156nteger(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),G),X2) ).

% apsnd_compose
tff(fact_4413_apsnd__compose,axiom,
    ! [F: fun_Co8499238673658658103nteger,G: fun_Co8499238673658658103nteger,X2: produc8923325533196201883nteger] : aa_Pro4693618923521437820nteger(aa_fun2509385170507305080nteger(produc6499014454317279255nteger,F),aa_Pro4693618923521437820nteger(aa_fun2509385170507305080nteger(produc6499014454317279255nteger,G),X2)) = aa_Pro4693618923521437820nteger(aa_fun2509385170507305080nteger(produc6499014454317279255nteger,aa_fun4435975922079263404nteger(comp_C7449957260575251196nteger(F),G)),X2) ).

% apsnd_compose
tff(fact_4414_prod__ge__1,axiom,
    ! [A2: set_o,F: fun_o_Code_integer] :
      ( ! [X3: $o] :
          ( member_o((X3),A2)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),aa_o_Code_integer(F,(X3))) )
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,F),A2)) ) ).

% prod_ge_1
tff(fact_4415_prod__ge__1,axiom,
    ! [A2: set_nat,F: fun_nat_Code_integer] :
      ( ! [X3: nat] :
          ( member_nat(X3,A2)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),aa_nat_Code_integer(F,X3)) )
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),groups3455450783089532116nteger(F,A2)) ) ).

% prod_ge_1
tff(fact_4416_prod__ge__1,axiom,
    ! [A2: set_int,F: fun_int_Code_integer] :
      ( ! [X3: int] :
          ( member_int(X3,A2)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),aa_int_Code_integer(F,X3)) )
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,F),A2)) ) ).

% prod_ge_1
tff(fact_4417_prod__ge__1,axiom,
    ! [A2: set_o,F: fun_o_rat] :
      ( ! [X3: $o] :
          ( member_o((X3),A2)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),aa_o_rat(F,(X3))) )
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),aa_set_o_rat(aa_fun7302669049306738524_o_rat(groups2869687844427037835_o_rat,F),A2)) ) ).

% prod_ge_1
tff(fact_4418_prod__ge__1,axiom,
    ! [A2: set_nat,F: fun_nat_rat] :
      ( ! [X3: nat] :
          ( member_nat(X3,A2)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),aa_nat_rat(F,X3)) )
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),groups73079841787564623at_rat(F,A2)) ) ).

% prod_ge_1
tff(fact_4419_prod__ge__1,axiom,
    ! [A2: set_int,F: fun_int_rat] :
      ( ! [X3: int] :
          ( member_int(X3,A2)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),aa_int_rat(F,X3)) )
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,F),A2)) ) ).

% prod_ge_1
tff(fact_4420_prod__ge__1,axiom,
    ! [A2: set_o,F: fun_o_nat] :
      ( ! [X3: $o] :
          ( member_o((X3),A2)
         => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),aa_o_nat(F,(X3))) )
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),aa_set_o_nat(aa_fun8470299178418016604_o_nat(groups3504817904513533571_o_nat,F),A2)) ) ).

% prod_ge_1
tff(fact_4421_prod__ge__1,axiom,
    ! [A2: set_int,F: fun_int_nat] :
      ( ! [X3: int] :
          ( member_int(X3,A2)
         => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),aa_int_nat(F,X3)) )
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),groups1707563613775114915nt_nat(F,A2)) ) ).

% prod_ge_1
tff(fact_4422_prod__ge__1,axiom,
    ! [A2: set_o,F: fun_o_int] :
      ( ! [X3: $o] :
          ( member_o((X3),A2)
         => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,one_one_int),aa_o_int(F,(X3))) )
     => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,one_one_int),groups3502327434004483295_o_int(F,A2)) ) ).

% prod_ge_1
tff(fact_4423_prod__ge__1,axiom,
    ! [A2: set_nat,F: fun_nat_nat] :
      ( ! [X3: nat] :
          ( member_nat(X3,A2)
         => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),aa_nat_nat(F,X3)) )
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),aa_set_nat_nat(groups708209901874060359at_nat(F),A2)) ) ).

% prod_ge_1
tff(fact_4424_int__of__integer__less__iff,axiom,
    ! [X2: code_integer,Y: code_integer] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_Code_integer_int(code_int_of_integer,X2)),aa_Code_integer_int(code_int_of_integer,Y))
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,X2),Y) ) ).

% int_of_integer_less_iff
tff(fact_4425_integer__less__iff,axiom,
    ! [K: code_integer,L: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,K),L)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,aa_Code_integer_int(code_int_of_integer,K)),aa_Code_integer_int(code_int_of_integer,L)) ) ).

% integer_less_iff
tff(fact_4426_less__integer_Orep__eq,axiom,
    ! [X2: code_integer,Xa: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,X2),Xa)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,aa_Code_integer_int(code_int_of_integer,X2)),aa_Code_integer_int(code_int_of_integer,Xa)) ) ).

% less_integer.rep_eq
tff(fact_4427_less__eq__integer_Orep__eq,axiom,
    ! [X2: code_integer,Xa: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,X2),Xa)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_Code_integer_int(code_int_of_integer,X2)),aa_Code_integer_int(code_int_of_integer,Xa)) ) ).

% less_eq_integer.rep_eq
tff(fact_4428_integer__less__eq__iff,axiom,
    ! [K: code_integer,L: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,K),L)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_Code_integer_int(code_int_of_integer,K)),aa_Code_integer_int(code_int_of_integer,L)) ) ).

% integer_less_eq_iff
tff(fact_4429_prod_Oshift__bounds__cl__Suc__ivl,axiom,
    ! [G: fun_nat_nat,M: nat,N2: nat] : aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,M)),aa_nat_nat(suc,N2))) = aa_set_nat_nat(groups708209901874060359at_nat(aTP_Lamm_dh(G)),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) ).

% prod.shift_bounds_cl_Suc_ivl
tff(fact_4430_prod_Oshift__bounds__cl__Suc__ivl,axiom,
    ! [G: fun_nat_int,M: nat,N2: nat] : groups705719431365010083at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,M)),aa_nat_nat(suc,N2))) = groups705719431365010083at_int(aTP_Lamm_dr(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) ).

% prod.shift_bounds_cl_Suc_ivl
tff(fact_4431_prod_Oshift__bounds__Suc__ivl,axiom,
    ! [G: fun_nat_nat,M: nat,N2: nat] : aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(suc,M)),aa_nat_nat(suc,N2))) = aa_set_nat_nat(groups708209901874060359at_nat(aTP_Lamm_dh(G)),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) ).

% prod.shift_bounds_Suc_ivl
tff(fact_4432_prod_Oshift__bounds__Suc__ivl,axiom,
    ! [G: fun_nat_int,M: nat,N2: nat] : groups705719431365010083at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(suc,M)),aa_nat_nat(suc,N2))) = groups705719431365010083at_int(aTP_Lamm_dr(G),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) ).

% prod.shift_bounds_Suc_ivl
tff(fact_4433_prod_Oshift__bounds__cl__nat__ivl,axiom,
    ! [G: fun_nat_nat,M: nat,K: nat,N2: nat] : aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),K))) = aa_set_nat_nat(groups708209901874060359at_nat(aa_nat_fun_nat_nat(aTP_Lamm_di(G),K)),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) ).

% prod.shift_bounds_cl_nat_ivl
tff(fact_4434_prod_Oshift__bounds__cl__nat__ivl,axiom,
    ! [G: fun_nat_int,M: nat,K: nat,N2: nat] : groups705719431365010083at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),K))) = groups705719431365010083at_int(aa_nat_fun_nat_int(aTP_Lamm_ks(G),K),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) ).

% prod.shift_bounds_cl_nat_ivl
tff(fact_4435_prod_Oshift__bounds__nat__ivl,axiom,
    ! [G: fun_nat_nat,M: nat,K: nat,N2: nat] : aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),K))) = aa_set_nat_nat(groups708209901874060359at_nat(aa_nat_fun_nat_nat(aTP_Lamm_di(G),K)),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) ).

% prod.shift_bounds_nat_ivl
tff(fact_4436_prod_Oshift__bounds__nat__ivl,axiom,
    ! [G: fun_nat_int,M: nat,K: nat,N2: nat] : groups705719431365010083at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),K))) = groups705719431365010083at_int(aa_nat_fun_nat_int(aTP_Lamm_ks(G),K),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) ).

% prod.shift_bounds_nat_ivl
tff(fact_4437_atLeastLessThanPlusOne__atLeastAtMost__integer,axiom,
    ! [L: code_integer,U: code_integer] : aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(L),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,U),one_one_Code_integer)) = aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(L),U) ).

% atLeastLessThanPlusOne_atLeastAtMost_integer
tff(fact_4438_prod__le__1,axiom,
    ! [A2: set_o,F: fun_o_Code_integer] :
      ( ! [X3: $o] :
          ( member_o((X3),A2)
         => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_o_Code_integer(F,(X3)))
            & aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_o_Code_integer(F,(X3))),one_one_Code_integer) ) )
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,F),A2)),one_one_Code_integer) ) ).

% prod_le_1
tff(fact_4439_prod__le__1,axiom,
    ! [A2: set_nat,F: fun_nat_Code_integer] :
      ( ! [X3: nat] :
          ( member_nat(X3,A2)
         => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_nat_Code_integer(F,X3))
            & aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_nat_Code_integer(F,X3)),one_one_Code_integer) ) )
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,groups3455450783089532116nteger(F,A2)),one_one_Code_integer) ) ).

% prod_le_1
tff(fact_4440_prod__le__1,axiom,
    ! [A2: set_int,F: fun_int_Code_integer] :
      ( ! [X3: int] :
          ( member_int(X3,A2)
         => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_int_Code_integer(F,X3))
            & aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_int_Code_integer(F,X3)),one_one_Code_integer) ) )
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,F),A2)),one_one_Code_integer) ) ).

% prod_le_1
tff(fact_4441_prod__le__1,axiom,
    ! [A2: set_o,F: fun_o_rat] :
      ( ! [X3: $o] :
          ( member_o((X3),A2)
         => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),aa_o_rat(F,(X3)))
            & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_o_rat(F,(X3))),one_one_rat) ) )
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_set_o_rat(aa_fun7302669049306738524_o_rat(groups2869687844427037835_o_rat,F),A2)),one_one_rat) ) ).

% prod_le_1
tff(fact_4442_prod__le__1,axiom,
    ! [A2: set_nat,F: fun_nat_rat] :
      ( ! [X3: nat] :
          ( member_nat(X3,A2)
         => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),aa_nat_rat(F,X3))
            & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_nat_rat(F,X3)),one_one_rat) ) )
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,groups73079841787564623at_rat(F,A2)),one_one_rat) ) ).

% prod_le_1
tff(fact_4443_prod__le__1,axiom,
    ! [A2: set_int,F: fun_int_rat] :
      ( ! [X3: int] :
          ( member_int(X3,A2)
         => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),aa_int_rat(F,X3))
            & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_int_rat(F,X3)),one_one_rat) ) )
     => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,F),A2)),one_one_rat) ) ).

% prod_le_1
tff(fact_4444_prod__le__1,axiom,
    ! [A2: set_o,F: fun_o_nat] :
      ( ! [X3: $o] :
          ( member_o((X3),A2)
         => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),aa_o_nat(F,(X3)))
            & aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_o_nat(F,(X3))),one_one_nat) ) )
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_set_o_nat(aa_fun8470299178418016604_o_nat(groups3504817904513533571_o_nat,F),A2)),one_one_nat) ) ).

% prod_le_1
tff(fact_4445_prod__le__1,axiom,
    ! [A2: set_int,F: fun_int_nat] :
      ( ! [X3: int] :
          ( member_int(X3,A2)
         => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),aa_int_nat(F,X3))
            & aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_int_nat(F,X3)),one_one_nat) ) )
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,groups1707563613775114915nt_nat(F,A2)),one_one_nat) ) ).

% prod_le_1
tff(fact_4446_prod__le__1,axiom,
    ! [A2: set_o,F: fun_o_int] :
      ( ! [X3: $o] :
          ( member_o((X3),A2)
         => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),aa_o_int(F,(X3)))
            & aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_o_int(F,(X3))),one_one_int) ) )
     => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,groups3502327434004483295_o_int(F,A2)),one_one_int) ) ).

% prod_le_1
tff(fact_4447_prod__le__1,axiom,
    ! [A2: set_nat,F: fun_nat_nat] :
      ( ! [X3: nat] :
          ( member_nat(X3,A2)
         => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),aa_nat_nat(F,X3))
            & aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(F,X3)),one_one_nat) ) )
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_set_nat_nat(groups708209901874060359at_nat(F),A2)),one_one_nat) ) ).

% prod_le_1
tff(fact_4448_prod_Oivl__cong,axiom,
    ! [A: nat,C: nat,B: nat,D2: nat,G: fun_nat_nat,Ha: fun_nat_nat] :
      ( ( A = C )
     => ( ( B = D2 )
       => ( ! [X3: nat] :
              ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,C),X3)
             => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,X3),D2)
               => ( aa_nat_nat(G,X3) = aa_nat_nat(Ha,X3) ) ) )
         => ( aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(A),B)) = aa_set_nat_nat(groups708209901874060359at_nat(Ha),aa_nat_set_nat(set_or4665077453230672383an_nat(C),D2)) ) ) ) ) ).

% prod.ivl_cong
tff(fact_4449_prod_Oivl__cong,axiom,
    ! [A: nat,C: nat,B: nat,D2: nat,G: fun_nat_int,Ha: fun_nat_int] :
      ( ( A = C )
     => ( ( B = D2 )
       => ( ! [X3: nat] :
              ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,C),X3)
             => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,X3),D2)
               => ( aa_nat_int(G,X3) = aa_nat_int(Ha,X3) ) ) )
         => ( groups705719431365010083at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(A),B)) = groups705719431365010083at_int(Ha,aa_nat_set_nat(set_or4665077453230672383an_nat(C),D2)) ) ) ) ) ).

% prod.ivl_cong
tff(fact_4450_prod_Oivl__cong,axiom,
    ! [A: int,C: int,B: int,D2: int,G: fun_int_int,Ha: fun_int_int] :
      ( ( A = C )
     => ( ( B = D2 )
       => ( ! [X3: int] :
              ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,C),X3)
             => ( aa_int_o(aa_int_fun_int_o(ord_less_int,X3),D2)
               => ( aa_int_int(G,X3) = aa_int_int(Ha,X3) ) ) )
         => ( aa_set_int_int(groups1705073143266064639nt_int(G),aa_int_set_int(set_or4662586982721622107an_int(A),B)) = aa_set_int_int(groups1705073143266064639nt_int(Ha),aa_int_set_int(set_or4662586982721622107an_int(C),D2)) ) ) ) ) ).

% prod.ivl_cong
tff(fact_4451_take__bit__integer_Orep__eq,axiom,
    ! [X2: nat,Xa: code_integer] : aa_Code_integer_int(code_int_of_integer,aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,X2),Xa)) = aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,X2),aa_Code_integer_int(code_int_of_integer,Xa)) ).

% take_bit_integer.rep_eq
tff(fact_4452_and__integer_Orep__eq,axiom,
    ! [X2: code_integer,Xa: code_integer] : aa_Code_integer_int(code_int_of_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3949692690581998587nteger,X2),Xa)) = aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,aa_Code_integer_int(code_int_of_integer,X2)),aa_Code_integer_int(code_int_of_integer,Xa)) ).

% and_integer.rep_eq
tff(fact_4453_bit__integer_Orep__eq,axiom,
    ! [X2: code_integer] : aa_Cod1075288278386115654_nat_o(bit_se9216721137139052372nteger,X2) = aa_int_fun_nat_o(bit_se1146084159140164899it_int,aa_Code_integer_int(code_int_of_integer,X2)) ).

% bit_integer.rep_eq
tff(fact_4454_prod_OatLeastLessThan__concat,axiom,
    ! [M: nat,N2: nat,P2: nat,G: fun_nat_assn] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),P2)
       => ( aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))),groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or4665077453230672383an_nat(N2),P2))) = groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),P2)) ) ) ) ).

% prod.atLeastLessThan_concat
tff(fact_4455_prod_OatLeastLessThan__concat,axiom,
    ! [M: nat,N2: nat,P2: nat,G: fun_nat_rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),P2)
       => ( aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,groups73079841787564623at_rat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))),groups73079841787564623at_rat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(N2),P2))) = groups73079841787564623at_rat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),P2)) ) ) ) ).

% prod.atLeastLessThan_concat
tff(fact_4456_prod_OatLeastLessThan__concat,axiom,
    ! [M: nat,N2: nat,P2: nat,G: fun_nat_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),P2)
       => ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))),aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(N2),P2))) = aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(M),P2)) ) ) ) ).

% prod.atLeastLessThan_concat
tff(fact_4457_prod_OatLeastLessThan__concat,axiom,
    ! [M: nat,N2: nat,P2: nat,G: fun_nat_int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),P2)
       => ( aa_int_int(aa_int_fun_int_int(times_times_int,groups705719431365010083at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))),groups705719431365010083at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(N2),P2))) = groups705719431365010083at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),P2)) ) ) ) ).

% prod.atLeastLessThan_concat
tff(fact_4458_mask__integer_Orep__eq,axiom,
    ! [X2: nat] : aa_Code_integer_int(code_int_of_integer,aa_nat_Code_integer(bit_se2119862282449309892nteger,X2)) = aa_nat_int(bit_se2000444600071755411sk_int,X2) ).

% mask_integer.rep_eq
tff(fact_4459_integer__of__num__def,axiom,
    code_integer_of_num = numera6620942414471956472nteger ).

% integer_of_num_def
tff(fact_4460_unset__bit__integer_Orep__eq,axiom,
    ! [X2: nat,Xa: code_integer] : aa_Code_integer_int(code_int_of_integer,aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se8260200283734997820nteger,X2),Xa)) = aa_int_int(aa_nat_fun_int_int(bit_se4203085406695923979it_int,X2),aa_Code_integer_int(code_int_of_integer,Xa)) ).

% unset_bit_integer.rep_eq
tff(fact_4461_set__bit__integer_Orep__eq,axiom,
    ! [X2: nat,Xa: code_integer] : aa_Code_integer_int(code_int_of_integer,aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se2793503036327961859nteger,X2),Xa)) = aa_int_int(aa_nat_fun_int_int(bit_se7879613467334960850it_int,X2),aa_Code_integer_int(code_int_of_integer,Xa)) ).

% set_bit_integer.rep_eq
tff(fact_4462_flip__bit__integer_Orep__eq,axiom,
    ! [X2: nat,Xa: code_integer] : aa_Code_integer_int(code_int_of_integer,aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1345352211410354436nteger,X2),Xa)) = aa_int_int(aa_nat_fun_int_int(bit_se2159334234014336723it_int,X2),aa_Code_integer_int(code_int_of_integer,Xa)) ).

% flip_bit_integer.rep_eq
tff(fact_4463_prod_OatLeast__Suc__atMost__Suc__shift,axiom,
    ! [G: fun_nat_nat,M: nat,N2: nat] : aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,M)),aa_nat_nat(suc,N2))) = aa_set_nat_nat(groups708209901874060359at_nat(comp_nat_nat_nat(G,suc)),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) ).

% prod.atLeast_Suc_atMost_Suc_shift
tff(fact_4464_prod_OatLeast__Suc__atMost__Suc__shift,axiom,
    ! [G: fun_nat_int,M: nat,N2: nat] : groups705719431365010083at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,M)),aa_nat_nat(suc,N2))) = groups705719431365010083at_int(comp_nat_int_nat(G,suc),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) ).

% prod.atLeast_Suc_atMost_Suc_shift
tff(fact_4465_prod_OatLeast__Suc__lessThan__Suc__shift,axiom,
    ! [G: fun_nat_nat,M: nat,N2: nat] : aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(suc,M)),aa_nat_nat(suc,N2))) = aa_set_nat_nat(groups708209901874060359at_nat(comp_nat_nat_nat(G,suc)),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) ).

% prod.atLeast_Suc_lessThan_Suc_shift
tff(fact_4466_prod_OatLeast__Suc__lessThan__Suc__shift,axiom,
    ! [G: fun_nat_int,M: nat,N2: nat] : groups705719431365010083at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(suc,M)),aa_nat_nat(suc,N2))) = groups705719431365010083at_int(comp_nat_int_nat(G,suc),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) ).

% prod.atLeast_Suc_lessThan_Suc_shift
tff(fact_4467_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
    ! [L: int,U: int] : aa_int_set_int(set_or4662586982721622107an_int(L),aa_int_int(aa_int_fun_int_int(plus_plus_int,U),one_one_int)) = aa_int_set_int(set_or1266510415728281911st_int(L),U) ).

% atLeastLessThanPlusOne_atLeastAtMost_int
tff(fact_4468_prod_OatLeastAtMost__shift__bounds,axiom,
    ! [G: fun_nat_nat,M: nat,K: nat,N2: nat] : aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),K))) = aa_set_nat_nat(groups708209901874060359at_nat(comp_nat_nat_nat(G,aa_nat_fun_nat_nat(plus_plus_nat,K))),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) ).

% prod.atLeastAtMost_shift_bounds
tff(fact_4469_prod_OatLeastAtMost__shift__bounds,axiom,
    ! [G: fun_nat_int,M: nat,K: nat,N2: nat] : groups705719431365010083at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),K))) = groups705719431365010083at_int(comp_nat_int_nat(G,aa_nat_fun_nat_nat(plus_plus_nat,K)),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) ).

% prod.atLeastAtMost_shift_bounds
tff(fact_4470_prod_OatLeastLessThan__shift__bounds,axiom,
    ! [G: fun_nat_nat,M: nat,K: nat,N2: nat] : aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),K))) = aa_set_nat_nat(groups708209901874060359at_nat(comp_nat_nat_nat(G,aa_nat_fun_nat_nat(plus_plus_nat,K))),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) ).

% prod.atLeastLessThan_shift_bounds
tff(fact_4471_prod_OatLeastLessThan__shift__bounds,axiom,
    ! [G: fun_nat_int,M: nat,K: nat,N2: nat] : groups705719431365010083at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),K))) = groups705719431365010083at_int(comp_nat_int_nat(G,aa_nat_fun_nat_nat(plus_plus_nat,K)),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) ).

% prod.atLeastLessThan_shift_bounds
tff(fact_4472_prod_OatLeastAtMost__rev,axiom,
    ! [G: fun_nat_nat,N2: nat,M: nat] : aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(N2),M)) = aa_set_nat_nat(groups708209901874060359at_nat(aa_nat_fun_nat_nat(aa_nat3783148529270815480at_nat(aTP_Lamm_do(G),N2),M)),aa_nat_set_nat(set_or1269000886237332187st_nat(N2),M)) ).

% prod.atLeastAtMost_rev
tff(fact_4473_prod_OatLeastAtMost__rev,axiom,
    ! [G: fun_nat_int,N2: nat,M: nat] : groups705719431365010083at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(N2),M)) = groups705719431365010083at_int(aa_nat_fun_nat_int(aa_nat1293065384339088724at_int(aTP_Lamm_kt(G),N2),M),aa_nat_set_nat(set_or1269000886237332187st_nat(N2),M)) ).

% prod.atLeastAtMost_rev
tff(fact_4474_prod_Onat__diff__reindex,axiom,
    ! [G: fun_nat_nat,N2: nat] : aa_set_nat_nat(groups708209901874060359at_nat(aa_nat_fun_nat_nat(aTP_Lamm_ix(G),N2)),aa_nat_set_nat(set_ord_lessThan_nat,N2)) = aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_ord_lessThan_nat,N2)) ).

% prod.nat_diff_reindex
tff(fact_4475_prod_Onat__diff__reindex,axiom,
    ! [G: fun_nat_int,N2: nat] : groups705719431365010083at_int(aa_nat_fun_nat_int(aTP_Lamm_ku(G),N2),aa_nat_set_nat(set_ord_lessThan_nat,N2)) = groups705719431365010083at_int(G,aa_nat_set_nat(set_ord_lessThan_nat,N2)) ).

% prod.nat_diff_reindex
tff(fact_4476_nat__of__integer_Oabs__eq,axiom,
    ! [X2: int] : aa_Code_integer_nat(code_nat_of_integer,aa_int_Code_integer(code_integer_of_int,X2)) = aa_int_nat(nat2,X2) ).

% nat_of_integer.abs_eq
tff(fact_4477_num__of__integer_Orep__eq,axiom,
    ! [X2: code_integer] : aa_Code_integer_num(code_num_of_integer,X2) = aa_nat_num(num_of_nat,aa_int_nat(nat2,aa_Code_integer_int(code_int_of_integer,X2))) ).

% num_of_integer.rep_eq
tff(fact_4478_prod_OatLeast0__atMost__Suc,axiom,
    ! [G: fun_nat_assn,N2: nat] : groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2))),aa_nat_assn(G,aa_nat_nat(suc,N2))) ).

% prod.atLeast0_atMost_Suc
tff(fact_4479_prod_OatLeast0__atMost__Suc,axiom,
    ! [G: fun_nat_rat,N2: nat] : groups73079841787564623at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,groups73079841787564623at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2))),aa_nat_rat(G,aa_nat_nat(suc,N2))) ).

% prod.atLeast0_atMost_Suc
tff(fact_4480_prod_OatLeast0__atMost__Suc,axiom,
    ! [G: fun_nat_nat,N2: nat] : aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2))),aa_nat_nat(G,aa_nat_nat(suc,N2))) ).

% prod.atLeast0_atMost_Suc
tff(fact_4481_prod_OatLeast0__atMost__Suc,axiom,
    ! [G: fun_nat_int,N2: nat] : groups705719431365010083at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_int_int(aa_int_fun_int_int(times_times_int,groups705719431365010083at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2))),aa_nat_int(G,aa_nat_nat(suc,N2))) ).

% prod.atLeast0_atMost_Suc
tff(fact_4482_prod_OatLeast0__lessThan__Suc,axiom,
    ! [G: fun_nat_assn,N2: nat] : groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2))),aa_nat_assn(G,N2)) ).

% prod.atLeast0_lessThan_Suc
tff(fact_4483_prod_OatLeast0__lessThan__Suc,axiom,
    ! [G: fun_nat_rat,N2: nat] : groups73079841787564623at_rat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,groups73079841787564623at_rat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2))),aa_nat_rat(G,N2)) ).

% prod.atLeast0_lessThan_Suc
tff(fact_4484_prod_OatLeast0__lessThan__Suc,axiom,
    ! [G: fun_nat_nat,N2: nat] : aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2))),aa_nat_nat(G,N2)) ).

% prod.atLeast0_lessThan_Suc
tff(fact_4485_prod_OatLeast0__lessThan__Suc,axiom,
    ! [G: fun_nat_int,N2: nat] : groups705719431365010083at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_int_int(aa_int_fun_int_int(times_times_int,groups705719431365010083at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2))),aa_nat_int(G,N2)) ).

% prod.atLeast0_lessThan_Suc
tff(fact_4486_prod_OatLeast__Suc__lessThan,axiom,
    ! [M: nat,N2: nat,G: fun_nat_assn] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M),N2)
     => ( groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_nat_assn(G,M)),groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(suc,M)),N2))) ) ) ).

% prod.atLeast_Suc_lessThan
tff(fact_4487_prod_OatLeast__Suc__lessThan,axiom,
    ! [M: nat,N2: nat,G: fun_nat_rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M),N2)
     => ( groups73079841787564623at_rat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(G,M)),groups73079841787564623at_rat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(suc,M)),N2))) ) ) ).

% prod.atLeast_Suc_lessThan
tff(fact_4488_prod_OatLeast__Suc__lessThan,axiom,
    ! [M: nat,N2: nat,G: fun_nat_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M),N2)
     => ( aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(G,M)),aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(suc,M)),N2))) ) ) ).

% prod.atLeast_Suc_lessThan
tff(fact_4489_prod_OatLeast__Suc__lessThan,axiom,
    ! [M: nat,N2: nat,G: fun_nat_int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M),N2)
     => ( groups705719431365010083at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(G,M)),groups705719431365010083at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(suc,M)),N2))) ) ) ).

% prod.atLeast_Suc_lessThan
tff(fact_4490_prod_Onat__ivl__Suc_H,axiom,
    ! [M: nat,N2: nat,G: fun_nat_assn] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),aa_nat_nat(suc,N2))
     => ( groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),aa_nat_nat(suc,N2))) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_nat_assn(G,aa_nat_nat(suc,N2))),groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))) ) ) ).

% prod.nat_ivl_Suc'
tff(fact_4491_prod_Onat__ivl__Suc_H,axiom,
    ! [M: nat,N2: nat,G: fun_nat_rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),aa_nat_nat(suc,N2))
     => ( groups73079841787564623at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),aa_nat_nat(suc,N2))) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(G,aa_nat_nat(suc,N2))),groups73079841787564623at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))) ) ) ).

% prod.nat_ivl_Suc'
tff(fact_4492_prod_Onat__ivl__Suc_H,axiom,
    ! [M: nat,N2: nat,G: fun_nat_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),aa_nat_nat(suc,N2))
     => ( aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),aa_nat_nat(suc,N2))) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(G,aa_nat_nat(suc,N2))),aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))) ) ) ).

% prod.nat_ivl_Suc'
tff(fact_4493_prod_Onat__ivl__Suc_H,axiom,
    ! [M: nat,N2: nat,G: fun_nat_int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),aa_nat_nat(suc,N2))
     => ( groups705719431365010083at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),aa_nat_nat(suc,N2))) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(G,aa_nat_nat(suc,N2))),groups705719431365010083at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))) ) ) ).

% prod.nat_ivl_Suc'
tff(fact_4494_prod_OatLeast__Suc__atMost,axiom,
    ! [M: nat,N2: nat,G: fun_nat_assn] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_nat_assn(G,M)),groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,M)),N2))) ) ) ).

% prod.atLeast_Suc_atMost
tff(fact_4495_prod_OatLeast__Suc__atMost,axiom,
    ! [M: nat,N2: nat,G: fun_nat_rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( groups73079841787564623at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(G,M)),groups73079841787564623at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,M)),N2))) ) ) ).

% prod.atLeast_Suc_atMost
tff(fact_4496_prod_OatLeast__Suc__atMost,axiom,
    ! [M: nat,N2: nat,G: fun_nat_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(G,M)),aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,M)),N2))) ) ) ).

% prod.atLeast_Suc_atMost
tff(fact_4497_prod_OatLeast__Suc__atMost,axiom,
    ! [M: nat,N2: nat,G: fun_nat_int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( groups705719431365010083at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(G,M)),groups705719431365010083at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,M)),N2))) ) ) ).

% prod.atLeast_Suc_atMost
tff(fact_4498_prod_OatLeastLessThan__Suc,axiom,
    ! [A: nat,B: nat,G: fun_nat_assn] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
     => ( groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or4665077453230672383an_nat(A),aa_nat_nat(suc,B))) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or4665077453230672383an_nat(A),B))),aa_nat_assn(G,B)) ) ) ).

% prod.atLeastLessThan_Suc
tff(fact_4499_prod_OatLeastLessThan__Suc,axiom,
    ! [A: nat,B: nat,G: fun_nat_rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
     => ( groups73079841787564623at_rat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(A),aa_nat_nat(suc,B))) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,groups73079841787564623at_rat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(A),B))),aa_nat_rat(G,B)) ) ) ).

% prod.atLeastLessThan_Suc
tff(fact_4500_prod_OatLeastLessThan__Suc,axiom,
    ! [A: nat,B: nat,G: fun_nat_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
     => ( aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(A),aa_nat_nat(suc,B))) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(A),B))),aa_nat_nat(G,B)) ) ) ).

% prod.atLeastLessThan_Suc
tff(fact_4501_prod_OatLeastLessThan__Suc,axiom,
    ! [A: nat,B: nat,G: fun_nat_int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
     => ( groups705719431365010083at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(A),aa_nat_nat(suc,B))) = aa_int_int(aa_int_fun_int_int(times_times_int,groups705719431365010083at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(A),B))),aa_nat_int(G,B)) ) ) ).

% prod.atLeastLessThan_Suc
tff(fact_4502_divmod__abs__code_I6_J,axiom,
    ! [J: code_integer] : aa_Cod6977894654539884864nteger(code_divmod_abs(zero_z3403309356797280102nteger),J) = aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(zero_z3403309356797280102nteger),zero_z3403309356797280102nteger) ).

% divmod_abs_code(6)
tff(fact_4503_prod_Olast__plus,axiom,
    ! [M: nat,N2: nat,G: fun_nat_assn] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_nat_assn(G,N2)),groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))) ) ) ).

% prod.last_plus
tff(fact_4504_prod_Olast__plus,axiom,
    ! [M: nat,N2: nat,G: fun_nat_rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( groups73079841787564623at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(G,N2)),groups73079841787564623at_rat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))) ) ) ).

% prod.last_plus
tff(fact_4505_prod_Olast__plus,axiom,
    ! [M: nat,N2: nat,G: fun_nat_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(G,N2)),aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))) ) ) ).

% prod.last_plus
tff(fact_4506_prod_Olast__plus,axiom,
    ! [M: nat,N2: nat,G: fun_nat_int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( groups705719431365010083at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(G,N2)),groups705719431365010083at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))) ) ) ).

% prod.last_plus
tff(fact_4507_prod_OSuc__reindex__ivl,axiom,
    ! [M: nat,N2: nat,G: fun_nat_assn] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))),aa_nat_assn(G,aa_nat_nat(suc,N2))) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_nat_assn(G,M)),groups6906906614972039071t_assn(aTP_Lamm_kv(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))) ) ) ).

% prod.Suc_reindex_ivl
tff(fact_4508_prod_OSuc__reindex__ivl,axiom,
    ! [M: nat,N2: nat,G: fun_nat_rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,groups73079841787564623at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))),aa_nat_rat(G,aa_nat_nat(suc,N2))) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(G,M)),groups73079841787564623at_rat(aTP_Lamm_dq(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))) ) ) ).

% prod.Suc_reindex_ivl
tff(fact_4509_prod_OSuc__reindex__ivl,axiom,
    ! [M: nat,N2: nat,G: fun_nat_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))),aa_nat_nat(G,aa_nat_nat(suc,N2))) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(G,M)),aa_set_nat_nat(groups708209901874060359at_nat(aTP_Lamm_dh(G)),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))) ) ) ).

% prod.Suc_reindex_ivl
tff(fact_4510_prod_OSuc__reindex__ivl,axiom,
    ! [M: nat,N2: nat,G: fun_nat_int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_int_int(aa_int_fun_int_int(times_times_int,groups705719431365010083at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))),aa_nat_int(G,aa_nat_nat(suc,N2))) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(G,M)),groups705719431365010083at_int(aTP_Lamm_dr(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))) ) ) ).

% prod.Suc_reindex_ivl
tff(fact_4511_prod_OatMost__Suc__shift,axiom,
    ! [G: fun_nat_assn,N2: nat] : groups6906906614972039071t_assn(G,aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(suc,N2))) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_nat_assn(G,zero_zero_nat)),groups6906906614972039071t_assn(aTP_Lamm_kv(G),aa_nat_set_nat(set_ord_atMost_nat,N2))) ).

% prod.atMost_Suc_shift
tff(fact_4512_prod_OatMost__Suc__shift,axiom,
    ! [G: fun_nat_rat,N2: nat] : groups73079841787564623at_rat(G,aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(suc,N2))) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(G,zero_zero_nat)),groups73079841787564623at_rat(aTP_Lamm_dq(G),aa_nat_set_nat(set_ord_atMost_nat,N2))) ).

% prod.atMost_Suc_shift
tff(fact_4513_prod_OatMost__Suc__shift,axiom,
    ! [G: fun_nat_nat,N2: nat] : aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(suc,N2))) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(G,zero_zero_nat)),aa_set_nat_nat(groups708209901874060359at_nat(aTP_Lamm_dh(G)),aa_nat_set_nat(set_ord_atMost_nat,N2))) ).

% prod.atMost_Suc_shift
tff(fact_4514_prod_OatMost__Suc__shift,axiom,
    ! [G: fun_nat_int,N2: nat] : groups705719431365010083at_int(G,aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(suc,N2))) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(G,zero_zero_nat)),groups705719431365010083at_int(aTP_Lamm_dr(G),aa_nat_set_nat(set_ord_atMost_nat,N2))) ).

% prod.atMost_Suc_shift
tff(fact_4515_prod_OlessThan__Suc__shift,axiom,
    ! [G: fun_nat_assn,N2: nat] : groups6906906614972039071t_assn(G,aa_nat_set_nat(set_ord_lessThan_nat,aa_nat_nat(suc,N2))) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_nat_assn(G,zero_zero_nat)),groups6906906614972039071t_assn(aTP_Lamm_kv(G),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% prod.lessThan_Suc_shift
tff(fact_4516_prod_OlessThan__Suc__shift,axiom,
    ! [G: fun_nat_rat,N2: nat] : groups73079841787564623at_rat(G,aa_nat_set_nat(set_ord_lessThan_nat,aa_nat_nat(suc,N2))) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(G,zero_zero_nat)),groups73079841787564623at_rat(aTP_Lamm_dq(G),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% prod.lessThan_Suc_shift
tff(fact_4517_prod_OlessThan__Suc__shift,axiom,
    ! [G: fun_nat_nat,N2: nat] : aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_ord_lessThan_nat,aa_nat_nat(suc,N2))) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(G,zero_zero_nat)),aa_set_nat_nat(groups708209901874060359at_nat(aTP_Lamm_dh(G)),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% prod.lessThan_Suc_shift
tff(fact_4518_prod_OlessThan__Suc__shift,axiom,
    ! [G: fun_nat_int,N2: nat] : groups705719431365010083at_int(G,aa_nat_set_nat(set_ord_lessThan_nat,aa_nat_nat(suc,N2))) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(G,zero_zero_nat)),groups705719431365010083at_int(aTP_Lamm_dr(G),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% prod.lessThan_Suc_shift
tff(fact_4519_prod_OatLeastLessThan__rev,axiom,
    ! [G: fun_nat_nat,N2: nat,M: nat] : aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(N2),M)) = aa_set_nat_nat(groups708209901874060359at_nat(aa_nat_fun_nat_nat(aa_nat3783148529270815480at_nat(aTP_Lamm_kc(G),N2),M)),aa_nat_set_nat(set_or4665077453230672383an_nat(N2),M)) ).

% prod.atLeastLessThan_rev
tff(fact_4520_prod_OatLeastLessThan__rev,axiom,
    ! [G: fun_nat_int,N2: nat,M: nat] : groups705719431365010083at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(N2),M)) = groups705719431365010083at_int(aa_nat_fun_nat_int(aa_nat1293065384339088724at_int(aTP_Lamm_kw(G),N2),M),aa_nat_set_nat(set_or4665077453230672383an_nat(N2),M)) ).

% prod.atLeastLessThan_rev
tff(fact_4521_prod_Onested__swap,axiom,
    ! [A: fun_nat_fun_nat_nat,N2: nat] : aa_set_nat_nat(groups708209901874060359at_nat(aTP_Lamm_kx(A)),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2)) = aa_set_nat_nat(groups708209901874060359at_nat(aa_nat_fun_nat_nat(aTP_Lamm_ky(A),N2)),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2)) ).

% prod.nested_swap
tff(fact_4522_prod_Onested__swap,axiom,
    ! [A: fun_nat_fun_nat_int,N2: nat] : groups705719431365010083at_int(aTP_Lamm_kz(A),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2)) = groups705719431365010083at_int(aa_nat_fun_nat_int(aTP_Lamm_lb(A),N2),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2)) ).

% prod.nested_swap
tff(fact_4523_prod_OatLeast1__atMost__eq,axiom,
    ! [G: fun_nat_nat,N2: nat] : aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,zero_zero_nat)),N2)) = aa_set_nat_nat(groups708209901874060359at_nat(aTP_Lamm_dh(G)),aa_nat_set_nat(set_ord_lessThan_nat,N2)) ).

% prod.atLeast1_atMost_eq
tff(fact_4524_prod_OatLeast1__atMost__eq,axiom,
    ! [G: fun_nat_int,N2: nat] : groups705719431365010083at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,zero_zero_nat)),N2)) = groups705719431365010083at_int(aTP_Lamm_dr(G),aa_nat_set_nat(set_ord_lessThan_nat,N2)) ).

% prod.atLeast1_atMost_eq
tff(fact_4525_prod_Onat__group,axiom,
    ! [G: fun_nat_nat,K: nat,N2: nat] : aa_set_nat_nat(groups708209901874060359at_nat(aa_nat_fun_nat_nat(aTP_Lamm_lc(G),K)),aa_nat_set_nat(set_ord_lessThan_nat,N2)) = aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_ord_lessThan_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,N2),K))) ).

% prod.nat_group
tff(fact_4526_prod_Onat__group,axiom,
    ! [G: fun_nat_int,K: nat,N2: nat] : groups705719431365010083at_int(aa_nat_fun_nat_int(aTP_Lamm_ld(G),K),aa_nat_set_nat(set_ord_lessThan_nat,N2)) = groups705719431365010083at_int(G,aa_nat_set_nat(set_ord_lessThan_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,N2),K))) ).

% prod.nat_group
tff(fact_4527_fact__prod,axiom,
    ! [N2: nat] : aa_nat_int(semiri1406184849735516958ct_int,N2) = aa_nat_int(semiri1314217659103216013at_int,aa_set_nat_nat(groups708209901874060359at_nat(aTP_Lamm_co),aa_nat_set_nat(set_or1269000886237332187st_nat(one_one_nat),N2))) ).

% fact_prod
tff(fact_4528_fact__prod,axiom,
    ! [N2: nat] : aa_nat_Code_integer(semiri3624122377584611663nteger,N2) = aa_nat_Code_integer(semiri4939895301339042750nteger,aa_set_nat_nat(groups708209901874060359at_nat(aTP_Lamm_co),aa_nat_set_nat(set_or1269000886237332187st_nat(one_one_nat),N2))) ).

% fact_prod
tff(fact_4529_fact__prod,axiom,
    ! [N2: nat] : aa_nat_Code_natural(semiri2447717529341329178atural,N2) = aa_nat_Code_natural(semiri3763490453095760265atural,aa_set_nat_nat(groups708209901874060359at_nat(aTP_Lamm_co),aa_nat_set_nat(set_or1269000886237332187st_nat(one_one_nat),N2))) ).

% fact_prod
tff(fact_4530_fact__prod,axiom,
    ! [N2: nat] : aa_nat_nat(semiri1408675320244567234ct_nat,N2) = aa_nat_nat(semiri1316708129612266289at_nat,aa_set_nat_nat(groups708209901874060359at_nat(aTP_Lamm_co),aa_nat_set_nat(set_or1269000886237332187st_nat(one_one_nat),N2))) ).

% fact_prod
tff(fact_4531_prod_Onested__swap_H,axiom,
    ! [A: fun_nat_fun_nat_nat,N2: nat] : aa_set_nat_nat(groups708209901874060359at_nat(aTP_Lamm_le(A)),aa_nat_set_nat(set_ord_atMost_nat,N2)) = aa_set_nat_nat(groups708209901874060359at_nat(aa_nat_fun_nat_nat(aTP_Lamm_ky(A),N2)),aa_nat_set_nat(set_ord_lessThan_nat,N2)) ).

% prod.nested_swap'
tff(fact_4532_prod_Onested__swap_H,axiom,
    ! [A: fun_nat_fun_nat_int,N2: nat] : groups705719431365010083at_int(aTP_Lamm_lf(A),aa_nat_set_nat(set_ord_atMost_nat,N2)) = groups705719431365010083at_int(aa_nat_fun_nat_int(aTP_Lamm_lb(A),N2),aa_nat_set_nat(set_ord_lessThan_nat,N2)) ).

% prod.nested_swap'
tff(fact_4533_prod__atLeastAtMost__code,axiom,
    ! [F: fun_nat_Code_integer,A: nat,B: nat] : groups3455450783089532116nteger(F,aa_nat_set_nat(set_or1269000886237332187st_nat(A),B)) = aa_Cod1783974652533396728nteger(set_fo1084959871951514735nteger(aTP_Lamm_lg(F),A,B),one_one_Code_integer) ).

% prod_atLeastAtMost_code
tff(fact_4534_prod__atLeastAtMost__code,axiom,
    ! [F: fun_nat_assn,A: nat,B: nat] : groups6906906614972039071t_assn(F,aa_nat_set_nat(set_or1269000886237332187st_nat(A),B)) = set_fo1959793692361082170t_assn(aTP_Lamm_lh(F),A,B,one_one_assn) ).

% prod_atLeastAtMost_code
tff(fact_4535_prod__atLeastAtMost__code,axiom,
    ! [F: fun_nat_rat,A: nat,B: nat] : groups73079841787564623at_rat(F,aa_nat_set_nat(set_or1269000886237332187st_nat(A),B)) = aa_rat_rat(set_fo1949268297981939178at_rat(aTP_Lamm_li(F),A,B),one_one_rat) ).

% prod_atLeastAtMost_code
tff(fact_4536_prod__atLeastAtMost__code,axiom,
    ! [F: fun_nat_nat,A: nat,B: nat] : aa_set_nat_nat(groups708209901874060359at_nat(F),aa_nat_set_nat(set_or1269000886237332187st_nat(A),B)) = aa_nat_nat(aa_nat_fun_nat_nat(set_fo2584398358068434914at_nat(aTP_Lamm_lj(F),A),B),one_one_nat) ).

% prod_atLeastAtMost_code
tff(fact_4537_prod__atLeastAtMost__code,axiom,
    ! [F: fun_nat_int,A: nat,B: nat] : groups705719431365010083at_int(F,aa_nat_set_nat(set_or1269000886237332187st_nat(A),B)) = aa_int_int(set_fo2581907887559384638at_int(aTP_Lamm_lk(F),A,B),one_one_int) ).

% prod_atLeastAtMost_code
tff(fact_4538_prod_Ohead__if,axiom,
    ! [G: fun_nat_Code_integer,M: nat,N2: nat] :
      groups3455450783089532116nteger(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),M),one_one_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,groups3455450783089532116nteger(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))),aa_nat_Code_integer(G,N2))) ).

% prod.head_if
tff(fact_4539_prod_Ohead__if,axiom,
    ! [G: fun_nat_assn,M: nat,N2: nat] :
      groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),M),one_one_assn,aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))),aa_nat_assn(G,N2))) ).

% prod.head_if
tff(fact_4540_prod_Ohead__if,axiom,
    ! [G: fun_nat_rat,M: nat,N2: nat] :
      groups73079841787564623at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),M),one_one_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,groups73079841787564623at_rat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))),aa_nat_rat(G,N2))) ).

% prod.head_if
tff(fact_4541_prod_Ohead__if,axiom,
    ! [G: fun_nat_nat,M: nat,N2: nat] :
      aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),M),one_one_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))),aa_nat_nat(G,N2))) ).

% prod.head_if
tff(fact_4542_prod_Ohead__if,axiom,
    ! [G: fun_nat_int,M: nat,N2: nat] :
      groups705719431365010083at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),M),one_one_int,aa_int_int(aa_int_fun_int_int(times_times_int,groups705719431365010083at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2))),aa_nat_int(G,N2))) ).

% prod.head_if
tff(fact_4543_prod_Oub__add__nat,axiom,
    ! [M: nat,N2: nat,G: fun_nat_assn,P2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),one_one_nat))
     => ( groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),P2))) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))),groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),one_one_nat)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),P2)))) ) ) ).

% prod.ub_add_nat
tff(fact_4544_prod_Oub__add__nat,axiom,
    ! [M: nat,N2: nat,G: fun_nat_rat,P2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),one_one_nat))
     => ( groups73079841787564623at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),P2))) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,groups73079841787564623at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))),groups73079841787564623at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),one_one_nat)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),P2)))) ) ) ).

% prod.ub_add_nat
tff(fact_4545_prod_Oub__add__nat,axiom,
    ! [M: nat,N2: nat,G: fun_nat_nat,P2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),one_one_nat))
     => ( aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),P2))) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))),aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),one_one_nat)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),P2)))) ) ) ).

% prod.ub_add_nat
tff(fact_4546_prod_Oub__add__nat,axiom,
    ! [M: nat,N2: nat,G: fun_nat_int,P2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),one_one_nat))
     => ( groups705719431365010083at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),P2))) = aa_int_int(aa_int_fun_int_int(times_times_int,groups705719431365010083at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2))),groups705719431365010083at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),one_one_nat)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),P2)))) ) ) ).

% prod.ub_add_nat
tff(fact_4547_prod_OatLeast0__atMost__Suc__shift,axiom,
    ! [G: fun_nat_assn,N2: nat] : groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_nat_assn(G,zero_zero_nat)),groups6906906614972039071t_assn(comp_nat_assn_nat(G,suc),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2))) ).

% prod.atLeast0_atMost_Suc_shift
tff(fact_4548_prod_OatLeast0__atMost__Suc__shift,axiom,
    ! [G: fun_nat_rat,N2: nat] : groups73079841787564623at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(G,zero_zero_nat)),groups73079841787564623at_rat(comp_nat_rat_nat(G,suc),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2))) ).

% prod.atLeast0_atMost_Suc_shift
tff(fact_4549_prod_OatLeast0__atMost__Suc__shift,axiom,
    ! [G: fun_nat_nat,N2: nat] : aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(G,zero_zero_nat)),aa_set_nat_nat(groups708209901874060359at_nat(comp_nat_nat_nat(G,suc)),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2))) ).

% prod.atLeast0_atMost_Suc_shift
tff(fact_4550_prod_OatLeast0__atMost__Suc__shift,axiom,
    ! [G: fun_nat_int,N2: nat] : groups705719431365010083at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(G,zero_zero_nat)),groups705719431365010083at_int(comp_nat_int_nat(G,suc),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2))) ).

% prod.atLeast0_atMost_Suc_shift
tff(fact_4551_prod_OatLeast0__lessThan__Suc__shift,axiom,
    ! [G: fun_nat_assn,N2: nat] : groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_nat_assn(G,zero_zero_nat)),groups6906906614972039071t_assn(comp_nat_assn_nat(G,suc),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2))) ).

% prod.atLeast0_lessThan_Suc_shift
tff(fact_4552_prod_OatLeast0__lessThan__Suc__shift,axiom,
    ! [G: fun_nat_rat,N2: nat] : groups73079841787564623at_rat(G,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(G,zero_zero_nat)),groups73079841787564623at_rat(comp_nat_rat_nat(G,suc),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2))) ).

% prod.atLeast0_lessThan_Suc_shift
tff(fact_4553_prod_OatLeast0__lessThan__Suc__shift,axiom,
    ! [G: fun_nat_nat,N2: nat] : aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(G,zero_zero_nat)),aa_set_nat_nat(groups708209901874060359at_nat(comp_nat_nat_nat(G,suc)),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2))) ).

% prod.atLeast0_lessThan_Suc_shift
tff(fact_4554_prod_OatLeast0__lessThan__Suc__shift,axiom,
    ! [G: fun_nat_int,N2: nat] : groups705719431365010083at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),aa_nat_nat(suc,N2))) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(G,zero_zero_nat)),groups705719431365010083at_int(comp_nat_int_nat(G,suc),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2))) ).

% prod.atLeast0_lessThan_Suc_shift
tff(fact_4555_prod_OatLeastLessThan__shift__0,axiom,
    ! [G: fun_nat_nat,M: nat,N2: nat] : aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) = aa_set_nat_nat(groups708209901874060359at_nat(comp_nat_nat_nat(G,aa_nat_fun_nat_nat(plus_plus_nat,M))),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),M))) ).

% prod.atLeastLessThan_shift_0
tff(fact_4556_prod_OatLeastLessThan__shift__0,axiom,
    ! [G: fun_nat_int,M: nat,N2: nat] : groups705719431365010083at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) = groups705719431365010083at_int(comp_nat_int_nat(G,aa_nat_fun_nat_nat(plus_plus_nat,M)),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),M))) ).

% prod.atLeastLessThan_shift_0
tff(fact_4557_integer__of__num__triv_I1_J,axiom,
    aa_num_Code_integer(code_integer_of_num,one) = one_one_Code_integer ).

% integer_of_num_triv(1)
tff(fact_4558_prod_OatLeastLessThan__rev__at__least__Suc__atMost,axiom,
    ! [G: fun_nat_nat,N2: nat,M: nat] : aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(N2),M)) = aa_set_nat_nat(groups708209901874060359at_nat(aa_nat_fun_nat_nat(aa_nat3783148529270815480at_nat(aTP_Lamm_do(G),N2),M)),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,N2)),M)) ).

% prod.atLeastLessThan_rev_at_least_Suc_atMost
tff(fact_4559_prod_OatLeastLessThan__rev__at__least__Suc__atMost,axiom,
    ! [G: fun_nat_int,N2: nat,M: nat] : groups705719431365010083at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(N2),M)) = groups705719431365010083at_int(aa_nat_fun_nat_int(aa_nat1293065384339088724at_int(aTP_Lamm_kt(G),N2),M),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,N2)),M)) ).

% prod.atLeastLessThan_rev_at_least_Suc_atMost
tff(fact_4560_prod_OatMost__shift,axiom,
    ! [G: fun_nat_assn,N2: nat] : groups6906906614972039071t_assn(G,aa_nat_set_nat(set_ord_atMost_nat,N2)) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_nat_assn(G,zero_zero_nat)),groups6906906614972039071t_assn(aTP_Lamm_kv(G),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% prod.atMost_shift
tff(fact_4561_prod_OatMost__shift,axiom,
    ! [G: fun_nat_rat,N2: nat] : groups73079841787564623at_rat(G,aa_nat_set_nat(set_ord_atMost_nat,N2)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(G,zero_zero_nat)),groups73079841787564623at_rat(aTP_Lamm_dq(G),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% prod.atMost_shift
tff(fact_4562_prod_OatMost__shift,axiom,
    ! [G: fun_nat_nat,N2: nat] : aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_ord_atMost_nat,N2)) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(G,zero_zero_nat)),aa_set_nat_nat(groups708209901874060359at_nat(aTP_Lamm_dh(G)),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% prod.atMost_shift
tff(fact_4563_prod_OatMost__shift,axiom,
    ! [G: fun_nat_int,N2: nat] : groups705719431365010083at_int(G,aa_nat_set_nat(set_ord_atMost_nat,N2)) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(G,zero_zero_nat)),groups705719431365010083at_int(aTP_Lamm_dr(G),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% prod.atMost_shift
tff(fact_4564_pochhammer__prod,axiom,
    ! [A: rat,N2: nat] : aa_nat_rat(comm_s4028243227959126397er_rat(A),N2) = groups73079841787564623at_rat(aTP_Lamm_ll(A),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2)) ).

% pochhammer_prod
tff(fact_4565_pochhammer__prod,axiom,
    ! [A: code_integer,N2: nat] : aa_nat_Code_integer(comm_s8582702949713902594nteger(A),N2) = groups3455450783089532116nteger(aTP_Lamm_lm(A),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2)) ).

% pochhammer_prod
tff(fact_4566_pochhammer__prod,axiom,
    ! [A: code_natural,N2: nat] : aa_nat_Code_natural(comm_s7406298101470620109atural(A),N2) = groups2279045934846249631atural(aTP_Lamm_ln(A),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2)) ).

% pochhammer_prod
tff(fact_4567_pochhammer__prod,axiom,
    ! [A: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(comm_s4663373288045622133er_nat,A),N2) = aa_set_nat_nat(groups708209901874060359at_nat(aa_nat_fun_nat_nat(aTP_Lamm_lo,A)),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2)) ).

% pochhammer_prod
tff(fact_4568_pochhammer__prod,axiom,
    ! [A: int,N2: nat] : aa_nat_int(comm_s4660882817536571857er_int(A),N2) = groups705719431365010083at_int(aTP_Lamm_lp(A),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2)) ).

% pochhammer_prod
tff(fact_4569_prod_OatLeast__atMost__pred__shift,axiom,
    ! [G: fun_nat_nat,M: nat,N2: nat] : aa_set_nat_nat(groups708209901874060359at_nat(comp_nat_nat_nat(G,aTP_Lamm_dx)),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,M)),aa_nat_nat(suc,N2))) = aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) ).

% prod.atLeast_atMost_pred_shift
tff(fact_4570_prod_OatLeast__atMost__pred__shift,axiom,
    ! [G: fun_nat_int,M: nat,N2: nat] : groups705719431365010083at_int(comp_nat_int_nat(G,aTP_Lamm_dx),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,M)),aa_nat_nat(suc,N2))) = groups705719431365010083at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) ).

% prod.atLeast_atMost_pred_shift
tff(fact_4571_prod_OatLeast__lessThan__pred__shift,axiom,
    ! [G: fun_nat_nat,M: nat,N2: nat] : aa_set_nat_nat(groups708209901874060359at_nat(comp_nat_nat_nat(G,aTP_Lamm_dx)),aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(suc,M)),aa_nat_nat(suc,N2))) = aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) ).

% prod.atLeast_lessThan_pred_shift
tff(fact_4572_prod_OatLeast__lessThan__pred__shift,axiom,
    ! [G: fun_nat_int,M: nat,N2: nat] : groups705719431365010083at_int(comp_nat_int_nat(G,aTP_Lamm_dx),aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(suc,M)),aa_nat_nat(suc,N2))) = groups705719431365010083at_int(G,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) ).

% prod.atLeast_lessThan_pred_shift
tff(fact_4573_integer__of__num_I2_J,axiom,
    ! [N2: num] :
      aa_num_Code_integer(code_integer_of_num,aa_num_num(bit0,N2)) = $let(
        k: code_integer,
        k:= aa_num_Code_integer(code_integer_of_num,N2),
        aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,k),k) ) ).

% integer_of_num(2)
tff(fact_4574_divmod__abs__code_I5_J,axiom,
    ! [J: code_integer] : aa_Cod6977894654539884864nteger(code_divmod_abs(J),zero_z3403309356797280102nteger) = aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(abs_abs_Code_integer,J)) ).

% divmod_abs_code(5)
tff(fact_4575_prod_OatLeastAtMost__shift__0,axiom,
    ! [M: nat,N2: nat,G: fun_nat_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = aa_set_nat_nat(groups708209901874060359at_nat(comp_nat_nat_nat(G,aa_nat_fun_nat_nat(plus_plus_nat,M))),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),M))) ) ) ).

% prod.atLeastAtMost_shift_0
tff(fact_4576_prod_OatLeastAtMost__shift__0,axiom,
    ! [M: nat,N2: nat,G: fun_nat_int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( groups705719431365010083at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) = groups705719431365010083at_int(comp_nat_int_nat(G,aa_nat_fun_nat_nat(plus_plus_nat,M)),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),M))) ) ) ).

% prod.atLeastAtMost_shift_0
tff(fact_4577_sum_OatLeast__int__lessThan__int__shift,axiom,
    ! [G: fun_int_nat,M: nat,N2: nat] : groups4541462559716669496nt_nat(G,aa_int_set_int(set_or4662586982721622107an_int(aa_nat_int(semiri1314217659103216013at_int,M)),aa_nat_int(semiri1314217659103216013at_int,N2))) = aa_set_nat_nat(groups3542108847815614940at_nat(comp_int_nat_nat(G,semiri1314217659103216013at_int)),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) ).

% sum.atLeast_int_lessThan_int_shift
tff(fact_4578_sum_OatLeast__int__lessThan__int__shift,axiom,
    ! [G: fun_int_int,M: nat,N2: nat] : aa_set_int_int(groups4538972089207619220nt_int(G),aa_int_set_int(set_or4662586982721622107an_int(aa_nat_int(semiri1314217659103216013at_int,M)),aa_nat_int(semiri1314217659103216013at_int,N2))) = groups3539618377306564664at_int(comp_int_int_nat(G,semiri1314217659103216013at_int),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) ).

% sum.atLeast_int_lessThan_int_shift
tff(fact_4579_pochhammer__Suc__prod,axiom,
    ! [A: rat,N2: nat] : aa_nat_rat(comm_s4028243227959126397er_rat(A),aa_nat_nat(suc,N2)) = groups73079841787564623at_rat(aTP_Lamm_ll(A),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2)) ).

% pochhammer_Suc_prod
tff(fact_4580_pochhammer__Suc__prod,axiom,
    ! [A: code_integer,N2: nat] : aa_nat_Code_integer(comm_s8582702949713902594nteger(A),aa_nat_nat(suc,N2)) = groups3455450783089532116nteger(aTP_Lamm_lm(A),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2)) ).

% pochhammer_Suc_prod
tff(fact_4581_pochhammer__Suc__prod,axiom,
    ! [A: code_natural,N2: nat] : aa_nat_Code_natural(comm_s7406298101470620109atural(A),aa_nat_nat(suc,N2)) = groups2279045934846249631atural(aTP_Lamm_ln(A),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2)) ).

% pochhammer_Suc_prod
tff(fact_4582_pochhammer__Suc__prod,axiom,
    ! [A: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(comm_s4663373288045622133er_nat,A),aa_nat_nat(suc,N2)) = aa_set_nat_nat(groups708209901874060359at_nat(aa_nat_fun_nat_nat(aTP_Lamm_lo,A)),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2)) ).

% pochhammer_Suc_prod
tff(fact_4583_pochhammer__Suc__prod,axiom,
    ! [A: int,N2: nat] : aa_nat_int(comm_s4660882817536571857er_int(A),aa_nat_nat(suc,N2)) = groups705719431365010083at_int(aTP_Lamm_lp(A),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2)) ).

% pochhammer_Suc_prod
tff(fact_4584_pochhammer__prod__rev,axiom,
    ! [A: rat,N2: nat] : aa_nat_rat(comm_s4028243227959126397er_rat(A),N2) = groups73079841787564623at_rat(aa_nat_fun_nat_rat(aTP_Lamm_lq(A),N2),aa_nat_set_nat(set_or1269000886237332187st_nat(one_one_nat),N2)) ).

% pochhammer_prod_rev
tff(fact_4585_pochhammer__prod__rev,axiom,
    ! [A: code_integer,N2: nat] : aa_nat_Code_integer(comm_s8582702949713902594nteger(A),N2) = groups3455450783089532116nteger(aa_nat2010205248571845816nteger(aTP_Lamm_lr(A),N2),aa_nat_set_nat(set_or1269000886237332187st_nat(one_one_nat),N2)) ).

% pochhammer_prod_rev
tff(fact_4586_pochhammer__prod__rev,axiom,
    ! [A: code_natural,N2: nat] : aa_nat_Code_natural(comm_s7406298101470620109atural(A),N2) = groups2279045934846249631atural(aa_nat6468655069083034883atural(aTP_Lamm_ls(A),N2),aa_nat_set_nat(set_or1269000886237332187st_nat(one_one_nat),N2)) ).

% pochhammer_prod_rev
tff(fact_4587_pochhammer__prod__rev,axiom,
    ! [A: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(comm_s4663373288045622133er_nat,A),N2) = aa_set_nat_nat(groups708209901874060359at_nat(aa_nat_fun_nat_nat(aTP_Lamm_lt(A),N2)),aa_nat_set_nat(set_or1269000886237332187st_nat(one_one_nat),N2)) ).

% pochhammer_prod_rev
tff(fact_4588_pochhammer__prod__rev,axiom,
    ! [A: int,N2: nat] : aa_nat_int(comm_s4660882817536571857er_int(A),N2) = groups705719431365010083at_int(aa_nat_fun_nat_int(aTP_Lamm_lu(A),N2),aa_nat_set_nat(set_or1269000886237332187st_nat(one_one_nat),N2)) ).

% pochhammer_prod_rev
tff(fact_4589_fact__div__fact,axiom,
    ! [N2: nat,M: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),M)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_nat_nat(semiri1408675320244567234ct_nat,M)),aa_nat_nat(semiri1408675320244567234ct_nat,N2)) = aa_set_nat_nat(groups708209901874060359at_nat(aTP_Lamm_co),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),one_one_nat)),M)) ) ) ).

% fact_div_fact
tff(fact_4590_integer__of__num__triv_I2_J,axiom,
    aa_num_Code_integer(code_integer_of_num,aa_num_num(bit0,one)) = aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)) ).

% integer_of_num_triv(2)
tff(fact_4591_prod_Oin__pairs,axiom,
    ! [G: fun_nat_assn,M: nat,N2: nat] : groups6906906614972039071t_assn(G,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),M)),aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)))) = groups6906906614972039071t_assn(aTP_Lamm_lv(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) ).

% prod.in_pairs
tff(fact_4592_prod_Oin__pairs,axiom,
    ! [G: fun_nat_rat,M: nat,N2: nat] : groups73079841787564623at_rat(G,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),M)),aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)))) = groups73079841787564623at_rat(aTP_Lamm_lw(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) ).

% prod.in_pairs
tff(fact_4593_prod_Oin__pairs,axiom,
    ! [G: fun_nat_nat,M: nat,N2: nat] : aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),M)),aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)))) = aa_set_nat_nat(groups708209901874060359at_nat(aTP_Lamm_lx(G)),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) ).

% prod.in_pairs
tff(fact_4594_prod_Oin__pairs,axiom,
    ! [G: fun_nat_int,M: nat,N2: nat] : groups705719431365010083at_int(G,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),M)),aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)))) = groups705719431365010083at_int(aTP_Lamm_ly(G),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) ).

% prod.in_pairs
tff(fact_4595_prod_Oin__pairs__0,axiom,
    ! [G: fun_nat_assn,N2: nat] : groups6906906614972039071t_assn(G,aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)))) = groups6906906614972039071t_assn(aTP_Lamm_lv(G),aa_nat_set_nat(set_ord_atMost_nat,N2)) ).

% prod.in_pairs_0
tff(fact_4596_prod_Oin__pairs__0,axiom,
    ! [G: fun_nat_rat,N2: nat] : groups73079841787564623at_rat(G,aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)))) = groups73079841787564623at_rat(aTP_Lamm_lw(G),aa_nat_set_nat(set_ord_atMost_nat,N2)) ).

% prod.in_pairs_0
tff(fact_4597_prod_Oin__pairs__0,axiom,
    ! [G: fun_nat_nat,N2: nat] : aa_set_nat_nat(groups708209901874060359at_nat(G),aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)))) = aa_set_nat_nat(groups708209901874060359at_nat(aTP_Lamm_lx(G)),aa_nat_set_nat(set_ord_atMost_nat,N2)) ).

% prod.in_pairs_0
tff(fact_4598_prod_Oin__pairs__0,axiom,
    ! [G: fun_nat_int,N2: nat] : groups705719431365010083at_int(G,aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)))) = groups705719431365010083at_int(aTP_Lamm_ly(G),aa_nat_set_nat(set_ord_atMost_nat,N2)) ).

% prod.in_pairs_0
tff(fact_4599_nat__of__integer__less__iff,axiom,
    ! [X2: code_integer,Y: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),X2)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),Y)
       => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_Code_integer_nat(code_nat_of_integer,X2)),aa_Code_integer_nat(code_nat_of_integer,Y))
        <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,X2),Y) ) ) ) ).

% nat_of_integer_less_iff
tff(fact_4600_pochhammer__Suc__prod__rev,axiom,
    ! [A: rat,N2: nat] : aa_nat_rat(comm_s4028243227959126397er_rat(A),aa_nat_nat(suc,N2)) = groups73079841787564623at_rat(aa_nat_fun_nat_rat(aTP_Lamm_lq(A),N2),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2)) ).

% pochhammer_Suc_prod_rev
tff(fact_4601_pochhammer__Suc__prod__rev,axiom,
    ! [A: code_integer,N2: nat] : aa_nat_Code_integer(comm_s8582702949713902594nteger(A),aa_nat_nat(suc,N2)) = groups3455450783089532116nteger(aa_nat2010205248571845816nteger(aTP_Lamm_lr(A),N2),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2)) ).

% pochhammer_Suc_prod_rev
tff(fact_4602_pochhammer__Suc__prod__rev,axiom,
    ! [A: code_natural,N2: nat] : aa_nat_Code_natural(comm_s7406298101470620109atural(A),aa_nat_nat(suc,N2)) = groups2279045934846249631atural(aa_nat6468655069083034883atural(aTP_Lamm_ls(A),N2),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2)) ).

% pochhammer_Suc_prod_rev
tff(fact_4603_pochhammer__Suc__prod__rev,axiom,
    ! [A: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(comm_s4663373288045622133er_nat,A),aa_nat_nat(suc,N2)) = aa_set_nat_nat(groups708209901874060359at_nat(aa_nat_fun_nat_nat(aTP_Lamm_lt(A),N2)),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2)) ).

% pochhammer_Suc_prod_rev
tff(fact_4604_pochhammer__Suc__prod__rev,axiom,
    ! [A: int,N2: nat] : aa_nat_int(comm_s4660882817536571857er_int(A),aa_nat_nat(suc,N2)) = groups705719431365010083at_int(aa_nat_fun_nat_int(aTP_Lamm_lu(A),N2),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2)) ).

% pochhammer_Suc_prod_rev
tff(fact_4605_divmod__integer__code,axiom,
    ! [K: code_integer,L: code_integer] :
      aa_Cod6977894654539884864nteger(code_divmod_integer(K),L) = $ite(
        K = zero_z3403309356797280102nteger,
        aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(zero_z3403309356797280102nteger),zero_z3403309356797280102nteger),
        $ite(
          aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),L),
          $ite(aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),K),aa_Cod6977894654539884864nteger(code_divmod_abs(K),L),aa_Pro4693618923521437820nteger(produc6916734918728496179nteger(aTP_Lamm_lz(L)),aa_Cod6977894654539884864nteger(code_divmod_abs(K),L))),
          $ite(
            L = zero_z3403309356797280102nteger,
            aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(zero_z3403309356797280102nteger),K),
            aa_Pro4693618923521437820nteger(aa_fun2509385170507305080nteger(produc6499014454317279255nteger,uminus1351360451143612070nteger),
              $ite(aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,K),zero_z3403309356797280102nteger),aa_Cod6977894654539884864nteger(code_divmod_abs(K),L),aa_Pro4693618923521437820nteger(produc6916734918728496179nteger(aTP_Lamm_ma(L)),aa_Cod6977894654539884864nteger(code_divmod_abs(K),L)))) ) ) ) ).

% divmod_integer_code
tff(fact_4606_bit__cut__integer__code,axiom,
    ! [K: code_integer] :
      code_bit_cut_integer(K) = $ite(K = zero_z3403309356797280102nteger,produc6677183202524767010eger_o(zero_z3403309356797280102nteger,$false),produc9125791028180074456eger_o(aTP_Lamm_mb(K),aa_Cod6977894654539884864nteger(code_divmod_abs(K),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))))) ).

% bit_cut_integer_code
tff(fact_4607_prod_Ozero__middle,axiom,
    ! [P2: nat,K: nat,G: fun_nat_Code_integer,Ha: fun_nat_Code_integer] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),P2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),P2)
       => ( groups3455450783089532116nteger(aa_fun589076786913273746nteger(aa_fun3918145391673965625nteger(aTP_Lamm_mc(K),G),Ha),aa_nat_set_nat(set_ord_atMost_nat,P2)) = groups3455450783089532116nteger(aa_fun589076786913273746nteger(aa_fun3918145391673965625nteger(aTP_Lamm_hz(K),G),Ha),aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,P2),aa_nat_nat(suc,zero_zero_nat)))) ) ) ) ).

% prod.zero_middle
tff(fact_4608_prod_Ozero__middle,axiom,
    ! [P2: nat,K: nat,G: fun_nat_assn,Ha: fun_nat_assn] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),P2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),P2)
       => ( groups6906906614972039071t_assn(aa_fun785744391571715112t_assn(aa_fun6591345337174305434t_assn(aTP_Lamm_md(K),G),Ha),aa_nat_set_nat(set_ord_atMost_nat,P2)) = groups6906906614972039071t_assn(aa_fun785744391571715112t_assn(aa_fun6591345337174305434t_assn(aTP_Lamm_me(K),G),Ha),aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,P2),aa_nat_nat(suc,zero_zero_nat)))) ) ) ) ).

% prod.zero_middle
tff(fact_4609_prod_Ozero__middle,axiom,
    ! [P2: nat,K: nat,G: fun_nat_rat,Ha: fun_nat_rat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),P2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),P2)
       => ( groups73079841787564623at_rat(aa_fun765758790203053448at_rat(aa_fun3638354034882855594at_rat(aTP_Lamm_mf(K),G),Ha),aa_nat_set_nat(set_ord_atMost_nat,P2)) = groups73079841787564623at_rat(aa_fun765758790203053448at_rat(aa_fun3638354034882855594at_rat(aTP_Lamm_id(K),G),Ha),aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,P2),aa_nat_nat(suc,zero_zero_nat)))) ) ) ) ).

% prod.zero_middle
tff(fact_4610_prod_Ozero__middle,axiom,
    ! [P2: nat,K: nat,G: fun_nat_nat,Ha: fun_nat_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),P2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),P2)
       => ( aa_set_nat_nat(groups708209901874060359at_nat(aa_fun5791449513213591928at_nat(aa_fun6854695580826382482at_nat(aTP_Lamm_mg(K),G),Ha)),aa_nat_set_nat(set_ord_atMost_nat,P2)) = aa_set_nat_nat(groups708209901874060359at_nat(aa_fun5791449513213591928at_nat(aa_fun6854695580826382482at_nat(aTP_Lamm_ih(K),G),Ha)),aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,P2),aa_nat_nat(suc,zero_zero_nat)))) ) ) ) ).

% prod.zero_middle
tff(fact_4611_prod_Ozero__middle,axiom,
    ! [P2: nat,K: nat,G: fun_nat_int,Ha: fun_nat_int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),P2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K),P2)
       => ( groups705719431365010083at_int(aa_fun5565043122120104496at_int(aa_fun5140708168904641446at_int(aTP_Lamm_mh(K),G),Ha),aa_nat_set_nat(set_ord_atMost_nat,P2)) = groups705719431365010083at_int(aa_fun5565043122120104496at_int(aa_fun5140708168904641446at_int(aTP_Lamm_if(K),G),Ha),aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,P2),aa_nat_nat(suc,zero_zero_nat)))) ) ) ) ).

% prod.zero_middle
tff(fact_4612_xor__int__rec,axiom,
    ! [K: int,L: int] :
      aa_int_int(aa_int_fun_int_int(bit_se6526347334894502574or_int,K),L) = aa_int_int(aa_int_fun_int_int(plus_plus_int,
          aa_o_int(zero_n2684676970156552555ol_int,
            ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),K) != ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),L))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(bit_se6526347334894502574or_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,K),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),aa_int_int(aa_int_fun_int_int(divide_divide_int,L),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))))) ).

% xor_int_rec
tff(fact_4613_divmod__abs__def,axiom,
    ! [K: code_integer,L: code_integer] : aa_Cod6977894654539884864nteger(code_divmod_abs(K),L) = aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,K)),aa_Cod1783974652533396728nteger(abs_abs_Code_integer,L))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,K)),aa_Cod1783974652533396728nteger(abs_abs_Code_integer,L))) ).

% divmod_abs_def
tff(fact_4614_less__int_Orep__eq,axiom,
    ! [X2: int,Xa: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,X2),Xa)
    <=> aa_Pro6150637604445964947_nat_o(aa_Pro989595756709598047_nat_o(aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,aTP_Lamm_fe),aa_int1417691210696471063at_nat(rep_Integ,X2)),aa_int1417691210696471063at_nat(rep_Integ,Xa)) ) ).

% less_int.rep_eq
tff(fact_4615_xor__int__unfold,axiom,
    ! [K: int,L: int] :
      aa_int_int(aa_int_fun_int_int(bit_se6526347334894502574or_int,K),L) = $ite(
        K = aa_int_int(uminus_uminus_int,one_one_int),
        aa_int_int(bit_ri7919022796975470100ot_int,L),
        $ite(
          L = aa_int_int(uminus_uminus_int,one_one_int),
          aa_int_int(bit_ri7919022796975470100ot_int,K),
          $ite(
            K = zero_zero_int,
            L,
            $ite(L = zero_zero_int,K,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(abs_abs_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(aa_int_fun_int_int(modulo_modulo_int,K),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,L),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(bit_se6526347334894502574or_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,K),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),aa_int_int(aa_int_fun_int_int(divide_divide_int,L),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))))))) ) ) ) ).

% xor_int_unfold
tff(fact_4616_take__bit__num__code,axiom,
    ! [N2: nat,M: num] : aa_num_option_num(bit_take_bit_num(N2),M) = produc478579273971653890on_num(aTP_Lamm_ml,product_Pair_nat_num(N2,M)) ).

% take_bit_num_code
tff(fact_4617_prod_Otriangle__reindex,axiom,
    ! [G: fun_nat_fun_nat_nat,N2: nat] : aa_set4749074711808745205at_nat(groups4077766827762148844at_nat(aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,G)),aa_fun7046812543386002057at_nat(collec3392354462482085612at_nat,aa_fun7564604662015400456_nat_o(produc6081775807080527818_nat_o,aTP_Lamm_iw(N2)))) = aa_set_nat_nat(groups708209901874060359at_nat(aTP_Lamm_mm(G)),aa_nat_set_nat(set_ord_lessThan_nat,N2)) ).

% prod.triangle_reindex
tff(fact_4618_prod_Otriangle__reindex,axiom,
    ! [G: fun_nat_fun_nat_int,N2: nat] : groups4075276357253098568at_int(produc6840382203811409530at_int(G),aa_fun7046812543386002057at_nat(collec3392354462482085612at_nat,aa_fun7564604662015400456_nat_o(produc6081775807080527818_nat_o,aTP_Lamm_iw(N2)))) = groups705719431365010083at_int(aTP_Lamm_mo(G),aa_nat_set_nat(set_ord_lessThan_nat,N2)) ).

% prod.triangle_reindex
tff(fact_4619_case__nat__add__eq__if,axiom,
    ! [A: option_num,F: fun_nat_option_num,V: num,N2: nat] : aa_nat_option_num(case_nat_option_num(A,F),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(numeral_numeral_nat,V)),N2)) = aa_nat_option_num(F,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(pred_numeral,V)),N2)) ).

% case_nat_add_eq_if
tff(fact_4620_bit_Ocompl__zero,axiom,
    aa_int_int(bit_ri7919022796975470100ot_int,zero_zero_int) = aa_int_int(uminus_uminus_int,one_one_int) ).

% bit.compl_zero
tff(fact_4621_bit_Ocompl__zero,axiom,
    aa_Cod1783974652533396728nteger(bit_ri7632146776885996613nteger,zero_z3403309356797280102nteger) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) ).

% bit.compl_zero
tff(fact_4622_bit_Ocompl__one,axiom,
    aa_int_int(bit_ri7919022796975470100ot_int,aa_int_int(uminus_uminus_int,one_one_int)) = zero_zero_int ).

% bit.compl_one
tff(fact_4623_bit_Ocompl__one,axiom,
    aa_Cod1783974652533396728nteger(bit_ri7632146776885996613nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) = zero_z3403309356797280102nteger ).

% bit.compl_one
tff(fact_4624_bit_Oxor__cancel__right,axiom,
    ! [X2: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3222712562003087583nteger,X2),aa_Cod1783974652533396728nteger(bit_ri7632146776885996613nteger,X2)) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) ).

% bit.xor_cancel_right
tff(fact_4625_bit_Oxor__cancel__right,axiom,
    ! [X2: int] : aa_int_int(aa_int_fun_int_int(bit_se6526347334894502574or_int,X2),aa_int_int(bit_ri7919022796975470100ot_int,X2)) = aa_int_int(uminus_uminus_int,one_one_int) ).

% bit.xor_cancel_right
tff(fact_4626_bit_Oxor__cancel__left,axiom,
    ! [X2: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3222712562003087583nteger,aa_Cod1783974652533396728nteger(bit_ri7632146776885996613nteger,X2)),X2) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) ).

% bit.xor_cancel_left
tff(fact_4627_bit_Oxor__cancel__left,axiom,
    ! [X2: int] : aa_int_int(aa_int_fun_int_int(bit_se6526347334894502574or_int,aa_int_int(bit_ri7919022796975470100ot_int,X2)),X2) = aa_int_int(uminus_uminus_int,one_one_int) ).

% bit.xor_cancel_left
tff(fact_4628_bit_Oxor__one__right,axiom,
    ! [X2: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3222712562003087583nteger,X2),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) = aa_Cod1783974652533396728nteger(bit_ri7632146776885996613nteger,X2) ).

% bit.xor_one_right
tff(fact_4629_bit_Oxor__one__right,axiom,
    ! [X2: int] : aa_int_int(aa_int_fun_int_int(bit_se6526347334894502574or_int,X2),aa_int_int(uminus_uminus_int,one_one_int)) = aa_int_int(bit_ri7919022796975470100ot_int,X2) ).

% bit.xor_one_right
tff(fact_4630_bit_Oxor__one__left,axiom,
    ! [X2: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3222712562003087583nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),X2) = aa_Cod1783974652533396728nteger(bit_ri7632146776885996613nteger,X2) ).

% bit.xor_one_left
tff(fact_4631_bit_Oxor__one__left,axiom,
    ! [X2: int] : aa_int_int(aa_int_fun_int_int(bit_se6526347334894502574or_int,aa_int_int(uminus_uminus_int,one_one_int)),X2) = aa_int_int(bit_ri7919022796975470100ot_int,X2) ).

% bit.xor_one_left
tff(fact_4632_push__bit__minus__one__eq__not__mask,axiom,
    ! [N2: nat] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se7788150548672797655nteger,N2),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) = aa_Cod1783974652533396728nteger(bit_ri7632146776885996613nteger,aa_nat_Code_integer(bit_se2119862282449309892nteger,N2)) ).

% push_bit_minus_one_eq_not_mask
tff(fact_4633_push__bit__minus__one__eq__not__mask,axiom,
    ! [N2: nat] : aa_int_int(aa_nat_fun_int_int(bit_se545348938243370406it_int,N2),aa_int_int(uminus_uminus_int,one_one_int)) = aa_int_int(bit_ri7919022796975470100ot_int,aa_nat_int(bit_se2000444600071755411sk_int,N2)) ).

% push_bit_minus_one_eq_not_mask
tff(fact_4634_not__one__eq,axiom,
    aa_int_int(bit_ri7919022796975470100ot_int,one_one_int) = aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))) ).

% not_one_eq
tff(fact_4635_not__one__eq,axiom,
    aa_Cod1783974652533396728nteger(bit_ri7632146776885996613nteger,one_one_Code_integer) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))) ).

% not_one_eq
tff(fact_4636_not__add__distrib,axiom,
    ! [A: int,B: int] : aa_int_int(bit_ri7919022796975470100ot_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B)) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(bit_ri7919022796975470100ot_int,A)),B) ).

% not_add_distrib
tff(fact_4637_not__add__distrib,axiom,
    ! [A: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(bit_ri7632146776885996613nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(bit_ri7632146776885996613nteger,A)),B) ).

% not_add_distrib
tff(fact_4638_not__diff__distrib,axiom,
    ! [A: int,B: int] : aa_int_int(bit_ri7919022796975470100ot_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),B)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(bit_ri7919022796975470100ot_int,A)),B) ).

% not_diff_distrib
tff(fact_4639_not__diff__distrib,axiom,
    ! [A: code_integer,B: code_integer] : aa_Cod1783974652533396728nteger(bit_ri7632146776885996613nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),B)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(bit_ri7632146776885996613nteger,A)),B) ).

% not_diff_distrib
tff(fact_4640_minus__eq__not__plus__1,axiom,
    ! [A: int] : aa_int_int(uminus_uminus_int,A) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(bit_ri7919022796975470100ot_int,A)),one_one_int) ).

% minus_eq_not_plus_1
tff(fact_4641_minus__eq__not__plus__1,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(bit_ri7632146776885996613nteger,A)),one_one_Code_integer) ).

% minus_eq_not_plus_1
tff(fact_4642_minus__eq__not__minus__1,axiom,
    ! [A: int] : aa_int_int(uminus_uminus_int,A) = aa_int_int(bit_ri7919022796975470100ot_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,A),one_one_int)) ).

% minus_eq_not_minus_1
tff(fact_4643_minus__eq__not__minus__1,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A) = aa_Cod1783974652533396728nteger(bit_ri7632146776885996613nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),one_one_Code_integer)) ).

% minus_eq_not_minus_1
tff(fact_4644_not__eq__complement,axiom,
    ! [A: int] : aa_int_int(bit_ri7919022796975470100ot_int,A) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(uminus_uminus_int,A)),one_one_int) ).

% not_eq_complement
tff(fact_4645_not__eq__complement,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(bit_ri7632146776885996613nteger,A) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,A)),one_one_Code_integer) ).

% not_eq_complement
tff(fact_4646_prod__int__eq,axiom,
    ! [I: nat,J: nat] : groups705719431365010083at_int(semiri1314217659103216013at_int,aa_nat_set_nat(set_or1269000886237332187st_nat(I),J)) = aa_set_int_int(groups1705073143266064639nt_int(aTP_Lamm_cp),aa_int_set_int(set_or1266510415728281911st_int(aa_nat_int(semiri1314217659103216013at_int,I)),aa_nat_int(semiri1314217659103216013at_int,J))) ).

% prod_int_eq
tff(fact_4647_prod__int__plus__eq,axiom,
    ! [I: nat,J: nat] : groups705719431365010083at_int(semiri1314217659103216013at_int,aa_nat_set_nat(set_or1269000886237332187st_nat(I),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),J))) = aa_set_int_int(groups1705073143266064639nt_int(aTP_Lamm_cp),aa_int_set_int(set_or1266510415728281911st_int(aa_nat_int(semiri1314217659103216013at_int,I)),aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),J)))) ).

% prod_int_plus_eq
tff(fact_4648_push__bit__mask__eq,axiom,
    ! [M: nat,N2: nat] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se7788150548672797655nteger,M),aa_nat_Code_integer(bit_se2119862282449309892nteger,N2)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3949692690581998587nteger,aa_nat_Code_integer(bit_se2119862282449309892nteger,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),M))),aa_Cod1783974652533396728nteger(bit_ri7632146776885996613nteger,aa_nat_Code_integer(bit_se2119862282449309892nteger,M))) ).

% push_bit_mask_eq
tff(fact_4649_push__bit__mask__eq,axiom,
    ! [M: nat,N2: nat] : aa_int_int(aa_nat_fun_int_int(bit_se545348938243370406it_int,M),aa_nat_int(bit_se2000444600071755411sk_int,N2)) = aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,aa_nat_int(bit_se2000444600071755411sk_int,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),M))),aa_int_int(bit_ri7919022796975470100ot_int,aa_nat_int(bit_se2000444600071755411sk_int,M))) ).

% push_bit_mask_eq
tff(fact_4650_prod_OatLeast__int__lessThan__int__shift,axiom,
    ! [G: fun_int_nat,M: nat,N2: nat] : groups1707563613775114915nt_nat(G,aa_int_set_int(set_or4662586982721622107an_int(aa_nat_int(semiri1314217659103216013at_int,M)),aa_nat_int(semiri1314217659103216013at_int,N2))) = aa_set_nat_nat(groups708209901874060359at_nat(comp_int_nat_nat(G,semiri1314217659103216013at_int)),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) ).

% prod.atLeast_int_lessThan_int_shift
tff(fact_4651_prod_OatLeast__int__lessThan__int__shift,axiom,
    ! [G: fun_int_int,M: nat,N2: nat] : aa_set_int_int(groups1705073143266064639nt_int(G),aa_int_set_int(set_or4662586982721622107an_int(aa_nat_int(semiri1314217659103216013at_int,M)),aa_nat_int(semiri1314217659103216013at_int,N2))) = groups705719431365010083at_int(comp_int_int_nat(G,semiri1314217659103216013at_int),aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)) ).

% prod.atLeast_int_lessThan_int_shift
tff(fact_4652_unset__bit__eq__and__not,axiom,
    ! [N2: nat,A: code_integer] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se8260200283734997820nteger,N2),A) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3949692690581998587nteger,A),aa_Cod1783974652533396728nteger(bit_ri7632146776885996613nteger,aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se7788150548672797655nteger,N2),one_one_Code_integer))) ).

% unset_bit_eq_and_not
tff(fact_4653_unset__bit__eq__and__not,axiom,
    ! [N2: nat,A: int] : aa_int_int(aa_nat_fun_int_int(bit_se4203085406695923979it_int,N2),A) = aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,A),aa_int_int(bit_ri7919022796975470100ot_int,aa_int_int(aa_nat_fun_int_int(bit_se545348938243370406it_int,N2),one_one_int))) ).

% unset_bit_eq_and_not
tff(fact_4654_prod_OatLeast__int__atMost__int__shift,axiom,
    ! [G: fun_int_nat,M: nat,N2: nat] : groups1707563613775114915nt_nat(G,aa_int_set_int(set_or1266510415728281911st_int(aa_nat_int(semiri1314217659103216013at_int,M)),aa_nat_int(semiri1314217659103216013at_int,N2))) = aa_set_nat_nat(groups708209901874060359at_nat(comp_int_nat_nat(G,semiri1314217659103216013at_int)),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) ).

% prod.atLeast_int_atMost_int_shift
tff(fact_4655_prod_OatLeast__int__atMost__int__shift,axiom,
    ! [G: fun_int_int,M: nat,N2: nat] : aa_set_int_int(groups1705073143266064639nt_int(G),aa_int_set_int(set_or1266510415728281911st_int(aa_nat_int(semiri1314217659103216013at_int,M)),aa_nat_int(semiri1314217659103216013at_int,N2))) = groups705719431365010083at_int(comp_int_int_nat(G,semiri1314217659103216013at_int),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) ).

% prod.atLeast_int_atMost_int_shift
tff(fact_4656_int__numeral__not__and__num,axiom,
    ! [M: num,N2: num] : aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,aa_int_int(bit_ri7919022796975470100ot_int,aa_num_int(numeral_numeral_int,M))),aa_num_int(numeral_numeral_int,N2)) = aa_option_num_int(case_option_int_num(zero_zero_int,numeral_numeral_int),aa_num_option_num(bit_and_not_num(N2),M)) ).

% int_numeral_not_and_num
tff(fact_4657_int__numeral__and__not__num,axiom,
    ! [M: num,N2: num] : aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,aa_num_int(numeral_numeral_int,M)),aa_int_int(bit_ri7919022796975470100ot_int,aa_num_int(numeral_numeral_int,N2))) = aa_option_num_int(case_option_int_num(zero_zero_int,numeral_numeral_int),aa_num_option_num(bit_and_not_num(M),N2)) ).

% int_numeral_and_not_num
tff(fact_4658_prod_Otriangle__reindex__eq,axiom,
    ! [G: fun_nat_fun_nat_nat,N2: nat] : aa_set4749074711808745205at_nat(groups4077766827762148844at_nat(aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,G)),aa_fun7046812543386002057at_nat(collec3392354462482085612at_nat,aa_fun7564604662015400456_nat_o(produc6081775807080527818_nat_o,aTP_Lamm_hv(N2)))) = aa_set_nat_nat(groups708209901874060359at_nat(aTP_Lamm_mm(G)),aa_nat_set_nat(set_ord_atMost_nat,N2)) ).

% prod.triangle_reindex_eq
tff(fact_4659_prod_Otriangle__reindex__eq,axiom,
    ! [G: fun_nat_fun_nat_int,N2: nat] : groups4075276357253098568at_int(produc6840382203811409530at_int(G),aa_fun7046812543386002057at_nat(collec3392354462482085612at_nat,aa_fun7564604662015400456_nat_o(produc6081775807080527818_nat_o,aTP_Lamm_hv(N2)))) = groups705719431365010083at_int(aTP_Lamm_mo(G),aa_nat_set_nat(set_ord_atMost_nat,N2)) ).

% prod.triangle_reindex_eq
tff(fact_4660_and__not__numerals_I8_J,axiom,
    ! [M: num,N2: num] : aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit1,M))),aa_int_int(bit_ri7919022796975470100ot_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,N2)))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,aa_num_int(numeral_numeral_int,M)),aa_int_int(bit_ri7919022796975470100ot_int,aa_num_int(numeral_numeral_int,N2))))) ).

% and_not_numerals(8)
tff(fact_4661_not__int__rec,axiom,
    ! [K: int] : aa_int_int(bit_ri7919022796975470100ot_int,K) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_o_int(zero_n2684676970156552555ol_int,aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),K))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(bit_ri7919022796975470100ot_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,K),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))))) ).

% not_int_rec
tff(fact_4662_Nitpick_Ocase__nat__unfold,axiom,
    ! [X2: option_num,F: fun_nat_option_num,N2: nat] :
      aa_nat_option_num(case_nat_option_num(X2,F),N2) = $ite(N2 = zero_zero_nat,X2,aa_nat_option_num(F,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat))) ).

% Nitpick.case_nat_unfold
tff(fact_4663_or__int__rec,axiom,
    ! [K: int,L: int] :
      aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,K),L) = aa_int_int(aa_int_fun_int_int(plus_plus_int,
          aa_o_int(zero_n2684676970156552555ol_int,
            ( ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),K)
            | ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),L) ))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,K),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),aa_int_int(aa_int_fun_int_int(divide_divide_int,L),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))))) ).

% or_int_rec
tff(fact_4664_or__numerals_I4_J,axiom,
    ! [X2: num,Y: num] : aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,X2))),aa_num_int(numeral_numeral_int,aa_num_num(bit1,Y))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,aa_num_int(numeral_numeral_int,X2)),aa_num_int(numeral_numeral_int,Y)))) ).

% or_numerals(4)
tff(fact_4665_or__numerals_I4_J,axiom,
    ! [X2: num,Y: num] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se1412395901928357646or_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,X2))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,Y))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(bit_se1412395901928357646or_nat,aa_num_nat(numeral_numeral_nat,X2)),aa_num_nat(numeral_numeral_nat,Y)))) ).

% or_numerals(4)
tff(fact_4666_or__numerals_I4_J,axiom,
    ! [X2: num,Y: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se1080825931792720795nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,X2))),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit1,Y))) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,one_one_Code_integer),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se1080825931792720795nteger,aa_num_Code_integer(numera6620942414471956472nteger,X2)),aa_num_Code_integer(numera6620942414471956472nteger,Y)))) ).

% or_numerals(4)
tff(fact_4667_or__numerals_I4_J,axiom,
    ! [X2: num,Y: num] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se9127793120404214118atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,X2))),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,Y))) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,one_one_Code_natural),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se9127793120404214118atural,aa_num_Code_natural(numera5444537566228673987atural,X2)),aa_num_Code_natural(numera5444537566228673987atural,Y)))) ).

% or_numerals(4)
tff(fact_4668_or__numerals_I6_J,axiom,
    ! [X2: num,Y: num] : aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,aa_num_int(numeral_numeral_int,aa_num_num(bit1,X2))),aa_num_int(numeral_numeral_int,aa_num_num(bit0,Y))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,aa_num_int(numeral_numeral_int,X2)),aa_num_int(numeral_numeral_int,Y)))) ).

% or_numerals(6)
tff(fact_4669_or__numerals_I6_J,axiom,
    ! [X2: num,Y: num] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se1412395901928357646or_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,X2))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,Y))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(bit_se1412395901928357646or_nat,aa_num_nat(numeral_numeral_nat,X2)),aa_num_nat(numeral_numeral_nat,Y)))) ).

% or_numerals(6)
tff(fact_4670_or__numerals_I6_J,axiom,
    ! [X2: num,Y: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se1080825931792720795nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit1,X2))),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,Y))) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,one_one_Code_integer),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se1080825931792720795nteger,aa_num_Code_integer(numera6620942414471956472nteger,X2)),aa_num_Code_integer(numera6620942414471956472nteger,Y)))) ).

% or_numerals(6)
tff(fact_4671_or__numerals_I6_J,axiom,
    ! [X2: num,Y: num] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se9127793120404214118atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,X2))),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,Y))) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,one_one_Code_natural),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se9127793120404214118atural,aa_num_Code_natural(numera5444537566228673987atural,X2)),aa_num_Code_natural(numera5444537566228673987atural,Y)))) ).

% or_numerals(6)
tff(fact_4672_or__numerals_I7_J,axiom,
    ! [X2: num,Y: num] : aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,aa_num_int(numeral_numeral_int,aa_num_num(bit1,X2))),aa_num_int(numeral_numeral_int,aa_num_num(bit1,Y))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,aa_num_int(numeral_numeral_int,X2)),aa_num_int(numeral_numeral_int,Y)))) ).

% or_numerals(7)
tff(fact_4673_or__numerals_I7_J,axiom,
    ! [X2: num,Y: num] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se1412395901928357646or_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,X2))),aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,Y))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(bit_se1412395901928357646or_nat,aa_num_nat(numeral_numeral_nat,X2)),aa_num_nat(numeral_numeral_nat,Y)))) ).

% or_numerals(7)
tff(fact_4674_or__numerals_I7_J,axiom,
    ! [X2: num,Y: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se1080825931792720795nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit1,X2))),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit1,Y))) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,one_one_Code_integer),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se1080825931792720795nteger,aa_num_Code_integer(numera6620942414471956472nteger,X2)),aa_num_Code_integer(numera6620942414471956472nteger,Y)))) ).

% or_numerals(7)
tff(fact_4675_or__numerals_I7_J,axiom,
    ! [X2: num,Y: num] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se9127793120404214118atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,X2))),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,Y))) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,one_one_Code_natural),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se9127793120404214118atural,aa_num_Code_natural(numera5444537566228673987atural,X2)),aa_num_Code_natural(numera5444537566228673987atural,Y)))) ).

% or_numerals(7)
tff(fact_4676_or__nat__rec,axiom,
    ! [M: nat,N2: nat] :
      aa_nat_nat(aa_nat_fun_nat_nat(bit_se1412395901928357646or_nat,M),N2) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,
          aa_o_nat(zero_n2687167440665602831ol_nat,
            ( ~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),M)
            | ~ aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2) ))),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(bit_se1412395901928357646or_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,M),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,N2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))) ).

% or_nat_rec
tff(fact_4677_or__not__numerals_I9_J,axiom,
    ! [M: num,N2: num] : aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,aa_num_int(numeral_numeral_int,aa_num_num(bit1,M))),aa_int_int(bit_ri7919022796975470100ot_int,aa_num_int(numeral_numeral_int,aa_num_num(bit1,N2)))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,aa_num_int(numeral_numeral_int,M)),aa_int_int(bit_ri7919022796975470100ot_int,aa_num_int(numeral_numeral_int,N2))))) ).

% or_not_numerals(9)
tff(fact_4678_bit_Odisj__one__left,axiom,
    ! [X2: int] : aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,aa_int_int(uminus_uminus_int,one_one_int)),X2) = aa_int_int(uminus_uminus_int,one_one_int) ).

% bit.disj_one_left
tff(fact_4679_bit_Odisj__one__left,axiom,
    ! [X2: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se1080825931792720795nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),X2) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) ).

% bit.disj_one_left
tff(fact_4680_bit_Odisj__one__right,axiom,
    ! [X2: int] : aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,X2),aa_int_int(uminus_uminus_int,one_one_int)) = aa_int_int(uminus_uminus_int,one_one_int) ).

% bit.disj_one_right
tff(fact_4681_bit_Odisj__one__right,axiom,
    ! [X2: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se1080825931792720795nteger,X2),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) ).

% bit.disj_one_right
tff(fact_4682_or__numerals_I8_J,axiom,
    ! [X2: num] : aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,aa_num_int(numeral_numeral_int,aa_num_num(bit1,X2))),one_one_int) = aa_num_int(numeral_numeral_int,aa_num_num(bit1,X2)) ).

% or_numerals(8)
tff(fact_4683_or__numerals_I8_J,axiom,
    ! [X2: num] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se1412395901928357646or_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,X2))),one_one_nat) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,X2)) ).

% or_numerals(8)
tff(fact_4684_or__numerals_I8_J,axiom,
    ! [X2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se1080825931792720795nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit1,X2))),one_one_Code_integer) = aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit1,X2)) ).

% or_numerals(8)
tff(fact_4685_or__numerals_I8_J,axiom,
    ! [X2: num] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se9127793120404214118atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,X2))),one_one_Code_natural) = aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,X2)) ).

% or_numerals(8)
tff(fact_4686_or__numerals_I2_J,axiom,
    ! [Y: num] : aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,one_one_int),aa_num_int(numeral_numeral_int,aa_num_num(bit1,Y))) = aa_num_int(numeral_numeral_int,aa_num_num(bit1,Y)) ).

% or_numerals(2)
tff(fact_4687_or__numerals_I2_J,axiom,
    ! [Y: num] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se1412395901928357646or_nat,one_one_nat),aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,Y))) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,Y)) ).

% or_numerals(2)
tff(fact_4688_or__numerals_I2_J,axiom,
    ! [Y: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se1080825931792720795nteger,one_one_Code_integer),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit1,Y))) = aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit1,Y)) ).

% or_numerals(2)
tff(fact_4689_or__numerals_I2_J,axiom,
    ! [Y: num] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se9127793120404214118atural,one_one_Code_natural),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,Y))) = aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,Y)) ).

% or_numerals(2)
tff(fact_4690_bit_Odisj__cancel__left,axiom,
    ! [X2: int] : aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,aa_int_int(bit_ri7919022796975470100ot_int,X2)),X2) = aa_int_int(uminus_uminus_int,one_one_int) ).

% bit.disj_cancel_left
tff(fact_4691_bit_Odisj__cancel__left,axiom,
    ! [X2: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se1080825931792720795nteger,aa_Cod1783974652533396728nteger(bit_ri7632146776885996613nteger,X2)),X2) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) ).

% bit.disj_cancel_left
tff(fact_4692_bit_Odisj__cancel__right,axiom,
    ! [X2: int] : aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,X2),aa_int_int(bit_ri7919022796975470100ot_int,X2)) = aa_int_int(uminus_uminus_int,one_one_int) ).

% bit.disj_cancel_right
tff(fact_4693_bit_Odisj__cancel__right,axiom,
    ! [X2: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se1080825931792720795nteger,X2),aa_Cod1783974652533396728nteger(bit_ri7632146776885996613nteger,X2)) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) ).

% bit.disj_cancel_right
tff(fact_4694_or__numerals_I5_J,axiom,
    ! [X2: num] : aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,X2))),one_one_int) = aa_num_int(numeral_numeral_int,aa_num_num(bit1,X2)) ).

% or_numerals(5)
tff(fact_4695_or__numerals_I5_J,axiom,
    ! [X2: num] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se1412395901928357646or_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,X2))),one_one_nat) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,X2)) ).

% or_numerals(5)
tff(fact_4696_or__numerals_I5_J,axiom,
    ! [X2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se1080825931792720795nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,X2))),one_one_Code_integer) = aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit1,X2)) ).

% or_numerals(5)
tff(fact_4697_or__numerals_I5_J,axiom,
    ! [X2: num] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se9127793120404214118atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,X2))),one_one_Code_natural) = aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,X2)) ).

% or_numerals(5)
tff(fact_4698_or__numerals_I1_J,axiom,
    ! [Y: num] : aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,one_one_int),aa_num_int(numeral_numeral_int,aa_num_num(bit0,Y))) = aa_num_int(numeral_numeral_int,aa_num_num(bit1,Y)) ).

% or_numerals(1)
tff(fact_4699_or__numerals_I1_J,axiom,
    ! [Y: num] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se1412395901928357646or_nat,one_one_nat),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,Y))) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,Y)) ).

% or_numerals(1)
tff(fact_4700_or__numerals_I1_J,axiom,
    ! [Y: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se1080825931792720795nteger,one_one_Code_integer),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,Y))) = aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit1,Y)) ).

% or_numerals(1)
tff(fact_4701_or__numerals_I1_J,axiom,
    ! [Y: num] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se9127793120404214118atural,one_one_Code_natural),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,Y))) = aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,Y)) ).

% or_numerals(1)
tff(fact_4702_or__integer_Oabs__eq,axiom,
    ! [Xa: int,X2: int] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se1080825931792720795nteger,aa_int_Code_integer(code_integer_of_int,Xa)),aa_int_Code_integer(code_integer_of_int,X2)) = aa_int_Code_integer(code_integer_of_int,aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,Xa),X2)) ).

% or_integer.abs_eq
tff(fact_4703_or__integer_Orep__eq,axiom,
    ! [X2: code_integer,Xa: code_integer] : aa_Code_integer_int(code_int_of_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se1080825931792720795nteger,X2),Xa)) = aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,aa_Code_integer_int(code_int_of_integer,X2)),aa_Code_integer_int(code_int_of_integer,Xa)) ).

% or_integer.rep_eq
tff(fact_4704_disjunctive__add,axiom,
    ! [A: int,B: int] :
      ( ! [N: nat] :
          ( ~ aa_nat_o(aa_int_fun_nat_o(bit_se1146084159140164899it_int,A),N)
          | ~ aa_nat_o(aa_int_fun_nat_o(bit_se1146084159140164899it_int,B),N) )
     => ( aa_int_int(aa_int_fun_int_int(plus_plus_int,A),B) = aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,A),B) ) ) ).

% disjunctive_add
tff(fact_4705_disjunctive__add,axiom,
    ! [A: nat,B: nat] :
      ( ! [N: nat] :
          ( ~ aa_nat_o(aa_nat_fun_nat_o(bit_se1148574629649215175it_nat,A),N)
          | ~ aa_nat_o(aa_nat_fun_nat_o(bit_se1148574629649215175it_nat,B),N) )
     => ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),B) = aa_nat_nat(aa_nat_fun_nat_nat(bit_se1412395901928357646or_nat,A),B) ) ) ).

% disjunctive_add
tff(fact_4706_disjunctive__add,axiom,
    ! [A: code_integer,B: code_integer] :
      ( ! [N: nat] :
          ( ~ aa_nat_o(aa_Cod1075288278386115654_nat_o(bit_se9216721137139052372nteger,A),N)
          | ~ aa_nat_o(aa_Cod1075288278386115654_nat_o(bit_se9216721137139052372nteger,B),N) )
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),B) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se1080825931792720795nteger,A),B) ) ) ).

% disjunctive_add
tff(fact_4707_disjunctive__add,axiom,
    ! [A: code_natural,B: code_natural] :
      ( ! [N: nat] :
          ( ~ aa_nat_o(aa_Cod9120328075896114107_nat_o(bit_se8040316288895769887atural,A),N)
          | ~ aa_nat_o(aa_Cod9120328075896114107_nat_o(bit_se8040316288895769887atural,B),N) )
     => ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),B) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se9127793120404214118atural,A),B) ) ) ).

% disjunctive_add
tff(fact_4708_plus__and__or,axiom,
    ! [X2: int,Y: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,X2),Y)),aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,X2),Y)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),Y) ).

% plus_and_or
tff(fact_4709_not__integer_Orep__eq,axiom,
    ! [X2: code_integer] : aa_Code_integer_int(code_int_of_integer,aa_Cod1783974652533396728nteger(bit_ri7632146776885996613nteger,X2)) = aa_int_int(bit_ri7919022796975470100ot_int,aa_Code_integer_int(code_int_of_integer,X2)) ).

% not_integer.rep_eq
tff(fact_4710_set__bit__nat__def,axiom,
    ! [M: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se7882103937844011126it_nat,M),N2) = aa_nat_nat(aa_nat_fun_nat_nat(bit_se1412395901928357646or_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(bit_se547839408752420682it_nat,M),one_one_nat)) ).

% set_bit_nat_def
tff(fact_4711_not__integer_Oabs__eq,axiom,
    ! [X2: int] : aa_Cod1783974652533396728nteger(bit_ri7632146776885996613nteger,aa_int_Code_integer(code_integer_of_int,X2)) = aa_int_Code_integer(code_integer_of_int,aa_int_int(bit_ri7919022796975470100ot_int,X2)) ).

% not_integer.abs_eq
tff(fact_4712_set__bit__eq__or,axiom,
    ! [N2: nat,A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se7882103937844011126it_nat,N2),A) = aa_nat_nat(aa_nat_fun_nat_nat(bit_se1412395901928357646or_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(bit_se547839408752420682it_nat,N2),one_one_nat)) ).

% set_bit_eq_or
tff(fact_4713_set__bit__eq__or,axiom,
    ! [N2: nat,A: code_integer] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se2793503036327961859nteger,N2),A) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se1080825931792720795nteger,A),aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se7788150548672797655nteger,N2),one_one_Code_integer)) ).

% set_bit_eq_or
tff(fact_4714_set__bit__eq__or,axiom,
    ! [N2: nat,A: int] : aa_int_int(aa_nat_fun_int_int(bit_se7879613467334960850it_int,N2),A) = aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,A),aa_int_int(aa_nat_fun_int_int(bit_se545348938243370406it_int,N2),one_one_int)) ).

% set_bit_eq_or
tff(fact_4715_set__bit__eq__or,axiom,
    ! [N2: nat,A: code_natural] : aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se1617098188084679374atural,N2),A) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se9127793120404214118atural,A),aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se6611745700429515170atural,N2),one_one_Code_natural)) ).

% set_bit_eq_or
tff(fact_4716_bit_Ocomplement__unique,axiom,
    ! [A: int,X2: int,Y: int] :
      ( ( aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,A),X2) = zero_zero_int )
     => ( ( aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,A),X2) = aa_int_int(uminus_uminus_int,one_one_int) )
       => ( ( aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,A),Y) = zero_zero_int )
         => ( ( aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,A),Y) = aa_int_int(uminus_uminus_int,one_one_int) )
           => ( X2 = Y ) ) ) ) ) ).

% bit.complement_unique
tff(fact_4717_bit_Ocomplement__unique,axiom,
    ! [A: code_integer,X2: code_integer,Y: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3949692690581998587nteger,A),X2) = zero_z3403309356797280102nteger )
     => ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se1080825931792720795nteger,A),X2) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) )
       => ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3949692690581998587nteger,A),Y) = zero_z3403309356797280102nteger )
         => ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se1080825931792720795nteger,A),Y) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) )
           => ( X2 = Y ) ) ) ) ) ).

% bit.complement_unique
tff(fact_4718_bit_Ocompl__unique,axiom,
    ! [X2: int,Y: int] :
      ( ( aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,X2),Y) = zero_zero_int )
     => ( ( aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,X2),Y) = aa_int_int(uminus_uminus_int,one_one_int) )
       => ( aa_int_int(bit_ri7919022796975470100ot_int,X2) = Y ) ) ) ).

% bit.compl_unique
tff(fact_4719_bit_Ocompl__unique,axiom,
    ! [X2: code_integer,Y: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3949692690581998587nteger,X2),Y) = zero_z3403309356797280102nteger )
     => ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se1080825931792720795nteger,X2),Y) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer) )
       => ( aa_Cod1783974652533396728nteger(bit_ri7632146776885996613nteger,X2) = Y ) ) ) ).

% bit.compl_unique
tff(fact_4720_or__one__eq,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,A),one_one_int) = aa_int_int(aa_int_fun_int_int(plus_plus_int,A),aa_o_int(zero_n2684676970156552555ol_int,aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A))) ).

% or_one_eq
tff(fact_4721_or__one__eq,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se1412395901928357646or_nat,A),one_one_nat) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),aa_o_nat(zero_n2687167440665602831ol_nat,aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A))) ).

% or_one_eq
tff(fact_4722_or__one__eq,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se1080825931792720795nteger,A),one_one_Code_integer) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),aa_o_Code_integer(zero_n356916108424825756nteger,aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A))) ).

% or_one_eq
tff(fact_4723_or__one__eq,axiom,
    ! [A: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se9127793120404214118atural,A),one_one_Code_natural) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),zero_n8403883297036319079atural(aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A))) ).

% or_one_eq
tff(fact_4724_one__or__eq,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,one_one_int),A) = aa_int_int(aa_int_fun_int_int(plus_plus_int,A),aa_o_int(zero_n2684676970156552555ol_int,aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),A))) ).

% one_or_eq
tff(fact_4725_one__or__eq,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se1412395901928357646or_nat,one_one_nat),A) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),aa_o_nat(zero_n2687167440665602831ol_nat,aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),A))) ).

% one_or_eq
tff(fact_4726_one__or__eq,axiom,
    ! [A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se1080825931792720795nteger,one_one_Code_integer),A) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,A),aa_o_Code_integer(zero_n356916108424825756nteger,aa_Code_integer_o(aa_Cod326357343816142457eger_o(dvd_dvd_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),A))) ).

% one_or_eq
tff(fact_4727_one__or__eq,axiom,
    ! [A: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se9127793120404214118atural,one_one_Code_natural),A) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,A),zero_n8403883297036319079atural(aa_Code_natural_o(dvd_dvd_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),A))) ).

% one_or_eq
tff(fact_4728_mask__Suc__double,axiom,
    ! [N2: nat] : aa_nat_int(bit_se2000444600071755411sk_int,aa_nat_nat(suc,N2)) = aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,one_one_int),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_nat_int(bit_se2000444600071755411sk_int,N2))) ).

% mask_Suc_double
tff(fact_4729_mask__Suc__double,axiom,
    ! [N2: nat] : aa_nat_Code_integer(bit_se2119862282449309892nteger,aa_nat_nat(suc,N2)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se1080825931792720795nteger,one_one_Code_integer),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_nat_Code_integer(bit_se2119862282449309892nteger,N2))) ).

% mask_Suc_double
tff(fact_4730_mask__Suc__double,axiom,
    ! [N2: nat] : aa_nat_nat(bit_se2002935070580805687sk_nat,aa_nat_nat(suc,N2)) = aa_nat_nat(aa_nat_fun_nat_nat(bit_se1412395901928357646or_nat,one_one_nat),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(bit_se2002935070580805687sk_nat,N2))) ).

% mask_Suc_double
tff(fact_4731_mask__Suc__double,axiom,
    ! [N2: nat] : aa_nat_Code_natural(bit_se943457434206027407atural,aa_nat_nat(suc,N2)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se9127793120404214118atural,one_one_Code_natural),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),aa_nat_Code_natural(bit_se943457434206027407atural,N2))) ).

% mask_Suc_double
tff(fact_4732_or__not__numerals_I5_J,axiom,
    ! [M: num,N2: num] : aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,M))),aa_int_int(bit_ri7919022796975470100ot_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,N2)))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,aa_num_int(numeral_numeral_int,M)),aa_int_int(bit_ri7919022796975470100ot_int,aa_num_int(numeral_numeral_int,N2))))) ).

% or_not_numerals(5)
tff(fact_4733_Suc__0__or__eq,axiom,
    ! [N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se1412395901928357646or_nat,aa_nat_nat(suc,zero_zero_nat)),N2) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),aa_o_nat(zero_n2687167440665602831ol_nat,aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2))) ).

% Suc_0_or_eq
tff(fact_4734_or__Suc__0__eq,axiom,
    ! [N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se1412395901928357646or_nat,N2),aa_nat_nat(suc,zero_zero_nat)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),aa_o_nat(zero_n2687167440665602831ol_nat,aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2))) ).

% or_Suc_0_eq
tff(fact_4735_or__not__numerals_I8_J,axiom,
    ! [M: num,N2: num] : aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,aa_num_int(numeral_numeral_int,aa_num_num(bit1,M))),aa_int_int(bit_ri7919022796975470100ot_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,N2)))) = aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,aa_num_int(numeral_numeral_int,M)),aa_int_int(bit_ri7919022796975470100ot_int,aa_num_int(numeral_numeral_int,N2))))) ).

% or_not_numerals(8)
tff(fact_4736_or__int__unfold,axiom,
    ! [K: int,L: int] :
      aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,K),L) = $ite(
        ( ( K = aa_int_int(uminus_uminus_int,one_one_int) )
        | ( L = aa_int_int(uminus_uminus_int,one_one_int) ) ),
        aa_int_int(uminus_uminus_int,one_one_int),
        $ite(
          K = zero_zero_int,
          L,
          $ite(L = zero_zero_int,K,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(ord_max_int,aa_int_int(aa_int_fun_int_int(modulo_modulo_int,K),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),aa_int_int(aa_int_fun_int_int(modulo_modulo_int,L),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(bit_se1409905431419307370or_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,K),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),aa_int_int(aa_int_fun_int_int(divide_divide_int,L),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))))))) ) ) ).

% or_int_unfold
tff(fact_4737_bit_Oabstract__boolean__algebra__sym__diff__axioms,axiom,
    boolea2445317508997433345nteger(bit_se3949692690581998587nteger,bit_se1080825931792720795nteger,bit_ri7632146776885996613nteger,zero_z3403309356797280102nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer),bit_se3222712562003087583nteger) ).

% bit.abstract_boolean_algebra_sym_diff_axioms
tff(fact_4738_bit_Oabstract__boolean__algebra__sym__diff__axioms,axiom,
    boolea8527374999097803216ff_int(bit_se725231765392027082nd_int,bit_se1409905431419307370or_int,bit_ri7919022796975470100ot_int,zero_zero_int,aa_int_int(uminus_uminus_int,one_one_int),bit_se6526347334894502574or_int) ).

% bit.abstract_boolean_algebra_sym_diff_axioms
tff(fact_4739_or__nat__unfold,axiom,
    ! [M: nat,N2: nat] :
      aa_nat_nat(aa_nat_fun_nat_nat(bit_se1412395901928357646or_nat,M),N2) = $ite(
        M = zero_zero_nat,
        N2,
        $ite(N2 = zero_zero_nat,M,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(ord_max_nat,aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,M),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,N2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(bit_se1412395901928357646or_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,M),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,N2),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))))) ) ).

% or_nat_unfold
tff(fact_4740_drop__bit__rec,axiom,
    ! [N2: nat,A: code_integer] :
      aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se3928097537394005634nteger,N2),A) = $ite(N2 = zero_zero_nat,A,aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se3928097537394005634nteger,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))))) ).

% drop_bit_rec
tff(fact_4741_drop__bit__rec,axiom,
    ! [N2: nat,A: int] :
      aa_int_int(aa_nat_fun_int_int(bit_se8568078237143864401it_int,N2),A) = $ite(N2 = zero_zero_nat,A,aa_int_int(aa_nat_fun_int_int(bit_se8568078237143864401it_int,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)),aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))))) ).

% drop_bit_rec
tff(fact_4742_drop__bit__rec,axiom,
    ! [N2: nat,A: nat] :
      aa_nat_nat(aa_nat_fun_nat_nat(bit_se8570568707652914677it_nat,N2),A) = $ite(N2 = zero_zero_nat,A,aa_nat_nat(aa_nat_fun_nat_nat(bit_se8570568707652914677it_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))))) ).

% drop_bit_rec
tff(fact_4743_drop__bit__rec,axiom,
    ! [N2: nat,A: code_natural] :
      aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se2751692689150723149atural,N2),A) = $ite(N2 = zero_zero_nat,A,aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se2751692689150723149atural,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))))) ).

% drop_bit_rec
tff(fact_4744_image__atLeastZeroLessThan__integer,axiom,
    ! [U: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),U)
     => ( aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(zero_z3403309356797280102nteger),U) = image_1215581382706833972nteger(semiri4939895301339042750nteger,aa_nat_set_nat(set_ord_lessThan_nat,aa_Code_integer_nat(code_nat_of_integer,U))) ) ) ).

% image_atLeastZeroLessThan_integer
tff(fact_4745_uminus__int__def,axiom,
    uminus_uminus_int = aa_fun8399641135911395862nt_int(map_fu3667384564859982768at_int(rep_Integ,abs_Integ),produc2626176000494625587at_nat(aTP_Lamm_dg)) ).

% uminus_int_def
tff(fact_4746_bit_Oabstract__boolean__algebra__axioms,axiom,
    aa_int_o(aa_int_fun_int_o(boolea5469654029284665142ra_int(bit_se725231765392027082nd_int,bit_se1409905431419307370or_int,bit_ri7919022796975470100ot_int),zero_zero_int),aa_int_int(uminus_uminus_int,one_one_int)) ).

% bit.abstract_boolean_algebra_axioms
tff(fact_4747_bit_Oabstract__boolean__algebra__axioms,axiom,
    aa_Code_integer_o(aa_Cod326357343816142457eger_o(boolea5643492148547655015nteger(bit_se3949692690581998587nteger,bit_se1080825931792720795nteger,bit_ri7632146776885996613nteger),zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) ).

% bit.abstract_boolean_algebra_axioms
tff(fact_4748_map__fun__apply,axiom,
    ! [F: fun_in4514472496968388910at_nat,G: fun_o_o,Ha: fun_Pr4796943543331071514_nat_o,X2: int] :
      ( aa_int_o(aa_fun1490936263268389485_int_o(map_fu4826362097070443709at_o_o(F,G),Ha),X2)
    <=> aa_o_o(G,aa_Pro6150637604445964947_nat_o(Ha,aa_int1417691210696471063at_nat(F,X2))) ) ).

% map_fun_apply
tff(fact_4749_map__fun__apply,axiom,
    ! [F: fun_in4514472496968388910at_nat,G: fun_fu3064074204415222357nt_int,Ha: fun_Pr2477239776880934807at_nat,X2: int] : aa_int_fun_int_int(map_fu8294830438409148311nt_int(F,G,Ha),X2) = aa_fun8399641135911395862nt_int(G,aa_Pro8023792847356852296at_nat(Ha,aa_int1417691210696471063at_nat(F,X2))) ).

% map_fun_apply
tff(fact_4750_map__fun__apply,axiom,
    ! [F: fun_in4514472496968388910at_nat,G: fun_fu7075445697382584196_int_o,Ha: fun_Pr2028404973800837934_nat_o,X2: int] : aa_int_fun_int_o(map_fu3191548434056052140_int_o(F,G,Ha),X2) = aa_fun1490936263268389485_int_o(G,aa_Pro989595756709598047_nat_o(Ha,aa_int1417691210696471063at_nat(F,X2))) ).

% map_fun_apply
tff(fact_4751_map__fun__apply,axiom,
    ! [F: fun_int_int,G: fun_Pr1652463973008025892nt_rat,Ha: fun_in4211310926729683942nt_int,X2: int] : aa_int_rat(aa_fun1809696235935464875nt_rat(map_fu3424225382358772769nt_rat(F,G),Ha),X2) = aa_Pro6166618844887768661nt_rat(G,aa_int7462565939943104719nt_int(Ha,aa_int_int(F,X2))) ).

% map_fun_apply
tff(fact_4752_map__fun__apply,axiom,
    ! [F: fun_int_int,G: fun_fu7460908759652350970nt_rat,Ha: fun_in1696471567231710611nt_int,X2: int] : aa_int_fun_int_rat(map_fu7945985449245211511nt_rat(F,G,Ha),X2) = aa_fun1809696235935464875nt_rat(G,aa_int2565445551602696444nt_int(Ha,aa_int_int(F,X2))) ).

% map_fun_apply
tff(fact_4753_drop__bit__drop__bit,axiom,
    ! [M: nat,N2: nat,A: code_integer] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se3928097537394005634nteger,M),aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se3928097537394005634nteger,N2),A)) = aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se3928097537394005634nteger,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)),A) ).

% drop_bit_drop_bit
tff(fact_4754_drop__bit__drop__bit,axiom,
    ! [M: nat,N2: nat,A: int] : aa_int_int(aa_nat_fun_int_int(bit_se8568078237143864401it_int,M),aa_int_int(aa_nat_fun_int_int(bit_se8568078237143864401it_int,N2),A)) = aa_int_int(aa_nat_fun_int_int(bit_se8568078237143864401it_int,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)),A) ).

% drop_bit_drop_bit
tff(fact_4755_drop__bit__drop__bit,axiom,
    ! [M: nat,N2: nat,A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se8570568707652914677it_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(bit_se8570568707652914677it_nat,N2),A)) = aa_nat_nat(aa_nat_fun_nat_nat(bit_se8570568707652914677it_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)),A) ).

% drop_bit_drop_bit
tff(fact_4756_drop__bit__drop__bit,axiom,
    ! [M: nat,N2: nat,A: code_natural] : aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se2751692689150723149atural,M),aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se2751692689150723149atural,N2),A)) = aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se2751692689150723149atural,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)),A) ).

% drop_bit_drop_bit
tff(fact_4757_image__add__atLeastAtMost,axiom,
    ! [K: rat,I: rat,J: rat] : image_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,K),set_or633870826150836451st_rat(I,J)) = set_or633870826150836451st_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,I),K),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,J),K)) ).

% image_add_atLeastAtMost
tff(fact_4758_image__add__atLeastAtMost,axiom,
    ! [K: int,I: int,J: int] : aa_set_int_set_int(image_int_int(aa_int_fun_int_int(plus_plus_int,K)),aa_int_set_int(set_or1266510415728281911st_int(I),J)) = aa_int_set_int(set_or1266510415728281911st_int(aa_int_int(aa_int_fun_int_int(plus_plus_int,I),K)),aa_int_int(aa_int_fun_int_int(plus_plus_int,J),K)) ).

% image_add_atLeastAtMost
tff(fact_4759_image__add__atLeastAtMost,axiom,
    ! [K: nat,I: nat,J: nat] : aa_set_nat_set_nat(image_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,K)),aa_nat_set_nat(set_or1269000886237332187st_nat(I),J)) = aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),K)) ).

% image_add_atLeastAtMost
tff(fact_4760_image__add__atLeastAtMost,axiom,
    ! [K: code_integer,I: code_integer,J: code_integer] : image_4470545334726330049nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,K),aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(I),J)) = aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,I),K)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,J),K)) ).

% image_add_atLeastAtMost
tff(fact_4761_image__diff__atLeastAtMost,axiom,
    ! [D2: rat,A: rat,B: rat] : image_rat_rat(minus_minus_rat(D2),set_or633870826150836451st_rat(A,B)) = set_or633870826150836451st_rat(aa_rat_rat(minus_minus_rat(D2),B),aa_rat_rat(minus_minus_rat(D2),A)) ).

% image_diff_atLeastAtMost
tff(fact_4762_image__diff__atLeastAtMost,axiom,
    ! [D2: int,A: int,B: int] : aa_set_int_set_int(image_int_int(aa_int_fun_int_int(minus_minus_int,D2)),aa_int_set_int(set_or1266510415728281911st_int(A),B)) = aa_int_set_int(set_or1266510415728281911st_int(aa_int_int(aa_int_fun_int_int(minus_minus_int,D2),B)),aa_int_int(aa_int_fun_int_int(minus_minus_int,D2),A)) ).

% image_diff_atLeastAtMost
tff(fact_4763_image__diff__atLeastAtMost,axiom,
    ! [D2: code_integer,A: code_integer,B: code_integer] : image_4470545334726330049nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,D2),aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(A),B)) = aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,D2),B)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,D2),A)) ).

% image_diff_atLeastAtMost
tff(fact_4764_image__add__atLeastLessThan,axiom,
    ! [K: rat,I: rat,J: rat] : image_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,K),set_or4029947393144176647an_rat(I,J)) = set_or4029947393144176647an_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,I),K),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,J),K)) ).

% image_add_atLeastLessThan
tff(fact_4765_image__add__atLeastLessThan,axiom,
    ! [K: nat,I: nat,J: nat] : aa_set_nat_set_nat(image_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,K)),aa_nat_set_nat(set_or4665077453230672383an_nat(I),J)) = aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),K)) ).

% image_add_atLeastLessThan
tff(fact_4766_image__add__atLeastLessThan,axiom,
    ! [K: code_integer,I: code_integer,J: code_integer] : image_4470545334726330049nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,K),aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(I),J)) = aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,I),K)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,J),K)) ).

% image_add_atLeastLessThan
tff(fact_4767_image__add__atLeastLessThan,axiom,
    ! [K: int,I: int,J: int] : aa_set_int_set_int(image_int_int(aa_int_fun_int_int(plus_plus_int,K)),aa_int_set_int(set_or4662586982721622107an_int(I),J)) = aa_int_set_int(set_or4662586982721622107an_int(aa_int_int(aa_int_fun_int_int(plus_plus_int,I),K)),aa_int_int(aa_int_fun_int_int(plus_plus_int,J),K)) ).

% image_add_atLeastLessThan
tff(fact_4768_max__0__1_I1_J,axiom,
    aa_rat_rat(ord_max_rat(zero_zero_rat),one_one_rat) = one_one_rat ).

% max_0_1(1)
tff(fact_4769_max__0__1_I1_J,axiom,
    aa_int_int(aa_int_fun_int_int(ord_max_int,zero_zero_int),one_one_int) = one_one_int ).

% max_0_1(1)
tff(fact_4770_max__0__1_I1_J,axiom,
    aa_nat_nat(aa_nat_fun_nat_nat(ord_max_nat,zero_zero_nat),one_one_nat) = one_one_nat ).

% max_0_1(1)
tff(fact_4771_max__0__1_I1_J,axiom,
    aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_max_Code_integer,zero_z3403309356797280102nteger),one_one_Code_integer) = one_one_Code_integer ).

% max_0_1(1)
tff(fact_4772_max__0__1_I1_J,axiom,
    aa_Cod4272041906116450446atural(ord_max_Code_natural(zero_z2226904508553997617atural),one_one_Code_natural) = one_one_Code_natural ).

% max_0_1(1)
tff(fact_4773_max__0__1_I2_J,axiom,
    aa_rat_rat(ord_max_rat(one_one_rat),zero_zero_rat) = one_one_rat ).

% max_0_1(2)
tff(fact_4774_max__0__1_I2_J,axiom,
    aa_int_int(aa_int_fun_int_int(ord_max_int,one_one_int),zero_zero_int) = one_one_int ).

% max_0_1(2)
tff(fact_4775_max__0__1_I2_J,axiom,
    aa_nat_nat(aa_nat_fun_nat_nat(ord_max_nat,one_one_nat),zero_zero_nat) = one_one_nat ).

% max_0_1(2)
tff(fact_4776_max__0__1_I2_J,axiom,
    aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_max_Code_integer,one_one_Code_integer),zero_z3403309356797280102nteger) = one_one_Code_integer ).

% max_0_1(2)
tff(fact_4777_max__0__1_I2_J,axiom,
    aa_Cod4272041906116450446atural(ord_max_Code_natural(one_one_Code_natural),zero_z2226904508553997617atural) = one_one_Code_natural ).

% max_0_1(2)
tff(fact_4778_image__uminus__atLeastAtMost,axiom,
    ! [X2: rat,Y: rat] : image_rat_rat(uminus_uminus_rat,set_or633870826150836451st_rat(X2,Y)) = set_or633870826150836451st_rat(aa_rat_rat(uminus_uminus_rat,Y),aa_rat_rat(uminus_uminus_rat,X2)) ).

% image_uminus_atLeastAtMost
tff(fact_4779_image__uminus__atLeastAtMost,axiom,
    ! [X2: int,Y: int] : aa_set_int_set_int(image_int_int(uminus_uminus_int),aa_int_set_int(set_or1266510415728281911st_int(X2),Y)) = aa_int_set_int(set_or1266510415728281911st_int(aa_int_int(uminus_uminus_int,Y)),aa_int_int(uminus_uminus_int,X2)) ).

% image_uminus_atLeastAtMost
tff(fact_4780_image__uminus__atLeastAtMost,axiom,
    ! [X2: code_integer,Y: code_integer] : image_4470545334726330049nteger(uminus1351360451143612070nteger,aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(X2),Y)) = aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,Y)),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,X2)) ).

% image_uminus_atLeastAtMost
tff(fact_4781_max__0__1_I6_J,axiom,
    ! [X2: num] : aa_nat_nat(aa_nat_fun_nat_nat(ord_max_nat,aa_num_nat(numeral_numeral_nat,X2)),one_one_nat) = aa_num_nat(numeral_numeral_nat,X2) ).

% max_0_1(6)
tff(fact_4782_max__0__1_I6_J,axiom,
    ! [X2: num] : aa_int_int(aa_int_fun_int_int(ord_max_int,aa_num_int(numeral_numeral_int,X2)),one_one_int) = aa_num_int(numeral_numeral_int,X2) ).

% max_0_1(6)
tff(fact_4783_max__0__1_I6_J,axiom,
    ! [X2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_max_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,X2)),one_one_Code_integer) = aa_num_Code_integer(numera6620942414471956472nteger,X2) ).

% max_0_1(6)
tff(fact_4784_max__0__1_I6_J,axiom,
    ! [X2: num] : aa_rat_rat(ord_max_rat(aa_num_rat(numeral_numeral_rat,X2)),one_one_rat) = aa_num_rat(numeral_numeral_rat,X2) ).

% max_0_1(6)
tff(fact_4785_max__0__1_I6_J,axiom,
    ! [X2: num] : aa_Cod4272041906116450446atural(ord_max_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,X2)),one_one_Code_natural) = aa_num_Code_natural(numera5444537566228673987atural,X2) ).

% max_0_1(6)
tff(fact_4786_max__0__1_I5_J,axiom,
    ! [X2: num] : aa_nat_nat(aa_nat_fun_nat_nat(ord_max_nat,one_one_nat),aa_num_nat(numeral_numeral_nat,X2)) = aa_num_nat(numeral_numeral_nat,X2) ).

% max_0_1(5)
tff(fact_4787_max__0__1_I5_J,axiom,
    ! [X2: num] : aa_int_int(aa_int_fun_int_int(ord_max_int,one_one_int),aa_num_int(numeral_numeral_int,X2)) = aa_num_int(numeral_numeral_int,X2) ).

% max_0_1(5)
tff(fact_4788_max__0__1_I5_J,axiom,
    ! [X2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_max_Code_integer,one_one_Code_integer),aa_num_Code_integer(numera6620942414471956472nteger,X2)) = aa_num_Code_integer(numera6620942414471956472nteger,X2) ).

% max_0_1(5)
tff(fact_4789_max__0__1_I5_J,axiom,
    ! [X2: num] : aa_rat_rat(ord_max_rat(one_one_rat),aa_num_rat(numeral_numeral_rat,X2)) = aa_num_rat(numeral_numeral_rat,X2) ).

% max_0_1(5)
tff(fact_4790_max__0__1_I5_J,axiom,
    ! [X2: num] : aa_Cod4272041906116450446atural(ord_max_Code_natural(one_one_Code_natural),aa_num_Code_natural(numera5444537566228673987atural,X2)) = aa_num_Code_natural(numera5444537566228673987atural,X2) ).

% max_0_1(5)
tff(fact_4791_image__add__atMost,axiom,
    ! [C: rat,A: rat] : image_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,C),set_ord_atMost_rat(A)) = set_ord_atMost_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,C),A)) ).

% image_add_atMost
tff(fact_4792_image__add__atMost,axiom,
    ! [C: int,A: int] : aa_set_int_set_int(image_int_int(aa_int_fun_int_int(plus_plus_int,C)),aa_int_set_int(set_ord_atMost_int,A)) = aa_int_set_int(set_ord_atMost_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,C),A)) ).

% image_add_atMost
tff(fact_4793_image__add__atLeastAtMost_H,axiom,
    ! [K: rat,I: rat,J: rat] : image_rat_rat(aTP_Lamm_mp(K),set_or633870826150836451st_rat(I,J)) = set_or633870826150836451st_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,I),K),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,J),K)) ).

% image_add_atLeastAtMost'
tff(fact_4794_image__add__atLeastAtMost_H,axiom,
    ! [K: int,I: int,J: int] : aa_set_int_set_int(image_int_int(aa_int_fun_int_int(aTP_Lamm_mq,K)),aa_int_set_int(set_or1266510415728281911st_int(I),J)) = aa_int_set_int(set_or1266510415728281911st_int(aa_int_int(aa_int_fun_int_int(plus_plus_int,I),K)),aa_int_int(aa_int_fun_int_int(plus_plus_int,J),K)) ).

% image_add_atLeastAtMost'
tff(fact_4795_image__add__atLeastAtMost_H,axiom,
    ! [K: nat,I: nat,J: nat] : aa_set_nat_set_nat(image_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_mr,K)),aa_nat_set_nat(set_or1269000886237332187st_nat(I),J)) = aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),K)) ).

% image_add_atLeastAtMost'
tff(fact_4796_image__add__atLeastAtMost_H,axiom,
    ! [K: code_integer,I: code_integer,J: code_integer] : image_4470545334726330049nteger(aa_Cod4161879620478718930nteger(aTP_Lamm_ms,K),aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(I),J)) = aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,I),K)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,J),K)) ).

% image_add_atLeastAtMost'
tff(fact_4797_image__minus__const__atLeastAtMost_H,axiom,
    ! [D2: rat,A: rat,B: rat] : image_rat_rat(aTP_Lamm_mt(D2),set_or633870826150836451st_rat(A,B)) = set_or633870826150836451st_rat(aa_rat_rat(minus_minus_rat(A),D2),aa_rat_rat(minus_minus_rat(B),D2)) ).

% image_minus_const_atLeastAtMost'
tff(fact_4798_image__minus__const__atLeastAtMost_H,axiom,
    ! [D2: int,A: int,B: int] : aa_set_int_set_int(image_int_int(aa_int_fun_int_int(aTP_Lamm_mu,D2)),aa_int_set_int(set_or1266510415728281911st_int(A),B)) = aa_int_set_int(set_or1266510415728281911st_int(aa_int_int(aa_int_fun_int_int(minus_minus_int,A),D2)),aa_int_int(aa_int_fun_int_int(minus_minus_int,B),D2)) ).

% image_minus_const_atLeastAtMost'
tff(fact_4799_image__minus__const__atLeastAtMost_H,axiom,
    ! [D2: code_integer,A: code_integer,B: code_integer] : image_4470545334726330049nteger(aa_Cod4161879620478718930nteger(aTP_Lamm_mv,D2),aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(A),B)) = aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,A),D2)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,B),D2)) ).

% image_minus_const_atLeastAtMost'
tff(fact_4800_image__add__atLeastLessThan_H,axiom,
    ! [K: rat,I: rat,J: rat] : image_rat_rat(aTP_Lamm_mp(K),set_or4029947393144176647an_rat(I,J)) = set_or4029947393144176647an_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,I),K),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,J),K)) ).

% image_add_atLeastLessThan'
tff(fact_4801_image__add__atLeastLessThan_H,axiom,
    ! [K: nat,I: nat,J: nat] : aa_set_nat_set_nat(image_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_mr,K)),aa_nat_set_nat(set_or4665077453230672383an_nat(I),J)) = aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),K)) ).

% image_add_atLeastLessThan'
tff(fact_4802_image__add__atLeastLessThan_H,axiom,
    ! [K: code_integer,I: code_integer,J: code_integer] : image_4470545334726330049nteger(aa_Cod4161879620478718930nteger(aTP_Lamm_ms,K),aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(I),J)) = aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,I),K)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,J),K)) ).

% image_add_atLeastLessThan'
tff(fact_4803_image__add__atLeastLessThan_H,axiom,
    ! [K: int,I: int,J: int] : aa_set_int_set_int(image_int_int(aa_int_fun_int_int(aTP_Lamm_mq,K)),aa_int_set_int(set_or4662586982721622107an_int(I),J)) = aa_int_set_int(set_or4662586982721622107an_int(aa_int_int(aa_int_fun_int_int(plus_plus_int,I),K)),aa_int_int(aa_int_fun_int_int(plus_plus_int,J),K)) ).

% image_add_atLeastLessThan'
tff(fact_4804_drop__bit__of__1,axiom,
    ! [N2: nat] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se3928097537394005634nteger,N2),one_one_Code_integer) = aa_o_Code_integer(zero_n356916108424825756nteger,N2 = zero_zero_nat) ).

% drop_bit_of_1
tff(fact_4805_drop__bit__of__1,axiom,
    ! [N2: nat] : aa_int_int(aa_nat_fun_int_int(bit_se8568078237143864401it_int,N2),one_one_int) = aa_o_int(zero_n2684676970156552555ol_int,N2 = zero_zero_nat) ).

% drop_bit_of_1
tff(fact_4806_drop__bit__of__1,axiom,
    ! [N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se8570568707652914677it_nat,N2),one_one_nat) = aa_o_nat(zero_n2687167440665602831ol_nat,N2 = zero_zero_nat) ).

% drop_bit_of_1
tff(fact_4807_drop__bit__of__1,axiom,
    ! [N2: nat] : aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se2751692689150723149atural,N2),one_one_Code_natural) = zero_n8403883297036319079atural(N2 = zero_zero_nat) ).

% drop_bit_of_1
tff(fact_4808_image__mult__atLeastAtMost,axiom,
    ! [D2: rat,A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),D2)
     => ( image_rat_rat(aa_rat_fun_rat_rat(times_times_rat,D2),set_or633870826150836451st_rat(A,B)) = set_or633870826150836451st_rat(aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,D2),A),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,D2),B)) ) ) ).

% image_mult_atLeastAtMost
tff(fact_4809_image__divide__atLeastAtMost,axiom,
    ! [D2: rat,A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),D2)
     => ( image_rat_rat(aTP_Lamm_mw(D2),set_or633870826150836451st_rat(A,B)) = set_or633870826150836451st_rat(aa_rat_rat(divide_divide_rat(A),D2),aa_rat_rat(divide_divide_rat(B),D2)) ) ) ).

% image_divide_atLeastAtMost
tff(fact_4810_drop__bit__integer_Orep__eq,axiom,
    ! [X2: nat,Xa: code_integer] : aa_Code_integer_int(code_int_of_integer,aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se3928097537394005634nteger,X2),Xa)) = aa_int_int(aa_nat_fun_int_int(bit_se8568078237143864401it_int,X2),aa_Code_integer_int(code_int_of_integer,Xa)) ).

% drop_bit_integer.rep_eq
tff(fact_4811_drop__bit__integer_Oabs__eq,axiom,
    ! [Xa: nat,X2: int] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se3928097537394005634nteger,Xa),aa_int_Code_integer(code_integer_of_int,X2)) = aa_int_Code_integer(code_integer_of_int,aa_int_int(aa_nat_fun_int_int(bit_se8568078237143864401it_int,Xa),X2)) ).

% drop_bit_integer.abs_eq
tff(fact_4812_max__add__distrib__left,axiom,
    ! [X2: rat,Y: rat,Z: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(ord_max_rat(X2),Y)),Z) = aa_rat_rat(ord_max_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),Z)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,Y),Z)) ).

% max_add_distrib_left
tff(fact_4813_max__add__distrib__left,axiom,
    ! [X2: int,Y: int,Z: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(ord_max_int,X2),Y)),Z) = aa_int_int(aa_int_fun_int_int(ord_max_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),Z)),aa_int_int(aa_int_fun_int_int(plus_plus_int,Y),Z)) ).

% max_add_distrib_left
tff(fact_4814_max__add__distrib__left,axiom,
    ! [X2: nat,Y: nat,Z: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(ord_max_nat,X2),Y)),Z) = aa_nat_nat(aa_nat_fun_nat_nat(ord_max_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X2),Z)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Y),Z)) ).

% max_add_distrib_left
tff(fact_4815_max__add__distrib__left,axiom,
    ! [X2: code_integer,Y: code_integer,Z: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_max_Code_integer,X2),Y)),Z) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_max_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X2),Z)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,Y),Z)) ).

% max_add_distrib_left
tff(fact_4816_max__add__distrib__left,axiom,
    ! [X2: code_natural,Y: code_natural,Z: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(ord_max_Code_natural(X2),Y)),Z) = aa_Cod4272041906116450446atural(ord_max_Code_natural(aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,X2),Z)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,Y),Z)) ).

% max_add_distrib_left
tff(fact_4817_max__add__distrib__right,axiom,
    ! [X2: rat,Y: rat,Z: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),aa_rat_rat(ord_max_rat(Y),Z)) = aa_rat_rat(ord_max_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),Y)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),Z)) ).

% max_add_distrib_right
tff(fact_4818_max__add__distrib__right,axiom,
    ! [X2: int,Y: int,Z: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),aa_int_int(aa_int_fun_int_int(ord_max_int,Y),Z)) = aa_int_int(aa_int_fun_int_int(ord_max_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),Y)),aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),Z)) ).

% max_add_distrib_right
tff(fact_4819_max__add__distrib__right,axiom,
    ! [X2: nat,Y: nat,Z: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X2),aa_nat_nat(aa_nat_fun_nat_nat(ord_max_nat,Y),Z)) = aa_nat_nat(aa_nat_fun_nat_nat(ord_max_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X2),Y)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X2),Z)) ).

% max_add_distrib_right
tff(fact_4820_max__add__distrib__right,axiom,
    ! [X2: code_integer,Y: code_integer,Z: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_max_Code_integer,Y),Z)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_max_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X2),Y)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X2),Z)) ).

% max_add_distrib_right
tff(fact_4821_max__add__distrib__right,axiom,
    ! [X2: code_natural,Y: code_natural,Z: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,X2),aa_Cod4272041906116450446atural(ord_max_Code_natural(Y),Z)) = aa_Cod4272041906116450446atural(ord_max_Code_natural(aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,X2),Y)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,X2),Z)) ).

% max_add_distrib_right
tff(fact_4822_max__diff__distrib__left,axiom,
    ! [X2: code_integer,Y: code_integer,Z: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_max_Code_integer,X2),Y)),Z) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_max_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,X2),Z)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,Y),Z)) ).

% max_diff_distrib_left
tff(fact_4823_max__diff__distrib__left,axiom,
    ! [X2: rat,Y: rat,Z: rat] : aa_rat_rat(minus_minus_rat(aa_rat_rat(ord_max_rat(X2),Y)),Z) = aa_rat_rat(ord_max_rat(aa_rat_rat(minus_minus_rat(X2),Z)),aa_rat_rat(minus_minus_rat(Y),Z)) ).

% max_diff_distrib_left
tff(fact_4824_max__diff__distrib__left,axiom,
    ! [X2: int,Y: int,Z: int] : aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(aa_int_fun_int_int(ord_max_int,X2),Y)),Z) = aa_int_int(aa_int_fun_int_int(ord_max_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,X2),Z)),aa_int_int(aa_int_fun_int_int(minus_minus_int,Y),Z)) ).

% max_diff_distrib_left
tff(fact_4825_translation__Compl,axiom,
    ! [A: rat,T: set_rat] : image_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),uminus2201863774496077783et_rat(T)) = uminus2201863774496077783et_rat(image_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),T)) ).

% translation_Compl
tff(fact_4826_translation__Compl,axiom,
    ! [A: int,T: set_int] : aa_set_int_set_int(image_int_int(aa_int_fun_int_int(plus_plus_int,A)),uminus1532241313380277803et_int(T)) = uminus1532241313380277803et_int(aa_set_int_set_int(image_int_int(aa_int_fun_int_int(plus_plus_int,A)),T)) ).

% translation_Compl
tff(fact_4827_nat__add__max__right,axiom,
    ! [M: nat,N2: nat,Q3: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(ord_max_nat,N2),Q3)) = aa_nat_nat(aa_nat_fun_nat_nat(ord_max_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),Q3)) ).

% nat_add_max_right
tff(fact_4828_nat__add__max__left,axiom,
    ! [M: nat,N2: nat,Q3: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(ord_max_nat,M),N2)),Q3) = aa_nat_nat(aa_nat_fun_nat_nat(ord_max_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),Q3)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),Q3)) ).

% nat_add_max_left
tff(fact_4829_image__eq__imp__comp,axiom,
    ! [F: fun_num_Code_integer,A2: set_num,G: fun_num_Code_integer,B4: set_num,Ha: fun_Co8499238673658658103nteger] :
      ( ( image_8379761247532268670nteger(F,A2) = image_8379761247532268670nteger(G,B4) )
     => ( image_8379761247532268670nteger(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,Ha),F),A2) = image_8379761247532268670nteger(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,Ha),G),B4) ) ) ).

% image_eq_imp_comp
tff(fact_4830_image__eq__imp__comp,axiom,
    ! [F: fun_int_nat,A2: set_int,G: fun_int_nat,B4: set_int,Ha: fun_nat_num] :
      ( ( image_int_nat(F,A2) = image_int_nat(G,B4) )
     => ( image_int_num(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,Ha),F),A2) = image_int_num(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,Ha),G),B4) ) ) ).

% image_eq_imp_comp
tff(fact_4831_image__eq__imp__comp,axiom,
    ! [F: fun_num_Code_integer,A2: set_num,G: fun_nat_Code_integer,B4: set_nat,Ha: fun_Co8499238673658658103nteger] :
      ( ( image_8379761247532268670nteger(F,A2) = image_1215581382706833972nteger(G,B4) )
     => ( image_8379761247532268670nteger(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,Ha),F),A2) = image_1215581382706833972nteger(comp_C6974050283906349679er_nat(Ha,G),B4) ) ) ).

% image_eq_imp_comp
tff(fact_4832_image__eq__imp__comp,axiom,
    ! [F: fun_int_Code_integer,A2: set_int,G: fun_nat_Code_integer,B4: set_nat,Ha: fun_Code_integer_int] :
      ( ( image_1587234942943678608nteger(F,A2) = image_1215581382706833972nteger(G,B4) )
     => ( aa_set_int_set_int(image_int_int(comp_C5046419837055054490nt_int(Ha,F)),A2) = image_nat_int(comp_C5048910307564104766nt_nat(Ha,G),B4) ) ) ).

% image_eq_imp_comp
tff(fact_4833_image__eq__imp__comp,axiom,
    ! [F: fun_int_nat,A2: set_int,G: fun_nat_nat,B4: set_nat,Ha: fun_nat_num] :
      ( ( image_int_nat(F,A2) = aa_set_nat_set_nat(image_nat_nat(G),B4) )
     => ( image_int_num(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,Ha),F),A2) = image_nat_num(comp_nat_num_nat(Ha,G),B4) ) ) ).

% image_eq_imp_comp
tff(fact_4834_image__eq__imp__comp,axiom,
    ! [F: fun_int_nat,A2: set_int,G: fun_nat_nat,B4: set_nat,Ha: fun_nat_int] :
      ( ( image_int_nat(F,A2) = aa_set_nat_set_nat(image_nat_nat(G),B4) )
     => ( aa_set_int_set_int(image_int_int(comp_nat_int_int(Ha,F)),A2) = image_nat_int(comp_nat_int_nat(Ha,G),B4) ) ) ).

% image_eq_imp_comp
tff(fact_4835_image__eq__imp__comp,axiom,
    ! [F: fun_nat_Code_integer,A2: set_nat,G: fun_num_Code_integer,B4: set_num,Ha: fun_Co8499238673658658103nteger] :
      ( ( image_1215581382706833972nteger(F,A2) = image_8379761247532268670nteger(G,B4) )
     => ( image_1215581382706833972nteger(comp_C6974050283906349679er_nat(Ha,F),A2) = image_8379761247532268670nteger(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,Ha),G),B4) ) ) ).

% image_eq_imp_comp
tff(fact_4836_image__eq__imp__comp,axiom,
    ! [F: fun_nat_Code_integer,A2: set_nat,G: fun_int_Code_integer,B4: set_int,Ha: fun_Code_integer_int] :
      ( ( image_1215581382706833972nteger(F,A2) = image_1587234942943678608nteger(G,B4) )
     => ( image_nat_int(comp_C5048910307564104766nt_nat(Ha,F),A2) = aa_set_int_set_int(image_int_int(comp_C5046419837055054490nt_int(Ha,G)),B4) ) ) ).

% image_eq_imp_comp
tff(fact_4837_image__eq__imp__comp,axiom,
    ! [F: fun_nat_Code_integer,A2: set_nat,G: fun_nat_Code_integer,B4: set_nat,Ha: fun_Co8499238673658658103nteger] :
      ( ( image_1215581382706833972nteger(F,A2) = image_1215581382706833972nteger(G,B4) )
     => ( image_1215581382706833972nteger(comp_C6974050283906349679er_nat(Ha,F),A2) = image_1215581382706833972nteger(comp_C6974050283906349679er_nat(Ha,G),B4) ) ) ).

% image_eq_imp_comp
tff(fact_4838_image__eq__imp__comp,axiom,
    ! [F: fun_nat_Code_integer,A2: set_nat,G: fun_nat_Code_integer,B4: set_nat,Ha: fun_Code_integer_nat] :
      ( ( image_1215581382706833972nteger(F,A2) = image_1215581382706833972nteger(G,B4) )
     => ( aa_set_nat_set_nat(image_nat_nat(comp_C4049556595663050210at_nat(Ha,F)),A2) = aa_set_nat_set_nat(image_nat_nat(comp_C4049556595663050210at_nat(Ha,G)),B4) ) ) ).

% image_eq_imp_comp
tff(fact_4839_image__comp,axiom,
    ! [F: fun_Co8499238673658658103nteger,G: fun_num_Code_integer,R2: set_num] : image_4470545334726330049nteger(F,image_8379761247532268670nteger(G,R2)) = image_8379761247532268670nteger(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),G),R2) ).

% image_comp
tff(fact_4840_image__comp,axiom,
    ! [F: fun_nat_num,G: fun_int_nat,R2: set_int] : image_nat_num(F,image_int_nat(G,R2)) = image_int_num(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),G),R2) ).

% image_comp
tff(fact_4841_image__comp,axiom,
    ! [F: fun_Co8499238673658658103nteger,G: fun_nat_Code_integer,R2: set_nat] : image_4470545334726330049nteger(F,image_1215581382706833972nteger(G,R2)) = image_1215581382706833972nteger(comp_C6974050283906349679er_nat(F,G),R2) ).

% image_comp
tff(fact_4842_image__comp,axiom,
    ! [F: fun_Code_integer_nat,G: fun_nat_Code_integer,R2: set_nat] : image_951025933927791156er_nat(F,image_1215581382706833972nteger(G,R2)) = aa_set_nat_set_nat(image_nat_nat(comp_C4049556595663050210at_nat(F,G)),R2) ).

% image_comp
tff(fact_4843_image__comp,axiom,
    ! [F: fun_Code_integer_int,G: fun_nat_Code_integer,R2: set_nat] : image_948535463418740880er_int(F,image_1215581382706833972nteger(G,R2)) = image_nat_int(comp_C5048910307564104766nt_nat(F,G),R2) ).

% image_comp
tff(fact_4844_image__comp,axiom,
    ! [F: fun_int_Code_integer,G: fun_nat_int,R2: set_nat] : image_1587234942943678608nteger(F,image_nat_int(G,R2)) = image_1215581382706833972nteger(comp_i1588355021709917246er_nat(F,G),R2) ).

% image_comp
tff(fact_4845_image__comp,axiom,
    ! [F: fun_int_nat,G: fun_nat_int,R2: set_nat] : image_int_nat(F,image_nat_int(G,R2)) = aa_set_nat_set_nat(image_nat_nat(comp_int_nat_nat(F,G)),R2) ).

% image_comp
tff(fact_4846_image__comp,axiom,
    ! [F: fun_nat_Code_integer,G: fun_nat_nat,R2: set_nat] : image_1215581382706833972nteger(F,aa_set_nat_set_nat(image_nat_nat(G),R2)) = image_1215581382706833972nteger(comp_n3898172953802868194er_nat(F,G),R2) ).

% image_comp
tff(fact_4847_image__comp,axiom,
    ! [F: fun_nat_nat,G: fun_nat_nat,R2: set_nat] : aa_set_nat_set_nat(image_nat_nat(F),aa_set_nat_set_nat(image_nat_nat(G),R2)) = aa_set_nat_set_nat(image_nat_nat(comp_nat_nat_nat(F,G)),R2) ).

% image_comp
tff(fact_4848_image__comp,axiom,
    ! [F: fun_nat_int,G: fun_int_nat,R2: set_int] : image_nat_int(F,image_int_nat(G,R2)) = aa_set_int_set_int(image_int_int(comp_nat_int_int(F,G)),R2) ).

% image_comp
tff(fact_4849_map__fun__def,axiom,
    ! [F: fun_Co8499238673658658103nteger,G: fun_Co1561183069634336733nteger,Ha: fun_Co8499238673658658103nteger] : map_fu5403962169733074228nteger(F,G,Ha) = aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,G),Ha)),F) ).

% map_fun_def
tff(fact_4850_map__fun__def,axiom,
    ! [F: fun_Co8499238673658658103nteger,G: fun_fu4800041728187187127nteger,Ha: fun_Co1981900195452921617nteger] : map_fu4199360331771201806nteger(F,G,Ha) = aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,comp_f6739083541385432444nteger(G,Ha)),F) ).

% map_fun_def
tff(fact_4851_map__fun__def,axiom,
    ! [F: fun_in4514472496968388910at_nat,G: fun_o_o,Ha: fun_Pr4796943543331071514_nat_o] : aa_fun1490936263268389485_int_o(map_fu4826362097070443709at_o_o(F,G),Ha) = comp_P1289042343629989734_o_int(aa_fun359341089595923442_nat_o(comp_o8022916681612831582at_nat(G),Ha),F) ).

% map_fun_def
tff(fact_4852_map__fun__def,axiom,
    ! [F: fun_in4514472496968388910at_nat,G: fun_fu3064074204415222357nt_int,Ha: fun_Pr2477239776880934807at_nat] : map_fu8294830438409148311nt_int(F,G,Ha) = comp_P1001692864575718241nt_int(comp_f6758108398856490500at_nat(G,Ha),F) ).

% map_fun_def
tff(fact_4853_map__fun__def,axiom,
    ! [F: fun_in4514472496968388910at_nat,G: fun_fu7075445697382584196_int_o,Ha: fun_Pr2028404973800837934_nat_o] : map_fu3191548434056052140_int_o(F,G,Ha) = comp_P2528745837942451219_o_int(comp_f803626508496913273at_nat(G,Ha),F) ).

% map_fun_def
tff(fact_4854_map__fun__def,axiom,
    ! [F: fun_int_int,G: fun_Pr1652463973008025892nt_rat,Ha: fun_in4211310926729683942nt_int] : aa_fun1809696235935464875nt_rat(map_fu3424225382358772769nt_rat(F,G),Ha) = comp_int_rat_int(aa_fun1809696235935464875nt_rat(comp_P5335556815845735580at_int(G),Ha),F) ).

% map_fun_def
tff(fact_4855_map__fun__def,axiom,
    ! [F: fun_int_int,G: fun_fu7460908759652350970nt_rat,Ha: fun_in1696471567231710611nt_int] : map_fu7945985449245211511nt_rat(F,G,Ha) = aa_fun2021421678210538301nt_rat(aa_fun3093514174373113060nt_rat(comp_i2769097025877698878at_int,comp_f5638830786481540082at_int(G,Ha)),F) ).

% map_fun_def
tff(fact_4856_map__fun_Ocompositionality,axiom,
    ! [F: fun_num_Code_integer,G: fun_Co8499238673658658103nteger,Ha: fun_Co8499238673658658103nteger,I: fun_num_Code_integer,Fun: fun_Code_integer_num] : aa_fun4882090679079481449nteger(map_fu5269526691104299083nteger(F,G),aa_fun8156166258484938729nteger(map_fu603974984455542859nteger(Ha,I),Fun)) = aa_fun7431108047665086886nteger(map_fu8223014087597717000nteger(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,Ha),F),aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),I)),Fun) ).

% map_fun.compositionality
tff(fact_4857_map__fun_Ocompositionality,axiom,
    ! [F: fun_num_Code_integer,G: fun_nat_num,Ha: fun_Co8499238673658658103nteger,I: fun_int_nat,Fun: fun_Code_integer_int] : aa_fun546377469102339993um_num(map_fu7479816331989151099at_num(F,G),aa_fun7469330169275180270er_nat(map_fu5423760287386111952nt_nat(Ha,I),Fun)) = aa_fun4497822097518049269um_num(map_fu8479170043890205655nt_num(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,Ha),F),aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,G),I)),Fun) ).

% map_fun.compositionality
tff(fact_4858_map__fun_Ocompositionality,axiom,
    ! [F: fun_int_nat,G: fun_Co8499238673658658103nteger,Ha: fun_nat_num,I: fun_num_Code_integer,Fun: fun_num_num] : aa_fun960730347150118382nteger(map_fu1717202910479192016nteger(F,G),aa_fun3342615978627461913nteger(map_fu1090464068875036027nteger(Ha,I),Fun)) = aa_fun3714269538864306549nteger(map_fu229184005524548567nteger(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,Ha),F),aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),I)),Fun) ).

% map_fun.compositionality
tff(fact_4859_map__fun_Ocompositionality,axiom,
    ! [F: fun_int_nat,G: fun_nat_num,Ha: fun_nat_num,I: fun_int_nat,Fun: fun_num_int] : aa_fun7499047162063484190nt_num(map_fu3669222299741785344at_num(F,G),aa_fun6377295008136452126at_nat(map_fu8361869985550671104nt_nat(Ha,I),Fun)) = aa_fun8084892656986344388nt_num(map_fu2609383839613498790nt_num(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,Ha),F),aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,G),I)),Fun) ).

% map_fun.compositionality
tff(fact_4860_map__fun_Ocompositionality,axiom,
    ! [F: fun_int_int,G: fun_o_o,Ha: fun_in4514472496968388910at_nat,I: fun_o_o,Fun: fun_Pr4796943543331071514_nat_o] : aa_fun6243517787477317628_int_o(map_fun_int_int_o_o(F,G),aa_fun1490936263268389485_int_o(map_fu4826362097070443709at_o_o(Ha,I),Fun)) = aa_fun1490936263268389485_int_o(map_fu4826362097070443709at_o_o(comp_i1108739374719436894at_int(Ha,F),comp_o_o_o(G,I)),Fun) ).

% map_fun.compositionality
tff(fact_4861_map__fun_Ocompositionality,axiom,
    ! [F: fun_int_int,G: fun_rat_rat,Ha: fun_int_int,I: fun_Pr1652463973008025892nt_rat,Fun: fun_in4211310926729683942nt_int] : aa_fun1481061427733998144nt_rat(map_fu6531859369801489698at_rat(F,G),aa_fun1809696235935464875nt_rat(map_fu3424225382358772769nt_rat(Ha,I),Fun)) = aa_fun1809696235935464875nt_rat(map_fu3424225382358772769nt_rat(aa_fun6280345759651049192nt_int(comp_int_int_int(Ha),F),comp_r4727614531642239972nt_int(G,I)),Fun) ).

% map_fun.compositionality
tff(fact_4862_map__fun_Ocompositionality,axiom,
    ! [F: fun_in4514472496968388910at_nat,G: fun_o_o,Ha: fun_Pr2118491707810114563at_nat,I: fun_o_o,Fun: fun_Pr4796943543331071514_nat_o] : aa_fun1490936263268389485_int_o(map_fu4826362097070443709at_o_o(F,G),aa_fun359341089595923442_nat_o(map_fu1707080289169145046at_o_o(Ha,I),Fun)) = aa_fun1490936263268389485_int_o(map_fu4826362097070443709at_o_o(comp_P7428279379633703887at_int(Ha,F),comp_o_o_o(G,I)),Fun) ).

% map_fun.compositionality
tff(fact_4863_map__fun_Ocompositionality,axiom,
    ! [F: fun_int_int,G: fun_Pr1652463973008025892nt_rat,Ha: fun_int_int,I: fun_Pr2478283820680522243nt_int,Fun: fun_in4211310926729683942nt_int] : aa_fun1809696235935464875nt_rat(map_fu3424225382358772769nt_rat(F,G),aa_fun6626262031093723324nt_int(map_fu2180209013632630320nt_int(Ha,I),Fun)) = aa_fun1809696235935464875nt_rat(map_fu3424225382358772769nt_rat(aa_fun6280345759651049192nt_int(comp_int_int_int(Ha),F),comp_P5648219952011055433nt_int(G,I)),Fun) ).

% map_fun.compositionality
tff(fact_4864_map__fun_Ocompositionality,axiom,
    ! [F: fun_num_Code_integer,G: fun_Co1561183069634336733nteger,Ha: fun_Co8499238673658658103nteger,I: fun_Co8499238673658658103nteger,Fun: fun_Co8499238673658658103nteger] : aa_fun4796990323277771791nteger(map_fu1595501404987506033nteger(F,G),aa_fun4435975922079263404nteger(map_fu5082455417554595470nteger(Ha,I),Fun)) = aa_fun4796990323277771791nteger(map_fu1595501404987506033nteger(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,Ha),F),aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,G),I)),Fun) ).

% map_fun.compositionality
tff(fact_4865_map__fun_Ocompositionality,axiom,
    ! [F: fun_Co8499238673658658103nteger,G: fun_Co8499238673658658103nteger,Ha: fun_Co1561183069634336733nteger,I: fun_num_Code_integer,Fun: fun_fu8347129338434488602er_num] : aa_fun4435975922079263404nteger(map_fu5082455417554595470nteger(F,G),aa_fun4497772300331625231nteger(map_fu2459088713202864369nteger(Ha,I),Fun)) = aa_fun4497772300331625231nteger(map_fu2459088713202864369nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,Ha),F),aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),I)),Fun) ).

% map_fun.compositionality
tff(fact_4866_map__fun_Ocomp,axiom,
    ! [F: fun_num_Code_integer,G: fun_Co8499238673658658103nteger,Ha: fun_Co8499238673658658103nteger,I: fun_num_Code_integer] : comp_f6909282360848428676er_num(map_fu5269526691104299083nteger(F,G),map_fu603974984455542859nteger(Ha,I)) = map_fu8223014087597717000nteger(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,Ha),F),aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),I)) ).

% map_fun.comp
tff(fact_4867_map__fun_Ocomp,axiom,
    ! [F: fun_num_Code_integer,G: fun_nat_num,Ha: fun_Co8499238673658658103nteger,I: fun_int_nat] : comp_f2587153255520370886er_int(map_fu7479816331989151099at_num(F,G),map_fu5423760287386111952nt_nat(Ha,I)) = map_fu8479170043890205655nt_num(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,Ha),F),aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,G),I)) ).

% map_fun.comp
tff(fact_4868_map__fun_Ocomp,axiom,
    ! [F: fun_int_nat,G: fun_Co8499238673658658103nteger,Ha: fun_nat_num,I: fun_num_Code_integer] : comp_f6195931460900804550um_num(map_fu1717202910479192016nteger(F,G),map_fu1090464068875036027nteger(Ha,I)) = map_fu229184005524548567nteger(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,Ha),F),aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),I)) ).

% map_fun.comp
tff(fact_4869_map__fun_Ocomp,axiom,
    ! [F: fun_int_nat,G: fun_nat_num,Ha: fun_nat_num,I: fun_int_nat] : comp_f6389250438540085768um_int(map_fu3669222299741785344at_num(F,G),map_fu8361869985550671104nt_nat(Ha,I)) = map_fu2609383839613498790nt_num(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,Ha),F),aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,G),I)) ).

% map_fun.comp
tff(fact_4870_map__fun_Ocomp,axiom,
    ! [F: fun_int_int,G: fun_o_o,Ha: fun_in4514472496968388910at_nat,I: fun_o_o] : comp_f4873873558822606653_nat_o(map_fun_int_int_o_o(F,G),map_fu4826362097070443709at_o_o(Ha,I)) = map_fu4826362097070443709at_o_o(comp_i1108739374719436894at_int(Ha,F),comp_o_o_o(G,I)) ).

% map_fun.comp
tff(fact_4871_map__fun_Ocomp,axiom,
    ! [F: fun_int_int,G: fun_rat_rat,Ha: fun_int_int,I: fun_Pr1652463973008025892nt_rat] : comp_f8575242358056807743nt_int(map_fu6531859369801489698at_rat(F,G),map_fu3424225382358772769nt_rat(Ha,I)) = map_fu3424225382358772769nt_rat(aa_fun6280345759651049192nt_int(comp_int_int_int(Ha),F),comp_r4727614531642239972nt_int(G,I)) ).

% map_fun.comp
tff(fact_4872_map__fun_Ocomp,axiom,
    ! [F: fun_in4514472496968388910at_nat,G: fun_o_o,Ha: fun_Pr2118491707810114563at_nat,I: fun_o_o] : comp_f3219779300056495522_nat_o(map_fu4826362097070443709at_o_o(F,G),map_fu1707080289169145046at_o_o(Ha,I)) = map_fu4826362097070443709at_o_o(comp_P7428279379633703887at_int(Ha,F),comp_o_o_o(G,I)) ).

% map_fun.comp
tff(fact_4873_map__fun_Ocomp,axiom,
    ! [F: fun_int_int,G: fun_Pr1652463973008025892nt_rat,Ha: fun_int_int,I: fun_Pr2478283820680522243nt_int] : comp_f3282907328706250400nt_int(map_fu3424225382358772769nt_rat(F,G),map_fu2180209013632630320nt_int(Ha,I)) = map_fu3424225382358772769nt_rat(aa_fun6280345759651049192nt_int(comp_int_int_int(Ha),F),comp_P5648219952011055433nt_int(G,I)) ).

% map_fun.comp
tff(fact_4874_map__fun_Ocomp,axiom,
    ! [F: fun_num_Code_integer,G: fun_Co1561183069634336733nteger,Ha: fun_Co8499238673658658103nteger,I: fun_Co8499238673658658103nteger] : comp_f4895884909053068781nteger(map_fu1595501404987506033nteger(F,G),map_fu5082455417554595470nteger(Ha,I)) = map_fu1595501404987506033nteger(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,Ha),F),aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,G),I)) ).

% map_fun.comp
tff(fact_4875_map__fun_Ocomp,axiom,
    ! [F: fun_Co8499238673658658103nteger,G: fun_Co8499238673658658103nteger,Ha: fun_Co1561183069634336733nteger,I: fun_num_Code_integer] : comp_f1360117556308984045er_num(map_fu5082455417554595470nteger(F,G),map_fu2459088713202864369nteger(Ha,I)) = map_fu2459088713202864369nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,Ha),F),aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),I)) ).

% map_fun.comp
tff(fact_4876_translation__subtract__Compl,axiom,
    ! [A: code_integer,T: set_Code_integer] : image_4470545334726330049nteger(aa_Cod4161879620478718930nteger(aTP_Lamm_mv,A),uminus804700908173204444nteger(T)) = uminus804700908173204444nteger(image_4470545334726330049nteger(aa_Cod4161879620478718930nteger(aTP_Lamm_mv,A),T)) ).

% translation_subtract_Compl
tff(fact_4877_translation__subtract__Compl,axiom,
    ! [A: rat,T: set_rat] : image_rat_rat(aTP_Lamm_mt(A),uminus2201863774496077783et_rat(T)) = uminus2201863774496077783et_rat(image_rat_rat(aTP_Lamm_mt(A),T)) ).

% translation_subtract_Compl
tff(fact_4878_translation__subtract__Compl,axiom,
    ! [A: int,T: set_int] : aa_set_int_set_int(image_int_int(aa_int_fun_int_int(aTP_Lamm_mu,A)),uminus1532241313380277803et_int(T)) = uminus1532241313380277803et_int(aa_set_int_set_int(image_int_int(aa_int_fun_int_int(aTP_Lamm_mu,A)),T)) ).

% translation_subtract_Compl
tff(fact_4879_nat__minus__add__max,axiom,
    ! [N2: nat,M: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),M)),M) = aa_nat_nat(aa_nat_fun_nat_nat(ord_max_nat,N2),M) ).

% nat_minus_add_max
tff(fact_4880_translation__diff,axiom,
    ! [A: rat,S: set_rat,T: set_rat] : image_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),minus_minus_set_rat(S,T)) = minus_minus_set_rat(image_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),S),image_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),T)) ).

% translation_diff
tff(fact_4881_translation__diff,axiom,
    ! [A: int,S: set_int,T: set_int] : aa_set_int_set_int(image_int_int(aa_int_fun_int_int(plus_plus_int,A)),minus_minus_set_int(S,T)) = minus_minus_set_int(aa_set_int_set_int(image_int_int(aa_int_fun_int_int(plus_plus_int,A)),S),aa_set_int_set_int(image_int_int(aa_int_fun_int_int(plus_plus_int,A)),T)) ).

% translation_diff
tff(fact_4882_translation__subtract__diff,axiom,
    ! [A: code_integer,S: set_Code_integer,T: set_Code_integer] : image_4470545334726330049nteger(aa_Cod4161879620478718930nteger(aTP_Lamm_mv,A),minus_2355218937544613996nteger(S,T)) = minus_2355218937544613996nteger(image_4470545334726330049nteger(aa_Cod4161879620478718930nteger(aTP_Lamm_mv,A),S),image_4470545334726330049nteger(aa_Cod4161879620478718930nteger(aTP_Lamm_mv,A),T)) ).

% translation_subtract_diff
tff(fact_4883_translation__subtract__diff,axiom,
    ! [A: rat,S: set_rat,T: set_rat] : image_rat_rat(aTP_Lamm_mt(A),minus_minus_set_rat(S,T)) = minus_minus_set_rat(image_rat_rat(aTP_Lamm_mt(A),S),image_rat_rat(aTP_Lamm_mt(A),T)) ).

% translation_subtract_diff
tff(fact_4884_translation__subtract__diff,axiom,
    ! [A: int,S: set_int,T: set_int] : aa_set_int_set_int(image_int_int(aa_int_fun_int_int(aTP_Lamm_mu,A)),minus_minus_set_int(S,T)) = minus_minus_set_int(aa_set_int_set_int(image_int_int(aa_int_fun_int_int(aTP_Lamm_mu,A)),S),aa_set_int_set_int(image_int_int(aa_int_fun_int_int(aTP_Lamm_mu,A)),T)) ).

% translation_subtract_diff
tff(fact_4885_take__bit__drop__bit,axiom,
    ! [M: nat,N2: nat,A: code_integer] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,M),aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se3928097537394005634nteger,N2),A)) = aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se3928097537394005634nteger,N2),aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)),A)) ).

% take_bit_drop_bit
tff(fact_4886_take__bit__drop__bit,axiom,
    ! [M: nat,N2: nat,A: int] : aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,M),aa_int_int(aa_nat_fun_int_int(bit_se8568078237143864401it_int,N2),A)) = aa_int_int(aa_nat_fun_int_int(bit_se8568078237143864401it_int,N2),aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)),A)) ).

% take_bit_drop_bit
tff(fact_4887_take__bit__drop__bit,axiom,
    ! [M: nat,N2: nat,A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(bit_se8570568707652914677it_nat,N2),A)) = aa_nat_nat(aa_nat_fun_nat_nat(bit_se8570568707652914677it_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)),A)) ).

% take_bit_drop_bit
tff(fact_4888_take__bit__drop__bit,axiom,
    ! [M: nat,N2: nat,A: code_natural] : aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se569199155075624693atural,M),aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se2751692689150723149atural,N2),A)) = aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se2751692689150723149atural,N2),aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se569199155075624693atural,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)),A)) ).

% take_bit_drop_bit
tff(fact_4889_bit__drop__bit__eq,axiom,
    ! [N2: nat,A: code_integer] : aa_Cod1075288278386115654_nat_o(bit_se9216721137139052372nteger,aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se3928097537394005634nteger,N2),A)) = comp_nat_o_nat(aa_Cod1075288278386115654_nat_o(bit_se9216721137139052372nteger,A),aa_nat_fun_nat_nat(plus_plus_nat,N2)) ).

% bit_drop_bit_eq
tff(fact_4890_bit__drop__bit__eq,axiom,
    ! [N2: nat,A: int] : aa_int_fun_nat_o(bit_se1146084159140164899it_int,aa_int_int(aa_nat_fun_int_int(bit_se8568078237143864401it_int,N2),A)) = comp_nat_o_nat(aa_int_fun_nat_o(bit_se1146084159140164899it_int,A),aa_nat_fun_nat_nat(plus_plus_nat,N2)) ).

% bit_drop_bit_eq
tff(fact_4891_bit__drop__bit__eq,axiom,
    ! [N2: nat,A: nat] : aa_nat_fun_nat_o(bit_se1148574629649215175it_nat,aa_nat_nat(aa_nat_fun_nat_nat(bit_se8570568707652914677it_nat,N2),A)) = comp_nat_o_nat(aa_nat_fun_nat_o(bit_se1148574629649215175it_nat,A),aa_nat_fun_nat_nat(plus_plus_nat,N2)) ).

% bit_drop_bit_eq
tff(fact_4892_bit__drop__bit__eq,axiom,
    ! [N2: nat,A: code_natural] : aa_Cod9120328075896114107_nat_o(bit_se8040316288895769887atural,aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se2751692689150723149atural,N2),A)) = comp_nat_o_nat(aa_Cod9120328075896114107_nat_o(bit_se8040316288895769887atural,A),aa_nat_fun_nat_nat(plus_plus_nat,N2)) ).

% bit_drop_bit_eq
tff(fact_4893_div__push__bit__of__1__eq__drop__bit,axiom,
    ! [A: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,A),aa_nat_nat(aa_nat_fun_nat_nat(bit_se547839408752420682it_nat,N2),one_one_nat)) = aa_nat_nat(aa_nat_fun_nat_nat(bit_se8570568707652914677it_nat,N2),A) ).

% div_push_bit_of_1_eq_drop_bit
tff(fact_4894_div__push__bit__of__1__eq__drop__bit,axiom,
    ! [A: code_integer,N2: nat] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,A),aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se7788150548672797655nteger,N2),one_one_Code_integer)) = aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se3928097537394005634nteger,N2),A) ).

% div_push_bit_of_1_eq_drop_bit
tff(fact_4895_div__push__bit__of__1__eq__drop__bit,axiom,
    ! [A: int,N2: nat] : aa_int_int(aa_int_fun_int_int(divide_divide_int,A),aa_int_int(aa_nat_fun_int_int(bit_se545348938243370406it_int,N2),one_one_int)) = aa_int_int(aa_nat_fun_int_int(bit_se8568078237143864401it_int,N2),A) ).

% div_push_bit_of_1_eq_drop_bit
tff(fact_4896_div__push__bit__of__1__eq__drop__bit,axiom,
    ! [A: code_natural,N2: nat] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,A),aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se6611745700429515170atural,N2),one_one_Code_natural)) = aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se2751692689150723149atural,N2),A) ).

% div_push_bit_of_1_eq_drop_bit
tff(fact_4897_bit__iff__and__drop__bit__eq__1,axiom,
    ! [A: code_integer,N2: nat] :
      ( aa_nat_o(aa_Cod1075288278386115654_nat_o(bit_se9216721137139052372nteger,A),N2)
    <=> ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3949692690581998587nteger,aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se3928097537394005634nteger,N2),A)),one_one_Code_integer) = one_one_Code_integer ) ) ).

% bit_iff_and_drop_bit_eq_1
tff(fact_4898_bit__iff__and__drop__bit__eq__1,axiom,
    ! [A: int,N2: nat] :
      ( aa_nat_o(aa_int_fun_nat_o(bit_se1146084159140164899it_int,A),N2)
    <=> ( aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,aa_int_int(aa_nat_fun_int_int(bit_se8568078237143864401it_int,N2),A)),one_one_int) = one_one_int ) ) ).

% bit_iff_and_drop_bit_eq_1
tff(fact_4899_bit__iff__and__drop__bit__eq__1,axiom,
    ! [A: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(bit_se1148574629649215175it_nat,A),N2)
    <=> ( aa_nat_nat(aa_nat_fun_nat_nat(bit_se727722235901077358nd_nat,aa_nat_nat(aa_nat_fun_nat_nat(bit_se8570568707652914677it_nat,N2),A)),one_one_nat) = one_one_nat ) ) ).

% bit_iff_and_drop_bit_eq_1
tff(fact_4900_bit__iff__and__drop__bit__eq__1,axiom,
    ! [A: code_natural,N2: nat] :
      ( aa_nat_o(aa_Cod9120328075896114107_nat_o(bit_se8040316288895769887atural,A),N2)
    <=> ( aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se2773287842338716102atural,aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se2751692689150723149atural,N2),A)),one_one_Code_natural) = one_one_Code_natural ) ) ).

% bit_iff_and_drop_bit_eq_1
tff(fact_4901_bits__ident,axiom,
    ! [N2: nat,A: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se7788150548672797655nteger,N2),aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se3928097537394005634nteger,N2),A))),aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,N2),A)) = A ).

% bits_ident
tff(fact_4902_bits__ident,axiom,
    ! [N2: nat,A: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_nat_fun_int_int(bit_se545348938243370406it_int,N2),aa_int_int(aa_nat_fun_int_int(bit_se8568078237143864401it_int,N2),A))),aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,N2),A)) = A ).

% bits_ident
tff(fact_4903_bits__ident,axiom,
    ! [N2: nat,A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(bit_se547839408752420682it_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(bit_se8570568707652914677it_nat,N2),A))),aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,N2),A)) = A ).

% bits_ident
tff(fact_4904_bits__ident,axiom,
    ! [N2: nat,A: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se6611745700429515170atural,N2),aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se2751692689150723149atural,N2),A))),aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se569199155075624693atural,N2),A)) = A ).

% bits_ident
tff(fact_4905_slice__eq__mask,axiom,
    ! [N2: nat,M: nat,A: code_integer] : aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se7788150548672797655nteger,N2),aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se1745604003318907178nteger,M),aa_Cod1783974652533396728nteger(aa_nat6383147911832638789nteger(bit_se3928097537394005634nteger,N2),A))) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3949692690581998587nteger,A),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(bit_se3949692690581998587nteger,aa_nat_Code_integer(bit_se2119862282449309892nteger,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2))),aa_Cod1783974652533396728nteger(bit_ri7632146776885996613nteger,aa_nat_Code_integer(bit_se2119862282449309892nteger,N2)))) ).

% slice_eq_mask
tff(fact_4906_slice__eq__mask,axiom,
    ! [N2: nat,M: nat,A: int] : aa_int_int(aa_nat_fun_int_int(bit_se545348938243370406it_int,N2),aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,M),aa_int_int(aa_nat_fun_int_int(bit_se8568078237143864401it_int,N2),A))) = aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,A),aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,aa_nat_int(bit_se2000444600071755411sk_int,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2))),aa_int_int(bit_ri7919022796975470100ot_int,aa_nat_int(bit_se2000444600071755411sk_int,N2)))) ).

% slice_eq_mask
tff(fact_4907_image__add__0,axiom,
    ! [S2: set_Code_integer] : image_4470545334726330049nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,zero_z3403309356797280102nteger),S2) = S2 ).

% image_add_0
tff(fact_4908_image__add__0,axiom,
    ! [S2: set_mu2057375006010111271at_nat] : image_2516384619306764229at_nat(plus_p7104986032573967614at_nat(zero_z1048942125864253310at_nat),S2) = S2 ).

% image_add_0
tff(fact_4909_image__add__0,axiom,
    ! [S2: set_rat] : image_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,zero_zero_rat),S2) = S2 ).

% image_add_0
tff(fact_4910_image__add__0,axiom,
    ! [S2: set_nat] : aa_set_nat_set_nat(image_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat)),S2) = S2 ).

% image_add_0
tff(fact_4911_image__add__0,axiom,
    ! [S2: set_int] : aa_set_int_set_int(image_int_int(aa_int_fun_int_int(plus_plus_int,zero_zero_int)),S2) = S2 ).

% image_add_0
tff(fact_4912_times__int__def,axiom,
    times_times_int = map_fu8294830438409148311nt_int(rep_Integ,map_fu3667384564859982768at_int(rep_Integ,abs_Integ),aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,aTP_Lamm_gd)) ).

% times_int_def
tff(fact_4913_minus__int__def,axiom,
    minus_minus_int = map_fu8294830438409148311nt_int(rep_Integ,map_fu3667384564859982768at_int(rep_Integ,abs_Integ),aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,aTP_Lamm_gb)) ).

% minus_int_def
tff(fact_4914_plus__int__def,axiom,
    plus_plus_int = map_fu8294830438409148311nt_int(rep_Integ,map_fu3667384564859982768at_int(rep_Integ,abs_Integ),aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,aTP_Lamm_fz)) ).

% plus_int_def
tff(fact_4915_rat__minus__code,axiom,
    ! [P2: rat,Q3: rat] : quotient_of(aa_rat_rat(minus_minus_rat(P2),Q3)) = aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,aTP_Lamm_my(Q3)),quotient_of(P2)) ).

% rat_minus_code
tff(fact_4916_rat__plus__code,axiom,
    ! [P2: rat,Q3: rat] : quotient_of(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,P2),Q3)) = aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,aTP_Lamm_na(Q3)),quotient_of(P2)) ).

% rat_plus_code
tff(fact_4917_image__Suc__atLeastAtMost,axiom,
    ! [I: nat,J: nat] : aa_set_nat_set_nat(image_nat_nat(suc),aa_nat_set_nat(set_or1269000886237332187st_nat(I),J)) = aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,I)),aa_nat_nat(suc,J)) ).

% image_Suc_atLeastAtMost
tff(fact_4918_image__Suc__atLeastLessThan,axiom,
    ! [I: nat,J: nat] : aa_set_nat_set_nat(image_nat_nat(suc),aa_nat_set_nat(set_or4665077453230672383an_nat(I),J)) = aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(suc,I)),aa_nat_nat(suc,J)) ).

% image_Suc_atLeastLessThan
tff(fact_4919_in__inv__image,axiom,
    ! [X2: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,R2: set_Pr4329608150637261639at_nat,F: fun_se320340636488258563at_nat] :
      ( member8757157785044589968at_nat(produc2922128104949294807at_nat(X2,Y),inv_im7023619800666061458at_nat(R2,F))
    <=> member8757157785044589968at_nat(produc2922128104949294807at_nat(aa_set8868280134176360700at_nat(F,X2),aa_set8868280134176360700at_nat(F,Y)),R2) ) ).

% in_inv_image
tff(fact_4920_in__inv__image,axiom,
    ! [X2: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,R2: set_Pr1261947904930325089at_nat,F: fun_se4097146774670233028at_nat] :
      ( member8757157785044589968at_nat(produc2922128104949294807at_nat(X2,Y),inv_im6750873321330482877at_nat(R2,F))
    <=> member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_set4749074711808745205at_nat(F,X2)),aa_set4749074711808745205at_nat(F,Y)),R2) ) ).

% in_inv_image
tff(fact_4921_in__inv__image,axiom,
    ! [X2: nat,Y: nat,R2: set_Pr4329608150637261639at_nat,F: fun_na7044673412300895210at_nat] :
      ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X2),Y),inv_im4437241714082187487at_nat(R2,F))
    <=> member8757157785044589968at_nat(produc2922128104949294807at_nat(aa_nat7062706319057040595at_nat(F,X2),aa_nat7062706319057040595at_nat(F,Y)),R2) ) ).

% in_inv_image
tff(fact_4922_in__inv__image,axiom,
    ! [X2: nat,Y: nat,R2: set_Pr1261947904930325089at_nat,F: fun_nat_nat] :
      ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X2),Y),inv_image_nat_nat(R2,F))
    <=> member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_nat_nat(F,X2)),aa_nat_nat(F,Y)),R2) ) ).

% in_inv_image
tff(fact_4923_pair__imageI,axiom,
    ! [A: nat,B: nat,A2: set_Pr1261947904930325089at_nat,F: fun_nat_fun_nat_o] :
      ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B),A2)
     => member_o(aa_nat_o(aa_nat_fun_nat_o(F,A),B),image_3693632289388996572_nat_o(aa_fun7564604662015400456_nat_o(produc6081775807080527818_nat_o,F),A2)) ) ).

% pair_imageI
tff(fact_4924_pair__imageI,axiom,
    ! [A: nat,B: nat,A2: set_Pr1261947904930325089at_nat,F: fun_nat_fun_nat_int] :
      ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B),A2)
     => member_int(aa_nat_int(aa_nat_fun_nat_int(F,A),B),image_2483585944268220136at_int(produc6840382203811409530at_int(F),A2)) ) ).

% pair_imageI
tff(fact_4925_pair__imageI,axiom,
    ! [A: nat,B: nat,A2: set_Pr1261947904930325089at_nat,F: fun_nat_fun_nat_nat] :
      ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B),A2)
     => member_nat(aa_nat_nat(aa_nat_fun_nat_nat(F,A),B),image_2486076414777270412at_nat(aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,F),A2)) ) ).

% pair_imageI
tff(fact_4926_pair__imageI,axiom,
    ! [A: int,B: int,A2: set_Pr958786334691620121nt_int,F: fun_int_fun_int_int] :
      ( member5262025264175285858nt_int(aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A),B),A2)
     => member_int(aa_int_int(aa_int_fun_int_int(F,A),B),image_5042161079198086560nt_int(aa_fun914008879417524284nt_int(produc8211389475949308722nt_int,F),A2)) ) ).

% pair_imageI
tff(fact_4927_pair__imageI,axiom,
    ! [A: nat,B: nat,A2: set_Pr1261947904930325089at_nat,F: fun_na4138050610385705875at_nat] :
      ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B),A2)
     => member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(F,A),B),aa_set8868280134176360700at_nat(image_5168914502847457605at_nat(produc2626176000494625587at_nat(F)),A2)) ) ).

% pair_imageI
tff(fact_4928_pair__imageI,axiom,
    ! [A: int,B: int,A2: set_Pr958786334691620121nt_int,F: fun_in1696471567231710611nt_int] :
      ( member5262025264175285858nt_int(aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A),B),A2)
     => member5262025264175285858nt_int(aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(F,A),B),image_2653370878348428101nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,F),A2)) ) ).

% pair_imageI
tff(fact_4929_pair__imageI,axiom,
    ! [A: nat,B: nat,A2: set_Pr1261947904930325089at_nat,F: fun_na5914473681949881652_nat_o] :
      ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B),A2)
     => member485394258709547313_nat_o(aa_nat7695548938202568488_nat_o(aa_nat4259715169212259317_nat_o(F,A),B),image_2420546460570504406_nat_o(aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,F),A2)) ) ).

% pair_imageI
tff(fact_4930_pair__imageI,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_Pr4329608150637261639at_nat,F: fun_se5639961202347202350_nat_o] :
      ( member8757157785044589968at_nat(produc2922128104949294807at_nat(A,B),A2)
     => member_o(aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(F,A),B),image_3500134854233901558_nat_o(aa_fun762164075915671590_nat_o(produc410239310623530412_nat_o,F),A2)) ) ).

% pair_imageI
tff(fact_4931_pair__imageI,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_Pr4329608150637261639at_nat,F: fun_se7776568131818451942at_nat] :
      ( member8757157785044589968at_nat(produc2922128104949294807at_nat(A,B),A2)
     => member_nat(aa_set4749074711808745205at_nat(aa_set6616311349231096415at_nat(F,A),B),image_3198525501578754290at_nat(produc4001655692221972156at_nat(F),A2)) ) ).

% pair_imageI
tff(fact_4932_pair__imageI,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_Pr4329608150637261639at_nat,F: fun_se5286484986886725186at_int] :
      ( member8757157785044589968at_nat(produc2922128104949294807at_nat(A,B),A2)
     => member_int(aa_set4746584241299694929at_int(aa_set2438460329721899707at_int(F,A),B),image_3196035031069704014at_int(produc3999165221712921880at_int(F),A2)) ) ).

% pair_imageI
tff(fact_4933_int__of__integer__max,axiom,
    ! [K: code_integer,L: code_integer] : aa_Code_integer_int(code_int_of_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_max_Code_integer,K),L)) = aa_int_int(aa_int_fun_int_int(ord_max_int,aa_Code_integer_int(code_int_of_integer,K)),aa_Code_integer_int(code_int_of_integer,L)) ).

% int_of_integer_max
tff(fact_4934_rat__one__code,axiom,
    quotient_of(one_one_rat) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,one_one_int),one_one_int) ).

% rat_one_code
tff(fact_4935_of__nat__of__integer,axiom,
    ! [K: code_integer] : aa_nat_Code_integer(semiri4939895301339042750nteger,aa_Code_integer_nat(code_nat_of_integer,K)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_max_Code_integer,zero_z3403309356797280102nteger),K) ).

% of_nat_of_integer
tff(fact_4936_rat__zero__code,axiom,
    quotient_of(zero_zero_rat) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,zero_zero_int),one_one_int) ).

% rat_zero_code
tff(fact_4937_quotient__of__number_I3_J,axiom,
    ! [K: num] : quotient_of(aa_num_rat(numeral_numeral_rat,K)) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_num_int(numeral_numeral_int,K)),one_one_int) ).

% quotient_of_number(3)
tff(fact_4938_quotient__of__number_I4_J,axiom,
    quotient_of(aa_rat_rat(uminus_uminus_rat,one_one_rat)) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_int_int(uminus_uminus_int,one_one_int)),one_one_int) ).

% quotient_of_number(4)
tff(fact_4939_quotient__of__number_I5_J,axiom,
    ! [K: num] : quotient_of(aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,K))) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,K))),one_one_int) ).

% quotient_of_number(5)
tff(fact_4940_diff__rat__def,axiom,
    ! [Q3: rat,R2: rat] : aa_rat_rat(minus_minus_rat(Q3),R2) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,Q3),aa_rat_rat(uminus_uminus_rat,R2)) ).

% diff_rat_def
tff(fact_4941_quotient__of__div,axiom,
    ! [R2: rat,N2: int,D2: int] :
      ( ( quotient_of(R2) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,N2),D2) )
     => ( R2 = aa_rat_rat(divide_divide_rat(aa_int_rat(ring_1_of_int_rat,N2)),aa_int_rat(ring_1_of_int_rat,D2)) ) ) ).

% quotient_of_div
tff(fact_4942_zero__notin__Suc__image,axiom,
    ! [A2: set_nat] : ~ member_nat(zero_zero_nat,aa_set_nat_set_nat(image_nat_nat(suc),A2)) ).

% zero_notin_Suc_image
tff(fact_4943_None__notin__image__Some,axiom,
    ! [A2: set_Pr5142436192348053284it_nat] : ~ member3517700364412436275it_nat(none_P2587165478634041381it_nat,image_4799632500972785611it_nat(some_P6105628898608307625it_nat,A2)) ).

% None_notin_image_Some
tff(fact_4944_None__notin__image__Some,axiom,
    ! [A2: set_num] : ~ member_option_num(none_num,image_num_option_num(some_num,A2)) ).

% None_notin_image_Some
tff(fact_4945_None__notin__image__Some,axiom,
    ! [A2: set_Pr1354866905816374718it_nat] : ~ member5596548051065438575it_nat(none_P9117596204409417319it_nat,image_3455408117458022631it_nat(some_P1914260805536162275it_nat,A2)) ).

% None_notin_image_Some
tff(fact_4946_plus__integer__def,axiom,
    plus_p5714425477246183910nteger = map_fu1034890151506530863nteger(code_int_of_integer,map_fu2599414010547811884nteger(code_int_of_integer,code_integer_of_int),plus_plus_int) ).

% plus_integer_def
tff(fact_4947_times__integer__def,axiom,
    times_3573771949741848930nteger = map_fu1034890151506530863nteger(code_int_of_integer,map_fu2599414010547811884nteger(code_int_of_integer,code_integer_of_int),times_times_int) ).

% times_integer_def
tff(fact_4948_minus__integer__def,axiom,
    minus_8373710615458151222nteger = map_fu1034890151506530863nteger(code_int_of_integer,map_fu2599414010547811884nteger(code_int_of_integer,code_integer_of_int),minus_minus_int) ).

% minus_integer_def
tff(fact_4949_divide__integer__def,axiom,
    divide6298287555418463151nteger = map_fu1034890151506530863nteger(code_int_of_integer,map_fu2599414010547811884nteger(code_int_of_integer,code_integer_of_int),divide_divide_int) ).

% divide_integer_def
tff(fact_4950_modulo__integer__def,axiom,
    modulo364778990260209775nteger = map_fu1034890151506530863nteger(code_int_of_integer,map_fu2599414010547811884nteger(code_int_of_integer,code_integer_of_int),modulo_modulo_int) ).

% modulo_integer_def
tff(fact_4951_and__integer__def,axiom,
    bit_se3949692690581998587nteger = map_fu1034890151506530863nteger(code_int_of_integer,map_fu2599414010547811884nteger(code_int_of_integer,code_integer_of_int),bit_se725231765392027082nd_int) ).

% and_integer_def
tff(fact_4952_or__integer__def,axiom,
    bit_se1080825931792720795nteger = map_fu1034890151506530863nteger(code_int_of_integer,map_fu2599414010547811884nteger(code_int_of_integer,code_integer_of_int),bit_se1409905431419307370or_int) ).

% or_integer_def
tff(fact_4953_xor__integer__def,axiom,
    bit_se3222712562003087583nteger = map_fu1034890151506530863nteger(code_int_of_integer,map_fu2599414010547811884nteger(code_int_of_integer,code_integer_of_int),bit_se6526347334894502574or_int) ).

% xor_integer_def
tff(fact_4954_image__int__atLeastAtMost,axiom,
    ! [A: nat,B: nat] : image_nat_int(semiri1314217659103216013at_int,aa_nat_set_nat(set_or1269000886237332187st_nat(A),B)) = aa_int_set_int(set_or1266510415728281911st_int(aa_nat_int(semiri1314217659103216013at_int,A)),aa_nat_int(semiri1314217659103216013at_int,B)) ).

% image_int_atLeastAtMost
tff(fact_4955_image__int__atLeastLessThan,axiom,
    ! [A: nat,B: nat] : image_nat_int(semiri1314217659103216013at_int,aa_nat_set_nat(set_or4665077453230672383an_nat(A),B)) = aa_int_set_int(set_or4662586982721622107an_int(aa_nat_int(semiri1314217659103216013at_int,A)),aa_nat_int(semiri1314217659103216013at_int,B)) ).

% image_int_atLeastLessThan
tff(fact_4956_quotient__of__denom__pos,axiom,
    ! [R2: rat,P2: int,Q3: int] :
      ( ( quotient_of(R2) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,P2),Q3) )
     => aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),Q3) ) ).

% quotient_of_denom_pos
tff(fact_4957_image__Suc__atMost,axiom,
    ! [N2: nat] : aa_set_nat_set_nat(image_nat_nat(suc),aa_nat_set_nat(set_ord_atMost_nat,N2)) = aa_nat_set_nat(set_or1269000886237332187st_nat(one_one_nat),aa_nat_nat(suc,N2)) ).

% image_Suc_atMost
tff(fact_4958_image__Suc__lessThan,axiom,
    ! [N2: nat] : aa_set_nat_set_nat(image_nat_nat(suc),aa_nat_set_nat(set_ord_lessThan_nat,N2)) = aa_nat_set_nat(set_or1269000886237332187st_nat(one_one_nat),N2) ).

% image_Suc_lessThan
tff(fact_4959_rat__uminus__code,axiom,
    ! [P2: rat] : quotient_of(aa_rat_rat(uminus_uminus_rat,P2)) = aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,aTP_Lamm_nb),quotient_of(P2)) ).

% rat_uminus_code
tff(fact_4960_rat__abs__code,axiom,
    ! [P2: rat] : quotient_of(aa_rat_rat(abs_abs_rat,P2)) = aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,aTP_Lamm_nc),quotient_of(P2)) ).

% rat_abs_code
tff(fact_4961_uminus__integer__def,axiom,
    uminus1351360451143612070nteger = aa_fun8964553180794676938nteger(map_fu2599414010547811884nteger(code_int_of_integer,code_integer_of_int),uminus_uminus_int) ).

% uminus_integer_def
tff(fact_4962_abs__integer__def,axiom,
    abs_abs_Code_integer = aa_fun8964553180794676938nteger(map_fu2599414010547811884nteger(code_int_of_integer,code_integer_of_int),abs_abs_int) ).

% abs_integer_def
tff(fact_4963_image__add__int__atLeastLessThan,axiom,
    ! [L: int,U: int] : aa_set_int_set_int(image_int_int(aa_int_fun_int_int(aTP_Lamm_mq,L)),aa_int_set_int(set_or4662586982721622107an_int(zero_zero_int),aa_int_int(aa_int_fun_int_int(minus_minus_int,U),L))) = aa_int_set_int(set_or4662586982721622107an_int(L),U) ).

% image_add_int_atLeastLessThan
tff(fact_4964_sgn__integer__def,axiom,
    sgn_sgn_Code_integer = aa_fun8964553180794676938nteger(map_fu2599414010547811884nteger(code_int_of_integer,code_integer_of_int),sgn_sgn_int) ).

% sgn_integer_def
tff(fact_4965_not__integer__def,axiom,
    bit_ri7632146776885996613nteger = aa_fun8964553180794676938nteger(map_fu2599414010547811884nteger(code_int_of_integer,code_integer_of_int),bit_ri7919022796975470100ot_int) ).

% not_integer_def
tff(fact_4966_image__add__integer__atLeastLessThan,axiom,
    ! [L: code_integer,U: code_integer] : image_4470545334726330049nteger(aa_Cod4161879620478718930nteger(aTP_Lamm_ms,L),aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,U),L))) = aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(L),U) ).

% image_add_integer_atLeastLessThan
tff(fact_4967_rat__times__code,axiom,
    ! [P2: rat,Q3: rat] : quotient_of(aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,P2),Q3)) = aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,aTP_Lamm_ne(Q3)),quotient_of(P2)) ).

% rat_times_code
tff(fact_4968_rat__divide__code,axiom,
    ! [P2: rat,Q3: rat] : quotient_of(aa_rat_rat(divide_divide_rat(P2),Q3)) = aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,aTP_Lamm_ng(Q3)),quotient_of(P2)) ).

% rat_divide_code
tff(fact_4969_image__atLeastZeroLessThan__int,axiom,
    ! [U: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),U)
     => ( aa_int_set_int(set_or4662586982721622107an_int(zero_zero_int),U) = image_nat_int(semiri1314217659103216013at_int,aa_nat_set_nat(set_ord_lessThan_nat,aa_int_nat(nat2,U))) ) ) ).

% image_atLeastZeroLessThan_int
tff(fact_4970_quotient__of__int,axiom,
    ! [A: int] : quotient_of(aa_int_rat(of_int,A)) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A),one_one_int) ).

% quotient_of_int
tff(fact_4971_rat__inverse__code,axiom,
    ! [P2: rat] : quotient_of(aa_rat_rat(inverse_inverse_rat,P2)) = aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,aTP_Lamm_nh),quotient_of(P2)) ).

% rat_inverse_code
tff(fact_4972_diff__numeral__special_I8_J,axiom,
    ! [M: num] : aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,M))),aa_int_int(uminus_uminus_int,one_one_int)) = aa_num_int(neg_numeral_sub_int(one),M) ).

% diff_numeral_special(8)
tff(fact_4973_diff__numeral__special_I8_J,axiom,
    ! [M: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,M))),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) = aa_num_Code_integer(neg_nu5755505904847501662nteger(one),M) ).

% diff_numeral_special(8)
tff(fact_4974_diff__numeral__special_I8_J,axiom,
    ! [M: num] : aa_rat_rat(minus_minus_rat(aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,M))),aa_rat_rat(uminus_uminus_rat,one_one_rat)) = neg_numeral_sub_rat(one,M) ).

% diff_numeral_special(8)
tff(fact_4975_diff__numeral__special_I7_J,axiom,
    ! [N2: num] : aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(uminus_uminus_int,one_one_int)),aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,N2))) = aa_num_int(neg_numeral_sub_int(N2),one) ).

% diff_numeral_special(7)
tff(fact_4976_diff__numeral__special_I7_J,axiom,
    ! [N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,N2))) = aa_num_Code_integer(neg_nu5755505904847501662nteger(N2),one) ).

% diff_numeral_special(7)
tff(fact_4977_diff__numeral__special_I7_J,axiom,
    ! [N2: num] : aa_rat_rat(minus_minus_rat(aa_rat_rat(uminus_uminus_rat,one_one_rat)),aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,N2))) = neg_numeral_sub_rat(N2,one) ).

% diff_numeral_special(7)
tff(fact_4978_minus__sub__one__diff__one,axiom,
    ! [M: num] : aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(uminus_uminus_int,aa_num_int(neg_numeral_sub_int(M),one))),one_one_int) = aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,M)) ).

% minus_sub_one_diff_one
tff(fact_4979_minus__sub__one__diff__one,axiom,
    ! [M: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(neg_nu5755505904847501662nteger(M),one))),one_one_Code_integer) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,M)) ).

% minus_sub_one_diff_one
tff(fact_4980_minus__sub__one__diff__one,axiom,
    ! [M: num] : aa_rat_rat(minus_minus_rat(aa_rat_rat(uminus_uminus_rat,neg_numeral_sub_rat(M,one))),one_one_rat) = aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,M)) ).

% minus_sub_one_diff_one
tff(fact_4981_add__neg__numeral__special_I4_J,axiom,
    ! [N2: num] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(uminus_uminus_int,one_one_int)),aa_num_int(numeral_numeral_int,N2)) = aa_num_int(neg_numeral_sub_int(N2),one) ).

% add_neg_numeral_special(4)
tff(fact_4982_add__neg__numeral__special_I4_J,axiom,
    ! [N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),aa_num_Code_integer(numera6620942414471956472nteger,N2)) = aa_num_Code_integer(neg_nu5755505904847501662nteger(N2),one) ).

% add_neg_numeral_special(4)
tff(fact_4983_add__neg__numeral__special_I4_J,axiom,
    ! [N2: num] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),aa_num_rat(numeral_numeral_rat,N2)) = neg_numeral_sub_rat(N2,one) ).

% add_neg_numeral_special(4)
tff(fact_4984_int__of__integer__sub,axiom,
    ! [K: num,L: num] : aa_Code_integer_int(code_int_of_integer,aa_num_Code_integer(neg_nu5755505904847501662nteger(K),L)) = aa_num_int(neg_numeral_sub_int(K),L) ).

% int_of_integer_sub
tff(fact_4985_inverse__1,axiom,
    aa_rat_rat(inverse_inverse_rat,one_one_rat) = one_one_rat ).

% inverse_1
tff(fact_4986_inverse__eq__1__iff,axiom,
    ! [X2: rat] :
      ( ( aa_rat_rat(inverse_inverse_rat,X2) = one_one_rat )
    <=> ( X2 = one_one_rat ) ) ).

% inverse_eq_1_iff
tff(fact_4987_right__inverse,axiom,
    ! [A: rat] :
      ( ( A != zero_zero_rat )
     => ( aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),aa_rat_rat(inverse_inverse_rat,A)) = one_one_rat ) ) ).

% right_inverse
tff(fact_4988_left__inverse,axiom,
    ! [A: rat] :
      ( ( A != zero_zero_rat )
     => ( aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(inverse_inverse_rat,A)),A) = one_one_rat ) ) ).

% left_inverse
tff(fact_4989_inverse__eq__divide__numeral,axiom,
    ! [W: num] : aa_rat_rat(inverse_inverse_rat,aa_num_rat(numeral_numeral_rat,W)) = aa_rat_rat(divide_divide_rat(one_one_rat),aa_num_rat(numeral_numeral_rat,W)) ).

% inverse_eq_divide_numeral
tff(fact_4990_add__neg__numeral__simps_I2_J,axiom,
    ! [M: num,N2: num] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,M))),aa_num_int(numeral_numeral_int,N2)) = aa_num_int(neg_numeral_sub_int(N2),M) ).

% add_neg_numeral_simps(2)
tff(fact_4991_add__neg__numeral__simps_I2_J,axiom,
    ! [M: num,N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,M))),aa_num_Code_integer(numera6620942414471956472nteger,N2)) = aa_num_Code_integer(neg_nu5755505904847501662nteger(N2),M) ).

% add_neg_numeral_simps(2)
tff(fact_4992_add__neg__numeral__simps_I2_J,axiom,
    ! [M: num,N2: num] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,M))),aa_num_rat(numeral_numeral_rat,N2)) = neg_numeral_sub_rat(N2,M) ).

% add_neg_numeral_simps(2)
tff(fact_4993_add__neg__numeral__simps_I1_J,axiom,
    ! [M: num,N2: num] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_num_int(numeral_numeral_int,M)),aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,N2))) = aa_num_int(neg_numeral_sub_int(M),N2) ).

% add_neg_numeral_simps(1)
tff(fact_4994_add__neg__numeral__simps_I1_J,axiom,
    ! [M: num,N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_num_Code_integer(numera6620942414471956472nteger,M)),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,N2))) = aa_num_Code_integer(neg_nu5755505904847501662nteger(M),N2) ).

% add_neg_numeral_simps(1)
tff(fact_4995_add__neg__numeral__simps_I1_J,axiom,
    ! [M: num,N2: num] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_num_rat(numeral_numeral_rat,M)),aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,N2))) = neg_numeral_sub_rat(M,N2) ).

% add_neg_numeral_simps(1)
tff(fact_4996_semiring__norm_I166_J,axiom,
    ! [V: num,W: num,Y: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_num_int(numeral_numeral_int,V)),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,W))),Y)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_num_int(neg_numeral_sub_int(V),W)),Y) ).

% semiring_norm(166)
tff(fact_4997_semiring__norm_I166_J,axiom,
    ! [V: num,W: num,Y: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_num_Code_integer(numera6620942414471956472nteger,V)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,W))),Y)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_num_Code_integer(neg_nu5755505904847501662nteger(V),W)),Y) ).

% semiring_norm(166)
tff(fact_4998_semiring__norm_I166_J,axiom,
    ! [V: num,W: num,Y: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_num_rat(numeral_numeral_rat,V)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,W))),Y)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,neg_numeral_sub_rat(V,W)),Y) ).

% semiring_norm(166)
tff(fact_4999_semiring__norm_I167_J,axiom,
    ! [V: num,W: num,Y: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,V))),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_num_int(numeral_numeral_int,W)),Y)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_num_int(neg_numeral_sub_int(W),V)),Y) ).

% semiring_norm(167)
tff(fact_5000_semiring__norm_I167_J,axiom,
    ! [V: num,W: num,Y: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,V))),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_num_Code_integer(numera6620942414471956472nteger,W)),Y)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_num_Code_integer(neg_nu5755505904847501662nteger(W),V)),Y) ).

% semiring_norm(167)
tff(fact_5001_semiring__norm_I167_J,axiom,
    ! [V: num,W: num,Y: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,V))),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_num_rat(numeral_numeral_rat,W)),Y)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,neg_numeral_sub_rat(W,V)),Y) ).

% semiring_norm(167)
tff(fact_5002_inverse__eq__divide__neg__numeral,axiom,
    ! [W: num] : aa_rat_rat(inverse_inverse_rat,aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,W))) = aa_rat_rat(divide_divide_rat(one_one_rat),aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,W))) ).

% inverse_eq_divide_neg_numeral
tff(fact_5003_diff__numeral__special_I2_J,axiom,
    ! [M: num] : aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_num_int(numeral_numeral_int,M)),one_one_int) = aa_num_int(neg_numeral_sub_int(M),one) ).

% diff_numeral_special(2)
tff(fact_5004_diff__numeral__special_I2_J,axiom,
    ! [M: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_num_Code_integer(numera6620942414471956472nteger,M)),one_one_Code_integer) = aa_num_Code_integer(neg_nu5755505904847501662nteger(M),one) ).

% diff_numeral_special(2)
tff(fact_5005_diff__numeral__special_I2_J,axiom,
    ! [M: num] : aa_rat_rat(minus_minus_rat(aa_num_rat(numeral_numeral_rat,M)),one_one_rat) = neg_numeral_sub_rat(M,one) ).

% diff_numeral_special(2)
tff(fact_5006_diff__numeral__special_I1_J,axiom,
    ! [N2: num] : aa_int_int(aa_int_fun_int_int(minus_minus_int,one_one_int),aa_num_int(numeral_numeral_int,N2)) = aa_num_int(neg_numeral_sub_int(one),N2) ).

% diff_numeral_special(1)
tff(fact_5007_diff__numeral__special_I1_J,axiom,
    ! [N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,one_one_Code_integer),aa_num_Code_integer(numera6620942414471956472nteger,N2)) = aa_num_Code_integer(neg_nu5755505904847501662nteger(one),N2) ).

% diff_numeral_special(1)
tff(fact_5008_diff__numeral__special_I1_J,axiom,
    ! [N2: num] : aa_rat_rat(minus_minus_rat(one_one_rat),aa_num_rat(numeral_numeral_rat,N2)) = neg_numeral_sub_rat(one,N2) ).

% diff_numeral_special(1)
tff(fact_5009_add__neg__numeral__special_I1_J,axiom,
    ! [M: num] : aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,M))) = aa_num_int(neg_numeral_sub_int(one),M) ).

% add_neg_numeral_special(1)
tff(fact_5010_add__neg__numeral__special_I1_J,axiom,
    ! [M: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,one_one_Code_integer),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,M))) = aa_num_Code_integer(neg_nu5755505904847501662nteger(one),M) ).

% add_neg_numeral_special(1)
tff(fact_5011_add__neg__numeral__special_I1_J,axiom,
    ! [M: num] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,one_one_rat),aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,M))) = neg_numeral_sub_rat(one,M) ).

% add_neg_numeral_special(1)
tff(fact_5012_add__neg__numeral__special_I2_J,axiom,
    ! [M: num] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,M))),one_one_int) = aa_num_int(neg_numeral_sub_int(one),M) ).

% add_neg_numeral_special(2)
tff(fact_5013_add__neg__numeral__special_I2_J,axiom,
    ! [M: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,M))),one_one_Code_integer) = aa_num_Code_integer(neg_nu5755505904847501662nteger(one),M) ).

% add_neg_numeral_special(2)
tff(fact_5014_add__neg__numeral__special_I2_J,axiom,
    ! [M: num] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,M))),one_one_rat) = neg_numeral_sub_rat(one,M) ).

% add_neg_numeral_special(2)
tff(fact_5015_add__neg__numeral__special_I3_J,axiom,
    ! [M: num] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_num_int(numeral_numeral_int,M)),aa_int_int(uminus_uminus_int,one_one_int)) = aa_num_int(neg_numeral_sub_int(M),one) ).

% add_neg_numeral_special(3)
tff(fact_5016_add__neg__numeral__special_I3_J,axiom,
    ! [M: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_num_Code_integer(numera6620942414471956472nteger,M)),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) = aa_num_Code_integer(neg_nu5755505904847501662nteger(M),one) ).

% add_neg_numeral_special(3)
tff(fact_5017_add__neg__numeral__special_I3_J,axiom,
    ! [M: num] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_num_rat(numeral_numeral_rat,M)),aa_rat_rat(uminus_uminus_rat,one_one_rat)) = neg_numeral_sub_rat(M,one) ).

% add_neg_numeral_special(3)
tff(fact_5018_inverse__unique,axiom,
    ! [A: rat,B: rat] :
      ( ( aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,A),B) = one_one_rat )
     => ( aa_rat_rat(inverse_inverse_rat,A) = B ) ) ).

% inverse_unique
tff(fact_5019_inverse__eq__divide,axiom,
    ! [A: rat] : aa_rat_rat(inverse_inverse_rat,A) = aa_rat_rat(divide_divide_rat(one_one_rat),A) ).

% inverse_eq_divide
tff(fact_5020_inverse__le__1__iff,axiom,
    ! [X2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_rat_rat(inverse_inverse_rat,X2)),one_one_rat)
    <=> ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,X2),zero_zero_rat)
        | aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),X2) ) ) ).

% inverse_le_1_iff
tff(fact_5021_one__less__inverse__iff,axiom,
    ! [X2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),aa_rat_rat(inverse_inverse_rat,X2))
    <=> ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),X2)
        & aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,X2),one_one_rat) ) ) ).

% one_less_inverse_iff
tff(fact_5022_one__less__inverse,axiom,
    ! [A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),A)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),one_one_rat)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),aa_rat_rat(inverse_inverse_rat,A)) ) ) ).

% one_less_inverse
tff(fact_5023_division__ring__inverse__add,axiom,
    ! [A: rat,B: rat] :
      ( ( A != zero_zero_rat )
     => ( ( B != zero_zero_rat )
       => ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(inverse_inverse_rat,A)),aa_rat_rat(inverse_inverse_rat,B)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(inverse_inverse_rat,A)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B))),aa_rat_rat(inverse_inverse_rat,B)) ) ) ) ).

% division_ring_inverse_add
tff(fact_5024_inverse__add,axiom,
    ! [A: rat,B: rat] :
      ( ( A != zero_zero_rat )
     => ( ( B != zero_zero_rat )
       => ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(inverse_inverse_rat,A)),aa_rat_rat(inverse_inverse_rat,B)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),B)),aa_rat_rat(inverse_inverse_rat,A))),aa_rat_rat(inverse_inverse_rat,B)) ) ) ) ).

% inverse_add
tff(fact_5025_field__class_Ofield__inverse,axiom,
    ! [A: rat] :
      ( ( A != zero_zero_rat )
     => ( aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(inverse_inverse_rat,A)),A) = one_one_rat ) ) ).

% field_class.field_inverse
tff(fact_5026_nonzero__inverse__eq__divide,axiom,
    ! [A: rat] :
      ( ( A != zero_zero_rat )
     => ( aa_rat_rat(inverse_inverse_rat,A) = aa_rat_rat(divide_divide_rat(one_one_rat),A) ) ) ).

% nonzero_inverse_eq_divide
tff(fact_5027_one__le__inverse__iff,axiom,
    ! [X2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),aa_rat_rat(inverse_inverse_rat,X2))
    <=> ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),X2)
        & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,X2),one_one_rat) ) ) ).

% one_le_inverse_iff
tff(fact_5028_inverse__less__1__iff,axiom,
    ! [X2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(inverse_inverse_rat,X2)),one_one_rat)
    <=> ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,X2),zero_zero_rat)
        | aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),X2) ) ) ).

% inverse_less_1_iff
tff(fact_5029_one__le__inverse,axiom,
    ! [A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),A)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),one_one_rat)
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),aa_rat_rat(inverse_inverse_rat,A)) ) ) ).

% one_le_inverse
tff(fact_5030_Frct__code__post_I5_J,axiom,
    ! [K: num] : aa_Pro6166618844887768661nt_rat(frct,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,one_one_int),aa_num_int(numeral_numeral_int,K))) = aa_rat_rat(divide_divide_rat(one_one_rat),aa_num_rat(numeral_numeral_rat,K)) ).

% Frct_code_post(5)
tff(fact_5031_Code__Numeral_Odup__def,axiom,
    code_dup = aa_fun8964553180794676938nteger(map_fu2599414010547811884nteger(code_int_of_integer,code_integer_of_int),aTP_Lamm_ni) ).

% Code_Numeral.dup_def
tff(fact_5032_Frct__code__post_I6_J,axiom,
    ! [K: num,L: num] : aa_Pro6166618844887768661nt_rat(frct,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_num_int(numeral_numeral_int,K)),aa_num_int(numeral_numeral_int,L))) = aa_rat_rat(divide_divide_rat(aa_num_rat(numeral_numeral_rat,K)),aa_num_rat(numeral_numeral_rat,L)) ).

% Frct_code_post(6)
tff(fact_5033_Frct__code__post_I4_J,axiom,
    ! [K: num] : aa_Pro6166618844887768661nt_rat(frct,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_num_int(numeral_numeral_int,K)),one_one_int)) = aa_num_rat(numeral_numeral_rat,K) ).

% Frct_code_post(4)
tff(fact_5034_eq__numeral__iff__iszero_I8_J,axiom,
    ! [Y: num] :
      ( ( one_one_int = aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,Y)) )
    <=> aa_int_o(ring_1_iszero_int,aa_num_int(numeral_numeral_int,aa_num_num(aa_num_fun_num_num(plus_plus_num,one),Y))) ) ).

% eq_numeral_iff_iszero(8)
tff(fact_5035_eq__numeral__iff__iszero_I8_J,axiom,
    ! [Y: num] :
      ( ( one_one_Code_integer = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,Y)) )
    <=> aa_Code_integer_o(ring_16219924574208605041nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(aa_num_fun_num_num(plus_plus_num,one),Y))) ) ).

% eq_numeral_iff_iszero(8)
tff(fact_5036_eq__numeral__iff__iszero_I8_J,axiom,
    ! [Y: num] :
      ( ( one_one_rat = aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,Y)) )
    <=> aa_rat_o(ring_1_iszero_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(aa_num_fun_num_num(plus_plus_num,one),Y))) ) ).

% eq_numeral_iff_iszero(8)
tff(fact_5037_eq__numeral__iff__iszero_I7_J,axiom,
    ! [X2: num] :
      ( ( aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,X2)) = one_one_int )
    <=> aa_int_o(ring_1_iszero_int,aa_num_int(numeral_numeral_int,aa_num_num(aa_num_fun_num_num(plus_plus_num,X2),one))) ) ).

% eq_numeral_iff_iszero(7)
tff(fact_5038_eq__numeral__iff__iszero_I7_J,axiom,
    ! [X2: num] :
      ( ( aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,X2)) = one_one_Code_integer )
    <=> aa_Code_integer_o(ring_16219924574208605041nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(aa_num_fun_num_num(plus_plus_num,X2),one))) ) ).

% eq_numeral_iff_iszero(7)
tff(fact_5039_eq__numeral__iff__iszero_I7_J,axiom,
    ! [X2: num] :
      ( ( aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,X2)) = one_one_rat )
    <=> aa_rat_o(ring_1_iszero_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(aa_num_fun_num_num(plus_plus_num,X2),one))) ) ).

% eq_numeral_iff_iszero(7)
tff(fact_5040_Inf_OINF__image,axiom,
    ! [Inf: fun_se3773019727686582893nteger,G: fun_Co8499238673658658103nteger,F: fun_num_Code_integer,A2: set_num] : aa_set8546232603906849326nteger(Inf,image_4470545334726330049nteger(G,image_8379761247532268670nteger(F,A2))) = aa_set8546232603906849326nteger(Inf,image_8379761247532268670nteger(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),F),A2)) ).

% Inf.INF_image
tff(fact_5041_Inf_OINF__image,axiom,
    ! [Inf: fun_set_num_num,G: fun_nat_num,F: fun_int_nat,A2: set_int] : aa_set_num_num(Inf,image_nat_num(G,image_int_nat(F,A2))) = aa_set_num_num(Inf,image_int_num(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,G),F),A2)) ).

% Inf.INF_image
tff(fact_5042_Inf_OINF__image,axiom,
    ! [Inf: fun_se3773019727686582893nteger,G: fun_Co8499238673658658103nteger,F: fun_nat_Code_integer,A2: set_nat] : aa_set8546232603906849326nteger(Inf,image_4470545334726330049nteger(G,image_1215581382706833972nteger(F,A2))) = aa_set8546232603906849326nteger(Inf,image_1215581382706833972nteger(comp_C6974050283906349679er_nat(G,F),A2)) ).

% Inf.INF_image
tff(fact_5043_Inf_OINF__image,axiom,
    ! [Inf: fun_set_nat_nat,G: fun_Code_integer_nat,F: fun_nat_Code_integer,A2: set_nat] : aa_set_nat_nat(Inf,image_951025933927791156er_nat(G,image_1215581382706833972nteger(F,A2))) = aa_set_nat_nat(Inf,aa_set_nat_set_nat(image_nat_nat(comp_C4049556595663050210at_nat(G,F)),A2)) ).

% Inf.INF_image
tff(fact_5044_Inf_OINF__image,axiom,
    ! [Inf: fun_set_int_int,G: fun_Code_integer_int,F: fun_nat_Code_integer,A2: set_nat] : aa_set_int_int(Inf,image_948535463418740880er_int(G,image_1215581382706833972nteger(F,A2))) = aa_set_int_int(Inf,image_nat_int(comp_C5048910307564104766nt_nat(G,F),A2)) ).

% Inf.INF_image
tff(fact_5045_Inf_OINF__image,axiom,
    ! [Inf: fun_se3773019727686582893nteger,G: fun_int_Code_integer,F: fun_nat_int,A2: set_nat] : aa_set8546232603906849326nteger(Inf,image_1587234942943678608nteger(G,image_nat_int(F,A2))) = aa_set8546232603906849326nteger(Inf,image_1215581382706833972nteger(comp_i1588355021709917246er_nat(G,F),A2)) ).

% Inf.INF_image
tff(fact_5046_Inf_OINF__image,axiom,
    ! [Inf: fun_set_nat_nat,G: fun_int_nat,F: fun_nat_int,A2: set_nat] : aa_set_nat_nat(Inf,image_int_nat(G,image_nat_int(F,A2))) = aa_set_nat_nat(Inf,aa_set_nat_set_nat(image_nat_nat(comp_int_nat_nat(G,F)),A2)) ).

% Inf.INF_image
tff(fact_5047_Inf_OINF__image,axiom,
    ! [Inf: fun_se3773019727686582893nteger,G: fun_nat_Code_integer,F: fun_nat_nat,A2: set_nat] : aa_set8546232603906849326nteger(Inf,image_1215581382706833972nteger(G,aa_set_nat_set_nat(image_nat_nat(F),A2))) = aa_set8546232603906849326nteger(Inf,image_1215581382706833972nteger(comp_n3898172953802868194er_nat(G,F),A2)) ).

% Inf.INF_image
tff(fact_5048_Inf_OINF__image,axiom,
    ! [Inf: fun_set_nat_nat,G: fun_nat_nat,F: fun_nat_nat,A2: set_nat] : aa_set_nat_nat(Inf,aa_set_nat_set_nat(image_nat_nat(G),aa_set_nat_set_nat(image_nat_nat(F),A2))) = aa_set_nat_nat(Inf,aa_set_nat_set_nat(image_nat_nat(comp_nat_nat_nat(G,F)),A2)) ).

% Inf.INF_image
tff(fact_5049_Inf_OINF__image,axiom,
    ! [Inf: fun_set_int_int,G: fun_nat_int,F: fun_int_nat,A2: set_int] : aa_set_int_int(Inf,image_nat_int(G,image_int_nat(F,A2))) = aa_set_int_int(Inf,aa_set_int_set_int(image_int_int(comp_nat_int_int(G,F)),A2)) ).

% Inf.INF_image
tff(fact_5050_not__iszero__1,axiom,
    ~ aa_Code_integer_o(ring_16219924574208605041nteger,one_one_Code_integer) ).

% not_iszero_1
tff(fact_5051_not__iszero__1,axiom,
    ~ aa_rat_o(ring_1_iszero_rat,one_one_rat) ).

% not_iszero_1
tff(fact_5052_not__iszero__1,axiom,
    ~ aa_int_o(ring_1_iszero_int,one_one_int) ).

% not_iszero_1
tff(fact_5053_Code__Numeral_Odup__code_I1_J,axiom,
    aa_Cod1783974652533396728nteger(code_dup,zero_z3403309356797280102nteger) = zero_z3403309356797280102nteger ).

% Code_Numeral.dup_code(1)
tff(fact_5054_not__iszero__neg__1,axiom,
    ~ aa_int_o(ring_1_iszero_int,aa_int_int(uminus_uminus_int,one_one_int)) ).

% not_iszero_neg_1
tff(fact_5055_not__iszero__neg__1,axiom,
    ~ aa_Code_integer_o(ring_16219924574208605041nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)) ).

% not_iszero_neg_1
tff(fact_5056_not__iszero__neg__1,axiom,
    ~ aa_rat_o(ring_1_iszero_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)) ).

% not_iszero_neg_1
tff(fact_5057_dup_Orep__eq,axiom,
    ! [X2: code_integer] : aa_Code_integer_int(code_int_of_integer,aa_Cod1783974652533396728nteger(code_dup,X2)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_Code_integer_int(code_int_of_integer,X2)),aa_Code_integer_int(code_int_of_integer,X2)) ).

% dup.rep_eq
tff(fact_5058_dup_Oabs__eq,axiom,
    ! [X2: int] : aa_Cod1783974652533396728nteger(code_dup,aa_int_Code_integer(code_integer_of_int,X2)) = aa_int_Code_integer(code_integer_of_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),X2)) ).

% dup.abs_eq
tff(fact_5059_eq__numeral__iff__iszero_I2_J,axiom,
    ! [X2: num,Y: num] :
      ( ( aa_num_int(numeral_numeral_int,X2) = aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,Y)) )
    <=> aa_int_o(ring_1_iszero_int,aa_num_int(numeral_numeral_int,aa_num_num(aa_num_fun_num_num(plus_plus_num,X2),Y))) ) ).

% eq_numeral_iff_iszero(2)
tff(fact_5060_eq__numeral__iff__iszero_I2_J,axiom,
    ! [X2: num,Y: num] :
      ( ( aa_num_Code_integer(numera6620942414471956472nteger,X2) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,Y)) )
    <=> aa_Code_integer_o(ring_16219924574208605041nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(aa_num_fun_num_num(plus_plus_num,X2),Y))) ) ).

% eq_numeral_iff_iszero(2)
tff(fact_5061_eq__numeral__iff__iszero_I2_J,axiom,
    ! [X2: num,Y: num] :
      ( ( aa_num_rat(numeral_numeral_rat,X2) = aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,Y)) )
    <=> aa_rat_o(ring_1_iszero_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(aa_num_fun_num_num(plus_plus_num,X2),Y))) ) ).

% eq_numeral_iff_iszero(2)
tff(fact_5062_eq__numeral__iff__iszero_I3_J,axiom,
    ! [X2: num,Y: num] :
      ( ( aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,X2)) = aa_num_int(numeral_numeral_int,Y) )
    <=> aa_int_o(ring_1_iszero_int,aa_num_int(numeral_numeral_int,aa_num_num(aa_num_fun_num_num(plus_plus_num,X2),Y))) ) ).

% eq_numeral_iff_iszero(3)
tff(fact_5063_eq__numeral__iff__iszero_I3_J,axiom,
    ! [X2: num,Y: num] :
      ( ( aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(numera6620942414471956472nteger,X2)) = aa_num_Code_integer(numera6620942414471956472nteger,Y) )
    <=> aa_Code_integer_o(ring_16219924574208605041nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(aa_num_fun_num_num(plus_plus_num,X2),Y))) ) ).

% eq_numeral_iff_iszero(3)
tff(fact_5064_eq__numeral__iff__iszero_I3_J,axiom,
    ! [X2: num,Y: num] :
      ( ( aa_rat_rat(uminus_uminus_rat,aa_num_rat(numeral_numeral_rat,X2)) = aa_num_rat(numeral_numeral_rat,Y) )
    <=> aa_rat_o(ring_1_iszero_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(aa_num_fun_num_num(plus_plus_num,X2),Y))) ) ).

% eq_numeral_iff_iszero(3)
tff(fact_5065_Frct__code__post_I2_J,axiom,
    ! [A: int] : aa_Pro6166618844887768661nt_rat(frct,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A),zero_zero_int)) = zero_zero_rat ).

% Frct_code_post(2)
tff(fact_5066_Frct__code__post_I1_J,axiom,
    ! [A: int] : aa_Pro6166618844887768661nt_rat(frct,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,zero_zero_int),A)) = zero_zero_rat ).

% Frct_code_post(1)
tff(fact_5067_Frct__code__post_I3_J,axiom,
    aa_Pro6166618844887768661nt_rat(frct,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,one_one_int),one_one_int)) = one_one_rat ).

% Frct_code_post(3)
tff(fact_5068_eq__numeral__iff__iszero_I6_J,axiom,
    ! [Y: num] :
      ( ( one_one_int = aa_num_int(numeral_numeral_int,Y) )
    <=> aa_int_o(ring_1_iszero_int,aa_num_int(neg_numeral_sub_int(one),Y)) ) ).

% eq_numeral_iff_iszero(6)
tff(fact_5069_eq__numeral__iff__iszero_I6_J,axiom,
    ! [Y: num] :
      ( ( one_one_Code_integer = aa_num_Code_integer(numera6620942414471956472nteger,Y) )
    <=> aa_Code_integer_o(ring_16219924574208605041nteger,aa_num_Code_integer(neg_nu5755505904847501662nteger(one),Y)) ) ).

% eq_numeral_iff_iszero(6)
tff(fact_5070_eq__numeral__iff__iszero_I6_J,axiom,
    ! [Y: num] :
      ( ( one_one_rat = aa_num_rat(numeral_numeral_rat,Y) )
    <=> aa_rat_o(ring_1_iszero_rat,neg_numeral_sub_rat(one,Y)) ) ).

% eq_numeral_iff_iszero(6)
tff(fact_5071_eq__numeral__iff__iszero_I5_J,axiom,
    ! [X2: num] :
      ( ( aa_num_int(numeral_numeral_int,X2) = one_one_int )
    <=> aa_int_o(ring_1_iszero_int,aa_num_int(neg_numeral_sub_int(X2),one)) ) ).

% eq_numeral_iff_iszero(5)
tff(fact_5072_eq__numeral__iff__iszero_I5_J,axiom,
    ! [X2: num] :
      ( ( aa_num_Code_integer(numera6620942414471956472nteger,X2) = one_one_Code_integer )
    <=> aa_Code_integer_o(ring_16219924574208605041nteger,aa_num_Code_integer(neg_nu5755505904847501662nteger(X2),one)) ) ).

% eq_numeral_iff_iszero(5)
tff(fact_5073_eq__numeral__iff__iszero_I5_J,axiom,
    ! [X2: num] :
      ( ( aa_num_rat(numeral_numeral_rat,X2) = one_one_rat )
    <=> aa_rat_o(ring_1_iszero_rat,neg_numeral_sub_rat(X2,one)) ) ).

% eq_numeral_iff_iszero(5)
tff(fact_5074_Frct__code__post_I7_J,axiom,
    ! [A: int,B: int] : aa_Pro6166618844887768661nt_rat(frct,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_int_int(uminus_uminus_int,A)),B)) = aa_rat_rat(uminus_uminus_rat,aa_Pro6166618844887768661nt_rat(frct,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A),B))) ).

% Frct_code_post(7)
tff(fact_5075_Frct__code__post_I8_J,axiom,
    ! [A: int,B: int] : aa_Pro6166618844887768661nt_rat(frct,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A),aa_int_int(uminus_uminus_int,B))) = aa_rat_rat(uminus_uminus_rat,aa_Pro6166618844887768661nt_rat(frct,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A),B))) ).

% Frct_code_post(8)
tff(fact_5076_Sup_OSUP__image,axiom,
    ! [Sup: fun_se3773019727686582893nteger,G: fun_Co8499238673658658103nteger,F: fun_num_Code_integer,A2: set_num] : aa_set8546232603906849326nteger(Sup,image_4470545334726330049nteger(G,image_8379761247532268670nteger(F,A2))) = aa_set8546232603906849326nteger(Sup,image_8379761247532268670nteger(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),F),A2)) ).

% Sup.SUP_image
tff(fact_5077_Sup_OSUP__image,axiom,
    ! [Sup: fun_set_num_num,G: fun_nat_num,F: fun_int_nat,A2: set_int] : aa_set_num_num(Sup,image_nat_num(G,image_int_nat(F,A2))) = aa_set_num_num(Sup,image_int_num(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,G),F),A2)) ).

% Sup.SUP_image
tff(fact_5078_Sup_OSUP__image,axiom,
    ! [Sup: fun_se3773019727686582893nteger,G: fun_Co8499238673658658103nteger,F: fun_nat_Code_integer,A2: set_nat] : aa_set8546232603906849326nteger(Sup,image_4470545334726330049nteger(G,image_1215581382706833972nteger(F,A2))) = aa_set8546232603906849326nteger(Sup,image_1215581382706833972nteger(comp_C6974050283906349679er_nat(G,F),A2)) ).

% Sup.SUP_image
tff(fact_5079_Sup_OSUP__image,axiom,
    ! [Sup: fun_set_nat_nat,G: fun_Code_integer_nat,F: fun_nat_Code_integer,A2: set_nat] : aa_set_nat_nat(Sup,image_951025933927791156er_nat(G,image_1215581382706833972nteger(F,A2))) = aa_set_nat_nat(Sup,aa_set_nat_set_nat(image_nat_nat(comp_C4049556595663050210at_nat(G,F)),A2)) ).

% Sup.SUP_image
tff(fact_5080_Sup_OSUP__image,axiom,
    ! [Sup: fun_set_int_int,G: fun_Code_integer_int,F: fun_nat_Code_integer,A2: set_nat] : aa_set_int_int(Sup,image_948535463418740880er_int(G,image_1215581382706833972nteger(F,A2))) = aa_set_int_int(Sup,image_nat_int(comp_C5048910307564104766nt_nat(G,F),A2)) ).

% Sup.SUP_image
tff(fact_5081_Sup_OSUP__image,axiom,
    ! [Sup: fun_se3773019727686582893nteger,G: fun_int_Code_integer,F: fun_nat_int,A2: set_nat] : aa_set8546232603906849326nteger(Sup,image_1587234942943678608nteger(G,image_nat_int(F,A2))) = aa_set8546232603906849326nteger(Sup,image_1215581382706833972nteger(comp_i1588355021709917246er_nat(G,F),A2)) ).

% Sup.SUP_image
tff(fact_5082_Sup_OSUP__image,axiom,
    ! [Sup: fun_set_nat_nat,G: fun_int_nat,F: fun_nat_int,A2: set_nat] : aa_set_nat_nat(Sup,image_int_nat(G,image_nat_int(F,A2))) = aa_set_nat_nat(Sup,aa_set_nat_set_nat(image_nat_nat(comp_int_nat_nat(G,F)),A2)) ).

% Sup.SUP_image
tff(fact_5083_Sup_OSUP__image,axiom,
    ! [Sup: fun_se3773019727686582893nteger,G: fun_nat_Code_integer,F: fun_nat_nat,A2: set_nat] : aa_set8546232603906849326nteger(Sup,image_1215581382706833972nteger(G,aa_set_nat_set_nat(image_nat_nat(F),A2))) = aa_set8546232603906849326nteger(Sup,image_1215581382706833972nteger(comp_n3898172953802868194er_nat(G,F),A2)) ).

% Sup.SUP_image
tff(fact_5084_Sup_OSUP__image,axiom,
    ! [Sup: fun_set_nat_nat,G: fun_nat_nat,F: fun_nat_nat,A2: set_nat] : aa_set_nat_nat(Sup,aa_set_nat_set_nat(image_nat_nat(G),aa_set_nat_set_nat(image_nat_nat(F),A2))) = aa_set_nat_nat(Sup,aa_set_nat_set_nat(image_nat_nat(comp_nat_nat_nat(G,F)),A2)) ).

% Sup.SUP_image
tff(fact_5085_Sup_OSUP__image,axiom,
    ! [Sup: fun_set_int_int,G: fun_nat_int,F: fun_int_nat,A2: set_int] : aa_set_int_int(Sup,image_nat_int(G,image_int_nat(F,A2))) = aa_set_int_int(Sup,aa_set_int_set_int(image_int_int(comp_nat_int_int(G,F)),A2)) ).

% Sup.SUP_image
tff(fact_5086_Code__Numeral_Osub__code_I9_J,axiom,
    ! [M: num,N2: num] : aa_num_Code_integer(aa_num5808785979904431436nteger(code_sub,aa_num_num(bit0,M)),aa_num_num(bit1,N2)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(code_dup,aa_num_Code_integer(aa_num5808785979904431436nteger(code_sub,M),N2))),one_one_Code_integer) ).

% Code_Numeral.sub_code(9)
tff(fact_5087_Code__Numeral_Osub__code_I8_J,axiom,
    ! [M: num,N2: num] : aa_num_Code_integer(aa_num5808785979904431436nteger(code_sub,aa_num_num(bit1,M)),aa_num_num(bit0,N2)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(code_dup,aa_num_Code_integer(aa_num5808785979904431436nteger(code_sub,M),N2))),one_one_Code_integer) ).

% Code_Numeral.sub_code(8)
tff(fact_5088_less__eq__int__def,axiom,
    ord_less_eq_int = map_fu3191548434056052140_int_o(rep_Integ,map_fu4826362097070443709at_o_o(rep_Integ,id_o),aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,aTP_Lamm_fg)) ).

% less_eq_int_def
tff(fact_5089_less__int__def,axiom,
    ord_less_int = map_fu3191548434056052140_int_o(rep_Integ,map_fu4826362097070443709at_o_o(rep_Integ,id_o),aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,aTP_Lamm_fe)) ).

% less_int_def
tff(fact_5090_image__affinity__atLeastAtMost__div__diff,axiom,
    ! [M: rat,C: rat,A: rat,B: rat] :
      image_rat_rat(aa_rat_fun_rat_rat(aTP_Lamm_nj(M),C),set_or633870826150836451st_rat(A,B)) = $ite(
        set_or633870826150836451st_rat(A,B) = bot_bot_set_rat,
        bot_bot_set_rat,
        $ite(aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),M),set_or633870826150836451st_rat(aa_rat_rat(minus_minus_rat(aa_rat_rat(divide_divide_rat(A),M)),C),aa_rat_rat(minus_minus_rat(aa_rat_rat(divide_divide_rat(B),M)),C)),set_or633870826150836451st_rat(aa_rat_rat(minus_minus_rat(aa_rat_rat(divide_divide_rat(B),M)),C),aa_rat_rat(minus_minus_rat(aa_rat_rat(divide_divide_rat(A),M)),C))) ) ).

% image_affinity_atLeastAtMost_div_diff
tff(fact_5091_image__affinity__atLeastAtMost__div,axiom,
    ! [M: rat,C: rat,A: rat,B: rat] :
      image_rat_rat(aa_rat_fun_rat_rat(aTP_Lamm_nk(M),C),set_or633870826150836451st_rat(A,B)) = $ite(
        set_or633870826150836451st_rat(A,B) = bot_bot_set_rat,
        bot_bot_set_rat,
        $ite(aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),M),set_or633870826150836451st_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(divide_divide_rat(A),M)),C),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(divide_divide_rat(B),M)),C)),set_or633870826150836451st_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(divide_divide_rat(B),M)),C),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(divide_divide_rat(A),M)),C))) ) ).

% image_affinity_atLeastAtMost_div
tff(fact_5092_image__affinity__atLeastAtMost__diff,axiom,
    ! [M: rat,C: rat,A: rat,B: rat] :
      image_rat_rat(aa_rat_fun_rat_rat(aTP_Lamm_nl(M),C),set_or633870826150836451st_rat(A,B)) = $ite(
        set_or633870826150836451st_rat(A,B) = bot_bot_set_rat,
        bot_bot_set_rat,
        $ite(aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),M),set_or633870826150836451st_rat(aa_rat_rat(minus_minus_rat(aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,M),A)),C),aa_rat_rat(minus_minus_rat(aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,M),B)),C)),set_or633870826150836451st_rat(aa_rat_rat(minus_minus_rat(aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,M),B)),C),aa_rat_rat(minus_minus_rat(aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,M),A)),C))) ) ).

% image_affinity_atLeastAtMost_diff
tff(fact_5093_id__apply,axiom,
    ! [X2: $o] :
      ( aa_o_o(id_o,(X2))
    <=> (X2) ) ).

% id_apply
tff(fact_5094_id__apply,axiom,
    ! [X2: nat] : aa_nat_nat(id_nat,X2) = X2 ).

% id_apply
tff(fact_5095_id__apply,axiom,
    ! [X2: fun_nat_o] : aa_fun5937193402907943164_nat_o(id_fun_nat_o,X2) = X2 ).

% id_apply
tff(fact_5096_id__apply,axiom,
    ! [X2: num] : aa_num_num(id_num,X2) = X2 ).

% id_apply
tff(fact_5097_id__apply,axiom,
    ! [X2: int] : aa_int_int(id_int,X2) = X2 ).

% id_apply
tff(fact_5098_bijective__Empty,axiom,
    biject3388518990857851981at_nat(bot_bo228742789529271731at_nat) ).

% bijective_Empty
tff(fact_5099_bijective__Empty,axiom,
    bijective_nat_nat(bot_bo2099793752762293965at_nat) ).

% bijective_Empty
tff(fact_5100_image__id,axiom,
    image_o_o(id_o) = id_set_o ).

% image_id
tff(fact_5101_image__id,axiom,
    image_2153120922742433605_nat_o(id_fun_nat_o) = id_set_fun_nat_o ).

% image_id
tff(fact_5102_image__id,axiom,
    image_num_num(id_num) = id_set_num ).

% image_id
tff(fact_5103_image__id,axiom,
    image_nat_nat(id_nat) = id_set_nat ).

% image_id
tff(fact_5104_image__id,axiom,
    image_int_int(id_int) = id_set_int ).

% image_id
tff(fact_5105_fun_Omap__id,axiom,
    ! [T: fun_num_Code_integer] : aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,id_Code_integer),T) = T ).

% fun.map_id
tff(fact_5106_id__comp,axiom,
    ! [G: fun_num_Code_integer] : aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,id_Code_integer),G) = G ).

% id_comp
tff(fact_5107_comp__id,axiom,
    ! [F: fun_Co1561183069634336733nteger] : aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),id_Code_integer) = F ).

% comp_id
tff(fact_5108_lessThan__0,axiom,
    aa_nat_set_nat(set_ord_lessThan_nat,zero_zero_nat) = bot_bot_set_nat ).

% lessThan_0
tff(fact_5109_apsnd__id,axiom,
    aa_fun2509385170507305080nteger(produc6499014454317279255nteger,id_Code_integer) = id_Pro2309048762231606924nteger ).

% apsnd_id
tff(fact_5110_set__to__map__empty,axiom,
    ! [X: set_Pr1261947904930325089at_nat] : aa_set2934564513904597954at_nat(set_to4447731662395764663at_nat(bot_bo228742789529271731at_nat),X) = none_s625347054029921090at_nat ).

% set_to_map_empty
tff(fact_5111_set__to__map__empty,axiom,
    ! [X: nat] : aa_nat_option_nat(set_to_map_nat_nat(bot_bo2099793752762293965at_nat),X) = none_nat ).

% set_to_map_empty
tff(fact_5112_atLeastatMost__empty__iff2,axiom,
    ! [A: $o,B: $o] :
      ( ( bot_bot_set_o = aa_o_set_o(set_or8904488021354931149Most_o((A)),(B)) )
    <=> ~ aa_o_o(aa_o_fun_o_o(ord_less_eq_o,(A)),(B)) ) ).

% atLeastatMost_empty_iff2
tff(fact_5113_atLeastatMost__empty__iff2,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( bot_bot_set_set_nat = set_or4548717258645045905et_nat(A,B) )
    <=> ~ aa_set_nat_o(ord_less_eq_set_nat(A),B) ) ).

% atLeastatMost_empty_iff2
tff(fact_5114_atLeastatMost__empty__iff2,axiom,
    ! [A: rat,B: rat] :
      ( ( bot_bot_set_rat = set_or633870826150836451st_rat(A,B) )
    <=> ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),B) ) ).

% atLeastatMost_empty_iff2
tff(fact_5115_atLeastatMost__empty__iff2,axiom,
    ! [A: num,B: num] :
      ( ( bot_bot_set_num = set_or7049704709247886629st_num(A,B) )
    <=> ~ aa_num_o(aa_num_fun_num_o(ord_less_eq_num,A),B) ) ).

% atLeastatMost_empty_iff2
tff(fact_5116_atLeastatMost__empty__iff2,axiom,
    ! [A: int,B: int] :
      ( ( bot_bot_set_int = aa_int_set_int(set_or1266510415728281911st_int(A),B) )
    <=> ~ aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),B) ) ).

% atLeastatMost_empty_iff2
tff(fact_5117_atLeastatMost__empty__iff2,axiom,
    ! [A: nat,B: nat] :
      ( ( bot_bot_set_nat = aa_nat_set_nat(set_or1269000886237332187st_nat(A),B) )
    <=> ~ aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B) ) ).

% atLeastatMost_empty_iff2
tff(fact_5118_atLeastatMost__empty__iff2,axiom,
    ! [A: code_integer,B: code_integer] :
      ( ( bot_bo3990330152332043303nteger = aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(A),B) )
    <=> ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),B) ) ).

% atLeastatMost_empty_iff2
tff(fact_5119_atLeastatMost__empty__iff,axiom,
    ! [A: $o,B: $o] :
      ( ( aa_o_set_o(set_or8904488021354931149Most_o((A)),(B)) = bot_bot_set_o )
    <=> ~ aa_o_o(aa_o_fun_o_o(ord_less_eq_o,(A)),(B)) ) ).

% atLeastatMost_empty_iff
tff(fact_5120_atLeastatMost__empty__iff,axiom,
    ! [A: set_nat,B: set_nat] :
      ( ( set_or4548717258645045905et_nat(A,B) = bot_bot_set_set_nat )
    <=> ~ aa_set_nat_o(ord_less_eq_set_nat(A),B) ) ).

% atLeastatMost_empty_iff
tff(fact_5121_atLeastatMost__empty__iff,axiom,
    ! [A: rat,B: rat] :
      ( ( set_or633870826150836451st_rat(A,B) = bot_bot_set_rat )
    <=> ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,A),B) ) ).

% atLeastatMost_empty_iff
tff(fact_5122_atLeastatMost__empty__iff,axiom,
    ! [A: num,B: num] :
      ( ( set_or7049704709247886629st_num(A,B) = bot_bot_set_num )
    <=> ~ aa_num_o(aa_num_fun_num_o(ord_less_eq_num,A),B) ) ).

% atLeastatMost_empty_iff
tff(fact_5123_atLeastatMost__empty__iff,axiom,
    ! [A: int,B: int] :
      ( ( aa_int_set_int(set_or1266510415728281911st_int(A),B) = bot_bot_set_int )
    <=> ~ aa_int_o(aa_int_fun_int_o(ord_less_eq_int,A),B) ) ).

% atLeastatMost_empty_iff
tff(fact_5124_atLeastatMost__empty__iff,axiom,
    ! [A: nat,B: nat] :
      ( ( aa_nat_set_nat(set_or1269000886237332187st_nat(A),B) = bot_bot_set_nat )
    <=> ~ aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B) ) ).

% atLeastatMost_empty_iff
tff(fact_5125_atLeastatMost__empty__iff,axiom,
    ! [A: code_integer,B: code_integer] :
      ( ( aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(A),B) = bot_bo3990330152332043303nteger )
    <=> ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,A),B) ) ).

% atLeastatMost_empty_iff
tff(fact_5126_atLeastatMost__empty,axiom,
    ! [B: $o,A: $o] :
      ( aa_o_o(aa_o_fun_o_o(ord_less_o,(B)),(A))
     => ( aa_o_set_o(set_or8904488021354931149Most_o((A)),(B)) = bot_bot_set_o ) ) ).

% atLeastatMost_empty
tff(fact_5127_atLeastatMost__empty,axiom,
    ! [B: rat,A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,B),A)
     => ( set_or633870826150836451st_rat(A,B) = bot_bot_set_rat ) ) ).

% atLeastatMost_empty
tff(fact_5128_atLeastatMost__empty,axiom,
    ! [B: num,A: num] :
      ( aa_num_o(aa_num_fun_num_o(ord_less_num,B),A)
     => ( set_or7049704709247886629st_num(A,B) = bot_bot_set_num ) ) ).

% atLeastatMost_empty
tff(fact_5129_atLeastatMost__empty,axiom,
    ! [B: int,A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,B),A)
     => ( aa_int_set_int(set_or1266510415728281911st_int(A),B) = bot_bot_set_int ) ) ).

% atLeastatMost_empty
tff(fact_5130_atLeastatMost__empty,axiom,
    ! [B: nat,A: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,B),A)
     => ( aa_nat_set_nat(set_or1269000886237332187st_nat(A),B) = bot_bot_set_nat ) ) ).

% atLeastatMost_empty
tff(fact_5131_atLeastatMost__empty,axiom,
    ! [B: code_integer,A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,B),A)
     => ( aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(A),B) = bot_bo3990330152332043303nteger ) ) ).

% atLeastatMost_empty
tff(fact_5132_atLeastLessThan__empty,axiom,
    ! [B: $o,A: $o] :
      ( aa_o_o(aa_o_fun_o_o(ord_less_eq_o,(B)),(A))
     => ( aa_o_set_o(set_or7139685690850216873Than_o((A)),(B)) = bot_bot_set_o ) ) ).

% atLeastLessThan_empty
tff(fact_5133_atLeastLessThan__empty,axiom,
    ! [B: set_nat,A: set_nat] :
      ( aa_set_nat_o(ord_less_eq_set_nat(B),A)
     => ( set_or3540276404033026485et_nat(A,B) = bot_bot_set_set_nat ) ) ).

% atLeastLessThan_empty
tff(fact_5134_atLeastLessThan__empty,axiom,
    ! [B: rat,A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),A)
     => ( set_or4029947393144176647an_rat(A,B) = bot_bot_set_rat ) ) ).

% atLeastLessThan_empty
tff(fact_5135_atLeastLessThan__empty,axiom,
    ! [B: num,A: num] :
      ( aa_num_o(aa_num_fun_num_o(ord_less_eq_num,B),A)
     => ( set_or1222409239386451017an_num(A,B) = bot_bot_set_num ) ) ).

% atLeastLessThan_empty
tff(fact_5136_atLeastLessThan__empty,axiom,
    ! [B: nat,A: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,B),A)
     => ( aa_nat_set_nat(set_or4665077453230672383an_nat(A),B) = bot_bot_set_nat ) ) ).

% atLeastLessThan_empty
tff(fact_5137_atLeastLessThan__empty,axiom,
    ! [B: code_integer,A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,B),A)
     => ( aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(A),B) = bot_bo3990330152332043303nteger ) ) ).

% atLeastLessThan_empty
tff(fact_5138_atLeastLessThan__empty,axiom,
    ! [B: int,A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,B),A)
     => ( aa_int_set_int(set_or4662586982721622107an_int(A),B) = bot_bot_set_int ) ) ).

% atLeastLessThan_empty
tff(fact_5139_atLeastLessThan__empty__iff,axiom,
    ! [A: $o,B: $o] :
      ( ( aa_o_set_o(set_or7139685690850216873Than_o((A)),(B)) = bot_bot_set_o )
    <=> ~ aa_o_o(aa_o_fun_o_o(ord_less_o,(A)),(B)) ) ).

% atLeastLessThan_empty_iff
tff(fact_5140_atLeastLessThan__empty__iff,axiom,
    ! [A: rat,B: rat] :
      ( ( set_or4029947393144176647an_rat(A,B) = bot_bot_set_rat )
    <=> ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B) ) ).

% atLeastLessThan_empty_iff
tff(fact_5141_atLeastLessThan__empty__iff,axiom,
    ! [A: num,B: num] :
      ( ( set_or1222409239386451017an_num(A,B) = bot_bot_set_num )
    <=> ~ aa_num_o(aa_num_fun_num_o(ord_less_num,A),B) ) ).

% atLeastLessThan_empty_iff
tff(fact_5142_atLeastLessThan__empty__iff,axiom,
    ! [A: nat,B: nat] :
      ( ( aa_nat_set_nat(set_or4665077453230672383an_nat(A),B) = bot_bot_set_nat )
    <=> ~ aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),B) ) ).

% atLeastLessThan_empty_iff
tff(fact_5143_atLeastLessThan__empty__iff,axiom,
    ! [A: code_integer,B: code_integer] :
      ( ( aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(A),B) = bot_bo3990330152332043303nteger )
    <=> ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),B) ) ).

% atLeastLessThan_empty_iff
tff(fact_5144_atLeastLessThan__empty__iff,axiom,
    ! [A: int,B: int] :
      ( ( aa_int_set_int(set_or4662586982721622107an_int(A),B) = bot_bot_set_int )
    <=> ~ aa_int_o(aa_int_fun_int_o(ord_less_int,A),B) ) ).

% atLeastLessThan_empty_iff
tff(fact_5145_atLeastLessThan__empty__iff2,axiom,
    ! [A: $o,B: $o] :
      ( ( bot_bot_set_o = aa_o_set_o(set_or7139685690850216873Than_o((A)),(B)) )
    <=> ~ aa_o_o(aa_o_fun_o_o(ord_less_o,(A)),(B)) ) ).

% atLeastLessThan_empty_iff2
tff(fact_5146_atLeastLessThan__empty__iff2,axiom,
    ! [A: rat,B: rat] :
      ( ( bot_bot_set_rat = set_or4029947393144176647an_rat(A,B) )
    <=> ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B) ) ).

% atLeastLessThan_empty_iff2
tff(fact_5147_atLeastLessThan__empty__iff2,axiom,
    ! [A: num,B: num] :
      ( ( bot_bot_set_num = set_or1222409239386451017an_num(A,B) )
    <=> ~ aa_num_o(aa_num_fun_num_o(ord_less_num,A),B) ) ).

% atLeastLessThan_empty_iff2
tff(fact_5148_atLeastLessThan__empty__iff2,axiom,
    ! [A: nat,B: nat] :
      ( ( bot_bot_set_nat = aa_nat_set_nat(set_or4665077453230672383an_nat(A),B) )
    <=> ~ aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),B) ) ).

% atLeastLessThan_empty_iff2
tff(fact_5149_atLeastLessThan__empty__iff2,axiom,
    ! [A: code_integer,B: code_integer] :
      ( ( bot_bo3990330152332043303nteger = aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(A),B) )
    <=> ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),B) ) ).

% atLeastLessThan_empty_iff2
tff(fact_5150_atLeastLessThan__empty__iff2,axiom,
    ! [A: int,B: int] :
      ( ( bot_bot_set_int = aa_int_set_int(set_or4662586982721622107an_int(A),B) )
    <=> ~ aa_int_o(aa_int_fun_int_o(ord_less_int,A),B) ) ).

% atLeastLessThan_empty_iff2
tff(fact_5151_prod_Oempty,axiom,
    ! [G: fun_o_Code_integer] : aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,G),bot_bot_set_o) = one_one_Code_integer ).

% prod.empty
tff(fact_5152_prod_Oempty,axiom,
    ! [G: fun_o_assn] : aa_set_o_assn(aa_fun1914167119812169564o_assn(groups5301882518646026715o_assn,G),bot_bot_set_o) = one_one_assn ).

% prod.empty
tff(fact_5153_prod_Oempty,axiom,
    ! [G: fun_o_rat] : aa_set_o_rat(aa_fun7302669049306738524_o_rat(groups2869687844427037835_o_rat,G),bot_bot_set_o) = one_one_rat ).

% prod.empty
tff(fact_5154_prod_Oempty,axiom,
    ! [G: fun_o_nat] : aa_set_o_nat(aa_fun8470299178418016604_o_nat(groups3504817904513533571_o_nat,G),bot_bot_set_o) = one_one_nat ).

% prod.empty
tff(fact_5155_prod_Oempty,axiom,
    ! [G: fun_o_int] : groups3502327434004483295_o_int(G,bot_bot_set_o) = one_one_int ).

% prod.empty
tff(fact_5156_prod_Oempty,axiom,
    ! [G: fun_nat_Code_integer] : groups3455450783089532116nteger(G,bot_bot_set_nat) = one_one_Code_integer ).

% prod.empty
tff(fact_5157_prod_Oempty,axiom,
    ! [G: fun_nat_assn] : groups6906906614972039071t_assn(G,bot_bot_set_nat) = one_one_assn ).

% prod.empty
tff(fact_5158_prod_Oempty,axiom,
    ! [G: fun_nat_rat] : groups73079841787564623at_rat(G,bot_bot_set_nat) = one_one_rat ).

% prod.empty
tff(fact_5159_prod_Oempty,axiom,
    ! [G: fun_int_Code_integer] : aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,G),bot_bot_set_int) = one_one_Code_integer ).

% prod.empty
tff(fact_5160_prod_Oempty,axiom,
    ! [G: fun_int_assn] : aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,G),bot_bot_set_int) = one_one_assn ).

% prod.empty
tff(fact_5161_group__add__class_Ominus__comp__minus,axiom,
    aa_fun6280345759651049192nt_int(comp_int_int_int(uminus_uminus_int),uminus_uminus_int) = id_int ).

% group_add_class.minus_comp_minus
tff(fact_5162_group__add__class_Ominus__comp__minus,axiom,
    aa_fun4435975922079263404nteger(comp_C7449957260575251196nteger(uminus1351360451143612070nteger),uminus1351360451143612070nteger) = id_Code_integer ).

% group_add_class.minus_comp_minus
tff(fact_5163_group__add__class_Ominus__comp__minus,axiom,
    comp_rat_rat_rat(uminus_uminus_rat,uminus_uminus_rat) = id_rat ).

% group_add_class.minus_comp_minus
tff(fact_5164_boolean__algebra__class_Ominus__comp__minus,axiom,
    comp_o_o_o(uminus_uminus_o,uminus_uminus_o) = id_o ).

% boolean_algebra_class.minus_comp_minus
tff(fact_5165_boolean__algebra__class_Ominus__comp__minus,axiom,
    comp_f9002688672733719870_nat_o(uminus6183504819137795864_nat_o,uminus6183504819137795864_nat_o) = id_fun_nat_o ).

% boolean_algebra_class.minus_comp_minus
tff(fact_5166_boolean__algebra__class_Ominus__comp__minus,axiom,
    comp_P7645380973975430442t_unit(uminus2952777764628376836t_unit,uminus2952777764628376836t_unit) = id_Product_unit ).

% boolean_algebra_class.minus_comp_minus
tff(fact_5167_rel__of__empty,axiom,
    ! [P: fun_Pr3059359313727237556_nat_o] : rel_of6563097375766832824at_nat(aTP_Lamm_nm,P) = bot_bo228742789529271731at_nat ).

% rel_of_empty
tff(fact_5168_rel__of__empty,axiom,
    ! [P: fun_Pr4796943543331071514_nat_o] : rel_of_nat_nat(aTP_Lamm_nn,P) = bot_bo2099793752762293965at_nat ).

% rel_of_empty
tff(fact_5169_comp__the__Some,axiom,
    comp_option_o_o_o(the_o,some_o) = id_o ).

% comp_the_Some
tff(fact_5170_comp__the__Some,axiom,
    comp_o4663963155070737957at_nat(the_nat,some_nat) = id_nat ).

% comp_the_Some
tff(fact_5171_comp__the__Some,axiom,
    comp_o311737599745908996_nat_o(the_fun_nat_o,some_fun_nat_o) = id_fun_nat_o ).

% comp_the_Some
tff(fact_5172_comp__the__Some,axiom,
    comp_o2446264010603541305nt_int(the_int2,some_int) = id_int ).

% comp_the_Some
tff(fact_5173_comp__the__Some,axiom,
    comp_o6342398210560591875um_num(the_num,some_num) = id_num ).

% comp_the_Some
tff(fact_5174_comp__the__Some,axiom,
    comp_o279924169626513613it_nat(the_Pr7776125533777466484it_nat,some_P1914260805536162275it_nat) = id_Pro1159712480615372887it_nat ).

% comp_the_Some
tff(fact_5175_fun_Omap__id0,axiom,
    comp_o_o_nat(id_o) = id_fun_nat_o ).

% fun.map_id0
tff(fact_5176_fun_Omap__id0,axiom,
    aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,id_Code_integer) = id_fun2933211968975237955nteger ).

% fun.map_id0
tff(fact_5177_Iio__eq__empty__iff,axiom,
    ! [N2: $o] :
      ( ( aa_o_set_o(set_ord_lessThan_o,(N2)) = bot_bot_set_o )
    <=> ( (N2)
      <=> bot_bot_o ) ) ).

% Iio_eq_empty_iff
tff(fact_5178_Iio__eq__empty__iff,axiom,
    ! [N2: nat] :
      ( ( aa_nat_set_nat(set_ord_lessThan_nat,N2) = bot_bot_set_nat )
    <=> ( N2 = bot_bot_nat ) ) ).

% Iio_eq_empty_iff
tff(fact_5179_option_Omap__id0,axiom,
    map_option_o_o(id_o) = id_option_o ).

% option.map_id0
tff(fact_5180_option_Omap__id0,axiom,
    map_option_nat_nat(id_nat) = id_option_nat ).

% option.map_id0
tff(fact_5181_option_Omap__id0,axiom,
    map_op4725796707522037195_nat_o(id_fun_nat_o) = id_option_fun_nat_o ).

% option.map_id0
tff(fact_5182_option_Omap__id0,axiom,
    map_option_int_int(id_int) = id_option_int ).

% option.map_id0
tff(fact_5183_option_Omap__id0,axiom,
    map_option_num_num(id_num) = id_option_num ).

% option.map_id0
tff(fact_5184_set__notEmptyE,axiom,
    ! [S2: set_Pr4329608150637261639at_nat] :
      ( ( S2 != bot_bo228742789529271731at_nat )
     => ~ ! [X3: produc3843707927480180839at_nat] : ~ member8757157785044589968at_nat(X3,S2) ) ).

% set_notEmptyE
tff(fact_5185_set__notEmptyE,axiom,
    ! [S2: set_Pr1261947904930325089at_nat] :
      ( ( S2 != bot_bo2099793752762293965at_nat )
     => ~ ! [X3: product_prod_nat_nat] : ~ member8440522571783428010at_nat(X3,S2) ) ).

% set_notEmptyE
tff(fact_5186_set__notEmptyE,axiom,
    ! [S2: set_o] :
      ( ( S2 != bot_bot_set_o )
     => ~ ! [X3: $o] : ~ member_o((X3),S2) ) ).

% set_notEmptyE
tff(fact_5187_set__notEmptyE,axiom,
    ! [S2: set_nat] :
      ( ( S2 != bot_bot_set_nat )
     => ~ ! [X3: nat] : ~ member_nat(X3,S2) ) ).

% set_notEmptyE
tff(fact_5188_set__notEmptyE,axiom,
    ! [S2: set_int] :
      ( ( S2 != bot_bot_set_int )
     => ~ ! [X3: int] : ~ member_int(X3,S2) ) ).

% set_notEmptyE
tff(fact_5189_memb__imp__not__empty,axiom,
    ! [X2: produc3843707927480180839at_nat,S2: set_Pr4329608150637261639at_nat] :
      ( member8757157785044589968at_nat(X2,S2)
     => ( S2 != bot_bo228742789529271731at_nat ) ) ).

% memb_imp_not_empty
tff(fact_5190_memb__imp__not__empty,axiom,
    ! [X2: product_prod_nat_nat,S2: set_Pr1261947904930325089at_nat] :
      ( member8440522571783428010at_nat(X2,S2)
     => ( S2 != bot_bo2099793752762293965at_nat ) ) ).

% memb_imp_not_empty
tff(fact_5191_memb__imp__not__empty,axiom,
    ! [X2: $o,S2: set_o] :
      ( member_o((X2),S2)
     => ( S2 != bot_bot_set_o ) ) ).

% memb_imp_not_empty
tff(fact_5192_memb__imp__not__empty,axiom,
    ! [X2: nat,S2: set_nat] :
      ( member_nat(X2,S2)
     => ( S2 != bot_bot_set_nat ) ) ).

% memb_imp_not_empty
tff(fact_5193_memb__imp__not__empty,axiom,
    ! [X2: int,S2: set_int] :
      ( member_int(X2,S2)
     => ( S2 != bot_bot_set_int ) ) ).

% memb_imp_not_empty
tff(fact_5194_id__def,axiom,
    ! [X: $o] :
      ( aa_o_o(id_o,(X))
    <=> (X) ) ).

% id_def
tff(fact_5195_id__def,axiom,
    ! [X: nat] : aa_nat_nat(id_nat,X) = X ).

% id_def
tff(fact_5196_id__def,axiom,
    ! [X: fun_nat_o] : aa_fun5937193402907943164_nat_o(id_fun_nat_o,X) = X ).

% id_def
tff(fact_5197_id__def,axiom,
    ! [X: num] : aa_num_num(id_num,X) = X ).

% id_def
tff(fact_5198_id__def,axiom,
    ! [X: int] : aa_int_int(id_int,X) = X ).

% id_def
tff(fact_5199_eq__id__iff,axiom,
    ! [F: fun_o_o] :
      ( ! [X4: $o] :
          ( aa_o_o(F,(X4))
        <=> (X4) )
    <=> ( F = id_o ) ) ).

% eq_id_iff
tff(fact_5200_eq__id__iff,axiom,
    ! [F: fun_nat_nat] :
      ( ! [X4: nat] : aa_nat_nat(F,X4) = X4
    <=> ( F = id_nat ) ) ).

% eq_id_iff
tff(fact_5201_eq__id__iff,axiom,
    ! [F: fun_fu4001317426178549763_nat_o] :
      ( ! [X4: fun_nat_o] : aa_fun5937193402907943164_nat_o(F,X4) = X4
    <=> ( F = id_fun_nat_o ) ) ).

% eq_id_iff
tff(fact_5202_eq__id__iff,axiom,
    ! [F: fun_num_num] :
      ( ! [X4: num] : aa_num_num(F,X4) = X4
    <=> ( F = id_num ) ) ).

% eq_id_iff
tff(fact_5203_eq__id__iff,axiom,
    ! [F: fun_int_int] :
      ( ! [X4: int] : aa_int_int(F,X4) = X4
    <=> ( F = id_int ) ) ).

% eq_id_iff
tff(fact_5204_comp__eq__id__dest,axiom,
    ! [A: fun_Co8499238673658658103nteger,B: fun_num_Code_integer,C: fun_num_Code_integer,V: num] :
      ( ( aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,A),B) = aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,id_Code_integer),C) )
     => ( aa_Cod1783974652533396728nteger(A,aa_num_Code_integer(B,V)) = aa_num_Code_integer(C,V) ) ) ).

% comp_eq_id_dest
tff(fact_5205_comp__eq__id__dest,axiom,
    ! [A: fun_Co1561183069634336733nteger,B: fun_Co8499238673658658103nteger,C: fun_Co1561183069634336733nteger,V: code_integer] :
      ( ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,A),B) = comp_f6855635597449841736nteger(id_fun8244602250740870226nteger,C) )
     => ( aa_Cod1978467581589928094nteger(A,aa_Cod1783974652533396728nteger(B,V)) = aa_Cod1978467581589928094nteger(C,V) ) ) ).

% comp_eq_id_dest
tff(fact_5206_comp__eq__id__dest,axiom,
    ! [A: fun_fu4800041728187187127nteger,B: fun_Co1981900195452921617nteger,C: fun_Co1561183069634336733nteger,V: code_integer] :
      ( ( comp_f6739083541385432444nteger(A,B) = comp_f6855635597449841736nteger(id_fun8244602250740870226nteger,C) )
     => ( aa_fun2509385170507305080nteger(A,aa_Cod4161879620478718930nteger(B,V)) = aa_Cod1978467581589928094nteger(C,V) ) ) ).

% comp_eq_id_dest
tff(fact_5207_comp__eq__id__dest,axiom,
    ! [A: fun_nat_num,B: fun_int_nat,C: fun_int_num,V: int] :
      ( ( aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,A),B) = comp_num_num_int(id_num,C) )
     => ( aa_nat_num(A,aa_int_nat(B,V)) = aa_int_num(C,V) ) ) ).

% comp_eq_id_dest
tff(fact_5208_option_Omap__id,axiom,
    ! [T: option_o] : aa_option_o_option_o(map_option_o_o(id_o),T) = T ).

% option.map_id
tff(fact_5209_option_Omap__id,axiom,
    ! [T: option_nat] : aa_opt1882420858203594238on_nat(map_option_nat_nat(id_nat),T) = T ).

% option.map_id
tff(fact_5210_option_Omap__id,axiom,
    ! [T: option_fun_nat_o] : aa_opt7724086761683053692_nat_o(map_op4725796707522037195_nat_o(id_fun_nat_o),T) = T ).

% option.map_id
tff(fact_5211_option_Omap__id,axiom,
    ! [T: option_int] : aa_opt3115652020397860022on_int(map_option_int_int(id_int),T) = T ).

% option.map_id
tff(fact_5212_option_Omap__id,axiom,
    ! [T: option_num] : aa_opt5369159329878751634on_num(map_option_num_num(id_num),T) = T ).

% option.map_id
tff(fact_5213_not__empty__eq__Iic__eq__empty,axiom,
    ! [Ha: $o] : bot_bot_set_o != aa_o_set_o(set_ord_atMost_o,(Ha)) ).

% not_empty_eq_Iic_eq_empty
tff(fact_5214_not__empty__eq__Iic__eq__empty,axiom,
    ! [Ha: int] : bot_bot_set_int != aa_int_set_int(set_ord_atMost_int,Ha) ).

% not_empty_eq_Iic_eq_empty
tff(fact_5215_not__empty__eq__Iic__eq__empty,axiom,
    ! [Ha: nat] : bot_bot_set_nat != aa_nat_set_nat(set_ord_atMost_nat,Ha) ).

% not_empty_eq_Iic_eq_empty
tff(fact_5216_lessThan__non__empty,axiom,
    ! [X2: int] : aa_int_set_int(set_ord_lessThan_int,X2) != bot_bot_set_int ).

% lessThan_non_empty
tff(fact_5217_subset__minus__empty,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,B4: set_Pr4329608150637261639at_nat] :
      ( ord_le1268244103169919719at_nat(A2,B4)
     => ( minus_3314409938677909166at_nat(A2,B4) = bot_bo228742789529271731at_nat ) ) ).

% subset_minus_empty
tff(fact_5218_subset__minus__empty,axiom,
    ! [A2: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] :
      ( aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(ord_le3146513528884898305at_nat,A2),B4)
     => ( aa_set8868280134176360700at_nat(minus_1356011639430497352at_nat(A2),B4) = bot_bo2099793752762293965at_nat ) ) ).

% subset_minus_empty
tff(fact_5219_subset__minus__empty,axiom,
    ! [A2: set_o,B4: set_o] :
      ( ord_less_eq_set_o(A2,B4)
     => ( minus_minus_set_o(A2,B4) = bot_bot_set_o ) ) ).

% subset_minus_empty
tff(fact_5220_subset__minus__empty,axiom,
    ! [A2: set_int,B4: set_int] :
      ( ord_less_eq_set_int(A2,B4)
     => ( minus_minus_set_int(A2,B4) = bot_bot_set_int ) ) ).

% subset_minus_empty
tff(fact_5221_subset__minus__empty,axiom,
    ! [A2: set_nat,B4: set_nat] :
      ( aa_set_nat_o(ord_less_eq_set_nat(A2),B4)
     => ( minus_minus_set_nat(A2,B4) = bot_bot_set_nat ) ) ).

% subset_minus_empty
tff(fact_5222_atLeastLessThan0,axiom,
    ! [M: nat] : aa_nat_set_nat(set_or4665077453230672383an_nat(M),zero_zero_nat) = bot_bot_set_nat ).

% atLeastLessThan0
tff(fact_5223_lessThan__empty__iff,axiom,
    ! [N2: nat] :
      ( ( aa_nat_set_nat(set_ord_lessThan_nat,N2) = bot_bot_set_nat )
    <=> ( N2 = zero_zero_nat ) ) ).

% lessThan_empty_iff
tff(fact_5224_set__to__map__empty__iff_I1_J,axiom,
    ! [S2: set_Pr4329608150637261639at_nat] :
      ( ! [X4: set_Pr1261947904930325089at_nat] : aa_set2934564513904597954at_nat(set_to4447731662395764663at_nat(S2),X4) = none_s625347054029921090at_nat
    <=> ( S2 = bot_bo228742789529271731at_nat ) ) ).

% set_to_map_empty_iff(1)
tff(fact_5225_set__to__map__empty__iff_I1_J,axiom,
    ! [S2: set_Pr1261947904930325089at_nat] :
      ( ! [X4: nat] : aa_nat_option_nat(set_to_map_nat_nat(S2),X4) = none_nat
    <=> ( S2 = bot_bo2099793752762293965at_nat ) ) ).

% set_to_map_empty_iff(1)
tff(fact_5226_Code__Numeral_Osub__code_I1_J,axiom,
    aa_num_Code_integer(aa_num5808785979904431436nteger(code_sub,one),one) = zero_z3403309356797280102nteger ).

% Code_Numeral.sub_code(1)
tff(fact_5227_set__to__map__empty__iff_I2_J,axiom,
    ! [S2: set_Pr4329608150637261639at_nat] :
      ( ( aTP_Lamm_nm = set_to4447731662395764663at_nat(S2) )
    <=> ( S2 = bot_bo228742789529271731at_nat ) ) ).

% set_to_map_empty_iff(2)
tff(fact_5228_set__to__map__empty__iff_I2_J,axiom,
    ! [S2: set_Pr1261947904930325089at_nat] :
      ( ( aTP_Lamm_nn = set_to_map_nat_nat(S2) )
    <=> ( S2 = bot_bo2099793752762293965at_nat ) ) ).

% set_to_map_empty_iff(2)
tff(fact_5229_less__integer__def,axiom,
    ord_le6747313008572928689nteger = map_fu4249723513525335408eger_o(code_int_of_integer,map_fu6957801986076833569nt_o_o(code_int_of_integer,id_o),ord_less_int) ).

% less_integer_def
tff(fact_5230_less__eq__integer__def,axiom,
    ord_le3102999989581377725nteger = map_fu4249723513525335408eger_o(code_int_of_integer,map_fu6957801986076833569nt_o_o(code_int_of_integer,id_o),ord_less_eq_int) ).

% less_eq_integer_def
tff(fact_5231_Code__Numeral_Osub__code_I6_J,axiom,
    ! [M: num,N2: num] : aa_num_Code_integer(aa_num5808785979904431436nteger(code_sub,aa_num_num(bit0,M)),aa_num_num(bit0,N2)) = aa_Cod1783974652533396728nteger(code_dup,aa_num_Code_integer(aa_num5808785979904431436nteger(code_sub,M),N2)) ).

% Code_Numeral.sub_code(6)
tff(fact_5232_Code__Numeral_Osub__code_I7_J,axiom,
    ! [M: num,N2: num] : aa_num_Code_integer(aa_num5808785979904431436nteger(code_sub,aa_num_num(bit1,M)),aa_num_num(bit1,N2)) = aa_Cod1783974652533396728nteger(code_dup,aa_num_Code_integer(aa_num5808785979904431436nteger(code_sub,M),N2)) ).

% Code_Numeral.sub_code(7)
tff(fact_5233_sub_Orep__eq,axiom,
    ! [X2: num,Xa: num] : aa_Code_integer_int(code_int_of_integer,aa_num_Code_integer(aa_num5808785979904431436nteger(code_sub,X2),Xa)) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_num_int(numeral_numeral_int,X2)),aa_num_int(numeral_numeral_int,Xa)) ).

% sub.rep_eq
tff(fact_5234_sub_Oabs__eq,axiom,
    ! [Xa: num,X2: num] : aa_num_Code_integer(aa_num5808785979904431436nteger(code_sub,Xa),X2) = aa_int_Code_integer(code_integer_of_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_num_int(numeral_numeral_int,Xa)),aa_num_int(numeral_numeral_int,X2))) ).

% sub.abs_eq
tff(fact_5235_image__mult__atLeastAtMost__if,axiom,
    ! [C: rat,X2: rat,Y: rat] :
      image_rat_rat(aa_rat_fun_rat_rat(times_times_rat,C),set_or633870826150836451st_rat(X2,Y)) = $ite(
        aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),C),
        set_or633870826150836451st_rat(aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,C),X2),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,C),Y)),
        $ite(aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,X2),Y),set_or633870826150836451st_rat(aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,C),Y),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,C),X2)),bot_bot_set_rat) ) ).

% image_mult_atLeastAtMost_if
tff(fact_5236_image__mult__atLeastAtMost__if_H,axiom,
    ! [C: rat,X2: rat,Y: rat] :
      image_rat_rat(aTP_Lamm_no(C),set_or633870826150836451st_rat(X2,Y)) = $ite(
        aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,X2),Y),
        $ite(aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,zero_zero_rat),C),set_or633870826150836451st_rat(aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,X2),C),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,Y),C)),set_or633870826150836451st_rat(aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,Y),C),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,X2),C))),
        bot_bot_set_rat ) ).

% image_mult_atLeastAtMost_if'
tff(fact_5237_image__affinity__atLeastAtMost,axiom,
    ! [M: rat,C: rat,A: rat,B: rat] :
      image_rat_rat(aa_rat_fun_rat_rat(aTP_Lamm_np(M),C),set_or633870826150836451st_rat(A,B)) = $ite(
        set_or633870826150836451st_rat(A,B) = bot_bot_set_rat,
        bot_bot_set_rat,
        $ite(aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),M),set_or633870826150836451st_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,M),A)),C),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,M),B)),C)),set_or633870826150836451st_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,M),B)),C),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,M),A)),C))) ) ).

% image_affinity_atLeastAtMost
tff(fact_5238_and__int_Osimps,axiom,
    ! [K: int,L: int] :
      aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,K),L) = $ite(
        ( member_int(K,insert_int(zero_zero_int,insert_int(aa_int_int(uminus_uminus_int,one_one_int),bot_bot_set_int)))
        & member_int(L,insert_int(zero_zero_int,insert_int(aa_int_int(uminus_uminus_int,one_one_int),bot_bot_set_int))) ),
        aa_int_int(uminus_uminus_int,
          aa_o_int(zero_n2684676970156552555ol_int,
            ( ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),K)
            & ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),L) ))),
        aa_int_int(aa_int_fun_int_int(plus_plus_int,
            aa_o_int(zero_n2684676970156552555ol_int,
              ( ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),K)
              & ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),L) ))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,K),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),aa_int_int(aa_int_fun_int_int(divide_divide_int,L),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))))) ) ).

% and_int.simps
tff(fact_5239_and__int_Oelims,axiom,
    ! [X2: int,Xa: int,Y: int] :
      ( ( aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,X2),Xa) = Y )
     => ( Y = $ite(
            ( member_int(X2,insert_int(zero_zero_int,insert_int(aa_int_int(uminus_uminus_int,one_one_int),bot_bot_set_int)))
            & member_int(Xa,insert_int(zero_zero_int,insert_int(aa_int_int(uminus_uminus_int,one_one_int),bot_bot_set_int))) ),
            aa_int_int(uminus_uminus_int,
              aa_o_int(zero_n2684676970156552555ol_int,
                ( ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),X2)
                & ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),Xa) ))),
            aa_int_int(aa_int_fun_int_int(plus_plus_int,
                aa_o_int(zero_n2684676970156552555ol_int,
                  ( ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),X2)
                  & ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),Xa) ))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,X2),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),aa_int_int(aa_int_fun_int_int(divide_divide_int,Xa),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))))) ) ) ) ).

% and_int.elims
tff(fact_5240_and__int_Opelims,axiom,
    ! [X2: int,Xa: int,Y: int] :
      ( ( aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,X2),Xa) = Y )
     => ( aa_Pro4592068669816069595_int_o(accp_P1096762738010456898nt_int(bit_and_int_rel),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X2),Xa))
       => ~ ( ( Y = $ite(
                  ( member_int(X2,insert_int(zero_zero_int,insert_int(aa_int_int(uminus_uminus_int,one_one_int),bot_bot_set_int)))
                  & member_int(Xa,insert_int(zero_zero_int,insert_int(aa_int_int(uminus_uminus_int,one_one_int),bot_bot_set_int))) ),
                  aa_int_int(uminus_uminus_int,
                    aa_o_int(zero_n2684676970156552555ol_int,
                      ( ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),X2)
                      & ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),Xa) ))),
                  aa_int_int(aa_int_fun_int_int(plus_plus_int,
                      aa_o_int(zero_n2684676970156552555ol_int,
                        ( ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),X2)
                        & ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),Xa) ))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,X2),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),aa_int_int(aa_int_fun_int_int(divide_divide_int,Xa),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))))) ) )
           => ~ aa_Pro4592068669816069595_int_o(accp_P1096762738010456898nt_int(bit_and_int_rel),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X2),Xa)) ) ) ) ).

% and_int.pelims
tff(fact_5241_and__int_Opsimps,axiom,
    ! [K: int,L: int] :
      ( aa_Pro4592068669816069595_int_o(accp_P1096762738010456898nt_int(bit_and_int_rel),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,K),L))
     => ( aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,K),L) = $ite(
            ( member_int(K,insert_int(zero_zero_int,insert_int(aa_int_int(uminus_uminus_int,one_one_int),bot_bot_set_int)))
            & member_int(L,insert_int(zero_zero_int,insert_int(aa_int_int(uminus_uminus_int,one_one_int),bot_bot_set_int))) ),
            aa_int_int(uminus_uminus_int,
              aa_o_int(zero_n2684676970156552555ol_int,
                ( ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),K)
                & ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),L) ))),
            aa_int_int(aa_int_fun_int_int(plus_plus_int,
                aa_o_int(zero_n2684676970156552555ol_int,
                  ( ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),K)
                  & ~ aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),L) ))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_int_int(aa_int_fun_int_int(bit_se725231765392027082nd_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,K),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),aa_int_int(aa_int_fun_int_int(divide_divide_int,L),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))))) ) ) ) ).

% and_int.psimps
tff(fact_5242_and__int_Opinduct,axiom,
    ! [A0: int,A1: int,P: fun_int_fun_int_o] :
      ( aa_Pro4592068669816069595_int_o(accp_P1096762738010456898nt_int(bit_and_int_rel),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A0),A1))
     => ( ! [K3: int,L5: int] :
            ( aa_Pro4592068669816069595_int_o(accp_P1096762738010456898nt_int(bit_and_int_rel),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,K3),L5))
           => ( ( ~ ( member_int(K3,insert_int(zero_zero_int,insert_int(aa_int_int(uminus_uminus_int,one_one_int),bot_bot_set_int)))
                    & member_int(L5,insert_int(zero_zero_int,insert_int(aa_int_int(uminus_uminus_int,one_one_int),bot_bot_set_int))) )
               => aa_int_o(aa_int_fun_int_o(P,aa_int_int(aa_int_fun_int_int(divide_divide_int,K3),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))),aa_int_int(aa_int_fun_int_int(divide_divide_int,L5),aa_num_int(numeral_numeral_int,aa_num_num(bit0,one)))) )
             => aa_int_o(aa_int_fun_int_o(P,K3),L5) ) )
       => aa_int_o(aa_int_fun_int_o(P,A0),A1) ) ) ).

% and_int.pinduct
tff(fact_5243_mask__mod__exp,axiom,
    ! [N2: nat,M: nat] : aa_int_int(aa_int_fun_int_int(modulo_modulo_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),N2)),one_one_int)),aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),M)) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,M),N2))),one_one_int) ).

% mask_mod_exp
tff(fact_5244_mask__mod__exp,axiom,
    ! [N2: nat,M: nat] : aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)),one_one_nat)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),M)) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,M),N2))),one_one_nat) ).

% mask_mod_exp
tff(fact_5245_mask__mod__exp,axiom,
    ! [N2: nat,M: nat] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),N2)),one_one_Code_integer)),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),M)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,M),N2))),one_one_Code_integer) ).

% mask_mod_exp
tff(fact_5246_mask__mod__exp,axiom,
    ! [N2: nat,M: nat] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(minus_7197305767214868737atural,aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),N2)),one_one_Code_natural)),aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),M)) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(minus_7197305767214868737atural,aa_nat_Code_natural(power_7079662738309270450atural(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,M),N2))),one_one_Code_natural) ).

% mask_mod_exp
tff(fact_5247_pair__leqI2,axiom,
    ! [A: nat,B: nat,S: nat,T: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),B)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,S),T)
       => member8206827879206165904at_nat(produc6161850002892822231at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),S),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,B),T)),fun_pair_leq) ) ) ).

% pair_leqI2
tff(fact_5248_min__eq__arg_I1_J,axiom,
    ! [M: code_integer,N2: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_min_Code_integer,M),N2) = M )
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,M),N2) ) ).

% min_eq_arg(1)
tff(fact_5249_min__eq__arg_I1_J,axiom,
    ! [M: code_natural,N2: code_natural] :
      ( ( aa_Cod4272041906116450446atural(ord_min_Code_natural(M),N2) = M )
    <=> aa_Code_natural_o(aa_Cod1485054954640246627ural_o(ord_le1926595141338095240atural,M),N2) ) ).

% min_eq_arg(1)
tff(fact_5250_min__eq__arg_I1_J,axiom,
    ! [M: rat,N2: rat] :
      ( ( aa_rat_rat(ord_min_rat(M),N2) = M )
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,M),N2) ) ).

% min_eq_arg(1)
tff(fact_5251_min__eq__arg_I1_J,axiom,
    ! [M: num,N2: num] :
      ( ( aa_num_num(aa_num_fun_num_num(ord_min_num,M),N2) = M )
    <=> aa_num_o(aa_num_fun_num_o(ord_less_eq_num,M),N2) ) ).

% min_eq_arg(1)
tff(fact_5252_min__eq__arg_I1_J,axiom,
    ! [M: nat,N2: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,M),N2) = M )
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2) ) ).

% min_eq_arg(1)
tff(fact_5253_min__eq__arg_I1_J,axiom,
    ! [M: int,N2: int] :
      ( ( aa_int_int(aa_int_fun_int_int(ord_min_int,M),N2) = M )
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,M),N2) ) ).

% min_eq_arg(1)
tff(fact_5254_min__eq__arg_I2_J,axiom,
    ! [M: code_integer,N2: code_integer] :
      ( ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_min_Code_integer,M),N2) = N2 )
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,N2),M) ) ).

% min_eq_arg(2)
tff(fact_5255_min__eq__arg_I2_J,axiom,
    ! [M: code_natural,N2: code_natural] :
      ( ( aa_Cod4272041906116450446atural(ord_min_Code_natural(M),N2) = N2 )
    <=> aa_Code_natural_o(aa_Cod1485054954640246627ural_o(ord_le1926595141338095240atural,N2),M) ) ).

% min_eq_arg(2)
tff(fact_5256_min__eq__arg_I2_J,axiom,
    ! [M: rat,N2: rat] :
      ( ( aa_rat_rat(ord_min_rat(M),N2) = N2 )
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,N2),M) ) ).

% min_eq_arg(2)
tff(fact_5257_min__eq__arg_I2_J,axiom,
    ! [M: num,N2: num] :
      ( ( aa_num_num(aa_num_fun_num_num(ord_min_num,M),N2) = N2 )
    <=> aa_num_o(aa_num_fun_num_o(ord_less_eq_num,N2),M) ) ).

% min_eq_arg(2)
tff(fact_5258_min__eq__arg_I2_J,axiom,
    ! [M: nat,N2: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,M),N2) = N2 )
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),M) ) ).

% min_eq_arg(2)
tff(fact_5259_min__eq__arg_I2_J,axiom,
    ! [M: int,N2: int] :
      ( ( aa_int_int(aa_int_fun_int_int(ord_min_int,M),N2) = N2 )
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,N2),M) ) ).

% min_eq_arg(2)
tff(fact_5260_min__arg__le_I1_J,axiom,
    ! [N2: code_integer,M: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,N2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_min_Code_integer,M),N2))
    <=> ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_min_Code_integer,M),N2) = N2 ) ) ).

% min_arg_le(1)
tff(fact_5261_min__arg__le_I1_J,axiom,
    ! [N2: code_natural,M: code_natural] :
      ( aa_Code_natural_o(aa_Cod1485054954640246627ural_o(ord_le1926595141338095240atural,N2),aa_Cod4272041906116450446atural(ord_min_Code_natural(M),N2))
    <=> ( aa_Cod4272041906116450446atural(ord_min_Code_natural(M),N2) = N2 ) ) ).

% min_arg_le(1)
tff(fact_5262_min__arg__le_I1_J,axiom,
    ! [N2: set_nat,M: set_nat] :
      ( aa_set_nat_o(ord_less_eq_set_nat(N2),ord_min_set_nat(M,N2))
    <=> ( ord_min_set_nat(M,N2) = N2 ) ) ).

% min_arg_le(1)
tff(fact_5263_min__arg__le_I1_J,axiom,
    ! [N2: rat,M: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,N2),aa_rat_rat(ord_min_rat(M),N2))
    <=> ( aa_rat_rat(ord_min_rat(M),N2) = N2 ) ) ).

% min_arg_le(1)
tff(fact_5264_min__arg__le_I1_J,axiom,
    ! [N2: num,M: num] :
      ( aa_num_o(aa_num_fun_num_o(ord_less_eq_num,N2),aa_num_num(aa_num_fun_num_num(ord_min_num,M),N2))
    <=> ( aa_num_num(aa_num_fun_num_num(ord_min_num,M),N2) = N2 ) ) ).

% min_arg_le(1)
tff(fact_5265_min__arg__le_I1_J,axiom,
    ! [N2: nat,M: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,M),N2))
    <=> ( aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,M),N2) = N2 ) ) ).

% min_arg_le(1)
tff(fact_5266_min__arg__le_I1_J,axiom,
    ! [N2: int,M: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,N2),aa_int_int(aa_int_fun_int_int(ord_min_int,M),N2))
    <=> ( aa_int_int(aa_int_fun_int_int(ord_min_int,M),N2) = N2 ) ) ).

% min_arg_le(1)
tff(fact_5267_min__arg__le_I2_J,axiom,
    ! [M: code_integer,N2: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,M),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_min_Code_integer,M),N2))
    <=> ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_min_Code_integer,M),N2) = M ) ) ).

% min_arg_le(2)
tff(fact_5268_min__arg__le_I2_J,axiom,
    ! [M: code_natural,N2: code_natural] :
      ( aa_Code_natural_o(aa_Cod1485054954640246627ural_o(ord_le1926595141338095240atural,M),aa_Cod4272041906116450446atural(ord_min_Code_natural(M),N2))
    <=> ( aa_Cod4272041906116450446atural(ord_min_Code_natural(M),N2) = M ) ) ).

% min_arg_le(2)
tff(fact_5269_min__arg__le_I2_J,axiom,
    ! [M: set_nat,N2: set_nat] :
      ( aa_set_nat_o(ord_less_eq_set_nat(M),ord_min_set_nat(M,N2))
    <=> ( ord_min_set_nat(M,N2) = M ) ) ).

% min_arg_le(2)
tff(fact_5270_min__arg__le_I2_J,axiom,
    ! [M: rat,N2: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,M),aa_rat_rat(ord_min_rat(M),N2))
    <=> ( aa_rat_rat(ord_min_rat(M),N2) = M ) ) ).

% min_arg_le(2)
tff(fact_5271_min__arg__le_I2_J,axiom,
    ! [M: num,N2: num] :
      ( aa_num_o(aa_num_fun_num_o(ord_less_eq_num,M),aa_num_num(aa_num_fun_num_num(ord_min_num,M),N2))
    <=> ( aa_num_num(aa_num_fun_num_num(ord_min_num,M),N2) = M ) ) ).

% min_arg_le(2)
tff(fact_5272_min__arg__le_I2_J,axiom,
    ! [M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,M),N2))
    <=> ( aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,M),N2) = M ) ) ).

% min_arg_le(2)
tff(fact_5273_min__arg__le_I2_J,axiom,
    ! [M: int,N2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,M),aa_int_int(aa_int_fun_int_int(ord_min_int,M),N2))
    <=> ( aa_int_int(aa_int_fun_int_int(ord_min_int,M),N2) = M ) ) ).

% min_arg_le(2)
tff(fact_5274_min__arg__not__ge_I1_J,axiom,
    ! [M: code_natural,N2: code_natural] :
      ( ~ aa_Code_natural_o(aa_Cod1485054954640246627ural_o(ord_le5570908160329646204atural,aa_Cod4272041906116450446atural(ord_min_Code_natural(M),N2)),M)
    <=> ( aa_Cod4272041906116450446atural(ord_min_Code_natural(M),N2) = M ) ) ).

% min_arg_not_ge(1)
tff(fact_5275_min__arg__not__ge_I1_J,axiom,
    ! [M: code_integer,N2: code_integer] :
      ( ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_min_Code_integer,M),N2)),M)
    <=> ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_min_Code_integer,M),N2) = M ) ) ).

% min_arg_not_ge(1)
tff(fact_5276_min__arg__not__ge_I1_J,axiom,
    ! [M: rat,N2: rat] :
      ( ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(ord_min_rat(M),N2)),M)
    <=> ( aa_rat_rat(ord_min_rat(M),N2) = M ) ) ).

% min_arg_not_ge(1)
tff(fact_5277_min__arg__not__ge_I1_J,axiom,
    ! [M: num,N2: num] :
      ( ~ aa_num_o(aa_num_fun_num_o(ord_less_num,aa_num_num(aa_num_fun_num_num(ord_min_num,M),N2)),M)
    <=> ( aa_num_num(aa_num_fun_num_num(ord_min_num,M),N2) = M ) ) ).

% min_arg_not_ge(1)
tff(fact_5278_min__arg__not__ge_I1_J,axiom,
    ! [M: nat,N2: nat] :
      ( ~ aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,M),N2)),M)
    <=> ( aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,M),N2) = M ) ) ).

% min_arg_not_ge(1)
tff(fact_5279_min__arg__not__ge_I1_J,axiom,
    ! [M: int,N2: int] :
      ( ~ aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(ord_min_int,M),N2)),M)
    <=> ( aa_int_int(aa_int_fun_int_int(ord_min_int,M),N2) = M ) ) ).

% min_arg_not_ge(1)
tff(fact_5280_min__arg__not__ge_I2_J,axiom,
    ! [M: code_natural,N2: code_natural] :
      ( ~ aa_Code_natural_o(aa_Cod1485054954640246627ural_o(ord_le5570908160329646204atural,aa_Cod4272041906116450446atural(ord_min_Code_natural(M),N2)),N2)
    <=> ( aa_Cod4272041906116450446atural(ord_min_Code_natural(M),N2) = N2 ) ) ).

% min_arg_not_ge(2)
tff(fact_5281_min__arg__not__ge_I2_J,axiom,
    ! [M: code_integer,N2: code_integer] :
      ( ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_min_Code_integer,M),N2)),N2)
    <=> ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_min_Code_integer,M),N2) = N2 ) ) ).

% min_arg_not_ge(2)
tff(fact_5282_min__arg__not__ge_I2_J,axiom,
    ! [M: rat,N2: rat] :
      ( ~ aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(ord_min_rat(M),N2)),N2)
    <=> ( aa_rat_rat(ord_min_rat(M),N2) = N2 ) ) ).

% min_arg_not_ge(2)
tff(fact_5283_min__arg__not__ge_I2_J,axiom,
    ! [M: num,N2: num] :
      ( ~ aa_num_o(aa_num_fun_num_o(ord_less_num,aa_num_num(aa_num_fun_num_num(ord_min_num,M),N2)),N2)
    <=> ( aa_num_num(aa_num_fun_num_num(ord_min_num,M),N2) = N2 ) ) ).

% min_arg_not_ge(2)
tff(fact_5284_min__arg__not__ge_I2_J,axiom,
    ! [M: nat,N2: nat] :
      ( ~ aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,M),N2)),N2)
    <=> ( aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,M),N2) = N2 ) ) ).

% min_arg_not_ge(2)
tff(fact_5285_min__arg__not__ge_I2_J,axiom,
    ! [M: int,N2: int] :
      ( ~ aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(ord_min_int,M),N2)),N2)
    <=> ( aa_int_int(aa_int_fun_int_int(ord_min_int,M),N2) = N2 ) ) ).

% min_arg_not_ge(2)
tff(fact_5286_min__less__self__conv_I1_J,axiom,
    ! [A: code_natural,B: code_natural] :
      ( aa_Code_natural_o(aa_Cod1485054954640246627ural_o(ord_le5570908160329646204atural,aa_Cod4272041906116450446atural(ord_min_Code_natural(A),B)),A)
    <=> aa_Code_natural_o(aa_Cod1485054954640246627ural_o(ord_le5570908160329646204atural,B),A) ) ).

% min_less_self_conv(1)
tff(fact_5287_min__less__self__conv_I1_J,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_min_Code_integer,A),B)),A)
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,B),A) ) ).

% min_less_self_conv(1)
tff(fact_5288_min__less__self__conv_I1_J,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(ord_min_rat(A),B)),A)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,B),A) ) ).

% min_less_self_conv(1)
tff(fact_5289_min__less__self__conv_I1_J,axiom,
    ! [A: num,B: num] :
      ( aa_num_o(aa_num_fun_num_o(ord_less_num,aa_num_num(aa_num_fun_num_num(ord_min_num,A),B)),A)
    <=> aa_num_o(aa_num_fun_num_o(ord_less_num,B),A) ) ).

% min_less_self_conv(1)
tff(fact_5290_min__less__self__conv_I1_J,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,A),B)),A)
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,B),A) ) ).

% min_less_self_conv(1)
tff(fact_5291_min__less__self__conv_I1_J,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(ord_min_int,A),B)),A)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,B),A) ) ).

% min_less_self_conv(1)
tff(fact_5292_min__less__self__conv_I2_J,axiom,
    ! [A: code_natural,B: code_natural] :
      ( aa_Code_natural_o(aa_Cod1485054954640246627ural_o(ord_le5570908160329646204atural,aa_Cod4272041906116450446atural(ord_min_Code_natural(A),B)),B)
    <=> aa_Code_natural_o(aa_Cod1485054954640246627ural_o(ord_le5570908160329646204atural,A),B) ) ).

% min_less_self_conv(2)
tff(fact_5293_min__less__self__conv_I2_J,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_min_Code_integer,A),B)),B)
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),B) ) ).

% min_less_self_conv(2)
tff(fact_5294_min__less__self__conv_I2_J,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_rat_rat(ord_min_rat(A),B)),B)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B) ) ).

% min_less_self_conv(2)
tff(fact_5295_min__less__self__conv_I2_J,axiom,
    ! [A: num,B: num] :
      ( aa_num_o(aa_num_fun_num_o(ord_less_num,aa_num_num(aa_num_fun_num_num(ord_min_num,A),B)),B)
    <=> aa_num_o(aa_num_fun_num_o(ord_less_num,A),B) ) ).

% min_less_self_conv(2)
tff(fact_5296_min__less__self__conv_I2_J,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,A),B)),B)
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),B) ) ).

% min_less_self_conv(2)
tff(fact_5297_min__less__self__conv_I2_J,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,aa_int_int(aa_int_fun_int_int(ord_min_int,A),B)),B)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,A),B) ) ).

% min_less_self_conv(2)
tff(fact_5298_min__simps_I1_J,axiom,
    ! [A: code_natural,B: code_natural] :
      ( aa_Code_natural_o(aa_Cod1485054954640246627ural_o(ord_le5570908160329646204atural,A),B)
     => ( aa_Cod4272041906116450446atural(ord_min_Code_natural(A),B) = A ) ) ).

% min_simps(1)
tff(fact_5299_min__simps_I1_J,axiom,
    ! [A: code_integer,B: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,A),B)
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_min_Code_integer,A),B) = A ) ) ).

% min_simps(1)
tff(fact_5300_min__simps_I1_J,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B)
     => ( aa_rat_rat(ord_min_rat(A),B) = A ) ) ).

% min_simps(1)
tff(fact_5301_min__simps_I1_J,axiom,
    ! [A: num,B: num] :
      ( aa_num_o(aa_num_fun_num_o(ord_less_num,A),B)
     => ( aa_num_num(aa_num_fun_num_num(ord_min_num,A),B) = A ) ) ).

% min_simps(1)
tff(fact_5302_min__simps_I1_J,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),B)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,A),B) = A ) ) ).

% min_simps(1)
tff(fact_5303_min__simps_I1_J,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,A),B)
     => ( aa_int_int(aa_int_fun_int_int(ord_min_int,A),B) = A ) ) ).

% min_simps(1)
tff(fact_5304_min__simps_I2_J,axiom,
    ! [B: code_natural,A: code_natural] :
      ( aa_Code_natural_o(aa_Cod1485054954640246627ural_o(ord_le5570908160329646204atural,B),A)
     => ( aa_Cod4272041906116450446atural(ord_min_Code_natural(A),B) = B ) ) ).

% min_simps(2)
tff(fact_5305_min__simps_I2_J,axiom,
    ! [B: code_integer,A: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,B),A)
     => ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_min_Code_integer,A),B) = B ) ) ).

% min_simps(2)
tff(fact_5306_min__simps_I2_J,axiom,
    ! [B: rat,A: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,B),A)
     => ( aa_rat_rat(ord_min_rat(A),B) = B ) ) ).

% min_simps(2)
tff(fact_5307_min__simps_I2_J,axiom,
    ! [B: num,A: num] :
      ( aa_num_o(aa_num_fun_num_o(ord_less_num,B),A)
     => ( aa_num_num(aa_num_fun_num_num(ord_min_num,A),B) = B ) ) ).

% min_simps(2)
tff(fact_5308_min__simps_I2_J,axiom,
    ! [B: nat,A: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,B),A)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,A),B) = B ) ) ).

% min_simps(2)
tff(fact_5309_min__simps_I2_J,axiom,
    ! [B: int,A: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,B),A)
     => ( aa_int_int(aa_int_fun_int_int(ord_min_int,A),B) = B ) ) ).

% min_simps(2)
tff(fact_5310_min__0__1_I2_J,axiom,
    aa_rat_rat(ord_min_rat(one_one_rat),zero_zero_rat) = zero_zero_rat ).

% min_0_1(2)
tff(fact_5311_min__0__1_I2_J,axiom,
    aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,one_one_nat),zero_zero_nat) = zero_zero_nat ).

% min_0_1(2)
tff(fact_5312_min__0__1_I2_J,axiom,
    aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_min_Code_integer,one_one_Code_integer),zero_z3403309356797280102nteger) = zero_z3403309356797280102nteger ).

% min_0_1(2)
tff(fact_5313_min__0__1_I2_J,axiom,
    aa_int_int(aa_int_fun_int_int(ord_min_int,one_one_int),zero_zero_int) = zero_zero_int ).

% min_0_1(2)
tff(fact_5314_min__0__1_I2_J,axiom,
    aa_Cod4272041906116450446atural(ord_min_Code_natural(one_one_Code_natural),zero_z2226904508553997617atural) = zero_z2226904508553997617atural ).

% min_0_1(2)
tff(fact_5315_min__0__1_I1_J,axiom,
    aa_rat_rat(ord_min_rat(zero_zero_rat),one_one_rat) = zero_zero_rat ).

% min_0_1(1)
tff(fact_5316_min__0__1_I1_J,axiom,
    aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,zero_zero_nat),one_one_nat) = zero_zero_nat ).

% min_0_1(1)
tff(fact_5317_min__0__1_I1_J,axiom,
    aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_min_Code_integer,zero_z3403309356797280102nteger),one_one_Code_integer) = zero_z3403309356797280102nteger ).

% min_0_1(1)
tff(fact_5318_min__0__1_I1_J,axiom,
    aa_int_int(aa_int_fun_int_int(ord_min_int,zero_zero_int),one_one_int) = zero_zero_int ).

% min_0_1(1)
tff(fact_5319_min__0__1_I1_J,axiom,
    aa_Cod4272041906116450446atural(ord_min_Code_natural(zero_z2226904508553997617atural),one_one_Code_natural) = zero_z2226904508553997617atural ).

% min_0_1(1)
tff(fact_5320_min__0__1_I5_J,axiom,
    ! [X2: num] : aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,one_one_nat),aa_num_nat(numeral_numeral_nat,X2)) = one_one_nat ).

% min_0_1(5)
tff(fact_5321_min__0__1_I5_J,axiom,
    ! [X2: num] : aa_int_int(aa_int_fun_int_int(ord_min_int,one_one_int),aa_num_int(numeral_numeral_int,X2)) = one_one_int ).

% min_0_1(5)
tff(fact_5322_min__0__1_I5_J,axiom,
    ! [X2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_min_Code_integer,one_one_Code_integer),aa_num_Code_integer(numera6620942414471956472nteger,X2)) = one_one_Code_integer ).

% min_0_1(5)
tff(fact_5323_min__0__1_I5_J,axiom,
    ! [X2: num] : aa_rat_rat(ord_min_rat(one_one_rat),aa_num_rat(numeral_numeral_rat,X2)) = one_one_rat ).

% min_0_1(5)
tff(fact_5324_min__0__1_I5_J,axiom,
    ! [X2: num] : aa_Cod4272041906116450446atural(ord_min_Code_natural(one_one_Code_natural),aa_num_Code_natural(numera5444537566228673987atural,X2)) = one_one_Code_natural ).

% min_0_1(5)
tff(fact_5325_min__0__1_I6_J,axiom,
    ! [X2: num] : aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,aa_num_nat(numeral_numeral_nat,X2)),one_one_nat) = one_one_nat ).

% min_0_1(6)
tff(fact_5326_min__0__1_I6_J,axiom,
    ! [X2: num] : aa_int_int(aa_int_fun_int_int(ord_min_int,aa_num_int(numeral_numeral_int,X2)),one_one_int) = one_one_int ).

% min_0_1(6)
tff(fact_5327_min__0__1_I6_J,axiom,
    ! [X2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_min_Code_integer,aa_num_Code_integer(numera6620942414471956472nteger,X2)),one_one_Code_integer) = one_one_Code_integer ).

% min_0_1(6)
tff(fact_5328_min__0__1_I6_J,axiom,
    ! [X2: num] : aa_rat_rat(ord_min_rat(aa_num_rat(numeral_numeral_rat,X2)),one_one_rat) = one_one_rat ).

% min_0_1(6)
tff(fact_5329_min__0__1_I6_J,axiom,
    ! [X2: num] : aa_Cod4272041906116450446atural(ord_min_Code_natural(aa_num_Code_natural(numera5444537566228673987atural,X2)),one_one_Code_natural) = one_one_Code_natural ).

% min_0_1(6)
tff(fact_5330_atLeastAtMost__singleton__iff,axiom,
    ! [A: $o,B: $o,C: $o] :
      ( ( aa_o_set_o(set_or8904488021354931149Most_o((A)),(B)) = insert_o((C),bot_bot_set_o) )
    <=> ( ( (A)
        <=> (B) )
        & ( (B)
        <=> (C) ) ) ) ).

% atLeastAtMost_singleton_iff
tff(fact_5331_atLeastAtMost__singleton__iff,axiom,
    ! [A: int,B: int,C: int] :
      ( ( aa_int_set_int(set_or1266510415728281911st_int(A),B) = insert_int(C,bot_bot_set_int) )
    <=> ( ( A = B )
        & ( B = C ) ) ) ).

% atLeastAtMost_singleton_iff
tff(fact_5332_atLeastAtMost__singleton__iff,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( aa_nat_set_nat(set_or1269000886237332187st_nat(A),B) = insert_nat(C,bot_bot_set_nat) )
    <=> ( ( A = B )
        & ( B = C ) ) ) ).

% atLeastAtMost_singleton_iff
tff(fact_5333_atLeastAtMost__singleton__iff,axiom,
    ! [A: code_integer,B: code_integer,C: code_integer] :
      ( ( aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(A),B) = insert_Code_integer(C,bot_bo3990330152332043303nteger) )
    <=> ( ( A = B )
        & ( B = C ) ) ) ).

% atLeastAtMost_singleton_iff
tff(fact_5334_atLeastAtMost__singleton,axiom,
    ! [A: $o] : aa_o_set_o(set_or8904488021354931149Most_o((A)),(A)) = insert_o((A),bot_bot_set_o) ).

% atLeastAtMost_singleton
tff(fact_5335_atLeastAtMost__singleton,axiom,
    ! [A: int] : aa_int_set_int(set_or1266510415728281911st_int(A),A) = insert_int(A,bot_bot_set_int) ).

% atLeastAtMost_singleton
tff(fact_5336_atLeastAtMost__singleton,axiom,
    ! [A: nat] : aa_nat_set_nat(set_or1269000886237332187st_nat(A),A) = insert_nat(A,bot_bot_set_nat) ).

% atLeastAtMost_singleton
tff(fact_5337_atLeastAtMost__singleton,axiom,
    ! [A: code_integer] : aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(A),A) = insert_Code_integer(A,bot_bo3990330152332043303nteger) ).

% atLeastAtMost_singleton
tff(fact_5338_min__Suc__gt_I2_J,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),B)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,B),aa_nat_nat(suc,A)) = aa_nat_nat(suc,A) ) ) ).

% min_Suc_gt(2)
tff(fact_5339_min__Suc__gt_I1_J,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),B)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,aa_nat_nat(suc,A)),B) = aa_nat_nat(suc,A) ) ) ).

% min_Suc_gt(1)
tff(fact_5340_case__prod__Pair,axiom,
    produc697581972998607883nteger(produc565448451787809096nteger) = id_Pro1988134236931701989nteger ).

% case_prod_Pair
tff(fact_5341_case__prod__Pair,axiom,
    produc1949718844479134567et_nat(produc6017135503889078682et_nat) = id_Pro1868950919225201135et_nat ).

% case_prod_Pair
tff(fact_5342_case__prod__Pair,axiom,
    produc2255458887868536227et_nat(produc7291855603632349880et_nat) = id_Pro6241762429208028941et_nat ).

% case_prod_Pair
tff(fact_5343_case__prod__Pair,axiom,
    produc6823905543215200229nt_int(produc7320969046608631221nt_int) = id_Pro8963167613625125458nt_int ).

% case_prod_Pair
tff(fact_5344_case__prod__Pair,axiom,
    produc7102243260366339645nt_int(produc4729913460834754785nt_int) = id_Pro8454827939775161726nt_int ).

% case_prod_Pair
tff(fact_5345_case__prod__Pair,axiom,
    aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,product_Pair_int_int) = id_Pro4381231610383771306nt_int ).

% case_prod_Pair
tff(fact_5346_single__Diff__lessThan,axiom,
    ! [K: $o] : minus_minus_set_o(insert_o((K),bot_bot_set_o),aa_o_set_o(set_ord_lessThan_o,(K))) = insert_o((K),bot_bot_set_o) ).

% single_Diff_lessThan
tff(fact_5347_single__Diff__lessThan,axiom,
    ! [K: int] : minus_minus_set_int(insert_int(K,bot_bot_set_int),aa_int_set_int(set_ord_lessThan_int,K)) = insert_int(K,bot_bot_set_int) ).

% single_Diff_lessThan
tff(fact_5348_single__Diff__lessThan,axiom,
    ! [K: nat] : minus_minus_set_nat(insert_nat(K,bot_bot_set_nat),aa_nat_set_nat(set_ord_lessThan_nat,K)) = insert_nat(K,bot_bot_set_nat) ).

% single_Diff_lessThan
tff(fact_5349_min__add__distrib__right,axiom,
    ! [X2: rat,Y: rat,Z: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),aa_rat_rat(ord_min_rat(Y),Z)) = aa_rat_rat(ord_min_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),Y)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),Z)) ).

% min_add_distrib_right
tff(fact_5350_min__add__distrib__right,axiom,
    ! [X2: nat,Y: nat,Z: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X2),aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,Y),Z)) = aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X2),Y)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X2),Z)) ).

% min_add_distrib_right
tff(fact_5351_min__add__distrib__right,axiom,
    ! [X2: code_integer,Y: code_integer,Z: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X2),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_min_Code_integer,Y),Z)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_min_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X2),Y)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X2),Z)) ).

% min_add_distrib_right
tff(fact_5352_min__add__distrib__right,axiom,
    ! [X2: int,Y: int,Z: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),aa_int_int(aa_int_fun_int_int(ord_min_int,Y),Z)) = aa_int_int(aa_int_fun_int_int(ord_min_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),Y)),aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),Z)) ).

% min_add_distrib_right
tff(fact_5353_min__add__distrib__right,axiom,
    ! [X2: code_natural,Y: code_natural,Z: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,X2),aa_Cod4272041906116450446atural(ord_min_Code_natural(Y),Z)) = aa_Cod4272041906116450446atural(ord_min_Code_natural(aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,X2),Y)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,X2),Z)) ).

% min_add_distrib_right
tff(fact_5354_min__add__distrib__left,axiom,
    ! [X2: rat,Y: rat,Z: rat] : aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(ord_min_rat(X2),Y)),Z) = aa_rat_rat(ord_min_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),Z)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,Y),Z)) ).

% min_add_distrib_left
tff(fact_5355_min__add__distrib__left,axiom,
    ! [X2: nat,Y: nat,Z: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,X2),Y)),Z) = aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X2),Z)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Y),Z)) ).

% min_add_distrib_left
tff(fact_5356_min__add__distrib__left,axiom,
    ! [X2: code_integer,Y: code_integer,Z: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_min_Code_integer,X2),Y)),Z) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_min_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X2),Z)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,Y),Z)) ).

% min_add_distrib_left
tff(fact_5357_min__add__distrib__left,axiom,
    ! [X2: int,Y: int,Z: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(ord_min_int,X2),Y)),Z) = aa_int_int(aa_int_fun_int_int(ord_min_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),Z)),aa_int_int(aa_int_fun_int_int(plus_plus_int,Y),Z)) ).

% min_add_distrib_left
tff(fact_5358_min__add__distrib__left,axiom,
    ! [X2: code_natural,Y: code_natural,Z: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(ord_min_Code_natural(X2),Y)),Z) = aa_Cod4272041906116450446atural(ord_min_Code_natural(aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,X2),Z)),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,Y),Z)) ).

% min_add_distrib_left
tff(fact_5359_min__diff__distrib__left,axiom,
    ! [X2: code_integer,Y: code_integer,Z: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_min_Code_integer,X2),Y)),Z) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_min_Code_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,X2),Z)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,Y),Z)) ).

% min_diff_distrib_left
tff(fact_5360_min__diff__distrib__left,axiom,
    ! [X2: rat,Y: rat,Z: rat] : aa_rat_rat(minus_minus_rat(aa_rat_rat(ord_min_rat(X2),Y)),Z) = aa_rat_rat(ord_min_rat(aa_rat_rat(minus_minus_rat(X2),Z)),aa_rat_rat(minus_minus_rat(Y),Z)) ).

% min_diff_distrib_left
tff(fact_5361_min__diff__distrib__left,axiom,
    ! [X2: int,Y: int,Z: int] : aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(aa_int_fun_int_int(ord_min_int,X2),Y)),Z) = aa_int_int(aa_int_fun_int_int(ord_min_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,X2),Z)),aa_int_int(aa_int_fun_int_int(minus_minus_int,Y),Z)) ).

% min_diff_distrib_left
tff(fact_5362_bot__option__def,axiom,
    bot_bot_option_num = none_num ).

% bot_option_def
tff(fact_5363_bot__empty__eq2,axiom,
    ! [X: fun_Pr5098669352780829690e_term,Xa3: produc8923325533196201883nteger] :
      ( aa_Pro4926521453222654329eger_o(aa_fun4505422719058378424eger_o(bot_bo4567088895781559819eger_o,X),Xa3)
    <=> member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X),Xa3),bot_bo9050247954524366304nteger) ) ).

% bot_empty_eq2
tff(fact_5364_bot__empty__eq2,axiom,
    ! [X: fun_Pr6460944699146269935_nat_o,Xa3: produc3658429121746597890et_nat] :
      ( aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(bot_bo3509460380234399255_nat_o,X),Xa3)
    <=> member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X),Xa3),bot_bo1493351289776401898et_nat) ) ).

% bot_empty_eq2
tff(fact_5365_bot__empty__eq2,axiom,
    ! [X: fun_Pr6460944699146269935_nat_o,Xa3: produc8799533983703829792et_nat] :
      ( aa_Pro5643009357358181178_nat_o(aa_fun912680268133416158_nat_o(bot_bo5031374944739956857_nat_o,X),Xa3)
    <=> member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X),Xa3),bot_bo6121529163330120712et_nat) ) ).

% bot_empty_eq2
tff(fact_5366_bot__empty__eq2,axiom,
    ! [X: fun_Pr7763680713840462443e_term,Xa3: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(aa_fun3538162476766722827_int_o(bot_bo1117279750869432670_int_o,X),Xa3)
    <=> member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X),Xa3),bot_bo2501116328598523085nt_int) ) ).

% bot_empty_eq2
tff(fact_5367_bot__empty__eq2,axiom,
    ! [X: fun_in5730379987311621695e_term,Xa3: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(aa_fun586359091965693151_int_o(bot_bo6524246659364023090_int_o,X),Xa3)
    <=> member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X),Xa3),bot_bo5189594446080201209nt_int) ) ).

% bot_empty_eq2
tff(fact_5368_bot__empty__eq2,axiom,
    ! [X: set_Pr1261947904930325089at_nat,Xa3: set_Pr1261947904930325089at_nat] :
      ( aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(bot_bo1070391751820557722_nat_o,X),Xa3)
    <=> member8757157785044589968at_nat(produc2922128104949294807at_nat(X,Xa3),bot_bo228742789529271731at_nat) ) ).

% bot_empty_eq2
tff(fact_5369_bot__empty__eq2,axiom,
    ! [X: nat,Xa3: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(bot_bo1118997454112379798_nat_o,X),Xa3)
    <=> member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X),Xa3),bot_bo2099793752762293965at_nat) ) ).

% bot_empty_eq2
tff(fact_5370_map__fun_Oidentity,axiom,
    map_fun_nat_nat_o_o(aTP_Lamm_co,aTP_Lamm_nq) = id_fun_nat_o ).

% map_fun.identity
tff(fact_5371_map__option_Oidentity,axiom,
    map_option_num_num(aTP_Lamm_cg) = id_option_num ).

% map_option.identity
tff(fact_5372_minus__max__eq__min,axiom,
    ! [X2: int,Y: int] : aa_int_int(uminus_uminus_int,aa_int_int(aa_int_fun_int_int(ord_max_int,X2),Y)) = aa_int_int(aa_int_fun_int_int(ord_min_int,aa_int_int(uminus_uminus_int,X2)),aa_int_int(uminus_uminus_int,Y)) ).

% minus_max_eq_min
tff(fact_5373_minus__max__eq__min,axiom,
    ! [X2: code_integer,Y: code_integer] : aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_max_Code_integer,X2),Y)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_min_Code_integer,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,X2)),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,Y)) ).

% minus_max_eq_min
tff(fact_5374_minus__max__eq__min,axiom,
    ! [X2: rat,Y: rat] : aa_rat_rat(uminus_uminus_rat,aa_rat_rat(ord_max_rat(X2),Y)) = aa_rat_rat(ord_min_rat(aa_rat_rat(uminus_uminus_rat,X2)),aa_rat_rat(uminus_uminus_rat,Y)) ).

% minus_max_eq_min
tff(fact_5375_minus__min__eq__max,axiom,
    ! [X2: int,Y: int] : aa_int_int(uminus_uminus_int,aa_int_int(aa_int_fun_int_int(ord_min_int,X2),Y)) = aa_int_int(aa_int_fun_int_int(ord_max_int,aa_int_int(uminus_uminus_int,X2)),aa_int_int(uminus_uminus_int,Y)) ).

% minus_min_eq_max
tff(fact_5376_minus__min__eq__max,axiom,
    ! [X2: code_integer,Y: code_integer] : aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_min_Code_integer,X2),Y)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_max_Code_integer,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,X2)),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,Y)) ).

% minus_min_eq_max
tff(fact_5377_minus__min__eq__max,axiom,
    ! [X2: rat,Y: rat] : aa_rat_rat(uminus_uminus_rat,aa_rat_rat(ord_min_rat(X2),Y)) = aa_rat_rat(ord_max_rat(aa_rat_rat(uminus_uminus_rat,X2)),aa_rat_rat(uminus_uminus_rat,Y)) ).

% minus_min_eq_max
tff(fact_5378_insert__minus__eq,axiom,
    ! [X2: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
      ( ( X2 != Y )
     => ( minus_3314409938677909166at_nat(aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(X2),A2),aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(Y),bot_bo228742789529271731at_nat)) = aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(X2),minus_3314409938677909166at_nat(A2,aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(Y),bot_bo228742789529271731at_nat))) ) ) ).

% insert_minus_eq
tff(fact_5379_insert__minus__eq,axiom,
    ! [X2: product_prod_nat_nat,Y: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
      ( ( X2 != Y )
     => ( aa_set8868280134176360700at_nat(minus_1356011639430497352at_nat(aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(X2),A2)),aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(Y),bot_bo2099793752762293965at_nat)) = aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(X2),aa_set8868280134176360700at_nat(minus_1356011639430497352at_nat(A2),aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(Y),bot_bo2099793752762293965at_nat))) ) ) ).

% insert_minus_eq
tff(fact_5380_insert__minus__eq,axiom,
    ! [X2: $o,Y: $o,A2: set_o] :
      ( ~ ( (X2)
        <=> (Y) )
     => ( minus_minus_set_o(insert_o((X2),A2),insert_o((Y),bot_bot_set_o)) = insert_o((X2),minus_minus_set_o(A2,insert_o((Y),bot_bot_set_o))) ) ) ).

% insert_minus_eq
tff(fact_5381_insert__minus__eq,axiom,
    ! [X2: int,Y: int,A2: set_int] :
      ( ( X2 != Y )
     => ( minus_minus_set_int(insert_int(X2,A2),insert_int(Y,bot_bot_set_int)) = insert_int(X2,minus_minus_set_int(A2,insert_int(Y,bot_bot_set_int))) ) ) ).

% insert_minus_eq
tff(fact_5382_insert__minus__eq,axiom,
    ! [X2: nat,Y: nat,A2: set_nat] :
      ( ( X2 != Y )
     => ( minus_minus_set_nat(insert_nat(X2,A2),insert_nat(Y,bot_bot_set_nat)) = insert_nat(X2,minus_minus_set_nat(A2,insert_nat(Y,bot_bot_set_nat))) ) ) ).

% insert_minus_eq
tff(fact_5383_set__minus__singleton__eq,axiom,
    ! [X2: produc3843707927480180839at_nat,X7: set_Pr4329608150637261639at_nat] :
      ( ~ member8757157785044589968at_nat(X2,X7)
     => ( minus_3314409938677909166at_nat(X7,aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(X2),bot_bo228742789529271731at_nat)) = X7 ) ) ).

% set_minus_singleton_eq
tff(fact_5384_set__minus__singleton__eq,axiom,
    ! [X2: product_prod_nat_nat,X7: set_Pr1261947904930325089at_nat] :
      ( ~ member8440522571783428010at_nat(X2,X7)
     => ( aa_set8868280134176360700at_nat(minus_1356011639430497352at_nat(X7),aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(X2),bot_bo2099793752762293965at_nat)) = X7 ) ) ).

% set_minus_singleton_eq
tff(fact_5385_set__minus__singleton__eq,axiom,
    ! [X2: $o,X7: set_o] :
      ( ~ member_o((X2),X7)
     => ( minus_minus_set_o(X7,insert_o((X2),bot_bot_set_o)) = X7 ) ) ).

% set_minus_singleton_eq
tff(fact_5386_set__minus__singleton__eq,axiom,
    ! [X2: int,X7: set_int] :
      ( ~ member_int(X2,X7)
     => ( minus_minus_set_int(X7,insert_int(X2,bot_bot_set_int)) = X7 ) ) ).

% set_minus_singleton_eq
tff(fact_5387_set__minus__singleton__eq,axiom,
    ! [X2: nat,X7: set_nat] :
      ( ~ member_nat(X2,X7)
     => ( minus_minus_set_nat(X7,insert_nat(X2,bot_bot_set_nat)) = X7 ) ) ).

% set_minus_singleton_eq
tff(fact_5388_atLeastAtMost__singleton_H,axiom,
    ! [A: $o,B: $o] :
      ( ( (A)
      <=> (B) )
     => ( aa_o_set_o(set_or8904488021354931149Most_o((A)),(B)) = insert_o((A),bot_bot_set_o) ) ) ).

% atLeastAtMost_singleton'
tff(fact_5389_atLeastAtMost__singleton_H,axiom,
    ! [A: int,B: int] :
      ( ( A = B )
     => ( aa_int_set_int(set_or1266510415728281911st_int(A),B) = insert_int(A,bot_bot_set_int) ) ) ).

% atLeastAtMost_singleton'
tff(fact_5390_atLeastAtMost__singleton_H,axiom,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( aa_nat_set_nat(set_or1269000886237332187st_nat(A),B) = insert_nat(A,bot_bot_set_nat) ) ) ).

% atLeastAtMost_singleton'
tff(fact_5391_atLeastAtMost__singleton_H,axiom,
    ! [A: code_integer,B: code_integer] :
      ( ( A = B )
     => ( aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(A),B) = insert_Code_integer(A,bot_bo3990330152332043303nteger) ) ) ).

% atLeastAtMost_singleton'
tff(fact_5392_remove__subset,axiom,
    ! [X2: produc3843707927480180839at_nat,S2: set_Pr4329608150637261639at_nat] :
      ( member8757157785044589968at_nat(X2,S2)
     => ord_le2604355607129572851at_nat(minus_3314409938677909166at_nat(S2,aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(X2),bot_bo228742789529271731at_nat)),S2) ) ).

% remove_subset
tff(fact_5393_remove__subset,axiom,
    ! [X2: product_prod_nat_nat,S2: set_Pr1261947904930325089at_nat] :
      ( member8440522571783428010at_nat(X2,S2)
     => aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(ord_le7866589430770878221at_nat,aa_set8868280134176360700at_nat(minus_1356011639430497352at_nat(S2),aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(X2),bot_bo2099793752762293965at_nat))),S2) ) ).

% remove_subset
tff(fact_5394_remove__subset,axiom,
    ! [X2: $o,S2: set_o] :
      ( member_o((X2),S2)
     => ord_less_set_o(minus_minus_set_o(S2,insert_o((X2),bot_bot_set_o)),S2) ) ).

% remove_subset
tff(fact_5395_remove__subset,axiom,
    ! [X2: int,S2: set_int] :
      ( member_int(X2,S2)
     => ord_less_set_int(minus_minus_set_int(S2,insert_int(X2,bot_bot_set_int)),S2) ) ).

% remove_subset
tff(fact_5396_remove__subset,axiom,
    ! [X2: nat,S2: set_nat] :
      ( member_nat(X2,S2)
     => ord_less_set_nat(minus_minus_set_nat(S2,insert_nat(X2,bot_bot_set_nat)),S2) ) ).

% remove_subset
tff(fact_5397_nat__of__integer__def,axiom,
    code_nat_of_integer = map_fu6539832666145259331at_nat(code_int_of_integer,id_nat,nat2) ).

% nat_of_integer_def
tff(fact_5398_bit__integer__def,axiom,
    bit_se9216721137139052372nteger = map_fu2913747595474184929_nat_o(code_int_of_integer,id_fun_nat_o,bit_se1146084159140164899it_int) ).

% bit_integer_def
tff(fact_5399_mask__integer__def,axiom,
    bit_se2119862282449309892nteger = map_fu6290471996055670595nteger(id_nat,code_integer_of_int,bit_se2000444600071755411sk_int) ).

% mask_integer_def
tff(fact_5400_atLeastLessThan__eq__atLeastAtMost__diff,axiom,
    ! [A: $o,B: $o] : aa_o_set_o(set_or7139685690850216873Than_o((A)),(B)) = minus_minus_set_o(aa_o_set_o(set_or8904488021354931149Most_o((A)),(B)),insert_o((B),bot_bot_set_o)) ).

% atLeastLessThan_eq_atLeastAtMost_diff
tff(fact_5401_atLeastLessThan__eq__atLeastAtMost__diff,axiom,
    ! [A: nat,B: nat] : aa_nat_set_nat(set_or4665077453230672383an_nat(A),B) = minus_minus_set_nat(aa_nat_set_nat(set_or1269000886237332187st_nat(A),B),insert_nat(B,bot_bot_set_nat)) ).

% atLeastLessThan_eq_atLeastAtMost_diff
tff(fact_5402_atLeastLessThan__eq__atLeastAtMost__diff,axiom,
    ! [A: code_integer,B: code_integer] : aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(A),B) = minus_2355218937544613996nteger(aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(A),B),insert_Code_integer(B,bot_bo3990330152332043303nteger)) ).

% atLeastLessThan_eq_atLeastAtMost_diff
tff(fact_5403_atLeastLessThan__eq__atLeastAtMost__diff,axiom,
    ! [A: int,B: int] : aa_int_set_int(set_or4662586982721622107an_int(A),B) = minus_minus_set_int(aa_int_set_int(set_or1266510415728281911st_int(A),B),insert_int(B,bot_bot_set_int)) ).

% atLeastLessThan_eq_atLeastAtMost_diff
tff(fact_5404_atLeastAtMostPlus1__int__conv,axiom,
    ! [M: int,N2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,M),aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),N2))
     => ( aa_int_set_int(set_or1266510415728281911st_int(M),aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),N2)) = insert_int(aa_int_int(aa_int_fun_int_int(plus_plus_int,one_one_int),N2),aa_int_set_int(set_or1266510415728281911st_int(M),N2)) ) ) ).

% atLeastAtMostPlus1_int_conv
tff(fact_5405_simp__from__to,axiom,
    ! [I: int,J: int] :
      aa_int_set_int(set_or1266510415728281911st_int(I),J) = $ite(aa_int_o(aa_int_fun_int_o(ord_less_int,J),I),bot_bot_set_int,insert_int(I,aa_int_set_int(set_or1266510415728281911st_int(aa_int_int(aa_int_fun_int_int(plus_plus_int,I),one_one_int)),J))) ).

% simp_from_to
tff(fact_5406_Code__Numeral_Osub__def,axiom,
    code_sub = map_fu8540202848259802501nteger(id_num,map_fu8638147718074629079nteger(id_num,code_integer_of_int),aTP_Lamm_nr) ).

% Code_Numeral.sub_def
tff(fact_5407_num__of__integer__def,axiom,
    code_num_of_integer = map_fu1227494855608507351um_num(code_int_of_integer,id_num,aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,num_of_nat),nat2)) ).

% num_of_integer_def
tff(fact_5408_take__bit__integer__def,axiom,
    bit_se1745604003318907178nteger = map_fu214667362969451334nteger(id_nat,map_fu2599414010547811884nteger(code_int_of_integer,code_integer_of_int),bit_se2923211474154528505it_int) ).

% take_bit_integer_def
tff(fact_5409_drop__bit__integer__def,axiom,
    bit_se3928097537394005634nteger = map_fu214667362969451334nteger(id_nat,map_fu2599414010547811884nteger(code_int_of_integer,code_integer_of_int),bit_se8568078237143864401it_int) ).

% drop_bit_integer_def
tff(fact_5410_push__bit__integer__def,axiom,
    bit_se7788150548672797655nteger = map_fu214667362969451334nteger(id_nat,map_fu2599414010547811884nteger(code_int_of_integer,code_integer_of_int),bit_se545348938243370406it_int) ).

% push_bit_integer_def
tff(fact_5411_unset__bit__integer__def,axiom,
    bit_se8260200283734997820nteger = map_fu214667362969451334nteger(id_nat,map_fu2599414010547811884nteger(code_int_of_integer,code_integer_of_int),bit_se4203085406695923979it_int) ).

% unset_bit_integer_def
tff(fact_5412_set__bit__integer__def,axiom,
    bit_se2793503036327961859nteger = map_fu214667362969451334nteger(id_nat,map_fu2599414010547811884nteger(code_int_of_integer,code_integer_of_int),bit_se7879613467334960850it_int) ).

% set_bit_integer_def
tff(fact_5413_flip__bit__integer__def,axiom,
    bit_se1345352211410354436nteger = map_fu214667362969451334nteger(id_nat,map_fu2599414010547811884nteger(code_int_of_integer,code_integer_of_int),bit_se2159334234014336723it_int) ).

% flip_bit_integer_def
tff(fact_5414_pair__leqI1,axiom,
    ! [A: nat,B: nat,S: nat,T: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,A),B)
     => member8206827879206165904at_nat(produc6161850002892822231at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),S),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,B),T)),fun_pair_leq) ) ).

% pair_leqI1
tff(fact_5415_image__minus__const__atLeastLessThan__nat,axiom,
    ! [C: nat,X2: nat,Y: nat] :
      aa_set_nat_set_nat(image_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_ns,C)),aa_nat_set_nat(set_or4665077453230672383an_nat(X2),Y)) = $ite(
        aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,C),Y),
        aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,X2),C)),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Y),C)),
        $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,X2),Y),insert_nat(zero_zero_nat,bot_bot_set_nat),bot_bot_set_nat) ) ).

% image_minus_const_atLeastLessThan_nat
tff(fact_5416_card__atLeastAtMost__int,axiom,
    ! [L: int,U: int] : finite_card_int(aa_int_set_int(set_or1266510415728281911st_int(L),U)) = aa_int_nat(nat2,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,U),L)),one_one_int)) ).

% card_atLeastAtMost_int
tff(fact_5417_range__mod,axiom,
    ! [N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => ( aa_set_nat_set_nat(image_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_nt,N2)),top_top_set_nat) = aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2) ) ) ).

% range_mod
tff(fact_5418_Some__image__these__eq,axiom,
    ! [A2: set_op3940070208846178154it_nat] : image_4799632500972785611it_nat(some_P6105628898608307625it_nat,these_6645423997822192641it_nat(A2)) = collec8141831914148684149it_nat(aTP_Lamm_nu(A2)) ).

% Some_image_these_eq
tff(fact_5419_Some__image__these__eq,axiom,
    ! [A2: set_option_num] : image_num_option_num(some_num,these_num(A2)) = collect_option_num(aTP_Lamm_nv(A2)) ).

% Some_image_these_eq
tff(fact_5420_Some__image__these__eq,axiom,
    ! [A2: set_op239864471688321678it_nat] : image_3455408117458022631it_nat(some_P1914260805536162275it_nat,these_3407724651694999947it_nat(A2)) = collec5742531119322951597it_nat(aTP_Lamm_nw(A2)) ).

% Some_image_these_eq
tff(fact_5421_prod__mono2,axiom,
    ! [B4: set_o,A2: set_o,F: fun_o_Code_integer] :
      ( finite_finite_o(B4)
     => ( ord_less_eq_set_o(A2,B4)
       => ( ! [B2: $o] :
              ( member_o((B2),minus_minus_set_o(B4,A2))
             => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),aa_o_Code_integer(F,(B2))) )
         => ( ! [A3: $o] :
                ( member_o((A3),A2)
               => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_o_Code_integer(F,(A3))) )
           => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,F),A2)),aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,F),B4)) ) ) ) ) ).

% prod_mono2
tff(fact_5422_prod__mono2,axiom,
    ! [B4: set_int,A2: set_int,F: fun_int_Code_integer] :
      ( finite_finite_int(B4)
     => ( ord_less_eq_set_int(A2,B4)
       => ( ! [B2: int] :
              ( member_int(B2,minus_minus_set_int(B4,A2))
             => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),aa_int_Code_integer(F,B2)) )
         => ( ! [A3: int] :
                ( member_int(A3,A2)
               => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_int_Code_integer(F,A3)) )
           => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,F),A2)),aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,F),B4)) ) ) ) ) ).

% prod_mono2
tff(fact_5423_prod__mono2,axiom,
    ! [B4: set_Code_integer,A2: set_Code_integer,F: fun_Co8499238673658658103nteger] :
      ( finite6017078050557962740nteger(B4)
     => ( ord_le7084787975880047091nteger(A2,B4)
       => ( ! [B2: code_integer] :
              ( member_Code_integer(B2,minus_2355218937544613996nteger(B4,A2))
             => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),aa_Cod1783974652533396728nteger(F,B2)) )
         => ( ! [A3: code_integer] :
                ( member_Code_integer(A3,A2)
               => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(F,A3)) )
           => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,F),A2)),aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,F),B4)) ) ) ) ) ).

% prod_mono2
tff(fact_5424_prod__mono2,axiom,
    ! [B4: set_o,A2: set_o,F: fun_o_rat] :
      ( finite_finite_o(B4)
     => ( ord_less_eq_set_o(A2,B4)
       => ( ! [B2: $o] :
              ( member_o((B2),minus_minus_set_o(B4,A2))
             => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),aa_o_rat(F,(B2))) )
         => ( ! [A3: $o] :
                ( member_o((A3),A2)
               => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),aa_o_rat(F,(A3))) )
           => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_set_o_rat(aa_fun7302669049306738524_o_rat(groups2869687844427037835_o_rat,F),A2)),aa_set_o_rat(aa_fun7302669049306738524_o_rat(groups2869687844427037835_o_rat,F),B4)) ) ) ) ) ).

% prod_mono2
tff(fact_5425_prod__mono2,axiom,
    ! [B4: set_int,A2: set_int,F: fun_int_rat] :
      ( finite_finite_int(B4)
     => ( ord_less_eq_set_int(A2,B4)
       => ( ! [B2: int] :
              ( member_int(B2,minus_minus_set_int(B4,A2))
             => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),aa_int_rat(F,B2)) )
         => ( ! [A3: int] :
                ( member_int(A3,A2)
               => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),aa_int_rat(F,A3)) )
           => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,F),A2)),aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,F),B4)) ) ) ) ) ).

% prod_mono2
tff(fact_5426_prod__mono2,axiom,
    ! [B4: set_Code_integer,A2: set_Code_integer,F: fun_Code_integer_rat] :
      ( finite6017078050557962740nteger(B4)
     => ( ord_le7084787975880047091nteger(A2,B4)
       => ( ! [B2: code_integer] :
              ( member_Code_integer(B2,minus_2355218937544613996nteger(B4,A2))
             => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),aa_Code_integer_rat(F,B2)) )
         => ( ! [A3: code_integer] :
                ( member_Code_integer(A3,A2)
               => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),aa_Code_integer_rat(F,A3)) )
           => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_set3519029356358064041er_rat(aa_fun5443269377828775384er_rat(groups2555765274223993564er_rat,F),A2)),aa_set3519029356358064041er_rat(aa_fun5443269377828775384er_rat(groups2555765274223993564er_rat,F),B4)) ) ) ) ) ).

% prod_mono2
tff(fact_5427_prod__mono2,axiom,
    ! [B4: set_o,A2: set_o,F: fun_o_int] :
      ( finite_finite_o(B4)
     => ( ord_less_eq_set_o(A2,B4)
       => ( ! [B2: $o] :
              ( member_o((B2),minus_minus_set_o(B4,A2))
             => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,one_one_int),aa_o_int(F,(B2))) )
         => ( ! [A3: $o] :
                ( member_o((A3),A2)
               => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),aa_o_int(F,(A3))) )
           => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,groups3502327434004483295_o_int(F,A2)),groups3502327434004483295_o_int(F,B4)) ) ) ) ) ).

% prod_mono2
tff(fact_5428_prod__mono2,axiom,
    ! [B4: set_Code_integer,A2: set_Code_integer,F: fun_Code_integer_int] :
      ( finite6017078050557962740nteger(B4)
     => ( ord_le7084787975880047091nteger(A2,B4)
       => ( ! [B2: code_integer] :
              ( member_Code_integer(B2,minus_2355218937544613996nteger(B4,A2))
             => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,one_one_int),aa_Code_integer_int(F,B2)) )
         => ( ! [A3: code_integer] :
                ( member_Code_integer(A3,A2)
               => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,zero_zero_int),aa_Code_integer_int(F,A3)) )
           => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,groups3188404863801439024er_int(F,A2)),groups3188404863801439024er_int(F,B4)) ) ) ) ) ).

% prod_mono2
tff(fact_5429_prod__mono2,axiom,
    ! [B4: set_nat,A2: set_nat,F: fun_nat_Code_integer] :
      ( finite_finite_nat(B4)
     => ( aa_set_nat_o(ord_less_eq_set_nat(A2),B4)
       => ( ! [B2: nat] :
              ( member_nat(B2,minus_minus_set_nat(B4,A2))
             => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),aa_nat_Code_integer(F,B2)) )
         => ( ! [A3: nat] :
                ( member_nat(A3,A2)
               => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_nat_Code_integer(F,A3)) )
           => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,groups3455450783089532116nteger(F,A2)),groups3455450783089532116nteger(F,B4)) ) ) ) ) ).

% prod_mono2
tff(fact_5430_prod__mono2,axiom,
    ! [B4: set_nat,A2: set_nat,F: fun_nat_rat] :
      ( finite_finite_nat(B4)
     => ( aa_set_nat_o(ord_less_eq_set_nat(A2),B4)
       => ( ! [B2: nat] :
              ( member_nat(B2,minus_minus_set_nat(B4,A2))
             => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),aa_nat_rat(F,B2)) )
         => ( ! [A3: nat] :
                ( member_nat(A3,A2)
               => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),aa_nat_rat(F,A3)) )
           => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,groups73079841787564623at_rat(F,A2)),groups73079841787564623at_rat(F,B4)) ) ) ) ) ).

% prod_mono2
tff(fact_5431_the__dflt__None__nonempty,axiom,
    ! [S2: set_Pr4329608150637261639at_nat] :
      ( ( S2 != bot_bo228742789529271731at_nat )
     => ( dflt_N3208751546879591902at_nat(S2) = some_s5890477192898017836at_nat(S2) ) ) ).

% the_dflt_None_nonempty
tff(fact_5432_the__dflt__None__nonempty,axiom,
    ! [S2: set_Pr1261947904930325089at_nat] :
      ( ( S2 != bot_bo2099793752762293965at_nat )
     => ( dflt_N6592383573632408824at_nat(S2) = some_s147305329494351046at_nat(S2) ) ) ).

% the_dflt_None_nonempty
tff(fact_5433_the__dflt__None__nonempty,axiom,
    ! [S2: set_o] :
      ( ( S2 != bot_bot_set_o )
     => ( dflt_None_set_o(S2) = some_set_o(S2) ) ) ).

% the_dflt_None_nonempty
tff(fact_5434_the__dflt__None__nonempty,axiom,
    ! [S2: set_nat] :
      ( ( S2 != bot_bot_set_nat )
     => ( dflt_None_set_nat(S2) = aa_set6119337032432945050et_nat(some_set_nat,S2) ) ) ).

% the_dflt_None_nonempty
tff(fact_5435_the__dflt__None__nonempty,axiom,
    ! [S2: set_int] :
      ( ( S2 != bot_bot_set_int )
     => ( dflt_None_set_int(S2) = some_set_int(S2) ) ) ).

% the_dflt_None_nonempty
tff(fact_5436_the__dflt__None__empty,axiom,
    dflt_N3208751546879591902at_nat(bot_bo228742789529271731at_nat) = none_s6518873173954064040at_nat ).

% the_dflt_None_empty
tff(fact_5437_the__dflt__None__empty,axiom,
    dflt_N6592383573632408824at_nat(bot_bo2099793752762293965at_nat) = none_s625347054029921090at_nat ).

% the_dflt_None_empty
tff(fact_5438_the__dflt__None__empty,axiom,
    dflt_None_set_o(bot_bot_set_o) = none_set_o ).

% the_dflt_None_empty
tff(fact_5439_the__dflt__None__empty,axiom,
    dflt_None_set_nat(bot_bot_set_nat) = none_set_nat ).

% the_dflt_None_empty
tff(fact_5440_the__dflt__None__empty,axiom,
    dflt_None_set_int(bot_bot_set_int) = none_set_int ).

% the_dflt_None_empty
tff(fact_5441_atMost__UNIV__triv,axiom,
    set_or4236626031148496127et_nat(top_top_set_nat) = top_top_set_set_nat ).

% atMost_UNIV_triv
tff(fact_5442_atMost__UNIV__triv,axiom,
    set_or2827140217781692084t_unit(top_to1996260823553986621t_unit) = top_to1767297665138865437t_unit ).

% atMost_UNIV_triv
tff(fact_5443_atMost__UNIV__triv,axiom,
    set_or58775011639299419et_int(top_top_set_int) = top_top_set_set_int ).

% atMost_UNIV_triv
tff(fact_5444_finite__atLeastAtMost,axiom,
    ! [L: nat,U: nat] : finite_finite_nat(aa_nat_set_nat(set_or1269000886237332187st_nat(L),U)) ).

% finite_atLeastAtMost
tff(fact_5445_finite__atLeastLessThan,axiom,
    ! [L: nat,U: nat] : finite_finite_nat(aa_nat_set_nat(set_or4665077453230672383an_nat(L),U)) ).

% finite_atLeastLessThan
tff(fact_5446_int__of__integer__min,axiom,
    ! [K: code_integer,L: code_integer] : aa_Code_integer_int(code_int_of_integer,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_min_Code_integer,K),L)) = aa_int_int(aa_int_fun_int_int(ord_min_int,aa_Code_integer_int(code_int_of_integer,K)),aa_Code_integer_int(code_int_of_integer,L)) ).

% int_of_integer_min
tff(fact_5447_finite__atMost,axiom,
    ! [K: nat] : finite_finite_nat(aa_nat_set_nat(set_ord_atMost_nat,K)) ).

% finite_atMost
tff(fact_5448_finite__lessThan,axiom,
    ! [K: nat] : finite_finite_nat(aa_nat_set_nat(set_ord_lessThan_nat,K)) ).

% finite_lessThan
tff(fact_5449_finite__atLeastAtMost__int,axiom,
    ! [L: int,U: int] : finite_finite_int(aa_int_set_int(set_or1266510415728281911st_int(L),U)) ).

% finite_atLeastAtMost_int
tff(fact_5450_finite__atLeastLessThan__int,axiom,
    ! [L: int,U: int] : finite_finite_int(aa_int_set_int(set_or4662586982721622107an_int(L),U)) ).

% finite_atLeastLessThan_int
tff(fact_5451_finite__atLeastLessThan__integer,axiom,
    ! [L: code_integer,U: code_integer] : finite6017078050557962740nteger(aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(L),U)) ).

% finite_atLeastLessThan_integer
tff(fact_5452_finite__atLeastAtMost__integer,axiom,
    ! [L: code_integer,U: code_integer] : finite6017078050557962740nteger(aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(L),U)) ).

% finite_atLeastAtMost_integer
tff(fact_5453_finite__option__UNIV,axiom,
    ( finite6785661671136154180nteger(top_to5929521628599800467nteger)
  <=> finite6017078050557962740nteger(top_to4645266643341252675nteger) ) ).

% finite_option_UNIV
tff(fact_5454_finite__option__UNIV,axiom,
    ( finite6732403688824079472at_nat(top_to3251141154256563319at_nat)
  <=> finite6177210948735845034at_nat(top_to4669805908274784177at_nat) ) ).

% finite_option_UNIV
tff(fact_5455_finite__option__UNIV,axiom,
    ( finite5523153139673422903on_nat(top_to8920198386146353926on_nat)
  <=> finite_finite_nat(top_top_set_nat) ) ).

% finite_option_UNIV
tff(fact_5456_finite__option__UNIV,axiom,
    ( finite1445617369574913404t_unit(top_to2690860209552263555t_unit)
  <=> finite4290736615968046902t_unit(top_to1996260823553986621t_unit) ) ).

% finite_option_UNIV
tff(fact_5457_finite__option__UNIV,axiom,
    ( finite1345302120164226195on_int(top_to6430115241214627170on_int)
  <=> finite_finite_int(top_top_set_int) ) ).

% finite_option_UNIV
tff(fact_5458_card__eq__UNIV,axiom,
    ! [S2: set_Product_unit] :
      ( ( finite410649719033368117t_unit(S2) = finite410649719033368117t_unit(top_to1996260823553986621t_unit) )
    <=> ( S2 = top_to1996260823553986621t_unit ) ) ).

% card_eq_UNIV
tff(fact_5459_card__eq__UNIV2,axiom,
    ! [S2: set_Product_unit] :
      ( ( finite410649719033368117t_unit(top_to1996260823553986621t_unit) = finite410649719033368117t_unit(S2) )
    <=> ( S2 = top_to1996260823553986621t_unit ) ) ).

% card_eq_UNIV2
tff(fact_5460_these__empty,axiom,
    these_1872268174106123684at_nat(bot_bo1471150103859235065at_nat) = bot_bo228742789529271731at_nat ).

% these_empty
tff(fact_5461_these__empty,axiom,
    these_8061402112538453438at_nat(bot_bo3414888551220300179at_nat) = bot_bo2099793752762293965at_nat ).

% these_empty
tff(fact_5462_these__empty,axiom,
    these_o(bot_bot_set_option_o) = bot_bot_set_o ).

% these_empty
tff(fact_5463_these__empty,axiom,
    these_nat(bot_bo5009843511495006442on_nat) = bot_bot_set_nat ).

% these_empty
tff(fact_5464_these__empty,axiom,
    these_int(bot_bo2519760366563279686on_int) = bot_bot_set_int ).

% these_empty
tff(fact_5465_these__insert__None,axiom,
    ! [A2: set_op3940070208846178154it_nat] : these_6645423997822192641it_nat(insert7468008629046257882it_nat(none_P2587165478634041381it_nat,A2)) = these_6645423997822192641it_nat(A2) ).

% these_insert_None
tff(fact_5466_these__insert__None,axiom,
    ! [A2: set_option_num] : these_num(insert_option_num(none_num,A2)) = these_num(A2) ).

% these_insert_None
tff(fact_5467_these__insert__None,axiom,
    ! [A2: set_op239864471688321678it_nat] : these_3407724651694999947it_nat(insert2007652293347934600it_nat(none_P9117596204409417319it_nat,A2)) = these_3407724651694999947it_nat(A2) ).

% these_insert_None
tff(fact_5468_the__dflt__None__set,axiom,
    ! [X2: set_Pr4329608150637261639at_nat] : the_de6830073021511528542at_nat(bot_bo228742789529271731at_nat,dflt_N3208751546879591902at_nat(X2)) = X2 ).

% the_dflt_None_set
tff(fact_5469_the__dflt__None__set,axiom,
    ! [X2: set_Pr1261947904930325089at_nat] : the_de3668382347305825784at_nat(bot_bo2099793752762293965at_nat,dflt_N6592383573632408824at_nat(X2)) = X2 ).

% the_dflt_None_set
tff(fact_5470_the__dflt__None__set,axiom,
    ! [X2: set_o] : the_default_set_o(bot_bot_set_o,dflt_None_set_o(X2)) = X2 ).

% the_dflt_None_set
tff(fact_5471_the__dflt__None__set,axiom,
    ! [X2: set_nat] : the_default_set_nat(bot_bot_set_nat,dflt_None_set_nat(X2)) = X2 ).

% the_dflt_None_set
tff(fact_5472_the__dflt__None__set,axiom,
    ! [X2: set_int] : the_default_set_int(bot_bot_set_int,dflt_None_set_int(X2)) = X2 ).

% the_dflt_None_set
tff(fact_5473_surj__plus,axiom,
    ! [A: rat] : image_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,A),top_top_set_rat) = top_top_set_rat ).

% surj_plus
tff(fact_5474_surj__plus,axiom,
    ! [A: int] : aa_set_int_set_int(image_int_int(aa_int_fun_int_int(plus_plus_int,A)),top_top_set_int) = top_top_set_int ).

% surj_plus
tff(fact_5475_infinite__Icc__iff,axiom,
    ! [A: rat,B: rat] :
      ( ~ finite_finite_rat(set_or633870826150836451st_rat(A,B))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B) ) ).

% infinite_Icc_iff
tff(fact_5476_infinite__Ico__iff,axiom,
    ! [A: rat,B: rat] :
      ( ~ finite_finite_rat(set_or4029947393144176647an_rat(A,B))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B) ) ).

% infinite_Ico_iff
tff(fact_5477_prod_Oinfinite,axiom,
    ! [A2: set_nat,G: fun_nat_Code_integer] :
      ( ~ finite_finite_nat(A2)
     => ( groups3455450783089532116nteger(G,A2) = one_one_Code_integer ) ) ).

% prod.infinite
tff(fact_5478_prod_Oinfinite,axiom,
    ! [A2: set_int,G: fun_int_Code_integer] :
      ( ~ finite_finite_int(A2)
     => ( aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,G),A2) = one_one_Code_integer ) ) ).

% prod.infinite
tff(fact_5479_prod_Oinfinite,axiom,
    ! [A2: set_Code_integer,G: fun_Co8499238673658658103nteger] :
      ( ~ finite6017078050557962740nteger(A2)
     => ( aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,G),A2) = one_one_Code_integer ) ) ).

% prod.infinite
tff(fact_5480_prod_Oinfinite,axiom,
    ! [A2: set_nat,G: fun_nat_assn] :
      ( ~ finite_finite_nat(A2)
     => ( groups6906906614972039071t_assn(G,A2) = one_one_assn ) ) ).

% prod.infinite
tff(fact_5481_prod_Oinfinite,axiom,
    ! [A2: set_int,G: fun_int_assn] :
      ( ~ finite_finite_int(A2)
     => ( aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,G),A2) = one_one_assn ) ) ).

% prod.infinite
tff(fact_5482_prod_Oinfinite,axiom,
    ! [A2: set_Code_integer,G: fun_Co4490034186337852034r_assn] :
      ( ~ finite6017078050557962740nteger(A2)
     => ( aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,G),A2) = one_one_assn ) ) ).

% prod.infinite
tff(fact_5483_prod_Oinfinite,axiom,
    ! [A2: set_nat,G: fun_nat_rat] :
      ( ~ finite_finite_nat(A2)
     => ( groups73079841787564623at_rat(G,A2) = one_one_rat ) ) ).

% prod.infinite
tff(fact_5484_prod_Oinfinite,axiom,
    ! [A2: set_int,G: fun_int_rat] :
      ( ~ finite_finite_int(A2)
     => ( aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,G),A2) = one_one_rat ) ) ).

% prod.infinite
tff(fact_5485_prod_Oinfinite,axiom,
    ! [A2: set_Code_integer,G: fun_Code_integer_rat] :
      ( ~ finite6017078050557962740nteger(A2)
     => ( aa_set3519029356358064041er_rat(aa_fun5443269377828775384er_rat(groups2555765274223993564er_rat,G),A2) = one_one_rat ) ) ).

% prod.infinite
tff(fact_5486_prod_Oinfinite,axiom,
    ! [A2: set_int,G: fun_int_nat] :
      ( ~ finite_finite_int(A2)
     => ( groups1707563613775114915nt_nat(G,A2) = one_one_nat ) ) ).

% prod.infinite
tff(fact_5487_card__ge__UNIV,axiom,
    ! [S2: set_Product_unit] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite410649719033368117t_unit(top_to1996260823553986621t_unit)),finite410649719033368117t_unit(S2))
    <=> ( S2 = top_to1996260823553986621t_unit ) ) ).

% card_ge_UNIV
tff(fact_5488_surj__diff__right,axiom,
    ! [A: code_integer] : image_4470545334726330049nteger(aa_Cod4161879620478718930nteger(aTP_Lamm_mv,A),top_to4645266643341252675nteger) = top_to4645266643341252675nteger ).

% surj_diff_right
tff(fact_5489_surj__diff__right,axiom,
    ! [A: rat] : image_rat_rat(aTP_Lamm_mt(A),top_top_set_rat) = top_top_set_rat ).

% surj_diff_right
tff(fact_5490_surj__diff__right,axiom,
    ! [A: int] : aa_set_int_set_int(image_int_int(aa_int_fun_int_int(aTP_Lamm_mu,A)),top_top_set_int) = top_top_set_int ).

% surj_diff_right
tff(fact_5491_prod__eq__1__iff,axiom,
    ! [A2: set_int,F: fun_int_nat] :
      ( finite_finite_int(A2)
     => ( ( groups1707563613775114915nt_nat(F,A2) = one_one_nat )
      <=> ! [X4: int] :
            ( member_int(X4,A2)
           => ( aa_int_nat(F,X4) = one_one_nat ) ) ) ) ).

% prod_eq_1_iff
tff(fact_5492_prod__eq__1__iff,axiom,
    ! [A2: set_Code_integer,F: fun_Code_integer_nat] :
      ( finite6017078050557962740nteger(A2)
     => ( ( groups3190895334310489300er_nat(F,A2) = one_one_nat )
      <=> ! [X4: code_integer] :
            ( member_Code_integer(X4,A2)
           => ( aa_Code_integer_nat(F,X4) = one_one_nat ) ) ) ) ).

% prod_eq_1_iff
tff(fact_5493_prod__eq__1__iff,axiom,
    ! [A2: set_Pr1261947904930325089at_nat,F: fun_Pr2602117396471556196at_nat] :
      ( finite6177210948735845034at_nat(A2)
     => ( ( aa_set4749074711808745205at_nat(groups4077766827762148844at_nat(F),A2) = one_one_nat )
      <=> ! [X4: product_prod_nat_nat] :
            ( member8440522571783428010at_nat(X4,A2)
           => ( aa_Pro4243173770044397973at_nat(F,X4) = one_one_nat ) ) ) ) ).

% prod_eq_1_iff
tff(fact_5494_prod__eq__1__iff,axiom,
    ! [A2: set_nat,F: fun_nat_nat] :
      ( finite_finite_nat(A2)
     => ( ( aa_set_nat_nat(groups708209901874060359at_nat(F),A2) = one_one_nat )
      <=> ! [X4: nat] :
            ( member_nat(X4,A2)
           => ( aa_nat_nat(F,X4) = one_one_nat ) ) ) ) ).

% prod_eq_1_iff
tff(fact_5495_prod_Odelta,axiom,
    ! [S2: set_o,A: $o,B: fun_o_Code_integer] :
      ( finite_finite_o(S2)
     => ( aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,aa_fun8520278569782659900nteger(aTP_Lamm_nx((A)),B)),S2) = $ite(member_o((A),S2),aa_o_Code_integer(B,(A)),one_one_Code_integer) ) ) ).

% prod.delta
tff(fact_5496_prod_Odelta,axiom,
    ! [S2: set_nat,A: nat,B: fun_nat_Code_integer] :
      ( finite_finite_nat(S2)
     => ( groups3455450783089532116nteger(aa_fun589076786913273746nteger(aTP_Lamm_ny(A),B),S2) = $ite(member_nat(A,S2),aa_nat_Code_integer(B,A),one_one_Code_integer) ) ) ).

% prod.delta
tff(fact_5497_prod_Odelta,axiom,
    ! [S2: set_int,A: int,B: fun_int_Code_integer] :
      ( finite_finite_int(S2)
     => ( aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,aa_fun5304498221708291146nteger(aTP_Lamm_nz(A),B)),S2) = $ite(member_int(A,S2),aa_int_Code_integer(B,A),one_one_Code_integer) ) ) ).

% prod.delta
tff(fact_5498_prod_Odelta,axiom,
    ! [S2: set_Code_integer,A: code_integer,B: fun_Co8499238673658658103nteger] :
      ( finite6017078050557962740nteger(S2)
     => ( aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,aa_fun4435975922079263404nteger(aTP_Lamm_oa(A),B)),S2) = $ite(member_Code_integer(A,S2),aa_Cod1783974652533396728nteger(B,A),one_one_Code_integer) ) ) ).

% prod.delta
tff(fact_5499_prod_Odelta,axiom,
    ! [S2: set_o,A: $o,B: fun_o_assn] :
      ( finite_finite_o(S2)
     => ( aa_set_o_assn(aa_fun1914167119812169564o_assn(groups5301882518646026715o_assn,aa_fun4536517337817438332o_assn(aTP_Lamm_ob((A)),B)),S2) = $ite(member_o((A),S2),aa_o_assn(B,(A)),one_one_assn) ) ) ).

% prod.delta
tff(fact_5500_prod_Odelta,axiom,
    ! [S2: set_nat,A: nat,B: fun_nat_assn] :
      ( finite_finite_nat(S2)
     => ( groups6906906614972039071t_assn(aa_fun785744391571715112t_assn(aTP_Lamm_oc(A),B),S2) = $ite(member_nat(A,S2),aa_nat_assn(B,A),one_one_assn) ) ) ).

% prod.delta
tff(fact_5501_prod_Odelta,axiom,
    ! [S2: set_int,A: int,B: fun_int_assn] :
      ( finite_finite_int(S2)
     => ( aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,aa_fun919007281442365664t_assn(aTP_Lamm_od(A),B)),S2) = $ite(member_int(A,S2),aa_int_assn(B,A),one_one_assn) ) ) ).

% prod.delta
tff(fact_5502_prod_Odelta,axiom,
    ! [S2: set_Code_integer,A: code_integer,B: fun_Co4490034186337852034r_assn] :
      ( finite6017078050557962740nteger(S2)
     => ( aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,aa_fun4119713415300323650r_assn(aTP_Lamm_oe(A),B)),S2) = $ite(member_Code_integer(A,S2),aa_Code_integer_assn(B,A),one_one_assn) ) ) ).

% prod.delta
tff(fact_5503_prod_Odelta,axiom,
    ! [S2: set_o,A: $o,B: fun_o_rat] :
      ( finite_finite_o(S2)
     => ( aa_set_o_rat(aa_fun7302669049306738524_o_rat(groups2869687844427037835_o_rat,aa_fun4336163974892599420_o_rat(aTP_Lamm_of((A)),B)),S2) = $ite(member_o((A),S2),aa_o_rat(B,(A)),one_one_rat) ) ) ).

% prod.delta
tff(fact_5504_prod_Odelta,axiom,
    ! [S2: set_nat,A: nat,B: fun_nat_rat] :
      ( finite_finite_nat(S2)
     => ( groups73079841787564623at_rat(aa_fun765758790203053448at_rat(aTP_Lamm_og(A),B),S2) = $ite(member_nat(A,S2),aa_nat_rat(B,A),one_one_rat) ) ) ).

% prod.delta
tff(fact_5505_prod_Odelta_H,axiom,
    ! [S2: set_o,A: $o,B: fun_o_Code_integer] :
      ( finite_finite_o(S2)
     => ( aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,aa_fun8520278569782659900nteger(aTP_Lamm_oh((A)),B)),S2) = $ite(member_o((A),S2),aa_o_Code_integer(B,(A)),one_one_Code_integer) ) ) ).

% prod.delta'
tff(fact_5506_prod_Odelta_H,axiom,
    ! [S2: set_nat,A: nat,B: fun_nat_Code_integer] :
      ( finite_finite_nat(S2)
     => ( groups3455450783089532116nteger(aa_fun589076786913273746nteger(aTP_Lamm_oi(A),B),S2) = $ite(member_nat(A,S2),aa_nat_Code_integer(B,A),one_one_Code_integer) ) ) ).

% prod.delta'
tff(fact_5507_prod_Odelta_H,axiom,
    ! [S2: set_int,A: int,B: fun_int_Code_integer] :
      ( finite_finite_int(S2)
     => ( aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,aa_fun5304498221708291146nteger(aTP_Lamm_oj(A),B)),S2) = $ite(member_int(A,S2),aa_int_Code_integer(B,A),one_one_Code_integer) ) ) ).

% prod.delta'
tff(fact_5508_prod_Odelta_H,axiom,
    ! [S2: set_Code_integer,A: code_integer,B: fun_Co8499238673658658103nteger] :
      ( finite6017078050557962740nteger(S2)
     => ( aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,aa_fun4435975922079263404nteger(aTP_Lamm_ok(A),B)),S2) = $ite(member_Code_integer(A,S2),aa_Cod1783974652533396728nteger(B,A),one_one_Code_integer) ) ) ).

% prod.delta'
tff(fact_5509_prod_Odelta_H,axiom,
    ! [S2: set_o,A: $o,B: fun_o_assn] :
      ( finite_finite_o(S2)
     => ( aa_set_o_assn(aa_fun1914167119812169564o_assn(groups5301882518646026715o_assn,aa_fun4536517337817438332o_assn(aTP_Lamm_ol((A)),B)),S2) = $ite(member_o((A),S2),aa_o_assn(B,(A)),one_one_assn) ) ) ).

% prod.delta'
tff(fact_5510_prod_Odelta_H,axiom,
    ! [S2: set_nat,A: nat,B: fun_nat_assn] :
      ( finite_finite_nat(S2)
     => ( groups6906906614972039071t_assn(aa_fun785744391571715112t_assn(aTP_Lamm_om(A),B),S2) = $ite(member_nat(A,S2),aa_nat_assn(B,A),one_one_assn) ) ) ).

% prod.delta'
tff(fact_5511_prod_Odelta_H,axiom,
    ! [S2: set_int,A: int,B: fun_int_assn] :
      ( finite_finite_int(S2)
     => ( aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,aa_fun919007281442365664t_assn(aTP_Lamm_on(A),B)),S2) = $ite(member_int(A,S2),aa_int_assn(B,A),one_one_assn) ) ) ).

% prod.delta'
tff(fact_5512_prod_Odelta_H,axiom,
    ! [S2: set_Code_integer,A: code_integer,B: fun_Co4490034186337852034r_assn] :
      ( finite6017078050557962740nteger(S2)
     => ( aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,aa_fun4119713415300323650r_assn(aTP_Lamm_oo(A),B)),S2) = $ite(member_Code_integer(A,S2),aa_Code_integer_assn(B,A),one_one_assn) ) ) ).

% prod.delta'
tff(fact_5513_prod_Odelta_H,axiom,
    ! [S2: set_o,A: $o,B: fun_o_rat] :
      ( finite_finite_o(S2)
     => ( aa_set_o_rat(aa_fun7302669049306738524_o_rat(groups2869687844427037835_o_rat,aa_fun4336163974892599420_o_rat(aTP_Lamm_op((A)),B)),S2) = $ite(member_o((A),S2),aa_o_rat(B,(A)),one_one_rat) ) ) ).

% prod.delta'
tff(fact_5514_prod_Odelta_H,axiom,
    ! [S2: set_nat,A: nat,B: fun_nat_rat] :
      ( finite_finite_nat(S2)
     => ( groups73079841787564623at_rat(aa_fun765758790203053448at_rat(aTP_Lamm_oq(A),B),S2) = $ite(member_nat(A,S2),aa_nat_rat(B,A),one_one_rat) ) ) ).

% prod.delta'
tff(fact_5515_these__insert__Some,axiom,
    ! [X2: produc3843707927480180839at_nat,A2: set_op989438649584373901at_nat] : these_1872268174106123684at_nat(insert6833468608972679677at_nat(some_P131194445498448716at_nat(X2),A2)) = aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(X2),these_1872268174106123684at_nat(A2)) ).

% these_insert_Some
tff(fact_5516_these__insert__Some,axiom,
    ! [X2: product_prod_nat_nat,A2: set_op4508134149509766951at_nat] : these_8061402112538453438at_nat(insert6842972033726296599at_nat(aa_Pro4773402355715522498at_nat(some_P7363390416028606310at_nat,X2),A2)) = aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(X2),these_8061402112538453438at_nat(A2)) ).

% these_insert_Some
tff(fact_5517_these__insert__Some,axiom,
    ! [X2: $o,A2: set_option_o] : these_o(insert_option_o(aa_o_option_o(some_o,(X2)),A2)) = insert_o((X2),these_o(A2)) ).

% these_insert_Some
tff(fact_5518_these__insert__Some,axiom,
    ! [X2: nat,A2: set_option_nat] : these_nat(insert_option_nat(aa_nat_option_nat(some_nat,X2),A2)) = insert_nat(X2,these_nat(A2)) ).

% these_insert_Some
tff(fact_5519_these__insert__Some,axiom,
    ! [X2: int,A2: set_option_int] : these_int(insert_option_int(aa_int_option_int(some_int,X2),A2)) = insert_int(X2,these_int(A2)) ).

% these_insert_Some
tff(fact_5520_these__insert__Some,axiom,
    ! [X2: num,A2: set_option_num] : these_num(insert_option_num(aa_num_option_num(some_num,X2),A2)) = insert_num(X2,these_num(A2)) ).

% these_insert_Some
tff(fact_5521_these__insert__Some,axiom,
    ! [X2: produc8664842809031399944it_nat,A2: set_op239864471688321678it_nat] : these_3407724651694999947it_nat(insert2007652293347934600it_nat(aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X2),A2)) = insert5940566491043231800it_nat(X2,these_3407724651694999947it_nat(A2)) ).

% these_insert_Some
tff(fact_5522_these__image__Some__eq,axiom,
    ! [A2: set_num] : these_num(image_num_option_num(some_num,A2)) = A2 ).

% these_image_Some_eq
tff(fact_5523_these__image__Some__eq,axiom,
    ! [A2: set_Pr1354866905816374718it_nat] : these_3407724651694999947it_nat(image_3455408117458022631it_nat(some_P1914260805536162275it_nat,A2)) = A2 ).

% these_image_Some_eq
tff(fact_5524_sum_Oinsert,axiom,
    ! [A2: set_o,X2: $o,G: fun_o_rat] :
      ( finite_finite_o(A2)
     => ( ~ member_o((X2),A2)
       => ( groups7872700643590313910_o_rat(G,insert_o((X2),A2)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_o_rat(G,(X2))),groups7872700643590313910_o_rat(G,A2)) ) ) ) ).

% sum.insert
tff(fact_5525_sum_Oinsert,axiom,
    ! [A2: set_nat,X2: nat,G: fun_nat_rat] :
      ( finite_finite_nat(A2)
     => ( ~ member_nat(X2,A2)
       => ( groups2906978787729119204at_rat(G,insert_nat(X2,A2)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(G,X2)),groups2906978787729119204at_rat(G,A2)) ) ) ) ).

% sum.insert
tff(fact_5526_sum_Oinsert,axiom,
    ! [A2: set_int,X2: int,G: fun_int_rat] :
      ( finite_finite_int(A2)
     => ( ~ member_int(X2,A2)
       => ( groups3906332499630173760nt_rat(G,insert_int(X2,A2)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_int_rat(G,X2)),groups3906332499630173760nt_rat(G,A2)) ) ) ) ).

% sum.insert
tff(fact_5527_sum_Oinsert,axiom,
    ! [A2: set_Code_integer,X2: code_integer,G: fun_Code_integer_rat] :
      ( finite6017078050557962740nteger(A2)
     => ( ~ member_Code_integer(X2,A2)
       => ( groups6602215022474089585er_rat(G,insert_Code_integer(X2,A2)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_Code_integer_rat(G,X2)),groups6602215022474089585er_rat(G,A2)) ) ) ) ).

% sum.insert
tff(fact_5528_sum_Oinsert,axiom,
    ! [A2: set_o,X2: $o,G: fun_o_nat] :
      ( finite_finite_o(A2)
     => ( ~ member_o((X2),A2)
       => ( groups8507830703676809646_o_nat(G,insert_o((X2),A2)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_o_nat(G,(X2))),groups8507830703676809646_o_nat(G,A2)) ) ) ) ).

% sum.insert
tff(fact_5529_sum_Oinsert,axiom,
    ! [A2: set_int,X2: int,G: fun_int_nat] :
      ( finite_finite_int(A2)
     => ( ~ member_int(X2,A2)
       => ( groups4541462559716669496nt_nat(G,insert_int(X2,A2)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_int_nat(G,X2)),groups4541462559716669496nt_nat(G,A2)) ) ) ) ).

% sum.insert
tff(fact_5530_sum_Oinsert,axiom,
    ! [A2: set_Code_integer,X2: code_integer,G: fun_Code_integer_nat] :
      ( finite6017078050557962740nteger(A2)
     => ( ~ member_Code_integer(X2,A2)
       => ( groups7237345082560585321er_nat(G,insert_Code_integer(X2,A2)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_Code_integer_nat(G,X2)),groups7237345082560585321er_nat(G,A2)) ) ) ) ).

% sum.insert
tff(fact_5531_sum_Oinsert,axiom,
    ! [A2: set_o,X2: $o,G: fun_o_int] :
      ( finite_finite_o(A2)
     => ( ~ member_o((X2),A2)
       => ( groups8505340233167759370_o_int(G,insert_o((X2),A2)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_o_int(G,(X2))),groups8505340233167759370_o_int(G,A2)) ) ) ) ).

% sum.insert
tff(fact_5532_sum_Oinsert,axiom,
    ! [A2: set_nat,X2: nat,G: fun_nat_int] :
      ( finite_finite_nat(A2)
     => ( ~ member_nat(X2,A2)
       => ( groups3539618377306564664at_int(G,insert_nat(X2,A2)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(G,X2)),groups3539618377306564664at_int(G,A2)) ) ) ) ).

% sum.insert
tff(fact_5533_sum_Oinsert,axiom,
    ! [A2: set_Code_integer,X2: code_integer,G: fun_Code_integer_int] :
      ( finite6017078050557962740nteger(A2)
     => ( ~ member_Code_integer(X2,A2)
       => ( groups7234854612051535045er_int(G,insert_Code_integer(X2,A2)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_Code_integer_int(G,X2)),groups7234854612051535045er_int(G,A2)) ) ) ) ).

% sum.insert
tff(fact_5534_atLeastLessThan__singleton,axiom,
    ! [M: nat] : aa_nat_set_nat(set_or4665077453230672383an_nat(M),aa_nat_nat(suc,M)) = insert_nat(M,bot_bot_set_nat) ).

% atLeastLessThan_singleton
tff(fact_5535_atMost__0,axiom,
    aa_nat_set_nat(set_ord_atMost_nat,zero_zero_nat) = insert_nat(zero_zero_nat,bot_bot_set_nat) ).

% atMost_0
tff(fact_5536_card__atLeastLessThan__int,axiom,
    ! [L: int,U: int] : finite_card_int(aa_int_set_int(set_or4662586982721622107an_int(L),U)) = aa_int_nat(nat2,aa_int_int(aa_int_fun_int_int(minus_minus_int,U),L)) ).

% card_atLeastLessThan_int
tff(fact_5537_card__doubleton__eq__2__iff,axiom,
    ! [A: product_unit,B: product_unit] :
      ( ( finite410649719033368117t_unit(insert_Product_unit(A,insert_Product_unit(B,bot_bo3957492148770167129t_unit))) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)) )
    <=> ( A != B ) ) ).

% card_doubleton_eq_2_iff
tff(fact_5538_card__doubleton__eq__2__iff,axiom,
    ! [A: list_nat,B: list_nat] :
      ( ( finite_card_list_nat(insert_list_nat(A,insert_list_nat(B,bot_bot_set_list_nat))) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)) )
    <=> ( A != B ) ) ).

% card_doubleton_eq_2_iff
tff(fact_5539_card__doubleton__eq__2__iff,axiom,
    ! [A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat] :
      ( ( finite3771342082235030671at_nat(aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(A),aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(B),bot_bo228742789529271731at_nat))) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)) )
    <=> ( A != B ) ) ).

% card_doubleton_eq_2_iff
tff(fact_5540_card__doubleton__eq__2__iff,axiom,
    ! [A: product_prod_nat_nat,B: product_prod_nat_nat] :
      ( ( aa_set4749074711808745205at_nat(finite711546835091564841at_nat,aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(A),aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(B),bot_bo2099793752762293965at_nat))) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)) )
    <=> ( A != B ) ) ).

% card_doubleton_eq_2_iff
tff(fact_5541_card__doubleton__eq__2__iff,axiom,
    ! [A: $o,B: $o] :
      ( ( finite_card_o(insert_o((A),insert_o((B),bot_bot_set_o))) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)) )
    <=> ~ ( (A)
        <=> (B) ) ) ).

% card_doubleton_eq_2_iff
tff(fact_5542_card__doubleton__eq__2__iff,axiom,
    ! [A: nat,B: nat] :
      ( ( aa_set_nat_nat(finite_card_nat,insert_nat(A,insert_nat(B,bot_bot_set_nat))) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)) )
    <=> ( A != B ) ) ).

% card_doubleton_eq_2_iff
tff(fact_5543_card__doubleton__eq__2__iff,axiom,
    ! [A: int,B: int] :
      ( ( finite_card_int(insert_int(A,insert_int(B,bot_bot_set_int))) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)) )
    <=> ( A != B ) ) ).

% card_doubleton_eq_2_iff
tff(fact_5544_atMost__eq__UNIV__iff,axiom,
    ! [X2: set_nat] :
      ( ( set_or4236626031148496127et_nat(X2) = top_top_set_set_nat )
    <=> ( X2 = top_top_set_nat ) ) ).

% atMost_eq_UNIV_iff
tff(fact_5545_atMost__eq__UNIV__iff,axiom,
    ! [X2: set_Product_unit] :
      ( ( set_or2827140217781692084t_unit(X2) = top_to1767297665138865437t_unit )
    <=> ( X2 = top_to1996260823553986621t_unit ) ) ).

% atMost_eq_UNIV_iff
tff(fact_5546_atMost__eq__UNIV__iff,axiom,
    ! [X2: set_int] :
      ( ( set_or58775011639299419et_int(X2) = top_top_set_set_int )
    <=> ( X2 = top_top_set_int ) ) ).

% atMost_eq_UNIV_iff
tff(fact_5547_atMost__eq__UNIV__iff,axiom,
    ! [X2: assn] :
      ( ( set_ord_atMost_assn(X2) = top_top_set_assn )
    <=> ( X2 = top_top_assn ) ) ).

% atMost_eq_UNIV_iff
tff(fact_5548_atMost__eq__UNIV__iff,axiom,
    ! [X2: product_unit] :
      ( ( set_or8621721900777396692t_unit(X2) = top_to1996260823553986621t_unit )
    <=> ( X2 = top_top_Product_unit ) ) ).

% atMost_eq_UNIV_iff
tff(fact_5549_card__le__if__inj__on__rel,axiom,
    ! [B4: set_o,A2: set_o,R2: fun_o_fun_o_o] :
      ( finite_finite_o(B4)
     => ( ! [A3: $o] :
            ( member_o((A3),A2)
           => ? [B5: $o] :
                ( member_o((B5),B4)
                & aa_o_o(aa_o_fun_o_o(R2,(A3)),(B5)) ) )
       => ( ! [A12: $o,A23: $o,B2: $o] :
              ( member_o((A12),A2)
             => ( member_o((A23),A2)
               => ( member_o((B2),B4)
                 => ( aa_o_o(aa_o_fun_o_o(R2,(A12)),(B2))
                   => ( aa_o_o(aa_o_fun_o_o(R2,(A23)),(B2))
                     => ( (A12)
                      <=> (A23) ) ) ) ) ) )
         => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite_card_o(A2)),finite_card_o(B4)) ) ) ) ).

% card_le_if_inj_on_rel
tff(fact_5550_card__le__if__inj__on__rel,axiom,
    ! [B4: set_Product_unit,A2: set_o,R2: fun_o_6763651944650080953unit_o] :
      ( finite4290736615968046902t_unit(B4)
     => ( ! [A3: $o] :
            ( member_o((A3),A2)
           => ? [B5: product_unit] :
                ( member_Product_unit(B5,B4)
                & aa_Product_unit_o(aa_o_f4945551202706114282unit_o(R2,(A3)),B5) ) )
       => ( ! [A12: $o,A23: $o,B2: product_unit] :
              ( member_o((A12),A2)
             => ( member_o((A23),A2)
               => ( member_Product_unit(B2,B4)
                 => ( aa_Product_unit_o(aa_o_f4945551202706114282unit_o(R2,(A12)),B2)
                   => ( aa_Product_unit_o(aa_o_f4945551202706114282unit_o(R2,(A23)),B2)
                     => ( (A12)
                      <=> (A23) ) ) ) ) ) )
         => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite_card_o(A2)),finite410649719033368117t_unit(B4)) ) ) ) ).

% card_le_if_inj_on_rel
tff(fact_5551_card__le__if__inj__on__rel,axiom,
    ! [B4: set_o,A2: set_int,R2: fun_int_fun_o_o] :
      ( finite_finite_o(B4)
     => ( ! [A3: int] :
            ( member_int(A3,A2)
           => ? [B5: $o] :
                ( member_o((B5),B4)
                & aa_o_o(aa_int_fun_o_o(R2,A3),(B5)) ) )
       => ( ! [A12: int,A23: int,B2: $o] :
              ( member_int(A12,A2)
             => ( member_int(A23,A2)
               => ( member_o((B2),B4)
                 => ( aa_o_o(aa_int_fun_o_o(R2,A12),(B2))
                   => ( aa_o_o(aa_int_fun_o_o(R2,A23),(B2))
                     => ( A12 = A23 ) ) ) ) ) )
         => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite_card_int(A2)),finite_card_o(B4)) ) ) ) ).

% card_le_if_inj_on_rel
tff(fact_5552_card__le__if__inj__on__rel,axiom,
    ! [B4: set_Product_unit,A2: set_int,R2: fun_in8984369272479023031unit_o] :
      ( finite4290736615968046902t_unit(B4)
     => ( ! [A3: int] :
            ( member_int(A3,A2)
           => ? [B5: product_unit] :
                ( member_Product_unit(B5,B4)
                & aa_Product_unit_o(aa_int8968792772080532472unit_o(R2,A3),B5) ) )
       => ( ! [A12: int,A23: int,B2: product_unit] :
              ( member_int(A12,A2)
             => ( member_int(A23,A2)
               => ( member_Product_unit(B2,B4)
                 => ( aa_Product_unit_o(aa_int8968792772080532472unit_o(R2,A12),B2)
                   => ( aa_Product_unit_o(aa_int8968792772080532472unit_o(R2,A23),B2)
                     => ( A12 = A23 ) ) ) ) ) )
         => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite_card_int(A2)),finite410649719033368117t_unit(B4)) ) ) ) ).

% card_le_if_inj_on_rel
tff(fact_5553_card__le__if__inj__on__rel,axiom,
    ! [B4: set_o,A2: set_Product_unit,R2: fun_Pr616739963666181091un_o_o] :
      ( finite_finite_o(B4)
     => ( ! [A3: product_unit] :
            ( member_Product_unit(A3,A2)
           => ? [B5: $o] :
                ( member_o((B5),B4)
                & aa_o_o(aa_Pro7286578113964105876un_o_o(R2,A3),(B5)) ) )
       => ( ! [A12: product_unit,A23: product_unit,B2: $o] :
              ( member_Product_unit(A12,A2)
             => ( member_Product_unit(A23,A2)
               => ( member_o((B2),B4)
                 => ( aa_o_o(aa_Pro7286578113964105876un_o_o(R2,A12),(B2))
                   => ( aa_o_o(aa_Pro7286578113964105876un_o_o(R2,A23),(B2))
                     => ( A12 = A23 ) ) ) ) ) )
         => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite410649719033368117t_unit(A2)),finite_card_o(B4)) ) ) ) ).

% card_le_if_inj_on_rel
tff(fact_5554_card__le__if__inj__on__rel,axiom,
    ! [B4: set_Product_unit,A2: set_Product_unit,R2: fun_Pr1520749766685617582unit_o] :
      ( finite4290736615968046902t_unit(B4)
     => ( ! [A3: product_unit] :
            ( member_Product_unit(A3,A2)
           => ? [B5: product_unit] :
                ( member_Product_unit(B5,B4)
                & aa_Product_unit_o(aa_Pro4895447120693452255unit_o(R2,A3),B5) ) )
       => ( ! [A12: product_unit,A23: product_unit,B2: product_unit] :
              ( member_Product_unit(A12,A2)
             => ( member_Product_unit(A23,A2)
               => ( member_Product_unit(B2,B4)
                 => ( aa_Product_unit_o(aa_Pro4895447120693452255unit_o(R2,A12),B2)
                   => ( aa_Product_unit_o(aa_Pro4895447120693452255unit_o(R2,A23),B2)
                     => ( A12 = A23 ) ) ) ) ) )
         => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite410649719033368117t_unit(A2)),finite410649719033368117t_unit(B4)) ) ) ) ).

% card_le_if_inj_on_rel
tff(fact_5555_card__le__if__inj__on__rel,axiom,
    ! [B4: set_o,A2: set_nat,R2: fun_nat_fun_o_o] :
      ( finite_finite_o(B4)
     => ( ! [A3: nat] :
            ( member_nat(A3,A2)
           => ? [B5: $o] :
                ( member_o((B5),B4)
                & aa_o_o(aa_nat_fun_o_o(R2,A3),(B5)) ) )
       => ( ! [A12: nat,A23: nat,B2: $o] :
              ( member_nat(A12,A2)
             => ( member_nat(A23,A2)
               => ( member_o((B2),B4)
                 => ( aa_o_o(aa_nat_fun_o_o(R2,A12),(B2))
                   => ( aa_o_o(aa_nat_fun_o_o(R2,A23),(B2))
                     => ( A12 = A23 ) ) ) ) ) )
         => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_set_nat_nat(finite_card_nat,A2)),finite_card_o(B4)) ) ) ) ).

% card_le_if_inj_on_rel
tff(fact_5556_card__le__if__inj__on__rel,axiom,
    ! [B4: set_Product_unit,A2: set_nat,R2: fun_na5971062356810558811unit_o] :
      ( finite4290736615968046902t_unit(B4)
     => ( ! [A3: nat] :
            ( member_nat(A3,A2)
           => ? [B5: product_unit] :
                ( member_Product_unit(B5,B4)
                & aa_Product_unit_o(aa_nat5955485856412068252unit_o(R2,A3),B5) ) )
       => ( ! [A12: nat,A23: nat,B2: product_unit] :
              ( member_nat(A12,A2)
             => ( member_nat(A23,A2)
               => ( member_Product_unit(B2,B4)
                 => ( aa_Product_unit_o(aa_nat5955485856412068252unit_o(R2,A12),B2)
                   => ( aa_Product_unit_o(aa_nat5955485856412068252unit_o(R2,A23),B2)
                     => ( A12 = A23 ) ) ) ) ) )
         => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_set_nat_nat(finite_card_nat,A2)),finite410649719033368117t_unit(B4)) ) ) ) ).

% card_le_if_inj_on_rel
tff(fact_5557_card__le__if__inj__on__rel,axiom,
    ! [B4: set_nat,A2: set_o,R2: fun_o_fun_nat_o] :
      ( finite_finite_nat(B4)
     => ( ! [A3: $o] :
            ( member_o((A3),A2)
           => ? [B5: nat] :
                ( member_nat(B5,B4)
                & aa_nat_o(aa_o_fun_nat_o(R2,(A3)),B5) ) )
       => ( ! [A12: $o,A23: $o,B2: nat] :
              ( member_o((A12),A2)
             => ( member_o((A23),A2)
               => ( member_nat(B2,B4)
                 => ( aa_nat_o(aa_o_fun_nat_o(R2,(A12)),B2)
                   => ( aa_nat_o(aa_o_fun_nat_o(R2,(A23)),B2)
                     => ( (A12)
                      <=> (A23) ) ) ) ) ) )
         => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite_card_o(A2)),aa_set_nat_nat(finite_card_nat,B4)) ) ) ) ).

% card_le_if_inj_on_rel
tff(fact_5558_card__le__if__inj__on__rel,axiom,
    ! [B4: set_nat,A2: set_int,R2: fun_int_fun_nat_o] :
      ( finite_finite_nat(B4)
     => ( ! [A3: int] :
            ( member_int(A3,A2)
           => ? [B5: nat] :
                ( member_nat(B5,B4)
                & aa_nat_o(aa_int_fun_nat_o(R2,A3),B5) ) )
       => ( ! [A12: int,A23: int,B2: nat] :
              ( member_int(A12,A2)
             => ( member_int(A23,A2)
               => ( member_nat(B2,B4)
                 => ( aa_nat_o(aa_int_fun_nat_o(R2,A12),B2)
                   => ( aa_nat_o(aa_int_fun_nat_o(R2,A23),B2)
                     => ( A12 = A23 ) ) ) ) ) )
         => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite_card_int(A2)),aa_set_nat_nat(finite_card_nat,B4)) ) ) ) ).

% card_le_if_inj_on_rel
tff(fact_5559_top__option__def,axiom,
    top_to4826455019444611206et_nat = aa_set6119337032432945050et_nat(some_set_nat,top_top_set_nat) ).

% top_option_def
tff(fact_5560_top__option__def,axiom,
    top_to7662761140297458691t_unit = some_s8043159101241848530t_unit(top_to1996260823553986621t_unit) ).

% top_option_def
tff(fact_5561_top__option__def,axiom,
    top_to2336371874512884450et_int = some_set_int(top_top_set_int) ).

% top_option_def
tff(fact_5562_top__option__def,axiom,
    top_to4322782652514146083t_unit = aa_Pro7616171890175246658t_unit(some_Product_unit,top_top_Product_unit) ).

% top_option_def
tff(fact_5563_top__option__def,axiom,
    top_top_option_assn = some_assn(top_top_assn) ).

% top_option_def
tff(fact_5564_finite__if__eq__beyond__finite,axiom,
    ! [S2: set_int,S3: set_int] :
      ( finite_finite_int(S2)
     => finite6197958912794628473et_int(collect_set_int(aa_set5425576183772390127_int_o(aTP_Lamm_or(S2),S3))) ) ).

% finite_if_eq_beyond_finite
tff(fact_5565_finite__if__eq__beyond__finite,axiom,
    ! [S2: set_Code_integer,S3: set_Code_integer] :
      ( finite6017078050557962740nteger(S2)
     => finite6931041176100689706nteger(collec574505750873337192nteger(aa_set4044230130517860621eger_o(aTP_Lamm_os(S2),S3))) ) ).

% finite_if_eq_beyond_finite
tff(fact_5566_finite__if__eq__beyond__finite,axiom,
    ! [S2: set_Pr1261947904930325089at_nat,S3: set_Pr1261947904930325089at_nat] :
      ( finite6177210948735845034at_nat(S2)
     => finite9047747110432174090at_nat(collec5514110066124741708at_nat(aa_set7675215768510388063_nat_o(aTP_Lamm_ot(S2),S3))) ) ).

% finite_if_eq_beyond_finite
tff(fact_5567_finite__if__eq__beyond__finite,axiom,
    ! [S2: set_nat,S3: set_nat] :
      ( finite_finite_nat(S2)
     => finite1152437895449049373et_nat(collect_set_nat(aa_set7861427066675100071_nat_o(aTP_Lamm_ou(S2),S3))) ) ).

% finite_if_eq_beyond_finite
tff(fact_5568_finite__range__Some,axiom,
    ( finite6785661671136154180nteger(image_8960079959263999889nteger(some_Code_integer,top_to4645266643341252675nteger))
  <=> finite6017078050557962740nteger(top_to4645266643341252675nteger) ) ).

% finite_range_Some
tff(fact_5569_finite__range__Some,axiom,
    ( finite6732403688824079472at_nat(image_4198897800814241419at_nat(some_P7363390416028606310at_nat,top_to4669805908274784177at_nat))
  <=> finite6177210948735845034at_nat(top_to4669805908274784177at_nat) ) ).

% finite_range_Some
tff(fact_5570_finite__range__Some,axiom,
    ( finite6231397076622260609on_num(image_num_option_num(some_num,top_top_set_num))
  <=> finite_finite_num(top_top_set_num) ) ).

% finite_range_Some
tff(fact_5571_finite__range__Some,axiom,
    ( finite6292238467249657455it_nat(image_3455408117458022631it_nat(some_P1914260805536162275it_nat,top_to4082048134677576814it_nat))
  <=> finite6446286893012251551it_nat(top_to4082048134677576814it_nat) ) ).

% finite_range_Some
tff(fact_5572_finite__range__Some,axiom,
    ( finite5523153139673422903on_nat(image_nat_option_nat(some_nat,top_top_set_nat))
  <=> finite_finite_nat(top_top_set_nat) ) ).

% finite_range_Some
tff(fact_5573_finite__range__Some,axiom,
    ( finite1445617369574913404t_unit(image_7094380055901048587t_unit(some_Product_unit,top_to1996260823553986621t_unit))
  <=> finite4290736615968046902t_unit(top_to1996260823553986621t_unit) ) ).

% finite_range_Some
tff(fact_5574_finite__range__Some,axiom,
    ( finite1345302120164226195on_int(image_int_option_int(some_int,top_top_set_int))
  <=> finite_finite_int(top_top_set_int) ) ).

% finite_range_Some
tff(fact_5575_obtain__subset__with__card__n,axiom,
    ! [N2: nat,S2: set_Product_unit] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),finite410649719033368117t_unit(S2))
     => ~ ! [T2: set_Product_unit] :
            ( ord_le3507040750410214029t_unit(T2,S2)
           => ( ( finite410649719033368117t_unit(T2) = N2 )
             => ~ finite4290736615968046902t_unit(T2) ) ) ) ).

% obtain_subset_with_card_n
tff(fact_5576_obtain__subset__with__card__n,axiom,
    ! [N2: nat,S2: set_list_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),finite_card_list_nat(S2))
     => ~ ! [T2: set_list_nat] :
            ( ord_le6045566169113846134st_nat(T2,S2)
           => ( ( finite_card_list_nat(T2) = N2 )
             => ~ finite8100373058378681591st_nat(T2) ) ) ) ).

% obtain_subset_with_card_n
tff(fact_5577_obtain__subset__with__card__n,axiom,
    ! [N2: nat,S2: set_int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),finite_card_int(S2))
     => ~ ! [T2: set_int] :
            ( ord_less_eq_set_int(T2,S2)
           => ( ( finite_card_int(T2) = N2 )
             => ~ finite_finite_int(T2) ) ) ) ).

% obtain_subset_with_card_n
tff(fact_5578_obtain__subset__with__card__n,axiom,
    ! [N2: nat,S2: set_Code_integer] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),finite4902975817058060853nteger(S2))
     => ~ ! [T2: set_Code_integer] :
            ( ord_le7084787975880047091nteger(T2,S2)
           => ( ( finite4902975817058060853nteger(T2) = N2 )
             => ~ finite6017078050557962740nteger(T2) ) ) ) ).

% obtain_subset_with_card_n
tff(fact_5579_obtain__subset__with__card__n,axiom,
    ! [N2: nat,S2: set_Pr1261947904930325089at_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),aa_set4749074711808745205at_nat(finite711546835091564841at_nat,S2))
     => ~ ! [T2: set_Pr1261947904930325089at_nat] :
            ( aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(ord_le3146513528884898305at_nat,T2),S2)
           => ( ( aa_set4749074711808745205at_nat(finite711546835091564841at_nat,T2) = N2 )
             => ~ finite6177210948735845034at_nat(T2) ) ) ) ).

% obtain_subset_with_card_n
tff(fact_5580_obtain__subset__with__card__n,axiom,
    ! [N2: nat,S2: set_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N2),aa_set_nat_nat(finite_card_nat,S2))
     => ~ ! [T2: set_nat] :
            ( aa_set_nat_o(ord_less_eq_set_nat(T2),S2)
           => ( ( aa_set_nat_nat(finite_card_nat,T2) = N2 )
             => ~ finite_finite_nat(T2) ) ) ) ).

% obtain_subset_with_card_n
tff(fact_5581_atLeastAtMost__eq__UNIV__iff,axiom,
    ! [X2: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
      ( ( set_or4049648398082403068at_nat(X2,Y) = top_to1754375979021635447at_nat )
    <=> ( ( X2 = bot_bo228742789529271731at_nat )
        & ( Y = top_to6833984726390702231at_nat ) ) ) ).

% atLeastAtMost_eq_UNIV_iff
tff(fact_5582_atLeastAtMost__eq__UNIV__iff,axiom,
    ! [X2: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
      ( ( aa_set6242432332095302236at_nat(set_or2784603332384507286at_nat(X2),Y) = top_to7629004291339433233at_nat )
    <=> ( ( X2 = bot_bo2099793752762293965at_nat )
        & ( Y = top_to4669805908274784177at_nat ) ) ) ).

% atLeastAtMost_eq_UNIV_iff
tff(fact_5583_atLeastAtMost__eq__UNIV__iff,axiom,
    ! [X2: set_o,Y: set_o] :
      ( ( set_or266616469461849773_set_o(X2,Y) = top_top_set_set_o )
    <=> ( ( X2 = bot_bot_set_o )
        & ( Y = top_top_set_o ) ) ) ).

% atLeastAtMost_eq_UNIV_iff
tff(fact_5584_atLeastAtMost__eq__UNIV__iff,axiom,
    ! [X2: set_nat,Y: set_nat] :
      ( ( set_or4548717258645045905et_nat(X2,Y) = top_top_set_set_nat )
    <=> ( ( X2 = bot_bot_set_nat )
        & ( Y = top_top_set_nat ) ) ) ).

% atLeastAtMost_eq_UNIV_iff
tff(fact_5585_atLeastAtMost__eq__UNIV__iff,axiom,
    ! [X2: set_Product_unit,Y: set_Product_unit] :
      ( ( set_or269330187037242274t_unit(X2,Y) = top_to1767297665138865437t_unit )
    <=> ( ( X2 = bot_bo3957492148770167129t_unit )
        & ( Y = top_to1996260823553986621t_unit ) ) ) ).

% atLeastAtMost_eq_UNIV_iff
tff(fact_5586_atLeastAtMost__eq__UNIV__iff,axiom,
    ! [X2: set_int,Y: set_int] :
      ( ( set_or370866239135849197et_int(X2,Y) = top_top_set_set_int )
    <=> ( ( X2 = bot_bot_set_int )
        & ( Y = top_top_set_int ) ) ) ).

% atLeastAtMost_eq_UNIV_iff
tff(fact_5587_atLeastAtMost__eq__UNIV__iff,axiom,
    ! [X2: assn,Y: assn] :
      ( ( set_or7959216805967363635t_assn(X2,Y) = top_top_set_assn )
    <=> ( ( X2 = bot_bot_assn )
        & ( Y = top_top_assn ) ) ) ).

% atLeastAtMost_eq_UNIV_iff
tff(fact_5588_atLeastAtMost__eq__UNIV__iff,axiom,
    ! [X2: product_unit,Y: product_unit] :
      ( ( set_or5692540242118139586t_unit(X2,Y) = top_to1996260823553986621t_unit )
    <=> ( ( X2 = bot_bot_Product_unit )
        & ( Y = top_top_Product_unit ) ) ) ).

% atLeastAtMost_eq_UNIV_iff
tff(fact_5589_UNIV__option__conv,axiom,
    top_to7137183367772546234it_nat = insert7468008629046257882it_nat(none_P2587165478634041381it_nat,image_4799632500972785611it_nat(some_P6105628898608307625it_nat,top_to3995162779041354868it_nat)) ).

% UNIV_option_conv
tff(fact_5590_UNIV__option__conv,axiom,
    top_to4635417975585700688on_num = insert_option_num(none_num,image_num_option_num(some_num,top_top_set_num)) ).

% UNIV_option_conv
tff(fact_5591_UNIV__option__conv,axiom,
    top_to6632602878615679294it_nat = insert2007652293347934600it_nat(none_P9117596204409417319it_nat,image_3455408117458022631it_nat(some_P1914260805536162275it_nat,top_to4082048134677576814it_nat)) ).

% UNIV_option_conv
tff(fact_5592_UNIV__option__conv,axiom,
    top_to8920198386146353926on_nat = insert_option_nat(none_nat,image_nat_option_nat(some_nat,top_top_set_nat)) ).

% UNIV_option_conv
tff(fact_5593_UNIV__option__conv,axiom,
    top_to2690860209552263555t_unit = insert2866144167138965411t_unit(none_Product_unit,image_7094380055901048587t_unit(some_Product_unit,top_to1996260823553986621t_unit)) ).

% UNIV_option_conv
tff(fact_5594_UNIV__option__conv,axiom,
    top_to6430115241214627170on_int = insert_option_int(none_int,image_int_option_int(some_int,top_top_set_int)) ).

% UNIV_option_conv
tff(fact_5595_bounded__nat__set__is__finite,axiom,
    ! [N5: set_nat,N2: nat] :
      ( ! [X3: nat] :
          ( member_nat(X3,N5)
         => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,X3),N2) )
     => finite_finite_nat(N5) ) ).

% bounded_nat_set_is_finite
tff(fact_5596_finite__nat__set__iff__bounded,axiom,
    ! [N5: set_nat] :
      ( finite_finite_nat(N5)
    <=> ? [M6: nat] :
        ! [X4: nat] :
          ( member_nat(X4,N5)
         => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,X4),M6) ) ) ).

% finite_nat_set_iff_bounded
tff(fact_5597_finite__nat__set__iff__bounded__le,axiom,
    ! [N5: set_nat] :
      ( finite_finite_nat(N5)
    <=> ? [M6: nat] :
        ! [X4: nat] :
          ( member_nat(X4,N5)
         => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,X4),M6) ) ) ).

% finite_nat_set_iff_bounded_le
tff(fact_5598_surjD,axiom,
    ! [F: fun_nat_Code_integer,Y: code_integer] :
      ( ( image_1215581382706833972nteger(F,top_top_set_nat) = top_to4645266643341252675nteger )
     => ? [X3: nat] : Y = aa_nat_Code_integer(F,X3) ) ).

% surjD
tff(fact_5599_surjD,axiom,
    ! [F: fun_nat_nat,Y: nat] :
      ( ( aa_set_nat_set_nat(image_nat_nat(F),top_top_set_nat) = top_top_set_nat )
     => ? [X3: nat] : Y = aa_nat_nat(F,X3) ) ).

% surjD
tff(fact_5600_surjD,axiom,
    ! [F: fun_nat_Product_unit,Y: product_unit] :
      ( ( image_8730104196221521654t_unit(F,top_top_set_nat) = top_to1996260823553986621t_unit )
     => ? [X3: nat] : Y = aa_nat_Product_unit(F,X3) ) ).

% surjD
tff(fact_5601_surjD,axiom,
    ! [F: fun_nat_int,Y: int] :
      ( ( image_nat_int(F,top_top_set_nat) = top_top_set_int )
     => ? [X3: nat] : Y = aa_nat_int(F,X3) ) ).

% surjD
tff(fact_5602_surjD,axiom,
    ! [F: fun_Product_unit_nat,Y: nat] :
      ( ( image_875570014554754200it_nat(F,top_to1996260823553986621t_unit) = top_top_set_nat )
     => ? [X3: product_unit] : Y = aa_Product_unit_nat(F,X3) ) ).

% surjD
tff(fact_5603_surjD,axiom,
    ! [F: fun_Pr2191293291710260995t_unit,Y: product_unit] :
      ( ( image_405062704495631173t_unit(F,top_to1996260823553986621t_unit) = top_to1996260823553986621t_unit )
     => ? [X3: product_unit] : Y = aa_Pro8294289767544744956t_unit(F,X3) ) ).

% surjD
tff(fact_5604_surjD,axiom,
    ! [F: fun_Product_unit_int,Y: int] :
      ( ( image_873079544045703924it_int(F,top_to1996260823553986621t_unit) = top_top_set_int )
     => ? [X3: product_unit] : Y = aa_Product_unit_int(F,X3) ) ).

% surjD
tff(fact_5605_surjD,axiom,
    ! [F: fun_int_nat,Y: nat] :
      ( ( image_int_nat(F,top_top_set_int) = top_top_set_nat )
     => ? [X3: int] : Y = aa_int_nat(F,X3) ) ).

% surjD
tff(fact_5606_surjD,axiom,
    ! [F: fun_int_Product_unit,Y: product_unit] :
      ( ( image_5846526143423701914t_unit(F,top_top_set_int) = top_to1996260823553986621t_unit )
     => ? [X3: int] : Y = aa_int_Product_unit(F,X3) ) ).

% surjD
tff(fact_5607_surjD,axiom,
    ! [F: fun_int_int,Y: int] :
      ( ( aa_set_int_set_int(image_int_int(F),top_top_set_int) = top_top_set_int )
     => ? [X3: int] : Y = aa_int_int(F,X3) ) ).

% surjD
tff(fact_5608_surjE,axiom,
    ! [F: fun_nat_Code_integer,Y: code_integer] :
      ( ( image_1215581382706833972nteger(F,top_top_set_nat) = top_to4645266643341252675nteger )
     => ~ ! [X3: nat] : Y != aa_nat_Code_integer(F,X3) ) ).

% surjE
tff(fact_5609_surjE,axiom,
    ! [F: fun_nat_nat,Y: nat] :
      ( ( aa_set_nat_set_nat(image_nat_nat(F),top_top_set_nat) = top_top_set_nat )
     => ~ ! [X3: nat] : Y != aa_nat_nat(F,X3) ) ).

% surjE
tff(fact_5610_surjE,axiom,
    ! [F: fun_nat_Product_unit,Y: product_unit] :
      ( ( image_8730104196221521654t_unit(F,top_top_set_nat) = top_to1996260823553986621t_unit )
     => ~ ! [X3: nat] : Y != aa_nat_Product_unit(F,X3) ) ).

% surjE
tff(fact_5611_surjE,axiom,
    ! [F: fun_nat_int,Y: int] :
      ( ( image_nat_int(F,top_top_set_nat) = top_top_set_int )
     => ~ ! [X3: nat] : Y != aa_nat_int(F,X3) ) ).

% surjE
tff(fact_5612_surjE,axiom,
    ! [F: fun_Product_unit_nat,Y: nat] :
      ( ( image_875570014554754200it_nat(F,top_to1996260823553986621t_unit) = top_top_set_nat )
     => ~ ! [X3: product_unit] : Y != aa_Product_unit_nat(F,X3) ) ).

% surjE
tff(fact_5613_surjE,axiom,
    ! [F: fun_Pr2191293291710260995t_unit,Y: product_unit] :
      ( ( image_405062704495631173t_unit(F,top_to1996260823553986621t_unit) = top_to1996260823553986621t_unit )
     => ~ ! [X3: product_unit] : Y != aa_Pro8294289767544744956t_unit(F,X3) ) ).

% surjE
tff(fact_5614_surjE,axiom,
    ! [F: fun_Product_unit_int,Y: int] :
      ( ( image_873079544045703924it_int(F,top_to1996260823553986621t_unit) = top_top_set_int )
     => ~ ! [X3: product_unit] : Y != aa_Product_unit_int(F,X3) ) ).

% surjE
tff(fact_5615_surjE,axiom,
    ! [F: fun_int_nat,Y: nat] :
      ( ( image_int_nat(F,top_top_set_int) = top_top_set_nat )
     => ~ ! [X3: int] : Y != aa_int_nat(F,X3) ) ).

% surjE
tff(fact_5616_surjE,axiom,
    ! [F: fun_int_Product_unit,Y: product_unit] :
      ( ( image_5846526143423701914t_unit(F,top_top_set_int) = top_to1996260823553986621t_unit )
     => ~ ! [X3: int] : Y != aa_int_Product_unit(F,X3) ) ).

% surjE
tff(fact_5617_surjE,axiom,
    ! [F: fun_int_int,Y: int] :
      ( ( aa_set_int_set_int(image_int_int(F),top_top_set_int) = top_top_set_int )
     => ~ ! [X3: int] : Y != aa_int_int(F,X3) ) ).

% surjE
tff(fact_5618_surjI,axiom,
    ! [G: fun_nat_Code_integer,F: fun_Code_integer_nat] :
      ( ! [X3: code_integer] : aa_nat_Code_integer(G,aa_Code_integer_nat(F,X3)) = X3
     => ( image_1215581382706833972nteger(G,top_top_set_nat) = top_to4645266643341252675nteger ) ) ).

% surjI
tff(fact_5619_surjI,axiom,
    ! [G: fun_nat_nat,F: fun_nat_nat] :
      ( ! [X3: nat] : aa_nat_nat(G,aa_nat_nat(F,X3)) = X3
     => ( aa_set_nat_set_nat(image_nat_nat(G),top_top_set_nat) = top_top_set_nat ) ) ).

% surjI
tff(fact_5620_surjI,axiom,
    ! [G: fun_nat_Product_unit,F: fun_Product_unit_nat] :
      ( ! [X3: product_unit] : aa_nat_Product_unit(G,aa_Product_unit_nat(F,X3)) = X3
     => ( image_8730104196221521654t_unit(G,top_top_set_nat) = top_to1996260823553986621t_unit ) ) ).

% surjI
tff(fact_5621_surjI,axiom,
    ! [G: fun_nat_int,F: fun_int_nat] :
      ( ! [X3: int] : aa_nat_int(G,aa_int_nat(F,X3)) = X3
     => ( image_nat_int(G,top_top_set_nat) = top_top_set_int ) ) ).

% surjI
tff(fact_5622_surjI,axiom,
    ! [G: fun_Product_unit_nat,F: fun_nat_Product_unit] :
      ( ! [X3: nat] : aa_Product_unit_nat(G,aa_nat_Product_unit(F,X3)) = X3
     => ( image_875570014554754200it_nat(G,top_to1996260823553986621t_unit) = top_top_set_nat ) ) ).

% surjI
tff(fact_5623_surjI,axiom,
    ! [G: fun_Pr2191293291710260995t_unit,F: fun_Pr2191293291710260995t_unit] :
      ( ! [X3: product_unit] : aa_Pro8294289767544744956t_unit(G,aa_Pro8294289767544744956t_unit(F,X3)) = X3
     => ( image_405062704495631173t_unit(G,top_to1996260823553986621t_unit) = top_to1996260823553986621t_unit ) ) ).

% surjI
tff(fact_5624_surjI,axiom,
    ! [G: fun_Product_unit_int,F: fun_int_Product_unit] :
      ( ! [X3: int] : aa_Product_unit_int(G,aa_int_Product_unit(F,X3)) = X3
     => ( image_873079544045703924it_int(G,top_to1996260823553986621t_unit) = top_top_set_int ) ) ).

% surjI
tff(fact_5625_surjI,axiom,
    ! [G: fun_int_nat,F: fun_nat_int] :
      ( ! [X3: nat] : aa_int_nat(G,aa_nat_int(F,X3)) = X3
     => ( image_int_nat(G,top_top_set_int) = top_top_set_nat ) ) ).

% surjI
tff(fact_5626_surjI,axiom,
    ! [G: fun_int_Product_unit,F: fun_Product_unit_int] :
      ( ! [X3: product_unit] : aa_int_Product_unit(G,aa_Product_unit_int(F,X3)) = X3
     => ( image_5846526143423701914t_unit(G,top_top_set_int) = top_to1996260823553986621t_unit ) ) ).

% surjI
tff(fact_5627_surjI,axiom,
    ! [G: fun_int_int,F: fun_int_int] :
      ( ! [X3: int] : aa_int_int(G,aa_int_int(F,X3)) = X3
     => ( aa_set_int_set_int(image_int_int(G),top_top_set_int) = top_top_set_int ) ) ).

% surjI
tff(fact_5628_surj__def,axiom,
    ! [F: fun_nat_Code_integer] :
      ( ( image_1215581382706833972nteger(F,top_top_set_nat) = top_to4645266643341252675nteger )
    <=> ! [Y3: code_integer] :
        ? [X4: nat] : Y3 = aa_nat_Code_integer(F,X4) ) ).

% surj_def
tff(fact_5629_surj__def,axiom,
    ! [F: fun_nat_nat] :
      ( ( aa_set_nat_set_nat(image_nat_nat(F),top_top_set_nat) = top_top_set_nat )
    <=> ! [Y3: nat] :
        ? [X4: nat] : Y3 = aa_nat_nat(F,X4) ) ).

% surj_def
tff(fact_5630_surj__def,axiom,
    ! [F: fun_nat_Product_unit] :
      ( ( image_8730104196221521654t_unit(F,top_top_set_nat) = top_to1996260823553986621t_unit )
    <=> ! [Y3: product_unit] :
        ? [X4: nat] : Y3 = aa_nat_Product_unit(F,X4) ) ).

% surj_def
tff(fact_5631_surj__def,axiom,
    ! [F: fun_nat_int] :
      ( ( image_nat_int(F,top_top_set_nat) = top_top_set_int )
    <=> ! [Y3: int] :
        ? [X4: nat] : Y3 = aa_nat_int(F,X4) ) ).

% surj_def
tff(fact_5632_surj__def,axiom,
    ! [F: fun_Product_unit_nat] :
      ( ( image_875570014554754200it_nat(F,top_to1996260823553986621t_unit) = top_top_set_nat )
    <=> ! [Y3: nat] :
        ? [X4: product_unit] : Y3 = aa_Product_unit_nat(F,X4) ) ).

% surj_def
tff(fact_5633_surj__def,axiom,
    ! [F: fun_Pr2191293291710260995t_unit] :
      ( ( image_405062704495631173t_unit(F,top_to1996260823553986621t_unit) = top_to1996260823553986621t_unit )
    <=> ! [Y3: product_unit] :
        ? [X4: product_unit] : Y3 = aa_Pro8294289767544744956t_unit(F,X4) ) ).

% surj_def
tff(fact_5634_surj__def,axiom,
    ! [F: fun_Product_unit_int] :
      ( ( image_873079544045703924it_int(F,top_to1996260823553986621t_unit) = top_top_set_int )
    <=> ! [Y3: int] :
        ? [X4: product_unit] : Y3 = aa_Product_unit_int(F,X4) ) ).

% surj_def
tff(fact_5635_surj__def,axiom,
    ! [F: fun_int_nat] :
      ( ( image_int_nat(F,top_top_set_int) = top_top_set_nat )
    <=> ! [Y3: nat] :
        ? [X4: int] : Y3 = aa_int_nat(F,X4) ) ).

% surj_def
tff(fact_5636_surj__def,axiom,
    ! [F: fun_int_Product_unit] :
      ( ( image_5846526143423701914t_unit(F,top_top_set_int) = top_to1996260823553986621t_unit )
    <=> ! [Y3: product_unit] :
        ? [X4: int] : Y3 = aa_int_Product_unit(F,X4) ) ).

% surj_def
tff(fact_5637_surj__def,axiom,
    ! [F: fun_int_int] :
      ( ( aa_set_int_set_int(image_int_int(F),top_top_set_int) = top_top_set_int )
    <=> ! [Y3: int] :
        ? [X4: int] : Y3 = aa_int_int(F,X4) ) ).

% surj_def
tff(fact_5638_these__empty__eq,axiom,
    ! [B4: set_op3940070208846178154it_nat] :
      ( ( these_6645423997822192641it_nat(B4) = bot_bo6361524548789211024it_nat )
    <=> ( ( B4 = bot_bo8185009268211221974it_nat )
        | ( B4 = insert7468008629046257882it_nat(none_P2587165478634041381it_nat,bot_bo8185009268211221974it_nat) ) ) ) ).

% these_empty_eq
tff(fact_5639_these__empty__eq,axiom,
    ! [B4: set_option_num] :
      ( ( these_num(B4) = bot_bot_set_num )
    <=> ( ( B4 = bot_bo725063100934353204on_num )
        | ( B4 = insert_option_num(none_num,bot_bo725063100934353204on_num) ) ) ) ).

% these_empty_eq
tff(fact_5640_these__empty__eq,axiom,
    ! [B4: set_op239864471688321678it_nat] :
      ( ( these_3407724651694999947it_nat(B4) = bot_bo5696401558416705618it_nat )
    <=> ( ( B4 = bot_bo1172055076661450530it_nat )
        | ( B4 = insert2007652293347934600it_nat(none_P9117596204409417319it_nat,bot_bo1172055076661450530it_nat) ) ) ) ).

% these_empty_eq
tff(fact_5641_these__empty__eq,axiom,
    ! [B4: set_op989438649584373901at_nat] :
      ( ( these_1872268174106123684at_nat(B4) = bot_bo228742789529271731at_nat )
    <=> ( ( B4 = bot_bo1471150103859235065at_nat )
        | ( B4 = insert6833468608972679677at_nat(none_P5811896708078067656at_nat,bot_bo1471150103859235065at_nat) ) ) ) ).

% these_empty_eq
tff(fact_5642_these__empty__eq,axiom,
    ! [B4: set_op4508134149509766951at_nat] :
      ( ( these_8061402112538453438at_nat(B4) = bot_bo2099793752762293965at_nat )
    <=> ( ( B4 = bot_bo3414888551220300179at_nat )
        | ( B4 = insert6842972033726296599at_nat(none_P5556105721700978146at_nat,bot_bo3414888551220300179at_nat) ) ) ) ).

% these_empty_eq
tff(fact_5643_these__empty__eq,axiom,
    ! [B4: set_option_o] :
      ( ( these_o(B4) = bot_bot_set_o )
    <=> ( ( B4 = bot_bot_set_option_o )
        | ( B4 = insert_option_o(none_o,bot_bot_set_option_o) ) ) ) ).

% these_empty_eq
tff(fact_5644_these__empty__eq,axiom,
    ! [B4: set_option_nat] :
      ( ( these_nat(B4) = bot_bot_set_nat )
    <=> ( ( B4 = bot_bo5009843511495006442on_nat )
        | ( B4 = insert_option_nat(none_nat,bot_bo5009843511495006442on_nat) ) ) ) ).

% these_empty_eq
tff(fact_5645_these__empty__eq,axiom,
    ! [B4: set_option_int] :
      ( ( these_int(B4) = bot_bot_set_int )
    <=> ( ( B4 = bot_bo2519760366563279686on_int )
        | ( B4 = insert_option_int(none_int,bot_bo2519760366563279686on_int) ) ) ) ).

% these_empty_eq
tff(fact_5646_these__not__empty__eq,axiom,
    ! [B4: set_op3940070208846178154it_nat] :
      ( ( these_6645423997822192641it_nat(B4) != bot_bo6361524548789211024it_nat )
    <=> ( ( B4 != bot_bo8185009268211221974it_nat )
        & ( B4 != insert7468008629046257882it_nat(none_P2587165478634041381it_nat,bot_bo8185009268211221974it_nat) ) ) ) ).

% these_not_empty_eq
tff(fact_5647_these__not__empty__eq,axiom,
    ! [B4: set_option_num] :
      ( ( these_num(B4) != bot_bot_set_num )
    <=> ( ( B4 != bot_bo725063100934353204on_num )
        & ( B4 != insert_option_num(none_num,bot_bo725063100934353204on_num) ) ) ) ).

% these_not_empty_eq
tff(fact_5648_these__not__empty__eq,axiom,
    ! [B4: set_op239864471688321678it_nat] :
      ( ( these_3407724651694999947it_nat(B4) != bot_bo5696401558416705618it_nat )
    <=> ( ( B4 != bot_bo1172055076661450530it_nat )
        & ( B4 != insert2007652293347934600it_nat(none_P9117596204409417319it_nat,bot_bo1172055076661450530it_nat) ) ) ) ).

% these_not_empty_eq
tff(fact_5649_these__not__empty__eq,axiom,
    ! [B4: set_op989438649584373901at_nat] :
      ( ( these_1872268174106123684at_nat(B4) != bot_bo228742789529271731at_nat )
    <=> ( ( B4 != bot_bo1471150103859235065at_nat )
        & ( B4 != insert6833468608972679677at_nat(none_P5811896708078067656at_nat,bot_bo1471150103859235065at_nat) ) ) ) ).

% these_not_empty_eq
tff(fact_5650_these__not__empty__eq,axiom,
    ! [B4: set_op4508134149509766951at_nat] :
      ( ( these_8061402112538453438at_nat(B4) != bot_bo2099793752762293965at_nat )
    <=> ( ( B4 != bot_bo3414888551220300179at_nat )
        & ( B4 != insert6842972033726296599at_nat(none_P5556105721700978146at_nat,bot_bo3414888551220300179at_nat) ) ) ) ).

% these_not_empty_eq
tff(fact_5651_these__not__empty__eq,axiom,
    ! [B4: set_option_o] :
      ( ( these_o(B4) != bot_bot_set_o )
    <=> ( ( B4 != bot_bot_set_option_o )
        & ( B4 != insert_option_o(none_o,bot_bot_set_option_o) ) ) ) ).

% these_not_empty_eq
tff(fact_5652_these__not__empty__eq,axiom,
    ! [B4: set_option_nat] :
      ( ( these_nat(B4) != bot_bot_set_nat )
    <=> ( ( B4 != bot_bo5009843511495006442on_nat )
        & ( B4 != insert_option_nat(none_nat,bot_bo5009843511495006442on_nat) ) ) ) ).

% these_not_empty_eq
tff(fact_5653_these__not__empty__eq,axiom,
    ! [B4: set_option_int] :
      ( ( these_int(B4) != bot_bot_set_int )
    <=> ( ( B4 != bot_bo2519760366563279686on_int )
        & ( B4 != insert_option_int(none_int,bot_bo2519760366563279686on_int) ) ) ) ).

% these_not_empty_eq
tff(fact_5654_not__UNIV__eq__Icc,axiom,
    ! [L4: int,H3: int] : top_top_set_int != aa_int_set_int(set_or1266510415728281911st_int(L4),H3) ).

% not_UNIV_eq_Icc
tff(fact_5655_not__UNIV__eq__Icc,axiom,
    ! [L4: nat,H3: nat] : top_top_set_nat != aa_nat_set_nat(set_or1269000886237332187st_nat(L4),H3) ).

% not_UNIV_eq_Icc
tff(fact_5656_infinite__Iic,axiom,
    ! [A: int] : ~ finite_finite_int(aa_int_set_int(set_ord_atMost_int,A)) ).

% infinite_Iic
tff(fact_5657_infinite__Iio,axiom,
    ! [A: int] : ~ finite_finite_int(aa_int_set_int(set_ord_lessThan_int,A)) ).

% infinite_Iio
tff(fact_5658_not__UNIV__eq__Iic,axiom,
    ! [H3: int] : top_top_set_int != aa_int_set_int(set_ord_atMost_int,H3) ).

% not_UNIV_eq_Iic
tff(fact_5659_not__UNIV__eq__Iic,axiom,
    ! [H3: nat] : top_top_set_nat != aa_nat_set_nat(set_ord_atMost_nat,H3) ).

% not_UNIV_eq_Iic
tff(fact_5660_card__1__singletonI,axiom,
    ! [S2: set_Product_unit,X2: product_unit] :
      ( finite4290736615968046902t_unit(S2)
     => ( ( finite410649719033368117t_unit(S2) = one_one_nat )
       => ( member_Product_unit(X2,S2)
         => ( S2 = insert_Product_unit(X2,bot_bo3957492148770167129t_unit) ) ) ) ) ).

% card_1_singletonI
tff(fact_5661_card__1__singletonI,axiom,
    ! [S2: set_list_nat,X2: list_nat] :
      ( finite8100373058378681591st_nat(S2)
     => ( ( finite_card_list_nat(S2) = one_one_nat )
       => ( member_list_nat(X2,S2)
         => ( S2 = insert_list_nat(X2,bot_bot_set_list_nat) ) ) ) ) ).

% card_1_singletonI
tff(fact_5662_card__1__singletonI,axiom,
    ! [S2: set_Code_integer,X2: code_integer] :
      ( finite6017078050557962740nteger(S2)
     => ( ( finite4902975817058060853nteger(S2) = one_one_nat )
       => ( member_Code_integer(X2,S2)
         => ( S2 = insert_Code_integer(X2,bot_bo3990330152332043303nteger) ) ) ) ) ).

% card_1_singletonI
tff(fact_5663_card__1__singletonI,axiom,
    ! [S2: set_Pr4329608150637261639at_nat,X2: produc3843707927480180839at_nat] :
      ( finite4343798906461161616at_nat(S2)
     => ( ( finite3771342082235030671at_nat(S2) = one_one_nat )
       => ( member8757157785044589968at_nat(X2,S2)
         => ( S2 = aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(X2),bot_bo228742789529271731at_nat) ) ) ) ) ).

% card_1_singletonI
tff(fact_5664_card__1__singletonI,axiom,
    ! [S2: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat] :
      ( finite6177210948735845034at_nat(S2)
     => ( ( aa_set4749074711808745205at_nat(finite711546835091564841at_nat,S2) = one_one_nat )
       => ( member8440522571783428010at_nat(X2,S2)
         => ( S2 = aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(X2),bot_bo2099793752762293965at_nat) ) ) ) ) ).

% card_1_singletonI
tff(fact_5665_card__1__singletonI,axiom,
    ! [S2: set_o,X2: $o] :
      ( finite_finite_o(S2)
     => ( ( finite_card_o(S2) = one_one_nat )
       => ( member_o((X2),S2)
         => ( S2 = insert_o((X2),bot_bot_set_o) ) ) ) ) ).

% card_1_singletonI
tff(fact_5666_card__1__singletonI,axiom,
    ! [S2: set_nat,X2: nat] :
      ( finite_finite_nat(S2)
     => ( ( aa_set_nat_nat(finite_card_nat,S2) = one_one_nat )
       => ( member_nat(X2,S2)
         => ( S2 = insert_nat(X2,bot_bot_set_nat) ) ) ) ) ).

% card_1_singletonI
tff(fact_5667_card__1__singletonI,axiom,
    ! [S2: set_int,X2: int] :
      ( finite_finite_int(S2)
     => ( ( finite_card_int(S2) = one_one_nat )
       => ( member_int(X2,S2)
         => ( S2 = insert_int(X2,bot_bot_set_int) ) ) ) ) ).

% card_1_singletonI
tff(fact_5668_finite__M__bounded__by__nat,axiom,
    ! [P: fun_nat_o,I: nat] : finite_finite_nat(collect_nat(aa_nat_fun_nat_o(aTP_Lamm_ov(P),I))) ).

% finite_M_bounded_by_nat
tff(fact_5669_finite__less__ub,axiom,
    ! [F: fun_nat_nat,U: nat] :
      ( ! [N: nat] : aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,N),aa_nat_nat(F,N))
     => finite_finite_nat(collect_nat(aa_nat_fun_nat_o(aTP_Lamm_ow(F),U))) ) ).

% finite_less_ub
tff(fact_5670_card__insert__disjoint_H,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,X2: produc3843707927480180839at_nat] :
      ( finite4343798906461161616at_nat(A2)
     => ( ~ member8757157785044589968at_nat(X2,A2)
       => ( aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite3771342082235030671at_nat(aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(X2),A2))),aa_nat_nat(suc,zero_zero_nat)) = finite3771342082235030671at_nat(A2) ) ) ) ).

% card_insert_disjoint'
tff(fact_5671_card__insert__disjoint_H,axiom,
    ! [A2: set_o,X2: $o] :
      ( finite_finite_o(A2)
     => ( ~ member_o((X2),A2)
       => ( aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite_card_o(insert_o((X2),A2))),aa_nat_nat(suc,zero_zero_nat)) = finite_card_o(A2) ) ) ) ).

% card_insert_disjoint'
tff(fact_5672_card__insert__disjoint_H,axiom,
    ! [A2: set_Product_unit,X2: product_unit] :
      ( finite4290736615968046902t_unit(A2)
     => ( ~ member_Product_unit(X2,A2)
       => ( aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite410649719033368117t_unit(insert_Product_unit(X2,A2))),aa_nat_nat(suc,zero_zero_nat)) = finite410649719033368117t_unit(A2) ) ) ) ).

% card_insert_disjoint'
tff(fact_5673_card__insert__disjoint_H,axiom,
    ! [A2: set_list_nat,X2: list_nat] :
      ( finite8100373058378681591st_nat(A2)
     => ( ~ member_list_nat(X2,A2)
       => ( aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite_card_list_nat(insert_list_nat(X2,A2))),aa_nat_nat(suc,zero_zero_nat)) = finite_card_list_nat(A2) ) ) ) ).

% card_insert_disjoint'
tff(fact_5674_card__insert__disjoint_H,axiom,
    ! [A2: set_nat,X2: nat] :
      ( finite_finite_nat(A2)
     => ( ~ member_nat(X2,A2)
       => ( aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_set_nat_nat(finite_card_nat,insert_nat(X2,A2))),aa_nat_nat(suc,zero_zero_nat)) = aa_set_nat_nat(finite_card_nat,A2) ) ) ) ).

% card_insert_disjoint'
tff(fact_5675_card__insert__disjoint_H,axiom,
    ! [A2: set_int,X2: int] :
      ( finite_finite_int(A2)
     => ( ~ member_int(X2,A2)
       => ( aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite_card_int(insert_int(X2,A2))),aa_nat_nat(suc,zero_zero_nat)) = finite_card_int(A2) ) ) ) ).

% card_insert_disjoint'
tff(fact_5676_card__insert__disjoint_H,axiom,
    ! [A2: set_Code_integer,X2: code_integer] :
      ( finite6017078050557962740nteger(A2)
     => ( ~ member_Code_integer(X2,A2)
       => ( aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite4902975817058060853nteger(insert_Code_integer(X2,A2))),aa_nat_nat(suc,zero_zero_nat)) = finite4902975817058060853nteger(A2) ) ) ) ).

% card_insert_disjoint'
tff(fact_5677_card__insert__disjoint_H,axiom,
    ! [A2: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat] :
      ( finite6177210948735845034at_nat(A2)
     => ( ~ member8440522571783428010at_nat(X2,A2)
       => ( aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_set4749074711808745205at_nat(finite711546835091564841at_nat,aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(X2),A2))),aa_nat_nat(suc,zero_zero_nat)) = aa_set4749074711808745205at_nat(finite711546835091564841at_nat,A2) ) ) ) ).

% card_insert_disjoint'
tff(fact_5678_in__these__eq,axiom,
    ! [X2: produc3843707927480180839at_nat,A2: set_op989438649584373901at_nat] :
      ( member8757157785044589968at_nat(X2,these_1872268174106123684at_nat(A2))
    <=> member4288423094740844502at_nat(some_P131194445498448716at_nat(X2),A2) ) ).

% in_these_eq
tff(fact_5679_in__these__eq,axiom,
    ! [X2: product_prod_nat_nat,A2: set_op4508134149509766951at_nat] :
      ( member8440522571783428010at_nat(X2,these_8061402112538453438at_nat(A2))
    <=> member3954567711264315760at_nat(aa_Pro4773402355715522498at_nat(some_P7363390416028606310at_nat,X2),A2) ) ).

% in_these_eq
tff(fact_5680_in__these__eq,axiom,
    ! [X2: $o,A2: set_option_o] :
      ( member_o((X2),these_o(A2))
    <=> member_option_o(aa_o_option_o(some_o,(X2)),A2) ) ).

% in_these_eq
tff(fact_5681_in__these__eq,axiom,
    ! [X2: nat,A2: set_option_nat] :
      ( member_nat(X2,these_nat(A2))
    <=> member_option_nat(aa_nat_option_nat(some_nat,X2),A2) ) ).

% in_these_eq
tff(fact_5682_in__these__eq,axiom,
    ! [X2: int,A2: set_option_int] :
      ( member_int(X2,these_int(A2))
    <=> member_option_int(aa_int_option_int(some_int,X2),A2) ) ).

% in_these_eq
tff(fact_5683_in__these__eq,axiom,
    ! [X2: num,A2: set_option_num] :
      ( member_num(X2,these_num(A2))
    <=> member_option_num(aa_num_option_num(some_num,X2),A2) ) ).

% in_these_eq
tff(fact_5684_in__these__eq,axiom,
    ! [X2: produc8664842809031399944it_nat,A2: set_op239864471688321678it_nat] :
      ( member3421417852355157663it_nat(X2,these_3407724651694999947it_nat(A2))
    <=> member5596548051065438575it_nat(aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,X2),A2) ) ).

% in_these_eq
tff(fact_5685_infinite__Icc,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B)
     => ~ finite_finite_rat(set_or633870826150836451st_rat(A,B)) ) ).

% infinite_Icc
tff(fact_5686_infinite__Ico,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B)
     => ~ finite_finite_rat(set_or4029947393144176647an_rat(A,B)) ) ).

% infinite_Ico
tff(fact_5687_subset__eq__atLeast0__atMost__finite,axiom,
    ! [N5: set_nat,N2: nat] :
      ( aa_set_nat_o(ord_less_eq_set_nat(N5),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2))
     => finite_finite_nat(N5) ) ).

% subset_eq_atLeast0_atMost_finite
tff(fact_5688_subset__eq__atLeast0__lessThan__finite,axiom,
    ! [N5: set_nat,N2: nat] :
      ( aa_set_nat_o(ord_less_eq_set_nat(N5),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2))
     => finite_finite_nat(N5) ) ).

% subset_eq_atLeast0_lessThan_finite
tff(fact_5689_atMost__Suc,axiom,
    ! [K: nat] : aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(suc,K)) = insert_nat(aa_nat_nat(suc,K),aa_nat_set_nat(set_ord_atMost_nat,K)) ).

% atMost_Suc
tff(fact_5690_surj__fun__eq,axiom,
    ! [F: fun_num_Code_integer,X7: set_num,G1: fun_Co8499238673658658103nteger,G22: fun_Co8499238673658658103nteger] :
      ( ( image_8379761247532268670nteger(F,X7) = top_to4645266643341252675nteger )
     => ( ! [X3: num] :
            ( member_num(X3,X7)
           => ( aa_num_Code_integer(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G1),F),X3) = aa_num_Code_integer(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G22),F),X3) ) )
       => ( G1 = G22 ) ) ) ).

% surj_fun_eq
tff(fact_5691_surj__fun__eq,axiom,
    ! [F: fun_Co8499238673658658103nteger,X7: set_Code_integer,G1: fun_Co1561183069634336733nteger,G22: fun_Co1561183069634336733nteger] :
      ( ( image_4470545334726330049nteger(F,X7) = top_to4645266643341252675nteger )
     => ( ! [X3: code_integer] :
            ( member_Code_integer(X3,X7)
           => ( aa_Cod1978467581589928094nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,G1),F),X3) = aa_Cod1978467581589928094nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,G22),F),X3) ) )
       => ( G1 = G22 ) ) ) ).

% surj_fun_eq
tff(fact_5692_surj__fun__eq,axiom,
    ! [F: fun_Co1981900195452921617nteger,X7: set_Code_integer,G1: fun_fu4800041728187187127nteger,G22: fun_fu4800041728187187127nteger] :
      ( ( image_2716445779319712667nteger(F,X7) = top_to805621317456759325nteger )
     => ( ! [X3: code_integer] :
            ( member_Code_integer(X3,X7)
           => ( aa_Cod1978467581589928094nteger(comp_f6739083541385432444nteger(G1,F),X3) = aa_Cod1978467581589928094nteger(comp_f6739083541385432444nteger(G22,F),X3) ) )
       => ( G1 = G22 ) ) ) ).

% surj_fun_eq
tff(fact_5693_surj__fun__eq,axiom,
    ! [F: fun_int_nat,X7: set_int,G1: fun_nat_num,G22: fun_nat_num] :
      ( ( image_int_nat(F,X7) = top_top_set_nat )
     => ( ! [X3: int] :
            ( member_int(X3,X7)
           => ( aa_int_num(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,G1),F),X3) = aa_int_num(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,G22),F),X3) ) )
       => ( G1 = G22 ) ) ) ).

% surj_fun_eq
tff(fact_5694_comp__surj,axiom,
    ! [F: fun_num_Code_integer,G: fun_Co8499238673658658103nteger] :
      ( ( image_8379761247532268670nteger(F,top_top_set_num) = top_to4645266643341252675nteger )
     => ( ( image_4470545334726330049nteger(G,top_to4645266643341252675nteger) = top_to4645266643341252675nteger )
       => ( image_8379761247532268670nteger(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),F),top_top_set_num) = top_to4645266643341252675nteger ) ) ) ).

% comp_surj
tff(fact_5695_comp__surj,axiom,
    ! [F: fun_nat_Code_integer,G: fun_Co8499238673658658103nteger] :
      ( ( image_1215581382706833972nteger(F,top_top_set_nat) = top_to4645266643341252675nteger )
     => ( ( image_4470545334726330049nteger(G,top_to4645266643341252675nteger) = top_to4645266643341252675nteger )
       => ( image_1215581382706833972nteger(comp_C6974050283906349679er_nat(G,F),top_top_set_nat) = top_to4645266643341252675nteger ) ) ) ).

% comp_surj
tff(fact_5696_comp__surj,axiom,
    ! [F: fun_nat_Code_integer,G: fun_Code_integer_nat] :
      ( ( image_1215581382706833972nteger(F,top_top_set_nat) = top_to4645266643341252675nteger )
     => ( ( image_951025933927791156er_nat(G,top_to4645266643341252675nteger) = top_top_set_nat )
       => ( aa_set_nat_set_nat(image_nat_nat(comp_C4049556595663050210at_nat(G,F)),top_top_set_nat) = top_top_set_nat ) ) ) ).

% comp_surj
tff(fact_5697_comp__surj,axiom,
    ! [F: fun_nat_Code_integer,G: fun_Co1365676809456677961t_unit] :
      ( ( image_1215581382706833972nteger(F,top_top_set_nat) = top_to4645266643341252675nteger )
     => ( ( image_7182656606676592809t_unit(G,top_to4645266643341252675nteger) = top_to1996260823553986621t_unit )
       => ( image_8730104196221521654t_unit(comp_C8086623346886033437it_nat(G,F),top_top_set_nat) = top_to1996260823553986621t_unit ) ) ) ).

% comp_surj
tff(fact_5698_comp__surj,axiom,
    ! [F: fun_nat_Code_integer,G: fun_Code_integer_int] :
      ( ( image_1215581382706833972nteger(F,top_top_set_nat) = top_to4645266643341252675nteger )
     => ( ( image_948535463418740880er_int(G,top_to4645266643341252675nteger) = top_top_set_int )
       => ( image_nat_int(comp_C5048910307564104766nt_nat(G,F),top_top_set_nat) = top_top_set_int ) ) ) ).

% comp_surj
tff(fact_5699_comp__surj,axiom,
    ! [F: fun_nat_nat,G: fun_nat_Code_integer] :
      ( ( aa_set_nat_set_nat(image_nat_nat(F),top_top_set_nat) = top_top_set_nat )
     => ( ( image_1215581382706833972nteger(G,top_top_set_nat) = top_to4645266643341252675nteger )
       => ( image_1215581382706833972nteger(comp_n3898172953802868194er_nat(G,F),top_top_set_nat) = top_to4645266643341252675nteger ) ) ) ).

% comp_surj
tff(fact_5700_comp__surj,axiom,
    ! [F: fun_nat_nat,G: fun_nat_nat] :
      ( ( aa_set_nat_set_nat(image_nat_nat(F),top_top_set_nat) = top_top_set_nat )
     => ( ( aa_set_nat_set_nat(image_nat_nat(G),top_top_set_nat) = top_top_set_nat )
       => ( aa_set_nat_set_nat(image_nat_nat(comp_nat_nat_nat(G,F)),top_top_set_nat) = top_top_set_nat ) ) ) ).

% comp_surj
tff(fact_5701_comp__surj,axiom,
    ! [F: fun_nat_nat,G: fun_nat_Product_unit] :
      ( ( aa_set_nat_set_nat(image_nat_nat(F),top_top_set_nat) = top_top_set_nat )
     => ( ( image_8730104196221521654t_unit(G,top_top_set_nat) = top_to1996260823553986621t_unit )
       => ( image_8730104196221521654t_unit(comp_n9025697279074352746it_nat(G,F),top_top_set_nat) = top_to1996260823553986621t_unit ) ) ) ).

% comp_surj
tff(fact_5702_comp__surj,axiom,
    ! [F: fun_nat_nat,G: fun_nat_int] :
      ( ( aa_set_nat_set_nat(image_nat_nat(F),top_top_set_nat) = top_top_set_nat )
     => ( ( image_nat_int(G,top_top_set_nat) = top_top_set_int )
       => ( image_nat_int(comp_nat_int_nat(G,F),top_top_set_nat) = top_top_set_int ) ) ) ).

% comp_surj
tff(fact_5703_comp__surj,axiom,
    ! [F: fun_nat_Product_unit,G: fun_Pr1820225556744648189nteger] :
      ( ( image_8730104196221521654t_unit(F,top_top_set_nat) = top_to1996260823553986621t_unit )
     => ( ( image_3815118110082124069nteger(G,top_to1996260823553986621t_unit) = top_to4645266643341252675nteger )
       => ( image_1215581382706833972nteger(comp_P756492639069434009er_nat(G,F),top_top_set_nat) = top_to4645266643341252675nteger ) ) ) ).

% comp_surj
tff(fact_5704_fun_Oset__map,axiom,
    ! [F: fun_Co8499238673658658103nteger,V: fun_num_Code_integer] : image_8379761247532268670nteger(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),V),top_top_set_num) = image_4470545334726330049nteger(F,image_8379761247532268670nteger(V,top_top_set_num)) ).

% fun.set_map
tff(fact_5705_fun_Oset__map,axiom,
    ! [F: fun_Co8499238673658658103nteger,V: fun_nat_Code_integer] : image_1215581382706833972nteger(comp_C6974050283906349679er_nat(F,V),top_top_set_nat) = image_4470545334726330049nteger(F,image_1215581382706833972nteger(V,top_top_set_nat)) ).

% fun.set_map
tff(fact_5706_fun_Oset__map,axiom,
    ! [F: fun_int_Code_integer,V: fun_nat_int] : image_1215581382706833972nteger(comp_i1588355021709917246er_nat(F,V),top_top_set_nat) = image_1587234942943678608nteger(F,image_nat_int(V,top_top_set_nat)) ).

% fun.set_map
tff(fact_5707_fun_Oset__map,axiom,
    ! [F: fun_nat_Code_integer,V: fun_nat_nat] : image_1215581382706833972nteger(comp_n3898172953802868194er_nat(F,V),top_top_set_nat) = image_1215581382706833972nteger(F,aa_set_nat_set_nat(image_nat_nat(V),top_top_set_nat)) ).

% fun.set_map
tff(fact_5708_fun_Oset__map,axiom,
    ! [F: fun_Code_integer_nat,V: fun_nat_Code_integer] : aa_set_nat_set_nat(image_nat_nat(comp_C4049556595663050210at_nat(F,V)),top_top_set_nat) = image_951025933927791156er_nat(F,image_1215581382706833972nteger(V,top_top_set_nat)) ).

% fun.set_map
tff(fact_5709_fun_Oset__map,axiom,
    ! [F: fun_int_nat,V: fun_nat_int] : aa_set_nat_set_nat(image_nat_nat(comp_int_nat_nat(F,V)),top_top_set_nat) = image_int_nat(F,image_nat_int(V,top_top_set_nat)) ).

% fun.set_map
tff(fact_5710_fun_Oset__map,axiom,
    ! [F: fun_nat_nat,V: fun_nat_nat] : aa_set_nat_set_nat(image_nat_nat(comp_nat_nat_nat(F,V)),top_top_set_nat) = aa_set_nat_set_nat(image_nat_nat(F),aa_set_nat_set_nat(image_nat_nat(V),top_top_set_nat)) ).

% fun.set_map
tff(fact_5711_fun_Oset__map,axiom,
    ! [F: fun_Code_integer_int,V: fun_nat_Code_integer] : image_nat_int(comp_C5048910307564104766nt_nat(F,V),top_top_set_nat) = image_948535463418740880er_int(F,image_1215581382706833972nteger(V,top_top_set_nat)) ).

% fun.set_map
tff(fact_5712_fun_Oset__map,axiom,
    ! [F: fun_nat_int,V: fun_nat_nat] : image_nat_int(comp_nat_int_nat(F,V),top_top_set_nat) = image_nat_int(F,aa_set_nat_set_nat(image_nat_nat(V),top_top_set_nat)) ).

% fun.set_map
tff(fact_5713_fun_Oset__map,axiom,
    ! [F: fun_int_int,V: fun_nat_int] : image_nat_int(comp_int_int_nat(F,V),top_top_set_nat) = aa_set_int_set_int(image_int_int(F),image_nat_int(V,top_top_set_nat)) ).

% fun.set_map
tff(fact_5714_fun_Omap__cong,axiom,
    ! [X2: fun_num_Code_integer,Ya: fun_num_Code_integer,F: fun_Co8499238673658658103nteger,G: fun_Co8499238673658658103nteger] :
      ( ( X2 = Ya )
     => ( ! [Z2: code_integer] :
            ( member_Code_integer(Z2,image_8379761247532268670nteger(Ya,top_top_set_num))
           => ( aa_Cod1783974652533396728nteger(F,Z2) = aa_Cod1783974652533396728nteger(G,Z2) ) )
       => ( aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),X2) = aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),Ya) ) ) ) ).

% fun.map_cong
tff(fact_5715_fun_Omap__cong,axiom,
    ! [X2: fun_Co8499238673658658103nteger,Ya: fun_Co8499238673658658103nteger,F: fun_Co1561183069634336733nteger,G: fun_Co1561183069634336733nteger] :
      ( ( X2 = Ya )
     => ( ! [Z2: code_integer] :
            ( member_Code_integer(Z2,image_4470545334726330049nteger(Ya,top_to4645266643341252675nteger))
           => ( aa_Cod1978467581589928094nteger(F,Z2) = aa_Cod1978467581589928094nteger(G,Z2) ) )
       => ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),X2) = aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,G),Ya) ) ) ) ).

% fun.map_cong
tff(fact_5716_fun_Omap__cong,axiom,
    ! [X2: fun_Co1981900195452921617nteger,Ya: fun_Co1981900195452921617nteger,F: fun_fu4800041728187187127nteger,G: fun_fu4800041728187187127nteger] :
      ( ( X2 = Ya )
     => ( ! [Z2: fun_Co8499238673658658103nteger] :
            ( member8321684580148902862nteger(Z2,image_2716445779319712667nteger(Ya,top_to4645266643341252675nteger))
           => ( aa_fun2509385170507305080nteger(F,Z2) = aa_fun2509385170507305080nteger(G,Z2) ) )
       => ( comp_f6739083541385432444nteger(F,X2) = comp_f6739083541385432444nteger(G,Ya) ) ) ) ).

% fun.map_cong
tff(fact_5717_fun_Omap__cong,axiom,
    ! [X2: fun_int_nat,Ya: fun_int_nat,F: fun_nat_num,G: fun_nat_num] :
      ( ( X2 = Ya )
     => ( ! [Z2: nat] :
            ( member_nat(Z2,image_int_nat(Ya,top_top_set_int))
           => ( aa_nat_num(F,Z2) = aa_nat_num(G,Z2) ) )
       => ( aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),X2) = aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,G),Ya) ) ) ) ).

% fun.map_cong
tff(fact_5718_fun_Omap__cong0,axiom,
    ! [X2: fun_num_Code_integer,F: fun_Co8499238673658658103nteger,G: fun_Co8499238673658658103nteger] :
      ( ! [Z2: code_integer] :
          ( member_Code_integer(Z2,image_8379761247532268670nteger(X2,top_top_set_num))
         => ( aa_Cod1783974652533396728nteger(F,Z2) = aa_Cod1783974652533396728nteger(G,Z2) ) )
     => ( aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),X2) = aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),X2) ) ) ).

% fun.map_cong0
tff(fact_5719_fun_Omap__cong0,axiom,
    ! [X2: fun_Co8499238673658658103nteger,F: fun_Co1561183069634336733nteger,G: fun_Co1561183069634336733nteger] :
      ( ! [Z2: code_integer] :
          ( member_Code_integer(Z2,image_4470545334726330049nteger(X2,top_to4645266643341252675nteger))
         => ( aa_Cod1978467581589928094nteger(F,Z2) = aa_Cod1978467581589928094nteger(G,Z2) ) )
     => ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),X2) = aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,G),X2) ) ) ).

% fun.map_cong0
tff(fact_5720_fun_Omap__cong0,axiom,
    ! [X2: fun_Co1981900195452921617nteger,F: fun_fu4800041728187187127nteger,G: fun_fu4800041728187187127nteger] :
      ( ! [Z2: fun_Co8499238673658658103nteger] :
          ( member8321684580148902862nteger(Z2,image_2716445779319712667nteger(X2,top_to4645266643341252675nteger))
         => ( aa_fun2509385170507305080nteger(F,Z2) = aa_fun2509385170507305080nteger(G,Z2) ) )
     => ( comp_f6739083541385432444nteger(F,X2) = comp_f6739083541385432444nteger(G,X2) ) ) ).

% fun.map_cong0
tff(fact_5721_fun_Omap__cong0,axiom,
    ! [X2: fun_int_nat,F: fun_nat_num,G: fun_nat_num] :
      ( ! [Z2: nat] :
          ( member_nat(Z2,image_int_nat(X2,top_top_set_int))
         => ( aa_nat_num(F,Z2) = aa_nat_num(G,Z2) ) )
     => ( aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),X2) = aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,G),X2) ) ) ).

% fun.map_cong0
tff(fact_5722_fun_Oinj__map__strong,axiom,
    ! [X2: fun_num_Code_integer,Xa: fun_num_Code_integer,F: fun_Co8499238673658658103nteger,Fa: fun_Co8499238673658658103nteger] :
      ( ! [Z2: code_integer,Za: code_integer] :
          ( member_Code_integer(Z2,image_8379761247532268670nteger(X2,top_top_set_num))
         => ( member_Code_integer(Za,image_8379761247532268670nteger(Xa,top_top_set_num))
           => ( ( aa_Cod1783974652533396728nteger(F,Z2) = aa_Cod1783974652533396728nteger(Fa,Za) )
             => ( Z2 = Za ) ) ) )
     => ( ( aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),X2) = aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,Fa),Xa) )
       => ( X2 = Xa ) ) ) ).

% fun.inj_map_strong
tff(fact_5723_fun_Oinj__map__strong,axiom,
    ! [X2: fun_Co8499238673658658103nteger,Xa: fun_Co8499238673658658103nteger,F: fun_Co1561183069634336733nteger,Fa: fun_Co1561183069634336733nteger] :
      ( ! [Z2: code_integer,Za: code_integer] :
          ( member_Code_integer(Z2,image_4470545334726330049nteger(X2,top_to4645266643341252675nteger))
         => ( member_Code_integer(Za,image_4470545334726330049nteger(Xa,top_to4645266643341252675nteger))
           => ( ( aa_Cod1978467581589928094nteger(F,Z2) = aa_Cod1978467581589928094nteger(Fa,Za) )
             => ( Z2 = Za ) ) ) )
     => ( ( aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),X2) = aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,Fa),Xa) )
       => ( X2 = Xa ) ) ) ).

% fun.inj_map_strong
tff(fact_5724_fun_Oinj__map__strong,axiom,
    ! [X2: fun_Co1981900195452921617nteger,Xa: fun_Co1981900195452921617nteger,F: fun_fu4800041728187187127nteger,Fa: fun_fu4800041728187187127nteger] :
      ( ! [Z2: fun_Co8499238673658658103nteger,Za: fun_Co8499238673658658103nteger] :
          ( member8321684580148902862nteger(Z2,image_2716445779319712667nteger(X2,top_to4645266643341252675nteger))
         => ( member8321684580148902862nteger(Za,image_2716445779319712667nteger(Xa,top_to4645266643341252675nteger))
           => ( ( aa_fun2509385170507305080nteger(F,Z2) = aa_fun2509385170507305080nteger(Fa,Za) )
             => ( Z2 = Za ) ) ) )
     => ( ( comp_f6739083541385432444nteger(F,X2) = comp_f6739083541385432444nteger(Fa,Xa) )
       => ( X2 = Xa ) ) ) ).

% fun.inj_map_strong
tff(fact_5725_fun_Oinj__map__strong,axiom,
    ! [X2: fun_int_nat,Xa: fun_int_nat,F: fun_nat_num,Fa: fun_nat_num] :
      ( ! [Z2: nat,Za: nat] :
          ( member_nat(Z2,image_int_nat(X2,top_top_set_int))
         => ( member_nat(Za,image_int_nat(Xa,top_top_set_int))
           => ( ( aa_nat_num(F,Z2) = aa_nat_num(Fa,Za) )
             => ( Z2 = Za ) ) ) )
     => ( ( aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),X2) = aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,Fa),Xa) )
       => ( X2 = Xa ) ) ) ).

% fun.inj_map_strong
tff(fact_5726_lessThan__Suc,axiom,
    ! [K: nat] : aa_nat_set_nat(set_ord_lessThan_nat,aa_nat_nat(suc,K)) = insert_nat(K,aa_nat_set_nat(set_ord_lessThan_nat,K)) ).

% lessThan_Suc
tff(fact_5727_not__UNIV__le__Icc,axiom,
    ! [L: int,Ha: int] : ~ ord_less_eq_set_int(top_top_set_int,aa_int_set_int(set_or1266510415728281911st_int(L),Ha)) ).

% not_UNIV_le_Icc
tff(fact_5728_not__UNIV__le__Icc,axiom,
    ! [L: nat,Ha: nat] : ~ aa_set_nat_o(ord_less_eq_set_nat(top_top_set_nat),aa_nat_set_nat(set_or1269000886237332187st_nat(L),Ha)) ).

% not_UNIV_le_Icc
tff(fact_5729_surj__id,axiom,
    aa_set_o_set_o(image_o_o(id_o),top_top_set_o) = top_top_set_o ).

% surj_id
tff(fact_5730_surj__id,axiom,
    aa_set8811106445076359420_nat_o(image_2153120922742433605_nat_o(id_fun_nat_o),top_to8708385046839970129_nat_o) = top_to8708385046839970129_nat_o ).

% surj_id
tff(fact_5731_surj__id,axiom,
    aa_set_num_set_num(image_num_num(id_num),top_top_set_num) = top_top_set_num ).

% surj_id
tff(fact_5732_surj__id,axiom,
    aa_set_nat_set_nat(image_nat_nat(id_nat),top_top_set_nat) = top_top_set_nat ).

% surj_id
tff(fact_5733_surj__id,axiom,
    image_405062704495631173t_unit(id_Product_unit,top_to1996260823553986621t_unit) = top_to1996260823553986621t_unit ).

% surj_id
tff(fact_5734_surj__id,axiom,
    aa_set_int_set_int(image_int_int(id_int),top_top_set_int) = top_top_set_int ).

% surj_id
tff(fact_5735_not__UNIV__le__Iic,axiom,
    ! [Ha: int] : ~ ord_less_eq_set_int(top_top_set_int,aa_int_set_int(set_ord_atMost_int,Ha)) ).

% not_UNIV_le_Iic
tff(fact_5736_not__UNIV__le__Iic,axiom,
    ! [Ha: nat] : ~ aa_set_nat_o(ord_less_eq_set_nat(top_top_set_nat),aa_nat_set_nat(set_ord_atMost_nat,Ha)) ).

% not_UNIV_le_Iic
tff(fact_5737_sum_Ofinite__Collect__op,axiom,
    ! [I4: set_o,X2: fun_o_Code_integer,Y: fun_o_Code_integer] :
      ( finite_finite_o(collect_o(aa_fun8192762245619933327un_o_o(aTP_Lamm_ox(I4),X2)))
     => ( finite_finite_o(collect_o(aa_fun8192762245619933327un_o_o(aTP_Lamm_ox(I4),Y)))
       => finite_finite_o(collect_o(aa_fun8192762245619933327un_o_o(aa_fun1865401534164435218un_o_o(aTP_Lamm_oy(I4),X2),Y))) ) ) ).

% sum.finite_Collect_op
tff(fact_5738_sum_Ofinite__Collect__op,axiom,
    ! [I4: set_nat,X2: fun_nat_Code_integer,Y: fun_nat_Code_integer] :
      ( finite_finite_nat(collect_nat(aa_fun3480067038916266681_nat_o(aTP_Lamm_oz(I4),X2)))
     => ( finite_finite_nat(collect_nat(aa_fun3480067038916266681_nat_o(aTP_Lamm_oz(I4),Y)))
       => finite_finite_nat(collect_nat(aa_fun3480067038916266681_nat_o(aa_fun2745573882733218024_nat_o(aTP_Lamm_pa(I4),X2),Y))) ) ) ).

% sum.finite_Collect_op
tff(fact_5739_sum_Ofinite__Collect__op,axiom,
    ! [I4: set_int,X2: fun_int_Code_integer,Y: fun_int_Code_integer] :
      ( finite_finite_int(collect_int(aa_fun3336537925265328129_int_o(aTP_Lamm_pb(I4),X2)))
     => ( finite_finite_int(collect_int(aa_fun3336537925265328129_int_o(aTP_Lamm_pb(I4),Y)))
       => finite_finite_int(collect_int(aa_fun3336537925265328129_int_o(aa_fun8818272713621706452_int_o(aTP_Lamm_pc(I4),X2),Y))) ) ) ).

% sum.finite_Collect_op
tff(fact_5740_sum_Ofinite__Collect__op,axiom,
    ! [I4: set_Code_integer,X2: fun_Co8499238673658658103nteger,Y: fun_Co8499238673658658103nteger] :
      ( finite6017078050557962740nteger(collect_Code_integer(aa_fun7159535342743012639eger_o(aTP_Lamm_pd(I4),X2)))
     => ( finite6017078050557962740nteger(collect_Code_integer(aa_fun7159535342743012639eger_o(aTP_Lamm_pd(I4),Y)))
       => finite6017078050557962740nteger(collect_Code_integer(aa_fun7159535342743012639eger_o(aa_fun5296778454019918337eger_o(aTP_Lamm_pe(I4),X2),Y))) ) ) ).

% sum.finite_Collect_op
tff(fact_5741_sum_Ofinite__Collect__op,axiom,
    ! [I4: set_o,X2: fun_o_rat,Y: fun_o_rat] :
      ( finite_finite_o(collect_o(aa_fun_o_rat_fun_o_o(aTP_Lamm_pf(I4),X2)))
     => ( finite_finite_o(collect_o(aa_fun_o_rat_fun_o_o(aTP_Lamm_pf(I4),Y)))
       => finite_finite_o(collect_o(aa_fun_o_rat_fun_o_o(aa_fun5510981055783399506un_o_o(aTP_Lamm_pg(I4),X2),Y))) ) ) ).

% sum.finite_Collect_op
tff(fact_5742_sum_Ofinite__Collect__op,axiom,
    ! [I4: set_nat,X2: fun_nat_rat,Y: fun_nat_rat] :
      ( finite_finite_nat(collect_nat(aa_fun1118977351124560894_nat_o(aTP_Lamm_ph(I4),X2)))
     => ( finite_finite_nat(collect_nat(aa_fun1118977351124560894_nat_o(aTP_Lamm_ph(I4),Y)))
       => finite_finite_nat(collect_nat(aa_fun1118977351124560894_nat_o(aa_fun8314661095172591474_nat_o(aTP_Lamm_pi(I4),X2),Y))) ) ) ).

% sum.finite_Collect_op
tff(fact_5743_sum_Ofinite__Collect__op,axiom,
    ! [I4: set_int,X2: fun_int_rat,Y: fun_int_rat] :
      ( finite_finite_int(collect_int(aa_fun7094158214180239686_int_o(aTP_Lamm_pj(I4),X2)))
     => ( finite_finite_int(collect_int(aa_fun7094158214180239686_int_o(aTP_Lamm_pj(I4),Y)))
       => finite_finite_int(collect_int(aa_fun7094158214180239686_int_o(aa_fun1445893531507182942_int_o(aTP_Lamm_pk(I4),X2),Y))) ) ) ).

% sum.finite_Collect_op
tff(fact_5744_sum_Ofinite__Collect__op,axiom,
    ! [I4: set_Code_integer,X2: fun_Code_integer_rat,Y: fun_Code_integer_rat] :
      ( finite6017078050557962740nteger(collect_Code_integer(aa_fun6395433285121891940eger_o(aTP_Lamm_pl(I4),X2)))
     => ( finite6017078050557962740nteger(collect_Code_integer(aa_fun6395433285121891940eger_o(aTP_Lamm_pl(I4),Y)))
       => finite6017078050557962740nteger(collect_Code_integer(aa_fun6395433285121891940eger_o(aa_fun4095556841599367307eger_o(aTP_Lamm_pm(I4),X2),Y))) ) ) ).

% sum.finite_Collect_op
tff(fact_5745_sum_Ofinite__Collect__op,axiom,
    ! [I4: set_o,X2: fun_o_nat,Y: fun_o_nat] :
      ( finite_finite_o(collect_o(aa_fun_o_nat_fun_o_o(aTP_Lamm_pn(I4),X2)))
     => ( finite_finite_o(collect_o(aa_fun_o_nat_fun_o_o(aTP_Lamm_pn(I4),Y)))
       => finite_finite_o(collect_o(aa_fun_o_nat_fun_o_o(aa_fun5833554292436378194un_o_o(aTP_Lamm_po(I4),X2),Y))) ) ) ).

% sum.finite_Collect_op
tff(fact_5746_sum_Ofinite__Collect__op,axiom,
    ! [I4: set_nat,X2: fun_nat_nat,Y: fun_nat_nat] :
      ( finite_finite_nat(collect_nat(aa_fun8673969331427483654_nat_o(aTP_Lamm_pp(I4),X2)))
     => ( finite_finite_nat(collect_nat(aa_fun8673969331427483654_nat_o(aTP_Lamm_pp(I4),Y)))
       => finite_finite_nat(collect_nat(aa_fun8673969331427483654_nat_o(aa_fun6348600740168882050_nat_o(aTP_Lamm_pq(I4),X2),Y))) ) ) ).

% sum.finite_Collect_op
tff(fact_5747_prod_Ofinite__Collect__op,axiom,
    ! [I4: set_o,X2: fun_o_Code_integer,Y: fun_o_Code_integer] :
      ( finite_finite_o(collect_o(aa_fun8192762245619933327un_o_o(aTP_Lamm_pr(I4),X2)))
     => ( finite_finite_o(collect_o(aa_fun8192762245619933327un_o_o(aTP_Lamm_pr(I4),Y)))
       => finite_finite_o(collect_o(aa_fun8192762245619933327un_o_o(aa_fun1865401534164435218un_o_o(aTP_Lamm_ps(I4),X2),Y))) ) ) ).

% prod.finite_Collect_op
tff(fact_5748_prod_Ofinite__Collect__op,axiom,
    ! [I4: set_nat,X2: fun_nat_Code_integer,Y: fun_nat_Code_integer] :
      ( finite_finite_nat(collect_nat(aa_fun3480067038916266681_nat_o(aTP_Lamm_pt(I4),X2)))
     => ( finite_finite_nat(collect_nat(aa_fun3480067038916266681_nat_o(aTP_Lamm_pt(I4),Y)))
       => finite_finite_nat(collect_nat(aa_fun3480067038916266681_nat_o(aa_fun2745573882733218024_nat_o(aTP_Lamm_pu(I4),X2),Y))) ) ) ).

% prod.finite_Collect_op
tff(fact_5749_prod_Ofinite__Collect__op,axiom,
    ! [I4: set_int,X2: fun_int_Code_integer,Y: fun_int_Code_integer] :
      ( finite_finite_int(collect_int(aa_fun3336537925265328129_int_o(aTP_Lamm_pv(I4),X2)))
     => ( finite_finite_int(collect_int(aa_fun3336537925265328129_int_o(aTP_Lamm_pv(I4),Y)))
       => finite_finite_int(collect_int(aa_fun3336537925265328129_int_o(aa_fun8818272713621706452_int_o(aTP_Lamm_pw(I4),X2),Y))) ) ) ).

% prod.finite_Collect_op
tff(fact_5750_prod_Ofinite__Collect__op,axiom,
    ! [I4: set_Code_integer,X2: fun_Co8499238673658658103nteger,Y: fun_Co8499238673658658103nteger] :
      ( finite6017078050557962740nteger(collect_Code_integer(aa_fun7159535342743012639eger_o(aTP_Lamm_px(I4),X2)))
     => ( finite6017078050557962740nteger(collect_Code_integer(aa_fun7159535342743012639eger_o(aTP_Lamm_px(I4),Y)))
       => finite6017078050557962740nteger(collect_Code_integer(aa_fun7159535342743012639eger_o(aa_fun5296778454019918337eger_o(aTP_Lamm_py(I4),X2),Y))) ) ) ).

% prod.finite_Collect_op
tff(fact_5751_prod_Ofinite__Collect__op,axiom,
    ! [I4: set_o,X2: fun_o_assn,Y: fun_o_assn] :
      ( finite_finite_o(collect_o(aa_fun8382565201914911066un_o_o(aTP_Lamm_pz(I4),X2)))
     => ( finite_finite_o(collect_o(aa_fun8382565201914911066un_o_o(aTP_Lamm_pz(I4),Y)))
       => finite_finite_o(collect_o(aa_fun8382565201914911066un_o_o(aa_fun5794833117214906962un_o_o(aTP_Lamm_qa(I4),X2),Y))) ) ) ).

% prod.finite_Collect_op
tff(fact_5752_prod_Ofinite__Collect__op,axiom,
    ! [I4: set_nat,X2: fun_nat_assn,Y: fun_nat_assn] :
      ( finite_finite_nat(collect_nat(aa_fun7183233715851567790_nat_o(aTP_Lamm_qb(I4),X2)))
     => ( finite_finite_nat(collect_nat(aa_fun7183233715851567790_nat_o(aTP_Lamm_qb(I4),Y)))
       => finite_finite_nat(collect_nat(aa_fun7183233715851567790_nat_o(aa_fun8595640264602358482_nat_o(aTP_Lamm_qc(I4),X2),Y))) ) ) ).

% prod.finite_Collect_op
tff(fact_5753_prod_Ofinite__Collect__op,axiom,
    ! [I4: set_int,X2: fun_int_assn,Y: fun_int_assn] :
      ( finite_finite_int(collect_int(aa_fun202081646129719286_int_o(aTP_Lamm_qd(I4),X2)))
     => ( finite_finite_int(collect_int(aa_fun202081646129719286_int_o(aTP_Lamm_qd(I4),Y)))
       => finite_finite_int(collect_int(aa_fun202081646129719286_int_o(aa_fun871127997271750846_int_o(aTP_Lamm_qe(I4),X2),Y))) ) ) ).

% prod.finite_Collect_op
tff(fact_5754_prod_Ofinite__Collect__op,axiom,
    ! [I4: set_Code_integer,X2: fun_Co4490034186337852034r_assn,Y: fun_Co4490034186337852034r_assn] :
      ( finite6017078050557962740nteger(collect_Code_integer(aa_fun6538703224075513620eger_o(aTP_Lamm_qf(I4),X2)))
     => ( finite6017078050557962740nteger(collect_Code_integer(aa_fun6538703224075513620eger_o(aTP_Lamm_qf(I4),Y)))
       => finite6017078050557962740nteger(collect_Code_integer(aa_fun6538703224075513620eger_o(aa_fun4422309413433313771eger_o(aTP_Lamm_qg(I4),X2),Y))) ) ) ).

% prod.finite_Collect_op
tff(fact_5755_prod_Ofinite__Collect__op,axiom,
    ! [I4: set_o,X2: fun_o_rat,Y: fun_o_rat] :
      ( finite_finite_o(collect_o(aa_fun_o_rat_fun_o_o(aTP_Lamm_qh(I4),X2)))
     => ( finite_finite_o(collect_o(aa_fun_o_rat_fun_o_o(aTP_Lamm_qh(I4),Y)))
       => finite_finite_o(collect_o(aa_fun_o_rat_fun_o_o(aa_fun5510981055783399506un_o_o(aTP_Lamm_qi(I4),X2),Y))) ) ) ).

% prod.finite_Collect_op
tff(fact_5756_prod_Ofinite__Collect__op,axiom,
    ! [I4: set_nat,X2: fun_nat_rat,Y: fun_nat_rat] :
      ( finite_finite_nat(collect_nat(aa_fun1118977351124560894_nat_o(aTP_Lamm_qj(I4),X2)))
     => ( finite_finite_nat(collect_nat(aa_fun1118977351124560894_nat_o(aTP_Lamm_qj(I4),Y)))
       => finite_finite_nat(collect_nat(aa_fun1118977351124560894_nat_o(aa_fun8314661095172591474_nat_o(aTP_Lamm_qk(I4),X2),Y))) ) ) ).

% prod.finite_Collect_op
tff(fact_5757_finite__atLeastZeroLessThan__int,axiom,
    ! [U: int] : finite_finite_int(aa_int_set_int(set_or4662586982721622107an_int(zero_zero_int),U)) ).

% finite_atLeastZeroLessThan_int
tff(fact_5758_card__eq__sum,axiom,
    ! [A2: set_int] : finite_card_int(A2) = groups4541462559716669496nt_nat(aTP_Lamm_ql,A2) ).

% card_eq_sum
tff(fact_5759_card__eq__sum,axiom,
    ! [A2: set_Product_unit] : finite410649719033368117t_unit(A2) = groups8766797177574957219it_nat(aTP_Lamm_qm,A2) ).

% card_eq_sum
tff(fact_5760_card__eq__sum,axiom,
    ! [A2: set_list_nat] : finite_card_list_nat(A2) = groups4396056296759096172at_nat(aTP_Lamm_qn,A2) ).

% card_eq_sum
tff(fact_5761_card__eq__sum,axiom,
    ! [A2: set_nat] : aa_set_nat_nat(finite_card_nat,A2) = aa_set_nat_nat(groups3542108847815614940at_nat(aTP_Lamm_kp),A2) ).

% card_eq_sum
tff(fact_5762_prod_Ointer__filter,axiom,
    ! [A2: set_o,G: fun_o_Code_integer,P: fun_o_o] :
      ( finite_finite_o(A2)
     => ( aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,G),collect_o(aa_fun_o_o_fun_o_o(aTP_Lamm_qo(A2),P))) = aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,aa_fun6542514109734600263nteger(aTP_Lamm_qp(G),P)),A2) ) ) ).

% prod.inter_filter
tff(fact_5763_prod_Ointer__filter,axiom,
    ! [A2: set_nat,G: fun_nat_Code_integer,P: fun_nat_o] :
      ( finite_finite_nat(A2)
     => ( groups3455450783089532116nteger(G,collect_nat(aa_fun5937193402907943164_nat_o(aTP_Lamm_qq(A2),P))) = groups3455450783089532116nteger(aa_fun3969837373441324047nteger(aTP_Lamm_qr(G),P),A2) ) ) ).

% prod.inter_filter
tff(fact_5764_prod_Ointer__filter,axiom,
    ! [A2: set_int,G: fun_int_Code_integer,P: fun_int_o] :
      ( finite_finite_int(A2)
     => ( aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,G),collect_int(aa_fun6243517787477317628_int_o(aTP_Lamm_qs(A2),P))) = aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,aa_fun6019004165459918095nteger(aTP_Lamm_qt(G),P)),A2) ) ) ).

% prod.inter_filter
tff(fact_5765_prod_Ointer__filter,axiom,
    ! [A2: set_Code_integer,G: fun_Co8499238673658658103nteger,P: fun_Code_integer_o] :
      ( finite6017078050557962740nteger(A2)
     => ( aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,G),collect_Code_integer(aa_fun8214818745163655228eger_o(aTP_Lamm_qu(A2),P))) = aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,aa_fun791458909507501263nteger(aTP_Lamm_qv(G),P)),A2) ) ) ).

% prod.inter_filter
tff(fact_5766_prod_Ointer__filter,axiom,
    ! [A2: set_o,G: fun_o_assn,P: fun_o_o] :
      ( finite_finite_o(A2)
     => ( aa_set_o_assn(aa_fun1914167119812169564o_assn(groups5301882518646026715o_assn,G),collect_o(aa_fun_o_o_fun_o_o(aTP_Lamm_qo(A2),P))) = aa_set_o_assn(aa_fun1914167119812169564o_assn(groups5301882518646026715o_assn,aa_fun8560762093604944786o_assn(aTP_Lamm_qw(G),P)),A2) ) ) ).

% prod.inter_filter
tff(fact_5767_prod_Ointer__filter,axiom,
    ! [A2: set_nat,G: fun_nat_assn,P: fun_nat_o] :
      ( finite_finite_nat(A2)
     => ( groups6906906614972039071t_assn(G,collect_nat(aa_fun5937193402907943164_nat_o(aTP_Lamm_qq(A2),P))) = groups6906906614972039071t_assn(aa_fun3990007403578212698t_assn(aTP_Lamm_qx(G),P),A2) ) ) ).

% prod.inter_filter
tff(fact_5768_prod_Ointer__filter,axiom,
    ! [A2: set_int,G: fun_int_assn,P: fun_int_o] :
      ( finite_finite_int(A2)
     => ( aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,G),collect_int(aa_fun6243517787477317628_int_o(aTP_Lamm_qs(A2),P))) = aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,aa_fun9028805181350005338t_assn(aTP_Lamm_qy(G),P)),A2) ) ) ).

% prod.inter_filter
tff(fact_5769_prod_Ointer__filter,axiom,
    ! [A2: set_Code_integer,G: fun_Co4490034186337852034r_assn,P: fun_Code_integer_o] :
      ( finite6017078050557962740nteger(A2)
     => ( aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,G),collect_Code_integer(aa_fun8214818745163655228eger_o(aTP_Lamm_qu(A2),P))) = aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,aa_fun6392223008197429786r_assn(aTP_Lamm_qz(G),P)),A2) ) ) ).

% prod.inter_filter
tff(fact_5770_prod_Ointer__filter,axiom,
    ! [A2: set_o,G: fun_o_rat,P: fun_o_o] :
      ( finite_finite_o(A2)
     => ( aa_set_o_rat(aa_fun7302669049306738524_o_rat(groups2869687844427037835_o_rat,G),collect_o(aa_fun_o_o_fun_o_o(aTP_Lamm_qo(A2),P))) = aa_set_o_rat(aa_fun7302669049306738524_o_rat(groups2869687844427037835_o_rat,aa_fun_o_o_fun_o_rat(aTP_Lamm_ra(G),P)),A2) ) ) ).

% prod.inter_filter
tff(fact_5771_prod_Ointer__filter,axiom,
    ! [A2: set_nat,G: fun_nat_rat,P: fun_nat_o] :
      ( finite_finite_nat(A2)
     => ( groups73079841787564623at_rat(G,collect_nat(aa_fun5937193402907943164_nat_o(aTP_Lamm_qq(A2),P))) = groups73079841787564623at_rat(aa_fun696632391729880074at_rat(aTP_Lamm_rb(G),P),A2) ) ) ).

% prod.inter_filter
tff(fact_5772_prod__gen__delta,axiom,
    ! [S2: set_o,A: $o,B: fun_o_assn,C: assn] :
      ( finite_finite_o(S2)
     => ( aa_set_o_assn(aa_fun1914167119812169564o_assn(groups5301882518646026715o_assn,aa_assn_fun_o_assn(aa_fun7777267157241973165o_assn(aTP_Lamm_rc((A)),B),C)),S2) = $ite(member_o((A),S2),aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_o_assn(B,(A))),aa_nat_assn(aa_assn_fun_nat_assn(power_power_assn,C),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite_card_o(S2)),one_one_nat))),aa_nat_assn(aa_assn_fun_nat_assn(power_power_assn,C),finite_card_o(S2))) ) ) ).

% prod_gen_delta
tff(fact_5773_prod__gen__delta,axiom,
    ! [S2: set_Product_unit,A: product_unit,B: fun_Pr6626665806141890376t_assn,C: assn] :
      ( finite4290736615968046902t_unit(S2)
     => ( groups5360233303959380816t_assn(aa_ass3177796706412234594t_assn(aa_fun5779862164363648365t_assn(aTP_Lamm_rd(A),B),C),S2) = $ite(member_Product_unit(A,S2),aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_Product_unit_assn(B,A)),aa_nat_assn(aa_assn_fun_nat_assn(power_power_assn,C),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite410649719033368117t_unit(S2)),one_one_nat))),aa_nat_assn(aa_assn_fun_nat_assn(power_power_assn,C),finite410649719033368117t_unit(S2))) ) ) ).

% prod_gen_delta
tff(fact_5774_prod__gen__delta,axiom,
    ! [S2: set_nat,A: nat,B: fun_nat_assn,C: assn] :
      ( finite_finite_nat(S2)
     => ( groups6906906614972039071t_assn(aa_assn_fun_nat_assn(aa_fun2404858873066863565t_assn(aTP_Lamm_re(A),B),C),S2) = $ite(member_nat(A,S2),aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_nat_assn(B,A)),aa_nat_assn(aa_assn_fun_nat_assn(power_power_assn,C),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_set_nat_nat(finite_card_nat,S2)),one_one_nat))),aa_nat_assn(aa_assn_fun_nat_assn(power_power_assn,C),aa_set_nat_nat(finite_card_nat,S2))) ) ) ).

% prod_gen_delta
tff(fact_5775_prod__gen__delta,axiom,
    ! [S2: set_int,A: int,B: fun_int_assn,C: assn] :
      ( finite_finite_int(S2)
     => ( aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,aa_assn_fun_int_assn(aa_fun3470678483766860421t_assn(aTP_Lamm_rf(A),B),C)),S2) = $ite(member_int(A,S2),aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_int_assn(B,A)),aa_nat_assn(aa_assn_fun_nat_assn(power_power_assn,C),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite_card_int(S2)),one_one_nat))),aa_nat_assn(aa_assn_fun_nat_assn(power_power_assn,C),finite_card_int(S2))) ) ) ).

% prod_gen_delta
tff(fact_5776_prod__gen__delta,axiom,
    ! [S2: set_Code_integer,A: code_integer,B: fun_Co4490034186337852034r_assn,C: assn] :
      ( finite6017078050557962740nteger(S2)
     => ( aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,aa_ass6027779773078136296r_assn(aa_fun5785710901775686247r_assn(aTP_Lamm_rg(A),B),C)),S2) = $ite(member_Code_integer(A,S2),aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_Code_integer_assn(B,A)),aa_nat_assn(aa_assn_fun_nat_assn(power_power_assn,C),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite4902975817058060853nteger(S2)),one_one_nat))),aa_nat_assn(aa_assn_fun_nat_assn(power_power_assn,C),finite4902975817058060853nteger(S2))) ) ) ).

% prod_gen_delta
tff(fact_5777_prod__gen__delta,axiom,
    ! [S2: set_o,A: $o,B: fun_o_rat,C: rat] :
      ( finite_finite_o(S2)
     => ( aa_set_o_rat(aa_fun7302669049306738524_o_rat(groups2869687844427037835_o_rat,aa_rat_fun_o_rat(aa_fun5241534567979455741_o_rat(aTP_Lamm_rh((A)),B),C)),S2) = $ite(member_o((A),S2),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_o_rat(B,(A))),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,C),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite_card_o(S2)),one_one_nat))),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,C),finite_card_o(S2))) ) ) ).

% prod_gen_delta
tff(fact_5778_prod__gen__delta,axiom,
    ! [S2: set_Product_unit,A: product_unit,B: fun_Product_unit_rat,C: rat] :
      ( finite4290736615968046902t_unit(S2)
     => ( groups8984663225794451456it_rat(aa_rat6507435564262174562it_rat(aa_fun5217320890768598205it_rat(aTP_Lamm_ri(A),B),C),S2) = $ite(member_Product_unit(A,S2),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_Product_unit_rat(B,A)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,C),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite410649719033368117t_unit(S2)),one_one_nat))),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,C),finite410649719033368117t_unit(S2))) ) ) ).

% prod_gen_delta
tff(fact_5779_prod__gen__delta,axiom,
    ! [S2: set_nat,A: nat,B: fun_nat_rat,C: rat] :
      ( finite_finite_nat(S2)
     => ( groups73079841787564623at_rat(aa_rat_fun_nat_rat(aa_fun5559679822142647773at_rat(aTP_Lamm_rj(A),B),C),S2) = $ite(member_nat(A,S2),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(B,A)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,C),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_set_nat_nat(finite_card_nat,S2)),one_one_nat))),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,C),aa_set_nat_nat(finite_card_nat,S2))) ) ) ).

% prod_gen_delta
tff(fact_5780_prod__gen__delta,axiom,
    ! [S2: set_int,A: int,B: fun_int_rat,C: rat] :
      ( finite_finite_int(S2)
     => ( aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,aa_rat_fun_int_rat(aa_fun9155288305517341845nt_rat(aTP_Lamm_rk(A),B),C)),S2) = $ite(member_int(A,S2),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_int_rat(B,A)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,C),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite_card_int(S2)),one_one_nat))),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,C),finite_card_int(S2))) ) ) ).

% prod_gen_delta
tff(fact_5781_prod__gen__delta,axiom,
    ! [S2: set_Code_integer,A: code_integer,B: fun_Code_integer_rat,C: rat] :
      ( finite6017078050557962740nteger(S2)
     => ( aa_set3519029356358064041er_rat(aa_fun5443269377828775384er_rat(groups2555765274223993564er_rat,aa_rat6553461586499541832er_rat(aa_fun8320714231555830903er_rat(aTP_Lamm_rl(A),B),C)),S2) = $ite(member_Code_integer(A,S2),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_Code_integer_rat(B,A)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,C),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite4902975817058060853nteger(S2)),one_one_nat))),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,C),finite4902975817058060853nteger(S2))) ) ) ).

% prod_gen_delta
tff(fact_5782_finite__atLeastZeroLessThan__integer,axiom,
    ! [U: code_integer] : finite6017078050557962740nteger(aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(zero_z3403309356797280102nteger),U)) ).

% finite_atLeastZeroLessThan_integer
tff(fact_5783_card__2__iff_H,axiom,
    ! [S2: set_int] :
      ( ( finite_card_int(S2) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)) )
    <=> ? [X4: int] :
          ( member_int(X4,S2)
          & ? [Xa2: int] :
              ( member_int(Xa2,S2)
              & ( X4 != Xa2 )
              & ! [Xb4: int] :
                  ( member_int(Xb4,S2)
                 => ( ( Xb4 = X4 )
                    | ( Xb4 = Xa2 ) ) ) ) ) ) ).

% card_2_iff'
tff(fact_5784_card__2__iff_H,axiom,
    ! [S2: set_Product_unit] :
      ( ( finite410649719033368117t_unit(S2) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)) )
    <=> ? [X4: product_unit] :
          ( member_Product_unit(X4,S2)
          & ? [Xa2: product_unit] :
              ( member_Product_unit(Xa2,S2)
              & ( X4 != Xa2 )
              & ! [Xb4: product_unit] :
                  ( member_Product_unit(Xb4,S2)
                 => ( ( Xb4 = X4 )
                    | ( Xb4 = Xa2 ) ) ) ) ) ) ).

% card_2_iff'
tff(fact_5785_card__2__iff_H,axiom,
    ! [S2: set_nat] :
      ( ( aa_set_nat_nat(finite_card_nat,S2) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)) )
    <=> ? [X4: nat] :
          ( member_nat(X4,S2)
          & ? [Xa2: nat] :
              ( member_nat(Xa2,S2)
              & ( X4 != Xa2 )
              & ! [Xb4: nat] :
                  ( member_nat(Xb4,S2)
                 => ( ( Xb4 = X4 )
                    | ( Xb4 = Xa2 ) ) ) ) ) ) ).

% card_2_iff'
tff(fact_5786_card__2__iff_H,axiom,
    ! [S2: set_list_nat] :
      ( ( finite_card_list_nat(S2) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)) )
    <=> ? [X4: list_nat] :
          ( member_list_nat(X4,S2)
          & ? [Xa2: list_nat] :
              ( member_list_nat(Xa2,S2)
              & ( X4 != Xa2 )
              & ! [Xb4: list_nat] :
                  ( member_list_nat(Xb4,S2)
                 => ( ( Xb4 = X4 )
                    | ( Xb4 = Xa2 ) ) ) ) ) ) ).

% card_2_iff'
tff(fact_5787_sum_Orelated,axiom,
    ! [R3: fun_Co2081214437782444048eger_o,S2: set_nat,Ha: fun_nat_Code_integer,G: fun_nat_Code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,zero_z3403309356797280102nteger),zero_z3403309356797280102nteger)
     => ( ! [X12: code_integer,Y12: code_integer,X23: code_integer,Y22: code_integer] :
            ( ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,X12),X23)
              & aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,Y12),Y22) )
           => aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X12),Y12)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X23),Y22)) )
       => ( finite_finite_nat(S2)
         => ( ! [X3: nat] :
                ( member_nat(X3,S2)
               => aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,aa_nat_Code_integer(Ha,X3)),aa_nat_Code_integer(G,X3)) )
           => aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,groups7501900531339628137nteger(Ha,S2)),groups7501900531339628137nteger(G,S2)) ) ) ) ) ).

% sum.related
tff(fact_5788_sum_Orelated,axiom,
    ! [R3: fun_Co2081214437782444048eger_o,S2: set_int,Ha: fun_int_Code_integer,G: fun_int_Code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,zero_z3403309356797280102nteger),zero_z3403309356797280102nteger)
     => ( ! [X12: code_integer,Y12: code_integer,X23: code_integer,Y22: code_integer] :
            ( ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,X12),X23)
              & aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,Y12),Y22) )
           => aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X12),Y12)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X23),Y22)) )
       => ( finite_finite_int(S2)
         => ( ! [X3: int] :
                ( member_int(X3,S2)
               => aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,aa_int_Code_integer(Ha,X3)),aa_int_Code_integer(G,X3)) )
           => aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,groups7873554091576472773nteger(Ha,S2)),groups7873554091576472773nteger(G,S2)) ) ) ) ) ).

% sum.related
tff(fact_5789_sum_Orelated,axiom,
    ! [R3: fun_Co2081214437782444048eger_o,S2: set_Code_integer,Ha: fun_Co8499238673658658103nteger,G: fun_Co8499238673658658103nteger] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,zero_z3403309356797280102nteger),zero_z3403309356797280102nteger)
     => ( ! [X12: code_integer,Y12: code_integer,X23: code_integer,Y22: code_integer] :
            ( ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,X12),X23)
              & aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,Y12),Y22) )
           => aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X12),Y12)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,X23),Y22)) )
       => ( finite6017078050557962740nteger(S2)
         => ( ! [X3: code_integer] :
                ( member_Code_integer(X3,S2)
               => aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,aa_Cod1783974652533396728nteger(Ha,X3)),aa_Cod1783974652533396728nteger(G,X3)) )
           => aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,aa_set8546232603906849326nteger(groups879477027807139574nteger(Ha),S2)),aa_set8546232603906849326nteger(groups879477027807139574nteger(G),S2)) ) ) ) ) ).

% sum.related
tff(fact_5790_sum_Orelated,axiom,
    ! [R3: fun_rat_fun_rat_o,S2: set_nat,Ha: fun_nat_rat,G: fun_nat_rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(R3,zero_zero_rat),zero_zero_rat)
     => ( ! [X12: rat,Y12: rat,X23: rat,Y22: rat] :
            ( ( aa_rat_o(aa_rat_fun_rat_o(R3,X12),X23)
              & aa_rat_o(aa_rat_fun_rat_o(R3,Y12),Y22) )
           => aa_rat_o(aa_rat_fun_rat_o(R3,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X12),Y12)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X23),Y22)) )
       => ( finite_finite_nat(S2)
         => ( ! [X3: nat] :
                ( member_nat(X3,S2)
               => aa_rat_o(aa_rat_fun_rat_o(R3,aa_nat_rat(Ha,X3)),aa_nat_rat(G,X3)) )
           => aa_rat_o(aa_rat_fun_rat_o(R3,groups2906978787729119204at_rat(Ha,S2)),groups2906978787729119204at_rat(G,S2)) ) ) ) ) ).

% sum.related
tff(fact_5791_sum_Orelated,axiom,
    ! [R3: fun_rat_fun_rat_o,S2: set_int,Ha: fun_int_rat,G: fun_int_rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(R3,zero_zero_rat),zero_zero_rat)
     => ( ! [X12: rat,Y12: rat,X23: rat,Y22: rat] :
            ( ( aa_rat_o(aa_rat_fun_rat_o(R3,X12),X23)
              & aa_rat_o(aa_rat_fun_rat_o(R3,Y12),Y22) )
           => aa_rat_o(aa_rat_fun_rat_o(R3,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X12),Y12)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X23),Y22)) )
       => ( finite_finite_int(S2)
         => ( ! [X3: int] :
                ( member_int(X3,S2)
               => aa_rat_o(aa_rat_fun_rat_o(R3,aa_int_rat(Ha,X3)),aa_int_rat(G,X3)) )
           => aa_rat_o(aa_rat_fun_rat_o(R3,groups3906332499630173760nt_rat(Ha,S2)),groups3906332499630173760nt_rat(G,S2)) ) ) ) ) ).

% sum.related
tff(fact_5792_sum_Orelated,axiom,
    ! [R3: fun_rat_fun_rat_o,S2: set_Code_integer,Ha: fun_Code_integer_rat,G: fun_Code_integer_rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(R3,zero_zero_rat),zero_zero_rat)
     => ( ! [X12: rat,Y12: rat,X23: rat,Y22: rat] :
            ( ( aa_rat_o(aa_rat_fun_rat_o(R3,X12),X23)
              & aa_rat_o(aa_rat_fun_rat_o(R3,Y12),Y22) )
           => aa_rat_o(aa_rat_fun_rat_o(R3,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X12),Y12)),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X23),Y22)) )
       => ( finite6017078050557962740nteger(S2)
         => ( ! [X3: code_integer] :
                ( member_Code_integer(X3,S2)
               => aa_rat_o(aa_rat_fun_rat_o(R3,aa_Code_integer_rat(Ha,X3)),aa_Code_integer_rat(G,X3)) )
           => aa_rat_o(aa_rat_fun_rat_o(R3,groups6602215022474089585er_rat(Ha,S2)),groups6602215022474089585er_rat(G,S2)) ) ) ) ) ).

% sum.related
tff(fact_5793_sum_Orelated,axiom,
    ! [R3: fun_nat_fun_nat_o,S2: set_int,Ha: fun_int_nat,G: fun_int_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(R3,zero_zero_nat),zero_zero_nat)
     => ( ! [X12: nat,Y12: nat,X23: nat,Y22: nat] :
            ( ( aa_nat_o(aa_nat_fun_nat_o(R3,X12),X23)
              & aa_nat_o(aa_nat_fun_nat_o(R3,Y12),Y22) )
           => aa_nat_o(aa_nat_fun_nat_o(R3,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X12),Y12)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X23),Y22)) )
       => ( finite_finite_int(S2)
         => ( ! [X3: int] :
                ( member_int(X3,S2)
               => aa_nat_o(aa_nat_fun_nat_o(R3,aa_int_nat(Ha,X3)),aa_int_nat(G,X3)) )
           => aa_nat_o(aa_nat_fun_nat_o(R3,groups4541462559716669496nt_nat(Ha,S2)),groups4541462559716669496nt_nat(G,S2)) ) ) ) ) ).

% sum.related
tff(fact_5794_sum_Orelated,axiom,
    ! [R3: fun_nat_fun_nat_o,S2: set_Code_integer,Ha: fun_Code_integer_nat,G: fun_Code_integer_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(R3,zero_zero_nat),zero_zero_nat)
     => ( ! [X12: nat,Y12: nat,X23: nat,Y22: nat] :
            ( ( aa_nat_o(aa_nat_fun_nat_o(R3,X12),X23)
              & aa_nat_o(aa_nat_fun_nat_o(R3,Y12),Y22) )
           => aa_nat_o(aa_nat_fun_nat_o(R3,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X12),Y12)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X23),Y22)) )
       => ( finite6017078050557962740nteger(S2)
         => ( ! [X3: code_integer] :
                ( member_Code_integer(X3,S2)
               => aa_nat_o(aa_nat_fun_nat_o(R3,aa_Code_integer_nat(Ha,X3)),aa_Code_integer_nat(G,X3)) )
           => aa_nat_o(aa_nat_fun_nat_o(R3,groups7237345082560585321er_nat(Ha,S2)),groups7237345082560585321er_nat(G,S2)) ) ) ) ) ).

% sum.related
tff(fact_5795_sum_Orelated,axiom,
    ! [R3: fun_int_fun_int_o,S2: set_nat,Ha: fun_nat_int,G: fun_nat_int] :
      ( aa_int_o(aa_int_fun_int_o(R3,zero_zero_int),zero_zero_int)
     => ( ! [X12: int,Y12: int,X23: int,Y22: int] :
            ( ( aa_int_o(aa_int_fun_int_o(R3,X12),X23)
              & aa_int_o(aa_int_fun_int_o(R3,Y12),Y22) )
           => aa_int_o(aa_int_fun_int_o(R3,aa_int_int(aa_int_fun_int_int(plus_plus_int,X12),Y12)),aa_int_int(aa_int_fun_int_int(plus_plus_int,X23),Y22)) )
       => ( finite_finite_nat(S2)
         => ( ! [X3: nat] :
                ( member_nat(X3,S2)
               => aa_int_o(aa_int_fun_int_o(R3,aa_nat_int(Ha,X3)),aa_nat_int(G,X3)) )
           => aa_int_o(aa_int_fun_int_o(R3,groups3539618377306564664at_int(Ha,S2)),groups3539618377306564664at_int(G,S2)) ) ) ) ) ).

% sum.related
tff(fact_5796_sum_Orelated,axiom,
    ! [R3: fun_int_fun_int_o,S2: set_Code_integer,Ha: fun_Code_integer_int,G: fun_Code_integer_int] :
      ( aa_int_o(aa_int_fun_int_o(R3,zero_zero_int),zero_zero_int)
     => ( ! [X12: int,Y12: int,X23: int,Y22: int] :
            ( ( aa_int_o(aa_int_fun_int_o(R3,X12),X23)
              & aa_int_o(aa_int_fun_int_o(R3,Y12),Y22) )
           => aa_int_o(aa_int_fun_int_o(R3,aa_int_int(aa_int_fun_int_int(plus_plus_int,X12),Y12)),aa_int_int(aa_int_fun_int_int(plus_plus_int,X23),Y22)) )
       => ( finite6017078050557962740nteger(S2)
         => ( ! [X3: code_integer] :
                ( member_Code_integer(X3,S2)
               => aa_int_o(aa_int_fun_int_o(R3,aa_Code_integer_int(Ha,X3)),aa_Code_integer_int(G,X3)) )
           => aa_int_o(aa_int_fun_int_o(R3,groups7234854612051535045er_int(Ha,S2)),groups7234854612051535045er_int(G,S2)) ) ) ) ) ).

% sum.related
tff(fact_5797_prod_Orelated,axiom,
    ! [R3: fun_Co2081214437782444048eger_o,S2: set_nat,Ha: fun_nat_Code_integer,G: fun_nat_Code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,one_one_Code_integer),one_one_Code_integer)
     => ( ! [X12: code_integer,Y12: code_integer,X23: code_integer,Y22: code_integer] :
            ( ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,X12),X23)
              & aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,Y12),Y22) )
           => aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,X12),Y12)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,X23),Y22)) )
       => ( finite_finite_nat(S2)
         => ( ! [X3: nat] :
                ( member_nat(X3,S2)
               => aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,aa_nat_Code_integer(Ha,X3)),aa_nat_Code_integer(G,X3)) )
           => aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,groups3455450783089532116nteger(Ha,S2)),groups3455450783089532116nteger(G,S2)) ) ) ) ) ).

% prod.related
tff(fact_5798_prod_Orelated,axiom,
    ! [R3: fun_Co2081214437782444048eger_o,S2: set_int,Ha: fun_int_Code_integer,G: fun_int_Code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,one_one_Code_integer),one_one_Code_integer)
     => ( ! [X12: code_integer,Y12: code_integer,X23: code_integer,Y22: code_integer] :
            ( ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,X12),X23)
              & aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,Y12),Y22) )
           => aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,X12),Y12)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,X23),Y22)) )
       => ( finite_finite_int(S2)
         => ( ! [X3: int] :
                ( member_int(X3,S2)
               => aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,aa_int_Code_integer(Ha,X3)),aa_int_Code_integer(G,X3)) )
           => aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,Ha),S2)),aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,G),S2)) ) ) ) ) ).

% prod.related
tff(fact_5799_prod_Orelated,axiom,
    ! [R3: fun_Co2081214437782444048eger_o,S2: set_Code_integer,Ha: fun_Co8499238673658658103nteger,G: fun_Co8499238673658658103nteger] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,one_one_Code_integer),one_one_Code_integer)
     => ( ! [X12: code_integer,Y12: code_integer,X23: code_integer,Y22: code_integer] :
            ( ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,X12),X23)
              & aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,Y12),Y22) )
           => aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,X12),Y12)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,X23),Y22)) )
       => ( finite6017078050557962740nteger(S2)
         => ( ! [X3: code_integer] :
                ( member_Code_integer(X3,S2)
               => aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,aa_Cod1783974652533396728nteger(Ha,X3)),aa_Cod1783974652533396728nteger(G,X3)) )
           => aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,Ha),S2)),aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,G),S2)) ) ) ) ) ).

% prod.related
tff(fact_5800_prod_Orelated,axiom,
    ! [R3: fun_assn_fun_assn_o,S2: set_nat,Ha: fun_nat_assn,G: fun_nat_assn] :
      ( aa_assn_o(aa_assn_fun_assn_o(R3,one_one_assn),one_one_assn)
     => ( ! [X12: assn,Y12: assn,X23: assn,Y22: assn] :
            ( ( aa_assn_o(aa_assn_fun_assn_o(R3,X12),X23)
              & aa_assn_o(aa_assn_fun_assn_o(R3,Y12),Y22) )
           => aa_assn_o(aa_assn_fun_assn_o(R3,aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,X12),Y12)),aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,X23),Y22)) )
       => ( finite_finite_nat(S2)
         => ( ! [X3: nat] :
                ( member_nat(X3,S2)
               => aa_assn_o(aa_assn_fun_assn_o(R3,aa_nat_assn(Ha,X3)),aa_nat_assn(G,X3)) )
           => aa_assn_o(aa_assn_fun_assn_o(R3,groups6906906614972039071t_assn(Ha,S2)),groups6906906614972039071t_assn(G,S2)) ) ) ) ) ).

% prod.related
tff(fact_5801_prod_Orelated,axiom,
    ! [R3: fun_assn_fun_assn_o,S2: set_int,Ha: fun_int_assn,G: fun_int_assn] :
      ( aa_assn_o(aa_assn_fun_assn_o(R3,one_one_assn),one_one_assn)
     => ( ! [X12: assn,Y12: assn,X23: assn,Y22: assn] :
            ( ( aa_assn_o(aa_assn_fun_assn_o(R3,X12),X23)
              & aa_assn_o(aa_assn_fun_assn_o(R3,Y12),Y22) )
           => aa_assn_o(aa_assn_fun_assn_o(R3,aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,X12),Y12)),aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,X23),Y22)) )
       => ( finite_finite_int(S2)
         => ( ! [X3: int] :
                ( member_int(X3,S2)
               => aa_assn_o(aa_assn_fun_assn_o(R3,aa_int_assn(Ha,X3)),aa_int_assn(G,X3)) )
           => aa_assn_o(aa_assn_fun_assn_o(R3,aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,Ha),S2)),aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,G),S2)) ) ) ) ) ).

% prod.related
tff(fact_5802_prod_Orelated,axiom,
    ! [R3: fun_assn_fun_assn_o,S2: set_Code_integer,Ha: fun_Co4490034186337852034r_assn,G: fun_Co4490034186337852034r_assn] :
      ( aa_assn_o(aa_assn_fun_assn_o(R3,one_one_assn),one_one_assn)
     => ( ! [X12: assn,Y12: assn,X23: assn,Y22: assn] :
            ( ( aa_assn_o(aa_assn_fun_assn_o(R3,X12),X23)
              & aa_assn_o(aa_assn_fun_assn_o(R3,Y12),Y22) )
           => aa_assn_o(aa_assn_fun_assn_o(R3,aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,X12),Y12)),aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,X23),Y22)) )
       => ( finite6017078050557962740nteger(S2)
         => ( ! [X3: code_integer] :
                ( member_Code_integer(X3,S2)
               => aa_assn_o(aa_assn_fun_assn_o(R3,aa_Code_integer_assn(Ha,X3)),aa_Code_integer_assn(G,X3)) )
           => aa_assn_o(aa_assn_fun_assn_o(R3,aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,Ha),S2)),aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,G),S2)) ) ) ) ) ).

% prod.related
tff(fact_5803_prod_Orelated,axiom,
    ! [R3: fun_rat_fun_rat_o,S2: set_nat,Ha: fun_nat_rat,G: fun_nat_rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(R3,one_one_rat),one_one_rat)
     => ( ! [X12: rat,Y12: rat,X23: rat,Y22: rat] :
            ( ( aa_rat_o(aa_rat_fun_rat_o(R3,X12),X23)
              & aa_rat_o(aa_rat_fun_rat_o(R3,Y12),Y22) )
           => aa_rat_o(aa_rat_fun_rat_o(R3,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,X12),Y12)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,X23),Y22)) )
       => ( finite_finite_nat(S2)
         => ( ! [X3: nat] :
                ( member_nat(X3,S2)
               => aa_rat_o(aa_rat_fun_rat_o(R3,aa_nat_rat(Ha,X3)),aa_nat_rat(G,X3)) )
           => aa_rat_o(aa_rat_fun_rat_o(R3,groups73079841787564623at_rat(Ha,S2)),groups73079841787564623at_rat(G,S2)) ) ) ) ) ).

% prod.related
tff(fact_5804_prod_Orelated,axiom,
    ! [R3: fun_rat_fun_rat_o,S2: set_int,Ha: fun_int_rat,G: fun_int_rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(R3,one_one_rat),one_one_rat)
     => ( ! [X12: rat,Y12: rat,X23: rat,Y22: rat] :
            ( ( aa_rat_o(aa_rat_fun_rat_o(R3,X12),X23)
              & aa_rat_o(aa_rat_fun_rat_o(R3,Y12),Y22) )
           => aa_rat_o(aa_rat_fun_rat_o(R3,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,X12),Y12)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,X23),Y22)) )
       => ( finite_finite_int(S2)
         => ( ! [X3: int] :
                ( member_int(X3,S2)
               => aa_rat_o(aa_rat_fun_rat_o(R3,aa_int_rat(Ha,X3)),aa_int_rat(G,X3)) )
           => aa_rat_o(aa_rat_fun_rat_o(R3,aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,Ha),S2)),aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,G),S2)) ) ) ) ) ).

% prod.related
tff(fact_5805_prod_Orelated,axiom,
    ! [R3: fun_rat_fun_rat_o,S2: set_Code_integer,Ha: fun_Code_integer_rat,G: fun_Code_integer_rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(R3,one_one_rat),one_one_rat)
     => ( ! [X12: rat,Y12: rat,X23: rat,Y22: rat] :
            ( ( aa_rat_o(aa_rat_fun_rat_o(R3,X12),X23)
              & aa_rat_o(aa_rat_fun_rat_o(R3,Y12),Y22) )
           => aa_rat_o(aa_rat_fun_rat_o(R3,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,X12),Y12)),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,X23),Y22)) )
       => ( finite6017078050557962740nteger(S2)
         => ( ! [X3: code_integer] :
                ( member_Code_integer(X3,S2)
               => aa_rat_o(aa_rat_fun_rat_o(R3,aa_Code_integer_rat(Ha,X3)),aa_Code_integer_rat(G,X3)) )
           => aa_rat_o(aa_rat_fun_rat_o(R3,aa_set3519029356358064041er_rat(aa_fun5443269377828775384er_rat(groups2555765274223993564er_rat,Ha),S2)),aa_set3519029356358064041er_rat(aa_fun5443269377828775384er_rat(groups2555765274223993564er_rat,G),S2)) ) ) ) ) ).

% prod.related
tff(fact_5806_prod_Orelated,axiom,
    ! [R3: fun_nat_fun_nat_o,S2: set_int,Ha: fun_int_nat,G: fun_int_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(R3,one_one_nat),one_one_nat)
     => ( ! [X12: nat,Y12: nat,X23: nat,Y22: nat] :
            ( ( aa_nat_o(aa_nat_fun_nat_o(R3,X12),X23)
              & aa_nat_o(aa_nat_fun_nat_o(R3,Y12),Y22) )
           => aa_nat_o(aa_nat_fun_nat_o(R3,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X12),Y12)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X23),Y22)) )
       => ( finite_finite_int(S2)
         => ( ! [X3: int] :
                ( member_int(X3,S2)
               => aa_nat_o(aa_nat_fun_nat_o(R3,aa_int_nat(Ha,X3)),aa_int_nat(G,X3)) )
           => aa_nat_o(aa_nat_fun_nat_o(R3,groups1707563613775114915nt_nat(Ha,S2)),groups1707563613775114915nt_nat(G,S2)) ) ) ) ) ).

% prod.related
tff(fact_5807_sum_Oinsert__if,axiom,
    ! [A2: set_o,G: fun_o_rat,X2: $o] :
      ( finite_finite_o(A2)
     => ( groups7872700643590313910_o_rat(G,insert_o((X2),A2)) = $ite(member_o((X2),A2),groups7872700643590313910_o_rat(G,A2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_o_rat(G,(X2))),groups7872700643590313910_o_rat(G,A2))) ) ) ).

% sum.insert_if
tff(fact_5808_sum_Oinsert__if,axiom,
    ! [A2: set_nat,G: fun_nat_rat,X2: nat] :
      ( finite_finite_nat(A2)
     => ( groups2906978787729119204at_rat(G,insert_nat(X2,A2)) = $ite(member_nat(X2,A2),groups2906978787729119204at_rat(G,A2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(G,X2)),groups2906978787729119204at_rat(G,A2))) ) ) ).

% sum.insert_if
tff(fact_5809_sum_Oinsert__if,axiom,
    ! [A2: set_int,G: fun_int_rat,X2: int] :
      ( finite_finite_int(A2)
     => ( groups3906332499630173760nt_rat(G,insert_int(X2,A2)) = $ite(member_int(X2,A2),groups3906332499630173760nt_rat(G,A2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_int_rat(G,X2)),groups3906332499630173760nt_rat(G,A2))) ) ) ).

% sum.insert_if
tff(fact_5810_sum_Oinsert__if,axiom,
    ! [A2: set_Code_integer,G: fun_Code_integer_rat,X2: code_integer] :
      ( finite6017078050557962740nteger(A2)
     => ( groups6602215022474089585er_rat(G,insert_Code_integer(X2,A2)) = $ite(member_Code_integer(X2,A2),groups6602215022474089585er_rat(G,A2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_Code_integer_rat(G,X2)),groups6602215022474089585er_rat(G,A2))) ) ) ).

% sum.insert_if
tff(fact_5811_sum_Oinsert__if,axiom,
    ! [A2: set_o,G: fun_o_nat,X2: $o] :
      ( finite_finite_o(A2)
     => ( groups8507830703676809646_o_nat(G,insert_o((X2),A2)) = $ite(member_o((X2),A2),groups8507830703676809646_o_nat(G,A2),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_o_nat(G,(X2))),groups8507830703676809646_o_nat(G,A2))) ) ) ).

% sum.insert_if
tff(fact_5812_sum_Oinsert__if,axiom,
    ! [A2: set_int,G: fun_int_nat,X2: int] :
      ( finite_finite_int(A2)
     => ( groups4541462559716669496nt_nat(G,insert_int(X2,A2)) = $ite(member_int(X2,A2),groups4541462559716669496nt_nat(G,A2),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_int_nat(G,X2)),groups4541462559716669496nt_nat(G,A2))) ) ) ).

% sum.insert_if
tff(fact_5813_sum_Oinsert__if,axiom,
    ! [A2: set_Code_integer,G: fun_Code_integer_nat,X2: code_integer] :
      ( finite6017078050557962740nteger(A2)
     => ( groups7237345082560585321er_nat(G,insert_Code_integer(X2,A2)) = $ite(member_Code_integer(X2,A2),groups7237345082560585321er_nat(G,A2),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_Code_integer_nat(G,X2)),groups7237345082560585321er_nat(G,A2))) ) ) ).

% sum.insert_if
tff(fact_5814_sum_Oinsert__if,axiom,
    ! [A2: set_o,G: fun_o_int,X2: $o] :
      ( finite_finite_o(A2)
     => ( groups8505340233167759370_o_int(G,insert_o((X2),A2)) = $ite(member_o((X2),A2),groups8505340233167759370_o_int(G,A2),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_o_int(G,(X2))),groups8505340233167759370_o_int(G,A2))) ) ) ).

% sum.insert_if
tff(fact_5815_sum_Oinsert__if,axiom,
    ! [A2: set_nat,G: fun_nat_int,X2: nat] :
      ( finite_finite_nat(A2)
     => ( groups3539618377306564664at_int(G,insert_nat(X2,A2)) = $ite(member_nat(X2,A2),groups3539618377306564664at_int(G,A2),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(G,X2)),groups3539618377306564664at_int(G,A2))) ) ) ).

% sum.insert_if
tff(fact_5816_sum_Oinsert__if,axiom,
    ! [A2: set_Code_integer,G: fun_Code_integer_int,X2: code_integer] :
      ( finite6017078050557962740nteger(A2)
     => ( groups7234854612051535045er_int(G,insert_Code_integer(X2,A2)) = $ite(member_Code_integer(X2,A2),groups7234854612051535045er_int(G,A2),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_Code_integer_int(G,X2)),groups7234854612051535045er_int(G,A2))) ) ) ).

% sum.insert_if
tff(fact_5817_atLeast0__atMost__Suc,axiom,
    ! [N2: nat] : aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),aa_nat_nat(suc,N2)) = insert_nat(aa_nat_nat(suc,N2),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2)) ).

% atLeast0_atMost_Suc
tff(fact_5818_atLeast0__lessThan__Suc,axiom,
    ! [N2: nat] : aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),aa_nat_nat(suc,N2)) = insert_nat(N2,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2)) ).

% atLeast0_lessThan_Suc
tff(fact_5819_Icc__eq__insert__lb__nat,axiom,
    ! [M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2) = insert_nat(M,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,M)),N2)) ) ) ).

% Icc_eq_insert_lb_nat
tff(fact_5820_atLeastAtMostSuc__conv,axiom,
    ! [M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),aa_nat_nat(suc,N2))
     => ( aa_nat_set_nat(set_or1269000886237332187st_nat(M),aa_nat_nat(suc,N2)) = insert_nat(aa_nat_nat(suc,N2),aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2)) ) ) ).

% atLeastAtMostSuc_conv
tff(fact_5821_atLeastAtMost__insertL,axiom,
    ! [M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2)
     => ( insert_nat(M,aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,M)),N2)) = aa_nat_set_nat(set_or1269000886237332187st_nat(M),N2) ) ) ).

% atLeastAtMost_insertL
tff(fact_5822_prod_Oreindex__bij__witness__not__neutral,axiom,
    ! [S5: set_o,T3: set_o,S2: set_o,I: fun_o_o,J: fun_o_o,T4: set_o,G: fun_o_Code_integer,Ha: fun_o_Code_integer] :
      ( finite_finite_o(S5)
     => ( finite_finite_o(T3)
       => ( ! [A3: $o] :
              ( member_o((A3),minus_minus_set_o(S2,S5))
             => ( aa_o_o(I,aa_o_o(J,(A3)))
              <=> (A3) ) )
         => ( ! [A3: $o] :
                ( member_o((A3),minus_minus_set_o(S2,S5))
               => member_o(aa_o_o(J,(A3)),minus_minus_set_o(T4,T3)) )
           => ( ! [B2: $o] :
                  ( member_o((B2),minus_minus_set_o(T4,T3))
                 => ( aa_o_o(J,aa_o_o(I,(B2)))
                  <=> (B2) ) )
             => ( ! [B2: $o] :
                    ( member_o((B2),minus_minus_set_o(T4,T3))
                   => member_o(aa_o_o(I,(B2)),minus_minus_set_o(S2,S5)) )
               => ( ! [A3: $o] :
                      ( member_o((A3),S5)
                     => ( aa_o_Code_integer(G,(A3)) = one_one_Code_integer ) )
                 => ( ! [B2: $o] :
                        ( member_o((B2),T3)
                       => ( aa_o_Code_integer(Ha,(B2)) = one_one_Code_integer ) )
                   => ( ! [A3: $o] :
                          ( member_o((A3),S2)
                         => ( aa_o_Code_integer(Ha,aa_o_o(J,(A3))) = aa_o_Code_integer(G,(A3)) ) )
                     => ( aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,G),S2) = aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,Ha),T4) ) ) ) ) ) ) ) ) ) ) ).

% prod.reindex_bij_witness_not_neutral
tff(fact_5823_prod_Oreindex__bij__witness__not__neutral,axiom,
    ! [S5: set_o,T3: set_int,S2: set_o,I: fun_int_o,J: fun_o_int,T4: set_int,G: fun_o_Code_integer,Ha: fun_int_Code_integer] :
      ( finite_finite_o(S5)
     => ( finite_finite_int(T3)
       => ( ! [A3: $o] :
              ( member_o((A3),minus_minus_set_o(S2,S5))
             => ( aa_int_o(I,aa_o_int(J,(A3)))
              <=> (A3) ) )
         => ( ! [A3: $o] :
                ( member_o((A3),minus_minus_set_o(S2,S5))
               => member_int(aa_o_int(J,(A3)),minus_minus_set_int(T4,T3)) )
           => ( ! [B2: int] :
                  ( member_int(B2,minus_minus_set_int(T4,T3))
                 => ( aa_o_int(J,aa_int_o(I,B2)) = B2 ) )
             => ( ! [B2: int] :
                    ( member_int(B2,minus_minus_set_int(T4,T3))
                   => member_o(aa_int_o(I,B2),minus_minus_set_o(S2,S5)) )
               => ( ! [A3: $o] :
                      ( member_o((A3),S5)
                     => ( aa_o_Code_integer(G,(A3)) = one_one_Code_integer ) )
                 => ( ! [B2: int] :
                        ( member_int(B2,T3)
                       => ( aa_int_Code_integer(Ha,B2) = one_one_Code_integer ) )
                   => ( ! [A3: $o] :
                          ( member_o((A3),S2)
                         => ( aa_int_Code_integer(Ha,aa_o_int(J,(A3))) = aa_o_Code_integer(G,(A3)) ) )
                     => ( aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,G),S2) = aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,Ha),T4) ) ) ) ) ) ) ) ) ) ) ).

% prod.reindex_bij_witness_not_neutral
tff(fact_5824_prod_Oreindex__bij__witness__not__neutral,axiom,
    ! [S5: set_o,T3: set_Code_integer,S2: set_o,I: fun_Code_integer_o,J: fun_o_Code_integer,T4: set_Code_integer,G: fun_o_Code_integer,Ha: fun_Co8499238673658658103nteger] :
      ( finite_finite_o(S5)
     => ( finite6017078050557962740nteger(T3)
       => ( ! [A3: $o] :
              ( member_o((A3),minus_minus_set_o(S2,S5))
             => ( aa_Code_integer_o(I,aa_o_Code_integer(J,(A3)))
              <=> (A3) ) )
         => ( ! [A3: $o] :
                ( member_o((A3),minus_minus_set_o(S2,S5))
               => member_Code_integer(aa_o_Code_integer(J,(A3)),minus_2355218937544613996nteger(T4,T3)) )
           => ( ! [B2: code_integer] :
                  ( member_Code_integer(B2,minus_2355218937544613996nteger(T4,T3))
                 => ( aa_o_Code_integer(J,aa_Code_integer_o(I,B2)) = B2 ) )
             => ( ! [B2: code_integer] :
                    ( member_Code_integer(B2,minus_2355218937544613996nteger(T4,T3))
                   => member_o(aa_Code_integer_o(I,B2),minus_minus_set_o(S2,S5)) )
               => ( ! [A3: $o] :
                      ( member_o((A3),S5)
                     => ( aa_o_Code_integer(G,(A3)) = one_one_Code_integer ) )
                 => ( ! [B2: code_integer] :
                        ( member_Code_integer(B2,T3)
                       => ( aa_Cod1783974652533396728nteger(Ha,B2) = one_one_Code_integer ) )
                   => ( ! [A3: $o] :
                          ( member_o((A3),S2)
                         => ( aa_Cod1783974652533396728nteger(Ha,aa_o_Code_integer(J,(A3))) = aa_o_Code_integer(G,(A3)) ) )
                     => ( aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,G),S2) = aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,Ha),T4) ) ) ) ) ) ) ) ) ) ) ).

% prod.reindex_bij_witness_not_neutral
tff(fact_5825_prod_Oreindex__bij__witness__not__neutral,axiom,
    ! [S5: set_int,T3: set_o,S2: set_int,I: fun_o_int,J: fun_int_o,T4: set_o,G: fun_int_Code_integer,Ha: fun_o_Code_integer] :
      ( finite_finite_int(S5)
     => ( finite_finite_o(T3)
       => ( ! [A3: int] :
              ( member_int(A3,minus_minus_set_int(S2,S5))
             => ( aa_o_int(I,aa_int_o(J,A3)) = A3 ) )
         => ( ! [A3: int] :
                ( member_int(A3,minus_minus_set_int(S2,S5))
               => member_o(aa_int_o(J,A3),minus_minus_set_o(T4,T3)) )
           => ( ! [B2: $o] :
                  ( member_o((B2),minus_minus_set_o(T4,T3))
                 => ( aa_int_o(J,aa_o_int(I,(B2)))
                  <=> (B2) ) )
             => ( ! [B2: $o] :
                    ( member_o((B2),minus_minus_set_o(T4,T3))
                   => member_int(aa_o_int(I,(B2)),minus_minus_set_int(S2,S5)) )
               => ( ! [A3: int] :
                      ( member_int(A3,S5)
                     => ( aa_int_Code_integer(G,A3) = one_one_Code_integer ) )
                 => ( ! [B2: $o] :
                        ( member_o((B2),T3)
                       => ( aa_o_Code_integer(Ha,(B2)) = one_one_Code_integer ) )
                   => ( ! [A3: int] :
                          ( member_int(A3,S2)
                         => ( aa_o_Code_integer(Ha,aa_int_o(J,A3)) = aa_int_Code_integer(G,A3) ) )
                     => ( aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,G),S2) = aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,Ha),T4) ) ) ) ) ) ) ) ) ) ) ).

% prod.reindex_bij_witness_not_neutral
tff(fact_5826_prod_Oreindex__bij__witness__not__neutral,axiom,
    ! [S5: set_int,T3: set_int,S2: set_int,I: fun_int_int,J: fun_int_int,T4: set_int,G: fun_int_Code_integer,Ha: fun_int_Code_integer] :
      ( finite_finite_int(S5)
     => ( finite_finite_int(T3)
       => ( ! [A3: int] :
              ( member_int(A3,minus_minus_set_int(S2,S5))
             => ( aa_int_int(I,aa_int_int(J,A3)) = A3 ) )
         => ( ! [A3: int] :
                ( member_int(A3,minus_minus_set_int(S2,S5))
               => member_int(aa_int_int(J,A3),minus_minus_set_int(T4,T3)) )
           => ( ! [B2: int] :
                  ( member_int(B2,minus_minus_set_int(T4,T3))
                 => ( aa_int_int(J,aa_int_int(I,B2)) = B2 ) )
             => ( ! [B2: int] :
                    ( member_int(B2,minus_minus_set_int(T4,T3))
                   => member_int(aa_int_int(I,B2),minus_minus_set_int(S2,S5)) )
               => ( ! [A3: int] :
                      ( member_int(A3,S5)
                     => ( aa_int_Code_integer(G,A3) = one_one_Code_integer ) )
                 => ( ! [B2: int] :
                        ( member_int(B2,T3)
                       => ( aa_int_Code_integer(Ha,B2) = one_one_Code_integer ) )
                   => ( ! [A3: int] :
                          ( member_int(A3,S2)
                         => ( aa_int_Code_integer(Ha,aa_int_int(J,A3)) = aa_int_Code_integer(G,A3) ) )
                     => ( aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,G),S2) = aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,Ha),T4) ) ) ) ) ) ) ) ) ) ) ).

% prod.reindex_bij_witness_not_neutral
tff(fact_5827_prod_Oreindex__bij__witness__not__neutral,axiom,
    ! [S5: set_int,T3: set_Code_integer,S2: set_int,I: fun_Code_integer_int,J: fun_int_Code_integer,T4: set_Code_integer,G: fun_int_Code_integer,Ha: fun_Co8499238673658658103nteger] :
      ( finite_finite_int(S5)
     => ( finite6017078050557962740nteger(T3)
       => ( ! [A3: int] :
              ( member_int(A3,minus_minus_set_int(S2,S5))
             => ( aa_Code_integer_int(I,aa_int_Code_integer(J,A3)) = A3 ) )
         => ( ! [A3: int] :
                ( member_int(A3,minus_minus_set_int(S2,S5))
               => member_Code_integer(aa_int_Code_integer(J,A3),minus_2355218937544613996nteger(T4,T3)) )
           => ( ! [B2: code_integer] :
                  ( member_Code_integer(B2,minus_2355218937544613996nteger(T4,T3))
                 => ( aa_int_Code_integer(J,aa_Code_integer_int(I,B2)) = B2 ) )
             => ( ! [B2: code_integer] :
                    ( member_Code_integer(B2,minus_2355218937544613996nteger(T4,T3))
                   => member_int(aa_Code_integer_int(I,B2),minus_minus_set_int(S2,S5)) )
               => ( ! [A3: int] :
                      ( member_int(A3,S5)
                     => ( aa_int_Code_integer(G,A3) = one_one_Code_integer ) )
                 => ( ! [B2: code_integer] :
                        ( member_Code_integer(B2,T3)
                       => ( aa_Cod1783974652533396728nteger(Ha,B2) = one_one_Code_integer ) )
                   => ( ! [A3: int] :
                          ( member_int(A3,S2)
                         => ( aa_Cod1783974652533396728nteger(Ha,aa_int_Code_integer(J,A3)) = aa_int_Code_integer(G,A3) ) )
                     => ( aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,G),S2) = aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,Ha),T4) ) ) ) ) ) ) ) ) ) ) ).

% prod.reindex_bij_witness_not_neutral
tff(fact_5828_prod_Oreindex__bij__witness__not__neutral,axiom,
    ! [S5: set_Code_integer,T3: set_o,S2: set_Code_integer,I: fun_o_Code_integer,J: fun_Code_integer_o,T4: set_o,G: fun_Co8499238673658658103nteger,Ha: fun_o_Code_integer] :
      ( finite6017078050557962740nteger(S5)
     => ( finite_finite_o(T3)
       => ( ! [A3: code_integer] :
              ( member_Code_integer(A3,minus_2355218937544613996nteger(S2,S5))
             => ( aa_o_Code_integer(I,aa_Code_integer_o(J,A3)) = A3 ) )
         => ( ! [A3: code_integer] :
                ( member_Code_integer(A3,minus_2355218937544613996nteger(S2,S5))
               => member_o(aa_Code_integer_o(J,A3),minus_minus_set_o(T4,T3)) )
           => ( ! [B2: $o] :
                  ( member_o((B2),minus_minus_set_o(T4,T3))
                 => ( aa_Code_integer_o(J,aa_o_Code_integer(I,(B2)))
                  <=> (B2) ) )
             => ( ! [B2: $o] :
                    ( member_o((B2),minus_minus_set_o(T4,T3))
                   => member_Code_integer(aa_o_Code_integer(I,(B2)),minus_2355218937544613996nteger(S2,S5)) )
               => ( ! [A3: code_integer] :
                      ( member_Code_integer(A3,S5)
                     => ( aa_Cod1783974652533396728nteger(G,A3) = one_one_Code_integer ) )
                 => ( ! [B2: $o] :
                        ( member_o((B2),T3)
                       => ( aa_o_Code_integer(Ha,(B2)) = one_one_Code_integer ) )
                   => ( ! [A3: code_integer] :
                          ( member_Code_integer(A3,S2)
                         => ( aa_o_Code_integer(Ha,aa_Code_integer_o(J,A3)) = aa_Cod1783974652533396728nteger(G,A3) ) )
                     => ( aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,G),S2) = aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,Ha),T4) ) ) ) ) ) ) ) ) ) ) ).

% prod.reindex_bij_witness_not_neutral
tff(fact_5829_prod_Oreindex__bij__witness__not__neutral,axiom,
    ! [S5: set_Code_integer,T3: set_int,S2: set_Code_integer,I: fun_int_Code_integer,J: fun_Code_integer_int,T4: set_int,G: fun_Co8499238673658658103nteger,Ha: fun_int_Code_integer] :
      ( finite6017078050557962740nteger(S5)
     => ( finite_finite_int(T3)
       => ( ! [A3: code_integer] :
              ( member_Code_integer(A3,minus_2355218937544613996nteger(S2,S5))
             => ( aa_int_Code_integer(I,aa_Code_integer_int(J,A3)) = A3 ) )
         => ( ! [A3: code_integer] :
                ( member_Code_integer(A3,minus_2355218937544613996nteger(S2,S5))
               => member_int(aa_Code_integer_int(J,A3),minus_minus_set_int(T4,T3)) )
           => ( ! [B2: int] :
                  ( member_int(B2,minus_minus_set_int(T4,T3))
                 => ( aa_Code_integer_int(J,aa_int_Code_integer(I,B2)) = B2 ) )
             => ( ! [B2: int] :
                    ( member_int(B2,minus_minus_set_int(T4,T3))
                   => member_Code_integer(aa_int_Code_integer(I,B2),minus_2355218937544613996nteger(S2,S5)) )
               => ( ! [A3: code_integer] :
                      ( member_Code_integer(A3,S5)
                     => ( aa_Cod1783974652533396728nteger(G,A3) = one_one_Code_integer ) )
                 => ( ! [B2: int] :
                        ( member_int(B2,T3)
                       => ( aa_int_Code_integer(Ha,B2) = one_one_Code_integer ) )
                   => ( ! [A3: code_integer] :
                          ( member_Code_integer(A3,S2)
                         => ( aa_int_Code_integer(Ha,aa_Code_integer_int(J,A3)) = aa_Cod1783974652533396728nteger(G,A3) ) )
                     => ( aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,G),S2) = aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,Ha),T4) ) ) ) ) ) ) ) ) ) ) ).

% prod.reindex_bij_witness_not_neutral
tff(fact_5830_prod_Oreindex__bij__witness__not__neutral,axiom,
    ! [S5: set_Code_integer,T3: set_Code_integer,S2: set_Code_integer,I: fun_Co8499238673658658103nteger,J: fun_Co8499238673658658103nteger,T4: set_Code_integer,G: fun_Co8499238673658658103nteger,Ha: fun_Co8499238673658658103nteger] :
      ( finite6017078050557962740nteger(S5)
     => ( finite6017078050557962740nteger(T3)
       => ( ! [A3: code_integer] :
              ( member_Code_integer(A3,minus_2355218937544613996nteger(S2,S5))
             => ( aa_Cod1783974652533396728nteger(I,aa_Cod1783974652533396728nteger(J,A3)) = A3 ) )
         => ( ! [A3: code_integer] :
                ( member_Code_integer(A3,minus_2355218937544613996nteger(S2,S5))
               => member_Code_integer(aa_Cod1783974652533396728nteger(J,A3),minus_2355218937544613996nteger(T4,T3)) )
           => ( ! [B2: code_integer] :
                  ( member_Code_integer(B2,minus_2355218937544613996nteger(T4,T3))
                 => ( aa_Cod1783974652533396728nteger(J,aa_Cod1783974652533396728nteger(I,B2)) = B2 ) )
             => ( ! [B2: code_integer] :
                    ( member_Code_integer(B2,minus_2355218937544613996nteger(T4,T3))
                   => member_Code_integer(aa_Cod1783974652533396728nteger(I,B2),minus_2355218937544613996nteger(S2,S5)) )
               => ( ! [A3: code_integer] :
                      ( member_Code_integer(A3,S5)
                     => ( aa_Cod1783974652533396728nteger(G,A3) = one_one_Code_integer ) )
                 => ( ! [B2: code_integer] :
                        ( member_Code_integer(B2,T3)
                       => ( aa_Cod1783974652533396728nteger(Ha,B2) = one_one_Code_integer ) )
                   => ( ! [A3: code_integer] :
                          ( member_Code_integer(A3,S2)
                         => ( aa_Cod1783974652533396728nteger(Ha,aa_Cod1783974652533396728nteger(J,A3)) = aa_Cod1783974652533396728nteger(G,A3) ) )
                     => ( aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,G),S2) = aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,Ha),T4) ) ) ) ) ) ) ) ) ) ) ).

% prod.reindex_bij_witness_not_neutral
tff(fact_5831_prod_Oreindex__bij__witness__not__neutral,axiom,
    ! [S5: set_o,T3: set_o,S2: set_o,I: fun_o_o,J: fun_o_o,T4: set_o,G: fun_o_assn,Ha: fun_o_assn] :
      ( finite_finite_o(S5)
     => ( finite_finite_o(T3)
       => ( ! [A3: $o] :
              ( member_o((A3),minus_minus_set_o(S2,S5))
             => ( aa_o_o(I,aa_o_o(J,(A3)))
              <=> (A3) ) )
         => ( ! [A3: $o] :
                ( member_o((A3),minus_minus_set_o(S2,S5))
               => member_o(aa_o_o(J,(A3)),minus_minus_set_o(T4,T3)) )
           => ( ! [B2: $o] :
                  ( member_o((B2),minus_minus_set_o(T4,T3))
                 => ( aa_o_o(J,aa_o_o(I,(B2)))
                  <=> (B2) ) )
             => ( ! [B2: $o] :
                    ( member_o((B2),minus_minus_set_o(T4,T3))
                   => member_o(aa_o_o(I,(B2)),minus_minus_set_o(S2,S5)) )
               => ( ! [A3: $o] :
                      ( member_o((A3),S5)
                     => ( aa_o_assn(G,(A3)) = one_one_assn ) )
                 => ( ! [B2: $o] :
                        ( member_o((B2),T3)
                       => ( aa_o_assn(Ha,(B2)) = one_one_assn ) )
                   => ( ! [A3: $o] :
                          ( member_o((A3),S2)
                         => ( aa_o_assn(Ha,aa_o_o(J,(A3))) = aa_o_assn(G,(A3)) ) )
                     => ( aa_set_o_assn(aa_fun1914167119812169564o_assn(groups5301882518646026715o_assn,G),S2) = aa_set_o_assn(aa_fun1914167119812169564o_assn(groups5301882518646026715o_assn,Ha),T4) ) ) ) ) ) ) ) ) ) ) ).

% prod.reindex_bij_witness_not_neutral
tff(fact_5832_dflt__None__set__def,axiom,
    ! [S2: set_Pr4329608150637261639at_nat] :
      dflt_N3208751546879591902at_nat(S2) = $ite(S2 = bot_bo228742789529271731at_nat,none_s6518873173954064040at_nat,some_s5890477192898017836at_nat(S2)) ).

% dflt_None_set_def
tff(fact_5833_dflt__None__set__def,axiom,
    ! [S2: set_Pr1261947904930325089at_nat] :
      dflt_N6592383573632408824at_nat(S2) = $ite(S2 = bot_bo2099793752762293965at_nat,none_s625347054029921090at_nat,some_s147305329494351046at_nat(S2)) ).

% dflt_None_set_def
tff(fact_5834_dflt__None__set__def,axiom,
    ! [S2: set_o] :
      dflt_None_set_o(S2) = $ite(S2 = bot_bot_set_o,none_set_o,some_set_o(S2)) ).

% dflt_None_set_def
tff(fact_5835_dflt__None__set__def,axiom,
    ! [S2: set_nat] :
      dflt_None_set_nat(S2) = $ite(S2 = bot_bot_set_nat,none_set_nat,aa_set6119337032432945050et_nat(some_set_nat,S2)) ).

% dflt_None_set_def
tff(fact_5836_dflt__None__set__def,axiom,
    ! [S2: set_int] :
      dflt_None_set_int(S2) = $ite(S2 = bot_bot_set_int,none_set_int,some_set_int(S2)) ).

% dflt_None_set_def
tff(fact_5837_sum__eq__1__iff,axiom,
    ! [A2: set_int,F: fun_int_nat] :
      ( finite_finite_int(A2)
     => ( ( groups4541462559716669496nt_nat(F,A2) = one_one_nat )
      <=> ? [X4: int] :
            ( member_int(X4,A2)
            & ( aa_int_nat(F,X4) = one_one_nat )
            & ! [Xa2: int] :
                ( member_int(Xa2,A2)
               => ( ( X4 != Xa2 )
                 => ( aa_int_nat(F,Xa2) = zero_zero_nat ) ) ) ) ) ) ).

% sum_eq_1_iff
tff(fact_5838_sum__eq__1__iff,axiom,
    ! [A2: set_Code_integer,F: fun_Code_integer_nat] :
      ( finite6017078050557962740nteger(A2)
     => ( ( groups7237345082560585321er_nat(F,A2) = one_one_nat )
      <=> ? [X4: code_integer] :
            ( member_Code_integer(X4,A2)
            & ( aa_Code_integer_nat(F,X4) = one_one_nat )
            & ! [Xa2: code_integer] :
                ( member_Code_integer(Xa2,A2)
               => ( ( X4 != Xa2 )
                 => ( aa_Code_integer_nat(F,Xa2) = zero_zero_nat ) ) ) ) ) ) ).

% sum_eq_1_iff
tff(fact_5839_sum__eq__1__iff,axiom,
    ! [A2: set_Pr1261947904930325089at_nat,F: fun_Pr2602117396471556196at_nat] :
      ( finite6177210948735845034at_nat(A2)
     => ( ( aa_set4749074711808745205at_nat(groups977919841031483927at_nat(F),A2) = one_one_nat )
      <=> ? [X4: product_prod_nat_nat] :
            ( member8440522571783428010at_nat(X4,A2)
            & ( aa_Pro4243173770044397973at_nat(F,X4) = one_one_nat )
            & ! [Xa2: product_prod_nat_nat] :
                ( member8440522571783428010at_nat(Xa2,A2)
               => ( ( X4 != Xa2 )
                 => ( aa_Pro4243173770044397973at_nat(F,Xa2) = zero_zero_nat ) ) ) ) ) ) ).

% sum_eq_1_iff
tff(fact_5840_sum__eq__1__iff,axiom,
    ! [A2: set_nat,F: fun_nat_nat] :
      ( finite_finite_nat(A2)
     => ( ( aa_set_nat_nat(groups3542108847815614940at_nat(F),A2) = one_one_nat )
      <=> ? [X4: nat] :
            ( member_nat(X4,A2)
            & ( aa_nat_nat(F,X4) = one_one_nat )
            & ! [Xa2: nat] :
                ( member_nat(Xa2,A2)
               => ( ( X4 != Xa2 )
                 => ( aa_nat_nat(F,Xa2) = zero_zero_nat ) ) ) ) ) ) ).

% sum_eq_1_iff
tff(fact_5841_surj__Compl__image__subset,axiom,
    ! [F: fun_nat_Code_integer,A2: set_nat] :
      ( ( image_1215581382706833972nteger(F,top_top_set_nat) = top_to4645266643341252675nteger )
     => ord_le7084787975880047091nteger(uminus804700908173204444nteger(image_1215581382706833972nteger(F,A2)),image_1215581382706833972nteger(F,uminus5710092332889474511et_nat(A2))) ) ).

% surj_Compl_image_subset
tff(fact_5842_surj__Compl__image__subset,axiom,
    ! [F: fun_nat_Product_unit,A2: set_nat] :
      ( ( image_8730104196221521654t_unit(F,top_top_set_nat) = top_to1996260823553986621t_unit )
     => ord_le3507040750410214029t_unit(uminus5944136376168626660t_unit(image_8730104196221521654t_unit(F,A2)),image_8730104196221521654t_unit(F,uminus5710092332889474511et_nat(A2))) ) ).

% surj_Compl_image_subset
tff(fact_5843_surj__Compl__image__subset,axiom,
    ! [F: fun_nat_int,A2: set_nat] :
      ( ( image_nat_int(F,top_top_set_nat) = top_top_set_int )
     => ord_less_eq_set_int(uminus1532241313380277803et_int(image_nat_int(F,A2)),image_nat_int(F,uminus5710092332889474511et_nat(A2))) ) ).

% surj_Compl_image_subset
tff(fact_5844_surj__Compl__image__subset,axiom,
    ! [F: fun_Pr2191293291710260995t_unit,A2: set_Product_unit] :
      ( ( image_405062704495631173t_unit(F,top_to1996260823553986621t_unit) = top_to1996260823553986621t_unit )
     => ord_le3507040750410214029t_unit(uminus5944136376168626660t_unit(image_405062704495631173t_unit(F,A2)),image_405062704495631173t_unit(F,uminus5944136376168626660t_unit(A2))) ) ).

% surj_Compl_image_subset
tff(fact_5845_surj__Compl__image__subset,axiom,
    ! [F: fun_Product_unit_int,A2: set_Product_unit] :
      ( ( image_873079544045703924it_int(F,top_to1996260823553986621t_unit) = top_top_set_int )
     => ord_less_eq_set_int(uminus1532241313380277803et_int(image_873079544045703924it_int(F,A2)),image_873079544045703924it_int(F,uminus5944136376168626660t_unit(A2))) ) ).

% surj_Compl_image_subset
tff(fact_5846_surj__Compl__image__subset,axiom,
    ! [F: fun_int_Product_unit,A2: set_int] :
      ( ( image_5846526143423701914t_unit(F,top_top_set_int) = top_to1996260823553986621t_unit )
     => ord_le3507040750410214029t_unit(uminus5944136376168626660t_unit(image_5846526143423701914t_unit(F,A2)),image_5846526143423701914t_unit(F,uminus1532241313380277803et_int(A2))) ) ).

% surj_Compl_image_subset
tff(fact_5847_surj__Compl__image__subset,axiom,
    ! [F: fun_int_int,A2: set_int] :
      ( ( aa_set_int_set_int(image_int_int(F),top_top_set_int) = top_top_set_int )
     => ord_less_eq_set_int(uminus1532241313380277803et_int(aa_set_int_set_int(image_int_int(F),A2)),aa_set_int_set_int(image_int_int(F),uminus1532241313380277803et_int(A2))) ) ).

% surj_Compl_image_subset
tff(fact_5848_surj__Compl__image__subset,axiom,
    ! [F: fun_nat_nat,A2: set_nat] :
      ( ( aa_set_nat_set_nat(image_nat_nat(F),top_top_set_nat) = top_top_set_nat )
     => aa_set_nat_o(ord_less_eq_set_nat(uminus5710092332889474511et_nat(aa_set_nat_set_nat(image_nat_nat(F),A2))),aa_set_nat_set_nat(image_nat_nat(F),uminus5710092332889474511et_nat(A2))) ) ).

% surj_Compl_image_subset
tff(fact_5849_surj__Compl__image__subset,axiom,
    ! [F: fun_Product_unit_nat,A2: set_Product_unit] :
      ( ( image_875570014554754200it_nat(F,top_to1996260823553986621t_unit) = top_top_set_nat )
     => aa_set_nat_o(ord_less_eq_set_nat(uminus5710092332889474511et_nat(image_875570014554754200it_nat(F,A2))),image_875570014554754200it_nat(F,uminus5944136376168626660t_unit(A2))) ) ).

% surj_Compl_image_subset
tff(fact_5850_surj__Compl__image__subset,axiom,
    ! [F: fun_int_nat,A2: set_int] :
      ( ( image_int_nat(F,top_top_set_int) = top_top_set_nat )
     => aa_set_nat_o(ord_less_eq_set_nat(uminus5710092332889474511et_nat(image_int_nat(F,A2))),image_int_nat(F,uminus1532241313380277803et_int(A2))) ) ).

% surj_Compl_image_subset
tff(fact_5851_card__atLeastZeroLessThan__int,axiom,
    ! [U: int] : finite_card_int(aa_int_set_int(set_or4662586982721622107an_int(zero_zero_int),U)) = aa_int_nat(nat2,U) ).

% card_atLeastZeroLessThan_int
tff(fact_5852_atMost__nat__numeral,axiom,
    ! [K: num] : aa_nat_set_nat(set_ord_atMost_nat,aa_num_nat(numeral_numeral_nat,K)) = insert_nat(aa_num_nat(numeral_numeral_nat,K),aa_nat_set_nat(set_ord_atMost_nat,aa_num_nat(pred_numeral,K))) ).

% atMost_nat_numeral
tff(fact_5853_lessThan__nat__numeral,axiom,
    ! [K: num] : aa_nat_set_nat(set_ord_lessThan_nat,aa_num_nat(numeral_numeral_nat,K)) = insert_nat(aa_num_nat(pred_numeral,K),aa_nat_set_nat(set_ord_lessThan_nat,aa_num_nat(pred_numeral,K))) ).

% lessThan_nat_numeral
tff(fact_5854_sum__Suc,axiom,
    ! [F: fun_int_nat,A2: set_int] : groups4541462559716669496nt_nat(aTP_Lamm_rm(F),A2) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,groups4541462559716669496nt_nat(F,A2)),finite_card_int(A2)) ).

% sum_Suc
tff(fact_5855_sum__Suc,axiom,
    ! [F: fun_Product_unit_nat,A2: set_Product_unit] : groups8766797177574957219it_nat(aTP_Lamm_rn(F),A2) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,groups8766797177574957219it_nat(F,A2)),finite410649719033368117t_unit(A2)) ).

% sum_Suc
tff(fact_5856_sum__Suc,axiom,
    ! [F: fun_list_nat_nat,A2: set_list_nat] : groups4396056296759096172at_nat(aTP_Lamm_ro(F),A2) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,groups4396056296759096172at_nat(F,A2)),finite_card_list_nat(A2)) ).

% sum_Suc
tff(fact_5857_sum__Suc,axiom,
    ! [F: fun_nat_nat,A2: set_nat] : aa_set_nat_nat(groups3542108847815614940at_nat(aTP_Lamm_rp(F)),A2) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_set_nat_nat(groups3542108847815614940at_nat(F),A2)),aa_set_nat_nat(finite_card_nat,A2)) ).

% sum_Suc
tff(fact_5858_prod_Osetdiff__irrelevant,axiom,
    ! [A2: set_int,G: fun_int_Code_integer] :
      ( finite_finite_int(A2)
     => ( aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,G),minus_minus_set_int(A2,collect_int(aTP_Lamm_rq(G)))) = aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,G),A2) ) ) ).

% prod.setdiff_irrelevant
tff(fact_5859_prod_Osetdiff__irrelevant,axiom,
    ! [A2: set_Code_integer,G: fun_Co8499238673658658103nteger] :
      ( finite6017078050557962740nteger(A2)
     => ( aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,G),minus_2355218937544613996nteger(A2,collect_Code_integer(aTP_Lamm_rr(G)))) = aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,G),A2) ) ) ).

% prod.setdiff_irrelevant
tff(fact_5860_prod_Osetdiff__irrelevant,axiom,
    ! [A2: set_int,G: fun_int_assn] :
      ( finite_finite_int(A2)
     => ( aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,G),minus_minus_set_int(A2,collect_int(aTP_Lamm_rs(G)))) = aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,G),A2) ) ) ).

% prod.setdiff_irrelevant
tff(fact_5861_prod_Osetdiff__irrelevant,axiom,
    ! [A2: set_Code_integer,G: fun_Co4490034186337852034r_assn] :
      ( finite6017078050557962740nteger(A2)
     => ( aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,G),minus_2355218937544613996nteger(A2,collect_Code_integer(aTP_Lamm_rt(G)))) = aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,G),A2) ) ) ).

% prod.setdiff_irrelevant
tff(fact_5862_prod_Osetdiff__irrelevant,axiom,
    ! [A2: set_int,G: fun_int_rat] :
      ( finite_finite_int(A2)
     => ( aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,G),minus_minus_set_int(A2,collect_int(aTP_Lamm_ru(G)))) = aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,G),A2) ) ) ).

% prod.setdiff_irrelevant
tff(fact_5863_prod_Osetdiff__irrelevant,axiom,
    ! [A2: set_Code_integer,G: fun_Code_integer_rat] :
      ( finite6017078050557962740nteger(A2)
     => ( aa_set3519029356358064041er_rat(aa_fun5443269377828775384er_rat(groups2555765274223993564er_rat,G),minus_2355218937544613996nteger(A2,collect_Code_integer(aTP_Lamm_rv(G)))) = aa_set3519029356358064041er_rat(aa_fun5443269377828775384er_rat(groups2555765274223993564er_rat,G),A2) ) ) ).

% prod.setdiff_irrelevant
tff(fact_5864_prod_Osetdiff__irrelevant,axiom,
    ! [A2: set_int,G: fun_int_nat] :
      ( finite_finite_int(A2)
     => ( groups1707563613775114915nt_nat(G,minus_minus_set_int(A2,collect_int(aTP_Lamm_rw(G)))) = groups1707563613775114915nt_nat(G,A2) ) ) ).

% prod.setdiff_irrelevant
tff(fact_5865_prod_Osetdiff__irrelevant,axiom,
    ! [A2: set_Code_integer,G: fun_Code_integer_nat] :
      ( finite6017078050557962740nteger(A2)
     => ( groups3190895334310489300er_nat(G,minus_2355218937544613996nteger(A2,collect_Code_integer(aTP_Lamm_rx(G)))) = groups3190895334310489300er_nat(G,A2) ) ) ).

% prod.setdiff_irrelevant
tff(fact_5866_prod_Osetdiff__irrelevant,axiom,
    ! [A2: set_Code_integer,G: fun_Code_integer_int] :
      ( finite6017078050557962740nteger(A2)
     => ( groups3188404863801439024er_int(G,minus_2355218937544613996nteger(A2,collect_Code_integer(aTP_Lamm_ry(G)))) = groups3188404863801439024er_int(G,A2) ) ) ).

% prod.setdiff_irrelevant
tff(fact_5867_prod_Osetdiff__irrelevant,axiom,
    ! [A2: set_nat,G: fun_nat_Code_integer] :
      ( finite_finite_nat(A2)
     => ( groups3455450783089532116nteger(G,minus_minus_set_nat(A2,collect_nat(aTP_Lamm_rz(G)))) = groups3455450783089532116nteger(G,A2) ) ) ).

% prod.setdiff_irrelevant
tff(fact_5868_notin__range__Some,axiom,
    ! [X2: option3216581401566546698it_nat] :
      ( ~ member3517700364412436275it_nat(X2,image_4799632500972785611it_nat(some_P6105628898608307625it_nat,top_to3995162779041354868it_nat))
    <=> ( X2 = none_P2587165478634041381it_nat ) ) ).

% notin_range_Some
tff(fact_5869_notin__range__Some,axiom,
    ! [X2: option_num] :
      ( ~ member_option_num(X2,image_num_option_num(some_num,top_top_set_num))
    <=> ( X2 = none_num ) ) ).

% notin_range_Some
tff(fact_5870_notin__range__Some,axiom,
    ! [X2: option8956607266484857688it_nat] :
      ( ~ member5596548051065438575it_nat(X2,image_3455408117458022631it_nat(some_P1914260805536162275it_nat,top_to4082048134677576814it_nat))
    <=> ( X2 = none_P9117596204409417319it_nat ) ) ).

% notin_range_Some
tff(fact_5871_notin__range__Some,axiom,
    ! [X2: option_nat] :
      ( ~ member_option_nat(X2,image_nat_option_nat(some_nat,top_top_set_nat))
    <=> ( X2 = none_nat ) ) ).

% notin_range_Some
tff(fact_5872_notin__range__Some,axiom,
    ! [X2: option_Product_unit] :
      ( ~ member1378114217278917244t_unit(X2,image_7094380055901048587t_unit(some_Product_unit,top_to1996260823553986621t_unit))
    <=> ( X2 = none_Product_unit ) ) ).

% notin_range_Some
tff(fact_5873_notin__range__Some,axiom,
    ! [X2: option_int] :
      ( ~ member_option_int(X2,image_int_option_int(some_int,top_top_set_int))
    <=> ( X2 = none_int ) ) ).

% notin_range_Some
tff(fact_5874_less__1__prod2,axiom,
    ! [I4: set_o,I: $o,F: fun_o_Code_integer] :
      ( finite_finite_o(I4)
     => ( member_o((I),I4)
       => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),aa_o_Code_integer(F,(I)))
         => ( ! [I2: $o] :
                ( member_o((I2),I4)
               => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),aa_o_Code_integer(F,(I2))) )
           => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,F),I4)) ) ) ) ) ).

% less_1_prod2
tff(fact_5875_less__1__prod2,axiom,
    ! [I4: set_nat,I: nat,F: fun_nat_Code_integer] :
      ( finite_finite_nat(I4)
     => ( member_nat(I,I4)
       => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),aa_nat_Code_integer(F,I))
         => ( ! [I2: nat] :
                ( member_nat(I2,I4)
               => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),aa_nat_Code_integer(F,I2)) )
           => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),groups3455450783089532116nteger(F,I4)) ) ) ) ) ).

% less_1_prod2
tff(fact_5876_less__1__prod2,axiom,
    ! [I4: set_int,I: int,F: fun_int_Code_integer] :
      ( finite_finite_int(I4)
     => ( member_int(I,I4)
       => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),aa_int_Code_integer(F,I))
         => ( ! [I2: int] :
                ( member_int(I2,I4)
               => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),aa_int_Code_integer(F,I2)) )
           => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,F),I4)) ) ) ) ) ).

% less_1_prod2
tff(fact_5877_less__1__prod2,axiom,
    ! [I4: set_Code_integer,I: code_integer,F: fun_Co8499238673658658103nteger] :
      ( finite6017078050557962740nteger(I4)
     => ( member_Code_integer(I,I4)
       => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),aa_Cod1783974652533396728nteger(F,I))
         => ( ! [I2: code_integer] :
                ( member_Code_integer(I2,I4)
               => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),aa_Cod1783974652533396728nteger(F,I2)) )
           => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,F),I4)) ) ) ) ) ).

% less_1_prod2
tff(fact_5878_less__1__prod2,axiom,
    ! [I4: set_o,I: $o,F: fun_o_rat] :
      ( finite_finite_o(I4)
     => ( member_o((I),I4)
       => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),aa_o_rat(F,(I)))
         => ( ! [I2: $o] :
                ( member_o((I2),I4)
               => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),aa_o_rat(F,(I2))) )
           => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),aa_set_o_rat(aa_fun7302669049306738524_o_rat(groups2869687844427037835_o_rat,F),I4)) ) ) ) ) ).

% less_1_prod2
tff(fact_5879_less__1__prod2,axiom,
    ! [I4: set_nat,I: nat,F: fun_nat_rat] :
      ( finite_finite_nat(I4)
     => ( member_nat(I,I4)
       => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),aa_nat_rat(F,I))
         => ( ! [I2: nat] :
                ( member_nat(I2,I4)
               => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),aa_nat_rat(F,I2)) )
           => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),groups73079841787564623at_rat(F,I4)) ) ) ) ) ).

% less_1_prod2
tff(fact_5880_less__1__prod2,axiom,
    ! [I4: set_int,I: int,F: fun_int_rat] :
      ( finite_finite_int(I4)
     => ( member_int(I,I4)
       => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),aa_int_rat(F,I))
         => ( ! [I2: int] :
                ( member_int(I2,I4)
               => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),aa_int_rat(F,I2)) )
           => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,F),I4)) ) ) ) ) ).

% less_1_prod2
tff(fact_5881_less__1__prod2,axiom,
    ! [I4: set_Code_integer,I: code_integer,F: fun_Code_integer_rat] :
      ( finite6017078050557962740nteger(I4)
     => ( member_Code_integer(I,I4)
       => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),aa_Code_integer_rat(F,I))
         => ( ! [I2: code_integer] :
                ( member_Code_integer(I2,I4)
               => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),aa_Code_integer_rat(F,I2)) )
           => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),aa_set3519029356358064041er_rat(aa_fun5443269377828775384er_rat(groups2555765274223993564er_rat,F),I4)) ) ) ) ) ).

% less_1_prod2
tff(fact_5882_less__1__prod2,axiom,
    ! [I4: set_o,I: $o,F: fun_o_int] :
      ( finite_finite_o(I4)
     => ( member_o((I),I4)
       => ( aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),aa_o_int(F,(I)))
         => ( ! [I2: $o] :
                ( member_o((I2),I4)
               => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,one_one_int),aa_o_int(F,(I2))) )
           => aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),groups3502327434004483295_o_int(F,I4)) ) ) ) ) ).

% less_1_prod2
tff(fact_5883_less__1__prod2,axiom,
    ! [I4: set_Code_integer,I: code_integer,F: fun_Code_integer_int] :
      ( finite6017078050557962740nteger(I4)
     => ( member_Code_integer(I,I4)
       => ( aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),aa_Code_integer_int(F,I))
         => ( ! [I2: code_integer] :
                ( member_Code_integer(I2,I4)
               => aa_int_o(aa_int_fun_int_o(ord_less_eq_int,one_one_int),aa_Code_integer_int(F,I2)) )
           => aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),groups3188404863801439024er_int(F,I4)) ) ) ) ) ).

% less_1_prod2
tff(fact_5884_less__1__prod,axiom,
    ! [I4: set_Code_integer,F: fun_Co8499238673658658103nteger] :
      ( finite6017078050557962740nteger(I4)
     => ( ( I4 != bot_bo3990330152332043303nteger )
       => ( ! [I2: code_integer] :
              ( member_Code_integer(I2,I4)
             => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),aa_Cod1783974652533396728nteger(F,I2)) )
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,F),I4)) ) ) ) ).

% less_1_prod
tff(fact_5885_less__1__prod,axiom,
    ! [I4: set_o,F: fun_o_Code_integer] :
      ( finite_finite_o(I4)
     => ( ( I4 != bot_bot_set_o )
       => ( ! [I2: $o] :
              ( member_o((I2),I4)
             => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),aa_o_Code_integer(F,(I2))) )
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,F),I4)) ) ) ) ).

% less_1_prod
tff(fact_5886_less__1__prod,axiom,
    ! [I4: set_nat,F: fun_nat_Code_integer] :
      ( finite_finite_nat(I4)
     => ( ( I4 != bot_bot_set_nat )
       => ( ! [I2: nat] :
              ( member_nat(I2,I4)
             => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),aa_nat_Code_integer(F,I2)) )
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),groups3455450783089532116nteger(F,I4)) ) ) ) ).

% less_1_prod
tff(fact_5887_less__1__prod,axiom,
    ! [I4: set_int,F: fun_int_Code_integer] :
      ( finite_finite_int(I4)
     => ( ( I4 != bot_bot_set_int )
       => ( ! [I2: int] :
              ( member_int(I2,I4)
             => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),aa_int_Code_integer(F,I2)) )
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,one_one_Code_integer),aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,F),I4)) ) ) ) ).

% less_1_prod
tff(fact_5888_less__1__prod,axiom,
    ! [I4: set_Code_integer,F: fun_Code_integer_rat] :
      ( finite6017078050557962740nteger(I4)
     => ( ( I4 != bot_bo3990330152332043303nteger )
       => ( ! [I2: code_integer] :
              ( member_Code_integer(I2,I4)
             => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),aa_Code_integer_rat(F,I2)) )
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),aa_set3519029356358064041er_rat(aa_fun5443269377828775384er_rat(groups2555765274223993564er_rat,F),I4)) ) ) ) ).

% less_1_prod
tff(fact_5889_less__1__prod,axiom,
    ! [I4: set_o,F: fun_o_rat] :
      ( finite_finite_o(I4)
     => ( ( I4 != bot_bot_set_o )
       => ( ! [I2: $o] :
              ( member_o((I2),I4)
             => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),aa_o_rat(F,(I2))) )
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),aa_set_o_rat(aa_fun7302669049306738524_o_rat(groups2869687844427037835_o_rat,F),I4)) ) ) ) ).

% less_1_prod
tff(fact_5890_less__1__prod,axiom,
    ! [I4: set_nat,F: fun_nat_rat] :
      ( finite_finite_nat(I4)
     => ( ( I4 != bot_bot_set_nat )
       => ( ! [I2: nat] :
              ( member_nat(I2,I4)
             => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),aa_nat_rat(F,I2)) )
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),groups73079841787564623at_rat(F,I4)) ) ) ) ).

% less_1_prod
tff(fact_5891_less__1__prod,axiom,
    ! [I4: set_int,F: fun_int_rat] :
      ( finite_finite_int(I4)
     => ( ( I4 != bot_bot_set_int )
       => ( ! [I2: int] :
              ( member_int(I2,I4)
             => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),aa_int_rat(F,I2)) )
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,one_one_rat),aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,F),I4)) ) ) ) ).

% less_1_prod
tff(fact_5892_less__1__prod,axiom,
    ! [I4: set_Code_integer,F: fun_Code_integer_int] :
      ( finite6017078050557962740nteger(I4)
     => ( ( I4 != bot_bo3990330152332043303nteger )
       => ( ! [I2: code_integer] :
              ( member_Code_integer(I2,I4)
             => aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),aa_Code_integer_int(F,I2)) )
         => aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),groups3188404863801439024er_int(F,I4)) ) ) ) ).

% less_1_prod
tff(fact_5893_less__1__prod,axiom,
    ! [I4: set_o,F: fun_o_int] :
      ( finite_finite_o(I4)
     => ( ( I4 != bot_bot_set_o )
       => ( ! [I2: $o] :
              ( member_o((I2),I4)
             => aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),aa_o_int(F,(I2))) )
         => aa_int_o(aa_int_fun_int_o(ord_less_int,one_one_int),groups3502327434004483295_o_int(F,I4)) ) ) ) ).

% less_1_prod
tff(fact_5894_sum_Oreindex__nontrivial,axiom,
    ! [A2: set_num,Ha: fun_num_Code_integer,G: fun_Co8499238673658658103nteger] :
      ( finite_finite_num(A2)
     => ( ! [X3: num,Y4: num] :
            ( member_num(X3,A2)
           => ( member_num(Y4,A2)
             => ( ( X3 != Y4 )
               => ( ( aa_num_Code_integer(Ha,X3) = aa_num_Code_integer(Ha,Y4) )
                 => ( aa_Cod1783974652533396728nteger(G,aa_num_Code_integer(Ha,X3)) = zero_z3403309356797280102nteger ) ) ) ) )
       => ( aa_set8546232603906849326nteger(groups879477027807139574nteger(G),image_8379761247532268670nteger(Ha,A2)) = groups5442708359310287027nteger(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),Ha),A2) ) ) ) ).

% sum.reindex_nontrivial
tff(fact_5895_sum_Oreindex__nontrivial,axiom,
    ! [A2: set_nat,Ha: fun_nat_Code_integer,G: fun_Co8499238673658658103nteger] :
      ( finite_finite_nat(A2)
     => ( ! [X3: nat,Y4: nat] :
            ( member_nat(X3,A2)
           => ( member_nat(Y4,A2)
             => ( ( X3 != Y4 )
               => ( ( aa_nat_Code_integer(Ha,X3) = aa_nat_Code_integer(Ha,Y4) )
                 => ( aa_Cod1783974652533396728nteger(G,aa_nat_Code_integer(Ha,X3)) = zero_z3403309356797280102nteger ) ) ) ) )
       => ( aa_set8546232603906849326nteger(groups879477027807139574nteger(G),image_1215581382706833972nteger(Ha,A2)) = groups7501900531339628137nteger(comp_C6974050283906349679er_nat(G,Ha),A2) ) ) ) ).

% sum.reindex_nontrivial
tff(fact_5896_sum_Oreindex__nontrivial,axiom,
    ! [A2: set_nat,Ha: fun_nat_nat,G: fun_nat_Code_integer] :
      ( finite_finite_nat(A2)
     => ( ! [X3: nat,Y4: nat] :
            ( member_nat(X3,A2)
           => ( member_nat(Y4,A2)
             => ( ( X3 != Y4 )
               => ( ( aa_nat_nat(Ha,X3) = aa_nat_nat(Ha,Y4) )
                 => ( aa_nat_Code_integer(G,aa_nat_nat(Ha,X3)) = zero_z3403309356797280102nteger ) ) ) ) )
       => ( groups7501900531339628137nteger(G,aa_set_nat_set_nat(image_nat_nat(Ha),A2)) = groups7501900531339628137nteger(comp_n3898172953802868194er_nat(G,Ha),A2) ) ) ) ).

% sum.reindex_nontrivial
tff(fact_5897_sum_Oreindex__nontrivial,axiom,
    ! [A2: set_nat,Ha: fun_nat_int,G: fun_int_Code_integer] :
      ( finite_finite_nat(A2)
     => ( ! [X3: nat,Y4: nat] :
            ( member_nat(X3,A2)
           => ( member_nat(Y4,A2)
             => ( ( X3 != Y4 )
               => ( ( aa_nat_int(Ha,X3) = aa_nat_int(Ha,Y4) )
                 => ( aa_int_Code_integer(G,aa_nat_int(Ha,X3)) = zero_z3403309356797280102nteger ) ) ) ) )
       => ( groups7873554091576472773nteger(G,image_nat_int(Ha,A2)) = groups7501900531339628137nteger(comp_i1588355021709917246er_nat(G,Ha),A2) ) ) ) ).

% sum.reindex_nontrivial
tff(fact_5898_sum_Oreindex__nontrivial,axiom,
    ! [A2: set_int,Ha: fun_int_int,G: fun_int_Code_integer] :
      ( finite_finite_int(A2)
     => ( ! [X3: int,Y4: int] :
            ( member_int(X3,A2)
           => ( member_int(Y4,A2)
             => ( ( X3 != Y4 )
               => ( ( aa_int_int(Ha,X3) = aa_int_int(Ha,Y4) )
                 => ( aa_int_Code_integer(G,aa_int_int(Ha,X3)) = zero_z3403309356797280102nteger ) ) ) ) )
       => ( groups7873554091576472773nteger(G,aa_set_int_set_int(image_int_int(Ha),A2)) = groups7873554091576472773nteger(comp_i1585864551200866970er_int(G,Ha),A2) ) ) ) ).

% sum.reindex_nontrivial
tff(fact_5899_sum_Oreindex__nontrivial,axiom,
    ! [A2: set_nat,Ha: fun_nat_Code_integer,G: fun_Code_integer_rat] :
      ( finite_finite_nat(A2)
     => ( ! [X3: nat,Y4: nat] :
            ( member_nat(X3,A2)
           => ( member_nat(Y4,A2)
             => ( ( X3 != Y4 )
               => ( ( aa_nat_Code_integer(Ha,X3) = aa_nat_Code_integer(Ha,Y4) )
                 => ( aa_Code_integer_rat(G,aa_nat_Code_integer(Ha,X3)) = zero_zero_rat ) ) ) ) )
       => ( groups6602215022474089585er_rat(G,image_1215581382706833972nteger(Ha,A2)) = groups2906978787729119204at_rat(comp_C3733001951728184298at_nat(G,Ha),A2) ) ) ) ).

% sum.reindex_nontrivial
tff(fact_5900_sum_Oreindex__nontrivial,axiom,
    ! [A2: set_nat,Ha: fun_nat_nat,G: fun_nat_rat] :
      ( finite_finite_nat(A2)
     => ( ! [X3: nat,Y4: nat] :
            ( member_nat(X3,A2)
           => ( member_nat(Y4,A2)
             => ( ( X3 != Y4 )
               => ( ( aa_nat_nat(Ha,X3) = aa_nat_nat(Ha,Y4) )
                 => ( aa_nat_rat(G,aa_nat_nat(Ha,X3)) = zero_zero_rat ) ) ) ) )
       => ( groups2906978787729119204at_rat(G,aa_set_nat_set_nat(image_nat_nat(Ha),A2)) = groups2906978787729119204at_rat(comp_nat_rat_nat(G,Ha),A2) ) ) ) ).

% sum.reindex_nontrivial
tff(fact_5901_sum_Oreindex__nontrivial,axiom,
    ! [A2: set_nat,Ha: fun_nat_int,G: fun_int_rat] :
      ( finite_finite_nat(A2)
     => ( ! [X3: nat,Y4: nat] :
            ( member_nat(X3,A2)
           => ( member_nat(Y4,A2)
             => ( ( X3 != Y4 )
               => ( ( aa_nat_int(Ha,X3) = aa_nat_int(Ha,Y4) )
                 => ( aa_int_rat(G,aa_nat_int(Ha,X3)) = zero_zero_rat ) ) ) ) )
       => ( groups3906332499630173760nt_rat(G,image_nat_int(Ha,A2)) = groups2906978787729119204at_rat(comp_int_rat_nat(G,Ha),A2) ) ) ) ).

% sum.reindex_nontrivial
tff(fact_5902_sum_Oreindex__nontrivial,axiom,
    ! [A2: set_int,Ha: fun_int_int,G: fun_int_rat] :
      ( finite_finite_int(A2)
     => ( ! [X3: int,Y4: int] :
            ( member_int(X3,A2)
           => ( member_int(Y4,A2)
             => ( ( X3 != Y4 )
               => ( ( aa_int_int(Ha,X3) = aa_int_int(Ha,Y4) )
                 => ( aa_int_rat(G,aa_int_int(Ha,X3)) = zero_zero_rat ) ) ) ) )
       => ( groups3906332499630173760nt_rat(G,aa_set_int_set_int(image_int_int(Ha),A2)) = groups3906332499630173760nt_rat(comp_int_rat_int(G,Ha),A2) ) ) ) ).

% sum.reindex_nontrivial
tff(fact_5903_sum_Oreindex__nontrivial,axiom,
    ! [A2: set_int,Ha: fun_int_int,G: fun_int_nat] :
      ( finite_finite_int(A2)
     => ( ! [X3: int,Y4: int] :
            ( member_int(X3,A2)
           => ( member_int(Y4,A2)
             => ( ( X3 != Y4 )
               => ( ( aa_int_int(Ha,X3) = aa_int_int(Ha,Y4) )
                 => ( aa_int_nat(G,aa_int_int(Ha,X3)) = zero_zero_nat ) ) ) ) )
       => ( groups4541462559716669496nt_nat(G,aa_set_int_set_int(image_int_int(Ha),A2)) = groups4541462559716669496nt_nat(comp_int_nat_int(G,Ha),A2) ) ) ) ).

% sum.reindex_nontrivial
tff(fact_5904_prod_Oreindex__nontrivial,axiom,
    ! [A2: set_num,Ha: fun_num_Code_integer,G: fun_Co8499238673658658103nteger] :
      ( finite_finite_num(A2)
     => ( ! [X3: num,Y4: num] :
            ( member_num(X3,A2)
           => ( member_num(Y4,A2)
             => ( ( X3 != Y4 )
               => ( ( aa_num_Code_integer(Ha,X3) = aa_num_Code_integer(Ha,Y4) )
                 => ( aa_Cod1783974652533396728nteger(G,aa_num_Code_integer(Ha,X3)) = one_one_Code_integer ) ) ) ) )
       => ( aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,G),image_8379761247532268670nteger(Ha,A2)) = groups1396258611060191006nteger(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),Ha),A2) ) ) ) ).

% prod.reindex_nontrivial
tff(fact_5905_prod_Oreindex__nontrivial,axiom,
    ! [A2: set_nat,Ha: fun_nat_Code_integer,G: fun_Co8499238673658658103nteger] :
      ( finite_finite_nat(A2)
     => ( ! [X3: nat,Y4: nat] :
            ( member_nat(X3,A2)
           => ( member_nat(Y4,A2)
             => ( ( X3 != Y4 )
               => ( ( aa_nat_Code_integer(Ha,X3) = aa_nat_Code_integer(Ha,Y4) )
                 => ( aa_Cod1783974652533396728nteger(G,aa_nat_Code_integer(Ha,X3)) = one_one_Code_integer ) ) ) ) )
       => ( aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,G),image_1215581382706833972nteger(Ha,A2)) = groups3455450783089532116nteger(comp_C6974050283906349679er_nat(G,Ha),A2) ) ) ) ).

% prod.reindex_nontrivial
tff(fact_5906_prod_Oreindex__nontrivial,axiom,
    ! [A2: set_nat,Ha: fun_nat_nat,G: fun_nat_Code_integer] :
      ( finite_finite_nat(A2)
     => ( ! [X3: nat,Y4: nat] :
            ( member_nat(X3,A2)
           => ( member_nat(Y4,A2)
             => ( ( X3 != Y4 )
               => ( ( aa_nat_nat(Ha,X3) = aa_nat_nat(Ha,Y4) )
                 => ( aa_nat_Code_integer(G,aa_nat_nat(Ha,X3)) = one_one_Code_integer ) ) ) ) )
       => ( groups3455450783089532116nteger(G,aa_set_nat_set_nat(image_nat_nat(Ha),A2)) = groups3455450783089532116nteger(comp_n3898172953802868194er_nat(G,Ha),A2) ) ) ) ).

% prod.reindex_nontrivial
tff(fact_5907_prod_Oreindex__nontrivial,axiom,
    ! [A2: set_nat,Ha: fun_nat_int,G: fun_int_Code_integer] :
      ( finite_finite_nat(A2)
     => ( ! [X3: nat,Y4: nat] :
            ( member_nat(X3,A2)
           => ( member_nat(Y4,A2)
             => ( ( X3 != Y4 )
               => ( ( aa_nat_int(Ha,X3) = aa_nat_int(Ha,Y4) )
                 => ( aa_int_Code_integer(G,aa_nat_int(Ha,X3)) = one_one_Code_integer ) ) ) ) )
       => ( aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,G),image_nat_int(Ha,A2)) = groups3455450783089532116nteger(comp_i1588355021709917246er_nat(G,Ha),A2) ) ) ) ).

% prod.reindex_nontrivial
tff(fact_5908_prod_Oreindex__nontrivial,axiom,
    ! [A2: set_int,Ha: fun_int_int,G: fun_int_Code_integer] :
      ( finite_finite_int(A2)
     => ( ! [X3: int,Y4: int] :
            ( member_int(X3,A2)
           => ( member_int(Y4,A2)
             => ( ( X3 != Y4 )
               => ( ( aa_int_int(Ha,X3) = aa_int_int(Ha,Y4) )
                 => ( aa_int_Code_integer(G,aa_int_int(Ha,X3)) = one_one_Code_integer ) ) ) ) )
       => ( aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,G),aa_set_int_set_int(image_int_int(Ha),A2)) = aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,comp_i1585864551200866970er_int(G,Ha)),A2) ) ) ) ).

% prod.reindex_nontrivial
tff(fact_5909_prod_Oreindex__nontrivial,axiom,
    ! [A2: set_nat,Ha: fun_nat_Code_integer,G: fun_Co4490034186337852034r_assn] :
      ( finite_finite_nat(A2)
     => ( ! [X3: nat,Y4: nat] :
            ( member_nat(X3,A2)
           => ( member_nat(Y4,A2)
             => ( ( X3 != Y4 )
               => ( ( aa_nat_Code_integer(Ha,X3) = aa_nat_Code_integer(Ha,Y4) )
                 => ( aa_Code_integer_assn(G,aa_nat_Code_integer(Ha,X3)) = one_one_assn ) ) ) ) )
       => ( aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,G),image_1215581382706833972nteger(Ha,A2)) = groups6906906614972039071t_assn(comp_C8462447471145125178sn_nat(G,Ha),A2) ) ) ) ).

% prod.reindex_nontrivial
tff(fact_5910_prod_Oreindex__nontrivial,axiom,
    ! [A2: set_nat,Ha: fun_nat_nat,G: fun_nat_assn] :
      ( finite_finite_nat(A2)
     => ( ! [X3: nat,Y4: nat] :
            ( member_nat(X3,A2)
           => ( member_nat(Y4,A2)
             => ( ( X3 != Y4 )
               => ( ( aa_nat_nat(Ha,X3) = aa_nat_nat(Ha,Y4) )
                 => ( aa_nat_assn(G,aa_nat_nat(Ha,X3)) = one_one_assn ) ) ) ) )
       => ( groups6906906614972039071t_assn(G,aa_set_nat_set_nat(image_nat_nat(Ha),A2)) = groups6906906614972039071t_assn(comp_nat_assn_nat(G,Ha),A2) ) ) ) ).

% prod.reindex_nontrivial
tff(fact_5911_prod_Oreindex__nontrivial,axiom,
    ! [A2: set_nat,Ha: fun_nat_int,G: fun_int_assn] :
      ( finite_finite_nat(A2)
     => ( ! [X3: nat,Y4: nat] :
            ( member_nat(X3,A2)
           => ( member_nat(Y4,A2)
             => ( ( X3 != Y4 )
               => ( ( aa_nat_int(Ha,X3) = aa_nat_int(Ha,Y4) )
                 => ( aa_int_assn(G,aa_nat_int(Ha,X3)) = one_one_assn ) ) ) ) )
       => ( aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,G),image_nat_int(Ha,A2)) = groups6906906614972039071t_assn(comp_int_assn_nat(G,Ha),A2) ) ) ) ).

% prod.reindex_nontrivial
tff(fact_5912_prod_Oreindex__nontrivial,axiom,
    ! [A2: set_int,Ha: fun_int_int,G: fun_int_assn] :
      ( finite_finite_int(A2)
     => ( ! [X3: int,Y4: int] :
            ( member_int(X3,A2)
           => ( member_int(Y4,A2)
             => ( ( X3 != Y4 )
               => ( ( aa_int_int(Ha,X3) = aa_int_int(Ha,Y4) )
                 => ( aa_int_assn(G,aa_int_int(Ha,X3)) = one_one_assn ) ) ) ) )
       => ( aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,G),aa_set_int_set_int(image_int_int(Ha),A2)) = aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,comp_int_assn_int(G,Ha)),A2) ) ) ) ).

% prod.reindex_nontrivial
tff(fact_5913_prod_Oreindex__nontrivial,axiom,
    ! [A2: set_nat,Ha: fun_nat_Code_integer,G: fun_Code_integer_rat] :
      ( finite_finite_nat(A2)
     => ( ! [X3: nat,Y4: nat] :
            ( member_nat(X3,A2)
           => ( member_nat(Y4,A2)
             => ( ( X3 != Y4 )
               => ( ( aa_nat_Code_integer(Ha,X3) = aa_nat_Code_integer(Ha,Y4) )
                 => ( aa_Code_integer_rat(G,aa_nat_Code_integer(Ha,X3)) = one_one_rat ) ) ) ) )
       => ( aa_set3519029356358064041er_rat(aa_fun5443269377828775384er_rat(groups2555765274223993564er_rat,G),image_1215581382706833972nteger(Ha,A2)) = groups73079841787564623at_rat(comp_C3733001951728184298at_nat(G,Ha),A2) ) ) ) ).

% prod.reindex_nontrivial
tff(fact_5914_sum_Osubset__diff,axiom,
    ! [B4: set_int,A2: set_int,G: fun_int_rat] :
      ( ord_less_eq_set_int(B4,A2)
     => ( finite_finite_int(A2)
       => ( groups3906332499630173760nt_rat(G,A2) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,groups3906332499630173760nt_rat(G,minus_minus_set_int(A2,B4))),groups3906332499630173760nt_rat(G,B4)) ) ) ) ).

% sum.subset_diff
tff(fact_5915_sum_Osubset__diff,axiom,
    ! [B4: set_Code_integer,A2: set_Code_integer,G: fun_Code_integer_rat] :
      ( ord_le7084787975880047091nteger(B4,A2)
     => ( finite6017078050557962740nteger(A2)
       => ( groups6602215022474089585er_rat(G,A2) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,groups6602215022474089585er_rat(G,minus_2355218937544613996nteger(A2,B4))),groups6602215022474089585er_rat(G,B4)) ) ) ) ).

% sum.subset_diff
tff(fact_5916_sum_Osubset__diff,axiom,
    ! [B4: set_int,A2: set_int,G: fun_int_nat] :
      ( ord_less_eq_set_int(B4,A2)
     => ( finite_finite_int(A2)
       => ( groups4541462559716669496nt_nat(G,A2) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,groups4541462559716669496nt_nat(G,minus_minus_set_int(A2,B4))),groups4541462559716669496nt_nat(G,B4)) ) ) ) ).

% sum.subset_diff
tff(fact_5917_sum_Osubset__diff,axiom,
    ! [B4: set_Code_integer,A2: set_Code_integer,G: fun_Code_integer_nat] :
      ( ord_le7084787975880047091nteger(B4,A2)
     => ( finite6017078050557962740nteger(A2)
       => ( groups7237345082560585321er_nat(G,A2) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,groups7237345082560585321er_nat(G,minus_2355218937544613996nteger(A2,B4))),groups7237345082560585321er_nat(G,B4)) ) ) ) ).

% sum.subset_diff
tff(fact_5918_sum_Osubset__diff,axiom,
    ! [B4: set_Code_integer,A2: set_Code_integer,G: fun_Code_integer_int] :
      ( ord_le7084787975880047091nteger(B4,A2)
     => ( finite6017078050557962740nteger(A2)
       => ( groups7234854612051535045er_int(G,A2) = aa_int_int(aa_int_fun_int_int(plus_plus_int,groups7234854612051535045er_int(G,minus_2355218937544613996nteger(A2,B4))),groups7234854612051535045er_int(G,B4)) ) ) ) ).

% sum.subset_diff
tff(fact_5919_sum_Osubset__diff,axiom,
    ! [B4: set_nat,A2: set_nat,G: fun_nat_rat] :
      ( aa_set_nat_o(ord_less_eq_set_nat(B4),A2)
     => ( finite_finite_nat(A2)
       => ( groups2906978787729119204at_rat(G,A2) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,groups2906978787729119204at_rat(G,minus_minus_set_nat(A2,B4))),groups2906978787729119204at_rat(G,B4)) ) ) ) ).

% sum.subset_diff
tff(fact_5920_sum_Osubset__diff,axiom,
    ! [B4: set_nat,A2: set_nat,G: fun_nat_int] :
      ( aa_set_nat_o(ord_less_eq_set_nat(B4),A2)
     => ( finite_finite_nat(A2)
       => ( groups3539618377306564664at_int(G,A2) = aa_int_int(aa_int_fun_int_int(plus_plus_int,groups3539618377306564664at_int(G,minus_minus_set_nat(A2,B4))),groups3539618377306564664at_int(G,B4)) ) ) ) ).

% sum.subset_diff
tff(fact_5921_sum_Osubset__diff,axiom,
    ! [B4: set_nat,A2: set_nat,G: fun_nat_nat] :
      ( aa_set_nat_o(ord_less_eq_set_nat(B4),A2)
     => ( finite_finite_nat(A2)
       => ( aa_set_nat_nat(groups3542108847815614940at_nat(G),A2) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_set_nat_nat(groups3542108847815614940at_nat(G),minus_minus_set_nat(A2,B4))),aa_set_nat_nat(groups3542108847815614940at_nat(G),B4)) ) ) ) ).

% sum.subset_diff
tff(fact_5922_sum_Osubset__diff,axiom,
    ! [B4: set_int,A2: set_int,G: fun_int_int] :
      ( ord_less_eq_set_int(B4,A2)
     => ( finite_finite_int(A2)
       => ( aa_set_int_int(groups4538972089207619220nt_int(G),A2) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_set_int_int(groups4538972089207619220nt_int(G),minus_minus_set_int(A2,B4))),aa_set_int_int(groups4538972089207619220nt_int(G),B4)) ) ) ) ).

% sum.subset_diff
tff(fact_5923_sum_Osubset__diff,axiom,
    ! [B4: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,G: fun_Pr8317260874932935276at_rat] :
      ( aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(ord_le3146513528884898305at_nat,B4),A2)
     => ( finite6177210948735845034at_nat(A2)
       => ( groups342789780944988191at_rat(G,A2) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,groups342789780944988191at_rat(G,aa_set8868280134176360700at_nat(minus_1356011639430497352at_nat(A2),B4))),groups342789780944988191at_rat(G,B4)) ) ) ) ).

% sum.subset_diff
tff(fact_5924_prod_Osame__carrier,axiom,
    ! [C4: set_o,A2: set_o,B4: set_o,G: fun_o_Code_integer,Ha: fun_o_Code_integer] :
      ( finite_finite_o(C4)
     => ( ord_less_eq_set_o(A2,C4)
       => ( ord_less_eq_set_o(B4,C4)
         => ( ! [A3: $o] :
                ( member_o((A3),minus_minus_set_o(C4,A2))
               => ( aa_o_Code_integer(G,(A3)) = one_one_Code_integer ) )
           => ( ! [B2: $o] :
                  ( member_o((B2),minus_minus_set_o(C4,B4))
                 => ( aa_o_Code_integer(Ha,(B2)) = one_one_Code_integer ) )
             => ( ( aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,G),A2) = aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,Ha),B4) )
              <=> ( aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,G),C4) = aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,Ha),C4) ) ) ) ) ) ) ) ).

% prod.same_carrier
tff(fact_5925_prod_Osame__carrier,axiom,
    ! [C4: set_int,A2: set_int,B4: set_int,G: fun_int_Code_integer,Ha: fun_int_Code_integer] :
      ( finite_finite_int(C4)
     => ( ord_less_eq_set_int(A2,C4)
       => ( ord_less_eq_set_int(B4,C4)
         => ( ! [A3: int] :
                ( member_int(A3,minus_minus_set_int(C4,A2))
               => ( aa_int_Code_integer(G,A3) = one_one_Code_integer ) )
           => ( ! [B2: int] :
                  ( member_int(B2,minus_minus_set_int(C4,B4))
                 => ( aa_int_Code_integer(Ha,B2) = one_one_Code_integer ) )
             => ( ( aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,G),A2) = aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,Ha),B4) )
              <=> ( aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,G),C4) = aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,Ha),C4) ) ) ) ) ) ) ) ).

% prod.same_carrier
tff(fact_5926_prod_Osame__carrier,axiom,
    ! [C4: set_Code_integer,A2: set_Code_integer,B4: set_Code_integer,G: fun_Co8499238673658658103nteger,Ha: fun_Co8499238673658658103nteger] :
      ( finite6017078050557962740nteger(C4)
     => ( ord_le7084787975880047091nteger(A2,C4)
       => ( ord_le7084787975880047091nteger(B4,C4)
         => ( ! [A3: code_integer] :
                ( member_Code_integer(A3,minus_2355218937544613996nteger(C4,A2))
               => ( aa_Cod1783974652533396728nteger(G,A3) = one_one_Code_integer ) )
           => ( ! [B2: code_integer] :
                  ( member_Code_integer(B2,minus_2355218937544613996nteger(C4,B4))
                 => ( aa_Cod1783974652533396728nteger(Ha,B2) = one_one_Code_integer ) )
             => ( ( aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,G),A2) = aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,Ha),B4) )
              <=> ( aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,G),C4) = aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,Ha),C4) ) ) ) ) ) ) ) ).

% prod.same_carrier
tff(fact_5927_prod_Osame__carrier,axiom,
    ! [C4: set_o,A2: set_o,B4: set_o,G: fun_o_assn,Ha: fun_o_assn] :
      ( finite_finite_o(C4)
     => ( ord_less_eq_set_o(A2,C4)
       => ( ord_less_eq_set_o(B4,C4)
         => ( ! [A3: $o] :
                ( member_o((A3),minus_minus_set_o(C4,A2))
               => ( aa_o_assn(G,(A3)) = one_one_assn ) )
           => ( ! [B2: $o] :
                  ( member_o((B2),minus_minus_set_o(C4,B4))
                 => ( aa_o_assn(Ha,(B2)) = one_one_assn ) )
             => ( ( aa_set_o_assn(aa_fun1914167119812169564o_assn(groups5301882518646026715o_assn,G),A2) = aa_set_o_assn(aa_fun1914167119812169564o_assn(groups5301882518646026715o_assn,Ha),B4) )
              <=> ( aa_set_o_assn(aa_fun1914167119812169564o_assn(groups5301882518646026715o_assn,G),C4) = aa_set_o_assn(aa_fun1914167119812169564o_assn(groups5301882518646026715o_assn,Ha),C4) ) ) ) ) ) ) ) ).

% prod.same_carrier
tff(fact_5928_prod_Osame__carrier,axiom,
    ! [C4: set_int,A2: set_int,B4: set_int,G: fun_int_assn,Ha: fun_int_assn] :
      ( finite_finite_int(C4)
     => ( ord_less_eq_set_int(A2,C4)
       => ( ord_less_eq_set_int(B4,C4)
         => ( ! [A3: int] :
                ( member_int(A3,minus_minus_set_int(C4,A2))
               => ( aa_int_assn(G,A3) = one_one_assn ) )
           => ( ! [B2: int] :
                  ( member_int(B2,minus_minus_set_int(C4,B4))
                 => ( aa_int_assn(Ha,B2) = one_one_assn ) )
             => ( ( aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,G),A2) = aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,Ha),B4) )
              <=> ( aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,G),C4) = aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,Ha),C4) ) ) ) ) ) ) ) ).

% prod.same_carrier
tff(fact_5929_prod_Osame__carrier,axiom,
    ! [C4: set_Code_integer,A2: set_Code_integer,B4: set_Code_integer,G: fun_Co4490034186337852034r_assn,Ha: fun_Co4490034186337852034r_assn] :
      ( finite6017078050557962740nteger(C4)
     => ( ord_le7084787975880047091nteger(A2,C4)
       => ( ord_le7084787975880047091nteger(B4,C4)
         => ( ! [A3: code_integer] :
                ( member_Code_integer(A3,minus_2355218937544613996nteger(C4,A2))
               => ( aa_Code_integer_assn(G,A3) = one_one_assn ) )
           => ( ! [B2: code_integer] :
                  ( member_Code_integer(B2,minus_2355218937544613996nteger(C4,B4))
                 => ( aa_Code_integer_assn(Ha,B2) = one_one_assn ) )
             => ( ( aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,G),A2) = aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,Ha),B4) )
              <=> ( aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,G),C4) = aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,Ha),C4) ) ) ) ) ) ) ) ).

% prod.same_carrier
tff(fact_5930_prod_Osame__carrier,axiom,
    ! [C4: set_o,A2: set_o,B4: set_o,G: fun_o_rat,Ha: fun_o_rat] :
      ( finite_finite_o(C4)
     => ( ord_less_eq_set_o(A2,C4)
       => ( ord_less_eq_set_o(B4,C4)
         => ( ! [A3: $o] :
                ( member_o((A3),minus_minus_set_o(C4,A2))
               => ( aa_o_rat(G,(A3)) = one_one_rat ) )
           => ( ! [B2: $o] :
                  ( member_o((B2),minus_minus_set_o(C4,B4))
                 => ( aa_o_rat(Ha,(B2)) = one_one_rat ) )
             => ( ( aa_set_o_rat(aa_fun7302669049306738524_o_rat(groups2869687844427037835_o_rat,G),A2) = aa_set_o_rat(aa_fun7302669049306738524_o_rat(groups2869687844427037835_o_rat,Ha),B4) )
              <=> ( aa_set_o_rat(aa_fun7302669049306738524_o_rat(groups2869687844427037835_o_rat,G),C4) = aa_set_o_rat(aa_fun7302669049306738524_o_rat(groups2869687844427037835_o_rat,Ha),C4) ) ) ) ) ) ) ) ).

% prod.same_carrier
tff(fact_5931_prod_Osame__carrier,axiom,
    ! [C4: set_int,A2: set_int,B4: set_int,G: fun_int_rat,Ha: fun_int_rat] :
      ( finite_finite_int(C4)
     => ( ord_less_eq_set_int(A2,C4)
       => ( ord_less_eq_set_int(B4,C4)
         => ( ! [A3: int] :
                ( member_int(A3,minus_minus_set_int(C4,A2))
               => ( aa_int_rat(G,A3) = one_one_rat ) )
           => ( ! [B2: int] :
                  ( member_int(B2,minus_minus_set_int(C4,B4))
                 => ( aa_int_rat(Ha,B2) = one_one_rat ) )
             => ( ( aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,G),A2) = aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,Ha),B4) )
              <=> ( aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,G),C4) = aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,Ha),C4) ) ) ) ) ) ) ) ).

% prod.same_carrier
tff(fact_5932_prod_Osame__carrier,axiom,
    ! [C4: set_Code_integer,A2: set_Code_integer,B4: set_Code_integer,G: fun_Code_integer_rat,Ha: fun_Code_integer_rat] :
      ( finite6017078050557962740nteger(C4)
     => ( ord_le7084787975880047091nteger(A2,C4)
       => ( ord_le7084787975880047091nteger(B4,C4)
         => ( ! [A3: code_integer] :
                ( member_Code_integer(A3,minus_2355218937544613996nteger(C4,A2))
               => ( aa_Code_integer_rat(G,A3) = one_one_rat ) )
           => ( ! [B2: code_integer] :
                  ( member_Code_integer(B2,minus_2355218937544613996nteger(C4,B4))
                 => ( aa_Code_integer_rat(Ha,B2) = one_one_rat ) )
             => ( ( aa_set3519029356358064041er_rat(aa_fun5443269377828775384er_rat(groups2555765274223993564er_rat,G),A2) = aa_set3519029356358064041er_rat(aa_fun5443269377828775384er_rat(groups2555765274223993564er_rat,Ha),B4) )
              <=> ( aa_set3519029356358064041er_rat(aa_fun5443269377828775384er_rat(groups2555765274223993564er_rat,G),C4) = aa_set3519029356358064041er_rat(aa_fun5443269377828775384er_rat(groups2555765274223993564er_rat,Ha),C4) ) ) ) ) ) ) ) ).

% prod.same_carrier
tff(fact_5933_prod_Osame__carrier,axiom,
    ! [C4: set_o,A2: set_o,B4: set_o,G: fun_o_nat,Ha: fun_o_nat] :
      ( finite_finite_o(C4)
     => ( ord_less_eq_set_o(A2,C4)
       => ( ord_less_eq_set_o(B4,C4)
         => ( ! [A3: $o] :
                ( member_o((A3),minus_minus_set_o(C4,A2))
               => ( aa_o_nat(G,(A3)) = one_one_nat ) )
           => ( ! [B2: $o] :
                  ( member_o((B2),minus_minus_set_o(C4,B4))
                 => ( aa_o_nat(Ha,(B2)) = one_one_nat ) )
             => ( ( aa_set_o_nat(aa_fun8470299178418016604_o_nat(groups3504817904513533571_o_nat,G),A2) = aa_set_o_nat(aa_fun8470299178418016604_o_nat(groups3504817904513533571_o_nat,Ha),B4) )
              <=> ( aa_set_o_nat(aa_fun8470299178418016604_o_nat(groups3504817904513533571_o_nat,G),C4) = aa_set_o_nat(aa_fun8470299178418016604_o_nat(groups3504817904513533571_o_nat,Ha),C4) ) ) ) ) ) ) ) ).

% prod.same_carrier
tff(fact_5934_prod_Osame__carrierI,axiom,
    ! [C4: set_o,A2: set_o,B4: set_o,G: fun_o_Code_integer,Ha: fun_o_Code_integer] :
      ( finite_finite_o(C4)
     => ( ord_less_eq_set_o(A2,C4)
       => ( ord_less_eq_set_o(B4,C4)
         => ( ! [A3: $o] :
                ( member_o((A3),minus_minus_set_o(C4,A2))
               => ( aa_o_Code_integer(G,(A3)) = one_one_Code_integer ) )
           => ( ! [B2: $o] :
                  ( member_o((B2),minus_minus_set_o(C4,B4))
                 => ( aa_o_Code_integer(Ha,(B2)) = one_one_Code_integer ) )
             => ( ( aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,G),C4) = aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,Ha),C4) )
               => ( aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,G),A2) = aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,Ha),B4) ) ) ) ) ) ) ) ).

% prod.same_carrierI
tff(fact_5935_prod_Osame__carrierI,axiom,
    ! [C4: set_int,A2: set_int,B4: set_int,G: fun_int_Code_integer,Ha: fun_int_Code_integer] :
      ( finite_finite_int(C4)
     => ( ord_less_eq_set_int(A2,C4)
       => ( ord_less_eq_set_int(B4,C4)
         => ( ! [A3: int] :
                ( member_int(A3,minus_minus_set_int(C4,A2))
               => ( aa_int_Code_integer(G,A3) = one_one_Code_integer ) )
           => ( ! [B2: int] :
                  ( member_int(B2,minus_minus_set_int(C4,B4))
                 => ( aa_int_Code_integer(Ha,B2) = one_one_Code_integer ) )
             => ( ( aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,G),C4) = aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,Ha),C4) )
               => ( aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,G),A2) = aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,Ha),B4) ) ) ) ) ) ) ) ).

% prod.same_carrierI
tff(fact_5936_prod_Osame__carrierI,axiom,
    ! [C4: set_Code_integer,A2: set_Code_integer,B4: set_Code_integer,G: fun_Co8499238673658658103nteger,Ha: fun_Co8499238673658658103nteger] :
      ( finite6017078050557962740nteger(C4)
     => ( ord_le7084787975880047091nteger(A2,C4)
       => ( ord_le7084787975880047091nteger(B4,C4)
         => ( ! [A3: code_integer] :
                ( member_Code_integer(A3,minus_2355218937544613996nteger(C4,A2))
               => ( aa_Cod1783974652533396728nteger(G,A3) = one_one_Code_integer ) )
           => ( ! [B2: code_integer] :
                  ( member_Code_integer(B2,minus_2355218937544613996nteger(C4,B4))
                 => ( aa_Cod1783974652533396728nteger(Ha,B2) = one_one_Code_integer ) )
             => ( ( aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,G),C4) = aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,Ha),C4) )
               => ( aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,G),A2) = aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,Ha),B4) ) ) ) ) ) ) ) ).

% prod.same_carrierI
tff(fact_5937_prod_Osame__carrierI,axiom,
    ! [C4: set_o,A2: set_o,B4: set_o,G: fun_o_assn,Ha: fun_o_assn] :
      ( finite_finite_o(C4)
     => ( ord_less_eq_set_o(A2,C4)
       => ( ord_less_eq_set_o(B4,C4)
         => ( ! [A3: $o] :
                ( member_o((A3),minus_minus_set_o(C4,A2))
               => ( aa_o_assn(G,(A3)) = one_one_assn ) )
           => ( ! [B2: $o] :
                  ( member_o((B2),minus_minus_set_o(C4,B4))
                 => ( aa_o_assn(Ha,(B2)) = one_one_assn ) )
             => ( ( aa_set_o_assn(aa_fun1914167119812169564o_assn(groups5301882518646026715o_assn,G),C4) = aa_set_o_assn(aa_fun1914167119812169564o_assn(groups5301882518646026715o_assn,Ha),C4) )
               => ( aa_set_o_assn(aa_fun1914167119812169564o_assn(groups5301882518646026715o_assn,G),A2) = aa_set_o_assn(aa_fun1914167119812169564o_assn(groups5301882518646026715o_assn,Ha),B4) ) ) ) ) ) ) ) ).

% prod.same_carrierI
tff(fact_5938_prod_Osame__carrierI,axiom,
    ! [C4: set_int,A2: set_int,B4: set_int,G: fun_int_assn,Ha: fun_int_assn] :
      ( finite_finite_int(C4)
     => ( ord_less_eq_set_int(A2,C4)
       => ( ord_less_eq_set_int(B4,C4)
         => ( ! [A3: int] :
                ( member_int(A3,minus_minus_set_int(C4,A2))
               => ( aa_int_assn(G,A3) = one_one_assn ) )
           => ( ! [B2: int] :
                  ( member_int(B2,minus_minus_set_int(C4,B4))
                 => ( aa_int_assn(Ha,B2) = one_one_assn ) )
             => ( ( aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,G),C4) = aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,Ha),C4) )
               => ( aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,G),A2) = aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,Ha),B4) ) ) ) ) ) ) ) ).

% prod.same_carrierI
tff(fact_5939_prod_Osame__carrierI,axiom,
    ! [C4: set_Code_integer,A2: set_Code_integer,B4: set_Code_integer,G: fun_Co4490034186337852034r_assn,Ha: fun_Co4490034186337852034r_assn] :
      ( finite6017078050557962740nteger(C4)
     => ( ord_le7084787975880047091nteger(A2,C4)
       => ( ord_le7084787975880047091nteger(B4,C4)
         => ( ! [A3: code_integer] :
                ( member_Code_integer(A3,minus_2355218937544613996nteger(C4,A2))
               => ( aa_Code_integer_assn(G,A3) = one_one_assn ) )
           => ( ! [B2: code_integer] :
                  ( member_Code_integer(B2,minus_2355218937544613996nteger(C4,B4))
                 => ( aa_Code_integer_assn(Ha,B2) = one_one_assn ) )
             => ( ( aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,G),C4) = aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,Ha),C4) )
               => ( aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,G),A2) = aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,Ha),B4) ) ) ) ) ) ) ) ).

% prod.same_carrierI
tff(fact_5940_prod_Osame__carrierI,axiom,
    ! [C4: set_o,A2: set_o,B4: set_o,G: fun_o_rat,Ha: fun_o_rat] :
      ( finite_finite_o(C4)
     => ( ord_less_eq_set_o(A2,C4)
       => ( ord_less_eq_set_o(B4,C4)
         => ( ! [A3: $o] :
                ( member_o((A3),minus_minus_set_o(C4,A2))
               => ( aa_o_rat(G,(A3)) = one_one_rat ) )
           => ( ! [B2: $o] :
                  ( member_o((B2),minus_minus_set_o(C4,B4))
                 => ( aa_o_rat(Ha,(B2)) = one_one_rat ) )
             => ( ( aa_set_o_rat(aa_fun7302669049306738524_o_rat(groups2869687844427037835_o_rat,G),C4) = aa_set_o_rat(aa_fun7302669049306738524_o_rat(groups2869687844427037835_o_rat,Ha),C4) )
               => ( aa_set_o_rat(aa_fun7302669049306738524_o_rat(groups2869687844427037835_o_rat,G),A2) = aa_set_o_rat(aa_fun7302669049306738524_o_rat(groups2869687844427037835_o_rat,Ha),B4) ) ) ) ) ) ) ) ).

% prod.same_carrierI
tff(fact_5941_prod_Osame__carrierI,axiom,
    ! [C4: set_int,A2: set_int,B4: set_int,G: fun_int_rat,Ha: fun_int_rat] :
      ( finite_finite_int(C4)
     => ( ord_less_eq_set_int(A2,C4)
       => ( ord_less_eq_set_int(B4,C4)
         => ( ! [A3: int] :
                ( member_int(A3,minus_minus_set_int(C4,A2))
               => ( aa_int_rat(G,A3) = one_one_rat ) )
           => ( ! [B2: int] :
                  ( member_int(B2,minus_minus_set_int(C4,B4))
                 => ( aa_int_rat(Ha,B2) = one_one_rat ) )
             => ( ( aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,G),C4) = aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,Ha),C4) )
               => ( aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,G),A2) = aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,Ha),B4) ) ) ) ) ) ) ) ).

% prod.same_carrierI
tff(fact_5942_prod_Osame__carrierI,axiom,
    ! [C4: set_Code_integer,A2: set_Code_integer,B4: set_Code_integer,G: fun_Code_integer_rat,Ha: fun_Code_integer_rat] :
      ( finite6017078050557962740nteger(C4)
     => ( ord_le7084787975880047091nteger(A2,C4)
       => ( ord_le7084787975880047091nteger(B4,C4)
         => ( ! [A3: code_integer] :
                ( member_Code_integer(A3,minus_2355218937544613996nteger(C4,A2))
               => ( aa_Code_integer_rat(G,A3) = one_one_rat ) )
           => ( ! [B2: code_integer] :
                  ( member_Code_integer(B2,minus_2355218937544613996nteger(C4,B4))
                 => ( aa_Code_integer_rat(Ha,B2) = one_one_rat ) )
             => ( ( aa_set3519029356358064041er_rat(aa_fun5443269377828775384er_rat(groups2555765274223993564er_rat,G),C4) = aa_set3519029356358064041er_rat(aa_fun5443269377828775384er_rat(groups2555765274223993564er_rat,Ha),C4) )
               => ( aa_set3519029356358064041er_rat(aa_fun5443269377828775384er_rat(groups2555765274223993564er_rat,G),A2) = aa_set3519029356358064041er_rat(aa_fun5443269377828775384er_rat(groups2555765274223993564er_rat,Ha),B4) ) ) ) ) ) ) ) ).

% prod.same_carrierI
tff(fact_5943_prod_Osame__carrierI,axiom,
    ! [C4: set_o,A2: set_o,B4: set_o,G: fun_o_nat,Ha: fun_o_nat] :
      ( finite_finite_o(C4)
     => ( ord_less_eq_set_o(A2,C4)
       => ( ord_less_eq_set_o(B4,C4)
         => ( ! [A3: $o] :
                ( member_o((A3),minus_minus_set_o(C4,A2))
               => ( aa_o_nat(G,(A3)) = one_one_nat ) )
           => ( ! [B2: $o] :
                  ( member_o((B2),minus_minus_set_o(C4,B4))
                 => ( aa_o_nat(Ha,(B2)) = one_one_nat ) )
             => ( ( aa_set_o_nat(aa_fun8470299178418016604_o_nat(groups3504817904513533571_o_nat,G),C4) = aa_set_o_nat(aa_fun8470299178418016604_o_nat(groups3504817904513533571_o_nat,Ha),C4) )
               => ( aa_set_o_nat(aa_fun8470299178418016604_o_nat(groups3504817904513533571_o_nat,G),A2) = aa_set_o_nat(aa_fun8470299178418016604_o_nat(groups3504817904513533571_o_nat,Ha),B4) ) ) ) ) ) ) ) ).

% prod.same_carrierI
tff(fact_5944_prod_Omono__neutral__left,axiom,
    ! [T4: set_int,S2: set_int,G: fun_int_Code_integer] :
      ( finite_finite_int(T4)
     => ( ord_less_eq_set_int(S2,T4)
       => ( ! [X3: int] :
              ( member_int(X3,minus_minus_set_int(T4,S2))
             => ( aa_int_Code_integer(G,X3) = one_one_Code_integer ) )
         => ( aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,G),S2) = aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,G),T4) ) ) ) ) ).

% prod.mono_neutral_left
tff(fact_5945_prod_Omono__neutral__left,axiom,
    ! [T4: set_Code_integer,S2: set_Code_integer,G: fun_Co8499238673658658103nteger] :
      ( finite6017078050557962740nteger(T4)
     => ( ord_le7084787975880047091nteger(S2,T4)
       => ( ! [X3: code_integer] :
              ( member_Code_integer(X3,minus_2355218937544613996nteger(T4,S2))
             => ( aa_Cod1783974652533396728nteger(G,X3) = one_one_Code_integer ) )
         => ( aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,G),S2) = aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,G),T4) ) ) ) ) ).

% prod.mono_neutral_left
tff(fact_5946_prod_Omono__neutral__left,axiom,
    ! [T4: set_int,S2: set_int,G: fun_int_assn] :
      ( finite_finite_int(T4)
     => ( ord_less_eq_set_int(S2,T4)
       => ( ! [X3: int] :
              ( member_int(X3,minus_minus_set_int(T4,S2))
             => ( aa_int_assn(G,X3) = one_one_assn ) )
         => ( aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,G),S2) = aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,G),T4) ) ) ) ) ).

% prod.mono_neutral_left
tff(fact_5947_prod_Omono__neutral__left,axiom,
    ! [T4: set_Code_integer,S2: set_Code_integer,G: fun_Co4490034186337852034r_assn] :
      ( finite6017078050557962740nteger(T4)
     => ( ord_le7084787975880047091nteger(S2,T4)
       => ( ! [X3: code_integer] :
              ( member_Code_integer(X3,minus_2355218937544613996nteger(T4,S2))
             => ( aa_Code_integer_assn(G,X3) = one_one_assn ) )
         => ( aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,G),S2) = aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,G),T4) ) ) ) ) ).

% prod.mono_neutral_left
tff(fact_5948_prod_Omono__neutral__left,axiom,
    ! [T4: set_int,S2: set_int,G: fun_int_rat] :
      ( finite_finite_int(T4)
     => ( ord_less_eq_set_int(S2,T4)
       => ( ! [X3: int] :
              ( member_int(X3,minus_minus_set_int(T4,S2))
             => ( aa_int_rat(G,X3) = one_one_rat ) )
         => ( aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,G),S2) = aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,G),T4) ) ) ) ) ).

% prod.mono_neutral_left
tff(fact_5949_prod_Omono__neutral__left,axiom,
    ! [T4: set_Code_integer,S2: set_Code_integer,G: fun_Code_integer_rat] :
      ( finite6017078050557962740nteger(T4)
     => ( ord_le7084787975880047091nteger(S2,T4)
       => ( ! [X3: code_integer] :
              ( member_Code_integer(X3,minus_2355218937544613996nteger(T4,S2))
             => ( aa_Code_integer_rat(G,X3) = one_one_rat ) )
         => ( aa_set3519029356358064041er_rat(aa_fun5443269377828775384er_rat(groups2555765274223993564er_rat,G),S2) = aa_set3519029356358064041er_rat(aa_fun5443269377828775384er_rat(groups2555765274223993564er_rat,G),T4) ) ) ) ) ).

% prod.mono_neutral_left
tff(fact_5950_prod_Omono__neutral__left,axiom,
    ! [T4: set_int,S2: set_int,G: fun_int_nat] :
      ( finite_finite_int(T4)
     => ( ord_less_eq_set_int(S2,T4)
       => ( ! [X3: int] :
              ( member_int(X3,minus_minus_set_int(T4,S2))
             => ( aa_int_nat(G,X3) = one_one_nat ) )
         => ( groups1707563613775114915nt_nat(G,S2) = groups1707563613775114915nt_nat(G,T4) ) ) ) ) ).

% prod.mono_neutral_left
tff(fact_5951_prod_Omono__neutral__left,axiom,
    ! [T4: set_Code_integer,S2: set_Code_integer,G: fun_Code_integer_nat] :
      ( finite6017078050557962740nteger(T4)
     => ( ord_le7084787975880047091nteger(S2,T4)
       => ( ! [X3: code_integer] :
              ( member_Code_integer(X3,minus_2355218937544613996nteger(T4,S2))
             => ( aa_Code_integer_nat(G,X3) = one_one_nat ) )
         => ( groups3190895334310489300er_nat(G,S2) = groups3190895334310489300er_nat(G,T4) ) ) ) ) ).

% prod.mono_neutral_left
tff(fact_5952_prod_Omono__neutral__left,axiom,
    ! [T4: set_Code_integer,S2: set_Code_integer,G: fun_Code_integer_int] :
      ( finite6017078050557962740nteger(T4)
     => ( ord_le7084787975880047091nteger(S2,T4)
       => ( ! [X3: code_integer] :
              ( member_Code_integer(X3,minus_2355218937544613996nteger(T4,S2))
             => ( aa_Code_integer_int(G,X3) = one_one_int ) )
         => ( groups3188404863801439024er_int(G,S2) = groups3188404863801439024er_int(G,T4) ) ) ) ) ).

% prod.mono_neutral_left
tff(fact_5953_prod_Omono__neutral__left,axiom,
    ! [T4: set_nat,S2: set_nat,G: fun_nat_Code_integer] :
      ( finite_finite_nat(T4)
     => ( aa_set_nat_o(ord_less_eq_set_nat(S2),T4)
       => ( ! [X3: nat] :
              ( member_nat(X3,minus_minus_set_nat(T4,S2))
             => ( aa_nat_Code_integer(G,X3) = one_one_Code_integer ) )
         => ( groups3455450783089532116nteger(G,S2) = groups3455450783089532116nteger(G,T4) ) ) ) ) ).

% prod.mono_neutral_left
tff(fact_5954_prod_Omono__neutral__right,axiom,
    ! [T4: set_int,S2: set_int,G: fun_int_Code_integer] :
      ( finite_finite_int(T4)
     => ( ord_less_eq_set_int(S2,T4)
       => ( ! [X3: int] :
              ( member_int(X3,minus_minus_set_int(T4,S2))
             => ( aa_int_Code_integer(G,X3) = one_one_Code_integer ) )
         => ( aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,G),T4) = aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,G),S2) ) ) ) ) ).

% prod.mono_neutral_right
tff(fact_5955_prod_Omono__neutral__right,axiom,
    ! [T4: set_Code_integer,S2: set_Code_integer,G: fun_Co8499238673658658103nteger] :
      ( finite6017078050557962740nteger(T4)
     => ( ord_le7084787975880047091nteger(S2,T4)
       => ( ! [X3: code_integer] :
              ( member_Code_integer(X3,minus_2355218937544613996nteger(T4,S2))
             => ( aa_Cod1783974652533396728nteger(G,X3) = one_one_Code_integer ) )
         => ( aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,G),T4) = aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,G),S2) ) ) ) ) ).

% prod.mono_neutral_right
tff(fact_5956_prod_Omono__neutral__right,axiom,
    ! [T4: set_int,S2: set_int,G: fun_int_assn] :
      ( finite_finite_int(T4)
     => ( ord_less_eq_set_int(S2,T4)
       => ( ! [X3: int] :
              ( member_int(X3,minus_minus_set_int(T4,S2))
             => ( aa_int_assn(G,X3) = one_one_assn ) )
         => ( aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,G),T4) = aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,G),S2) ) ) ) ) ).

% prod.mono_neutral_right
tff(fact_5957_prod_Omono__neutral__right,axiom,
    ! [T4: set_Code_integer,S2: set_Code_integer,G: fun_Co4490034186337852034r_assn] :
      ( finite6017078050557962740nteger(T4)
     => ( ord_le7084787975880047091nteger(S2,T4)
       => ( ! [X3: code_integer] :
              ( member_Code_integer(X3,minus_2355218937544613996nteger(T4,S2))
             => ( aa_Code_integer_assn(G,X3) = one_one_assn ) )
         => ( aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,G),T4) = aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,G),S2) ) ) ) ) ).

% prod.mono_neutral_right
tff(fact_5958_prod_Omono__neutral__right,axiom,
    ! [T4: set_int,S2: set_int,G: fun_int_rat] :
      ( finite_finite_int(T4)
     => ( ord_less_eq_set_int(S2,T4)
       => ( ! [X3: int] :
              ( member_int(X3,minus_minus_set_int(T4,S2))
             => ( aa_int_rat(G,X3) = one_one_rat ) )
         => ( aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,G),T4) = aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,G),S2) ) ) ) ) ).

% prod.mono_neutral_right
tff(fact_5959_prod_Omono__neutral__right,axiom,
    ! [T4: set_Code_integer,S2: set_Code_integer,G: fun_Code_integer_rat] :
      ( finite6017078050557962740nteger(T4)
     => ( ord_le7084787975880047091nteger(S2,T4)
       => ( ! [X3: code_integer] :
              ( member_Code_integer(X3,minus_2355218937544613996nteger(T4,S2))
             => ( aa_Code_integer_rat(G,X3) = one_one_rat ) )
         => ( aa_set3519029356358064041er_rat(aa_fun5443269377828775384er_rat(groups2555765274223993564er_rat,G),T4) = aa_set3519029356358064041er_rat(aa_fun5443269377828775384er_rat(groups2555765274223993564er_rat,G),S2) ) ) ) ) ).

% prod.mono_neutral_right
tff(fact_5960_prod_Omono__neutral__right,axiom,
    ! [T4: set_int,S2: set_int,G: fun_int_nat] :
      ( finite_finite_int(T4)
     => ( ord_less_eq_set_int(S2,T4)
       => ( ! [X3: int] :
              ( member_int(X3,minus_minus_set_int(T4,S2))
             => ( aa_int_nat(G,X3) = one_one_nat ) )
         => ( groups1707563613775114915nt_nat(G,T4) = groups1707563613775114915nt_nat(G,S2) ) ) ) ) ).

% prod.mono_neutral_right
tff(fact_5961_prod_Omono__neutral__right,axiom,
    ! [T4: set_Code_integer,S2: set_Code_integer,G: fun_Code_integer_nat] :
      ( finite6017078050557962740nteger(T4)
     => ( ord_le7084787975880047091nteger(S2,T4)
       => ( ! [X3: code_integer] :
              ( member_Code_integer(X3,minus_2355218937544613996nteger(T4,S2))
             => ( aa_Code_integer_nat(G,X3) = one_one_nat ) )
         => ( groups3190895334310489300er_nat(G,T4) = groups3190895334310489300er_nat(G,S2) ) ) ) ) ).

% prod.mono_neutral_right
tff(fact_5962_prod_Omono__neutral__right,axiom,
    ! [T4: set_Code_integer,S2: set_Code_integer,G: fun_Code_integer_int] :
      ( finite6017078050557962740nteger(T4)
     => ( ord_le7084787975880047091nteger(S2,T4)
       => ( ! [X3: code_integer] :
              ( member_Code_integer(X3,minus_2355218937544613996nteger(T4,S2))
             => ( aa_Code_integer_int(G,X3) = one_one_int ) )
         => ( groups3188404863801439024er_int(G,T4) = groups3188404863801439024er_int(G,S2) ) ) ) ) ).

% prod.mono_neutral_right
tff(fact_5963_prod_Omono__neutral__right,axiom,
    ! [T4: set_nat,S2: set_nat,G: fun_nat_Code_integer] :
      ( finite_finite_nat(T4)
     => ( aa_set_nat_o(ord_less_eq_set_nat(S2),T4)
       => ( ! [X3: nat] :
              ( member_nat(X3,minus_minus_set_nat(T4,S2))
             => ( aa_nat_Code_integer(G,X3) = one_one_Code_integer ) )
         => ( groups3455450783089532116nteger(G,T4) = groups3455450783089532116nteger(G,S2) ) ) ) ) ).

% prod.mono_neutral_right
tff(fact_5964_prod_Omono__neutral__cong__left,axiom,
    ! [T4: set_o,S2: set_o,Ha: fun_o_Code_integer,G: fun_o_Code_integer] :
      ( finite_finite_o(T4)
     => ( ord_less_eq_set_o(S2,T4)
       => ( ! [X3: $o] :
              ( member_o((X3),minus_minus_set_o(T4,S2))
             => ( aa_o_Code_integer(Ha,(X3)) = one_one_Code_integer ) )
         => ( ! [X3: $o] :
                ( member_o((X3),S2)
               => ( aa_o_Code_integer(G,(X3)) = aa_o_Code_integer(Ha,(X3)) ) )
           => ( aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,G),S2) = aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,Ha),T4) ) ) ) ) ) ).

% prod.mono_neutral_cong_left
tff(fact_5965_prod_Omono__neutral__cong__left,axiom,
    ! [T4: set_int,S2: set_int,Ha: fun_int_Code_integer,G: fun_int_Code_integer] :
      ( finite_finite_int(T4)
     => ( ord_less_eq_set_int(S2,T4)
       => ( ! [X3: int] :
              ( member_int(X3,minus_minus_set_int(T4,S2))
             => ( aa_int_Code_integer(Ha,X3) = one_one_Code_integer ) )
         => ( ! [X3: int] :
                ( member_int(X3,S2)
               => ( aa_int_Code_integer(G,X3) = aa_int_Code_integer(Ha,X3) ) )
           => ( aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,G),S2) = aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,Ha),T4) ) ) ) ) ) ).

% prod.mono_neutral_cong_left
tff(fact_5966_prod_Omono__neutral__cong__left,axiom,
    ! [T4: set_Code_integer,S2: set_Code_integer,Ha: fun_Co8499238673658658103nteger,G: fun_Co8499238673658658103nteger] :
      ( finite6017078050557962740nteger(T4)
     => ( ord_le7084787975880047091nteger(S2,T4)
       => ( ! [X3: code_integer] :
              ( member_Code_integer(X3,minus_2355218937544613996nteger(T4,S2))
             => ( aa_Cod1783974652533396728nteger(Ha,X3) = one_one_Code_integer ) )
         => ( ! [X3: code_integer] :
                ( member_Code_integer(X3,S2)
               => ( aa_Cod1783974652533396728nteger(G,X3) = aa_Cod1783974652533396728nteger(Ha,X3) ) )
           => ( aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,G),S2) = aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,Ha),T4) ) ) ) ) ) ).

% prod.mono_neutral_cong_left
tff(fact_5967_prod_Omono__neutral__cong__left,axiom,
    ! [T4: set_o,S2: set_o,Ha: fun_o_assn,G: fun_o_assn] :
      ( finite_finite_o(T4)
     => ( ord_less_eq_set_o(S2,T4)
       => ( ! [X3: $o] :
              ( member_o((X3),minus_minus_set_o(T4,S2))
             => ( aa_o_assn(Ha,(X3)) = one_one_assn ) )
         => ( ! [X3: $o] :
                ( member_o((X3),S2)
               => ( aa_o_assn(G,(X3)) = aa_o_assn(Ha,(X3)) ) )
           => ( aa_set_o_assn(aa_fun1914167119812169564o_assn(groups5301882518646026715o_assn,G),S2) = aa_set_o_assn(aa_fun1914167119812169564o_assn(groups5301882518646026715o_assn,Ha),T4) ) ) ) ) ) ).

% prod.mono_neutral_cong_left
tff(fact_5968_prod_Omono__neutral__cong__left,axiom,
    ! [T4: set_int,S2: set_int,Ha: fun_int_assn,G: fun_int_assn] :
      ( finite_finite_int(T4)
     => ( ord_less_eq_set_int(S2,T4)
       => ( ! [X3: int] :
              ( member_int(X3,minus_minus_set_int(T4,S2))
             => ( aa_int_assn(Ha,X3) = one_one_assn ) )
         => ( ! [X3: int] :
                ( member_int(X3,S2)
               => ( aa_int_assn(G,X3) = aa_int_assn(Ha,X3) ) )
           => ( aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,G),S2) = aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,Ha),T4) ) ) ) ) ) ).

% prod.mono_neutral_cong_left
tff(fact_5969_prod_Omono__neutral__cong__left,axiom,
    ! [T4: set_Code_integer,S2: set_Code_integer,Ha: fun_Co4490034186337852034r_assn,G: fun_Co4490034186337852034r_assn] :
      ( finite6017078050557962740nteger(T4)
     => ( ord_le7084787975880047091nteger(S2,T4)
       => ( ! [X3: code_integer] :
              ( member_Code_integer(X3,minus_2355218937544613996nteger(T4,S2))
             => ( aa_Code_integer_assn(Ha,X3) = one_one_assn ) )
         => ( ! [X3: code_integer] :
                ( member_Code_integer(X3,S2)
               => ( aa_Code_integer_assn(G,X3) = aa_Code_integer_assn(Ha,X3) ) )
           => ( aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,G),S2) = aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,Ha),T4) ) ) ) ) ) ).

% prod.mono_neutral_cong_left
tff(fact_5970_prod_Omono__neutral__cong__left,axiom,
    ! [T4: set_o,S2: set_o,Ha: fun_o_rat,G: fun_o_rat] :
      ( finite_finite_o(T4)
     => ( ord_less_eq_set_o(S2,T4)
       => ( ! [X3: $o] :
              ( member_o((X3),minus_minus_set_o(T4,S2))
             => ( aa_o_rat(Ha,(X3)) = one_one_rat ) )
         => ( ! [X3: $o] :
                ( member_o((X3),S2)
               => ( aa_o_rat(G,(X3)) = aa_o_rat(Ha,(X3)) ) )
           => ( aa_set_o_rat(aa_fun7302669049306738524_o_rat(groups2869687844427037835_o_rat,G),S2) = aa_set_o_rat(aa_fun7302669049306738524_o_rat(groups2869687844427037835_o_rat,Ha),T4) ) ) ) ) ) ).

% prod.mono_neutral_cong_left
tff(fact_5971_prod_Omono__neutral__cong__left,axiom,
    ! [T4: set_int,S2: set_int,Ha: fun_int_rat,G: fun_int_rat] :
      ( finite_finite_int(T4)
     => ( ord_less_eq_set_int(S2,T4)
       => ( ! [X3: int] :
              ( member_int(X3,minus_minus_set_int(T4,S2))
             => ( aa_int_rat(Ha,X3) = one_one_rat ) )
         => ( ! [X3: int] :
                ( member_int(X3,S2)
               => ( aa_int_rat(G,X3) = aa_int_rat(Ha,X3) ) )
           => ( aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,G),S2) = aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,Ha),T4) ) ) ) ) ) ).

% prod.mono_neutral_cong_left
tff(fact_5972_prod_Omono__neutral__cong__left,axiom,
    ! [T4: set_Code_integer,S2: set_Code_integer,Ha: fun_Code_integer_rat,G: fun_Code_integer_rat] :
      ( finite6017078050557962740nteger(T4)
     => ( ord_le7084787975880047091nteger(S2,T4)
       => ( ! [X3: code_integer] :
              ( member_Code_integer(X3,minus_2355218937544613996nteger(T4,S2))
             => ( aa_Code_integer_rat(Ha,X3) = one_one_rat ) )
         => ( ! [X3: code_integer] :
                ( member_Code_integer(X3,S2)
               => ( aa_Code_integer_rat(G,X3) = aa_Code_integer_rat(Ha,X3) ) )
           => ( aa_set3519029356358064041er_rat(aa_fun5443269377828775384er_rat(groups2555765274223993564er_rat,G),S2) = aa_set3519029356358064041er_rat(aa_fun5443269377828775384er_rat(groups2555765274223993564er_rat,Ha),T4) ) ) ) ) ) ).

% prod.mono_neutral_cong_left
tff(fact_5973_prod_Omono__neutral__cong__left,axiom,
    ! [T4: set_o,S2: set_o,Ha: fun_o_nat,G: fun_o_nat] :
      ( finite_finite_o(T4)
     => ( ord_less_eq_set_o(S2,T4)
       => ( ! [X3: $o] :
              ( member_o((X3),minus_minus_set_o(T4,S2))
             => ( aa_o_nat(Ha,(X3)) = one_one_nat ) )
         => ( ! [X3: $o] :
                ( member_o((X3),S2)
               => ( aa_o_nat(G,(X3)) = aa_o_nat(Ha,(X3)) ) )
           => ( aa_set_o_nat(aa_fun8470299178418016604_o_nat(groups3504817904513533571_o_nat,G),S2) = aa_set_o_nat(aa_fun8470299178418016604_o_nat(groups3504817904513533571_o_nat,Ha),T4) ) ) ) ) ) ).

% prod.mono_neutral_cong_left
tff(fact_5974_prod_Omono__neutral__cong__right,axiom,
    ! [T4: set_o,S2: set_o,G: fun_o_Code_integer,Ha: fun_o_Code_integer] :
      ( finite_finite_o(T4)
     => ( ord_less_eq_set_o(S2,T4)
       => ( ! [X3: $o] :
              ( member_o((X3),minus_minus_set_o(T4,S2))
             => ( aa_o_Code_integer(G,(X3)) = one_one_Code_integer ) )
         => ( ! [X3: $o] :
                ( member_o((X3),S2)
               => ( aa_o_Code_integer(G,(X3)) = aa_o_Code_integer(Ha,(X3)) ) )
           => ( aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,G),T4) = aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,Ha),S2) ) ) ) ) ) ).

% prod.mono_neutral_cong_right
tff(fact_5975_prod_Omono__neutral__cong__right,axiom,
    ! [T4: set_int,S2: set_int,G: fun_int_Code_integer,Ha: fun_int_Code_integer] :
      ( finite_finite_int(T4)
     => ( ord_less_eq_set_int(S2,T4)
       => ( ! [X3: int] :
              ( member_int(X3,minus_minus_set_int(T4,S2))
             => ( aa_int_Code_integer(G,X3) = one_one_Code_integer ) )
         => ( ! [X3: int] :
                ( member_int(X3,S2)
               => ( aa_int_Code_integer(G,X3) = aa_int_Code_integer(Ha,X3) ) )
           => ( aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,G),T4) = aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,Ha),S2) ) ) ) ) ) ).

% prod.mono_neutral_cong_right
tff(fact_5976_prod_Omono__neutral__cong__right,axiom,
    ! [T4: set_Code_integer,S2: set_Code_integer,G: fun_Co8499238673658658103nteger,Ha: fun_Co8499238673658658103nteger] :
      ( finite6017078050557962740nteger(T4)
     => ( ord_le7084787975880047091nteger(S2,T4)
       => ( ! [X3: code_integer] :
              ( member_Code_integer(X3,minus_2355218937544613996nteger(T4,S2))
             => ( aa_Cod1783974652533396728nteger(G,X3) = one_one_Code_integer ) )
         => ( ! [X3: code_integer] :
                ( member_Code_integer(X3,S2)
               => ( aa_Cod1783974652533396728nteger(G,X3) = aa_Cod1783974652533396728nteger(Ha,X3) ) )
           => ( aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,G),T4) = aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,Ha),S2) ) ) ) ) ) ).

% prod.mono_neutral_cong_right
tff(fact_5977_prod_Omono__neutral__cong__right,axiom,
    ! [T4: set_o,S2: set_o,G: fun_o_assn,Ha: fun_o_assn] :
      ( finite_finite_o(T4)
     => ( ord_less_eq_set_o(S2,T4)
       => ( ! [X3: $o] :
              ( member_o((X3),minus_minus_set_o(T4,S2))
             => ( aa_o_assn(G,(X3)) = one_one_assn ) )
         => ( ! [X3: $o] :
                ( member_o((X3),S2)
               => ( aa_o_assn(G,(X3)) = aa_o_assn(Ha,(X3)) ) )
           => ( aa_set_o_assn(aa_fun1914167119812169564o_assn(groups5301882518646026715o_assn,G),T4) = aa_set_o_assn(aa_fun1914167119812169564o_assn(groups5301882518646026715o_assn,Ha),S2) ) ) ) ) ) ).

% prod.mono_neutral_cong_right
tff(fact_5978_prod_Omono__neutral__cong__right,axiom,
    ! [T4: set_int,S2: set_int,G: fun_int_assn,Ha: fun_int_assn] :
      ( finite_finite_int(T4)
     => ( ord_less_eq_set_int(S2,T4)
       => ( ! [X3: int] :
              ( member_int(X3,minus_minus_set_int(T4,S2))
             => ( aa_int_assn(G,X3) = one_one_assn ) )
         => ( ! [X3: int] :
                ( member_int(X3,S2)
               => ( aa_int_assn(G,X3) = aa_int_assn(Ha,X3) ) )
           => ( aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,G),T4) = aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,Ha),S2) ) ) ) ) ) ).

% prod.mono_neutral_cong_right
tff(fact_5979_prod_Omono__neutral__cong__right,axiom,
    ! [T4: set_Code_integer,S2: set_Code_integer,G: fun_Co4490034186337852034r_assn,Ha: fun_Co4490034186337852034r_assn] :
      ( finite6017078050557962740nteger(T4)
     => ( ord_le7084787975880047091nteger(S2,T4)
       => ( ! [X3: code_integer] :
              ( member_Code_integer(X3,minus_2355218937544613996nteger(T4,S2))
             => ( aa_Code_integer_assn(G,X3) = one_one_assn ) )
         => ( ! [X3: code_integer] :
                ( member_Code_integer(X3,S2)
               => ( aa_Code_integer_assn(G,X3) = aa_Code_integer_assn(Ha,X3) ) )
           => ( aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,G),T4) = aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,Ha),S2) ) ) ) ) ) ).

% prod.mono_neutral_cong_right
tff(fact_5980_prod_Omono__neutral__cong__right,axiom,
    ! [T4: set_o,S2: set_o,G: fun_o_rat,Ha: fun_o_rat] :
      ( finite_finite_o(T4)
     => ( ord_less_eq_set_o(S2,T4)
       => ( ! [X3: $o] :
              ( member_o((X3),minus_minus_set_o(T4,S2))
             => ( aa_o_rat(G,(X3)) = one_one_rat ) )
         => ( ! [X3: $o] :
                ( member_o((X3),S2)
               => ( aa_o_rat(G,(X3)) = aa_o_rat(Ha,(X3)) ) )
           => ( aa_set_o_rat(aa_fun7302669049306738524_o_rat(groups2869687844427037835_o_rat,G),T4) = aa_set_o_rat(aa_fun7302669049306738524_o_rat(groups2869687844427037835_o_rat,Ha),S2) ) ) ) ) ) ).

% prod.mono_neutral_cong_right
tff(fact_5981_prod_Omono__neutral__cong__right,axiom,
    ! [T4: set_int,S2: set_int,G: fun_int_rat,Ha: fun_int_rat] :
      ( finite_finite_int(T4)
     => ( ord_less_eq_set_int(S2,T4)
       => ( ! [X3: int] :
              ( member_int(X3,minus_minus_set_int(T4,S2))
             => ( aa_int_rat(G,X3) = one_one_rat ) )
         => ( ! [X3: int] :
                ( member_int(X3,S2)
               => ( aa_int_rat(G,X3) = aa_int_rat(Ha,X3) ) )
           => ( aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,G),T4) = aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,Ha),S2) ) ) ) ) ) ).

% prod.mono_neutral_cong_right
tff(fact_5982_prod_Omono__neutral__cong__right,axiom,
    ! [T4: set_Code_integer,S2: set_Code_integer,G: fun_Code_integer_rat,Ha: fun_Code_integer_rat] :
      ( finite6017078050557962740nteger(T4)
     => ( ord_le7084787975880047091nteger(S2,T4)
       => ( ! [X3: code_integer] :
              ( member_Code_integer(X3,minus_2355218937544613996nteger(T4,S2))
             => ( aa_Code_integer_rat(G,X3) = one_one_rat ) )
         => ( ! [X3: code_integer] :
                ( member_Code_integer(X3,S2)
               => ( aa_Code_integer_rat(G,X3) = aa_Code_integer_rat(Ha,X3) ) )
           => ( aa_set3519029356358064041er_rat(aa_fun5443269377828775384er_rat(groups2555765274223993564er_rat,G),T4) = aa_set3519029356358064041er_rat(aa_fun5443269377828775384er_rat(groups2555765274223993564er_rat,Ha),S2) ) ) ) ) ) ).

% prod.mono_neutral_cong_right
tff(fact_5983_prod_Omono__neutral__cong__right,axiom,
    ! [T4: set_o,S2: set_o,G: fun_o_nat,Ha: fun_o_nat] :
      ( finite_finite_o(T4)
     => ( ord_less_eq_set_o(S2,T4)
       => ( ! [X3: $o] :
              ( member_o((X3),minus_minus_set_o(T4,S2))
             => ( aa_o_nat(G,(X3)) = one_one_nat ) )
         => ( ! [X3: $o] :
                ( member_o((X3),S2)
               => ( aa_o_nat(G,(X3)) = aa_o_nat(Ha,(X3)) ) )
           => ( aa_set_o_nat(aa_fun8470299178418016604_o_nat(groups3504817904513533571_o_nat,G),T4) = aa_set_o_nat(aa_fun8470299178418016604_o_nat(groups3504817904513533571_o_nat,Ha),S2) ) ) ) ) ) ).

% prod.mono_neutral_cong_right
tff(fact_5984_atLeastLessThanSuc,axiom,
    ! [M: nat,N2: nat] :
      aa_nat_set_nat(set_or4665077453230672383an_nat(M),aa_nat_nat(suc,N2)) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2),insert_nat(N2,aa_nat_set_nat(set_or4665077453230672383an_nat(M),N2)),bot_bot_set_nat) ).

% atLeastLessThanSuc
tff(fact_5985_Option_Othese__def,axiom,
    ! [A2: set_op3940070208846178154it_nat] : these_6645423997822192641it_nat(A2) = image_5549452628634654015it_nat(the_Pr5856008525237892824it_nat,collec8141831914148684149it_nat(aTP_Lamm_nu(A2))) ).

% Option.these_def
tff(fact_5986_Option_Othese__def,axiom,
    ! [A2: set_option_num] : these_num(A2) = image_option_num_num(the_num,collect_option_num(aTP_Lamm_nv(A2))) ).

% Option.these_def
tff(fact_5987_Option_Othese__def,axiom,
    ! [A2: set_op239864471688321678it_nat] : these_3407724651694999947it_nat(A2) = image_1237920015125996135it_nat(the_Pr7776125533777466484it_nat,collec5742531119322951597it_nat(aTP_Lamm_nw(A2))) ).

% Option.these_def
tff(fact_5988_atLeast0__atMost__Suc__eq__insert__0,axiom,
    ! [N2: nat] : aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),aa_nat_nat(suc,N2)) = insert_nat(zero_zero_nat,aa_set_nat_set_nat(image_nat_nat(suc),aa_nat_set_nat(set_or1269000886237332187st_nat(zero_zero_nat),N2))) ).

% atLeast0_atMost_Suc_eq_insert_0
tff(fact_5989_atLeast0__lessThan__Suc__eq__insert__0,axiom,
    ! [N2: nat] : aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),aa_nat_nat(suc,N2)) = insert_nat(zero_zero_nat,aa_set_nat_set_nat(image_nat_nat(suc),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2))) ).

% atLeast0_lessThan_Suc_eq_insert_0
tff(fact_5990_atMost__Suc__eq__insert__0,axiom,
    ! [N2: nat] : aa_nat_set_nat(set_ord_atMost_nat,aa_nat_nat(suc,N2)) = insert_nat(zero_zero_nat,aa_set_nat_set_nat(image_nat_nat(suc),aa_nat_set_nat(set_ord_atMost_nat,N2))) ).

% atMost_Suc_eq_insert_0
tff(fact_5991_lessThan__Suc__eq__insert__0,axiom,
    ! [N2: nat] : aa_nat_set_nat(set_ord_lessThan_nat,aa_nat_nat(suc,N2)) = insert_nat(zero_zero_nat,aa_set_nat_set_nat(image_nat_nat(suc),aa_nat_set_nat(set_ord_lessThan_nat,N2))) ).

% lessThan_Suc_eq_insert_0
tff(fact_5992_card__2__iff,axiom,
    ! [S2: set_Product_unit] :
      ( ( finite410649719033368117t_unit(S2) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)) )
    <=> ? [X4: product_unit,Y3: product_unit] :
          ( ( S2 = insert_Product_unit(X4,insert_Product_unit(Y3,bot_bo3957492148770167129t_unit)) )
          & ( X4 != Y3 ) ) ) ).

% card_2_iff
tff(fact_5993_card__2__iff,axiom,
    ! [S2: set_list_nat] :
      ( ( finite_card_list_nat(S2) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)) )
    <=> ? [X4: list_nat,Y3: list_nat] :
          ( ( S2 = insert_list_nat(X4,insert_list_nat(Y3,bot_bot_set_list_nat)) )
          & ( X4 != Y3 ) ) ) ).

% card_2_iff
tff(fact_5994_card__2__iff,axiom,
    ! [S2: set_Pr4329608150637261639at_nat] :
      ( ( finite3771342082235030671at_nat(S2) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)) )
    <=> ? [X4: produc3843707927480180839at_nat,Y3: produc3843707927480180839at_nat] :
          ( ( S2 = aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(X4),aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(Y3),bot_bo228742789529271731at_nat)) )
          & ( X4 != Y3 ) ) ) ).

% card_2_iff
tff(fact_5995_card__2__iff,axiom,
    ! [S2: set_Pr1261947904930325089at_nat] :
      ( ( aa_set4749074711808745205at_nat(finite711546835091564841at_nat,S2) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)) )
    <=> ? [X4: product_prod_nat_nat,Y3: product_prod_nat_nat] :
          ( ( S2 = aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(X4),aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(Y3),bot_bo2099793752762293965at_nat)) )
          & ( X4 != Y3 ) ) ) ).

% card_2_iff
tff(fact_5996_card__2__iff,axiom,
    ! [S2: set_o] :
      ( ( finite_card_o(S2) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)) )
    <=> ? [X4: $o,Y3: $o] :
          ( ( S2 = insert_o((X4),insert_o((Y3),bot_bot_set_o)) )
          & ~ ( (X4)
            <=> (Y3) ) ) ) ).

% card_2_iff
tff(fact_5997_card__2__iff,axiom,
    ! [S2: set_nat] :
      ( ( aa_set_nat_nat(finite_card_nat,S2) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)) )
    <=> ? [X4: nat,Y3: nat] :
          ( ( S2 = insert_nat(X4,insert_nat(Y3,bot_bot_set_nat)) )
          & ( X4 != Y3 ) ) ) ).

% card_2_iff
tff(fact_5998_card__2__iff,axiom,
    ! [S2: set_int] :
      ( ( finite_card_int(S2) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)) )
    <=> ? [X4: int,Y3: int] :
          ( ( S2 = insert_int(X4,insert_int(Y3,bot_bot_set_int)) )
          & ( X4 != Y3 ) ) ) ).

% card_2_iff
tff(fact_5999_card__3__iff,axiom,
    ! [S2: set_Product_unit] :
      ( ( finite410649719033368117t_unit(S2) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,one)) )
    <=> ? [X4: product_unit,Y3: product_unit,Z3: product_unit] :
          ( ( S2 = insert_Product_unit(X4,insert_Product_unit(Y3,insert_Product_unit(Z3,bot_bo3957492148770167129t_unit))) )
          & ( X4 != Y3 )
          & ( Y3 != Z3 )
          & ( X4 != Z3 ) ) ) ).

% card_3_iff
tff(fact_6000_card__3__iff,axiom,
    ! [S2: set_list_nat] :
      ( ( finite_card_list_nat(S2) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,one)) )
    <=> ? [X4: list_nat,Y3: list_nat,Z3: list_nat] :
          ( ( S2 = insert_list_nat(X4,insert_list_nat(Y3,insert_list_nat(Z3,bot_bot_set_list_nat))) )
          & ( X4 != Y3 )
          & ( Y3 != Z3 )
          & ( X4 != Z3 ) ) ) ).

% card_3_iff
tff(fact_6001_card__3__iff,axiom,
    ! [S2: set_Pr4329608150637261639at_nat] :
      ( ( finite3771342082235030671at_nat(S2) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,one)) )
    <=> ? [X4: produc3843707927480180839at_nat,Y3: produc3843707927480180839at_nat,Z3: produc3843707927480180839at_nat] :
          ( ( S2 = aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(X4),aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(Y3),aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(Z3),bot_bo228742789529271731at_nat))) )
          & ( X4 != Y3 )
          & ( Y3 != Z3 )
          & ( X4 != Z3 ) ) ) ).

% card_3_iff
tff(fact_6002_card__3__iff,axiom,
    ! [S2: set_Pr1261947904930325089at_nat] :
      ( ( aa_set4749074711808745205at_nat(finite711546835091564841at_nat,S2) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,one)) )
    <=> ? [X4: product_prod_nat_nat,Y3: product_prod_nat_nat,Z3: product_prod_nat_nat] :
          ( ( S2 = aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(X4),aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(Y3),aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(Z3),bot_bo2099793752762293965at_nat))) )
          & ( X4 != Y3 )
          & ( Y3 != Z3 )
          & ( X4 != Z3 ) ) ) ).

% card_3_iff
tff(fact_6003_card__3__iff,axiom,
    ! [S2: set_o] :
      ( ( finite_card_o(S2) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,one)) )
    <=> ? [X4: $o,Y3: $o,Z3: $o] :
          ( ( S2 = insert_o((X4),insert_o((Y3),insert_o((Z3),bot_bot_set_o))) )
          & ~ ( (X4)
            <=> (Y3) )
          & ~ ( (Y3)
            <=> (Z3) )
          & ~ ( (X4)
            <=> (Z3) ) ) ) ).

% card_3_iff
tff(fact_6004_card__3__iff,axiom,
    ! [S2: set_nat] :
      ( ( aa_set_nat_nat(finite_card_nat,S2) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,one)) )
    <=> ? [X4: nat,Y3: nat,Z3: nat] :
          ( ( S2 = insert_nat(X4,insert_nat(Y3,insert_nat(Z3,bot_bot_set_nat))) )
          & ( X4 != Y3 )
          & ( Y3 != Z3 )
          & ( X4 != Z3 ) ) ) ).

% card_3_iff
tff(fact_6005_card__3__iff,axiom,
    ! [S2: set_int] :
      ( ( finite_card_int(S2) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit1,one)) )
    <=> ? [X4: int,Y3: int,Z3: int] :
          ( ( S2 = insert_int(X4,insert_int(Y3,insert_int(Z3,bot_bot_set_int))) )
          & ( X4 != Y3 )
          & ( Y3 != Z3 )
          & ( X4 != Z3 ) ) ) ).

% card_3_iff
tff(fact_6006_sum__image__le,axiom,
    ! [I4: set_num,G: fun_Co8499238673658658103nteger,F: fun_num_Code_integer] :
      ( finite_finite_num(I4)
     => ( ! [I2: num] :
            ( member_num(I2,I4)
           => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(G,aa_num_Code_integer(F,I2))) )
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_set8546232603906849326nteger(groups879477027807139574nteger(G),image_8379761247532268670nteger(F,I4))),groups5442708359310287027nteger(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,G),F),I4)) ) ) ).

% sum_image_le
tff(fact_6007_sum__image__le,axiom,
    ! [I4: set_nat,G: fun_Co8499238673658658103nteger,F: fun_nat_Code_integer] :
      ( finite_finite_nat(I4)
     => ( ! [I2: nat] :
            ( member_nat(I2,I4)
           => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_Cod1783974652533396728nteger(G,aa_nat_Code_integer(F,I2))) )
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_set8546232603906849326nteger(groups879477027807139574nteger(G),image_1215581382706833972nteger(F,I4))),groups7501900531339628137nteger(comp_C6974050283906349679er_nat(G,F),I4)) ) ) ).

% sum_image_le
tff(fact_6008_sum__image__le,axiom,
    ! [I4: set_nat,G: fun_nat_Code_integer,F: fun_nat_nat] :
      ( finite_finite_nat(I4)
     => ( ! [I2: nat] :
            ( member_nat(I2,I4)
           => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_nat_Code_integer(G,aa_nat_nat(F,I2))) )
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,groups7501900531339628137nteger(G,aa_set_nat_set_nat(image_nat_nat(F),I4))),groups7501900531339628137nteger(comp_n3898172953802868194er_nat(G,F),I4)) ) ) ).

% sum_image_le
tff(fact_6009_sum__image__le,axiom,
    ! [I4: set_nat,G: fun_int_Code_integer,F: fun_nat_int] :
      ( finite_finite_nat(I4)
     => ( ! [I2: nat] :
            ( member_nat(I2,I4)
           => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_int_Code_integer(G,aa_nat_int(F,I2))) )
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,groups7873554091576472773nteger(G,image_nat_int(F,I4))),groups7501900531339628137nteger(comp_i1588355021709917246er_nat(G,F),I4)) ) ) ).

% sum_image_le
tff(fact_6010_sum__image__le,axiom,
    ! [I4: set_int,G: fun_int_Code_integer,F: fun_int_int] :
      ( finite_finite_int(I4)
     => ( ! [I2: int] :
            ( member_int(I2,I4)
           => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_int_Code_integer(G,aa_int_int(F,I2))) )
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,groups7873554091576472773nteger(G,aa_set_int_set_int(image_int_int(F),I4))),groups7873554091576472773nteger(comp_i1585864551200866970er_int(G,F),I4)) ) ) ).

% sum_image_le
tff(fact_6011_sum__image__le,axiom,
    ! [I4: set_nat,G: fun_Code_integer_rat,F: fun_nat_Code_integer] :
      ( finite_finite_nat(I4)
     => ( ! [I2: nat] :
            ( member_nat(I2,I4)
           => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),aa_Code_integer_rat(G,aa_nat_Code_integer(F,I2))) )
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,groups6602215022474089585er_rat(G,image_1215581382706833972nteger(F,I4))),groups2906978787729119204at_rat(comp_C3733001951728184298at_nat(G,F),I4)) ) ) ).

% sum_image_le
tff(fact_6012_sum__image__le,axiom,
    ! [I4: set_nat,G: fun_nat_rat,F: fun_nat_nat] :
      ( finite_finite_nat(I4)
     => ( ! [I2: nat] :
            ( member_nat(I2,I4)
           => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),aa_nat_rat(G,aa_nat_nat(F,I2))) )
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,groups2906978787729119204at_rat(G,aa_set_nat_set_nat(image_nat_nat(F),I4))),groups2906978787729119204at_rat(comp_nat_rat_nat(G,F),I4)) ) ) ).

% sum_image_le
tff(fact_6013_sum__image__le,axiom,
    ! [I4: set_nat,G: fun_int_rat,F: fun_nat_int] :
      ( finite_finite_nat(I4)
     => ( ! [I2: nat] :
            ( member_nat(I2,I4)
           => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),aa_int_rat(G,aa_nat_int(F,I2))) )
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,groups3906332499630173760nt_rat(G,image_nat_int(F,I4))),groups2906978787729119204at_rat(comp_int_rat_nat(G,F),I4)) ) ) ).

% sum_image_le
tff(fact_6014_sum__image__le,axiom,
    ! [I4: set_int,G: fun_int_rat,F: fun_int_int] :
      ( finite_finite_int(I4)
     => ( ! [I2: int] :
            ( member_int(I2,I4)
           => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),aa_int_rat(G,aa_int_int(F,I2))) )
       => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,groups3906332499630173760nt_rat(G,aa_set_int_set_int(image_int_int(F),I4))),groups3906332499630173760nt_rat(comp_int_rat_int(G,F),I4)) ) ) ).

% sum_image_le
tff(fact_6015_sum__image__le,axiom,
    ! [I4: set_int,G: fun_int_nat,F: fun_int_int] :
      ( finite_finite_int(I4)
     => ( ! [I2: int] :
            ( member_int(I2,I4)
           => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),aa_int_nat(G,aa_int_int(F,I2))) )
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,groups4541462559716669496nt_nat(G,aa_set_int_set_int(image_int_int(F),I4))),groups4541462559716669496nt_nat(comp_int_nat_int(G,F),I4)) ) ) ).

% sum_image_le
tff(fact_6016_sum_Oremove,axiom,
    ! [A2: set_Code_integer,X2: code_integer,G: fun_Code_integer_rat] :
      ( finite6017078050557962740nteger(A2)
     => ( member_Code_integer(X2,A2)
       => ( groups6602215022474089585er_rat(G,A2) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_Code_integer_rat(G,X2)),groups6602215022474089585er_rat(G,minus_2355218937544613996nteger(A2,insert_Code_integer(X2,bot_bo3990330152332043303nteger)))) ) ) ) ).

% sum.remove
tff(fact_6017_sum_Oremove,axiom,
    ! [A2: set_Code_integer,X2: code_integer,G: fun_Code_integer_nat] :
      ( finite6017078050557962740nteger(A2)
     => ( member_Code_integer(X2,A2)
       => ( groups7237345082560585321er_nat(G,A2) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_Code_integer_nat(G,X2)),groups7237345082560585321er_nat(G,minus_2355218937544613996nteger(A2,insert_Code_integer(X2,bot_bo3990330152332043303nteger)))) ) ) ) ).

% sum.remove
tff(fact_6018_sum_Oremove,axiom,
    ! [A2: set_Code_integer,X2: code_integer,G: fun_Code_integer_int] :
      ( finite6017078050557962740nteger(A2)
     => ( member_Code_integer(X2,A2)
       => ( groups7234854612051535045er_int(G,A2) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_Code_integer_int(G,X2)),groups7234854612051535045er_int(G,minus_2355218937544613996nteger(A2,insert_Code_integer(X2,bot_bo3990330152332043303nteger)))) ) ) ) ).

% sum.remove
tff(fact_6019_sum_Oremove,axiom,
    ! [A2: set_o,X2: $o,G: fun_o_rat] :
      ( finite_finite_o(A2)
     => ( member_o((X2),A2)
       => ( groups7872700643590313910_o_rat(G,A2) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_o_rat(G,(X2))),groups7872700643590313910_o_rat(G,minus_minus_set_o(A2,insert_o((X2),bot_bot_set_o)))) ) ) ) ).

% sum.remove
tff(fact_6020_sum_Oremove,axiom,
    ! [A2: set_o,X2: $o,G: fun_o_nat] :
      ( finite_finite_o(A2)
     => ( member_o((X2),A2)
       => ( groups8507830703676809646_o_nat(G,A2) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_o_nat(G,(X2))),groups8507830703676809646_o_nat(G,minus_minus_set_o(A2,insert_o((X2),bot_bot_set_o)))) ) ) ) ).

% sum.remove
tff(fact_6021_sum_Oremove,axiom,
    ! [A2: set_o,X2: $o,G: fun_o_int] :
      ( finite_finite_o(A2)
     => ( member_o((X2),A2)
       => ( groups8505340233167759370_o_int(G,A2) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_o_int(G,(X2))),groups8505340233167759370_o_int(G,minus_minus_set_o(A2,insert_o((X2),bot_bot_set_o)))) ) ) ) ).

% sum.remove
tff(fact_6022_sum_Oremove,axiom,
    ! [A2: set_int,X2: int,G: fun_int_rat] :
      ( finite_finite_int(A2)
     => ( member_int(X2,A2)
       => ( groups3906332499630173760nt_rat(G,A2) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_int_rat(G,X2)),groups3906332499630173760nt_rat(G,minus_minus_set_int(A2,insert_int(X2,bot_bot_set_int)))) ) ) ) ).

% sum.remove
tff(fact_6023_sum_Oremove,axiom,
    ! [A2: set_int,X2: int,G: fun_int_nat] :
      ( finite_finite_int(A2)
     => ( member_int(X2,A2)
       => ( groups4541462559716669496nt_nat(G,A2) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_int_nat(G,X2)),groups4541462559716669496nt_nat(G,minus_minus_set_int(A2,insert_int(X2,bot_bot_set_int)))) ) ) ) ).

% sum.remove
tff(fact_6024_sum_Oremove,axiom,
    ! [A2: set_nat,X2: nat,G: fun_nat_rat] :
      ( finite_finite_nat(A2)
     => ( member_nat(X2,A2)
       => ( groups2906978787729119204at_rat(G,A2) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(G,X2)),groups2906978787729119204at_rat(G,minus_minus_set_nat(A2,insert_nat(X2,bot_bot_set_nat)))) ) ) ) ).

% sum.remove
tff(fact_6025_sum_Oremove,axiom,
    ! [A2: set_nat,X2: nat,G: fun_nat_int] :
      ( finite_finite_nat(A2)
     => ( member_nat(X2,A2)
       => ( groups3539618377306564664at_int(G,A2) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(G,X2)),groups3539618377306564664at_int(G,minus_minus_set_nat(A2,insert_nat(X2,bot_bot_set_nat)))) ) ) ) ).

% sum.remove
tff(fact_6026_sum_Oinsert__remove,axiom,
    ! [A2: set_Code_integer,G: fun_Code_integer_rat,X2: code_integer] :
      ( finite6017078050557962740nteger(A2)
     => ( groups6602215022474089585er_rat(G,insert_Code_integer(X2,A2)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_Code_integer_rat(G,X2)),groups6602215022474089585er_rat(G,minus_2355218937544613996nteger(A2,insert_Code_integer(X2,bot_bo3990330152332043303nteger)))) ) ) ).

% sum.insert_remove
tff(fact_6027_sum_Oinsert__remove,axiom,
    ! [A2: set_Code_integer,G: fun_Code_integer_nat,X2: code_integer] :
      ( finite6017078050557962740nteger(A2)
     => ( groups7237345082560585321er_nat(G,insert_Code_integer(X2,A2)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_Code_integer_nat(G,X2)),groups7237345082560585321er_nat(G,minus_2355218937544613996nteger(A2,insert_Code_integer(X2,bot_bo3990330152332043303nteger)))) ) ) ).

% sum.insert_remove
tff(fact_6028_sum_Oinsert__remove,axiom,
    ! [A2: set_Code_integer,G: fun_Code_integer_int,X2: code_integer] :
      ( finite6017078050557962740nteger(A2)
     => ( groups7234854612051535045er_int(G,insert_Code_integer(X2,A2)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_Code_integer_int(G,X2)),groups7234854612051535045er_int(G,minus_2355218937544613996nteger(A2,insert_Code_integer(X2,bot_bo3990330152332043303nteger)))) ) ) ).

% sum.insert_remove
tff(fact_6029_sum_Oinsert__remove,axiom,
    ! [A2: set_o,G: fun_o_rat,X2: $o] :
      ( finite_finite_o(A2)
     => ( groups7872700643590313910_o_rat(G,insert_o((X2),A2)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_o_rat(G,(X2))),groups7872700643590313910_o_rat(G,minus_minus_set_o(A2,insert_o((X2),bot_bot_set_o)))) ) ) ).

% sum.insert_remove
tff(fact_6030_sum_Oinsert__remove,axiom,
    ! [A2: set_o,G: fun_o_nat,X2: $o] :
      ( finite_finite_o(A2)
     => ( groups8507830703676809646_o_nat(G,insert_o((X2),A2)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_o_nat(G,(X2))),groups8507830703676809646_o_nat(G,minus_minus_set_o(A2,insert_o((X2),bot_bot_set_o)))) ) ) ).

% sum.insert_remove
tff(fact_6031_sum_Oinsert__remove,axiom,
    ! [A2: set_o,G: fun_o_int,X2: $o] :
      ( finite_finite_o(A2)
     => ( groups8505340233167759370_o_int(G,insert_o((X2),A2)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_o_int(G,(X2))),groups8505340233167759370_o_int(G,minus_minus_set_o(A2,insert_o((X2),bot_bot_set_o)))) ) ) ).

% sum.insert_remove
tff(fact_6032_sum_Oinsert__remove,axiom,
    ! [A2: set_int,G: fun_int_rat,X2: int] :
      ( finite_finite_int(A2)
     => ( groups3906332499630173760nt_rat(G,insert_int(X2,A2)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_int_rat(G,X2)),groups3906332499630173760nt_rat(G,minus_minus_set_int(A2,insert_int(X2,bot_bot_set_int)))) ) ) ).

% sum.insert_remove
tff(fact_6033_sum_Oinsert__remove,axiom,
    ! [A2: set_int,G: fun_int_nat,X2: int] :
      ( finite_finite_int(A2)
     => ( groups4541462559716669496nt_nat(G,insert_int(X2,A2)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_int_nat(G,X2)),groups4541462559716669496nt_nat(G,minus_minus_set_int(A2,insert_int(X2,bot_bot_set_int)))) ) ) ).

% sum.insert_remove
tff(fact_6034_sum_Oinsert__remove,axiom,
    ! [A2: set_nat,G: fun_nat_rat,X2: nat] :
      ( finite_finite_nat(A2)
     => ( groups2906978787729119204at_rat(G,insert_nat(X2,A2)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(G,X2)),groups2906978787729119204at_rat(G,minus_minus_set_nat(A2,insert_nat(X2,bot_bot_set_nat)))) ) ) ).

% sum.insert_remove
tff(fact_6035_sum_Oinsert__remove,axiom,
    ! [A2: set_nat,G: fun_nat_int,X2: nat] :
      ( finite_finite_nat(A2)
     => ( groups3539618377306564664at_int(G,insert_nat(X2,A2)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(G,X2)),groups3539618377306564664at_int(G,minus_minus_set_nat(A2,insert_nat(X2,bot_bot_set_nat)))) ) ) ).

% sum.insert_remove
tff(fact_6036_atLeast1__atMost__eq__remove0,axiom,
    ! [N2: nat] : aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,zero_zero_nat)),N2) = minus_minus_set_nat(aa_nat_set_nat(set_ord_atMost_nat,N2),insert_nat(zero_zero_nat,bot_bot_set_nat)) ).

% atLeast1_atMost_eq_remove0
tff(fact_6037_atLeast1__lessThan__eq__remove0,axiom,
    ! [N2: nat] : aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(suc,zero_zero_nat)),N2) = minus_minus_set_nat(aa_nat_set_nat(set_ord_lessThan_nat,N2),insert_nat(zero_zero_nat,bot_bot_set_nat)) ).

% atLeast1_lessThan_eq_remove0
tff(fact_6038_atLeastLessThan__nat__numeral,axiom,
    ! [M: nat,K: num] :
      aa_nat_set_nat(set_or4665077453230672383an_nat(M),aa_num_nat(numeral_numeral_nat,K)) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),aa_num_nat(pred_numeral,K)),insert_nat(aa_num_nat(pred_numeral,K),aa_nat_set_nat(set_or4665077453230672383an_nat(M),aa_num_nat(pred_numeral,K))),bot_bot_set_nat) ).

% atLeastLessThan_nat_numeral
tff(fact_6039_sum_Odelta__remove,axiom,
    ! [S2: set_Code_integer,A: code_integer,B: fun_Code_integer_rat,C: fun_Code_integer_rat] :
      ( finite6017078050557962740nteger(S2)
     => ( groups6602215022474089585er_rat(aa_fun8169474305930283170er_rat(aa_fun1894662059565830609er_rat(aTP_Lamm_sa(A),B),C),S2) = $ite(member_Code_integer(A,S2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_Code_integer_rat(B,A)),groups6602215022474089585er_rat(C,minus_2355218937544613996nteger(S2,insert_Code_integer(A,bot_bo3990330152332043303nteger)))),groups6602215022474089585er_rat(C,minus_2355218937544613996nteger(S2,insert_Code_integer(A,bot_bo3990330152332043303nteger)))) ) ) ).

% sum.delta_remove
tff(fact_6040_sum_Odelta__remove,axiom,
    ! [S2: set_Code_integer,A: code_integer,B: fun_Code_integer_nat,C: fun_Code_integer_nat] :
      ( finite6017078050557962740nteger(S2)
     => ( groups7237345082560585321er_nat(aa_fun3076867170244285586er_nat(aa_fun7635586485349294009er_nat(aTP_Lamm_sb(A),B),C),S2) = $ite(member_Code_integer(A,S2),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_Code_integer_nat(B,A)),groups7237345082560585321er_nat(C,minus_2355218937544613996nteger(S2,insert_Code_integer(A,bot_bo3990330152332043303nteger)))),groups7237345082560585321er_nat(C,minus_2355218937544613996nteger(S2,insert_Code_integer(A,bot_bo3990330152332043303nteger)))) ) ) ).

% sum.delta_remove
tff(fact_6041_sum_Odelta__remove,axiom,
    ! [S2: set_Code_integer,A: code_integer,B: fun_Code_integer_int,C: fun_Code_integer_int] :
      ( finite6017078050557962740nteger(S2)
     => ( groups7234854612051535045er_int(aa_fun3291479149765983562er_int(aa_fun4411173778969602765er_int(aTP_Lamm_sc(A),B),C),S2) = $ite(member_Code_integer(A,S2),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_Code_integer_int(B,A)),groups7234854612051535045er_int(C,minus_2355218937544613996nteger(S2,insert_Code_integer(A,bot_bo3990330152332043303nteger)))),groups7234854612051535045er_int(C,minus_2355218937544613996nteger(S2,insert_Code_integer(A,bot_bo3990330152332043303nteger)))) ) ) ).

% sum.delta_remove
tff(fact_6042_sum_Odelta__remove,axiom,
    ! [S2: set_o,A: $o,B: fun_o_rat,C: fun_o_rat] :
      ( finite_finite_o(S2)
     => ( groups7872700643590313910_o_rat(aa_fun4336163974892599420_o_rat(aa_fun2919298112881465802_o_rat(aTP_Lamm_sd((A)),B),C),S2) = $ite(member_o((A),S2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_o_rat(B,(A))),groups7872700643590313910_o_rat(C,minus_minus_set_o(S2,insert_o((A),bot_bot_set_o)))),groups7872700643590313910_o_rat(C,minus_minus_set_o(S2,insert_o((A),bot_bot_set_o)))) ) ) ).

% sum.delta_remove
tff(fact_6043_sum_Odelta__remove,axiom,
    ! [S2: set_o,A: $o,B: fun_o_nat,C: fun_o_nat] :
      ( finite_finite_o(S2)
     => ( groups8507830703676809646_o_nat(aa_fun6176012476734143100_o_nat(aa_fun6251207968994965954_o_nat(aTP_Lamm_se((A)),B),C),S2) = $ite(member_o((A),S2),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_o_nat(B,(A))),groups8507830703676809646_o_nat(C,minus_minus_set_o(S2,insert_o((A),bot_bot_set_o)))),groups8507830703676809646_o_nat(C,minus_minus_set_o(S2,insert_o((A),bot_bot_set_o)))) ) ) ).

% sum.delta_remove
tff(fact_6044_sum_Odelta__remove,axiom,
    ! [S2: set_o,A: $o,B: fun_o_int,C: fun_o_int] :
      ( finite_finite_o(S2)
     => ( groups8505340233167759370_o_int(aa_fun4727766026823762812_o_int(aa_fun5648456818326528798_o_int(aTP_Lamm_sf((A)),B),C),S2) = $ite(member_o((A),S2),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_o_int(B,(A))),groups8505340233167759370_o_int(C,minus_minus_set_o(S2,insert_o((A),bot_bot_set_o)))),groups8505340233167759370_o_int(C,minus_minus_set_o(S2,insert_o((A),bot_bot_set_o)))) ) ) ).

% sum.delta_remove
tff(fact_6045_sum_Odelta__remove,axiom,
    ! [S2: set_int,A: int,B: fun_int_rat,C: fun_int_rat] :
      ( finite_finite_int(S2)
     => ( groups3906332499630173760nt_rat(aa_fun1481061427733998144nt_rat(aa_fun2191249852558612414nt_rat(aTP_Lamm_sg(A),B),C),S2) = $ite(member_int(A,S2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_int_rat(B,A)),groups3906332499630173760nt_rat(C,minus_minus_set_int(S2,insert_int(A,bot_bot_set_int)))),groups3906332499630173760nt_rat(C,minus_minus_set_int(S2,insert_int(A,bot_bot_set_int)))) ) ) ).

% sum.delta_remove
tff(fact_6046_sum_Odelta__remove,axiom,
    ! [S2: set_int,A: int,B: fun_int_nat,C: fun_int_nat] :
      ( finite_finite_int(S2)
     => ( groups4541462559716669496nt_nat(aa_fun6506752150744536624nt_nat(aa_fun5407591398502139302nt_nat(aTP_Lamm_sh(A),B),C),S2) = $ite(member_int(A,S2),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_int_nat(B,A)),groups4541462559716669496nt_nat(C,minus_minus_set_int(S2,insert_int(A,bot_bot_set_int)))),groups4541462559716669496nt_nat(C,minus_minus_set_int(S2,insert_int(A,bot_bot_set_int)))) ) ) ).

% sum.delta_remove
tff(fact_6047_sum_Odelta__remove,axiom,
    ! [S2: set_nat,A: nat,B: fun_nat_rat,C: fun_nat_rat] :
      ( finite_finite_nat(S2)
     => ( groups2906978787729119204at_rat(aa_fun765758790203053448at_rat(aa_fun3638354034882855594at_rat(aTP_Lamm_si(A),B),C),S2) = $ite(member_nat(A,S2),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(B,A)),groups2906978787729119204at_rat(C,minus_minus_set_nat(S2,insert_nat(A,bot_bot_set_nat)))),groups2906978787729119204at_rat(C,minus_minus_set_nat(S2,insert_nat(A,bot_bot_set_nat)))) ) ) ).

% sum.delta_remove
tff(fact_6048_sum_Odelta__remove,axiom,
    ! [S2: set_nat,A: nat,B: fun_nat_int,C: fun_nat_int] :
      ( finite_finite_nat(S2)
     => ( groups3539618377306564664at_int(aa_fun5565043122120104496at_int(aa_fun5140708168904641446at_int(aTP_Lamm_sj(A),B),C),S2) = $ite(member_nat(A,S2),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(B,A)),groups3539618377306564664at_int(C,minus_minus_set_nat(S2,insert_nat(A,bot_bot_set_nat)))),groups3539618377306564664at_int(C,minus_minus_set_nat(S2,insert_nat(A,bot_bot_set_nat)))) ) ) ).

% sum.delta_remove
tff(fact_6049_prod__le__power,axiom,
    ! [A2: set_o,F: fun_o_Code_integer,N2: code_integer,K: nat] :
      ( ! [I2: $o] :
          ( member_o((I2),A2)
         => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_o_Code_integer(F,(I2)))
            & aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_o_Code_integer(F,(I2))),N2) ) )
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite_card_o(A2)),K)
       => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),N2)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,F),A2)),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,N2),K)) ) ) ) ).

% prod_le_power
tff(fact_6050_prod__le__power,axiom,
    ! [A2: set_int,F: fun_int_Code_integer,N2: code_integer,K: nat] :
      ( ! [I2: int] :
          ( member_int(I2,A2)
         => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_int_Code_integer(F,I2))
            & aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_int_Code_integer(F,I2)),N2) ) )
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite_card_int(A2)),K)
       => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),N2)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,F),A2)),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,N2),K)) ) ) ) ).

% prod_le_power
tff(fact_6051_prod__le__power,axiom,
    ! [A2: set_Product_unit,F: fun_Pr1820225556744648189nteger,N2: code_integer,K: nat] :
      ( ! [I2: product_unit] :
          ( member_Product_unit(I2,A2)
         => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_Pro1705297278780387758nteger(F,I2))
            & aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_Pro1705297278780387758nteger(F,I2)),N2) ) )
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite410649719033368117t_unit(A2)),K)
       => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),N2)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,groups8185359811944078981nteger(F,A2)),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,N2),K)) ) ) ) ).

% prod_le_power
tff(fact_6052_prod__le__power,axiom,
    ! [A2: set_nat,F: fun_nat_Code_integer,N2: code_integer,K: nat] :
      ( ! [I2: nat] :
          ( member_nat(I2,A2)
         => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_nat_Code_integer(F,I2))
            & aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_nat_Code_integer(F,I2)),N2) ) )
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_set_nat_nat(finite_card_nat,A2)),K)
       => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,one_one_Code_integer),N2)
         => aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,groups3455450783089532116nteger(F,A2)),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,N2),K)) ) ) ) ).

% prod_le_power
tff(fact_6053_prod__le__power,axiom,
    ! [A2: set_o,F: fun_o_rat,N2: rat,K: nat] :
      ( ! [I2: $o] :
          ( member_o((I2),A2)
         => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),aa_o_rat(F,(I2)))
            & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_o_rat(F,(I2))),N2) ) )
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite_card_o(A2)),K)
       => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),N2)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_set_o_rat(aa_fun7302669049306738524_o_rat(groups2869687844427037835_o_rat,F),A2)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,N2),K)) ) ) ) ).

% prod_le_power
tff(fact_6054_prod__le__power,axiom,
    ! [A2: set_int,F: fun_int_rat,N2: rat,K: nat] :
      ( ! [I2: int] :
          ( member_int(I2,A2)
         => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),aa_int_rat(F,I2))
            & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_int_rat(F,I2)),N2) ) )
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite_card_int(A2)),K)
       => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),N2)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,F),A2)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,N2),K)) ) ) ) ).

% prod_le_power
tff(fact_6055_prod__le__power,axiom,
    ! [A2: set_Product_unit,F: fun_Product_unit_rat,N2: rat,K: nat] :
      ( ! [I2: product_unit] :
          ( member_Product_unit(I2,A2)
         => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),aa_Product_unit_rat(F,I2))
            & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_Product_unit_rat(F,I2)),N2) ) )
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite410649719033368117t_unit(A2)),K)
       => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),N2)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,groups8984663225794451456it_rat(F,A2)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,N2),K)) ) ) ) ).

% prod_le_power
tff(fact_6056_prod__le__power,axiom,
    ! [A2: set_nat,F: fun_nat_rat,N2: rat,K: nat] :
      ( ! [I2: nat] :
          ( member_nat(I2,A2)
         => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,zero_zero_rat),aa_nat_rat(F,I2))
            & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_nat_rat(F,I2)),N2) ) )
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_set_nat_nat(finite_card_nat,A2)),K)
       => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,one_one_rat),N2)
         => aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,groups73079841787564623at_rat(F,A2)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,N2),K)) ) ) ) ).

% prod_le_power
tff(fact_6057_prod__le__power,axiom,
    ! [A2: set_o,F: fun_o_nat,N2: nat,K: nat] :
      ( ! [I2: $o] :
          ( member_o((I2),A2)
         => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),aa_o_nat(F,(I2)))
            & aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_o_nat(F,(I2))),N2) ) )
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite_card_o(A2)),K)
       => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),N2)
         => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_set_o_nat(aa_fun8470299178418016604_o_nat(groups3504817904513533571_o_nat,F),A2)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,N2),K)) ) ) ) ).

% prod_le_power
tff(fact_6058_prod__le__power,axiom,
    ! [A2: set_int,F: fun_int_nat,N2: nat,K: nat] :
      ( ! [I2: int] :
          ( member_int(I2,A2)
         => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,zero_zero_nat),aa_int_nat(F,I2))
            & aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_int_nat(F,I2)),N2) ) )
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite_card_int(A2)),K)
       => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),N2)
         => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,groups1707563613775114915nt_nat(F,A2)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,N2),K)) ) ) ) ).

% prod_le_power
tff(fact_6059_card__Diff__insert,axiom,
    ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B4: set_Pr4329608150637261639at_nat] :
      ( member8757157785044589968at_nat(A,A2)
     => ( ~ member8757157785044589968at_nat(A,B4)
       => ( finite3771342082235030671at_nat(minus_3314409938677909166at_nat(A2,aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(A),B4))) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite3771342082235030671at_nat(minus_3314409938677909166at_nat(A2,B4))),one_one_nat) ) ) ) ).

% card_Diff_insert
tff(fact_6060_card__Diff__insert,axiom,
    ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] :
      ( member8440522571783428010at_nat(A,A2)
     => ( ~ member8440522571783428010at_nat(A,B4)
       => ( aa_set4749074711808745205at_nat(finite711546835091564841at_nat,aa_set8868280134176360700at_nat(minus_1356011639430497352at_nat(A2),aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(A),B4))) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_set4749074711808745205at_nat(finite711546835091564841at_nat,aa_set8868280134176360700at_nat(minus_1356011639430497352at_nat(A2),B4))),one_one_nat) ) ) ) ).

% card_Diff_insert
tff(fact_6061_card__Diff__insert,axiom,
    ! [A: $o,A2: set_o,B4: set_o] :
      ( member_o((A),A2)
     => ( ~ member_o((A),B4)
       => ( finite_card_o(minus_minus_set_o(A2,insert_o((A),B4))) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite_card_o(minus_minus_set_o(A2,B4))),one_one_nat) ) ) ) ).

% card_Diff_insert
tff(fact_6062_card__Diff__insert,axiom,
    ! [A: int,A2: set_int,B4: set_int] :
      ( member_int(A,A2)
     => ( ~ member_int(A,B4)
       => ( finite_card_int(minus_minus_set_int(A2,insert_int(A,B4))) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite_card_int(minus_minus_set_int(A2,B4))),one_one_nat) ) ) ) ).

% card_Diff_insert
tff(fact_6063_card__Diff__insert,axiom,
    ! [A: product_unit,A2: set_Product_unit,B4: set_Product_unit] :
      ( member_Product_unit(A,A2)
     => ( ~ member_Product_unit(A,B4)
       => ( finite410649719033368117t_unit(minus_6452836326544984404t_unit(A2,insert_Product_unit(A,B4))) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite410649719033368117t_unit(minus_6452836326544984404t_unit(A2,B4))),one_one_nat) ) ) ) ).

% card_Diff_insert
tff(fact_6064_card__Diff__insert,axiom,
    ! [A: list_nat,A2: set_list_nat,B4: set_list_nat] :
      ( member_list_nat(A,A2)
     => ( ~ member_list_nat(A,B4)
       => ( finite_card_list_nat(minus_7954133019191499631st_nat(A2,insert_list_nat(A,B4))) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite_card_list_nat(minus_7954133019191499631st_nat(A2,B4))),one_one_nat) ) ) ) ).

% card_Diff_insert
tff(fact_6065_card__Diff__insert,axiom,
    ! [A: nat,A2: set_nat,B4: set_nat] :
      ( member_nat(A,A2)
     => ( ~ member_nat(A,B4)
       => ( aa_set_nat_nat(finite_card_nat,minus_minus_set_nat(A2,insert_nat(A,B4))) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_set_nat_nat(finite_card_nat,minus_minus_set_nat(A2,B4))),one_one_nat) ) ) ) ).

% card_Diff_insert
tff(fact_6066_card__insert__le__m1,axiom,
    ! [N2: nat,Y: set_Pr4329608150637261639at_nat,X2: produc3843707927480180839at_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite3771342082235030671at_nat(Y)),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat))
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite3771342082235030671at_nat(aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(X2),Y))),N2) ) ) ).

% card_insert_le_m1
tff(fact_6067_card__insert__le__m1,axiom,
    ! [N2: nat,Y: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_set4749074711808745205at_nat(finite711546835091564841at_nat,Y)),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat))
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_set4749074711808745205at_nat(finite711546835091564841at_nat,aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(X2),Y))),N2) ) ) ).

% card_insert_le_m1
tff(fact_6068_card__insert__le__m1,axiom,
    ! [N2: nat,Y: set_o,X2: $o] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite_card_o(Y)),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat))
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite_card_o(insert_o((X2),Y))),N2) ) ) ).

% card_insert_le_m1
tff(fact_6069_card__insert__le__m1,axiom,
    ! [N2: nat,Y: set_int,X2: int] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite_card_int(Y)),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat))
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite_card_int(insert_int(X2,Y))),N2) ) ) ).

% card_insert_le_m1
tff(fact_6070_card__insert__le__m1,axiom,
    ! [N2: nat,Y: set_Product_unit,X2: product_unit] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite410649719033368117t_unit(Y)),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat))
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite410649719033368117t_unit(insert_Product_unit(X2,Y))),N2) ) ) ).

% card_insert_le_m1
tff(fact_6071_card__insert__le__m1,axiom,
    ! [N2: nat,Y: set_nat,X2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_set_nat_nat(finite_card_nat,Y)),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat))
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_set_nat_nat(finite_card_nat,insert_nat(X2,Y))),N2) ) ) ).

% card_insert_le_m1
tff(fact_6072_card__insert__le__m1,axiom,
    ! [N2: nat,Y: set_list_nat,X2: list_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite_card_list_nat(Y)),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat))
       => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite_card_list_nat(insert_list_nat(X2,Y))),N2) ) ) ).

% card_insert_le_m1
tff(fact_6073_card__Diff__singleton__if,axiom,
    ! [A2: set_Product_unit,X2: product_unit] :
      finite410649719033368117t_unit(minus_6452836326544984404t_unit(A2,insert_Product_unit(X2,bot_bo3957492148770167129t_unit))) = $ite(member_Product_unit(X2,A2),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite410649719033368117t_unit(A2)),one_one_nat),finite410649719033368117t_unit(A2)) ).

% card_Diff_singleton_if
tff(fact_6074_card__Diff__singleton__if,axiom,
    ! [A2: set_list_nat,X2: list_nat] :
      finite_card_list_nat(minus_7954133019191499631st_nat(A2,insert_list_nat(X2,bot_bot_set_list_nat))) = $ite(member_list_nat(X2,A2),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite_card_list_nat(A2)),one_one_nat),finite_card_list_nat(A2)) ).

% card_Diff_singleton_if
tff(fact_6075_card__Diff__singleton__if,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,X2: produc3843707927480180839at_nat] :
      finite3771342082235030671at_nat(minus_3314409938677909166at_nat(A2,aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(X2),bot_bo228742789529271731at_nat))) = $ite(member8757157785044589968at_nat(X2,A2),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite3771342082235030671at_nat(A2)),one_one_nat),finite3771342082235030671at_nat(A2)) ).

% card_Diff_singleton_if
tff(fact_6076_card__Diff__singleton__if,axiom,
    ! [A2: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat] :
      aa_set4749074711808745205at_nat(finite711546835091564841at_nat,aa_set8868280134176360700at_nat(minus_1356011639430497352at_nat(A2),aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(X2),bot_bo2099793752762293965at_nat))) = $ite(member8440522571783428010at_nat(X2,A2),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_set4749074711808745205at_nat(finite711546835091564841at_nat,A2)),one_one_nat),aa_set4749074711808745205at_nat(finite711546835091564841at_nat,A2)) ).

% card_Diff_singleton_if
tff(fact_6077_card__Diff__singleton__if,axiom,
    ! [A2: set_o,X2: $o] :
      finite_card_o(minus_minus_set_o(A2,insert_o((X2),bot_bot_set_o))) = $ite(member_o((X2),A2),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite_card_o(A2)),one_one_nat),finite_card_o(A2)) ).

% card_Diff_singleton_if
tff(fact_6078_card__Diff__singleton__if,axiom,
    ! [A2: set_int,X2: int] :
      finite_card_int(minus_minus_set_int(A2,insert_int(X2,bot_bot_set_int))) = $ite(member_int(X2,A2),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite_card_int(A2)),one_one_nat),finite_card_int(A2)) ).

% card_Diff_singleton_if
tff(fact_6079_card__Diff__singleton__if,axiom,
    ! [A2: set_nat,X2: nat] :
      aa_set_nat_nat(finite_card_nat,minus_minus_set_nat(A2,insert_nat(X2,bot_bot_set_nat))) = $ite(member_nat(X2,A2),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_set_nat_nat(finite_card_nat,A2)),one_one_nat),aa_set_nat_nat(finite_card_nat,A2)) ).

% card_Diff_singleton_if
tff(fact_6080_card__Diff__singleton,axiom,
    ! [X2: product_unit,A2: set_Product_unit] :
      ( member_Product_unit(X2,A2)
     => ( finite410649719033368117t_unit(minus_6452836326544984404t_unit(A2,insert_Product_unit(X2,bot_bo3957492148770167129t_unit))) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite410649719033368117t_unit(A2)),one_one_nat) ) ) ).

% card_Diff_singleton
tff(fact_6081_card__Diff__singleton,axiom,
    ! [X2: list_nat,A2: set_list_nat] :
      ( member_list_nat(X2,A2)
     => ( finite_card_list_nat(minus_7954133019191499631st_nat(A2,insert_list_nat(X2,bot_bot_set_list_nat))) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite_card_list_nat(A2)),one_one_nat) ) ) ).

% card_Diff_singleton
tff(fact_6082_card__Diff__singleton,axiom,
    ! [X2: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
      ( member8757157785044589968at_nat(X2,A2)
     => ( finite3771342082235030671at_nat(minus_3314409938677909166at_nat(A2,aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(X2),bot_bo228742789529271731at_nat))) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite3771342082235030671at_nat(A2)),one_one_nat) ) ) ).

% card_Diff_singleton
tff(fact_6083_card__Diff__singleton,axiom,
    ! [X2: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
      ( member8440522571783428010at_nat(X2,A2)
     => ( aa_set4749074711808745205at_nat(finite711546835091564841at_nat,aa_set8868280134176360700at_nat(minus_1356011639430497352at_nat(A2),aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(X2),bot_bo2099793752762293965at_nat))) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_set4749074711808745205at_nat(finite711546835091564841at_nat,A2)),one_one_nat) ) ) ).

% card_Diff_singleton
tff(fact_6084_card__Diff__singleton,axiom,
    ! [X2: $o,A2: set_o] :
      ( member_o((X2),A2)
     => ( finite_card_o(minus_minus_set_o(A2,insert_o((X2),bot_bot_set_o))) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite_card_o(A2)),one_one_nat) ) ) ).

% card_Diff_singleton
tff(fact_6085_card__Diff__singleton,axiom,
    ! [X2: int,A2: set_int] :
      ( member_int(X2,A2)
     => ( finite_card_int(minus_minus_set_int(A2,insert_int(X2,bot_bot_set_int))) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,finite_card_int(A2)),one_one_nat) ) ) ).

% card_Diff_singleton
tff(fact_6086_card__Diff__singleton,axiom,
    ! [X2: nat,A2: set_nat] :
      ( member_nat(X2,A2)
     => ( aa_set_nat_nat(finite_card_nat,minus_minus_set_nat(A2,insert_nat(X2,bot_bot_set_nat))) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_set_nat_nat(finite_card_nat,A2)),one_one_nat) ) ) ).

% card_Diff_singleton
tff(fact_6087_in__finite__psubset,axiom,
    ! [A2: set_nat,B4: set_nat] :
      ( member8277197624267554838et_nat(produc4532415448927165861et_nat(A2,B4),finite_psubset_nat)
    <=> ( ord_less_set_nat(A2,B4)
        & finite_finite_nat(B4) ) ) ).

% in_finite_psubset
tff(fact_6088_in__finite__psubset,axiom,
    ! [A2: set_int,B4: set_int] :
      ( member2572552093476627150et_int(produc6363374080413544029et_int(A2,B4),finite_psubset_int)
    <=> ( ord_less_set_int(A2,B4)
        & finite_finite_int(B4) ) ) ).

% in_finite_psubset
tff(fact_6089_in__finite__psubset,axiom,
    ! [A2: set_Code_integer,B4: set_Code_integer] :
      ( member4307123515891402160nteger(produc7443773368509356479nteger(A2,B4),finite2416775604798480986nteger)
    <=> ( ord_le1307284697595431911nteger(A2,B4)
        & finite6017078050557962740nteger(B4) ) ) ).

% in_finite_psubset
tff(fact_6090_in__finite__psubset,axiom,
    ! [A2: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] :
      ( member8757157785044589968at_nat(produc2922128104949294807at_nat(A2,B4),finite469560695537375940at_nat)
    <=> ( aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(ord_le7866589430770878221at_nat,A2),B4)
        & finite6177210948735845034at_nat(B4) ) ) ).

% in_finite_psubset
tff(fact_6091_card__1__singletonE,axiom,
    ! [A2: set_Product_unit] :
      ( ( finite410649719033368117t_unit(A2) = one_one_nat )
     => ~ ! [X3: product_unit] : A2 != insert_Product_unit(X3,bot_bo3957492148770167129t_unit) ) ).

% card_1_singletonE
tff(fact_6092_card__1__singletonE,axiom,
    ! [A2: set_list_nat] :
      ( ( finite_card_list_nat(A2) = one_one_nat )
     => ~ ! [X3: list_nat] : A2 != insert_list_nat(X3,bot_bot_set_list_nat) ) ).

% card_1_singletonE
tff(fact_6093_card__1__singletonE,axiom,
    ! [A2: set_Pr4329608150637261639at_nat] :
      ( ( finite3771342082235030671at_nat(A2) = one_one_nat )
     => ~ ! [X3: produc3843707927480180839at_nat] : A2 != aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(X3),bot_bo228742789529271731at_nat) ) ).

% card_1_singletonE
tff(fact_6094_card__1__singletonE,axiom,
    ! [A2: set_Pr1261947904930325089at_nat] :
      ( ( aa_set4749074711808745205at_nat(finite711546835091564841at_nat,A2) = one_one_nat )
     => ~ ! [X3: product_prod_nat_nat] : A2 != aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(X3),bot_bo2099793752762293965at_nat) ) ).

% card_1_singletonE
tff(fact_6095_card__1__singletonE,axiom,
    ! [A2: set_o] :
      ( ( finite_card_o(A2) = one_one_nat )
     => ~ ! [X3: $o] : A2 != insert_o((X3),bot_bot_set_o) ) ).

% card_1_singletonE
tff(fact_6096_card__1__singletonE,axiom,
    ! [A2: set_nat] :
      ( ( aa_set_nat_nat(finite_card_nat,A2) = one_one_nat )
     => ~ ! [X3: nat] : A2 != insert_nat(X3,bot_bot_set_nat) ) ).

% card_1_singletonE
tff(fact_6097_card__1__singletonE,axiom,
    ! [A2: set_int] :
      ( ( finite_card_int(A2) = one_one_nat )
     => ~ ! [X3: int] : A2 != insert_int(X3,bot_bot_set_int) ) ).

% card_1_singletonE
tff(fact_6098_integer__of__nat__def,axiom,
    code_integer_of_nat = map_fu6290471996055670595nteger(id_nat,code_integer_of_int,semiri1314217659103216013at_int) ).

% integer_of_nat_def
tff(fact_6099_card__UNIV__unit,axiom,
    finite410649719033368117t_unit(top_to1996260823553986621t_unit) = one_one_nat ).

% card_UNIV_unit
tff(fact_6100_card__lessThan,axiom,
    ! [U: nat] : aa_set_nat_nat(finite_card_nat,aa_nat_set_nat(set_ord_lessThan_nat,U)) = U ).

% card_lessThan
tff(fact_6101_card__atLeastLessThan,axiom,
    ! [L: nat,U: nat] : aa_set_nat_nat(finite_card_nat,aa_nat_set_nat(set_or4665077453230672383an_nat(L),U)) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,U),L) ).

% card_atLeastLessThan
tff(fact_6102_card__atMost,axiom,
    ! [U: nat] : aa_set_nat_nat(finite_card_nat,aa_nat_set_nat(set_ord_atMost_nat,U)) = aa_nat_nat(suc,U) ).

% card_atMost
tff(fact_6103_Collect__const__case__prod,axiom,
    ! [P: $o] :
      aa_fun1965866159956205013at_nat(collec6321179662152712658at_nat,aa_fun762164075915671590_nat_o(produc410239310623530412_nat_o,aTP_Lamm_sk((P)))) = $ite((P),top_to6833984726390702231at_nat,bot_bo228742789529271731at_nat) ).

% Collect_const_case_prod
tff(fact_6104_Collect__const__case__prod,axiom,
    ! [P: $o] :
      aa_fun7046812543386002057at_nat(collec3392354462482085612at_nat,aa_fun7564604662015400456_nat_o(produc6081775807080527818_nat_o,aTP_Lamm_sl((P)))) = $ite((P),top_to4669805908274784177at_nat,bot_bo2099793752762293965at_nat) ).

% Collect_const_case_prod
tff(fact_6105_nat__of__integer__integer__of__nat,axiom,
    ! [N2: nat] : aa_Code_integer_nat(code_nat_of_integer,aa_nat_Code_integer(code_integer_of_nat,N2)) = N2 ).

% nat_of_integer_integer_of_nat
tff(fact_6106_card__atLeastAtMost,axiom,
    ! [L: nat,U: nat] : aa_set_nat_nat(finite_card_nat,aa_nat_set_nat(set_or1269000886237332187st_nat(L),U)) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(suc,U)),L) ).

% card_atLeastAtMost
tff(fact_6107_integer__of__nat_Orep__eq,axiom,
    ! [X2: nat] : aa_Code_integer_int(code_int_of_integer,aa_nat_Code_integer(code_integer_of_nat,X2)) = aa_nat_int(semiri1314217659103216013at_int,X2) ).

% integer_of_nat.rep_eq
tff(fact_6108_int__of__integer__integer__of__nat,axiom,
    ! [N2: nat] : aa_Code_integer_int(code_int_of_integer,aa_nat_Code_integer(code_integer_of_nat,N2)) = aa_nat_int(semiri1314217659103216013at_int,N2) ).

% int_of_integer_integer_of_nat
tff(fact_6109_top__empty__eq2,axiom,
    ! [X: set_Pr1261947904930325089at_nat,Xa3: set_Pr1261947904930325089at_nat] :
      ( aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(top_to7888465585648448638_nat_o,X),Xa3)
    <=> member8757157785044589968at_nat(produc2922128104949294807at_nat(X,Xa3),top_to6833984726390702231at_nat) ) ).

% top_empty_eq2
tff(fact_6110_top__empty__eq2,axiom,
    ! [X: nat,Xa3: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(top_to5288702739685986426_nat_o,X),Xa3)
    <=> member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X),Xa3),top_to4669805908274784177at_nat) ) ).

% top_empty_eq2
tff(fact_6111_top__empty__eq2,axiom,
    ! [X: fun_Pr5098669352780829690e_term,Xa3: produc8923325533196201883nteger] :
      ( aa_Pro4926521453222654329eger_o(aa_fun4505422719058378424eger_o(top_to2784585791485011495eger_o,X),Xa3)
    <=> member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X),Xa3),top_to7525899545246753276nteger) ) ).

% top_empty_eq2
tff(fact_6112_top__empty__eq2,axiom,
    ! [X: fun_Pr6460944699146269935_nat_o,Xa3: produc3658429121746597890et_nat] :
      ( aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(top_to2712223222597888051_nat_o,X),Xa3)
    <=> member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X),Xa3),top_to2987642378616949766et_nat) ) ).

% top_empty_eq2
tff(fact_6113_top__empty__eq2,axiom,
    ! [X: fun_Pr6460944699146269935_nat_o,Xa3: produc8799533983703829792et_nat] :
      ( aa_Pro5643009357358181178_nat_o(aa_fun912680268133416158_nat_o(top_to3067105749023872149_nat_o,X),Xa3)
    <=> member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X),Xa3),top_to2648389616742571044et_nat) ) ).

% top_empty_eq2
tff(fact_6114_top__empty__eq2,axiom,
    ! [X: fun_Pr7763680713840462443e_term,Xa3: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(aa_fun3538162476766722827_int_o(top_to1218662295448195450_int_o,X),Xa3)
    <=> member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X),Xa3),top_to6107225058432391401nt_int) ) ).

% top_empty_eq2
tff(fact_6115_top__empty__eq2,axiom,
    ! [X: fun_in5730379987311621695e_term,Xa3: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(aa_fun586359091965693151_int_o(top_to1089409542825796430_int_o,X),Xa3)
    <=> member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X),Xa3),top_to1212741241995312661nt_int) ) ).

% top_empty_eq2
tff(fact_6116_int__of__integer__induct,axiom,
    ! [Y: int,P: fun_int_o] :
      ( member_int(Y,top_top_set_int)
     => ( ! [X3: code_integer] : aa_int_o(P,aa_Code_integer_int(code_int_of_integer,X3))
       => aa_int_o(P,Y) ) ) ).

% int_of_integer_induct
tff(fact_6117_int__of__integer__cases,axiom,
    ! [Y: int] :
      ( member_int(Y,top_top_set_int)
     => ~ ! [X3: code_integer] : Y != aa_Code_integer_int(code_int_of_integer,X3) ) ).

% int_of_integer_cases
tff(fact_6118_int__of__integer,axiom,
    ! [X2: code_integer] : member_int(aa_Code_integer_int(code_int_of_integer,X2),top_top_set_int) ).

% int_of_integer
tff(fact_6119_integer__of__int__inject,axiom,
    ! [X2: int,Y: int] :
      ( member_int(X2,top_top_set_int)
     => ( member_int(Y,top_top_set_int)
       => ( ( aa_int_Code_integer(code_integer_of_int,X2) = aa_int_Code_integer(code_integer_of_int,Y) )
        <=> ( X2 = Y ) ) ) ) ).

% integer_of_int_inject
tff(fact_6120_integer__of__int__induct,axiom,
    ! [P: fun_Code_integer_o,X2: code_integer] :
      ( ! [Y4: int] :
          ( member_int(Y4,top_top_set_int)
         => aa_Code_integer_o(P,aa_int_Code_integer(code_integer_of_int,Y4)) )
     => aa_Code_integer_o(P,X2) ) ).

% integer_of_int_induct
tff(fact_6121_integer__of__int__cases,axiom,
    ! [X2: code_integer] :
      ~ ! [Y4: int] :
          ( ( X2 = aa_int_Code_integer(code_integer_of_int,Y4) )
         => ~ member_int(Y4,top_top_set_int) ) ).

% integer_of_int_cases
tff(fact_6122_subset__card__intvl__is__intvl,axiom,
    ! [A2: set_nat,K: nat] :
      ( aa_set_nat_o(ord_less_eq_set_nat(A2),aa_nat_set_nat(set_or4665077453230672383an_nat(K),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,K),aa_set_nat_nat(finite_card_nat,A2))))
     => ( A2 = aa_nat_set_nat(set_or4665077453230672383an_nat(K),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,K),aa_set_nat_nat(finite_card_nat,A2))) ) ) ).

% subset_card_intvl_is_intvl
tff(fact_6123_integer__of__int__inverse,axiom,
    ! [Y: int] :
      ( member_int(Y,top_top_set_int)
     => ( aa_Code_integer_int(code_int_of_integer,aa_int_Code_integer(code_integer_of_int,Y)) = Y ) ) ).

% integer_of_int_inverse
tff(fact_6124_subset__eq__atLeast0__lessThan__card,axiom,
    ! [N5: set_nat,N2: nat] :
      ( aa_set_nat_o(ord_less_eq_set_nat(N5),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N2))
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_set_nat_nat(finite_card_nat,N5)),N2) ) ).

% subset_eq_atLeast0_lessThan_card
tff(fact_6125_integer__of__nat__eq__of__nat,axiom,
    code_integer_of_nat = semiri4939895301339042750nteger ).

% integer_of_nat_eq_of_nat
tff(fact_6126_card__less__Suc2,axiom,
    ! [M2: set_nat,I: nat] :
      ( ~ member_nat(zero_zero_nat,M2)
     => ( aa_set_nat_nat(finite_card_nat,collect_nat(aa_nat_fun_nat_o(aTP_Lamm_sm(M2),I))) = aa_set_nat_nat(finite_card_nat,collect_nat(aa_nat_fun_nat_o(aTP_Lamm_sn(M2),I))) ) ) ).

% card_less_Suc2
tff(fact_6127_card__less__Suc,axiom,
    ! [M2: set_nat,I: nat] :
      ( member_nat(zero_zero_nat,M2)
     => ( aa_nat_nat(suc,aa_set_nat_nat(finite_card_nat,collect_nat(aa_nat_fun_nat_o(aTP_Lamm_sm(M2),I)))) = aa_set_nat_nat(finite_card_nat,collect_nat(aa_nat_fun_nat_o(aTP_Lamm_sn(M2),I))) ) ) ).

% card_less_Suc
tff(fact_6128_card__less,axiom,
    ! [M2: set_nat,I: nat] :
      ( member_nat(zero_zero_nat,M2)
     => ( aa_set_nat_nat(finite_card_nat,collect_nat(aa_nat_fun_nat_o(aTP_Lamm_sn(M2),I))) != zero_zero_nat ) ) ).

% card_less
tff(fact_6129_integer__of__nat__0,axiom,
    aa_nat_Code_integer(code_integer_of_nat,zero_zero_nat) = zero_z3403309356797280102nteger ).

% integer_of_nat_0
tff(fact_6130_integer__of__nat_Oabs__eq,axiom,
    ! [X2: nat] : aa_nat_Code_integer(code_integer_of_nat,X2) = aa_int_Code_integer(code_integer_of_int,aa_nat_int(semiri1314217659103216013at_int,X2)) ).

% integer_of_nat.abs_eq
tff(fact_6131_integer__of__nat__numeral,axiom,
    ! [N2: num] : aa_nat_Code_integer(code_integer_of_nat,aa_num_nat(numeral_numeral_nat,N2)) = aa_num_Code_integer(numera6620942414471956472nteger,N2) ).

% integer_of_nat_numeral
tff(fact_6132_integer__of__nat__1,axiom,
    aa_nat_Code_integer(code_integer_of_nat,one_one_nat) = one_one_Code_integer ).

% integer_of_nat_1
tff(fact_6133_card__sum__le__nat__sum,axiom,
    ! [S2: set_nat] : aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_set_nat_nat(groups3542108847815614940at_nat(aTP_Lamm_co),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),aa_set_nat_nat(finite_card_nat,S2)))),aa_set_nat_nat(groups3542108847815614940at_nat(aTP_Lamm_co),S2)) ).

% card_sum_le_nat_sum
tff(fact_6134_set__encode__insert,axiom,
    ! [A2: set_nat,N2: nat] :
      ( finite_finite_nat(A2)
     => ( ~ member_nat(N2,A2)
       => ( aa_set_nat_nat(nat_set_encode,insert_nat(N2,A2)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)),aa_set_nat_nat(nat_set_encode,A2)) ) ) ) ).

% set_encode_insert
tff(fact_6135_card__greaterThanLessThan__int,axiom,
    ! [L: int,U: int] : finite_card_int(aa_int_set_int(set_or5832277885323065728an_int(L),U)) = aa_int_nat(nat2,aa_int_int(aa_int_fun_int_int(minus_minus_int,U),aa_int_int(aa_int_fun_int_int(plus_plus_int,L),one_one_int))) ).

% card_greaterThanLessThan_int
tff(fact_6136_wmax__insertI,axiom,
    ! [Y: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat] :
      ( member8440522571783428010at_nat(Y,YS)
     => ( member8206827879206165904at_nat(produc6161850002892822231at_nat(X2,Y),fun_pair_leq)
       => ( member8757157785044589968at_nat(produc2922128104949294807at_nat(XS,YS),fun_max_weak)
         => member8757157785044589968at_nat(produc2922128104949294807at_nat(aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(X2),XS),YS),fun_max_weak) ) ) ) ).

% wmax_insertI
tff(fact_6137_wmin__insertI,axiom,
    ! [X2: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat,Y: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat] :
      ( member8440522571783428010at_nat(X2,XS)
     => ( member8206827879206165904at_nat(produc6161850002892822231at_nat(X2,Y),fun_pair_leq)
       => ( member8757157785044589968at_nat(produc2922128104949294807at_nat(XS,YS),fun_min_weak)
         => member8757157785044589968at_nat(produc2922128104949294807at_nat(XS,aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(Y),YS)),fun_min_weak) ) ) ) ).

% wmin_insertI
tff(fact_6138_smin__insertI,axiom,
    ! [X2: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat,Y: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat] :
      ( member8440522571783428010at_nat(X2,XS)
     => ( member8206827879206165904at_nat(produc6161850002892822231at_nat(X2,Y),fun_pair_less)
       => ( member8757157785044589968at_nat(produc2922128104949294807at_nat(XS,YS),fun_min_strict)
         => member8757157785044589968at_nat(produc2922128104949294807at_nat(XS,aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(Y),YS)),fun_min_strict) ) ) ) ).

% smin_insertI
tff(fact_6139_prod_Oinsert_H,axiom,
    ! [I4: set_o,P2: fun_o_Code_integer,I: $o] :
      ( finite_finite_o(collect_o(aa_fun8192762245619933327un_o_o(aTP_Lamm_pr(I4),P2)))
     => ( groups2836416601086271911nteger(P2,insert_o((I),I4)) = $ite(member_o((I),I4),groups2836416601086271911nteger(P2,I4),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_o_Code_integer(P2,(I))),groups2836416601086271911nteger(P2,I4))) ) ) ).

% prod.insert'
tff(fact_6140_prod_Oinsert_H,axiom,
    ! [I4: set_nat,P2: fun_nat_Code_integer,I: nat] :
      ( finite_finite_nat(collect_nat(aa_fun3480067038916266681_nat_o(aTP_Lamm_pt(I4),P2)))
     => ( groups8290090294887179773nteger(P2,insert_nat(I,I4)) = $ite(member_nat(I,I4),groups8290090294887179773nteger(P2,I4),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(P2,I)),groups8290090294887179773nteger(P2,I4))) ) ) ).

% prod.insert'
tff(fact_6141_prod_Oinsert_H,axiom,
    ! [I4: set_int,P2: fun_int_Code_integer,I: int] :
      ( finite_finite_int(collect_int(aa_fun3336537925265328129_int_o(aTP_Lamm_pv(I4),P2)))
     => ( groups8661743855124024409nteger(P2,insert_int(I,I4)) = $ite(member_int(I,I4),groups8661743855124024409nteger(P2,I4),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_int_Code_integer(P2,I)),groups8661743855124024409nteger(P2,I4))) ) ) ).

% prod.insert'
tff(fact_6142_prod_Oinsert_H,axiom,
    ! [I4: set_Code_integer,P2: fun_Co8499238673658658103nteger,I: code_integer] :
      ( finite6017078050557962740nteger(collect_Code_integer(aa_fun7159535342743012639eger_o(aTP_Lamm_px(I4),P2)))
     => ( aa_set8546232603906849326nteger(groups7219916603568234122nteger(P2),insert_Code_integer(I,I4)) = $ite(member_Code_integer(I,I4),aa_set8546232603906849326nteger(groups7219916603568234122nteger(P2),I4),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(P2,I)),aa_set8546232603906849326nteger(groups7219916603568234122nteger(P2),I4))) ) ) ).

% prod.insert'
tff(fact_6143_prod_Oinsert_H,axiom,
    ! [I4: set_o,P2: fun_o_assn,I: $o] :
      ( finite_finite_o(collect_o(aa_fun8382565201914911066un_o_o(aTP_Lamm_pz(I4),P2)))
     => ( groups12625163056032370o_assn(P2,insert_o((I),I4)) = $ite(member_o((I),I4),groups12625163056032370o_assn(P2,I4),aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_o_assn(P2,(I))),groups12625163056032370o_assn(P2,I4))) ) ) ).

% prod.insert'
tff(fact_6144_prod_Oinsert_H,axiom,
    ! [I4: set_nat,P2: fun_nat_assn,I: nat] :
      ( finite_finite_nat(collect_nat(aa_fun7183233715851567790_nat_o(aTP_Lamm_qb(I4),P2)))
     => ( groups3916077543535352520t_assn(P2,insert_nat(I,I4)) = $ite(member_nat(I,I4),groups3916077543535352520t_assn(P2,I4),aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_nat_assn(P2,I)),groups3916077543535352520t_assn(P2,I4))) ) ) ).

% prod.insert'
tff(fact_6145_prod_Oinsert_H,axiom,
    ! [I4: set_int,P2: fun_int_assn,I: int] :
      ( finite_finite_int(collect_int(aa_fun202081646129719286_int_o(aTP_Lamm_qd(I4),P2)))
     => ( groups4891613008741529892t_assn(P2,insert_int(I,I4)) = $ite(member_int(I,I4),groups4891613008741529892t_assn(P2,I4),aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_int_assn(P2,I)),groups4891613008741529892t_assn(P2,I4))) ) ) ).

% prod.insert'
tff(fact_6146_prod_Oinsert_H,axiom,
    ! [I4: set_Code_integer,P2: fun_Co4490034186337852034r_assn,I: code_integer] :
      ( finite6017078050557962740nteger(collect_Code_integer(aa_fun6538703224075513620eger_o(aTP_Lamm_qf(I4),P2)))
     => ( groups980104329299799381r_assn(P2,insert_Code_integer(I,I4)) = $ite(member_Code_integer(I,I4),groups980104329299799381r_assn(P2,I4),aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_Code_integer_assn(P2,I)),groups980104329299799381r_assn(P2,I4))) ) ) ).

% prod.insert'
tff(fact_6147_prod_Oinsert_H,axiom,
    ! [I4: set_o,P2: fun_o_rat,I: $o] :
      ( finite_finite_o(collect_o(aa_fun_o_rat_fun_o_o(aTP_Lamm_qh(I4),P2)))
     => ( groups4688112016125141794_o_rat(P2,insert_o((I),I4)) = $ite(member_o((I),I4),groups4688112016125141794_o_rat(P2,I4),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_o_rat(P2,(I))),groups4688112016125141794_o_rat(P2,I4))) ) ) ).

% prod.insert'
tff(fact_6148_prod_Oinsert_H,axiom,
    ! [I4: set_nat,P2: fun_nat_rat,I: nat] :
      ( finite_finite_nat(collect_nat(aa_fun1118977351124560894_nat_o(aTP_Lamm_qj(I4),P2)))
     => ( groups4112464933559648120at_rat(P2,insert_nat(I,I4)) = $ite(member_nat(I,I4),groups4112464933559648120at_rat(P2,I4),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(P2,I)),groups4112464933559648120at_rat(P2,I4))) ) ) ).

% prod.insert'
tff(fact_6149_greaterThanLessThan__iff,axiom,
    ! [I: $o,L: $o,U: $o] :
      ( member_o((I),aa_o_set_o(set_or1716231572884733764Than_o((L)),(U)))
    <=> ( aa_o_o(aa_o_fun_o_o(ord_less_o,(L)),(I))
        & aa_o_o(aa_o_fun_o_o(ord_less_o,(I)),(U)) ) ) ).

% greaterThanLessThan_iff
tff(fact_6150_greaterThanLessThan__iff,axiom,
    ! [I: rat,L: rat,U: rat] :
      ( member_rat(I,set_or5199638295745620268an_rat(L,U))
    <=> ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,L),I)
        & aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,I),U) ) ) ).

% greaterThanLessThan_iff
tff(fact_6151_greaterThanLessThan__iff,axiom,
    ! [I: num,L: num,U: num] :
      ( member_num(I,set_or2392100141987894638an_num(L,U))
    <=> ( aa_num_o(aa_num_fun_num_o(ord_less_num,L),I)
        & aa_num_o(aa_num_fun_num_o(ord_less_num,I),U) ) ) ).

% greaterThanLessThan_iff
tff(fact_6152_greaterThanLessThan__iff,axiom,
    ! [I: int,L: int,U: int] :
      ( member_int(I,aa_int_set_int(set_or5832277885323065728an_int(L),U))
    <=> ( aa_int_o(aa_int_fun_int_o(ord_less_int,L),I)
        & aa_int_o(aa_int_fun_int_o(ord_less_int,I),U) ) ) ).

% greaterThanLessThan_iff
tff(fact_6153_greaterThanLessThan__iff,axiom,
    ! [I: nat,L: nat,U: nat] :
      ( member_nat(I,aa_nat_set_nat(set_or5834768355832116004an_nat(L),U))
    <=> ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,L),I)
        & aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,I),U) ) ) ).

% greaterThanLessThan_iff
tff(fact_6154_greaterThanLessThan__iff,axiom,
    ! [I: code_integer,L: code_integer,U: code_integer] :
      ( member_Code_integer(I,aa_Cod2813182003028390446nteger(set_or4266950643985792945nteger(L),U))
    <=> ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,L),I)
        & aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,I),U) ) ) ).

% greaterThanLessThan_iff
tff(fact_6155_finite__greaterThanLessThan__int,axiom,
    ! [L: int,U: int] : finite_finite_int(aa_int_set_int(set_or5832277885323065728an_int(L),U)) ).

% finite_greaterThanLessThan_int
tff(fact_6156_greaterThanLessThan__empty__iff2,axiom,
    ! [A: rat,B: rat] :
      ( ( bot_bot_set_rat = set_or5199638295745620268an_rat(A,B) )
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),A) ) ).

% greaterThanLessThan_empty_iff2
tff(fact_6157_greaterThanLessThan__empty__iff,axiom,
    ! [A: rat,B: rat] :
      ( ( set_or5199638295745620268an_rat(A,B) = bot_bot_set_rat )
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),A) ) ).

% greaterThanLessThan_empty_iff
tff(fact_6158_greaterThanLessThan__empty,axiom,
    ! [L: $o,K: $o] :
      ( aa_o_o(aa_o_fun_o_o(ord_less_eq_o,(L)),(K))
     => ( aa_o_set_o(set_or1716231572884733764Than_o((K)),(L)) = bot_bot_set_o ) ) ).

% greaterThanLessThan_empty
tff(fact_6159_greaterThanLessThan__empty,axiom,
    ! [L: set_nat,K: set_nat] :
      ( aa_set_nat_o(ord_less_eq_set_nat(L),K)
     => ( set_or8625682525731655386et_nat(K,L) = bot_bot_set_set_nat ) ) ).

% greaterThanLessThan_empty
tff(fact_6160_greaterThanLessThan__empty,axiom,
    ! [L: rat,K: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,L),K)
     => ( set_or5199638295745620268an_rat(K,L) = bot_bot_set_rat ) ) ).

% greaterThanLessThan_empty
tff(fact_6161_greaterThanLessThan__empty,axiom,
    ! [L: num,K: num] :
      ( aa_num_o(aa_num_fun_num_o(ord_less_eq_num,L),K)
     => ( set_or2392100141987894638an_num(K,L) = bot_bot_set_num ) ) ).

% greaterThanLessThan_empty
tff(fact_6162_greaterThanLessThan__empty,axiom,
    ! [L: int,K: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,L),K)
     => ( aa_int_set_int(set_or5832277885323065728an_int(K),L) = bot_bot_set_int ) ) ).

% greaterThanLessThan_empty
tff(fact_6163_greaterThanLessThan__empty,axiom,
    ! [L: nat,K: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,L),K)
     => ( aa_nat_set_nat(set_or5834768355832116004an_nat(K),L) = bot_bot_set_nat ) ) ).

% greaterThanLessThan_empty
tff(fact_6164_greaterThanLessThan__empty,axiom,
    ! [L: code_integer,K: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,L),K)
     => ( aa_Cod2813182003028390446nteger(set_or4266950643985792945nteger(K),L) = bot_bo3990330152332043303nteger ) ) ).

% greaterThanLessThan_empty
tff(fact_6165_infinite__Ioo__iff,axiom,
    ! [A: rat,B: rat] :
      ( ~ finite_finite_rat(set_or5199638295745620268an_rat(A,B))
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B) ) ).

% infinite_Ioo_iff
tff(fact_6166_image__uminus__greaterThanLessThan,axiom,
    ! [X2: rat,Y: rat] : image_rat_rat(uminus_uminus_rat,set_or5199638295745620268an_rat(X2,Y)) = set_or5199638295745620268an_rat(aa_rat_rat(uminus_uminus_rat,Y),aa_rat_rat(uminus_uminus_rat,X2)) ).

% image_uminus_greaterThanLessThan
tff(fact_6167_image__uminus__greaterThanLessThan,axiom,
    ! [X2: int,Y: int] : aa_set_int_set_int(image_int_int(uminus_uminus_int),aa_int_set_int(set_or5832277885323065728an_int(X2),Y)) = aa_int_set_int(set_or5832277885323065728an_int(aa_int_int(uminus_uminus_int,Y)),aa_int_int(uminus_uminus_int,X2)) ).

% image_uminus_greaterThanLessThan
tff(fact_6168_image__uminus__greaterThanLessThan,axiom,
    ! [X2: code_integer,Y: code_integer] : image_4470545334726330049nteger(uminus1351360451143612070nteger,aa_Cod2813182003028390446nteger(set_or4266950643985792945nteger(X2),Y)) = aa_Cod2813182003028390446nteger(set_or4266950643985792945nteger(aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,Y)),aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,X2)) ).

% image_uminus_greaterThanLessThan
tff(fact_6169_prod_Oempty_H,axiom,
    ! [P2: fun_o_Code_integer] : groups2836416601086271911nteger(P2,bot_bot_set_o) = one_one_Code_integer ).

% prod.empty'
tff(fact_6170_prod_Oempty_H,axiom,
    ! [P2: fun_o_assn] : groups12625163056032370o_assn(P2,bot_bot_set_o) = one_one_assn ).

% prod.empty'
tff(fact_6171_prod_Oempty_H,axiom,
    ! [P2: fun_o_rat] : groups4688112016125141794_o_rat(P2,bot_bot_set_o) = one_one_rat ).

% prod.empty'
tff(fact_6172_prod_Oempty_H,axiom,
    ! [P2: fun_o_nat] : groups5323242076211637530_o_nat(P2,bot_bot_set_o) = one_one_nat ).

% prod.empty'
tff(fact_6173_prod_Oempty_H,axiom,
    ! [P2: fun_o_int] : groups5320751605702587254_o_int(P2,bot_bot_set_o) = one_one_int ).

% prod.empty'
tff(fact_6174_prod_Oempty_H,axiom,
    ! [P2: fun_nat_Code_integer] : groups8290090294887179773nteger(P2,bot_bot_set_nat) = one_one_Code_integer ).

% prod.empty'
tff(fact_6175_prod_Oempty_H,axiom,
    ! [P2: fun_nat_assn] : groups3916077543535352520t_assn(P2,bot_bot_set_nat) = one_one_assn ).

% prod.empty'
tff(fact_6176_prod_Oempty_H,axiom,
    ! [P2: fun_nat_rat] : groups4112464933559648120at_rat(P2,bot_bot_set_nat) = one_one_rat ).

% prod.empty'
tff(fact_6177_prod_Oempty_H,axiom,
    ! [P2: fun_nat_nat] : aa_set_nat_nat(groups4747594993646143856at_nat(P2),bot_bot_set_nat) = one_one_nat ).

% prod.empty'
tff(fact_6178_prod_Oempty_H,axiom,
    ! [P2: fun_nat_int] : groups4745104523137093580at_int(P2,bot_bot_set_nat) = one_one_int ).

% prod.empty'
tff(fact_6179_smin__emptyI,axiom,
    ! [X7: set_Pr1261947904930325089at_nat] :
      ( ( X7 != bot_bo2099793752762293965at_nat )
     => member8757157785044589968at_nat(produc2922128104949294807at_nat(X7,bot_bo2099793752762293965at_nat),fun_min_strict) ) ).

% smin_emptyI
tff(fact_6180_wmax__emptyI,axiom,
    ! [X7: set_Pr1261947904930325089at_nat] :
      ( finite6177210948735845034at_nat(X7)
     => member8757157785044589968at_nat(produc2922128104949294807at_nat(bot_bo2099793752762293965at_nat,X7),fun_max_weak) ) ).

% wmax_emptyI
tff(fact_6181_wmin__emptyI,axiom,
    ! [X7: set_Pr1261947904930325089at_nat] : member8757157785044589968at_nat(produc2922128104949294807at_nat(X7,bot_bo2099793752762293965at_nat),fun_min_weak) ).

% wmin_emptyI
tff(fact_6182_prod_Onon__neutral_H,axiom,
    ! [G: fun_o_Code_integer,I4: set_o] : groups2836416601086271911nteger(G,collect_o(aa_set_o_fun_o_o(aTP_Lamm_so(G),I4))) = groups2836416601086271911nteger(G,I4) ).

% prod.non_neutral'
tff(fact_6183_prod_Onon__neutral_H,axiom,
    ! [G: fun_int_Code_integer,I4: set_int] : groups8661743855124024409nteger(G,collect_int(aa_set_int_fun_int_o(aTP_Lamm_sp(G),I4))) = groups8661743855124024409nteger(G,I4) ).

% prod.non_neutral'
tff(fact_6184_prod_Onon__neutral_H,axiom,
    ! [G: fun_nat_Code_integer,I4: set_nat] : groups8290090294887179773nteger(G,collect_nat(aa_set_nat_fun_nat_o(aTP_Lamm_sq(G),I4))) = groups8290090294887179773nteger(G,I4) ).

% prod.non_neutral'
tff(fact_6185_prod_Onon__neutral_H,axiom,
    ! [G: fun_o_assn,I4: set_o] : groups12625163056032370o_assn(G,collect_o(aa_set_o_fun_o_o(aTP_Lamm_sr(G),I4))) = groups12625163056032370o_assn(G,I4) ).

% prod.non_neutral'
tff(fact_6186_prod_Onon__neutral_H,axiom,
    ! [G: fun_int_assn,I4: set_int] : groups4891613008741529892t_assn(G,collect_int(aa_set_int_fun_int_o(aTP_Lamm_ss(G),I4))) = groups4891613008741529892t_assn(G,I4) ).

% prod.non_neutral'
tff(fact_6187_prod_Onon__neutral_H,axiom,
    ! [G: fun_nat_assn,I4: set_nat] : groups3916077543535352520t_assn(G,collect_nat(aa_set_nat_fun_nat_o(aTP_Lamm_st(G),I4))) = groups3916077543535352520t_assn(G,I4) ).

% prod.non_neutral'
tff(fact_6188_prod_Onon__neutral_H,axiom,
    ! [G: fun_o_rat,I4: set_o] : groups4688112016125141794_o_rat(G,collect_o(aa_set_o_fun_o_o(aTP_Lamm_su(G),I4))) = groups4688112016125141794_o_rat(G,I4) ).

% prod.non_neutral'
tff(fact_6189_prod_Onon__neutral_H,axiom,
    ! [G: fun_int_rat,I4: set_int] : groups5111818645460702676nt_rat(G,collect_int(aa_set_int_fun_int_o(aTP_Lamm_sv(G),I4))) = groups5111818645460702676nt_rat(G,I4) ).

% prod.non_neutral'
tff(fact_6190_prod_Onon__neutral_H,axiom,
    ! [G: fun_nat_rat,I4: set_nat] : groups4112464933559648120at_rat(G,collect_nat(aa_set_nat_fun_nat_o(aTP_Lamm_sw(G),I4))) = groups4112464933559648120at_rat(G,I4) ).

% prod.non_neutral'
tff(fact_6191_prod_Onon__neutral_H,axiom,
    ! [G: fun_o_nat,I4: set_o] : groups5323242076211637530_o_nat(G,collect_o(aa_set_o_fun_o_o(aTP_Lamm_sx(G),I4))) = groups5323242076211637530_o_nat(G,I4) ).

% prod.non_neutral'
tff(fact_6192_infinite__Ioo,axiom,
    ! [A: rat,B: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B)
     => ~ finite_finite_rat(set_or5199638295745620268an_rat(A,B)) ) ).

% infinite_Ioo
tff(fact_6193_greaterThanLessThan__subseteq__greaterThanLessThan,axiom,
    ! [A: rat,B: rat,C: rat,D2: rat] :
      ( ord_less_eq_set_rat(set_or5199638295745620268an_rat(A,B),set_or5199638295745620268an_rat(C,D2))
    <=> ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B)
       => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,C),A)
          & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),D2) ) ) ) ).

% greaterThanLessThan_subseteq_greaterThanLessThan
tff(fact_6194_prod__decode__aux_Ocases,axiom,
    ! [X2: product_prod_nat_nat] :
      ~ ! [K3: nat,M4: nat] : X2 != aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,K3),M4) ).

% prod_decode_aux.cases
tff(fact_6195_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
    ! [L: int,U: int] : aa_int_set_int(set_or4662586982721622107an_int(aa_int_int(aa_int_fun_int_int(plus_plus_int,L),one_one_int)),U) = aa_int_set_int(set_or5832277885323065728an_int(L),U) ).

% atLeastPlusOneLessThan_greaterThanLessThan_int
tff(fact_6196_prod_Omono__neutral__left_H,axiom,
    ! [S2: set_nat,T4: set_nat,G: fun_nat_Code_integer] :
      ( aa_set_nat_o(ord_less_eq_set_nat(S2),T4)
     => ( ! [X3: nat] :
            ( member_nat(X3,minus_minus_set_nat(T4,S2))
           => ( aa_nat_Code_integer(G,X3) = one_one_Code_integer ) )
       => ( groups8290090294887179773nteger(G,S2) = groups8290090294887179773nteger(G,T4) ) ) ) ).

% prod.mono_neutral_left'
tff(fact_6197_prod_Omono__neutral__left_H,axiom,
    ! [S2: set_nat,T4: set_nat,G: fun_nat_assn] :
      ( aa_set_nat_o(ord_less_eq_set_nat(S2),T4)
     => ( ! [X3: nat] :
            ( member_nat(X3,minus_minus_set_nat(T4,S2))
           => ( aa_nat_assn(G,X3) = one_one_assn ) )
       => ( groups3916077543535352520t_assn(G,S2) = groups3916077543535352520t_assn(G,T4) ) ) ) ).

% prod.mono_neutral_left'
tff(fact_6198_prod_Omono__neutral__left_H,axiom,
    ! [S2: set_nat,T4: set_nat,G: fun_nat_rat] :
      ( aa_set_nat_o(ord_less_eq_set_nat(S2),T4)
     => ( ! [X3: nat] :
            ( member_nat(X3,minus_minus_set_nat(T4,S2))
           => ( aa_nat_rat(G,X3) = one_one_rat ) )
       => ( groups4112464933559648120at_rat(G,S2) = groups4112464933559648120at_rat(G,T4) ) ) ) ).

% prod.mono_neutral_left'
tff(fact_6199_prod_Omono__neutral__left_H,axiom,
    ! [S2: set_nat,T4: set_nat,G: fun_nat_nat] :
      ( aa_set_nat_o(ord_less_eq_set_nat(S2),T4)
     => ( ! [X3: nat] :
            ( member_nat(X3,minus_minus_set_nat(T4,S2))
           => ( aa_nat_nat(G,X3) = one_one_nat ) )
       => ( aa_set_nat_nat(groups4747594993646143856at_nat(G),S2) = aa_set_nat_nat(groups4747594993646143856at_nat(G),T4) ) ) ) ).

% prod.mono_neutral_left'
tff(fact_6200_prod_Omono__neutral__left_H,axiom,
    ! [S2: set_nat,T4: set_nat,G: fun_nat_int] :
      ( aa_set_nat_o(ord_less_eq_set_nat(S2),T4)
     => ( ! [X3: nat] :
            ( member_nat(X3,minus_minus_set_nat(T4,S2))
           => ( aa_nat_int(G,X3) = one_one_int ) )
       => ( groups4745104523137093580at_int(G,S2) = groups4745104523137093580at_int(G,T4) ) ) ) ).

% prod.mono_neutral_left'
tff(fact_6201_prod_Omono__neutral__right_H,axiom,
    ! [S2: set_nat,T4: set_nat,G: fun_nat_Code_integer] :
      ( aa_set_nat_o(ord_less_eq_set_nat(S2),T4)
     => ( ! [X3: nat] :
            ( member_nat(X3,minus_minus_set_nat(T4,S2))
           => ( aa_nat_Code_integer(G,X3) = one_one_Code_integer ) )
       => ( groups8290090294887179773nteger(G,T4) = groups8290090294887179773nteger(G,S2) ) ) ) ).

% prod.mono_neutral_right'
tff(fact_6202_prod_Omono__neutral__right_H,axiom,
    ! [S2: set_nat,T4: set_nat,G: fun_nat_assn] :
      ( aa_set_nat_o(ord_less_eq_set_nat(S2),T4)
     => ( ! [X3: nat] :
            ( member_nat(X3,minus_minus_set_nat(T4,S2))
           => ( aa_nat_assn(G,X3) = one_one_assn ) )
       => ( groups3916077543535352520t_assn(G,T4) = groups3916077543535352520t_assn(G,S2) ) ) ) ).

% prod.mono_neutral_right'
tff(fact_6203_prod_Omono__neutral__right_H,axiom,
    ! [S2: set_nat,T4: set_nat,G: fun_nat_rat] :
      ( aa_set_nat_o(ord_less_eq_set_nat(S2),T4)
     => ( ! [X3: nat] :
            ( member_nat(X3,minus_minus_set_nat(T4,S2))
           => ( aa_nat_rat(G,X3) = one_one_rat ) )
       => ( groups4112464933559648120at_rat(G,T4) = groups4112464933559648120at_rat(G,S2) ) ) ) ).

% prod.mono_neutral_right'
tff(fact_6204_prod_Omono__neutral__right_H,axiom,
    ! [S2: set_nat,T4: set_nat,G: fun_nat_nat] :
      ( aa_set_nat_o(ord_less_eq_set_nat(S2),T4)
     => ( ! [X3: nat] :
            ( member_nat(X3,minus_minus_set_nat(T4,S2))
           => ( aa_nat_nat(G,X3) = one_one_nat ) )
       => ( aa_set_nat_nat(groups4747594993646143856at_nat(G),T4) = aa_set_nat_nat(groups4747594993646143856at_nat(G),S2) ) ) ) ).

% prod.mono_neutral_right'
tff(fact_6205_prod_Omono__neutral__right_H,axiom,
    ! [S2: set_nat,T4: set_nat,G: fun_nat_int] :
      ( aa_set_nat_o(ord_less_eq_set_nat(S2),T4)
     => ( ! [X3: nat] :
            ( member_nat(X3,minus_minus_set_nat(T4,S2))
           => ( aa_nat_int(G,X3) = one_one_int ) )
       => ( groups4745104523137093580at_int(G,T4) = groups4745104523137093580at_int(G,S2) ) ) ) ).

% prod.mono_neutral_right'
tff(fact_6206_prod_Omono__neutral__cong__left_H,axiom,
    ! [S2: set_o,T4: set_o,Ha: fun_o_Code_integer,G: fun_o_Code_integer] :
      ( ord_less_eq_set_o(S2,T4)
     => ( ! [I2: $o] :
            ( member_o((I2),minus_minus_set_o(T4,S2))
           => ( aa_o_Code_integer(Ha,(I2)) = one_one_Code_integer ) )
       => ( ! [X3: $o] :
              ( member_o((X3),S2)
             => ( aa_o_Code_integer(G,(X3)) = aa_o_Code_integer(Ha,(X3)) ) )
         => ( groups2836416601086271911nteger(G,S2) = groups2836416601086271911nteger(Ha,T4) ) ) ) ) ).

% prod.mono_neutral_cong_left'
tff(fact_6207_prod_Omono__neutral__cong__left_H,axiom,
    ! [S2: set_int,T4: set_int,Ha: fun_int_Code_integer,G: fun_int_Code_integer] :
      ( ord_less_eq_set_int(S2,T4)
     => ( ! [I2: int] :
            ( member_int(I2,minus_minus_set_int(T4,S2))
           => ( aa_int_Code_integer(Ha,I2) = one_one_Code_integer ) )
       => ( ! [X3: int] :
              ( member_int(X3,S2)
             => ( aa_int_Code_integer(G,X3) = aa_int_Code_integer(Ha,X3) ) )
         => ( groups8661743855124024409nteger(G,S2) = groups8661743855124024409nteger(Ha,T4) ) ) ) ) ).

% prod.mono_neutral_cong_left'
tff(fact_6208_prod_Omono__neutral__cong__left_H,axiom,
    ! [S2: set_o,T4: set_o,Ha: fun_o_assn,G: fun_o_assn] :
      ( ord_less_eq_set_o(S2,T4)
     => ( ! [I2: $o] :
            ( member_o((I2),minus_minus_set_o(T4,S2))
           => ( aa_o_assn(Ha,(I2)) = one_one_assn ) )
       => ( ! [X3: $o] :
              ( member_o((X3),S2)
             => ( aa_o_assn(G,(X3)) = aa_o_assn(Ha,(X3)) ) )
         => ( groups12625163056032370o_assn(G,S2) = groups12625163056032370o_assn(Ha,T4) ) ) ) ) ).

% prod.mono_neutral_cong_left'
tff(fact_6209_prod_Omono__neutral__cong__left_H,axiom,
    ! [S2: set_int,T4: set_int,Ha: fun_int_assn,G: fun_int_assn] :
      ( ord_less_eq_set_int(S2,T4)
     => ( ! [I2: int] :
            ( member_int(I2,minus_minus_set_int(T4,S2))
           => ( aa_int_assn(Ha,I2) = one_one_assn ) )
       => ( ! [X3: int] :
              ( member_int(X3,S2)
             => ( aa_int_assn(G,X3) = aa_int_assn(Ha,X3) ) )
         => ( groups4891613008741529892t_assn(G,S2) = groups4891613008741529892t_assn(Ha,T4) ) ) ) ) ).

% prod.mono_neutral_cong_left'
tff(fact_6210_prod_Omono__neutral__cong__left_H,axiom,
    ! [S2: set_o,T4: set_o,Ha: fun_o_rat,G: fun_o_rat] :
      ( ord_less_eq_set_o(S2,T4)
     => ( ! [I2: $o] :
            ( member_o((I2),minus_minus_set_o(T4,S2))
           => ( aa_o_rat(Ha,(I2)) = one_one_rat ) )
       => ( ! [X3: $o] :
              ( member_o((X3),S2)
             => ( aa_o_rat(G,(X3)) = aa_o_rat(Ha,(X3)) ) )
         => ( groups4688112016125141794_o_rat(G,S2) = groups4688112016125141794_o_rat(Ha,T4) ) ) ) ) ).

% prod.mono_neutral_cong_left'
tff(fact_6211_prod_Omono__neutral__cong__left_H,axiom,
    ! [S2: set_int,T4: set_int,Ha: fun_int_rat,G: fun_int_rat] :
      ( ord_less_eq_set_int(S2,T4)
     => ( ! [I2: int] :
            ( member_int(I2,minus_minus_set_int(T4,S2))
           => ( aa_int_rat(Ha,I2) = one_one_rat ) )
       => ( ! [X3: int] :
              ( member_int(X3,S2)
             => ( aa_int_rat(G,X3) = aa_int_rat(Ha,X3) ) )
         => ( groups5111818645460702676nt_rat(G,S2) = groups5111818645460702676nt_rat(Ha,T4) ) ) ) ) ).

% prod.mono_neutral_cong_left'
tff(fact_6212_prod_Omono__neutral__cong__left_H,axiom,
    ! [S2: set_o,T4: set_o,Ha: fun_o_nat,G: fun_o_nat] :
      ( ord_less_eq_set_o(S2,T4)
     => ( ! [I2: $o] :
            ( member_o((I2),minus_minus_set_o(T4,S2))
           => ( aa_o_nat(Ha,(I2)) = one_one_nat ) )
       => ( ! [X3: $o] :
              ( member_o((X3),S2)
             => ( aa_o_nat(G,(X3)) = aa_o_nat(Ha,(X3)) ) )
         => ( groups5323242076211637530_o_nat(G,S2) = groups5323242076211637530_o_nat(Ha,T4) ) ) ) ) ).

% prod.mono_neutral_cong_left'
tff(fact_6213_prod_Omono__neutral__cong__left_H,axiom,
    ! [S2: set_int,T4: set_int,Ha: fun_int_nat,G: fun_int_nat] :
      ( ord_less_eq_set_int(S2,T4)
     => ( ! [I2: int] :
            ( member_int(I2,minus_minus_set_int(T4,S2))
           => ( aa_int_nat(Ha,I2) = one_one_nat ) )
       => ( ! [X3: int] :
              ( member_int(X3,S2)
             => ( aa_int_nat(G,X3) = aa_int_nat(Ha,X3) ) )
         => ( groups5746948705547198412nt_nat(G,S2) = groups5746948705547198412nt_nat(Ha,T4) ) ) ) ) ).

% prod.mono_neutral_cong_left'
tff(fact_6214_prod_Omono__neutral__cong__left_H,axiom,
    ! [S2: set_o,T4: set_o,Ha: fun_o_int,G: fun_o_int] :
      ( ord_less_eq_set_o(S2,T4)
     => ( ! [I2: $o] :
            ( member_o((I2),minus_minus_set_o(T4,S2))
           => ( aa_o_int(Ha,(I2)) = one_one_int ) )
       => ( ! [X3: $o] :
              ( member_o((X3),S2)
             => ( aa_o_int(G,(X3)) = aa_o_int(Ha,(X3)) ) )
         => ( groups5320751605702587254_o_int(G,S2) = groups5320751605702587254_o_int(Ha,T4) ) ) ) ) ).

% prod.mono_neutral_cong_left'
tff(fact_6215_prod_Omono__neutral__cong__left_H,axiom,
    ! [S2: set_int,T4: set_int,Ha: fun_int_int,G: fun_int_int] :
      ( ord_less_eq_set_int(S2,T4)
     => ( ! [I2: int] :
            ( member_int(I2,minus_minus_set_int(T4,S2))
           => ( aa_int_int(Ha,I2) = one_one_int ) )
       => ( ! [X3: int] :
              ( member_int(X3,S2)
             => ( aa_int_int(G,X3) = aa_int_int(Ha,X3) ) )
         => ( aa_set_int_int(groups5744458235038148136nt_int(G),S2) = aa_set_int_int(groups5744458235038148136nt_int(Ha),T4) ) ) ) ) ).

% prod.mono_neutral_cong_left'
tff(fact_6216_prod_Omono__neutral__cong__right_H,axiom,
    ! [S2: set_o,T4: set_o,G: fun_o_Code_integer,Ha: fun_o_Code_integer] :
      ( ord_less_eq_set_o(S2,T4)
     => ( ! [X3: $o] :
            ( member_o((X3),minus_minus_set_o(T4,S2))
           => ( aa_o_Code_integer(G,(X3)) = one_one_Code_integer ) )
       => ( ! [X3: $o] :
              ( member_o((X3),S2)
             => ( aa_o_Code_integer(G,(X3)) = aa_o_Code_integer(Ha,(X3)) ) )
         => ( groups2836416601086271911nteger(G,T4) = groups2836416601086271911nteger(Ha,S2) ) ) ) ) ).

% prod.mono_neutral_cong_right'
tff(fact_6217_prod_Omono__neutral__cong__right_H,axiom,
    ! [S2: set_int,T4: set_int,G: fun_int_Code_integer,Ha: fun_int_Code_integer] :
      ( ord_less_eq_set_int(S2,T4)
     => ( ! [X3: int] :
            ( member_int(X3,minus_minus_set_int(T4,S2))
           => ( aa_int_Code_integer(G,X3) = one_one_Code_integer ) )
       => ( ! [X3: int] :
              ( member_int(X3,S2)
             => ( aa_int_Code_integer(G,X3) = aa_int_Code_integer(Ha,X3) ) )
         => ( groups8661743855124024409nteger(G,T4) = groups8661743855124024409nteger(Ha,S2) ) ) ) ) ).

% prod.mono_neutral_cong_right'
tff(fact_6218_prod_Omono__neutral__cong__right_H,axiom,
    ! [S2: set_o,T4: set_o,G: fun_o_assn,Ha: fun_o_assn] :
      ( ord_less_eq_set_o(S2,T4)
     => ( ! [X3: $o] :
            ( member_o((X3),minus_minus_set_o(T4,S2))
           => ( aa_o_assn(G,(X3)) = one_one_assn ) )
       => ( ! [X3: $o] :
              ( member_o((X3),S2)
             => ( aa_o_assn(G,(X3)) = aa_o_assn(Ha,(X3)) ) )
         => ( groups12625163056032370o_assn(G,T4) = groups12625163056032370o_assn(Ha,S2) ) ) ) ) ).

% prod.mono_neutral_cong_right'
tff(fact_6219_prod_Omono__neutral__cong__right_H,axiom,
    ! [S2: set_int,T4: set_int,G: fun_int_assn,Ha: fun_int_assn] :
      ( ord_less_eq_set_int(S2,T4)
     => ( ! [X3: int] :
            ( member_int(X3,minus_minus_set_int(T4,S2))
           => ( aa_int_assn(G,X3) = one_one_assn ) )
       => ( ! [X3: int] :
              ( member_int(X3,S2)
             => ( aa_int_assn(G,X3) = aa_int_assn(Ha,X3) ) )
         => ( groups4891613008741529892t_assn(G,T4) = groups4891613008741529892t_assn(Ha,S2) ) ) ) ) ).

% prod.mono_neutral_cong_right'
tff(fact_6220_prod_Omono__neutral__cong__right_H,axiom,
    ! [S2: set_o,T4: set_o,G: fun_o_rat,Ha: fun_o_rat] :
      ( ord_less_eq_set_o(S2,T4)
     => ( ! [X3: $o] :
            ( member_o((X3),minus_minus_set_o(T4,S2))
           => ( aa_o_rat(G,(X3)) = one_one_rat ) )
       => ( ! [X3: $o] :
              ( member_o((X3),S2)
             => ( aa_o_rat(G,(X3)) = aa_o_rat(Ha,(X3)) ) )
         => ( groups4688112016125141794_o_rat(G,T4) = groups4688112016125141794_o_rat(Ha,S2) ) ) ) ) ).

% prod.mono_neutral_cong_right'
tff(fact_6221_prod_Omono__neutral__cong__right_H,axiom,
    ! [S2: set_int,T4: set_int,G: fun_int_rat,Ha: fun_int_rat] :
      ( ord_less_eq_set_int(S2,T4)
     => ( ! [X3: int] :
            ( member_int(X3,minus_minus_set_int(T4,S2))
           => ( aa_int_rat(G,X3) = one_one_rat ) )
       => ( ! [X3: int] :
              ( member_int(X3,S2)
             => ( aa_int_rat(G,X3) = aa_int_rat(Ha,X3) ) )
         => ( groups5111818645460702676nt_rat(G,T4) = groups5111818645460702676nt_rat(Ha,S2) ) ) ) ) ).

% prod.mono_neutral_cong_right'
tff(fact_6222_prod_Omono__neutral__cong__right_H,axiom,
    ! [S2: set_o,T4: set_o,G: fun_o_nat,Ha: fun_o_nat] :
      ( ord_less_eq_set_o(S2,T4)
     => ( ! [X3: $o] :
            ( member_o((X3),minus_minus_set_o(T4,S2))
           => ( aa_o_nat(G,(X3)) = one_one_nat ) )
       => ( ! [X3: $o] :
              ( member_o((X3),S2)
             => ( aa_o_nat(G,(X3)) = aa_o_nat(Ha,(X3)) ) )
         => ( groups5323242076211637530_o_nat(G,T4) = groups5323242076211637530_o_nat(Ha,S2) ) ) ) ) ).

% prod.mono_neutral_cong_right'
tff(fact_6223_prod_Omono__neutral__cong__right_H,axiom,
    ! [S2: set_int,T4: set_int,G: fun_int_nat,Ha: fun_int_nat] :
      ( ord_less_eq_set_int(S2,T4)
     => ( ! [X3: int] :
            ( member_int(X3,minus_minus_set_int(T4,S2))
           => ( aa_int_nat(G,X3) = one_one_nat ) )
       => ( ! [X3: int] :
              ( member_int(X3,S2)
             => ( aa_int_nat(G,X3) = aa_int_nat(Ha,X3) ) )
         => ( groups5746948705547198412nt_nat(G,T4) = groups5746948705547198412nt_nat(Ha,S2) ) ) ) ) ).

% prod.mono_neutral_cong_right'
tff(fact_6224_prod_Omono__neutral__cong__right_H,axiom,
    ! [S2: set_o,T4: set_o,G: fun_o_int,Ha: fun_o_int] :
      ( ord_less_eq_set_o(S2,T4)
     => ( ! [X3: $o] :
            ( member_o((X3),minus_minus_set_o(T4,S2))
           => ( aa_o_int(G,(X3)) = one_one_int ) )
       => ( ! [X3: $o] :
              ( member_o((X3),S2)
             => ( aa_o_int(G,(X3)) = aa_o_int(Ha,(X3)) ) )
         => ( groups5320751605702587254_o_int(G,T4) = groups5320751605702587254_o_int(Ha,S2) ) ) ) ) ).

% prod.mono_neutral_cong_right'
tff(fact_6225_prod_Omono__neutral__cong__right_H,axiom,
    ! [S2: set_int,T4: set_int,G: fun_int_int,Ha: fun_int_int] :
      ( ord_less_eq_set_int(S2,T4)
     => ( ! [X3: int] :
            ( member_int(X3,minus_minus_set_int(T4,S2))
           => ( aa_int_int(G,X3) = one_one_int ) )
       => ( ! [X3: int] :
              ( member_int(X3,S2)
             => ( aa_int_int(G,X3) = aa_int_int(Ha,X3) ) )
         => ( aa_set_int_int(groups5744458235038148136nt_int(G),T4) = aa_set_int_int(groups5744458235038148136nt_int(Ha),S2) ) ) ) ) ).

% prod.mono_neutral_cong_right'
tff(fact_6226_prod_Odistrib_H,axiom,
    ! [I4: set_o,G: fun_o_Code_integer,Ha: fun_o_Code_integer] :
      ( finite_finite_o(collect_o(aa_fun8192762245619933327un_o_o(aTP_Lamm_pr(I4),G)))
     => ( finite_finite_o(collect_o(aa_fun8192762245619933327un_o_o(aTP_Lamm_pr(I4),Ha)))
       => ( groups2836416601086271911nteger(aa_fun8520278569782659900nteger(aTP_Lamm_sy(G),Ha),I4) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,groups2836416601086271911nteger(G,I4)),groups2836416601086271911nteger(Ha,I4)) ) ) ) ).

% prod.distrib'
tff(fact_6227_prod_Odistrib_H,axiom,
    ! [I4: set_nat,G: fun_nat_Code_integer,Ha: fun_nat_Code_integer] :
      ( finite_finite_nat(collect_nat(aa_fun3480067038916266681_nat_o(aTP_Lamm_pt(I4),G)))
     => ( finite_finite_nat(collect_nat(aa_fun3480067038916266681_nat_o(aTP_Lamm_pt(I4),Ha)))
       => ( groups8290090294887179773nteger(aa_fun589076786913273746nteger(aTP_Lamm_sz(G),Ha),I4) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,groups8290090294887179773nteger(G,I4)),groups8290090294887179773nteger(Ha,I4)) ) ) ) ).

% prod.distrib'
tff(fact_6228_prod_Odistrib_H,axiom,
    ! [I4: set_int,G: fun_int_Code_integer,Ha: fun_int_Code_integer] :
      ( finite_finite_int(collect_int(aa_fun3336537925265328129_int_o(aTP_Lamm_pv(I4),G)))
     => ( finite_finite_int(collect_int(aa_fun3336537925265328129_int_o(aTP_Lamm_pv(I4),Ha)))
       => ( groups8661743855124024409nteger(aa_fun5304498221708291146nteger(aTP_Lamm_ta(G),Ha),I4) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,groups8661743855124024409nteger(G,I4)),groups8661743855124024409nteger(Ha,I4)) ) ) ) ).

% prod.distrib'
tff(fact_6229_prod_Odistrib_H,axiom,
    ! [I4: set_Code_integer,G: fun_Co8499238673658658103nteger,Ha: fun_Co8499238673658658103nteger] :
      ( finite6017078050557962740nteger(collect_Code_integer(aa_fun7159535342743012639eger_o(aTP_Lamm_px(I4),G)))
     => ( finite6017078050557962740nteger(collect_Code_integer(aa_fun7159535342743012639eger_o(aTP_Lamm_px(I4),Ha)))
       => ( aa_set8546232603906849326nteger(groups7219916603568234122nteger(aa_fun4435975922079263404nteger(aTP_Lamm_tb(G),Ha)),I4) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_set8546232603906849326nteger(groups7219916603568234122nteger(G),I4)),aa_set8546232603906849326nteger(groups7219916603568234122nteger(Ha),I4)) ) ) ) ).

% prod.distrib'
tff(fact_6230_prod_Odistrib_H,axiom,
    ! [I4: set_o,G: fun_o_assn,Ha: fun_o_assn] :
      ( finite_finite_o(collect_o(aa_fun8382565201914911066un_o_o(aTP_Lamm_pz(I4),G)))
     => ( finite_finite_o(collect_o(aa_fun8382565201914911066un_o_o(aTP_Lamm_pz(I4),Ha)))
       => ( groups12625163056032370o_assn(aa_fun4536517337817438332o_assn(aTP_Lamm_tc(G),Ha),I4) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,groups12625163056032370o_assn(G,I4)),groups12625163056032370o_assn(Ha,I4)) ) ) ) ).

% prod.distrib'
tff(fact_6231_prod_Odistrib_H,axiom,
    ! [I4: set_nat,G: fun_nat_assn,Ha: fun_nat_assn] :
      ( finite_finite_nat(collect_nat(aa_fun7183233715851567790_nat_o(aTP_Lamm_qb(I4),G)))
     => ( finite_finite_nat(collect_nat(aa_fun7183233715851567790_nat_o(aTP_Lamm_qb(I4),Ha)))
       => ( groups3916077543535352520t_assn(aa_fun785744391571715112t_assn(aTP_Lamm_td(G),Ha),I4) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,groups3916077543535352520t_assn(G,I4)),groups3916077543535352520t_assn(Ha,I4)) ) ) ) ).

% prod.distrib'
tff(fact_6232_prod_Odistrib_H,axiom,
    ! [I4: set_int,G: fun_int_assn,Ha: fun_int_assn] :
      ( finite_finite_int(collect_int(aa_fun202081646129719286_int_o(aTP_Lamm_qd(I4),G)))
     => ( finite_finite_int(collect_int(aa_fun202081646129719286_int_o(aTP_Lamm_qd(I4),Ha)))
       => ( groups4891613008741529892t_assn(aa_fun919007281442365664t_assn(aTP_Lamm_te(G),Ha),I4) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,groups4891613008741529892t_assn(G,I4)),groups4891613008741529892t_assn(Ha,I4)) ) ) ) ).

% prod.distrib'
tff(fact_6233_prod_Odistrib_H,axiom,
    ! [I4: set_Code_integer,G: fun_Co4490034186337852034r_assn,Ha: fun_Co4490034186337852034r_assn] :
      ( finite6017078050557962740nteger(collect_Code_integer(aa_fun6538703224075513620eger_o(aTP_Lamm_qf(I4),G)))
     => ( finite6017078050557962740nteger(collect_Code_integer(aa_fun6538703224075513620eger_o(aTP_Lamm_qf(I4),Ha)))
       => ( groups980104329299799381r_assn(aa_fun4119713415300323650r_assn(aTP_Lamm_tf(G),Ha),I4) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,groups980104329299799381r_assn(G,I4)),groups980104329299799381r_assn(Ha,I4)) ) ) ) ).

% prod.distrib'
tff(fact_6234_prod_Odistrib_H,axiom,
    ! [I4: set_o,G: fun_o_rat,Ha: fun_o_rat] :
      ( finite_finite_o(collect_o(aa_fun_o_rat_fun_o_o(aTP_Lamm_qh(I4),G)))
     => ( finite_finite_o(collect_o(aa_fun_o_rat_fun_o_o(aTP_Lamm_qh(I4),Ha)))
       => ( groups4688112016125141794_o_rat(aa_fun4336163974892599420_o_rat(aTP_Lamm_tg(G),Ha),I4) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,groups4688112016125141794_o_rat(G,I4)),groups4688112016125141794_o_rat(Ha,I4)) ) ) ) ).

% prod.distrib'
tff(fact_6235_prod_Odistrib_H,axiom,
    ! [I4: set_nat,G: fun_nat_rat,Ha: fun_nat_rat] :
      ( finite_finite_nat(collect_nat(aa_fun1118977351124560894_nat_o(aTP_Lamm_qj(I4),G)))
     => ( finite_finite_nat(collect_nat(aa_fun1118977351124560894_nat_o(aTP_Lamm_qj(I4),Ha)))
       => ( groups4112464933559648120at_rat(aa_fun765758790203053448at_rat(aTP_Lamm_th(G),Ha),I4) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,groups4112464933559648120at_rat(G,I4)),groups4112464933559648120at_rat(Ha,I4)) ) ) ) ).

% prod.distrib'
tff(fact_6236_prod_OG__def,axiom,
    ! [P2: fun_o_Code_integer,I4: set_o] :
      groups2836416601086271911nteger(P2,I4) = $ite(finite_finite_o(collect_o(aa_set_o_fun_o_o(aTP_Lamm_so(P2),I4))),aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,P2),collect_o(aa_set_o_fun_o_o(aTP_Lamm_so(P2),I4))),one_one_Code_integer) ).

% prod.G_def
tff(fact_6237_prod_OG__def,axiom,
    ! [P2: fun_nat_Code_integer,I4: set_nat] :
      groups8290090294887179773nteger(P2,I4) = $ite(finite_finite_nat(collect_nat(aa_set_nat_fun_nat_o(aTP_Lamm_sq(P2),I4))),groups3455450783089532116nteger(P2,collect_nat(aa_set_nat_fun_nat_o(aTP_Lamm_sq(P2),I4))),one_one_Code_integer) ).

% prod.G_def
tff(fact_6238_prod_OG__def,axiom,
    ! [P2: fun_int_Code_integer,I4: set_int] :
      groups8661743855124024409nteger(P2,I4) = $ite(finite_finite_int(collect_int(aa_set_int_fun_int_o(aTP_Lamm_sp(P2),I4))),aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,P2),collect_int(aa_set_int_fun_int_o(aTP_Lamm_sp(P2),I4))),one_one_Code_integer) ).

% prod.G_def
tff(fact_6239_prod_OG__def,axiom,
    ! [P2: fun_Co8499238673658658103nteger,I4: set_Code_integer] :
      aa_set8546232603906849326nteger(groups7219916603568234122nteger(P2),I4) = $ite(finite6017078050557962740nteger(collect_Code_integer(aa_set8032437628614644675eger_o(aTP_Lamm_ti(P2),I4))),aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,P2),collect_Code_integer(aa_set8032437628614644675eger_o(aTP_Lamm_ti(P2),I4))),one_one_Code_integer) ).

% prod.G_def
tff(fact_6240_prod_OG__def,axiom,
    ! [P2: fun_o_assn,I4: set_o] :
      groups12625163056032370o_assn(P2,I4) = $ite(finite_finite_o(collect_o(aa_set_o_fun_o_o(aTP_Lamm_sr(P2),I4))),aa_set_o_assn(aa_fun1914167119812169564o_assn(groups5301882518646026715o_assn,P2),collect_o(aa_set_o_fun_o_o(aTP_Lamm_sr(P2),I4))),one_one_assn) ).

% prod.G_def
tff(fact_6241_prod_OG__def,axiom,
    ! [P2: fun_nat_assn,I4: set_nat] :
      groups3916077543535352520t_assn(P2,I4) = $ite(finite_finite_nat(collect_nat(aa_set_nat_fun_nat_o(aTP_Lamm_st(P2),I4))),groups6906906614972039071t_assn(P2,collect_nat(aa_set_nat_fun_nat_o(aTP_Lamm_st(P2),I4))),one_one_assn) ).

% prod.G_def
tff(fact_6242_prod_OG__def,axiom,
    ! [P2: fun_int_assn,I4: set_int] :
      groups4891613008741529892t_assn(P2,I4) = $ite(finite_finite_int(collect_int(aa_set_int_fun_int_o(aTP_Lamm_ss(P2),I4))),aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,P2),collect_int(aa_set_int_fun_int_o(aTP_Lamm_ss(P2),I4))),one_one_assn) ).

% prod.G_def
tff(fact_6243_prod_OG__def,axiom,
    ! [P2: fun_Co4490034186337852034r_assn,I4: set_Code_integer] :
      groups980104329299799381r_assn(P2,I4) = $ite(finite6017078050557962740nteger(collect_Code_integer(aa_set8032437628614644675eger_o(aTP_Lamm_tj(P2),I4))),aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,P2),collect_Code_integer(aa_set8032437628614644675eger_o(aTP_Lamm_tj(P2),I4))),one_one_assn) ).

% prod.G_def
tff(fact_6244_prod_OG__def,axiom,
    ! [P2: fun_o_rat,I4: set_o] :
      groups4688112016125141794_o_rat(P2,I4) = $ite(finite_finite_o(collect_o(aa_set_o_fun_o_o(aTP_Lamm_su(P2),I4))),aa_set_o_rat(aa_fun7302669049306738524_o_rat(groups2869687844427037835_o_rat,P2),collect_o(aa_set_o_fun_o_o(aTP_Lamm_su(P2),I4))),one_one_rat) ).

% prod.G_def
tff(fact_6245_prod_OG__def,axiom,
    ! [P2: fun_nat_rat,I4: set_nat] :
      groups4112464933559648120at_rat(P2,I4) = $ite(finite_finite_nat(collect_nat(aa_set_nat_fun_nat_o(aTP_Lamm_sw(P2),I4))),groups73079841787564623at_rat(P2,collect_nat(aa_set_nat_fun_nat_o(aTP_Lamm_sw(P2),I4))),one_one_rat) ).

% prod.G_def
tff(fact_6246_greaterThanLessThan__subseteq__atLeastAtMost__iff,axiom,
    ! [A: rat,B: rat,C: rat,D2: rat] :
      ( ord_less_eq_set_rat(set_or5199638295745620268an_rat(A,B),set_or633870826150836451st_rat(C,D2))
    <=> ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B)
       => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,C),A)
          & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),D2) ) ) ) ).

% greaterThanLessThan_subseteq_atLeastAtMost_iff
tff(fact_6247_greaterThanLessThan__subseteq__atLeastLessThan__iff,axiom,
    ! [A: rat,B: rat,C: rat,D2: rat] :
      ( ord_less_eq_set_rat(set_or5199638295745620268an_rat(A,B),set_or4029947393144176647an_rat(C,D2))
    <=> ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,A),B)
       => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,C),A)
          & aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,B),D2) ) ) ) ).

% greaterThanLessThan_subseteq_atLeastLessThan_iff
tff(fact_6248_atLeastAtMost__diff__ends,axiom,
    ! [A: $o,B: $o] : minus_minus_set_o(aa_o_set_o(set_or8904488021354931149Most_o((A)),(B)),insert_o((A),insert_o((B),bot_bot_set_o))) = aa_o_set_o(set_or1716231572884733764Than_o((A)),(B)) ).

% atLeastAtMost_diff_ends
tff(fact_6249_atLeastAtMost__diff__ends,axiom,
    ! [A: int,B: int] : minus_minus_set_int(aa_int_set_int(set_or1266510415728281911st_int(A),B),insert_int(A,insert_int(B,bot_bot_set_int))) = aa_int_set_int(set_or5832277885323065728an_int(A),B) ).

% atLeastAtMost_diff_ends
tff(fact_6250_atLeastAtMost__diff__ends,axiom,
    ! [A: nat,B: nat] : minus_minus_set_nat(aa_nat_set_nat(set_or1269000886237332187st_nat(A),B),insert_nat(A,insert_nat(B,bot_bot_set_nat))) = aa_nat_set_nat(set_or5834768355832116004an_nat(A),B) ).

% atLeastAtMost_diff_ends
tff(fact_6251_atLeastAtMost__diff__ends,axiom,
    ! [A: code_integer,B: code_integer] : minus_2355218937544613996nteger(aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(A),B),insert_Code_integer(A,insert_Code_integer(B,bot_bo3990330152332043303nteger))) = aa_Cod2813182003028390446nteger(set_or4266950643985792945nteger(A),B) ).

% atLeastAtMost_diff_ends
tff(fact_6252_smax__insertI,axiom,
    ! [Y: product_prod_nat_nat,Y7: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat,X7: set_Pr1261947904930325089at_nat] :
      ( member8440522571783428010at_nat(Y,Y7)
     => ( member8206827879206165904at_nat(produc6161850002892822231at_nat(X2,Y),fun_pair_less)
       => ( member8757157785044589968at_nat(produc2922128104949294807at_nat(X7,Y7),fun_max_strict)
         => member8757157785044589968at_nat(produc2922128104949294807at_nat(aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(X2),X7),Y7),fun_max_strict) ) ) ) ).

% smax_insertI
tff(fact_6253_set__decode__plus__power__2,axiom,
    ! [N2: nat,Z: nat] :
      ( ~ member_nat(N2,aa_nat_set_nat(nat_set_decode,Z))
     => ( aa_nat_set_nat(nat_set_decode,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),N2)),Z)) = insert_nat(N2,aa_nat_set_nat(nat_set_decode,Z)) ) ) ).

% set_decode_plus_power_2
tff(fact_6254_prod__decode__aux_Osimps,axiom,
    ! [K: nat,M: nat] :
      aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(nat_prod_decode_aux,K),M) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),K),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,K),M)),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(nat_prod_decode_aux,aa_nat_nat(suc,K)),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,M),aa_nat_nat(suc,K)))) ).

% prod_decode_aux.simps
tff(fact_6255_prod__decode__aux_Oelims,axiom,
    ! [X2: nat,Xa: nat,Y: product_prod_nat_nat] :
      ( ( aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(nat_prod_decode_aux,X2),Xa) = Y )
     => ( Y = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,Xa),X2),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Xa),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,X2),Xa)),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(nat_prod_decode_aux,aa_nat_nat(suc,X2)),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Xa),aa_nat_nat(suc,X2)))) ) ) ).

% prod_decode_aux.elims
tff(fact_6256_min__rpair__set,axiom,
    fun_re2478310338295953701at_nat(produc9060074326276436823at_nat(fun_min_strict,fun_min_weak)) ).

% min_rpair_set
tff(fact_6257_triangle__Suc,axiom,
    ! [N2: nat] : aa_nat_nat(nat_triangle,aa_nat_nat(suc,N2)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(nat_triangle,N2)),aa_nat_nat(suc,N2)) ).

% triangle_Suc
tff(fact_6258_finite__greaterThanLessThan,axiom,
    ! [L: nat,U: nat] : finite_finite_nat(aa_nat_set_nat(set_or5834768355832116004an_nat(L),U)) ).

% finite_greaterThanLessThan
tff(fact_6259_finite__greaterThanLessThan__integer,axiom,
    ! [L: code_integer,U: code_integer] : finite6017078050557962740nteger(aa_Cod2813182003028390446nteger(set_or4266950643985792945nteger(L),U)) ).

% finite_greaterThanLessThan_integer
tff(fact_6260_card__greaterThanLessThan,axiom,
    ! [L: nat,U: nat] : aa_set_nat_nat(finite_card_nat,aa_nat_set_nat(set_or5834768355832116004an_nat(L),U)) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,U),aa_nat_nat(suc,L)) ).

% card_greaterThanLessThan
tff(fact_6261_max__rpair__set,axiom,
    fun_re2478310338295953701at_nat(produc9060074326276436823at_nat(fun_max_strict,fun_max_weak)) ).

% max_rpair_set
tff(fact_6262_atLeastSucLessThan__greaterThanLessThan,axiom,
    ! [L: nat,U: nat] : aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(suc,L)),U) = aa_nat_set_nat(set_or5834768355832116004an_nat(L),U) ).

% atLeastSucLessThan_greaterThanLessThan
tff(fact_6263_smax__emptyI,axiom,
    ! [Y7: set_Pr1261947904930325089at_nat] :
      ( finite6177210948735845034at_nat(Y7)
     => ( ( Y7 != bot_bo2099793752762293965at_nat )
       => member8757157785044589968at_nat(produc2922128104949294807at_nat(bot_bo2099793752762293965at_nat,Y7),fun_max_strict) ) ) ).

% smax_emptyI
tff(fact_6264_atLeastPlusOneLessThan__greaterThanLessThan__integer,axiom,
    ! [L: code_integer,U: code_integer] : aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,L),one_one_Code_integer)),U) = aa_Cod2813182003028390446nteger(set_or4266950643985792945nteger(L),U) ).

% atLeastPlusOneLessThan_greaterThanLessThan_integer
tff(fact_6265_prod__decode__aux_Opelims,axiom,
    ! [X2: nat,Xa: nat,Y: product_prod_nat_nat] :
      ( ( aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(nat_prod_decode_aux,X2),Xa) = Y )
     => ( aa_Pro6150637604445964947_nat_o(accp_P4275260045618599050at_nat(nat_pr5047031295181774490ux_rel),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X2),Xa))
       => ~ ( ( Y = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,Xa),X2),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Xa),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,X2),Xa)),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(nat_prod_decode_aux,aa_nat_nat(suc,X2)),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Xa),aa_nat_nat(suc,X2)))) )
           => ~ aa_Pro6150637604445964947_nat_o(accp_P4275260045618599050at_nat(nat_pr5047031295181774490ux_rel),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X2),Xa)) ) ) ) ).

% prod_decode_aux.pelims
tff(fact_6266_total__on__singleton,axiom,
    ! [X2: set_Pr1261947904930325089at_nat] : total_7212417256332265445at_nat(insert9200635055090092081at_nat(X2,bot_bo3083307316010499117at_nat),aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(produc2922128104949294807at_nat(X2,X2)),bot_bo228742789529271731at_nat)) ).

% total_on_singleton
tff(fact_6267_total__on__singleton,axiom,
    ! [X2: produc3843707927480180839at_nat] : total_1513685709984341995at_nat(aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(X2),bot_bo228742789529271731at_nat),insert398606708087465655at_nat(produc2335810615602371415at_nat(X2,X2),bot_bo7193250159860175667at_nat)) ).

% total_on_singleton
tff(fact_6268_total__on__singleton,axiom,
    ! [X2: product_prod_nat_nat] : total_3592101749530773125at_nat(aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(X2),bot_bo2099793752762293965at_nat),insert5050368324300391991at_nat(produc6161850002892822231at_nat(X2,X2),bot_bo5327735625951526323at_nat)) ).

% total_on_singleton
tff(fact_6269_total__on__singleton,axiom,
    ! [X2: $o] : total_on_o(insert_o((X2),bot_bot_set_o),insert6201435330877294327od_o_o(product_Pair_o_o((X2),(X2)),bot_bo7073875226086086771od_o_o)) ).

% total_on_singleton
tff(fact_6270_total__on__singleton,axiom,
    ! [X2: nat] : total_on_nat(insert_nat(X2,bot_bot_set_nat),aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X2),X2)),bot_bo2099793752762293965at_nat)) ).

% total_on_singleton
tff(fact_6271_total__on__singleton,axiom,
    ! [X2: int] : total_on_int(insert_int(X2,bot_bot_set_int),insert5033312907999012233nt_int(aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X2),X2),bot_bo1796632182523588997nt_int)) ).

% total_on_singleton
tff(fact_6272_prod__encode__prod__decode__aux,axiom,
    ! [K: nat,M: nat] : aa_Pro4243173770044397973at_nat(nat_prod_encode,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(nat_prod_decode_aux,K),M)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(nat_triangle,K)),M) ).

% prod_encode_prod_decode_aux
tff(fact_6273_sum_Oinsert_H,axiom,
    ! [I4: set_o,P2: fun_o_Code_integer,I: $o] :
      ( finite_finite_o(collect_o(aa_fun8192762245619933327un_o_o(aTP_Lamm_ox(I4),P2)))
     => ( groups1402912129352969042nteger(P2,insert_o((I),I4)) = $ite(member_o((I),I4),groups1402912129352969042nteger(P2,I4),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_o_Code_integer(P2,(I))),groups1402912129352969042nteger(P2,I4))) ) ) ).

% sum.insert'
tff(fact_6274_sum_Oinsert_H,axiom,
    ! [I4: set_nat,P2: fun_nat_Code_integer,I: nat] :
      ( finite_finite_nat(collect_nat(aa_fun3480067038916266681_nat_o(aTP_Lamm_oz(I4),P2)))
     => ( groups555127423416065298nteger(P2,insert_nat(I,I4)) = $ite(member_nat(I,I4),groups555127423416065298nteger(P2,I4),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_nat_Code_integer(P2,I)),groups555127423416065298nteger(P2,I4))) ) ) ).

% sum.insert'
tff(fact_6275_sum_Oinsert_H,axiom,
    ! [I4: set_int,P2: fun_int_Code_integer,I: int] :
      ( finite_finite_int(collect_int(aa_fun3336537925265328129_int_o(aTP_Lamm_pb(I4),P2)))
     => ( groups926780983652909934nteger(P2,insert_int(I,I4)) = $ite(member_int(I,I4),groups926780983652909934nteger(P2,I4),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_int_Code_integer(P2,I)),groups926780983652909934nteger(P2,I4))) ) ) ).

% sum.insert'
tff(fact_6276_sum_Oinsert_H,axiom,
    ! [I4: set_Code_integer,P2: fun_Co8499238673658658103nteger,I: code_integer] :
      ( finite6017078050557962740nteger(collect_Code_integer(aa_fun7159535342743012639eger_o(aTP_Lamm_pd(I4),P2)))
     => ( aa_set8546232603906849326nteger(groups910942671188738463nteger(P2),insert_Code_integer(I,I4)) = $ite(member_Code_integer(I,I4),aa_set8546232603906849326nteger(groups910942671188738463nteger(P2),I4),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(P2,I)),aa_set8546232603906849326nteger(groups910942671188738463nteger(P2),I4))) ) ) ).

% sum.insert'
tff(fact_6277_sum_Oinsert_H,axiom,
    ! [I4: set_o,P2: fun_o_rat,I: $o] :
      ( finite_finite_o(collect_o(aa_fun_o_rat_fun_o_o(aTP_Lamm_pf(I4),P2)))
     => ( groups3921277224699582669_o_rat(P2,insert_o((I),I4)) = $ite(member_o((I),I4),groups3921277224699582669_o_rat(P2,I4),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_o_rat(P2,(I))),groups3921277224699582669_o_rat(P2,I4))) ) ) ).

% sum.insert'
tff(fact_6278_sum_Oinsert_H,axiom,
    ! [I4: set_nat,P2: fun_nat_rat,I: nat] :
      ( finite_finite_nat(collect_nat(aa_fun1118977351124560894_nat_o(aTP_Lamm_ph(I4),P2)))
     => ( groups1351286907653491341at_rat(P2,insert_nat(I,I4)) = $ite(member_nat(I,I4),groups1351286907653491341at_rat(P2,I4),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(P2,I)),groups1351286907653491341at_rat(P2,I4))) ) ) ).

% sum.insert'
tff(fact_6279_sum_Oinsert_H,axiom,
    ! [I4: set_int,P2: fun_int_rat,I: int] :
      ( finite_finite_int(collect_int(aa_fun7094158214180239686_int_o(aTP_Lamm_pj(I4),P2)))
     => ( groups2350640619554545897nt_rat(P2,insert_int(I,I4)) = $ite(member_int(I,I4),groups2350640619554545897nt_rat(P2,I4),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_int_rat(P2,I)),groups2350640619554545897nt_rat(P2,I4))) ) ) ).

% sum.insert'
tff(fact_6280_sum_Oinsert_H,axiom,
    ! [I4: set_Code_integer,P2: fun_Code_integer_rat,I: code_integer] :
      ( finite6017078050557962740nteger(collect_Code_integer(aa_fun6395433285121891940eger_o(aTP_Lamm_pl(I4),P2)))
     => ( groups8878813951405302554er_rat(P2,insert_Code_integer(I,I4)) = $ite(member_Code_integer(I,I4),groups8878813951405302554er_rat(P2,I4),aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_Code_integer_rat(P2,I)),groups8878813951405302554er_rat(P2,I4))) ) ) ).

% sum.insert'
tff(fact_6281_sum_Oinsert_H,axiom,
    ! [I4: set_o,P2: fun_o_nat,I: $o] :
      ( finite_finite_o(collect_o(aa_fun_o_nat_fun_o_o(aTP_Lamm_pn(I4),P2)))
     => ( groups4556407284786078405_o_nat(P2,insert_o((I),I4)) = $ite(member_o((I),I4),groups4556407284786078405_o_nat(P2,I4),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_o_nat(P2,(I))),groups4556407284786078405_o_nat(P2,I4))) ) ) ).

% sum.insert'
tff(fact_6282_sum_Oinsert_H,axiom,
    ! [I4: set_nat,P2: fun_nat_nat,I: nat] :
      ( finite_finite_nat(collect_nat(aa_fun8673969331427483654_nat_o(aTP_Lamm_pp(I4),P2)))
     => ( aa_set_nat_nat(groups1986416967739987077at_nat(P2),insert_nat(I,I4)) = $ite(member_nat(I,I4),aa_set_nat_nat(groups1986416967739987077at_nat(P2),I4),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(P2,I)),aa_set_nat_nat(groups1986416967739987077at_nat(P2),I4))) ) ) ).

% sum.insert'
tff(fact_6283_max__ext_Omax__extI,axiom,
    ! [X7: set_se7855581050983116737at_nat,Y7: set_se7855581050983116737at_nat,R3: set_Pr4329608150637261639at_nat] :
      ( finite9047747110432174090at_nat(X7)
     => ( finite9047747110432174090at_nat(Y7)
       => ( ( Y7 != bot_bo3083307316010499117at_nat )
         => ( ! [X3: set_Pr1261947904930325089at_nat] :
                ( member2643936169264416010at_nat(X3,X7)
               => ? [Xa3: set_Pr1261947904930325089at_nat] :
                    ( member2643936169264416010at_nat(Xa3,Y7)
                    & member8757157785044589968at_nat(produc2922128104949294807at_nat(X3,Xa3),R3) ) )
           => member4300370950623927696at_nat(produc7462898802507495127at_nat(X7,Y7),max_ex4535816423174879388at_nat(R3)) ) ) ) ) ).

% max_ext.max_extI
tff(fact_6284_max__ext_Omax__extI,axiom,
    ! [X7: set_Code_integer,Y7: set_Code_integer,R3: set_Pr4811707699266497531nteger] :
      ( finite6017078050557962740nteger(X7)
     => ( finite6017078050557962740nteger(Y7)
       => ( ( Y7 != bot_bo3990330152332043303nteger )
         => ( ! [X3: code_integer] :
                ( member_Code_integer(X3,X7)
               => ? [Xa3: code_integer] :
                    ( member_Code_integer(Xa3,Y7)
                    & member157494554546826820nteger(aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(X3),Xa3),R3) ) )
           => member4307123515891402160nteger(produc7443773368509356479nteger(X7,Y7),max_ext_Code_integer(R3)) ) ) ) ) ).

% max_ext.max_extI
tff(fact_6285_max__ext_Omax__extI,axiom,
    ! [X7: set_Pr4329608150637261639at_nat,Y7: set_Pr4329608150637261639at_nat,R3: set_Pr5564308138774400199at_nat] :
      ( finite4343798906461161616at_nat(X7)
     => ( finite4343798906461161616at_nat(Y7)
       => ( ( Y7 != bot_bo228742789529271731at_nat )
         => ( ! [X3: produc3843707927480180839at_nat] :
                ( member8757157785044589968at_nat(X3,X7)
               => ? [Xa3: produc3843707927480180839at_nat] :
                    ( member8757157785044589968at_nat(Xa3,Y7)
                    & member6009668390874684176at_nat(produc2335810615602371415at_nat(X3,Xa3),R3) ) )
           => member1466754251312161552at_nat(produc9060074326276436823at_nat(X7,Y7),max_ex8833738776070432290at_nat(R3)) ) ) ) ) ).

% max_ext.max_extI
tff(fact_6286_max__ext_Omax__extI,axiom,
    ! [X7: set_Pr1261947904930325089at_nat,Y7: set_Pr1261947904930325089at_nat,R3: set_Pr8693737435421807431at_nat] :
      ( finite6177210948735845034at_nat(X7)
     => ( finite6177210948735845034at_nat(Y7)
       => ( ( Y7 != bot_bo2099793752762293965at_nat )
         => ( ! [X3: product_prod_nat_nat] :
                ( member8440522571783428010at_nat(X3,X7)
               => ? [Xa3: product_prod_nat_nat] :
                    ( member8440522571783428010at_nat(Xa3,Y7)
                    & member8206827879206165904at_nat(produc6161850002892822231at_nat(X3,Xa3),R3) ) )
           => member8757157785044589968at_nat(produc2922128104949294807at_nat(X7,Y7),max_ex8135407076693332796at_nat(R3)) ) ) ) ) ).

% max_ext.max_extI
tff(fact_6287_max__ext_Omax__extI,axiom,
    ! [X7: set_o,Y7: set_o,R3: set_Product_prod_o_o] :
      ( finite_finite_o(X7)
     => ( finite_finite_o(Y7)
       => ( ( Y7 != bot_bot_set_o )
         => ( ! [X3: $o] :
                ( member_o((X3),X7)
               => ? [Xa3: $o] :
                    ( member_o((Xa3),Y7)
                    & member7466972457876170832od_o_o(product_Pair_o_o((X3),(Xa3)),R3) ) )
           => member9116954335612470352_set_o(produc5838405689764958487_set_o(X7,Y7),max_ext_o(R3)) ) ) ) ) ).

% max_ext.max_extI
tff(fact_6288_max__ext_Omax__extI,axiom,
    ! [X7: set_nat,Y7: set_nat,R3: set_Pr1261947904930325089at_nat] :
      ( finite_finite_nat(X7)
     => ( finite_finite_nat(Y7)
       => ( ( Y7 != bot_bot_set_nat )
         => ( ! [X3: nat] :
                ( member_nat(X3,X7)
               => ? [Xa3: nat] :
                    ( member_nat(Xa3,Y7)
                    & member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),Xa3),R3) ) )
           => member8277197624267554838et_nat(produc4532415448927165861et_nat(X7,Y7),max_ext_nat(R3)) ) ) ) ) ).

% max_ext.max_extI
tff(fact_6289_max__ext_Omax__extI,axiom,
    ! [X7: set_int,Y7: set_int,R3: set_Pr958786334691620121nt_int] :
      ( finite_finite_int(X7)
     => ( finite_finite_int(Y7)
       => ( ( Y7 != bot_bot_set_int )
         => ( ! [X3: int] :
                ( member_int(X3,X7)
               => ? [Xa3: int] :
                    ( member_int(Xa3,Y7)
                    & member5262025264175285858nt_int(aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X3),Xa3),R3) ) )
           => member2572552093476627150et_int(produc6363374080413544029et_int(X7,Y7),max_ext_int(R3)) ) ) ) ) ).

% max_ext.max_extI
tff(fact_6290_total__on__def,axiom,
    ! [A2: set_se7855581050983116737at_nat,R2: set_Pr4329608150637261639at_nat] :
      ( total_7212417256332265445at_nat(A2,R2)
    <=> ! [X4: set_Pr1261947904930325089at_nat] :
          ( member2643936169264416010at_nat(X4,A2)
         => ! [Xa2: set_Pr1261947904930325089at_nat] :
              ( member2643936169264416010at_nat(Xa2,A2)
             => ( ( X4 != Xa2 )
               => ( member8757157785044589968at_nat(produc2922128104949294807at_nat(X4,Xa2),R2)
                  | member8757157785044589968at_nat(produc2922128104949294807at_nat(Xa2,X4),R2) ) ) ) ) ) ).

% total_on_def
tff(fact_6291_total__on__def,axiom,
    ! [A2: set_nat,R2: set_Pr1261947904930325089at_nat] :
      ( total_on_nat(A2,R2)
    <=> ! [X4: nat] :
          ( member_nat(X4,A2)
         => ! [Xa2: nat] :
              ( member_nat(Xa2,A2)
             => ( ( X4 != Xa2 )
               => ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X4),Xa2),R2)
                  | member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Xa2),X4),R2) ) ) ) ) ) ).

% total_on_def
tff(fact_6292_total__onI,axiom,
    ! [A2: set_se7855581050983116737at_nat,R2: set_Pr4329608150637261639at_nat] :
      ( ! [X3: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] :
          ( member2643936169264416010at_nat(X3,A2)
         => ( member2643936169264416010at_nat(Y4,A2)
           => ( ( X3 != Y4 )
             => ( member8757157785044589968at_nat(produc2922128104949294807at_nat(X3,Y4),R2)
                | member8757157785044589968at_nat(produc2922128104949294807at_nat(Y4,X3),R2) ) ) ) )
     => total_7212417256332265445at_nat(A2,R2) ) ).

% total_onI
tff(fact_6293_total__onI,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,R2: set_Pr5564308138774400199at_nat] :
      ( ! [X3: produc3843707927480180839at_nat,Y4: produc3843707927480180839at_nat] :
          ( member8757157785044589968at_nat(X3,A2)
         => ( member8757157785044589968at_nat(Y4,A2)
           => ( ( X3 != Y4 )
             => ( member6009668390874684176at_nat(produc2335810615602371415at_nat(X3,Y4),R2)
                | member6009668390874684176at_nat(produc2335810615602371415at_nat(Y4,X3),R2) ) ) ) )
     => total_1513685709984341995at_nat(A2,R2) ) ).

% total_onI
tff(fact_6294_total__onI,axiom,
    ! [A2: set_Pr1261947904930325089at_nat,R2: set_Pr8693737435421807431at_nat] :
      ( ! [X3: product_prod_nat_nat,Y4: product_prod_nat_nat] :
          ( member8440522571783428010at_nat(X3,A2)
         => ( member8440522571783428010at_nat(Y4,A2)
           => ( ( X3 != Y4 )
             => ( member8206827879206165904at_nat(produc6161850002892822231at_nat(X3,Y4),R2)
                | member8206827879206165904at_nat(produc6161850002892822231at_nat(Y4,X3),R2) ) ) ) )
     => total_3592101749530773125at_nat(A2,R2) ) ).

% total_onI
tff(fact_6295_total__onI,axiom,
    ! [A2: set_o,R2: set_Product_prod_o_o] :
      ( ! [X3: $o,Y4: $o] :
          ( member_o((X3),A2)
         => ( member_o((Y4),A2)
           => ( ~ ( (X3)
                <=> (Y4) )
             => ( member7466972457876170832od_o_o(product_Pair_o_o((X3),(Y4)),R2)
                | member7466972457876170832od_o_o(product_Pair_o_o((Y4),(X3)),R2) ) ) ) )
     => total_on_o(A2,R2) ) ).

% total_onI
tff(fact_6296_total__onI,axiom,
    ! [A2: set_nat,R2: set_Pr1261947904930325089at_nat] :
      ( ! [X3: nat,Y4: nat] :
          ( member_nat(X3,A2)
         => ( member_nat(Y4,A2)
           => ( ( X3 != Y4 )
             => ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),Y4),R2)
                | member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Y4),X3),R2) ) ) ) )
     => total_on_nat(A2,R2) ) ).

% total_onI
tff(fact_6297_total__onI,axiom,
    ! [A2: set_int,R2: set_Pr958786334691620121nt_int] :
      ( ! [X3: int,Y4: int] :
          ( member_int(X3,A2)
         => ( member_int(Y4,A2)
           => ( ( X3 != Y4 )
             => ( member5262025264175285858nt_int(aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X3),Y4),R2)
                | member5262025264175285858nt_int(aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Y4),X3),R2) ) ) ) )
     => total_on_int(A2,R2) ) ).

% total_onI
tff(fact_6298_sum_Odistrib__triv_H,axiom,
    ! [I4: set_nat,G: fun_nat_rat,Ha: fun_nat_rat] :
      ( finite_finite_nat(I4)
     => ( groups1351286907653491341at_rat(aa_fun765758790203053448at_rat(aTP_Lamm_tk(G),Ha),I4) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,groups1351286907653491341at_rat(G,I4)),groups1351286907653491341at_rat(Ha,I4)) ) ) ).

% sum.distrib_triv'
tff(fact_6299_sum_Odistrib__triv_H,axiom,
    ! [I4: set_int,G: fun_int_rat,Ha: fun_int_rat] :
      ( finite_finite_int(I4)
     => ( groups2350640619554545897nt_rat(aa_fun1481061427733998144nt_rat(aTP_Lamm_tl(G),Ha),I4) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,groups2350640619554545897nt_rat(G,I4)),groups2350640619554545897nt_rat(Ha,I4)) ) ) ).

% sum.distrib_triv'
tff(fact_6300_sum_Odistrib__triv_H,axiom,
    ! [I4: set_Code_integer,G: fun_Code_integer_rat,Ha: fun_Code_integer_rat] :
      ( finite6017078050557962740nteger(I4)
     => ( groups8878813951405302554er_rat(aa_fun8169474305930283170er_rat(aTP_Lamm_tm(G),Ha),I4) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,groups8878813951405302554er_rat(G,I4)),groups8878813951405302554er_rat(Ha,I4)) ) ) ).

% sum.distrib_triv'
tff(fact_6301_sum_Odistrib__triv_H,axiom,
    ! [I4: set_nat,G: fun_nat_nat,Ha: fun_nat_nat] :
      ( finite_finite_nat(I4)
     => ( aa_set_nat_nat(groups1986416967739987077at_nat(aa_fun5791449513213591928at_nat(aTP_Lamm_er(G),Ha)),I4) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_set_nat_nat(groups1986416967739987077at_nat(G),I4)),aa_set_nat_nat(groups1986416967739987077at_nat(Ha),I4)) ) ) ).

% sum.distrib_triv'
tff(fact_6302_sum_Odistrib__triv_H,axiom,
    ! [I4: set_int,G: fun_int_nat,Ha: fun_int_nat] :
      ( finite_finite_int(I4)
     => ( groups2985770679641041633nt_nat(aa_fun6506752150744536624nt_nat(aTP_Lamm_tn(G),Ha),I4) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,groups2985770679641041633nt_nat(G,I4)),groups2985770679641041633nt_nat(Ha,I4)) ) ) ).

% sum.distrib_triv'
tff(fact_6303_sum_Odistrib__triv_H,axiom,
    ! [I4: set_Code_integer,G: fun_Code_integer_nat,Ha: fun_Code_integer_nat] :
      ( finite6017078050557962740nteger(I4)
     => ( groups290571974637022482er_nat(aa_fun3076867170244285586er_nat(aTP_Lamm_to(G),Ha),I4) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,groups290571974637022482er_nat(G,I4)),groups290571974637022482er_nat(Ha,I4)) ) ) ).

% sum.distrib_triv'
tff(fact_6304_sum_Odistrib__triv_H,axiom,
    ! [I4: set_nat,G: fun_nat_int,Ha: fun_nat_int] :
      ( finite_finite_nat(I4)
     => ( groups1983926497230936801at_int(aa_fun5565043122120104496at_int(aTP_Lamm_tp(G),Ha),I4) = aa_int_int(aa_int_fun_int_int(plus_plus_int,groups1983926497230936801at_int(G,I4)),groups1983926497230936801at_int(Ha,I4)) ) ) ).

% sum.distrib_triv'
tff(fact_6305_sum_Odistrib__triv_H,axiom,
    ! [I4: set_int,G: fun_int_int,Ha: fun_int_int] :
      ( finite_finite_int(I4)
     => ( aa_set_int_int(groups2983280209131991357nt_int(aa_fun6280345759651049192nt_int(aTP_Lamm_es(G),Ha)),I4) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_set_int_int(groups2983280209131991357nt_int(G),I4)),aa_set_int_int(groups2983280209131991357nt_int(Ha),I4)) ) ) ).

% sum.distrib_triv'
tff(fact_6306_sum_Odistrib__triv_H,axiom,
    ! [I4: set_Code_integer,G: fun_Code_integer_int,Ha: fun_Code_integer_int] :
      ( finite6017078050557962740nteger(I4)
     => ( groups288081504127972206er_int(aa_fun3291479149765983562er_int(aTP_Lamm_tq(G),Ha),I4) = aa_int_int(aa_int_fun_int_int(plus_plus_int,groups288081504127972206er_int(G,I4)),groups288081504127972206er_int(Ha,I4)) ) ) ).

% sum.distrib_triv'
tff(fact_6307_sum_Odistrib__triv_H,axiom,
    ! [I4: set_Pr1261947904930325089at_nat,G: fun_Pr8317260874932935276at_rat,Ha: fun_Pr8317260874932935276at_rat] :
      ( finite6177210948735845034at_nat(I4)
     => ( groups3328076802468863542at_rat(aa_fun1488288443938188604at_rat(aTP_Lamm_tr(G),Ha),I4) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,groups3328076802468863542at_rat(G,I4)),groups3328076802468863542at_rat(Ha,I4)) ) ) ).

% sum.distrib_triv'
tff(fact_6308_le__prod__encode__1,axiom,
    ! [A: nat,B: nat] : aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,A),aa_Pro4243173770044397973at_nat(nat_prod_encode,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B))) ).

% le_prod_encode_1
tff(fact_6309_le__prod__encode__2,axiom,
    ! [B: nat,A: nat] : aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,B),aa_Pro4243173770044397973at_nat(nat_prod_encode,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B))) ).

% le_prod_encode_2
tff(fact_6310_sum_Odistrib_H,axiom,
    ! [I4: set_o,G: fun_o_Code_integer,Ha: fun_o_Code_integer] :
      ( finite_finite_o(collect_o(aa_fun8192762245619933327un_o_o(aTP_Lamm_ox(I4),G)))
     => ( finite_finite_o(collect_o(aa_fun8192762245619933327un_o_o(aTP_Lamm_ox(I4),Ha)))
       => ( groups1402912129352969042nteger(aa_fun8520278569782659900nteger(aTP_Lamm_ts(G),Ha),I4) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,groups1402912129352969042nteger(G,I4)),groups1402912129352969042nteger(Ha,I4)) ) ) ) ).

% sum.distrib'
tff(fact_6311_sum_Odistrib_H,axiom,
    ! [I4: set_nat,G: fun_nat_Code_integer,Ha: fun_nat_Code_integer] :
      ( finite_finite_nat(collect_nat(aa_fun3480067038916266681_nat_o(aTP_Lamm_oz(I4),G)))
     => ( finite_finite_nat(collect_nat(aa_fun3480067038916266681_nat_o(aTP_Lamm_oz(I4),Ha)))
       => ( groups555127423416065298nteger(aa_fun589076786913273746nteger(aTP_Lamm_tt(G),Ha),I4) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,groups555127423416065298nteger(G,I4)),groups555127423416065298nteger(Ha,I4)) ) ) ) ).

% sum.distrib'
tff(fact_6312_sum_Odistrib_H,axiom,
    ! [I4: set_int,G: fun_int_Code_integer,Ha: fun_int_Code_integer] :
      ( finite_finite_int(collect_int(aa_fun3336537925265328129_int_o(aTP_Lamm_pb(I4),G)))
     => ( finite_finite_int(collect_int(aa_fun3336537925265328129_int_o(aTP_Lamm_pb(I4),Ha)))
       => ( groups926780983652909934nteger(aa_fun5304498221708291146nteger(aTP_Lamm_tu(G),Ha),I4) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,groups926780983652909934nteger(G,I4)),groups926780983652909934nteger(Ha,I4)) ) ) ) ).

% sum.distrib'
tff(fact_6313_sum_Odistrib_H,axiom,
    ! [I4: set_Code_integer,G: fun_Co8499238673658658103nteger,Ha: fun_Co8499238673658658103nteger] :
      ( finite6017078050557962740nteger(collect_Code_integer(aa_fun7159535342743012639eger_o(aTP_Lamm_pd(I4),G)))
     => ( finite6017078050557962740nteger(collect_Code_integer(aa_fun7159535342743012639eger_o(aTP_Lamm_pd(I4),Ha)))
       => ( aa_set8546232603906849326nteger(groups910942671188738463nteger(aa_fun4435975922079263404nteger(aTP_Lamm_tv(G),Ha)),I4) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_set8546232603906849326nteger(groups910942671188738463nteger(G),I4)),aa_set8546232603906849326nteger(groups910942671188738463nteger(Ha),I4)) ) ) ) ).

% sum.distrib'
tff(fact_6314_sum_Odistrib_H,axiom,
    ! [I4: set_o,G: fun_o_rat,Ha: fun_o_rat] :
      ( finite_finite_o(collect_o(aa_fun_o_rat_fun_o_o(aTP_Lamm_pf(I4),G)))
     => ( finite_finite_o(collect_o(aa_fun_o_rat_fun_o_o(aTP_Lamm_pf(I4),Ha)))
       => ( groups3921277224699582669_o_rat(aa_fun4336163974892599420_o_rat(aTP_Lamm_tw(G),Ha),I4) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,groups3921277224699582669_o_rat(G,I4)),groups3921277224699582669_o_rat(Ha,I4)) ) ) ) ).

% sum.distrib'
tff(fact_6315_sum_Odistrib_H,axiom,
    ! [I4: set_nat,G: fun_nat_rat,Ha: fun_nat_rat] :
      ( finite_finite_nat(collect_nat(aa_fun1118977351124560894_nat_o(aTP_Lamm_ph(I4),G)))
     => ( finite_finite_nat(collect_nat(aa_fun1118977351124560894_nat_o(aTP_Lamm_ph(I4),Ha)))
       => ( groups1351286907653491341at_rat(aa_fun765758790203053448at_rat(aTP_Lamm_tk(G),Ha),I4) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,groups1351286907653491341at_rat(G,I4)),groups1351286907653491341at_rat(Ha,I4)) ) ) ) ).

% sum.distrib'
tff(fact_6316_sum_Odistrib_H,axiom,
    ! [I4: set_int,G: fun_int_rat,Ha: fun_int_rat] :
      ( finite_finite_int(collect_int(aa_fun7094158214180239686_int_o(aTP_Lamm_pj(I4),G)))
     => ( finite_finite_int(collect_int(aa_fun7094158214180239686_int_o(aTP_Lamm_pj(I4),Ha)))
       => ( groups2350640619554545897nt_rat(aa_fun1481061427733998144nt_rat(aTP_Lamm_tl(G),Ha),I4) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,groups2350640619554545897nt_rat(G,I4)),groups2350640619554545897nt_rat(Ha,I4)) ) ) ) ).

% sum.distrib'
tff(fact_6317_sum_Odistrib_H,axiom,
    ! [I4: set_Code_integer,G: fun_Code_integer_rat,Ha: fun_Code_integer_rat] :
      ( finite6017078050557962740nteger(collect_Code_integer(aa_fun6395433285121891940eger_o(aTP_Lamm_pl(I4),G)))
     => ( finite6017078050557962740nteger(collect_Code_integer(aa_fun6395433285121891940eger_o(aTP_Lamm_pl(I4),Ha)))
       => ( groups8878813951405302554er_rat(aa_fun8169474305930283170er_rat(aTP_Lamm_tm(G),Ha),I4) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,groups8878813951405302554er_rat(G,I4)),groups8878813951405302554er_rat(Ha,I4)) ) ) ) ).

% sum.distrib'
tff(fact_6318_sum_Odistrib_H,axiom,
    ! [I4: set_o,G: fun_o_nat,Ha: fun_o_nat] :
      ( finite_finite_o(collect_o(aa_fun_o_nat_fun_o_o(aTP_Lamm_pn(I4),G)))
     => ( finite_finite_o(collect_o(aa_fun_o_nat_fun_o_o(aTP_Lamm_pn(I4),Ha)))
       => ( groups4556407284786078405_o_nat(aa_fun6176012476734143100_o_nat(aTP_Lamm_tx(G),Ha),I4) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,groups4556407284786078405_o_nat(G,I4)),groups4556407284786078405_o_nat(Ha,I4)) ) ) ) ).

% sum.distrib'
tff(fact_6319_sum_Odistrib_H,axiom,
    ! [I4: set_nat,G: fun_nat_nat,Ha: fun_nat_nat] :
      ( finite_finite_nat(collect_nat(aa_fun8673969331427483654_nat_o(aTP_Lamm_pp(I4),G)))
     => ( finite_finite_nat(collect_nat(aa_fun8673969331427483654_nat_o(aTP_Lamm_pp(I4),Ha)))
       => ( aa_set_nat_nat(groups1986416967739987077at_nat(aa_fun5791449513213591928at_nat(aTP_Lamm_er(G),Ha)),I4) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_set_nat_nat(groups1986416967739987077at_nat(G),I4)),aa_set_nat_nat(groups1986416967739987077at_nat(Ha),I4)) ) ) ) ).

% sum.distrib'
tff(fact_6320_prod__encode__def,axiom,
    nat_prod_encode = aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,aTP_Lamm_ty) ).

% prod_encode_def
tff(fact_6321_max__ext_Ocases,axiom,
    ! [A1: set_se7855581050983116737at_nat,A22: set_se7855581050983116737at_nat,R3: set_Pr4329608150637261639at_nat] :
      ( member4300370950623927696at_nat(produc7462898802507495127at_nat(A1,A22),max_ex4535816423174879388at_nat(R3))
     => ~ ( finite9047747110432174090at_nat(A1)
         => ( finite9047747110432174090at_nat(A22)
           => ( ( A22 != bot_bo3083307316010499117at_nat )
             => ~ ! [X: set_Pr1261947904930325089at_nat] :
                    ( member2643936169264416010at_nat(X,A1)
                   => ? [Xa4: set_Pr1261947904930325089at_nat] :
                        ( member2643936169264416010at_nat(Xa4,A22)
                        & member8757157785044589968at_nat(produc2922128104949294807at_nat(X,Xa4),R3) ) ) ) ) ) ) ).

% max_ext.cases
tff(fact_6322_max__ext_Ocases,axiom,
    ! [A1: set_Code_integer,A22: set_Code_integer,R3: set_Pr4811707699266497531nteger] :
      ( member4307123515891402160nteger(produc7443773368509356479nteger(A1,A22),max_ext_Code_integer(R3))
     => ~ ( finite6017078050557962740nteger(A1)
         => ( finite6017078050557962740nteger(A22)
           => ( ( A22 != bot_bo3990330152332043303nteger )
             => ~ ! [X: code_integer] :
                    ( member_Code_integer(X,A1)
                   => ? [Xa4: code_integer] :
                        ( member_Code_integer(Xa4,A22)
                        & member157494554546826820nteger(aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(X),Xa4),R3) ) ) ) ) ) ) ).

% max_ext.cases
tff(fact_6323_max__ext_Ocases,axiom,
    ! [A1: set_Pr4329608150637261639at_nat,A22: set_Pr4329608150637261639at_nat,R3: set_Pr5564308138774400199at_nat] :
      ( member1466754251312161552at_nat(produc9060074326276436823at_nat(A1,A22),max_ex8833738776070432290at_nat(R3))
     => ~ ( finite4343798906461161616at_nat(A1)
         => ( finite4343798906461161616at_nat(A22)
           => ( ( A22 != bot_bo228742789529271731at_nat )
             => ~ ! [X: produc3843707927480180839at_nat] :
                    ( member8757157785044589968at_nat(X,A1)
                   => ? [Xa4: produc3843707927480180839at_nat] :
                        ( member8757157785044589968at_nat(Xa4,A22)
                        & member6009668390874684176at_nat(produc2335810615602371415at_nat(X,Xa4),R3) ) ) ) ) ) ) ).

% max_ext.cases
tff(fact_6324_max__ext_Ocases,axiom,
    ! [A1: set_Pr1261947904930325089at_nat,A22: set_Pr1261947904930325089at_nat,R3: set_Pr8693737435421807431at_nat] :
      ( member8757157785044589968at_nat(produc2922128104949294807at_nat(A1,A22),max_ex8135407076693332796at_nat(R3))
     => ~ ( finite6177210948735845034at_nat(A1)
         => ( finite6177210948735845034at_nat(A22)
           => ( ( A22 != bot_bo2099793752762293965at_nat )
             => ~ ! [X: product_prod_nat_nat] :
                    ( member8440522571783428010at_nat(X,A1)
                   => ? [Xa4: product_prod_nat_nat] :
                        ( member8440522571783428010at_nat(Xa4,A22)
                        & member8206827879206165904at_nat(produc6161850002892822231at_nat(X,Xa4),R3) ) ) ) ) ) ) ).

% max_ext.cases
tff(fact_6325_max__ext_Ocases,axiom,
    ! [A1: set_o,A22: set_o,R3: set_Product_prod_o_o] :
      ( member9116954335612470352_set_o(produc5838405689764958487_set_o(A1,A22),max_ext_o(R3))
     => ~ ( finite_finite_o(A1)
         => ( finite_finite_o(A22)
           => ( ( A22 != bot_bot_set_o )
             => ~ ! [X: $o] :
                    ( member_o((X),A1)
                   => ? [Xa4: $o] :
                        ( member_o((Xa4),A22)
                        & member7466972457876170832od_o_o(product_Pair_o_o((X),(Xa4)),R3) ) ) ) ) ) ) ).

% max_ext.cases
tff(fact_6326_max__ext_Ocases,axiom,
    ! [A1: set_nat,A22: set_nat,R3: set_Pr1261947904930325089at_nat] :
      ( member8277197624267554838et_nat(produc4532415448927165861et_nat(A1,A22),max_ext_nat(R3))
     => ~ ( finite_finite_nat(A1)
         => ( finite_finite_nat(A22)
           => ( ( A22 != bot_bot_set_nat )
             => ~ ! [X: nat] :
                    ( member_nat(X,A1)
                   => ? [Xa4: nat] :
                        ( member_nat(Xa4,A22)
                        & member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X),Xa4),R3) ) ) ) ) ) ) ).

% max_ext.cases
tff(fact_6327_max__ext_Ocases,axiom,
    ! [A1: set_int,A22: set_int,R3: set_Pr958786334691620121nt_int] :
      ( member2572552093476627150et_int(produc6363374080413544029et_int(A1,A22),max_ext_int(R3))
     => ~ ( finite_finite_int(A1)
         => ( finite_finite_int(A22)
           => ( ( A22 != bot_bot_set_int )
             => ~ ! [X: int] :
                    ( member_int(X,A1)
                   => ? [Xa4: int] :
                        ( member_int(Xa4,A22)
                        & member5262025264175285858nt_int(aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X),Xa4),R3) ) ) ) ) ) ) ).

% max_ext.cases
tff(fact_6328_max__ext_Osimps,axiom,
    ! [A1: set_se7855581050983116737at_nat,A22: set_se7855581050983116737at_nat,R3: set_Pr4329608150637261639at_nat] :
      ( member4300370950623927696at_nat(produc7462898802507495127at_nat(A1,A22),max_ex4535816423174879388at_nat(R3))
    <=> ( finite9047747110432174090at_nat(A1)
        & finite9047747110432174090at_nat(A22)
        & ( A22 != bot_bo3083307316010499117at_nat )
        & ! [X4: set_Pr1261947904930325089at_nat] :
            ( member2643936169264416010at_nat(X4,A1)
           => ? [Xa2: set_Pr1261947904930325089at_nat] :
                ( member2643936169264416010at_nat(Xa2,A22)
                & member8757157785044589968at_nat(produc2922128104949294807at_nat(X4,Xa2),R3) ) ) ) ) ).

% max_ext.simps
tff(fact_6329_max__ext_Osimps,axiom,
    ! [A1: set_Code_integer,A22: set_Code_integer,R3: set_Pr4811707699266497531nteger] :
      ( member4307123515891402160nteger(produc7443773368509356479nteger(A1,A22),max_ext_Code_integer(R3))
    <=> ( finite6017078050557962740nteger(A1)
        & finite6017078050557962740nteger(A22)
        & ( A22 != bot_bo3990330152332043303nteger )
        & ! [X4: code_integer] :
            ( member_Code_integer(X4,A1)
           => ? [Xa2: code_integer] :
                ( member_Code_integer(Xa2,A22)
                & member157494554546826820nteger(aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(X4),Xa2),R3) ) ) ) ) ).

% max_ext.simps
tff(fact_6330_max__ext_Osimps,axiom,
    ! [A1: set_Pr4329608150637261639at_nat,A22: set_Pr4329608150637261639at_nat,R3: set_Pr5564308138774400199at_nat] :
      ( member1466754251312161552at_nat(produc9060074326276436823at_nat(A1,A22),max_ex8833738776070432290at_nat(R3))
    <=> ( finite4343798906461161616at_nat(A1)
        & finite4343798906461161616at_nat(A22)
        & ( A22 != bot_bo228742789529271731at_nat )
        & ! [X4: produc3843707927480180839at_nat] :
            ( member8757157785044589968at_nat(X4,A1)
           => ? [Xa2: produc3843707927480180839at_nat] :
                ( member8757157785044589968at_nat(Xa2,A22)
                & member6009668390874684176at_nat(produc2335810615602371415at_nat(X4,Xa2),R3) ) ) ) ) ).

% max_ext.simps
tff(fact_6331_max__ext_Osimps,axiom,
    ! [A1: set_Pr1261947904930325089at_nat,A22: set_Pr1261947904930325089at_nat,R3: set_Pr8693737435421807431at_nat] :
      ( member8757157785044589968at_nat(produc2922128104949294807at_nat(A1,A22),max_ex8135407076693332796at_nat(R3))
    <=> ( finite6177210948735845034at_nat(A1)
        & finite6177210948735845034at_nat(A22)
        & ( A22 != bot_bo2099793752762293965at_nat )
        & ! [X4: product_prod_nat_nat] :
            ( member8440522571783428010at_nat(X4,A1)
           => ? [Xa2: product_prod_nat_nat] :
                ( member8440522571783428010at_nat(Xa2,A22)
                & member8206827879206165904at_nat(produc6161850002892822231at_nat(X4,Xa2),R3) ) ) ) ) ).

% max_ext.simps
tff(fact_6332_max__ext_Osimps,axiom,
    ! [A1: set_o,A22: set_o,R3: set_Product_prod_o_o] :
      ( member9116954335612470352_set_o(produc5838405689764958487_set_o(A1,A22),max_ext_o(R3))
    <=> ( finite_finite_o(A1)
        & finite_finite_o(A22)
        & ( A22 != bot_bot_set_o )
        & ! [X4: $o] :
            ( member_o((X4),A1)
           => ? [Xa2: $o] :
                ( member_o((Xa2),A22)
                & member7466972457876170832od_o_o(product_Pair_o_o((X4),(Xa2)),R3) ) ) ) ) ).

% max_ext.simps
tff(fact_6333_max__ext_Osimps,axiom,
    ! [A1: set_nat,A22: set_nat,R3: set_Pr1261947904930325089at_nat] :
      ( member8277197624267554838et_nat(produc4532415448927165861et_nat(A1,A22),max_ext_nat(R3))
    <=> ( finite_finite_nat(A1)
        & finite_finite_nat(A22)
        & ( A22 != bot_bot_set_nat )
        & ! [X4: nat] :
            ( member_nat(X4,A1)
           => ? [Xa2: nat] :
                ( member_nat(Xa2,A22)
                & member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X4),Xa2),R3) ) ) ) ) ).

% max_ext.simps
tff(fact_6334_max__ext_Osimps,axiom,
    ! [A1: set_int,A22: set_int,R3: set_Pr958786334691620121nt_int] :
      ( member2572552093476627150et_int(produc6363374080413544029et_int(A1,A22),max_ext_int(R3))
    <=> ( finite_finite_int(A1)
        & finite_finite_int(A22)
        & ( A22 != bot_bot_set_int )
        & ! [X4: int] :
            ( member_int(X4,A1)
           => ? [Xa2: int] :
                ( member_int(Xa2,A22)
                & member5262025264175285858nt_int(aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X4),Xa2),R3) ) ) ) ) ).

% max_ext.simps
tff(fact_6335_max__extp__eq,axiom,
    ! [R2: fun_Pr2028404973800837934_nat_o,X2: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
      ( aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(max_ex4864111882549613972at_nat(R2),X2),Y)
    <=> member8757157785044589968at_nat(produc2922128104949294807at_nat(X2,Y),max_ex8135407076693332796at_nat(collec7088162979684241874at_nat(produc6590410687421337004_nat_o(R2)))) ) ).

% max_extp_eq
tff(fact_6336_max__extp__max__ext__eq,axiom,
    ! [R3: set_Pr4329608150637261639at_nat,X: set_se7855581050983116737at_nat,Xa3: set_se7855581050983116737at_nat] :
      ( aa_set5218765425691562963_nat_o(aa_set8824140522937572191_nat_o(max_ex4845989503969680116at_nat(aa_set5605188905385065315_nat_o(aTP_Lamm_bu,R3)),X),Xa3)
    <=> member4300370950623927696at_nat(produc7462898802507495127at_nat(X,Xa3),max_ex4535816423174879388at_nat(R3)) ) ).

% max_extp_max_ext_eq
tff(fact_6337_max__extp__max__ext__eq,axiom,
    ! [R3: set_Pr1261947904930325089at_nat,X: set_nat,Xa3: set_nat] :
      ( aa_set_nat_o(aa_set7861427066675100071_nat_o(max_extp_nat(aa_set2634951030311766213_nat_o(aTP_Lamm_bv,R3)),X),Xa3)
    <=> member8277197624267554838et_nat(produc4532415448927165861et_nat(X,Xa3),max_ext_nat(R3)) ) ).

% max_extp_max_ext_eq
tff(fact_6338_max__extp__max__ext__eq,axiom,
    ! [R3: set_Pr8693737435421807431at_nat,X: set_Pr1261947904930325089at_nat,Xa3: set_Pr1261947904930325089at_nat] :
      ( aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(max_ex4864111882549613972at_nat(aTP_Lamm_tz(R3)),X),Xa3)
    <=> member8757157785044589968at_nat(produc2922128104949294807at_nat(X,Xa3),max_ex8135407076693332796at_nat(R3)) ) ).

% max_extp_max_ext_eq
tff(fact_6339_one__div__numeral,axiom,
    ! [N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,one_one_Code_integer),aa_num_Code_integer(numera6620942414471956472nteger,N2)) = aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,unique3479559517661332726nteger(one,N2)) ).

% one_div_numeral
tff(fact_6340_one__div__numeral,axiom,
    ! [N2: num] : aa_int_int(aa_int_fun_int_int(divide_divide_int,one_one_int),aa_num_int(numeral_numeral_int,N2)) = aa_Pro6799258434465214121nt_int(product_fst_int_int,unique5052692396658037445od_int(one,N2)) ).

% one_div_numeral
tff(fact_6341_one__div__numeral,axiom,
    ! [N2: num] : aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,one_one_nat),aa_num_nat(numeral_numeral_nat,N2)) = aa_Pro4243173770044397973at_nat(product_fst_nat_nat,unique5055182867167087721od_nat(one,N2)) ).

% one_div_numeral
tff(fact_6342_sqr_Osimps_I3_J,axiom,
    ! [N2: num] : aa_num_num(sqr,aa_num_num(bit1,N2)) = aa_num_num(bit1,aa_num_num(bit0,aa_num_num(aa_num_fun_num_num(plus_plus_num,aa_num_num(sqr,N2)),N2))) ).

% sqr.simps(3)
tff(fact_6343_one__mod__numeral,axiom,
    ! [N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,one_one_Code_integer),aa_num_Code_integer(numera6620942414471956472nteger,N2)) = aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,unique3479559517661332726nteger(one,N2)) ).

% one_mod_numeral
tff(fact_6344_one__mod__numeral,axiom,
    ! [N2: num] : aa_int_int(aa_int_fun_int_int(modulo_modulo_int,one_one_int),aa_num_int(numeral_numeral_int,N2)) = aa_Pro6799258434465214121nt_int(product_snd_int_int,unique5052692396658037445od_int(one,N2)) ).

% one_mod_numeral
tff(fact_6345_one__mod__numeral,axiom,
    ! [N2: num] : aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,one_one_nat),aa_num_nat(numeral_numeral_nat,N2)) = aa_Pro4243173770044397973at_nat(product_snd_nat_nat,unique5055182867167087721od_nat(one,N2)) ).

% one_mod_numeral
tff(fact_6346_card__UNION,axiom,
    ! [A2: set_set_Product_unit] :
      ( finite1772178364199683094t_unit(A2)
     => ( ! [X3: set_Product_unit] :
            ( member5877623283571906838t_unit(X3,A2)
           => finite4290736615968046902t_unit(X3) )
       => ( finite410649719033368117t_unit(comple3349607820504768346t_unit(A2)) = aa_int_nat(nat2,groups9212676010950626495it_int(aTP_Lamm_ua,collec4600646233855244344t_unit(aTP_Lamm_ub(A2)))) ) ) ) ).

% card_UNION
tff(fact_6347_card__UNION,axiom,
    ! [A2: set_set_list_nat] :
      ( finite7047420756378620717st_nat(A2)
     => ( ! [X3: set_list_nat] :
            ( member_set_list_nat(X3,A2)
           => finite8100373058378681591st_nat(X3) )
       => ( finite_card_list_nat(comple8404747032580312297st_nat(A2)) = aa_int_nat(nat2,groups7004213669654646580at_int(aTP_Lamm_uc,collec4691811733418234273st_nat(aTP_Lamm_ud(A2)))) ) ) ) ).

% card_UNION
tff(fact_6348_card__UNION,axiom,
    ! [A2: set_set_int] :
      ( finite6197958912794628473et_int(A2)
     => ( ! [X3: set_int] :
            ( member_set_int(X3,A2)
           => finite_finite_int(X3) )
       => ( finite_card_int(comple3221217463730067765et_int(A2)) = aa_int_nat(nat2,groups1080061135233207040nt_int(aTP_Lamm_ue,collect_set_set_int(aTP_Lamm_uf(A2)))) ) ) ) ).

% card_UNION
tff(fact_6349_card__UNION,axiom,
    ! [A2: set_set_Code_integer] :
      ( finite6931041176100689706nteger(A2)
     => ( ! [X3: set_Code_integer] :
            ( member1834298987299537450nteger(X3,A2)
           => finite6017078050557962740nteger(X3) )
       => ( finite4902975817058060853nteger(comple739944243200306918nteger(A2)) = aa_int_nat(nat2,groups2416162284031854641er_int(aTP_Lamm_ug,collec9208119312383884190nteger(aTP_Lamm_uh(A2)))) ) ) ) ).

% card_UNION
tff(fact_6350_card__UNION,axiom,
    ! [A2: set_se7855581050983116737at_nat] :
      ( finite9047747110432174090at_nat(A2)
     => ( ! [X3: set_Pr1261947904930325089at_nat] :
            ( member2643936169264416010at_nat(X3,A2)
           => finite6177210948735845034at_nat(X3) )
       => ( aa_set4749074711808745205at_nat(finite711546835091564841at_nat,comple5685304695842803022at_nat(A2)) = aa_int_nat(nat2,groups1759609815103008563at_int(aTP_Lamm_ui,collec6698286964019821996at_nat(aTP_Lamm_uj(A2)))) ) ) ) ).

% card_UNION
tff(fact_6351_card__UNION,axiom,
    ! [A2: set_set_nat] :
      ( finite1152437895449049373et_nat(A2)
     => ( ! [X3: set_nat] :
            ( member_set_nat(X3,A2)
           => finite_finite_nat(X3) )
       => ( aa_set_nat_nat(finite_card_nat,comple7399068483239264473et_nat(A2)) = aa_int_nat(nat2,groups7084729577923612836at_int(aTP_Lamm_uk,collect_set_set_nat(aTP_Lamm_ul(A2)))) ) ) ) ).

% card_UNION
tff(fact_6352_Sup__atMost,axiom,
    ! [Y: set_nat] : comple7399068483239264473et_nat(set_or4236626031148496127et_nat(Y)) = Y ).

% Sup_atMost
tff(fact_6353_Sup__atMost,axiom,
    ! [Y: product_unit] : comple4687483117567863418t_unit(set_or8621721900777396692t_unit(Y)) = Y ).

% Sup_atMost
tff(fact_6354_fst__apsnd,axiom,
    ! [F: fun_Co8499238673658658103nteger,X2: produc8923325533196201883nteger] : aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,aa_Pro4693618923521437820nteger(aa_fun2509385170507305080nteger(produc6499014454317279255nteger,F),X2)) = aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,X2) ).

% fst_apsnd
tff(fact_6355_fst__apsnd,axiom,
    ! [F: fun_int_int,X2: product_prod_int_int] : aa_Pro6799258434465214121nt_int(product_fst_int_int,aa_Pro6970504127699319548nt_int(produc4463282112584876420nt_int(F),X2)) = aa_Pro6799258434465214121nt_int(product_fst_int_int,X2) ).

% fst_apsnd
tff(fact_6356_fst__comp__apsnd,axiom,
    ! [F: fun_Co8499238673658658103nteger] : comp_P3428181540658402820nteger(produc8508995932063986495nteger,aa_fun2509385170507305080nteger(produc6499014454317279255nteger,F)) = produc8508995932063986495nteger ).

% fst_comp_apsnd
tff(fact_6357_fst__comp__apsnd,axiom,
    ! [F: fun_int_int] : comp_P5356232565778667509nt_int(product_fst_int_int,produc4463282112584876420nt_int(F)) = product_fst_int_int ).

% fst_comp_apsnd
tff(fact_6358_apsnd__eq__conv,axiom,
    ! [F: fun_Co8499238673658658103nteger,X2: produc8923325533196201883nteger,G: fun_Co8499238673658658103nteger] :
      ( ( aa_Pro4693618923521437820nteger(aa_fun2509385170507305080nteger(produc6499014454317279255nteger,F),X2) = aa_Pro4693618923521437820nteger(aa_fun2509385170507305080nteger(produc6499014454317279255nteger,G),X2) )
    <=> ( aa_Cod1783974652533396728nteger(F,aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,X2)) = aa_Cod1783974652533396728nteger(G,aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,X2)) ) ) ).

% apsnd_eq_conv
tff(fact_6359_snd__apsnd,axiom,
    ! [F: fun_Co8499238673658658103nteger,X2: produc8923325533196201883nteger] : aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,aa_Pro4693618923521437820nteger(aa_fun2509385170507305080nteger(produc6499014454317279255nteger,F),X2)) = aa_Cod1783974652533396728nteger(F,aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,X2)) ).

% snd_apsnd
tff(fact_6360_snd__apsnd,axiom,
    ! [F: fun_int_int,X2: product_prod_int_int] : aa_Pro6799258434465214121nt_int(product_snd_int_int,aa_Pro6970504127699319548nt_int(produc4463282112584876420nt_int(F),X2)) = aa_int_int(F,aa_Pro6799258434465214121nt_int(product_snd_int_int,X2)) ).

% snd_apsnd
tff(fact_6361_snd__apsnd,axiom,
    ! [F: fun_Pr74676805955934211atural,X2: produc5835291356934675326atural] : aa_Pro3673693039631929973atural(produc6591912806276919810atural,aa_Pro4026365172444991930atural(produc4464772112783624294atural(F),X2)) = aa_Pro4262726347734369532atural(F,aa_Pro3673693039631929973atural(produc6591912806276919810atural,X2)) ).

% snd_apsnd
tff(fact_6362_snd__comp__apsnd,axiom,
    ! [F: fun_Co8499238673658658103nteger] : comp_P3428181540658402820nteger(produc6174133586879617921nteger,aa_fun2509385170507305080nteger(produc6499014454317279255nteger,F)) = comp_C1043215000170864188nteger(F,produc6174133586879617921nteger) ).

% snd_comp_apsnd
tff(fact_6363_snd__comp__apsnd,axiom,
    ! [F: fun_int_int] : comp_P5356232565778667509nt_int(product_snd_int_int,produc4463282112584876420nt_int(F)) = comp_i4330622015127193916nt_int(F,product_snd_int_int) ).

% snd_comp_apsnd
tff(fact_6364_snd__comp__apsnd,axiom,
    ! [F: fun_Pr74676805955934211atural] : comp_P7610810914149544718atural(produc6591912806276919810atural,produc4464772112783624294atural(F)) = comp_P3067963646784605345atural(F,produc6591912806276919810atural) ).

% snd_comp_apsnd
tff(fact_6365_fst__divmod__integer,axiom,
    ! [K: code_integer,L: code_integer] : aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,aa_Cod6977894654539884864nteger(code_divmod_integer(K),L)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,K),L) ).

% fst_divmod_integer
tff(fact_6366_snd__divmod__integer,axiom,
    ! [K: code_integer,L: code_integer] : aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,aa_Cod6977894654539884864nteger(code_divmod_integer(K),L)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,K),L) ).

% snd_divmod_integer
tff(fact_6367_Sup__atLeastAtMost,axiom,
    ! [X2: set_nat,Y: set_nat] :
      ( aa_set_nat_o(ord_less_eq_set_nat(X2),Y)
     => ( comple7399068483239264473et_nat(set_or4548717258645045905et_nat(X2,Y)) = Y ) ) ).

% Sup_atLeastAtMost
tff(fact_6368_Sup__atLeastAtMost,axiom,
    ! [X2: product_unit,Y: product_unit] :
      ( aa_Product_unit_o(aa_Pro4895447120693452255unit_o(ord_le3221252021190050221t_unit,X2),Y)
     => ( comple4687483117567863418t_unit(set_or5692540242118139586t_unit(X2,Y)) = Y ) ) ).

% Sup_atLeastAtMost
tff(fact_6369_Inf__atLeastAtMost,axiom,
    ! [X2: set_nat,Y: set_nat] :
      ( aa_set_nat_o(ord_less_eq_set_nat(X2),Y)
     => ( comple7806235888213564991et_nat(set_or4548717258645045905et_nat(X2,Y)) = X2 ) ) ).

% Inf_atLeastAtMost
tff(fact_6370_Inf__atLeastAtMost,axiom,
    ! [X2: product_unit,Y: product_unit] :
      ( aa_Product_unit_o(aa_Pro4895447120693452255unit_o(ord_le3221252021190050221t_unit,X2),Y)
     => ( comple2584293577114468500t_unit(set_or5692540242118139586t_unit(X2,Y)) = X2 ) ) ).

% Inf_atLeastAtMost
tff(fact_6371_Inf__atLeastLessThan,axiom,
    ! [X2: set_nat,Y: set_nat] :
      ( ord_less_set_nat(X2,Y)
     => ( comple7806235888213564991et_nat(set_or3540276404033026485et_nat(X2,Y)) = X2 ) ) ).

% Inf_atLeastLessThan
tff(fact_6372_Inf__atLeastLessThan,axiom,
    ! [X2: product_unit,Y: product_unit] :
      ( aa_Product_unit_o(aa_Pro4895447120693452255unit_o(ord_le361264281704409273t_unit,X2),Y)
     => ( comple2584293577114468500t_unit(set_or4663484573592751262t_unit(X2,Y)) = X2 ) ) ).

% Inf_atLeastLessThan
tff(fact_6373_prod_Ocollapse,axiom,
    ! [Prod: produc2453742332425399446nteger] : aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,aa_Pro4276937008533432526e_term(produc2481150572478215260nteger,Prod)),aa_Pro4625778721341478855nteger(produc6589491691745714842nteger,Prod)) = Prod ).

% prod.collapse
tff(fact_6374_prod_Ocollapse,axiom,
    ! [Prod: produc8799533983703829792et_nat] : aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,aa_Pro8262445894397805713_nat_o(produc5325900173150335662et_nat,Prod)),aa_Pro5541488491759012064et_nat(produc4960056325182568940et_nat,Prod)) = Prod ).

% prod.collapse
tff(fact_6375_prod_Ocollapse,axiom,
    ! [Prod: produc3112576180687729086et_nat] : aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,aa_Pro2837773213478468339_nat_o(produc4078497350495916492et_nat,Prod)),aa_Pro7798056222271281692et_nat(produc9081944055658670602et_nat,Prod)) = Prod ).

% prod.collapse
tff(fact_6376_prod_Ocollapse,axiom,
    ! [Prod: produc3043004577601930755nt_int] : aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,aa_Pro4010435699744810540e_term(produc3130796691802200265nt_int,Prod)),aa_Pro2675344531184151096nt_int(produc1557020426977177351nt_int,Prod)) = Prod ).

% prod.collapse
tff(fact_6377_prod_Ocollapse,axiom,
    ! [Prod: produc4788131091073775919nt_int] : aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,aa_Pro2551989255418117932e_term(produc4463008262350210037nt_int,Prod)),aa_Pro4437156595432605708nt_int(produc7629796867588368947nt_int,Prod)) = Prod ).

% prod.collapse
tff(fact_6378_prod_Ocollapse,axiom,
    ! [Prod: produc8923325533196201883nteger] : aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,Prod)),aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,Prod)) = Prod ).

% prod.collapse
tff(fact_6379_prod_Ocollapse,axiom,
    ! [Prod: product_prod_int_int] : aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_Pro6799258434465214121nt_int(product_fst_int_int,Prod)),aa_Pro6799258434465214121nt_int(product_snd_int_int,Prod)) = Prod ).

% prod.collapse
tff(fact_6380_prod_Ocollapse,axiom,
    ! [Prod: produc5835291356934675326atural] : aa_Pro7165575656943818355atural(produc6639722614265839536atural(aa_Pro5806155842103967332atural(produc497848011034438852atural,Prod)),aa_Pro3673693039631929973atural(produc6591912806276919810atural,Prod)) = Prod ).

% prod.collapse
tff(fact_6381_Inf__atMost,axiom,
    ! [X2: set_Pr4329608150637261639at_nat] : comple6751905152567503566at_nat(set_or4071486571221009422at_nat(X2)) = bot_bo228742789529271731at_nat ).

% Inf_atMost
tff(fact_6382_Inf__atMost,axiom,
    ! [X2: set_Pr1261947904930325089at_nat] : comple1930127330929219688at_nat(aa_set6242432332095302236at_nat(set_or2762583123196137896at_nat,X2)) = bot_bo2099793752762293965at_nat ).

% Inf_atMost
tff(fact_6383_Inf__atMost,axiom,
    ! [X2: set_o] : comple3063163877087187839_set_o(set_ord_atMost_set_o(X2)) = bot_bot_set_o ).

% Inf_atMost
tff(fact_6384_Inf__atMost,axiom,
    ! [X2: set_int] : comple3628384868704368283et_int(set_or58775011639299419et_int(X2)) = bot_bot_set_int ).

% Inf_atMost
tff(fact_6385_Inf__atMost,axiom,
    ! [X2: set_nat] : comple7806235888213564991et_nat(set_or4236626031148496127et_nat(X2)) = bot_bot_set_nat ).

% Inf_atMost
tff(fact_6386_Inf__atMost,axiom,
    ! [X2: product_unit] : comple2584293577114468500t_unit(set_or8621721900777396692t_unit(X2)) = bot_bot_Product_unit ).

% Inf_atMost
tff(fact_6387_img__fst,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,S2: set_Pr4329608150637261639at_nat] :
      ( member8757157785044589968at_nat(produc2922128104949294807at_nat(A,B),S2)
     => member2643936169264416010at_nat(A,image_7979982168039674559at_nat(produc6011863565407846595at_nat,S2)) ) ).

% img_fst
tff(fact_6388_img__fst,axiom,
    ! [A: nat,B: nat,S2: set_Pr1261947904930325089at_nat] :
      ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B),S2)
     => member_nat(A,image_2486076414777270412at_nat(product_fst_nat_nat,S2)) ) ).

% img_fst
tff(fact_6389_img__fst,axiom,
    ! [A: fun_Pr5098669352780829690e_term,B: produc8923325533196201883nteger,S2: set_Pr3486312109254157132nteger] :
      ( member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A),B),S2)
     => member8464590939221061905e_term(A,image_5882744770105888791e_term(produc2481150572478215260nteger,S2)) ) ).

% img_fst
tff(fact_6390_img__fst,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,B: produc3658429121746597890et_nat,S2: set_Pr1312406793078187350et_nat] :
      ( member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A),B),S2)
     => member7544390268018397336_nat_o(A,image_4444162529858428168_nat_o(produc5325900173150335662et_nat,S2)) ) ).

% img_fst
tff(fact_6391_img__fst,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,B: produc8799533983703829792et_nat,S2: set_Pr4040394263813967220et_nat] :
      ( member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A),B),S2)
     => member7544390268018397336_nat_o(A,image_8400968272122294250_nat_o(produc4078497350495916492et_nat,S2)) ) ).

% img_fst
tff(fact_6392_img__fst,axiom,
    ! [A: fun_Pr7763680713840462443e_term,B: product_prod_int_int,S2: set_Pr6700895561065273913nt_int] :
      ( member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,A),B),S2)
     => member1495369047980753794e_term(A,image_143812984558558581e_term(produc3130796691802200265nt_int,S2)) ) ).

% img_fst
tff(fact_6393_img__fst,axiom,
    ! [A: fun_in5730379987311621695e_term,B: product_prod_int_int,S2: set_Pr4166680992137330533nt_int] :
      ( member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A),B),S2)
     => member4871225538671630166e_term(A,image_7516633138899002997e_term(produc4463008262350210037nt_int,S2)) ) ).

% img_fst
tff(fact_6394_img__fst,axiom,
    ! [A: code_integer,B: code_integer,S2: set_Pr4811707699266497531nteger] :
      ( member157494554546826820nteger(aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(A),B),S2)
     => member_Code_integer(A,image_6316824473203919795nteger(produc8508995932063986495nteger,S2)) ) ).

% img_fst
tff(fact_6395_img__fst,axiom,
    ! [A: int,B: int,S2: set_Pr958786334691620121nt_int] :
      ( member5262025264175285858nt_int(aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A),B),S2)
     => member_int(A,image_5042161079198086560nt_int(product_fst_int_int,S2)) ) ).

% img_fst
tff(fact_6396_img__snd,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,S2: set_Pr4329608150637261639at_nat] :
      ( member8757157785044589968at_nat(produc2922128104949294807at_nat(A,B),S2)
     => member2643936169264416010at_nat(B,image_7979982168039674559at_nat(produc2937545259423399429at_nat,S2)) ) ).

% img_snd
tff(fact_6397_img__snd,axiom,
    ! [A: nat,B: nat,S2: set_Pr1261947904930325089at_nat] :
      ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B),S2)
     => member_nat(B,image_2486076414777270412at_nat(product_snd_nat_nat,S2)) ) ).

% img_snd
tff(fact_6398_img__snd,axiom,
    ! [A: fun_Pr5098669352780829690e_term,B: produc8923325533196201883nteger,S2: set_Pr3486312109254157132nteger] :
      ( member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A),B),S2)
     => member157494554546826820nteger(B,image_2271979006234848446nteger(produc6589491691745714842nteger,S2)) ) ).

% img_snd
tff(fact_6399_img__snd,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,B: produc3658429121746597890et_nat,S2: set_Pr1312406793078187350et_nat] :
      ( member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A),B),S2)
     => member6260224972018164377et_nat(B,image_5643293374885392937et_nat(produc4960056325182568940et_nat,S2)) ) ).

% img_snd
tff(fact_6400_img__snd,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,B: produc8799533983703829792et_nat,S2: set_Pr4040394263813967220et_nat] :
      ( member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A),B),S2)
     => member4513763875858039863et_nat(B,image_1425188809386248805et_nat(produc9081944055658670602et_nat,S2)) ) ).

% img_snd
tff(fact_6401_img__snd,axiom,
    ! [A: fun_Pr7763680713840462443e_term,B: product_prod_int_int,S2: set_Pr6700895561065273913nt_int] :
      ( member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,A),B),S2)
     => member5262025264175285858nt_int(B,image_5003770246312495919nt_int(produc1557020426977177351nt_int,S2)) ) ).

% img_snd
tff(fact_6402_img__snd,axiom,
    ! [A: fun_in5730379987311621695e_term,B: product_prod_int_int,S2: set_Pr4166680992137330533nt_int] :
      ( member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A),B),S2)
     => member5262025264175285858nt_int(B,image_5733965904763621635nt_int(produc7629796867588368947nt_int,S2)) ) ).

% img_snd
tff(fact_6403_img__snd,axiom,
    ! [A: code_integer,B: code_integer,S2: set_Pr4811707699266497531nteger] :
      ( member157494554546826820nteger(aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(A),B),S2)
     => member_Code_integer(B,image_6316824473203919795nteger(produc6174133586879617921nteger,S2)) ) ).

% img_snd
tff(fact_6404_img__snd,axiom,
    ! [A: int,B: int,S2: set_Pr958786334691620121nt_int] :
      ( member5262025264175285858nt_int(aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A),B),S2)
     => member_int(B,image_5042161079198086560nt_int(product_snd_int_int,S2)) ) ).

% img_snd
tff(fact_6405_img__snd,axiom,
    ! [A: code_natural,B: produc7822875418678951345atural,S2: set_Pr2352657477744078772atural] :
      ( member2108296798382401941atural(aa_Pro7165575656943818355atural(produc6639722614265839536atural(A),B),S2)
     => member8280416476884352090atural(B,image_3837677093542026988atural(produc6591912806276919810atural,S2)) ) ).

% img_snd
tff(fact_6406_fst__divmod__abs,axiom,
    ! [K: code_integer,L: code_integer] : aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,aa_Cod6977894654539884864nteger(code_divmod_abs(K),L)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(divide6298287555418463151nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,K)),aa_Cod1783974652533396728nteger(abs_abs_Code_integer,L)) ).

% fst_divmod_abs
tff(fact_6407_snd__divmod__abs,axiom,
    ! [K: code_integer,L: code_integer] : aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,aa_Cod6977894654539884864nteger(code_divmod_abs(K),L)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(modulo364778990260209775nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,K)),aa_Cod1783974652533396728nteger(abs_abs_Code_integer,L)) ).

% snd_divmod_abs
tff(fact_6408_Inf__atMostLessThan,axiom,
    ! [X2: set_Pr4329608150637261639at_nat] :
      ( ord_le2604355607129572851at_nat(top_to6833984726390702231at_nat,X2)
     => ( comple6751905152567503566at_nat(set_or2137699863726836970at_nat(X2)) = bot_bo228742789529271731at_nat ) ) ).

% Inf_atMostLessThan
tff(fact_6409_Inf__atMostLessThan,axiom,
    ! [X2: set_Pr1261947904930325089at_nat] :
      ( aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(ord_le7866589430770878221at_nat,top_to4669805908274784177at_nat),X2)
     => ( comple1930127330929219688at_nat(aa_set6242432332095302236at_nat(set_or5243998310507771012at_nat,X2)) = bot_bo2099793752762293965at_nat ) ) ).

% Inf_atMostLessThan
tff(fact_6410_Inf__atMostLessThan,axiom,
    ! [X2: set_o] :
      ( ord_less_set_o(top_top_set_o,X2)
     => ( comple3063163877087187839_set_o(set_or3489638696441961371_set_o(X2)) = bot_bot_set_o ) ) ).

% Inf_atMostLessThan
tff(fact_6411_Inf__atMostLessThan,axiom,
    ! [X2: set_Product_unit] :
      ( ord_le8056459307392131481t_unit(top_to1996260823553986621t_unit,X2)
     => ( comple7216939928495492468t_unit(set_or3324826255835560848t_unit(X2)) = bot_bo3957492148770167129t_unit ) ) ).

% Inf_atMostLessThan
tff(fact_6412_Inf__atMostLessThan,axiom,
    ! [X2: set_int] :
      ( ord_less_set_int(top_top_set_int,X2)
     => ( comple3628384868704368283et_int(set_or5935648273017318783et_int(X2)) = bot_bot_set_int ) ) ).

% Inf_atMostLessThan
tff(fact_6413_Inf__atMostLessThan,axiom,
    ! [X2: set_nat] :
      ( ord_less_set_nat(top_top_set_nat,X2)
     => ( comple7806235888213564991et_nat(set_or890127255671739683et_nat(X2)) = bot_bot_set_nat ) ) ).

% Inf_atMostLessThan
tff(fact_6414_Inf__atMostLessThan,axiom,
    ! [X2: product_unit] :
      ( aa_Product_unit_o(aa_Pro4895447120693452255unit_o(ord_le361264281704409273t_unit,top_top_Product_unit),X2)
     => ( comple2584293577114468500t_unit(set_or8708608758551125680t_unit(X2)) = bot_bot_Product_unit ) ) ).

% Inf_atMostLessThan
tff(fact_6415_case__prod__beta_H,axiom,
    ! [F: fun_nat_fun_nat_nat,X: product_prod_nat_nat] : aa_Pro4243173770044397973at_nat(aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,F),X) = aa_nat_nat(aa_nat_fun_nat_nat(F,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,X)),aa_Pro4243173770044397973at_nat(product_snd_nat_nat,X)) ).

% case_prod_beta'
tff(fact_6416_case__prod__beta_H,axiom,
    ! [F: fun_na1668100129766719005at_nat,X: product_prod_nat_nat] : aa_Pro8023792847356852296at_nat(aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,F),X) = aa_nat7997280740862404369at_nat(aa_nat5682243440470347102at_nat(F,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,X)),aa_Pro4243173770044397973at_nat(product_snd_nat_nat,X)) ).

% case_prod_beta'
tff(fact_6417_case__prod__beta_H,axiom,
    ! [F: fun_na5914473681949881652_nat_o,X: product_prod_nat_nat] : aa_Pro989595756709598047_nat_o(aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,F),X) = aa_nat7695548938202568488_nat_o(aa_nat4259715169212259317_nat_o(F,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,X)),aa_Pro4243173770044397973at_nat(product_snd_nat_nat,X)) ).

% case_prod_beta'
tff(fact_6418_case__prod__beta_H,axiom,
    ! [F: fun_in1696471567231710611nt_int,X: product_prod_int_int] : aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,F),X) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(F,aa_Pro6799258434465214121nt_int(product_fst_int_int,X)),aa_Pro6799258434465214121nt_int(product_snd_int_int,X)) ).

% case_prod_beta'
tff(fact_6419_case__prod__beta_H,axiom,
    ! [F: fun_int_fun_int_int,X: product_prod_int_int] : aa_Pro6799258434465214121nt_int(aa_fun914008879417524284nt_int(produc8211389475949308722nt_int,F),X) = aa_int_int(aa_int_fun_int_int(F,aa_Pro6799258434465214121nt_int(product_fst_int_int,X)),aa_Pro6799258434465214121nt_int(product_snd_int_int,X)) ).

% case_prod_beta'
tff(fact_6420_case__prod__unfold,axiom,
    ! [X: fun_nat_fun_nat_nat,Xa3: product_prod_nat_nat] : aa_Pro4243173770044397973at_nat(aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,X),Xa3) = aa_nat_nat(aa_nat_fun_nat_nat(X,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,Xa3)),aa_Pro4243173770044397973at_nat(product_snd_nat_nat,Xa3)) ).

% case_prod_unfold
tff(fact_6421_case__prod__unfold,axiom,
    ! [X: fun_na1668100129766719005at_nat,Xa3: product_prod_nat_nat] : aa_Pro8023792847356852296at_nat(aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,X),Xa3) = aa_nat7997280740862404369at_nat(aa_nat5682243440470347102at_nat(X,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,Xa3)),aa_Pro4243173770044397973at_nat(product_snd_nat_nat,Xa3)) ).

% case_prod_unfold
tff(fact_6422_case__prod__unfold,axiom,
    ! [X: fun_na5914473681949881652_nat_o,Xa3: product_prod_nat_nat] : aa_Pro989595756709598047_nat_o(aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,X),Xa3) = aa_nat7695548938202568488_nat_o(aa_nat4259715169212259317_nat_o(X,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,Xa3)),aa_Pro4243173770044397973at_nat(product_snd_nat_nat,Xa3)) ).

% case_prod_unfold
tff(fact_6423_case__prod__unfold,axiom,
    ! [X: fun_in1696471567231710611nt_int,Xa3: product_prod_int_int] : aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,X),Xa3) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(X,aa_Pro6799258434465214121nt_int(product_fst_int_int,Xa3)),aa_Pro6799258434465214121nt_int(product_snd_int_int,Xa3)) ).

% case_prod_unfold
tff(fact_6424_case__prod__unfold,axiom,
    ! [X: fun_int_fun_int_int,Xa3: product_prod_int_int] : aa_Pro6799258434465214121nt_int(aa_fun914008879417524284nt_int(produc8211389475949308722nt_int,X),Xa3) = aa_int_int(aa_int_fun_int_int(X,aa_Pro6799258434465214121nt_int(product_fst_int_int,Xa3)),aa_Pro6799258434465214121nt_int(product_snd_int_int,Xa3)) ).

% case_prod_unfold
tff(fact_6425_Product__Type_OCollect__case__prodD,axiom,
    ! [X2: produc3843707927480180839at_nat,A2: fun_se5639961202347202350_nat_o] :
      ( member8757157785044589968at_nat(X2,aa_fun1965866159956205013at_nat(collec6321179662152712658at_nat,aa_fun762164075915671590_nat_o(produc410239310623530412_nat_o,A2)))
     => aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(A2,aa_Pro441628658106787830at_nat(produc6011863565407846595at_nat,X2)),aa_Pro441628658106787830at_nat(produc2937545259423399429at_nat,X2)) ) ).

% Product_Type.Collect_case_prodD
tff(fact_6426_Product__Type_OCollect__case__prodD,axiom,
    ! [X2: product_prod_nat_nat,A2: fun_nat_fun_nat_o] :
      ( member8440522571783428010at_nat(X2,aa_fun7046812543386002057at_nat(collec3392354462482085612at_nat,aa_fun7564604662015400456_nat_o(produc6081775807080527818_nat_o,A2)))
     => aa_nat_o(aa_nat_fun_nat_o(A2,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,X2)),aa_Pro4243173770044397973at_nat(product_snd_nat_nat,X2)) ) ).

% Product_Type.Collect_case_prodD
tff(fact_6427_Product__Type_OCollect__case__prodD,axiom,
    ! [X2: produc8923325533196201883nteger,A2: fun_Co2081214437782444048eger_o] :
      ( member157494554546826820nteger(X2,collec7766031446232907142nteger(produc2066375834425727024eger_o(A2)))
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(A2,aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,X2)),aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,X2)) ) ).

% Product_Type.Collect_case_prodD
tff(fact_6428_Product__Type_OCollect__case__prodD,axiom,
    ! [X2: product_prod_int_int,A2: fun_int_fun_int_o] :
      ( member5262025264175285858nt_int(X2,collec213857154873943460nt_int(produc4947309494688390418_int_o(A2)))
     => aa_int_o(aa_int_fun_int_o(A2,aa_Pro6799258434465214121nt_int(product_fst_int_int,X2)),aa_Pro6799258434465214121nt_int(product_snd_int_int,X2)) ) ).

% Product_Type.Collect_case_prodD
tff(fact_6429_Product__Type_OCollect__case__prodD,axiom,
    ! [X2: produc5835291356934675326atural,A2: fun_Co9066792663755620495ural_o] :
      ( member2108296798382401941atural(X2,collec1991479681304692691atural(produc7358226366420480123ural_o(A2)))
     => aa_Pro6073791466322389475ural_o(aa_Cod1393124287678120144ural_o(A2,aa_Pro5806155842103967332atural(produc497848011034438852atural,X2)),aa_Pro3673693039631929973atural(produc6591912806276919810atural,X2)) ) ).

% Product_Type.Collect_case_prodD
tff(fact_6430_case__prod__beta,axiom,
    ! [F: fun_nat_fun_nat_nat,P2: product_prod_nat_nat] : aa_Pro4243173770044397973at_nat(aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,F),P2) = aa_nat_nat(aa_nat_fun_nat_nat(F,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,P2)),aa_Pro4243173770044397973at_nat(product_snd_nat_nat,P2)) ).

% case_prod_beta
tff(fact_6431_case__prod__beta,axiom,
    ! [F: fun_na1668100129766719005at_nat,P2: product_prod_nat_nat] : aa_Pro8023792847356852296at_nat(aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,F),P2) = aa_nat7997280740862404369at_nat(aa_nat5682243440470347102at_nat(F,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,P2)),aa_Pro4243173770044397973at_nat(product_snd_nat_nat,P2)) ).

% case_prod_beta
tff(fact_6432_case__prod__beta,axiom,
    ! [F: fun_na5914473681949881652_nat_o,P2: product_prod_nat_nat] : aa_Pro989595756709598047_nat_o(aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,F),P2) = aa_nat7695548938202568488_nat_o(aa_nat4259715169212259317_nat_o(F,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,P2)),aa_Pro4243173770044397973at_nat(product_snd_nat_nat,P2)) ).

% case_prod_beta
tff(fact_6433_case__prod__beta,axiom,
    ! [F: fun_in1696471567231710611nt_int,P2: product_prod_int_int] : aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,F),P2) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(F,aa_Pro6799258434465214121nt_int(product_fst_int_int,P2)),aa_Pro6799258434465214121nt_int(product_snd_int_int,P2)) ).

% case_prod_beta
tff(fact_6434_case__prod__beta,axiom,
    ! [F: fun_int_fun_int_int,P2: product_prod_int_int] : aa_Pro6799258434465214121nt_int(aa_fun914008879417524284nt_int(produc8211389475949308722nt_int,F),P2) = aa_int_int(aa_int_fun_int_int(F,aa_Pro6799258434465214121nt_int(product_fst_int_int,P2)),aa_Pro6799258434465214121nt_int(product_snd_int_int,P2)) ).

% case_prod_beta
tff(fact_6435_split__beta,axiom,
    ! [F: fun_nat_fun_nat_nat,Prod: product_prod_nat_nat] : aa_Pro4243173770044397973at_nat(aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,F),Prod) = aa_nat_nat(aa_nat_fun_nat_nat(F,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,Prod)),aa_Pro4243173770044397973at_nat(product_snd_nat_nat,Prod)) ).

% split_beta
tff(fact_6436_split__beta,axiom,
    ! [F: fun_na1668100129766719005at_nat,Prod: product_prod_nat_nat] : aa_Pro8023792847356852296at_nat(aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,F),Prod) = aa_nat7997280740862404369at_nat(aa_nat5682243440470347102at_nat(F,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,Prod)),aa_Pro4243173770044397973at_nat(product_snd_nat_nat,Prod)) ).

% split_beta
tff(fact_6437_split__beta,axiom,
    ! [F: fun_na5914473681949881652_nat_o,Prod: product_prod_nat_nat] : aa_Pro989595756709598047_nat_o(aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,F),Prod) = aa_nat7695548938202568488_nat_o(aa_nat4259715169212259317_nat_o(F,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,Prod)),aa_Pro4243173770044397973at_nat(product_snd_nat_nat,Prod)) ).

% split_beta
tff(fact_6438_split__beta,axiom,
    ! [F: fun_in1696471567231710611nt_int,Prod: product_prod_int_int] : aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,F),Prod) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(F,aa_Pro6799258434465214121nt_int(product_fst_int_int,Prod)),aa_Pro6799258434465214121nt_int(product_snd_int_int,Prod)) ).

% split_beta
tff(fact_6439_split__beta,axiom,
    ! [F: fun_int_fun_int_int,Prod: product_prod_int_int] : aa_Pro6799258434465214121nt_int(aa_fun914008879417524284nt_int(produc8211389475949308722nt_int,F),Prod) = aa_int_int(aa_int_fun_int_int(F,aa_Pro6799258434465214121nt_int(product_fst_int_int,Prod)),aa_Pro6799258434465214121nt_int(product_snd_int_int,Prod)) ).

% split_beta
tff(fact_6440_effect__guardI,axiom,
    ! [P: fun_he8413527710729349838unit_o,Ha: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit,F: fun_he4944555133437423336it_nat,N2: nat,R2: product_unit] :
      ( aa_hea7994211679605476167unit_o(P,Ha)
     => ( ( H3 = produc2838810277069100634it_nat(produc8604850587836428116it_nat(aa_hea256619718444519449it_nat(F,Ha))) )
       => ( ( N2 = produc2594868675584459928it_nat(produc8604850587836428116it_nat(aa_hea256619718444519449it_nat(F,Ha))) )
         => ( ( R2 = produc4530234641508181270it_nat(aa_hea256619718444519449it_nat(F,Ha)) )
           => aa_nat_o(heap_T6553295506729943825t_unit(heap_T8440541562793052209t_unit(P,F),Ha,H3,R2),N2) ) ) ) ) ).

% effect_guardI
tff(fact_6441_effect__guardI,axiom,
    ! [P: fun_he8413527710729349838unit_o,Ha: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit,F: fun_he281446669002384250it_nat,N2: nat,R2: array_a] :
      ( aa_hea7994211679605476167unit_o(P,Ha)
     => ( ( H3 = produc2838810277069100634it_nat(produc6991280839920081578it_nat(aa_hea1118439097112461811it_nat(F,Ha))) )
       => ( ( N2 = produc2594868675584459928it_nat(produc6991280839920081578it_nat(aa_hea1118439097112461811it_nat(F,Ha))) )
         => ( ( R2 = produc491454361838572648it_nat(aa_hea1118439097112461811it_nat(F,Ha)) )
           => aa_nat_o(heap_T5830633491639066771rray_a(heap_T7685628758766326643rray_a(P,F),Ha,H3,R2),N2) ) ) ) ) ).

% effect_guardI
tff(fact_6442_effect__guardE,axiom,
    ! [P: fun_he8413527710729349838unit_o,F: fun_he4944555133437423336it_nat,Ha: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit,R2: product_unit,N2: nat] :
      ( aa_nat_o(heap_T6553295506729943825t_unit(heap_T8440541562793052209t_unit(P,F),Ha,H3,R2),N2)
     => ~ ( ( H3 = produc2838810277069100634it_nat(produc8604850587836428116it_nat(aa_hea256619718444519449it_nat(F,Ha))) )
         => ( ( N2 = produc2594868675584459928it_nat(produc8604850587836428116it_nat(aa_hea256619718444519449it_nat(F,Ha))) )
           => ( ( R2 = produc4530234641508181270it_nat(aa_hea256619718444519449it_nat(F,Ha)) )
             => ~ aa_hea7994211679605476167unit_o(P,Ha) ) ) ) ) ).

% effect_guardE
tff(fact_6443_effect__guardE,axiom,
    ! [P: fun_he8413527710729349838unit_o,F: fun_he281446669002384250it_nat,Ha: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit,R2: array_a,N2: nat] :
      ( aa_nat_o(heap_T5830633491639066771rray_a(heap_T7685628758766326643rray_a(P,F),Ha,H3,R2),N2)
     => ~ ( ( H3 = produc2838810277069100634it_nat(produc6991280839920081578it_nat(aa_hea1118439097112461811it_nat(F,Ha))) )
         => ( ( N2 = produc2594868675584459928it_nat(produc6991280839920081578it_nat(aa_hea1118439097112461811it_nat(F,Ha))) )
           => ( ( R2 = produc491454361838572648it_nat(aa_hea1118439097112461811it_nat(F,Ha)) )
             => ~ aa_hea7994211679605476167unit_o(P,Ha) ) ) ) ) ).

% effect_guardE
tff(fact_6444_effectE,axiom,
    ! [C: heap_T5738788834812785303t_unit,Ha: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit,R2: product_unit,N2: nat] :
      ( aa_nat_o(heap_T6553295506729943825t_unit(C,Ha,H3,R2),N2)
     => ~ ( ( R2 = produc4530234641508181270it_nat(aa_opt6779208767223616030it_nat(the_Pr7776125533777466484it_nat,aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(C),Ha))) )
         => ( ( H3 = produc2838810277069100634it_nat(produc8604850587836428116it_nat(aa_opt6779208767223616030it_nat(the_Pr7776125533777466484it_nat,aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(C),Ha)))) )
           => ( ( N2 = produc2594868675584459928it_nat(produc8604850587836428116it_nat(aa_opt6779208767223616030it_nat(the_Pr7776125533777466484it_nat,aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(C),Ha)))) )
             => ~ aa_hea7994211679605476167unit_o(heap_T584514906347983379t_unit(C),Ha) ) ) ) ) ).

% effectE
tff(fact_6445_effectE,axiom,
    ! [C: heap_T6362127782908069795rray_a,Ha: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit,R2: array_a,N2: nat] :
      ( aa_nat_o(heap_T5830633491639066771rray_a(C,Ha,H3,R2),N2)
     => ~ ( ( R2 = produc491454361838572648it_nat(aa_opt2040853179424174198it_nat(the_Pr5856008525237892824it_nat,aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(C),Ha))) )
         => ( ( H3 = produc2838810277069100634it_nat(produc6991280839920081578it_nat(aa_opt2040853179424174198it_nat(the_Pr5856008525237892824it_nat,aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(C),Ha)))) )
           => ( ( N2 = produc2594868675584459928it_nat(produc6991280839920081578it_nat(aa_opt2040853179424174198it_nat(the_Pr5856008525237892824it_nat,aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(C),Ha)))) )
             => ~ aa_hea7994211679605476167unit_o(heap_T6932021131025641745rray_a(C),Ha) ) ) ) ) ).

% effectE
tff(fact_6446_prod__eq__iff,axiom,
    ! [S: produc8923325533196201883nteger,T: produc8923325533196201883nteger] :
      ( ( S = T )
    <=> ( ( aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,S) = aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,T) )
        & ( aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,S) = aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,T) ) ) ) ).

% prod_eq_iff
tff(fact_6447_prod__eq__iff,axiom,
    ! [S: product_prod_int_int,T: product_prod_int_int] :
      ( ( S = T )
    <=> ( ( aa_Pro6799258434465214121nt_int(product_fst_int_int,S) = aa_Pro6799258434465214121nt_int(product_fst_int_int,T) )
        & ( aa_Pro6799258434465214121nt_int(product_snd_int_int,S) = aa_Pro6799258434465214121nt_int(product_snd_int_int,T) ) ) ) ).

% prod_eq_iff
tff(fact_6448_prod__eq__iff,axiom,
    ! [S: produc5835291356934675326atural,T: produc5835291356934675326atural] :
      ( ( S = T )
    <=> ( ( aa_Pro5806155842103967332atural(produc497848011034438852atural,S) = aa_Pro5806155842103967332atural(produc497848011034438852atural,T) )
        & ( aa_Pro3673693039631929973atural(produc6591912806276919810atural,S) = aa_Pro3673693039631929973atural(produc6591912806276919810atural,T) ) ) ) ).

% prod_eq_iff
tff(fact_6449_prod__eqI,axiom,
    ! [P2: produc8923325533196201883nteger,Q3: produc8923325533196201883nteger] :
      ( ( aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,P2) = aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,Q3) )
     => ( ( aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,P2) = aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,Q3) )
       => ( P2 = Q3 ) ) ) ).

% prod_eqI
tff(fact_6450_prod__eqI,axiom,
    ! [P2: product_prod_int_int,Q3: product_prod_int_int] :
      ( ( aa_Pro6799258434465214121nt_int(product_fst_int_int,P2) = aa_Pro6799258434465214121nt_int(product_fst_int_int,Q3) )
     => ( ( aa_Pro6799258434465214121nt_int(product_snd_int_int,P2) = aa_Pro6799258434465214121nt_int(product_snd_int_int,Q3) )
       => ( P2 = Q3 ) ) ) ).

% prod_eqI
tff(fact_6451_prod__eqI,axiom,
    ! [P2: produc5835291356934675326atural,Q3: produc5835291356934675326atural] :
      ( ( aa_Pro5806155842103967332atural(produc497848011034438852atural,P2) = aa_Pro5806155842103967332atural(produc497848011034438852atural,Q3) )
     => ( ( aa_Pro3673693039631929973atural(produc6591912806276919810atural,P2) = aa_Pro3673693039631929973atural(produc6591912806276919810atural,Q3) )
       => ( P2 = Q3 ) ) ) ).

% prod_eqI
tff(fact_6452_prod_Oexpand,axiom,
    ! [Prod: produc8923325533196201883nteger,Prod2: produc8923325533196201883nteger] :
      ( ( ( aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,Prod) = aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,Prod2) )
        & ( aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,Prod) = aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,Prod2) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
tff(fact_6453_prod_Oexpand,axiom,
    ! [Prod: product_prod_int_int,Prod2: product_prod_int_int] :
      ( ( ( aa_Pro6799258434465214121nt_int(product_fst_int_int,Prod) = aa_Pro6799258434465214121nt_int(product_fst_int_int,Prod2) )
        & ( aa_Pro6799258434465214121nt_int(product_snd_int_int,Prod) = aa_Pro6799258434465214121nt_int(product_snd_int_int,Prod2) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
tff(fact_6454_prod_Oexpand,axiom,
    ! [Prod: produc5835291356934675326atural,Prod2: produc5835291356934675326atural] :
      ( ( ( aa_Pro5806155842103967332atural(produc497848011034438852atural,Prod) = aa_Pro5806155842103967332atural(produc497848011034438852atural,Prod2) )
        & ( aa_Pro3673693039631929973atural(produc6591912806276919810atural,Prod) = aa_Pro3673693039631929973atural(produc6591912806276919810atural,Prod2) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
tff(fact_6455_All__prod__contract,axiom,
    ! [P: fun_Co2081214437782444048eger_o] :
      ( ! [A5: code_integer,X_1: code_integer] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(P,A5),X_1)
    <=> ! [Z3: produc8923325533196201883nteger] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(P,aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,Z3)),aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,Z3)) ) ).

% All_prod_contract
tff(fact_6456_All__prod__contract,axiom,
    ! [P: fun_int_fun_int_o] :
      ( ! [A5: int,X_1: int] : aa_int_o(aa_int_fun_int_o(P,A5),X_1)
    <=> ! [Z3: product_prod_int_int] : aa_int_o(aa_int_fun_int_o(P,aa_Pro6799258434465214121nt_int(product_fst_int_int,Z3)),aa_Pro6799258434465214121nt_int(product_snd_int_int,Z3)) ) ).

% All_prod_contract
tff(fact_6457_All__prod__contract,axiom,
    ! [P: fun_Co9066792663755620495ural_o] :
      ( ! [A5: code_natural,X_1: produc7822875418678951345atural] : aa_Pro6073791466322389475ural_o(aa_Cod1393124287678120144ural_o(P,A5),X_1)
    <=> ! [Z3: produc5835291356934675326atural] : aa_Pro6073791466322389475ural_o(aa_Cod1393124287678120144ural_o(P,aa_Pro5806155842103967332atural(produc497848011034438852atural,Z3)),aa_Pro3673693039631929973atural(produc6591912806276919810atural,Z3)) ) ).

% All_prod_contract
tff(fact_6458_Ex__prod__contract,axiom,
    ! [P: fun_Co2081214437782444048eger_o] :
      ( ? [A5: code_integer,X_1: code_integer] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(P,A5),X_1)
    <=> ? [Z3: produc8923325533196201883nteger] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(P,aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,Z3)),aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,Z3)) ) ).

% Ex_prod_contract
tff(fact_6459_Ex__prod__contract,axiom,
    ! [P: fun_int_fun_int_o] :
      ( ? [A5: int,X_1: int] : aa_int_o(aa_int_fun_int_o(P,A5),X_1)
    <=> ? [Z3: product_prod_int_int] : aa_int_o(aa_int_fun_int_o(P,aa_Pro6799258434465214121nt_int(product_fst_int_int,Z3)),aa_Pro6799258434465214121nt_int(product_snd_int_int,Z3)) ) ).

% Ex_prod_contract
tff(fact_6460_Ex__prod__contract,axiom,
    ! [P: fun_Co9066792663755620495ural_o] :
      ( ? [A5: code_natural,X_1: produc7822875418678951345atural] : aa_Pro6073791466322389475ural_o(aa_Cod1393124287678120144ural_o(P,A5),X_1)
    <=> ? [Z3: produc5835291356934675326atural] : aa_Pro6073791466322389475ural_o(aa_Cod1393124287678120144ural_o(P,aa_Pro5806155842103967332atural(produc497848011034438852atural,Z3)),aa_Pro3673693039631929973atural(produc6591912806276919810atural,Z3)) ) ).

% Ex_prod_contract
tff(fact_6461_prod_Osplit__sel,axiom,
    ! [P: fun_nat_o,F: fun_nat_fun_nat_nat,Prod: product_prod_nat_nat] :
      ( aa_nat_o(P,aa_Pro4243173770044397973at_nat(aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,F),Prod))
    <=> ( ( Prod = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,Prod)),aa_Pro4243173770044397973at_nat(product_snd_nat_nat,Prod)) )
       => aa_nat_o(P,aa_nat_nat(aa_nat_fun_nat_nat(F,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,Prod)),aa_Pro4243173770044397973at_nat(product_snd_nat_nat,Prod))) ) ) ).

% prod.split_sel
tff(fact_6462_prod_Osplit__sel,axiom,
    ! [P: fun_fu8391177546919232046_nat_o,F: fun_na1668100129766719005at_nat,Prod: product_prod_nat_nat] :
      ( aa_fun3538214411680374423_nat_o(P,aa_Pro8023792847356852296at_nat(aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,F),Prod))
    <=> ( ( Prod = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,Prod)),aa_Pro4243173770044397973at_nat(product_snd_nat_nat,Prod)) )
       => aa_fun3538214411680374423_nat_o(P,aa_nat7997280740862404369at_nat(aa_nat5682243440470347102at_nat(F,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,Prod)),aa_Pro4243173770044397973at_nat(product_snd_nat_nat,Prod))) ) ) ).

% prod.split_sel
tff(fact_6463_prod_Osplit__sel,axiom,
    ! [P: fun_fu6891447142836604759at_o_o,F: fun_na5914473681949881652_nat_o,Prod: product_prod_nat_nat] :
      ( aa_fun8408151826566693824at_o_o(P,aa_Pro989595756709598047_nat_o(aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,F),Prod))
    <=> ( ( Prod = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,Prod)),aa_Pro4243173770044397973at_nat(product_snd_nat_nat,Prod)) )
       => aa_fun8408151826566693824at_o_o(P,aa_nat7695548938202568488_nat_o(aa_nat4259715169212259317_nat_o(F,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,Prod)),aa_Pro4243173770044397973at_nat(product_snd_nat_nat,Prod))) ) ) ).

% prod.split_sel
tff(fact_6464_prod_Osplit__sel,axiom,
    ! [P: fun_Pr3238374608701176162_int_o,F: fun_in1696471567231710611nt_int,Prod: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(P,aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,F),Prod))
    <=> ( ( Prod = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_Pro6799258434465214121nt_int(product_fst_int_int,Prod)),aa_Pro6799258434465214121nt_int(product_snd_int_int,Prod)) )
       => aa_Pro4592068669816069595_int_o(P,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(F,aa_Pro6799258434465214121nt_int(product_fst_int_int,Prod)),aa_Pro6799258434465214121nt_int(product_snd_int_int,Prod))) ) ) ).

% prod.split_sel
tff(fact_6465_prod_Osplit__sel,axiom,
    ! [P: fun_int_o,F: fun_int_fun_int_int,Prod: product_prod_int_int] :
      ( aa_int_o(P,aa_Pro6799258434465214121nt_int(aa_fun914008879417524284nt_int(produc8211389475949308722nt_int,F),Prod))
    <=> ( ( Prod = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_Pro6799258434465214121nt_int(product_fst_int_int,Prod)),aa_Pro6799258434465214121nt_int(product_snd_int_int,Prod)) )
       => aa_int_o(P,aa_int_int(aa_int_fun_int_int(F,aa_Pro6799258434465214121nt_int(product_fst_int_int,Prod)),aa_Pro6799258434465214121nt_int(product_snd_int_int,Prod))) ) ) ).

% prod.split_sel
tff(fact_6466_prod_Osplit__sel__asm,axiom,
    ! [P: fun_nat_o,F: fun_nat_fun_nat_nat,Prod: product_prod_nat_nat] :
      ( aa_nat_o(P,aa_Pro4243173770044397973at_nat(aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,F),Prod))
    <=> ~ ( ( Prod = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,Prod)),aa_Pro4243173770044397973at_nat(product_snd_nat_nat,Prod)) )
          & ~ aa_nat_o(P,aa_nat_nat(aa_nat_fun_nat_nat(F,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,Prod)),aa_Pro4243173770044397973at_nat(product_snd_nat_nat,Prod))) ) ) ).

% prod.split_sel_asm
tff(fact_6467_prod_Osplit__sel__asm,axiom,
    ! [P: fun_fu8391177546919232046_nat_o,F: fun_na1668100129766719005at_nat,Prod: product_prod_nat_nat] :
      ( aa_fun3538214411680374423_nat_o(P,aa_Pro8023792847356852296at_nat(aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,F),Prod))
    <=> ~ ( ( Prod = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,Prod)),aa_Pro4243173770044397973at_nat(product_snd_nat_nat,Prod)) )
          & ~ aa_fun3538214411680374423_nat_o(P,aa_nat7997280740862404369at_nat(aa_nat5682243440470347102at_nat(F,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,Prod)),aa_Pro4243173770044397973at_nat(product_snd_nat_nat,Prod))) ) ) ).

% prod.split_sel_asm
tff(fact_6468_prod_Osplit__sel__asm,axiom,
    ! [P: fun_fu6891447142836604759at_o_o,F: fun_na5914473681949881652_nat_o,Prod: product_prod_nat_nat] :
      ( aa_fun8408151826566693824at_o_o(P,aa_Pro989595756709598047_nat_o(aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,F),Prod))
    <=> ~ ( ( Prod = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,Prod)),aa_Pro4243173770044397973at_nat(product_snd_nat_nat,Prod)) )
          & ~ aa_fun8408151826566693824at_o_o(P,aa_nat7695548938202568488_nat_o(aa_nat4259715169212259317_nat_o(F,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,Prod)),aa_Pro4243173770044397973at_nat(product_snd_nat_nat,Prod))) ) ) ).

% prod.split_sel_asm
tff(fact_6469_prod_Osplit__sel__asm,axiom,
    ! [P: fun_Pr3238374608701176162_int_o,F: fun_in1696471567231710611nt_int,Prod: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(P,aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,F),Prod))
    <=> ~ ( ( Prod = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_Pro6799258434465214121nt_int(product_fst_int_int,Prod)),aa_Pro6799258434465214121nt_int(product_snd_int_int,Prod)) )
          & ~ aa_Pro4592068669816069595_int_o(P,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(F,aa_Pro6799258434465214121nt_int(product_fst_int_int,Prod)),aa_Pro6799258434465214121nt_int(product_snd_int_int,Prod))) ) ) ).

% prod.split_sel_asm
tff(fact_6470_prod_Osplit__sel__asm,axiom,
    ! [P: fun_int_o,F: fun_int_fun_int_int,Prod: product_prod_int_int] :
      ( aa_int_o(P,aa_Pro6799258434465214121nt_int(aa_fun914008879417524284nt_int(produc8211389475949308722nt_int,F),Prod))
    <=> ~ ( ( Prod = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_Pro6799258434465214121nt_int(product_fst_int_int,Prod)),aa_Pro6799258434465214121nt_int(product_snd_int_int,Prod)) )
          & ~ aa_int_o(P,aa_int_int(aa_int_fun_int_int(F,aa_Pro6799258434465214121nt_int(product_fst_int_int,Prod)),aa_Pro6799258434465214121nt_int(product_snd_int_int,Prod))) ) ) ).

% prod.split_sel_asm
tff(fact_6471_surjective__pairing,axiom,
    ! [T: produc2453742332425399446nteger] : T = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,aa_Pro4276937008533432526e_term(produc2481150572478215260nteger,T)),aa_Pro4625778721341478855nteger(produc6589491691745714842nteger,T)) ).

% surjective_pairing
tff(fact_6472_surjective__pairing,axiom,
    ! [T: produc8799533983703829792et_nat] : T = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,aa_Pro8262445894397805713_nat_o(produc5325900173150335662et_nat,T)),aa_Pro5541488491759012064et_nat(produc4960056325182568940et_nat,T)) ).

% surjective_pairing
tff(fact_6473_surjective__pairing,axiom,
    ! [T: produc3112576180687729086et_nat] : T = aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,aa_Pro2837773213478468339_nat_o(produc4078497350495916492et_nat,T)),aa_Pro7798056222271281692et_nat(produc9081944055658670602et_nat,T)) ).

% surjective_pairing
tff(fact_6474_surjective__pairing,axiom,
    ! [T: produc3043004577601930755nt_int] : T = aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,aa_Pro4010435699744810540e_term(produc3130796691802200265nt_int,T)),aa_Pro2675344531184151096nt_int(produc1557020426977177351nt_int,T)) ).

% surjective_pairing
tff(fact_6475_surjective__pairing,axiom,
    ! [T: produc4788131091073775919nt_int] : T = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,aa_Pro2551989255418117932e_term(produc4463008262350210037nt_int,T)),aa_Pro4437156595432605708nt_int(produc7629796867588368947nt_int,T)) ).

% surjective_pairing
tff(fact_6476_surjective__pairing,axiom,
    ! [T: produc8923325533196201883nteger] : T = aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,T)),aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,T)) ).

% surjective_pairing
tff(fact_6477_surjective__pairing,axiom,
    ! [T: product_prod_int_int] : T = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_Pro6799258434465214121nt_int(product_fst_int_int,T)),aa_Pro6799258434465214121nt_int(product_snd_int_int,T)) ).

% surjective_pairing
tff(fact_6478_surjective__pairing,axiom,
    ! [T: produc5835291356934675326atural] : T = aa_Pro7165575656943818355atural(produc6639722614265839536atural(aa_Pro5806155842103967332atural(produc497848011034438852atural,T)),aa_Pro3673693039631929973atural(produc6591912806276919810atural,T)) ).

% surjective_pairing
tff(fact_6479_prod_Oexhaust__sel,axiom,
    ! [Prod: produc2453742332425399446nteger] : Prod = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,aa_Pro4276937008533432526e_term(produc2481150572478215260nteger,Prod)),aa_Pro4625778721341478855nteger(produc6589491691745714842nteger,Prod)) ).

% prod.exhaust_sel
tff(fact_6480_prod_Oexhaust__sel,axiom,
    ! [Prod: produc8799533983703829792et_nat] : Prod = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,aa_Pro8262445894397805713_nat_o(produc5325900173150335662et_nat,Prod)),aa_Pro5541488491759012064et_nat(produc4960056325182568940et_nat,Prod)) ).

% prod.exhaust_sel
tff(fact_6481_prod_Oexhaust__sel,axiom,
    ! [Prod: produc3112576180687729086et_nat] : Prod = aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,aa_Pro2837773213478468339_nat_o(produc4078497350495916492et_nat,Prod)),aa_Pro7798056222271281692et_nat(produc9081944055658670602et_nat,Prod)) ).

% prod.exhaust_sel
tff(fact_6482_prod_Oexhaust__sel,axiom,
    ! [Prod: produc3043004577601930755nt_int] : Prod = aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,aa_Pro4010435699744810540e_term(produc3130796691802200265nt_int,Prod)),aa_Pro2675344531184151096nt_int(produc1557020426977177351nt_int,Prod)) ).

% prod.exhaust_sel
tff(fact_6483_prod_Oexhaust__sel,axiom,
    ! [Prod: produc4788131091073775919nt_int] : Prod = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,aa_Pro2551989255418117932e_term(produc4463008262350210037nt_int,Prod)),aa_Pro4437156595432605708nt_int(produc7629796867588368947nt_int,Prod)) ).

% prod.exhaust_sel
tff(fact_6484_prod_Oexhaust__sel,axiom,
    ! [Prod: produc8923325533196201883nteger] : Prod = aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,Prod)),aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,Prod)) ).

% prod.exhaust_sel
tff(fact_6485_prod_Oexhaust__sel,axiom,
    ! [Prod: product_prod_int_int] : Prod = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_Pro6799258434465214121nt_int(product_fst_int_int,Prod)),aa_Pro6799258434465214121nt_int(product_snd_int_int,Prod)) ).

% prod.exhaust_sel
tff(fact_6486_prod_Oexhaust__sel,axiom,
    ! [Prod: produc5835291356934675326atural] : Prod = aa_Pro7165575656943818355atural(produc6639722614265839536atural(aa_Pro5806155842103967332atural(produc497848011034438852atural,Prod)),aa_Pro3673693039631929973atural(produc6591912806276919810atural,Prod)) ).

% prod.exhaust_sel
tff(fact_6487_exI__realizer,axiom,
    ! [P: fun_Pr4680327687137491167term_o,Y: produc8923325533196201883nteger,X2: fun_Pr5098669352780829690e_term] :
      ( aa_fun7993445754732355552term_o(aa_Pro9035772811636298456term_o(P,Y),X2)
     => aa_fun7993445754732355552term_o(aa_Pro9035772811636298456term_o(P,aa_Pro4625778721341478855nteger(produc6589491691745714842nteger,aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X2),Y))),aa_Pro4276937008533432526e_term(produc2481150572478215260nteger,aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X2),Y))) ) ).

% exI_realizer
tff(fact_6488_exI__realizer,axiom,
    ! [P: fun_Pr5843349257357397163at_o_o,Y: produc3658429121746597890et_nat,X2: fun_Pr6460944699146269935_nat_o] :
      ( aa_fun1675921005893230629at_o_o(aa_Pro3588693547670092268at_o_o(P,Y),X2)
     => aa_fun1675921005893230629at_o_o(aa_Pro3588693547670092268at_o_o(P,aa_Pro5541488491759012064et_nat(produc4960056325182568940et_nat,aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X2),Y))),aa_Pro8262445894397805713_nat_o(produc5325900173150335662et_nat,aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X2),Y))) ) ).

% exI_realizer
tff(fact_6489_exI__realizer,axiom,
    ! [P: fun_Pr2647030239595059785at_o_o,Y: produc8799533983703829792et_nat,X2: fun_Pr6460944699146269935_nat_o] :
      ( aa_fun1675921005893230629at_o_o(aa_Pro1702148226396177290at_o_o(P,Y),X2)
     => aa_fun1675921005893230629at_o_o(aa_Pro1702148226396177290at_o_o(P,aa_Pro7798056222271281692et_nat(produc9081944055658670602et_nat,aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X2),Y))),aa_Pro2837773213478468339_nat_o(produc4078497350495916492et_nat,aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X2),Y))) ) ).

% exI_realizer
tff(fact_6490_exI__realizer,axiom,
    ! [P: fun_Pr5526332658708858896term_o,Y: product_prod_int_int,X2: fun_Pr7763680713840462443e_term] :
      ( aa_fun7650857933016935215term_o(aa_Pro1023942307601852809term_o(P,Y),X2)
     => aa_fun7650857933016935215term_o(aa_Pro1023942307601852809term_o(P,aa_Pro2675344531184151096nt_int(produc1557020426977177351nt_int,aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X2),Y))),aa_Pro4010435699744810540e_term(produc3130796691802200265nt_int,aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X2),Y))) ) ).

% exI_realizer
tff(fact_6491_exI__realizer,axiom,
    ! [P: fun_Pr7145817153658775868term_o,Y: product_prod_int_int,X2: fun_in5730379987311621695e_term] :
      ( aa_fun3020711759848831579term_o(aa_Pro1235490124264145077term_o(P,Y),X2)
     => aa_fun3020711759848831579term_o(aa_Pro1235490124264145077term_o(P,aa_Pro4437156595432605708nt_int(produc7629796867588368947nt_int,aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X2),Y))),aa_Pro2551989255418117932e_term(produc4463008262350210037nt_int,aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X2),Y))) ) ).

% exI_realizer
tff(fact_6492_exI__realizer,axiom,
    ! [P: fun_Co2081214437782444048eger_o,Y: code_integer,X2: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(P,Y),X2)
     => aa_Code_integer_o(aa_Cod326357343816142457eger_o(P,aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(X2),Y))),aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(X2),Y))) ) ).

% exI_realizer
tff(fact_6493_exI__realizer,axiom,
    ! [P: fun_int_fun_int_o,Y: int,X2: int] :
      ( aa_int_o(aa_int_fun_int_o(P,Y),X2)
     => aa_int_o(aa_int_fun_int_o(P,aa_Pro6799258434465214121nt_int(product_snd_int_int,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X2),Y))),aa_Pro6799258434465214121nt_int(product_fst_int_int,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X2),Y))) ) ).

% exI_realizer
tff(fact_6494_exI__realizer,axiom,
    ! [P: fun_Pr3928691295121555099ural_o,Y: produc7822875418678951345atural,X2: code_natural] :
      ( aa_Code_natural_o(aa_Pro3271585298577294228ural_o(P,Y),X2)
     => aa_Code_natural_o(aa_Pro3271585298577294228ural_o(P,aa_Pro3673693039631929973atural(produc6591912806276919810atural,aa_Pro7165575656943818355atural(produc6639722614265839536atural(X2),Y))),aa_Pro5806155842103967332atural(produc497848011034438852atural,aa_Pro7165575656943818355atural(produc6639722614265839536atural(X2),Y))) ) ).

% exI_realizer
tff(fact_6495_conjI__realizer,axiom,
    ! [P: fun_fu4736795817735658359term_o,P2: fun_Pr5098669352780829690e_term,Q: fun_Pr7211993375558241536eger_o,Q3: produc8923325533196201883nteger] :
      ( aa_fun7993445754732355552term_o(P,P2)
     => ( aa_Pro4926521453222654329eger_o(Q,Q3)
       => ( aa_fun7993445754732355552term_o(P,aa_Pro4276937008533432526e_term(produc2481150572478215260nteger,aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,P2),Q3)))
          & aa_Pro4926521453222654329eger_o(Q,aa_Pro4625778721341478855nteger(produc6589491691745714842nteger,aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,P2),Q3))) ) ) ) ).

% conjI_realizer
tff(fact_6496_conjI__realizer,axiom,
    ! [P: fun_fu5135969500543783852at_o_o,P2: fun_Pr6460944699146269935_nat_o,Q: fun_Pr6460944699146269935_nat_o,Q3: produc3658429121746597890et_nat] :
      ( aa_fun1675921005893230629at_o_o(P,P2)
     => ( aa_Pro653082453696054616_nat_o(Q,Q3)
       => ( aa_fun1675921005893230629at_o_o(P,aa_Pro8262445894397805713_nat_o(produc5325900173150335662et_nat,aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,P2),Q3)))
          & aa_Pro653082453696054616_nat_o(Q,aa_Pro5541488491759012064et_nat(produc4960056325182568940et_nat,aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,P2),Q3))) ) ) ) ).

% conjI_realizer
tff(fact_6497_conjI__realizer,axiom,
    ! [P: fun_fu5135969500543783852at_o_o,P2: fun_Pr6460944699146269935_nat_o,Q: fun_Pr2620521676128474833_nat_o,Q3: produc8799533983703829792et_nat] :
      ( aa_fun1675921005893230629at_o_o(P,P2)
     => ( aa_Pro5643009357358181178_nat_o(Q,Q3)
       => ( aa_fun1675921005893230629at_o_o(P,aa_Pro2837773213478468339_nat_o(produc4078497350495916492et_nat,aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,P2),Q3)))
          & aa_Pro5643009357358181178_nat_o(Q,aa_Pro7798056222271281692et_nat(produc9081944055658670602et_nat,aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,P2),Q3))) ) ) ) ).

% conjI_realizer
tff(fact_6498_conjI__realizer,axiom,
    ! [P: fun_fu6378075912484669126term_o,P2: fun_Pr7763680713840462443e_term,Q: fun_Pr3238374608701176162_int_o,Q3: product_prod_int_int] :
      ( aa_fun7650857933016935215term_o(P,P2)
     => ( aa_Pro4592068669816069595_int_o(Q,Q3)
       => ( aa_fun7650857933016935215term_o(P,aa_Pro4010435699744810540e_term(produc3130796691802200265nt_int,aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,P2),Q3)))
          & aa_Pro4592068669816069595_int_o(Q,aa_Pro2675344531184151096nt_int(produc1557020426977177351nt_int,aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,P2),Q3))) ) ) ) ).

% conjI_realizer
tff(fact_6499_conjI__realizer,axiom,
    ! [P: fun_fu3265955482920998386term_o,P2: fun_in5730379987311621695e_term,Q: fun_Pr3238374608701176162_int_o,Q3: product_prod_int_int] :
      ( aa_fun3020711759848831579term_o(P,P2)
     => ( aa_Pro4592068669816069595_int_o(Q,Q3)
       => ( aa_fun3020711759848831579term_o(P,aa_Pro2551989255418117932e_term(produc4463008262350210037nt_int,aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,P2),Q3)))
          & aa_Pro4592068669816069595_int_o(Q,aa_Pro4437156595432605708nt_int(produc7629796867588368947nt_int,aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,P2),Q3))) ) ) ) ).

% conjI_realizer
tff(fact_6500_conjI__realizer,axiom,
    ! [P: fun_Code_integer_o,P2: code_integer,Q: fun_Code_integer_o,Q3: code_integer] :
      ( aa_Code_integer_o(P,P2)
     => ( aa_Code_integer_o(Q,Q3)
       => ( aa_Code_integer_o(P,aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(P2),Q3)))
          & aa_Code_integer_o(Q,aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(P2),Q3))) ) ) ) ).

% conjI_realizer
tff(fact_6501_conjI__realizer,axiom,
    ! [P: fun_int_o,P2: int,Q: fun_int_o,Q3: int] :
      ( aa_int_o(P,P2)
     => ( aa_int_o(Q,Q3)
       => ( aa_int_o(P,aa_Pro6799258434465214121nt_int(product_fst_int_int,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,P2),Q3)))
          & aa_int_o(Q,aa_Pro6799258434465214121nt_int(product_snd_int_int,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,P2),Q3))) ) ) ) ).

% conjI_realizer
tff(fact_6502_conjI__realizer,axiom,
    ! [P: fun_Code_natural_o,P2: code_natural,Q: fun_Pr8359263388657976682ural_o,Q3: produc7822875418678951345atural] :
      ( aa_Code_natural_o(P,P2)
     => ( aa_Pro6073791466322389475ural_o(Q,Q3)
       => ( aa_Code_natural_o(P,aa_Pro5806155842103967332atural(produc497848011034438852atural,aa_Pro7165575656943818355atural(produc6639722614265839536atural(P2),Q3)))
          & aa_Pro6073791466322389475ural_o(Q,aa_Pro3673693039631929973atural(produc6591912806276919810atural,aa_Pro7165575656943818355atural(produc6639722614265839536atural(P2),Q3))) ) ) ) ).

% conjI_realizer
tff(fact_6503_execute__bind__success,axiom,
    ! [F: heap_T5738788834812785303t_unit,Ha: heap_e7401611519738050253t_unit,G: fun_Pr5924905948197006361rray_a] :
      ( aa_hea7994211679605476167unit_o(heap_T584514906347983379t_unit(F),Ha)
     => ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(heap_T7158140910958840029rray_a(F,G)),Ha) = heap_T531568236820715630rray_a(produc2594868675584459928it_nat(produc8604850587836428116it_nat(aa_opt6779208767223616030it_nat(the_Pr7776125533777466484it_nat,aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(F),Ha)))),aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(aa_Pro755961224256580114rray_a(G,produc4530234641508181270it_nat(aa_opt6779208767223616030it_nat(the_Pr7776125533777466484it_nat,aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(F),Ha))))),produc2838810277069100634it_nat(produc8604850587836428116it_nat(aa_opt6779208767223616030it_nat(the_Pr7776125533777466484it_nat,aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(F),Ha)))))) ) ) ).

% execute_bind_success
tff(fact_6504_execute__bind__success,axiom,
    ! [F: heap_T5738788834812785303t_unit,Ha: heap_e7401611519738050253t_unit,G: fun_Pr292408699144966967t_unit] :
      ( aa_hea7994211679605476167unit_o(heap_T584514906347983379t_unit(F),Ha)
     => ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(heap_T2633723481742716231t_unit(F,G)),Ha) = heap_T3616969660504097270t_unit(produc2594868675584459928it_nat(produc8604850587836428116it_nat(aa_opt6779208767223616030it_nat(the_Pr7776125533777466484it_nat,aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(F),Ha)))),aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(aa_Pro1108561329362217960t_unit(G,produc4530234641508181270it_nat(aa_opt6779208767223616030it_nat(the_Pr7776125533777466484it_nat,aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(F),Ha))))),produc2838810277069100634it_nat(produc8604850587836428116it_nat(aa_opt6779208767223616030it_nat(the_Pr7776125533777466484it_nat,aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(F),Ha)))))) ) ) ).

% execute_bind_success
tff(fact_6505_execute__bind__success,axiom,
    ! [F: heap_T6362127782908069795rray_a,Ha: heap_e7401611519738050253t_unit,G: fun_ar3891948820113774757rray_a] :
      ( aa_hea7994211679605476167unit_o(heap_T6932021131025641745rray_a(F),Ha)
     => ( aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(heap_T2407400398799471159rray_a(F,G)),Ha) = heap_T531568236820715630rray_a(produc2594868675584459928it_nat(produc6991280839920081578it_nat(aa_opt2040853179424174198it_nat(the_Pr5856008525237892824it_nat,aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(F),Ha)))),aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(aa_arr1142863274018860686rray_a(G,produc491454361838572648it_nat(aa_opt2040853179424174198it_nat(the_Pr5856008525237892824it_nat,aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(F),Ha))))),produc2838810277069100634it_nat(produc6991280839920081578it_nat(aa_opt2040853179424174198it_nat(the_Pr5856008525237892824it_nat,aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(F),Ha)))))) ) ) ).

% execute_bind_success
tff(fact_6506_execute__bind__success,axiom,
    ! [F: heap_T6362127782908069795rray_a,Ha: heap_e7401611519738050253t_unit,G: fun_ar1074044450438384043t_unit] :
      ( aa_hea7994211679605476167unit_o(heap_T6932021131025641745rray_a(F),Ha)
     => ( aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(heap_T7324619625323989613t_unit(F,G)),Ha) = heap_T3616969660504097270t_unit(produc2594868675584459928it_nat(produc6991280839920081578it_nat(aa_opt2040853179424174198it_nat(the_Pr5856008525237892824it_nat,aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(F),Ha)))),aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(aa_arr7999650297717212780t_unit(G,produc491454361838572648it_nat(aa_opt2040853179424174198it_nat(the_Pr5856008525237892824it_nat,aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(F),Ha))))),produc2838810277069100634it_nat(produc6991280839920081578it_nat(aa_opt2040853179424174198it_nat(the_Pr5856008525237892824it_nat,aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(F),Ha)))))) ) ) ).

% execute_bind_success
tff(fact_6507_sndI,axiom,
    ! [X2: produc2453742332425399446nteger,Y: fun_Pr5098669352780829690e_term,Z: produc8923325533196201883nteger] :
      ( ( X2 = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,Y),Z) )
     => ( aa_Pro4625778721341478855nteger(produc6589491691745714842nteger,X2) = Z ) ) ).

% sndI
tff(fact_6508_sndI,axiom,
    ! [X2: produc8799533983703829792et_nat,Y: fun_Pr6460944699146269935_nat_o,Z: produc3658429121746597890et_nat] :
      ( ( X2 = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,Y),Z) )
     => ( aa_Pro5541488491759012064et_nat(produc4960056325182568940et_nat,X2) = Z ) ) ).

% sndI
tff(fact_6509_sndI,axiom,
    ! [X2: produc3112576180687729086et_nat,Y: fun_Pr6460944699146269935_nat_o,Z: produc8799533983703829792et_nat] :
      ( ( X2 = aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,Y),Z) )
     => ( aa_Pro7798056222271281692et_nat(produc9081944055658670602et_nat,X2) = Z ) ) ).

% sndI
tff(fact_6510_sndI,axiom,
    ! [X2: produc3043004577601930755nt_int,Y: fun_Pr7763680713840462443e_term,Z: product_prod_int_int] :
      ( ( X2 = aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,Y),Z) )
     => ( aa_Pro2675344531184151096nt_int(produc1557020426977177351nt_int,X2) = Z ) ) ).

% sndI
tff(fact_6511_sndI,axiom,
    ! [X2: produc4788131091073775919nt_int,Y: fun_in5730379987311621695e_term,Z: product_prod_int_int] :
      ( ( X2 = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,Y),Z) )
     => ( aa_Pro4437156595432605708nt_int(produc7629796867588368947nt_int,X2) = Z ) ) ).

% sndI
tff(fact_6512_sndI,axiom,
    ! [X2: produc8923325533196201883nteger,Y: code_integer,Z: code_integer] :
      ( ( X2 = aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(Y),Z) )
     => ( aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,X2) = Z ) ) ).

% sndI
tff(fact_6513_sndI,axiom,
    ! [X2: product_prod_int_int,Y: int,Z: int] :
      ( ( X2 = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Y),Z) )
     => ( aa_Pro6799258434465214121nt_int(product_snd_int_int,X2) = Z ) ) ).

% sndI
tff(fact_6514_sndI,axiom,
    ! [X2: produc5835291356934675326atural,Y: code_natural,Z: produc7822875418678951345atural] :
      ( ( X2 = aa_Pro7165575656943818355atural(produc6639722614265839536atural(Y),Z) )
     => ( aa_Pro3673693039631929973atural(produc6591912806276919810atural,X2) = Z ) ) ).

% sndI
tff(fact_6515_sndE,axiom,
    ! [X2: produc2453742332425399446nteger,A: fun_Pr5098669352780829690e_term,B: produc8923325533196201883nteger,P: fun_Pr7211993375558241536eger_o] :
      ( ( X2 = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A),B) )
     => ( aa_Pro4926521453222654329eger_o(P,aa_Pro4625778721341478855nteger(produc6589491691745714842nteger,X2))
       => aa_Pro4926521453222654329eger_o(P,B) ) ) ).

% sndE
tff(fact_6516_sndE,axiom,
    ! [X2: produc8799533983703829792et_nat,A: fun_Pr6460944699146269935_nat_o,B: produc3658429121746597890et_nat,P: fun_Pr6460944699146269935_nat_o] :
      ( ( X2 = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A),B) )
     => ( aa_Pro653082453696054616_nat_o(P,aa_Pro5541488491759012064et_nat(produc4960056325182568940et_nat,X2))
       => aa_Pro653082453696054616_nat_o(P,B) ) ) ).

% sndE
tff(fact_6517_sndE,axiom,
    ! [X2: produc3112576180687729086et_nat,A: fun_Pr6460944699146269935_nat_o,B: produc8799533983703829792et_nat,P: fun_Pr2620521676128474833_nat_o] :
      ( ( X2 = aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A),B) )
     => ( aa_Pro5643009357358181178_nat_o(P,aa_Pro7798056222271281692et_nat(produc9081944055658670602et_nat,X2))
       => aa_Pro5643009357358181178_nat_o(P,B) ) ) ).

% sndE
tff(fact_6518_sndE,axiom,
    ! [X2: produc3043004577601930755nt_int,A: fun_Pr7763680713840462443e_term,B: product_prod_int_int,P: fun_Pr3238374608701176162_int_o] :
      ( ( X2 = aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,A),B) )
     => ( aa_Pro4592068669816069595_int_o(P,aa_Pro2675344531184151096nt_int(produc1557020426977177351nt_int,X2))
       => aa_Pro4592068669816069595_int_o(P,B) ) ) ).

% sndE
tff(fact_6519_sndE,axiom,
    ! [X2: produc4788131091073775919nt_int,A: fun_in5730379987311621695e_term,B: product_prod_int_int,P: fun_Pr3238374608701176162_int_o] :
      ( ( X2 = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A),B) )
     => ( aa_Pro4592068669816069595_int_o(P,aa_Pro4437156595432605708nt_int(produc7629796867588368947nt_int,X2))
       => aa_Pro4592068669816069595_int_o(P,B) ) ) ).

% sndE
tff(fact_6520_sndE,axiom,
    ! [X2: produc8923325533196201883nteger,A: code_integer,B: code_integer,P: fun_Code_integer_o] :
      ( ( X2 = aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(A),B) )
     => ( aa_Code_integer_o(P,aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,X2))
       => aa_Code_integer_o(P,B) ) ) ).

% sndE
tff(fact_6521_sndE,axiom,
    ! [X2: product_prod_int_int,A: int,B: int,P: fun_int_o] :
      ( ( X2 = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A),B) )
     => ( aa_int_o(P,aa_Pro6799258434465214121nt_int(product_snd_int_int,X2))
       => aa_int_o(P,B) ) ) ).

% sndE
tff(fact_6522_sndE,axiom,
    ! [X2: produc5835291356934675326atural,A: code_natural,B: produc7822875418678951345atural,P: fun_Pr8359263388657976682ural_o] :
      ( ( X2 = aa_Pro7165575656943818355atural(produc6639722614265839536atural(A),B) )
     => ( aa_Pro6073791466322389475ural_o(P,aa_Pro3673693039631929973atural(produc6591912806276919810atural,X2))
       => aa_Pro6073791466322389475ural_o(P,B) ) ) ).

% sndE
tff(fact_6523_snd__eqD,axiom,
    ! [X2: fun_Pr5098669352780829690e_term,Y: produc8923325533196201883nteger,A: produc8923325533196201883nteger] :
      ( ( aa_Pro4625778721341478855nteger(produc6589491691745714842nteger,aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X2),Y)) = A )
     => ( Y = A ) ) ).

% snd_eqD
tff(fact_6524_snd__eqD,axiom,
    ! [X2: fun_Pr6460944699146269935_nat_o,Y: produc3658429121746597890et_nat,A: produc3658429121746597890et_nat] :
      ( ( aa_Pro5541488491759012064et_nat(produc4960056325182568940et_nat,aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X2),Y)) = A )
     => ( Y = A ) ) ).

% snd_eqD
tff(fact_6525_snd__eqD,axiom,
    ! [X2: fun_Pr6460944699146269935_nat_o,Y: produc8799533983703829792et_nat,A: produc8799533983703829792et_nat] :
      ( ( aa_Pro7798056222271281692et_nat(produc9081944055658670602et_nat,aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X2),Y)) = A )
     => ( Y = A ) ) ).

% snd_eqD
tff(fact_6526_snd__eqD,axiom,
    ! [X2: fun_Pr7763680713840462443e_term,Y: product_prod_int_int,A: product_prod_int_int] :
      ( ( aa_Pro2675344531184151096nt_int(produc1557020426977177351nt_int,aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X2),Y)) = A )
     => ( Y = A ) ) ).

% snd_eqD
tff(fact_6527_snd__eqD,axiom,
    ! [X2: fun_in5730379987311621695e_term,Y: product_prod_int_int,A: product_prod_int_int] :
      ( ( aa_Pro4437156595432605708nt_int(produc7629796867588368947nt_int,aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X2),Y)) = A )
     => ( Y = A ) ) ).

% snd_eqD
tff(fact_6528_snd__eqD,axiom,
    ! [X2: code_integer,Y: code_integer,A: code_integer] :
      ( ( aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(X2),Y)) = A )
     => ( Y = A ) ) ).

% snd_eqD
tff(fact_6529_snd__eqD,axiom,
    ! [X2: int,Y: int,A: int] :
      ( ( aa_Pro6799258434465214121nt_int(product_snd_int_int,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X2),Y)) = A )
     => ( Y = A ) ) ).

% snd_eqD
tff(fact_6530_snd__eqD,axiom,
    ! [X2: code_natural,Y: produc7822875418678951345atural,A: produc7822875418678951345atural] :
      ( ( aa_Pro3673693039631929973atural(produc6591912806276919810atural,aa_Pro7165575656943818355atural(produc6639722614265839536atural(X2),Y)) = A )
     => ( Y = A ) ) ).

% snd_eqD
tff(fact_6531_snd__conv,axiom,
    ! [X1: fun_Pr5098669352780829690e_term,X22: produc8923325533196201883nteger] : aa_Pro4625778721341478855nteger(produc6589491691745714842nteger,aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X1),X22)) = X22 ).

% snd_conv
tff(fact_6532_snd__conv,axiom,
    ! [X1: fun_Pr6460944699146269935_nat_o,X22: produc3658429121746597890et_nat] : aa_Pro5541488491759012064et_nat(produc4960056325182568940et_nat,aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X1),X22)) = X22 ).

% snd_conv
tff(fact_6533_snd__conv,axiom,
    ! [X1: fun_Pr6460944699146269935_nat_o,X22: produc8799533983703829792et_nat] : aa_Pro7798056222271281692et_nat(produc9081944055658670602et_nat,aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X1),X22)) = X22 ).

% snd_conv
tff(fact_6534_snd__conv,axiom,
    ! [X1: fun_Pr7763680713840462443e_term,X22: product_prod_int_int] : aa_Pro2675344531184151096nt_int(produc1557020426977177351nt_int,aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X1),X22)) = X22 ).

% snd_conv
tff(fact_6535_snd__conv,axiom,
    ! [X1: fun_in5730379987311621695e_term,X22: product_prod_int_int] : aa_Pro4437156595432605708nt_int(produc7629796867588368947nt_int,aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X1),X22)) = X22 ).

% snd_conv
tff(fact_6536_snd__conv,axiom,
    ! [X1: code_integer,X22: code_integer] : aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(X1),X22)) = X22 ).

% snd_conv
tff(fact_6537_snd__conv,axiom,
    ! [X1: int,X22: int] : aa_Pro6799258434465214121nt_int(product_snd_int_int,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X1),X22)) = X22 ).

% snd_conv
tff(fact_6538_snd__conv,axiom,
    ! [X1: code_natural,X22: produc7822875418678951345atural] : aa_Pro3673693039631929973atural(produc6591912806276919810atural,aa_Pro7165575656943818355atural(produc6639722614265839536atural(X1),X22)) = X22 ).

% snd_conv
tff(fact_6539_Some__Inf,axiom,
    ! [A2: set_set_nat] : aa_set6119337032432945050et_nat(some_set_nat,comple7806235888213564991et_nat(A2)) = comple3446467376476514063et_nat(image_838307146230912995et_nat(some_set_nat,A2)) ).

% Some_Inf
tff(fact_6540_Some__Inf,axiom,
    ! [A2: set_Product_unit] : aa_Pro7616171890175246658t_unit(some_Product_unit,comple2584293577114468500t_unit(A2)) = comple5564859526659248602t_unit(image_7094380055901048587t_unit(some_Product_unit,A2)) ).

% Some_Inf
tff(fact_6541_fstI,axiom,
    ! [X2: produc2453742332425399446nteger,Y: fun_Pr5098669352780829690e_term,Z: produc8923325533196201883nteger] :
      ( ( X2 = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,Y),Z) )
     => ( aa_Pro4276937008533432526e_term(produc2481150572478215260nteger,X2) = Y ) ) ).

% fstI
tff(fact_6542_fstI,axiom,
    ! [X2: produc8799533983703829792et_nat,Y: fun_Pr6460944699146269935_nat_o,Z: produc3658429121746597890et_nat] :
      ( ( X2 = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,Y),Z) )
     => ( aa_Pro8262445894397805713_nat_o(produc5325900173150335662et_nat,X2) = Y ) ) ).

% fstI
tff(fact_6543_fstI,axiom,
    ! [X2: produc3112576180687729086et_nat,Y: fun_Pr6460944699146269935_nat_o,Z: produc8799533983703829792et_nat] :
      ( ( X2 = aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,Y),Z) )
     => ( aa_Pro2837773213478468339_nat_o(produc4078497350495916492et_nat,X2) = Y ) ) ).

% fstI
tff(fact_6544_fstI,axiom,
    ! [X2: produc3043004577601930755nt_int,Y: fun_Pr7763680713840462443e_term,Z: product_prod_int_int] :
      ( ( X2 = aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,Y),Z) )
     => ( aa_Pro4010435699744810540e_term(produc3130796691802200265nt_int,X2) = Y ) ) ).

% fstI
tff(fact_6545_fstI,axiom,
    ! [X2: produc4788131091073775919nt_int,Y: fun_in5730379987311621695e_term,Z: product_prod_int_int] :
      ( ( X2 = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,Y),Z) )
     => ( aa_Pro2551989255418117932e_term(produc4463008262350210037nt_int,X2) = Y ) ) ).

% fstI
tff(fact_6546_fstI,axiom,
    ! [X2: produc8923325533196201883nteger,Y: code_integer,Z: code_integer] :
      ( ( X2 = aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(Y),Z) )
     => ( aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,X2) = Y ) ) ).

% fstI
tff(fact_6547_fstI,axiom,
    ! [X2: product_prod_int_int,Y: int,Z: int] :
      ( ( X2 = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Y),Z) )
     => ( aa_Pro6799258434465214121nt_int(product_fst_int_int,X2) = Y ) ) ).

% fstI
tff(fact_6548_fstE,axiom,
    ! [X2: produc2453742332425399446nteger,A: fun_Pr5098669352780829690e_term,B: produc8923325533196201883nteger,P: fun_fu4736795817735658359term_o] :
      ( ( X2 = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A),B) )
     => ( aa_fun7993445754732355552term_o(P,aa_Pro4276937008533432526e_term(produc2481150572478215260nteger,X2))
       => aa_fun7993445754732355552term_o(P,A) ) ) ).

% fstE
tff(fact_6549_fstE,axiom,
    ! [X2: produc8799533983703829792et_nat,A: fun_Pr6460944699146269935_nat_o,B: produc3658429121746597890et_nat,P: fun_fu5135969500543783852at_o_o] :
      ( ( X2 = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A),B) )
     => ( aa_fun1675921005893230629at_o_o(P,aa_Pro8262445894397805713_nat_o(produc5325900173150335662et_nat,X2))
       => aa_fun1675921005893230629at_o_o(P,A) ) ) ).

% fstE
tff(fact_6550_fstE,axiom,
    ! [X2: produc3112576180687729086et_nat,A: fun_Pr6460944699146269935_nat_o,B: produc8799533983703829792et_nat,P: fun_fu5135969500543783852at_o_o] :
      ( ( X2 = aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A),B) )
     => ( aa_fun1675921005893230629at_o_o(P,aa_Pro2837773213478468339_nat_o(produc4078497350495916492et_nat,X2))
       => aa_fun1675921005893230629at_o_o(P,A) ) ) ).

% fstE
tff(fact_6551_fstE,axiom,
    ! [X2: produc3043004577601930755nt_int,A: fun_Pr7763680713840462443e_term,B: product_prod_int_int,P: fun_fu6378075912484669126term_o] :
      ( ( X2 = aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,A),B) )
     => ( aa_fun7650857933016935215term_o(P,aa_Pro4010435699744810540e_term(produc3130796691802200265nt_int,X2))
       => aa_fun7650857933016935215term_o(P,A) ) ) ).

% fstE
tff(fact_6552_fstE,axiom,
    ! [X2: produc4788131091073775919nt_int,A: fun_in5730379987311621695e_term,B: product_prod_int_int,P: fun_fu3265955482920998386term_o] :
      ( ( X2 = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A),B) )
     => ( aa_fun3020711759848831579term_o(P,aa_Pro2551989255418117932e_term(produc4463008262350210037nt_int,X2))
       => aa_fun3020711759848831579term_o(P,A) ) ) ).

% fstE
tff(fact_6553_fstE,axiom,
    ! [X2: produc8923325533196201883nteger,A: code_integer,B: code_integer,P: fun_Code_integer_o] :
      ( ( X2 = aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(A),B) )
     => ( aa_Code_integer_o(P,aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,X2))
       => aa_Code_integer_o(P,A) ) ) ).

% fstE
tff(fact_6554_fstE,axiom,
    ! [X2: product_prod_int_int,A: int,B: int,P: fun_int_o] :
      ( ( X2 = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A),B) )
     => ( aa_int_o(P,aa_Pro6799258434465214121nt_int(product_fst_int_int,X2))
       => aa_int_o(P,A) ) ) ).

% fstE
tff(fact_6555_fst__eqD,axiom,
    ! [X2: fun_Pr5098669352780829690e_term,Y: produc8923325533196201883nteger,A: fun_Pr5098669352780829690e_term] :
      ( ( aa_Pro4276937008533432526e_term(produc2481150572478215260nteger,aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X2),Y)) = A )
     => ( X2 = A ) ) ).

% fst_eqD
tff(fact_6556_fst__eqD,axiom,
    ! [X2: fun_Pr6460944699146269935_nat_o,Y: produc3658429121746597890et_nat,A: fun_Pr6460944699146269935_nat_o] :
      ( ( aa_Pro8262445894397805713_nat_o(produc5325900173150335662et_nat,aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X2),Y)) = A )
     => ( X2 = A ) ) ).

% fst_eqD
tff(fact_6557_fst__eqD,axiom,
    ! [X2: fun_Pr6460944699146269935_nat_o,Y: produc8799533983703829792et_nat,A: fun_Pr6460944699146269935_nat_o] :
      ( ( aa_Pro2837773213478468339_nat_o(produc4078497350495916492et_nat,aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X2),Y)) = A )
     => ( X2 = A ) ) ).

% fst_eqD
tff(fact_6558_fst__eqD,axiom,
    ! [X2: fun_Pr7763680713840462443e_term,Y: product_prod_int_int,A: fun_Pr7763680713840462443e_term] :
      ( ( aa_Pro4010435699744810540e_term(produc3130796691802200265nt_int,aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X2),Y)) = A )
     => ( X2 = A ) ) ).

% fst_eqD
tff(fact_6559_fst__eqD,axiom,
    ! [X2: fun_in5730379987311621695e_term,Y: product_prod_int_int,A: fun_in5730379987311621695e_term] :
      ( ( aa_Pro2551989255418117932e_term(produc4463008262350210037nt_int,aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X2),Y)) = A )
     => ( X2 = A ) ) ).

% fst_eqD
tff(fact_6560_fst__eqD,axiom,
    ! [X2: code_integer,Y: code_integer,A: code_integer] :
      ( ( aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(X2),Y)) = A )
     => ( X2 = A ) ) ).

% fst_eqD
tff(fact_6561_fst__eqD,axiom,
    ! [X2: int,Y: int,A: int] :
      ( ( aa_Pro6799258434465214121nt_int(product_fst_int_int,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X2),Y)) = A )
     => ( X2 = A ) ) ).

% fst_eqD
tff(fact_6562_fst__conv,axiom,
    ! [X1: fun_Pr5098669352780829690e_term,X22: produc8923325533196201883nteger] : aa_Pro4276937008533432526e_term(produc2481150572478215260nteger,aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X1),X22)) = X1 ).

% fst_conv
tff(fact_6563_fst__conv,axiom,
    ! [X1: fun_Pr6460944699146269935_nat_o,X22: produc3658429121746597890et_nat] : aa_Pro8262445894397805713_nat_o(produc5325900173150335662et_nat,aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X1),X22)) = X1 ).

% fst_conv
tff(fact_6564_fst__conv,axiom,
    ! [X1: fun_Pr6460944699146269935_nat_o,X22: produc8799533983703829792et_nat] : aa_Pro2837773213478468339_nat_o(produc4078497350495916492et_nat,aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X1),X22)) = X1 ).

% fst_conv
tff(fact_6565_fst__conv,axiom,
    ! [X1: fun_Pr7763680713840462443e_term,X22: product_prod_int_int] : aa_Pro4010435699744810540e_term(produc3130796691802200265nt_int,aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X1),X22)) = X1 ).

% fst_conv
tff(fact_6566_fst__conv,axiom,
    ! [X1: fun_in5730379987311621695e_term,X22: product_prod_int_int] : aa_Pro2551989255418117932e_term(produc4463008262350210037nt_int,aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X1),X22)) = X1 ).

% fst_conv
tff(fact_6567_fst__conv,axiom,
    ! [X1: code_integer,X22: code_integer] : aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(X1),X22)) = X1 ).

% fst_conv
tff(fact_6568_fst__conv,axiom,
    ! [X1: int,X22: int] : aa_Pro6799258434465214121nt_int(product_fst_int_int,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X1),X22)) = X1 ).

% fst_conv
tff(fact_6569_snd__fst__flip,axiom,
    ! [Xy: produc592931078481472324e_term] : produc7766732615400916880e_term(Xy) = comp_P9209726524401416377e_term(produc2481150572478215260nteger,produc1137639668546780417nteger(aTP_Lamm_um),Xy) ).

% snd_fst_flip
tff(fact_6570_snd__fst__flip,axiom,
    ! [Xy: produc2739566037923759970_nat_o] : produc5282040756795020774_nat_o(Xy) = comp_P2439397525924500238_nat_o(produc5325900173150335662et_nat,produc1257024432443326049et_nat(aTP_Lamm_un),Xy) ).

% snd_fst_flip
tff(fact_6571_snd__fst__flip,axiom,
    ! [Xy: produc6858501863712832324_nat_o] : produc7941837674541168712_nat_o(Xy) = comp_P8320187926549339218_nat_o(produc4078497350495916492et_nat,produc5430029401411191265et_nat(aTP_Lamm_uo),Xy) ).

% snd_fst_flip
tff(fact_6572_snd__fst__flip,axiom,
    ! [Xy: produc4155239895104388691e_term] : produc7082206506123769631e_term(Xy) = comp_P4791264009094562086e_term(produc3130796691802200265nt_int,produc4605791130040086525nt_int(aTP_Lamm_up),Xy) ).

% snd_fst_flip
tff(fact_6573_snd__fst__flip,axiom,
    ! [Xy: produc5464280974217902119e_term] : produc1448379345012327155e_term(Xy) = comp_P7738237167614049274e_term(produc4463008262350210037nt_int,produc8624921108698535677nt_int(aTP_Lamm_uq),Xy) ).

% snd_fst_flip
tff(fact_6574_snd__fst__flip,axiom,
    ! [Xy: produc8923325533196201883nteger] : aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,Xy) = aa_Pro5245656335456409788nteger(comp_P3428181540658402820nteger(produc8508995932063986495nteger,produc6916734918728496179nteger(aTP_Lamm_ur)),Xy) ).

% snd_fst_flip
tff(fact_6575_snd__fst__flip,axiom,
    ! [Xy: produc5835291356934675326atural] : aa_Pro3673693039631929973atural(produc6591912806276919810atural,Xy) = comp_P3887058762840424708atural(produc4353917038236142998atural,produc6785097126449100389atural(aTP_Lamm_us),Xy) ).

% snd_fst_flip
tff(fact_6576_snd__fst__flip,axiom,
    ! [Xy: product_prod_int_int] : aa_Pro6799258434465214121nt_int(product_snd_int_int,Xy) = aa_Pro6799258434465214121nt_int(comp_P5356232565778667509nt_int(product_fst_int_int,aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,aTP_Lamm_ut)),Xy) ).

% snd_fst_flip
tff(fact_6577_fst__snd__flip,axiom,
    ! [Xy: produc592931078481472324e_term] : produc3658391496133417298e_term(Xy) = comp_P2694320290640119590e_term(produc6589491691745714842nteger,produc1137639668546780417nteger(aTP_Lamm_um),Xy) ).

% fst_snd_flip
tff(fact_6578_fst__snd__flip,axiom,
    ! [Xy: produc2739566037923759970_nat_o] : produc5647884604762787496_nat_o(Xy) = comp_P172845262850278761_nat_o(produc4960056325182568940et_nat,produc1257024432443326049et_nat(aTP_Lamm_un),Xy) ).

% fst_snd_flip
tff(fact_6579_fst__snd__flip,axiom,
    ! [Xy: produc6858501863712832324_nat_o] : produc2938390969378414602_nat_o(Xy) = comp_P2867375532623115527_nat_o(produc9081944055658670602et_nat,produc5430029401411191265et_nat(aTP_Lamm_uo),Xy) ).

% fst_snd_flip
tff(fact_6580_fst__snd__flip,axiom,
    ! [Xy: produc4155239895104388691e_term] : produc8655982770948792545e_term(Xy) = comp_P8873622951661117094e_term(produc1557020426977177351nt_int,produc4605791130040086525nt_int(aTP_Lamm_up),Xy) ).

% fst_snd_flip
tff(fact_6581_fst__snd__flip,axiom,
    ! [Xy: produc5464280974217902119e_term] : produc7504962776628944053e_term(Xy) = comp_P3263061180182656590e_term(produc7629796867588368947nt_int,produc8624921108698535677nt_int(aTP_Lamm_uq),Xy) ).

% fst_snd_flip
tff(fact_6582_fst__snd__flip,axiom,
    ! [Xy: produc8923325533196201883nteger] : aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,Xy) = aa_Pro5245656335456409788nteger(comp_P3428181540658402820nteger(produc6174133586879617921nteger,produc6916734918728496179nteger(aTP_Lamm_ur)),Xy) ).

% fst_snd_flip
tff(fact_6583_fst__snd__flip,axiom,
    ! [Xy: produc3981471736659609608atural] : aa_Pro8943840777669118315atural(produc4353917038236142998atural,Xy) = comp_P5756991293874479000atural(produc6591912806276919810atural,produc1198152457851389869atural(aTP_Lamm_uu),Xy) ).

% fst_snd_flip
tff(fact_6584_fst__snd__flip,axiom,
    ! [Xy: product_prod_int_int] : aa_Pro6799258434465214121nt_int(product_fst_int_int,Xy) = aa_Pro6799258434465214121nt_int(comp_P5356232565778667509nt_int(product_snd_int_int,aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,aTP_Lamm_ut)),Xy) ).

% fst_snd_flip
tff(fact_6585_finite__UNION__then__finite,axiom,
    ! [B4: fun_o_set_int,A2: set_o,A: $o] :
      ( finite_finite_int(comple3221217463730067765et_int(image_o_set_int(B4,A2)))
     => ( member_o((A),A2)
       => finite_finite_int(aa_o_set_int(B4,(A))) ) ) ).

% finite_UNION_then_finite
tff(fact_6586_finite__UNION__then__finite,axiom,
    ! [B4: fun_nat_set_int,A2: set_nat,A: nat] :
      ( finite_finite_int(comple3221217463730067765et_int(image_nat_set_int(B4,A2)))
     => ( member_nat(A,A2)
       => finite_finite_int(aa_nat_set_int(B4,A)) ) ) ).

% finite_UNION_then_finite
tff(fact_6587_finite__UNION__then__finite,axiom,
    ! [B4: fun_int_set_int,A2: set_int,A: int] :
      ( finite_finite_int(comple3221217463730067765et_int(image_int_set_int(B4,A2)))
     => ( member_int(A,A2)
       => finite_finite_int(aa_int_set_int(B4,A)) ) ) ).

% finite_UNION_then_finite
tff(fact_6588_finite__UNION__then__finite,axiom,
    ! [B4: fun_o_5240169576699714110nteger,A2: set_o,A: $o] :
      ( finite6017078050557962740nteger(comple739944243200306918nteger(image_6491638074533506790nteger(B4,A2)))
     => ( member_o((A),A2)
       => finite6017078050557962740nteger(aa_o_s5402425747378369775nteger(B4,(A))) ) ) ).

% finite_UNION_then_finite
tff(fact_6589_finite__UNION__then__finite,axiom,
    ! [B4: fun_na9118744110877893344nteger,A2: set_nat,A: nat] :
      ( finite6017078050557962740nteger(comple739944243200306918nteger(image_2385391725447763818nteger(B4,A2)))
     => ( member_nat(A,A2)
       => finite6017078050557962740nteger(aa_nat8922193080109606305nteger(B4,A)) ) ) ).

% finite_UNION_then_finite
tff(fact_6590_finite__UNION__then__finite,axiom,
    ! [B4: fun_in6808926178784942396nteger,A2: set_int,A: int] :
      ( finite6017078050557962740nteger(comple739944243200306918nteger(image_75573793354812870nteger(B4,A2)))
     => ( member_int(A,A2)
       => finite6017078050557962740nteger(aa_int6612375148016655357nteger(B4,A)) ) ) ).

% finite_UNION_then_finite
tff(fact_6591_finite__UNION__then__finite,axiom,
    ! [B4: fun_o_set_nat,A2: set_o,A: $o] :
      ( finite_finite_nat(comple7399068483239264473et_nat(image_o_set_nat(B4,A2)))
     => ( member_o((A),A2)
       => finite_finite_nat(aa_o_set_nat(B4,(A))) ) ) ).

% finite_UNION_then_finite
tff(fact_6592_finite__UNION__then__finite,axiom,
    ! [B4: fun_nat_set_nat,A2: set_nat,A: nat] :
      ( finite_finite_nat(comple7399068483239264473et_nat(image_nat_set_nat(B4,A2)))
     => ( member_nat(A,A2)
       => finite_finite_nat(aa_nat_set_nat(B4,A)) ) ) ).

% finite_UNION_then_finite
tff(fact_6593_finite__UNION__then__finite,axiom,
    ! [B4: fun_int_set_nat,A2: set_int,A: int] :
      ( finite_finite_nat(comple7399068483239264473et_nat(image_int_set_nat(B4,A2)))
     => ( member_int(A,A2)
       => finite_finite_nat(aa_int_set_nat(B4,A)) ) ) ).

% finite_UNION_then_finite
tff(fact_6594_finite__UNION__then__finite,axiom,
    ! [B4: fun_Pr6548035576365145974et_int,A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat] :
      ( finite_finite_int(comple3221217463730067765et_int(image_5061345727057949854et_int(B4,A2)))
     => ( member8440522571783428010at_nat(A,A2)
       => finite_finite_int(aa_Pro4945722294086666663et_int(B4,A)) ) ) ).

% finite_UNION_then_finite
tff(fact_6595_case__prod__comp,axiom,
    ! [F: fun_Co1561183069634336733nteger,G: fun_Co8499238673658658103nteger,X2: produc3346328345660746739nteger] : produc4281629032016041417nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),G),X2) = aa_Pro4693618923521437820nteger(aa_Cod1978467581589928094nteger(F,aa_Cod1783974652533396728nteger(G,produc1861665112190112313nteger(X2))),produc7955729907432593271nteger(X2)) ).

% case_prod_comp
tff(fact_6596_case__prod__comp,axiom,
    ! [F: fun_fu4800041728187187127nteger,G: fun_Co1981900195452921617nteger,X2: produc3346328345660746739nteger] : produc4281629032016041417nteger(comp_f6739083541385432444nteger(F,G),X2) = aa_Pro4693618923521437820nteger(aa_fun2509385170507305080nteger(F,aa_Cod4161879620478718930nteger(G,produc1861665112190112313nteger(X2))),produc7955729907432593271nteger(X2)) ).

% case_prod_comp
tff(fact_6597_fn__snd__conv,axiom,
    ! [F: fun_nat_nat] : aTP_Lamm_uv(F) = aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,aTP_Lamm_uw(F)) ).

% fn_snd_conv
tff(fact_6598_fn__snd__conv,axiom,
    ! [F: fun_na8713714802964096592at_nat] : aTP_Lamm_ux(F) = aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,aTP_Lamm_uy(F)) ).

% fn_snd_conv
tff(fact_6599_fn__snd__conv,axiom,
    ! [F: fun_na3970208099681795815_nat_o] : aTP_Lamm_uz(F) = aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,aTP_Lamm_va(F)) ).

% fn_snd_conv
tff(fact_6600_fn__snd__conv,axiom,
    ! [F: fun_in4211310926729683942nt_int] : aTP_Lamm_vb(F) = aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,aTP_Lamm_vc(F)) ).

% fn_snd_conv
tff(fact_6601_fn__snd__conv,axiom,
    ! [F: fun_int_int] : aTP_Lamm_vd(F) = aa_fun914008879417524284nt_int(produc8211389475949308722nt_int,aTP_Lamm_ve(F)) ).

% fn_snd_conv
tff(fact_6602_snd__def,axiom,
    ! [Prod: produc8923325533196201883nteger] : aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,Prod) = produc7469247390737344965nteger(aTP_Lamm_vf,Prod) ).

% snd_def
tff(fact_6603_snd__def,axiom,
    ! [Prod: produc5835291356934675326atural] : aa_Pro3673693039631929973atural(produc6591912806276919810atural,Prod) = produc6302656368764539796atural(aTP_Lamm_vg,Prod) ).

% snd_def
tff(fact_6604_snd__def,axiom,
    ! [Prod: product_prod_nat_nat] : aa_Pro4243173770044397973at_nat(product_snd_nat_nat,Prod) = aa_Pro4243173770044397973at_nat(aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,aTP_Lamm_vh),Prod) ).

% snd_def
tff(fact_6605_snd__def,axiom,
    ! [Prod: product_prod_int_int] : aa_Pro6799258434465214121nt_int(product_snd_int_int,Prod) = aa_Pro6799258434465214121nt_int(aa_fun914008879417524284nt_int(produc8211389475949308722nt_int,aTP_Lamm_vi),Prod) ).

% snd_def
tff(fact_6606_fn__fst__conv,axiom,
    ! [F: fun_nat_nat] : aTP_Lamm_vj(F) = aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,aTP_Lamm_vk(F)) ).

% fn_fst_conv
tff(fact_6607_fn__fst__conv,axiom,
    ! [F: fun_na8713714802964096592at_nat] : aTP_Lamm_vl(F) = aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,aTP_Lamm_vm(F)) ).

% fn_fst_conv
tff(fact_6608_fn__fst__conv,axiom,
    ! [F: fun_na3970208099681795815_nat_o] : aTP_Lamm_vn(F) = aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,aTP_Lamm_vo(F)) ).

% fn_fst_conv
tff(fact_6609_fn__fst__conv,axiom,
    ! [F: fun_in4211310926729683942nt_int] : aTP_Lamm_vp(F) = aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,aTP_Lamm_vq(F)) ).

% fn_fst_conv
tff(fact_6610_fn__fst__conv,axiom,
    ! [F: fun_int_int] : aTP_Lamm_vr(F) = aa_fun914008879417524284nt_int(produc8211389475949308722nt_int,aTP_Lamm_vs(F)) ).

% fn_fst_conv
tff(fact_6611_fst__def,axiom,
    ! [Prod: produc8923325533196201883nteger] : aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,Prod) = produc7469247390737344965nteger(aTP_Lamm_cb,Prod) ).

% fst_def
tff(fact_6612_fst__def,axiom,
    ! [Prod: product_prod_nat_nat] : aa_Pro4243173770044397973at_nat(product_fst_nat_nat,Prod) = aa_Pro4243173770044397973at_nat(aa_fun500577536901462844at_nat(produc6842872674320459806at_nat,aTP_Lamm_vt),Prod) ).

% fst_def
tff(fact_6613_fst__def,axiom,
    ! [Prod: product_prod_int_int] : aa_Pro6799258434465214121nt_int(product_fst_int_int,Prod) = aa_Pro6799258434465214121nt_int(aa_fun914008879417524284nt_int(produc8211389475949308722nt_int,aTP_Lamm_vu),Prod) ).

% fst_def
tff(fact_6614_Collect__split__mono__strong,axiom,
    ! [X7: set_Code_integer,A2: set_Pr4811707699266497531nteger,Y7: set_Code_integer,P: fun_Co2081214437782444048eger_o,Q: fun_Co2081214437782444048eger_o] :
      ( ( X7 = image_6316824473203919795nteger(produc8508995932063986495nteger,A2) )
     => ( ( Y7 = image_6316824473203919795nteger(produc6174133586879617921nteger,A2) )
       => ( ! [X3: code_integer] :
              ( member_Code_integer(X3,X7)
             => ! [Xa4: code_integer] :
                  ( member_Code_integer(Xa4,Y7)
                 => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(P,X3),Xa4)
                   => aa_Code_integer_o(aa_Cod326357343816142457eger_o(Q,X3),Xa4) ) ) )
         => ( ord_le3725938330318615451nteger(A2,collec7766031446232907142nteger(produc2066375834425727024eger_o(P)))
           => ord_le3725938330318615451nteger(A2,collec7766031446232907142nteger(produc2066375834425727024eger_o(Q))) ) ) ) ) ).

% Collect_split_mono_strong
tff(fact_6615_Collect__split__mono__strong,axiom,
    ! [X7: set_int,A2: set_Pr958786334691620121nt_int,Y7: set_int,P: fun_int_fun_int_o,Q: fun_int_fun_int_o] :
      ( ( X7 = image_5042161079198086560nt_int(product_fst_int_int,A2) )
     => ( ( Y7 = image_5042161079198086560nt_int(product_snd_int_int,A2) )
       => ( ! [X3: int] :
              ( member_int(X3,X7)
             => ! [Xa4: int] :
                  ( member_int(Xa4,Y7)
                 => ( aa_int_o(aa_int_fun_int_o(P,X3),Xa4)
                   => aa_int_o(aa_int_fun_int_o(Q,X3),Xa4) ) ) )
         => ( ord_le2843351958646193337nt_int(A2,collec213857154873943460nt_int(produc4947309494688390418_int_o(P)))
           => ord_le2843351958646193337nt_int(A2,collec213857154873943460nt_int(produc4947309494688390418_int_o(Q))) ) ) ) ) ).

% Collect_split_mono_strong
tff(fact_6616_Collect__split__mono__strong,axiom,
    ! [X7: set_Code_natural,A2: set_Pr2352657477744078772atural,Y7: set_Pr7564037697178849041atural,P: fun_Co9066792663755620495ural_o,Q: fun_Co9066792663755620495ural_o] :
      ( ( X7 = image_8194678751871465133atural(produc497848011034438852atural,A2) )
     => ( ( Y7 = image_3837677093542026988atural(produc6591912806276919810atural,A2) )
       => ( ! [X3: code_natural] :
              ( member_Code_natural(X3,X7)
             => ! [Xa4: produc7822875418678951345atural] :
                  ( member8280416476884352090atural(Xa4,Y7)
                 => ( aa_Pro6073791466322389475ural_o(aa_Cod1393124287678120144ural_o(P,X3),Xa4)
                   => aa_Pro6073791466322389475ural_o(aa_Cod1393124287678120144ural_o(Q,X3),Xa4) ) ) )
         => ( ord_le2202040463148982292atural(A2,collec1991479681304692691atural(produc7358226366420480123ural_o(P)))
           => ord_le2202040463148982292atural(A2,collec1991479681304692691atural(produc7358226366420480123ural_o(Q))) ) ) ) ) ).

% Collect_split_mono_strong
tff(fact_6617_Some__Sup,axiom,
    ! [A2: set_o] :
      ( ( A2 != bot_bot_set_o )
     => ( aa_o_option_o(some_o,complete_Sup_Sup_o(A2)) = comple4490649148004324043tion_o(image_o_option_o(some_o,A2)) ) ) ).

% Some_Sup
tff(fact_6618_Some__Sup,axiom,
    ! [A2: set_set_nat] :
      ( ( A2 != bot_bot_set_set_nat )
     => ( aa_set6119337032432945050et_nat(some_set_nat,comple7399068483239264473et_nat(A2)) = comple8455683388168444585et_nat(image_838307146230912995et_nat(some_set_nat,A2)) ) ) ).

% Some_Sup
tff(fact_6619_Some__Sup,axiom,
    ! [A2: set_Product_unit] :
      ( ( A2 != bot_bo3957492148770167129t_unit )
     => ( aa_Pro7616171890175246658t_unit(some_Product_unit,comple4687483117567863418t_unit(A2)) = comple7481738165189995200t_unit(image_7094380055901048587t_unit(some_Product_unit,A2)) ) ) ).

% Some_Sup
tff(fact_6620_Inf__option__def,axiom,
    ! [A2: set_option_set_nat] :
      comple3446467376476514063et_nat(A2) = $ite(member8989860449721436141et_nat(none_set_nat,A2),none_set_nat,aa_set6119337032432945050et_nat(some_set_nat,comple7806235888213564991et_nat(these_set_nat(A2)))) ).

% Inf_option_def
tff(fact_6621_Inf__option__def,axiom,
    ! [A2: set_op3165557761946182707t_unit] :
      comple5564859526659248602t_unit(A2) = $ite(member1378114217278917244t_unit(none_Product_unit,A2),none_Product_unit,aa_Pro7616171890175246658t_unit(some_Product_unit,comple2584293577114468500t_unit(these_Product_unit(A2)))) ).

% Inf_option_def
tff(fact_6622_Some__INF,axiom,
    ! [F: fun_nat_set_nat,A2: set_nat] : aa_set6119337032432945050et_nat(some_set_nat,comple7806235888213564991et_nat(image_nat_set_nat(F,A2))) = comple3446467376476514063et_nat(image_1085372205585808685et_nat(aTP_Lamm_vv(F),A2)) ).

% Some_INF
tff(fact_6623_INF__image,axiom,
    ! [G: fun_Code_integer_nat,F: fun_nat_Code_integer,A2: set_nat] : aa_set_nat_nat(complete_Inf_Inf_nat,image_951025933927791156er_nat(G,image_1215581382706833972nteger(F,A2))) = aa_set_nat_nat(complete_Inf_Inf_nat,aa_set_nat_set_nat(image_nat_nat(comp_C4049556595663050210at_nat(G,F)),A2)) ).

% INF_image
tff(fact_6624_INF__image,axiom,
    ! [G: fun_Code_integer_int,F: fun_nat_Code_integer,A2: set_nat] : aa_set_int_int(complete_Inf_Inf_int,image_948535463418740880er_int(G,image_1215581382706833972nteger(F,A2))) = aa_set_int_int(complete_Inf_Inf_int,image_nat_int(comp_C5048910307564104766nt_nat(G,F),A2)) ).

% INF_image
tff(fact_6625_INF__image,axiom,
    ! [G: fun_int_nat,F: fun_nat_int,A2: set_nat] : aa_set_nat_nat(complete_Inf_Inf_nat,image_int_nat(G,image_nat_int(F,A2))) = aa_set_nat_nat(complete_Inf_Inf_nat,aa_set_nat_set_nat(image_nat_nat(comp_int_nat_nat(G,F)),A2)) ).

% INF_image
tff(fact_6626_INF__image,axiom,
    ! [G: fun_nat_nat,F: fun_nat_nat,A2: set_nat] : aa_set_nat_nat(complete_Inf_Inf_nat,aa_set_nat_set_nat(image_nat_nat(G),aa_set_nat_set_nat(image_nat_nat(F),A2))) = aa_set_nat_nat(complete_Inf_Inf_nat,aa_set_nat_set_nat(image_nat_nat(comp_nat_nat_nat(G,F)),A2)) ).

% INF_image
tff(fact_6627_INF__image,axiom,
    ! [G: fun_nat_int,F: fun_int_nat,A2: set_int] : aa_set_int_int(complete_Inf_Inf_int,image_nat_int(G,image_int_nat(F,A2))) = aa_set_int_int(complete_Inf_Inf_int,aa_set_int_set_int(image_int_int(comp_nat_int_int(G,F)),A2)) ).

% INF_image
tff(fact_6628_INF__image,axiom,
    ! [G: fun_nat_int,F: fun_nat_nat,A2: set_nat] : aa_set_int_int(complete_Inf_Inf_int,image_nat_int(G,aa_set_nat_set_nat(image_nat_nat(F),A2))) = aa_set_int_int(complete_Inf_Inf_int,image_nat_int(comp_nat_int_nat(G,F),A2)) ).

% INF_image
tff(fact_6629_INF__image,axiom,
    ! [G: fun_int_int,F: fun_nat_int,A2: set_nat] : aa_set_int_int(complete_Inf_Inf_int,aa_set_int_set_int(image_int_int(G),image_nat_int(F,A2))) = aa_set_int_int(complete_Inf_Inf_int,image_nat_int(comp_int_int_nat(G,F),A2)) ).

% INF_image
tff(fact_6630_INF__image,axiom,
    ! [G: fun_int_int,F: fun_int_int,A2: set_int] : aa_set_int_int(complete_Inf_Inf_int,aa_set_int_set_int(image_int_int(G),aa_set_int_set_int(image_int_int(F),A2))) = aa_set_int_int(complete_Inf_Inf_int,aa_set_int_set_int(image_int_int(aa_fun6280345759651049192nt_int(comp_int_int_int(G),F)),A2)) ).

% INF_image
tff(fact_6631_INF__image,axiom,
    ! [G: fun_Co1365676809456677961t_unit,F: fun_nat_Code_integer,A2: set_nat] : comple2584293577114468500t_unit(image_7182656606676592809t_unit(G,image_1215581382706833972nteger(F,A2))) = comple2584293577114468500t_unit(image_8730104196221521654t_unit(comp_C8086623346886033437it_nat(G,F),A2)) ).

% INF_image
tff(fact_6632_INF__image,axiom,
    ! [G: fun_nat_Product_unit,F: fun_nat_nat,A2: set_nat] : comple2584293577114468500t_unit(image_8730104196221521654t_unit(G,aa_set_nat_set_nat(image_nat_nat(F),A2))) = comple2584293577114468500t_unit(image_8730104196221521654t_unit(comp_n9025697279074352746it_nat(G,F),A2)) ).

% INF_image
tff(fact_6633_SUP__image,axiom,
    ! [G: fun_Code_integer_nat,F: fun_nat_Code_integer,A2: set_nat] : aa_set_nat_nat(complete_Sup_Sup_nat,image_951025933927791156er_nat(G,image_1215581382706833972nteger(F,A2))) = aa_set_nat_nat(complete_Sup_Sup_nat,aa_set_nat_set_nat(image_nat_nat(comp_C4049556595663050210at_nat(G,F)),A2)) ).

% SUP_image
tff(fact_6634_SUP__image,axiom,
    ! [G: fun_Code_integer_int,F: fun_nat_Code_integer,A2: set_nat] : aa_set_int_int(complete_Sup_Sup_int,image_948535463418740880er_int(G,image_1215581382706833972nteger(F,A2))) = aa_set_int_int(complete_Sup_Sup_int,image_nat_int(comp_C5048910307564104766nt_nat(G,F),A2)) ).

% SUP_image
tff(fact_6635_SUP__image,axiom,
    ! [G: fun_int_nat,F: fun_nat_int,A2: set_nat] : aa_set_nat_nat(complete_Sup_Sup_nat,image_int_nat(G,image_nat_int(F,A2))) = aa_set_nat_nat(complete_Sup_Sup_nat,aa_set_nat_set_nat(image_nat_nat(comp_int_nat_nat(G,F)),A2)) ).

% SUP_image
tff(fact_6636_SUP__image,axiom,
    ! [G: fun_nat_nat,F: fun_nat_nat,A2: set_nat] : aa_set_nat_nat(complete_Sup_Sup_nat,aa_set_nat_set_nat(image_nat_nat(G),aa_set_nat_set_nat(image_nat_nat(F),A2))) = aa_set_nat_nat(complete_Sup_Sup_nat,aa_set_nat_set_nat(image_nat_nat(comp_nat_nat_nat(G,F)),A2)) ).

% SUP_image
tff(fact_6637_SUP__image,axiom,
    ! [G: fun_nat_int,F: fun_int_nat,A2: set_int] : aa_set_int_int(complete_Sup_Sup_int,image_nat_int(G,image_int_nat(F,A2))) = aa_set_int_int(complete_Sup_Sup_int,aa_set_int_set_int(image_int_int(comp_nat_int_int(G,F)),A2)) ).

% SUP_image
tff(fact_6638_SUP__image,axiom,
    ! [G: fun_nat_int,F: fun_nat_nat,A2: set_nat] : aa_set_int_int(complete_Sup_Sup_int,image_nat_int(G,aa_set_nat_set_nat(image_nat_nat(F),A2))) = aa_set_int_int(complete_Sup_Sup_int,image_nat_int(comp_nat_int_nat(G,F),A2)) ).

% SUP_image
tff(fact_6639_SUP__image,axiom,
    ! [G: fun_int_int,F: fun_nat_int,A2: set_nat] : aa_set_int_int(complete_Sup_Sup_int,aa_set_int_set_int(image_int_int(G),image_nat_int(F,A2))) = aa_set_int_int(complete_Sup_Sup_int,image_nat_int(comp_int_int_nat(G,F),A2)) ).

% SUP_image
tff(fact_6640_SUP__image,axiom,
    ! [G: fun_int_int,F: fun_int_int,A2: set_int] : aa_set_int_int(complete_Sup_Sup_int,aa_set_int_set_int(image_int_int(G),aa_set_int_set_int(image_int_int(F),A2))) = aa_set_int_int(complete_Sup_Sup_int,aa_set_int_set_int(image_int_int(aa_fun6280345759651049192nt_int(comp_int_int_int(G),F)),A2)) ).

% SUP_image
tff(fact_6641_SUP__image,axiom,
    ! [G: fun_Co1365676809456677961t_unit,F: fun_nat_Code_integer,A2: set_nat] : comple4687483117567863418t_unit(image_7182656606676592809t_unit(G,image_1215581382706833972nteger(F,A2))) = comple4687483117567863418t_unit(image_8730104196221521654t_unit(comp_C8086623346886033437it_nat(G,F),A2)) ).

% SUP_image
tff(fact_6642_SUP__image,axiom,
    ! [G: fun_nat_Product_unit,F: fun_nat_nat,A2: set_nat] : comple4687483117567863418t_unit(image_8730104196221521654t_unit(G,aa_set_nat_set_nat(image_nat_nat(F),A2))) = comple4687483117567863418t_unit(image_8730104196221521654t_unit(comp_n9025697279074352746it_nat(G,F),A2)) ).

% SUP_image
tff(fact_6643_in__snd__imageE,axiom,
    ! [Y: set_Pr1261947904930325089at_nat,S2: set_Pr4329608150637261639at_nat] :
      ( member2643936169264416010at_nat(Y,image_7979982168039674559at_nat(produc2937545259423399429at_nat,S2))
     => ~ ! [X3: set_Pr1261947904930325089at_nat] : ~ member8757157785044589968at_nat(produc2922128104949294807at_nat(X3,Y),S2) ) ).

% in_snd_imageE
tff(fact_6644_in__snd__imageE,axiom,
    ! [Y: nat,S2: set_Pr1261947904930325089at_nat] :
      ( member_nat(Y,image_2486076414777270412at_nat(product_snd_nat_nat,S2))
     => ~ ! [X3: nat] : ~ member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),Y),S2) ) ).

% in_snd_imageE
tff(fact_6645_in__snd__imageE,axiom,
    ! [Y: produc8923325533196201883nteger,S2: set_Pr3486312109254157132nteger] :
      ( member157494554546826820nteger(Y,image_2271979006234848446nteger(produc6589491691745714842nteger,S2))
     => ~ ! [X3: fun_Pr5098669352780829690e_term] : ~ member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X3),Y),S2) ) ).

% in_snd_imageE
tff(fact_6646_in__snd__imageE,axiom,
    ! [Y: produc3658429121746597890et_nat,S2: set_Pr1312406793078187350et_nat] :
      ( member6260224972018164377et_nat(Y,image_5643293374885392937et_nat(produc4960056325182568940et_nat,S2))
     => ~ ! [X3: fun_Pr6460944699146269935_nat_o] : ~ member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X3),Y),S2) ) ).

% in_snd_imageE
tff(fact_6647_in__snd__imageE,axiom,
    ! [Y: produc8799533983703829792et_nat,S2: set_Pr4040394263813967220et_nat] :
      ( member4513763875858039863et_nat(Y,image_1425188809386248805et_nat(produc9081944055658670602et_nat,S2))
     => ~ ! [X3: fun_Pr6460944699146269935_nat_o] : ~ member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X3),Y),S2) ) ).

% in_snd_imageE
tff(fact_6648_in__snd__imageE,axiom,
    ! [Y: product_prod_int_int,S2: set_Pr6700895561065273913nt_int] :
      ( member5262025264175285858nt_int(Y,image_5003770246312495919nt_int(produc1557020426977177351nt_int,S2))
     => ~ ! [X3: fun_Pr7763680713840462443e_term] : ~ member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X3),Y),S2) ) ).

% in_snd_imageE
tff(fact_6649_in__snd__imageE,axiom,
    ! [Y: product_prod_int_int,S2: set_Pr4166680992137330533nt_int] :
      ( member5262025264175285858nt_int(Y,image_5733965904763621635nt_int(produc7629796867588368947nt_int,S2))
     => ~ ! [X3: fun_in5730379987311621695e_term] : ~ member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X3),Y),S2) ) ).

% in_snd_imageE
tff(fact_6650_in__snd__imageE,axiom,
    ! [Y: code_integer,S2: set_Pr4811707699266497531nteger] :
      ( member_Code_integer(Y,image_6316824473203919795nteger(produc6174133586879617921nteger,S2))
     => ~ ! [X3: code_integer] : ~ member157494554546826820nteger(aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(X3),Y),S2) ) ).

% in_snd_imageE
tff(fact_6651_in__snd__imageE,axiom,
    ! [Y: int,S2: set_Pr958786334691620121nt_int] :
      ( member_int(Y,image_5042161079198086560nt_int(product_snd_int_int,S2))
     => ~ ! [X3: int] : ~ member5262025264175285858nt_int(aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X3),Y),S2) ) ).

% in_snd_imageE
tff(fact_6652_in__snd__imageE,axiom,
    ! [Y: produc7822875418678951345atural,S2: set_Pr2352657477744078772atural] :
      ( member8280416476884352090atural(Y,image_3837677093542026988atural(produc6591912806276919810atural,S2))
     => ~ ! [X3: code_natural] : ~ member2108296798382401941atural(aa_Pro7165575656943818355atural(produc6639722614265839536atural(X3),Y),S2) ) ).

% in_snd_imageE
tff(fact_6653_in__fst__imageE,axiom,
    ! [X2: set_Pr1261947904930325089at_nat,S2: set_Pr4329608150637261639at_nat] :
      ( member2643936169264416010at_nat(X2,image_7979982168039674559at_nat(produc6011863565407846595at_nat,S2))
     => ~ ! [Y4: set_Pr1261947904930325089at_nat] : ~ member8757157785044589968at_nat(produc2922128104949294807at_nat(X2,Y4),S2) ) ).

% in_fst_imageE
tff(fact_6654_in__fst__imageE,axiom,
    ! [X2: nat,S2: set_Pr1261947904930325089at_nat] :
      ( member_nat(X2,image_2486076414777270412at_nat(product_fst_nat_nat,S2))
     => ~ ! [Y4: nat] : ~ member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X2),Y4),S2) ) ).

% in_fst_imageE
tff(fact_6655_in__fst__imageE,axiom,
    ! [X2: fun_Pr5098669352780829690e_term,S2: set_Pr3486312109254157132nteger] :
      ( member8464590939221061905e_term(X2,image_5882744770105888791e_term(produc2481150572478215260nteger,S2))
     => ~ ! [Y4: produc8923325533196201883nteger] : ~ member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X2),Y4),S2) ) ).

% in_fst_imageE
tff(fact_6656_in__fst__imageE,axiom,
    ! [X2: fun_Pr6460944699146269935_nat_o,S2: set_Pr1312406793078187350et_nat] :
      ( member7544390268018397336_nat_o(X2,image_4444162529858428168_nat_o(produc5325900173150335662et_nat,S2))
     => ~ ! [Y4: produc3658429121746597890et_nat] : ~ member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X2),Y4),S2) ) ).

% in_fst_imageE
tff(fact_6657_in__fst__imageE,axiom,
    ! [X2: fun_Pr6460944699146269935_nat_o,S2: set_Pr4040394263813967220et_nat] :
      ( member7544390268018397336_nat_o(X2,image_8400968272122294250_nat_o(produc4078497350495916492et_nat,S2))
     => ~ ! [Y4: produc8799533983703829792et_nat] : ~ member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X2),Y4),S2) ) ).

% in_fst_imageE
tff(fact_6658_in__fst__imageE,axiom,
    ! [X2: fun_Pr7763680713840462443e_term,S2: set_Pr6700895561065273913nt_int] :
      ( member1495369047980753794e_term(X2,image_143812984558558581e_term(produc3130796691802200265nt_int,S2))
     => ~ ! [Y4: product_prod_int_int] : ~ member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X2),Y4),S2) ) ).

% in_fst_imageE
tff(fact_6659_in__fst__imageE,axiom,
    ! [X2: fun_in5730379987311621695e_term,S2: set_Pr4166680992137330533nt_int] :
      ( member4871225538671630166e_term(X2,image_7516633138899002997e_term(produc4463008262350210037nt_int,S2))
     => ~ ! [Y4: product_prod_int_int] : ~ member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X2),Y4),S2) ) ).

% in_fst_imageE
tff(fact_6660_in__fst__imageE,axiom,
    ! [X2: code_integer,S2: set_Pr4811707699266497531nteger] :
      ( member_Code_integer(X2,image_6316824473203919795nteger(produc8508995932063986495nteger,S2))
     => ~ ! [Y4: code_integer] : ~ member157494554546826820nteger(aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(X2),Y4),S2) ) ).

% in_fst_imageE
tff(fact_6661_in__fst__imageE,axiom,
    ! [X2: int,S2: set_Pr958786334691620121nt_int] :
      ( member_int(X2,image_5042161079198086560nt_int(product_fst_int_int,S2))
     => ~ ! [Y4: int] : ~ member5262025264175285858nt_int(aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X2),Y4),S2) ) ).

% in_fst_imageE
tff(fact_6662_Some__SUP,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,F: fun_Pr6764980218223570944et_nat] :
      ( ( A2 != bot_bo228742789529271731at_nat )
     => ( aa_set6119337032432945050et_nat(some_set_nat,comple7399068483239264473et_nat(image_3160451284896210088et_nat(F,A2))) = comple8455683388168444585et_nat(image_934083234596377592et_nat(aTP_Lamm_vw(F),A2)) ) ) ).

% Some_SUP
tff(fact_6663_Some__SUP,axiom,
    ! [A2: set_Pr1261947904930325089at_nat,F: fun_Pr9038118721296872730et_nat] :
      ( ( A2 != bot_bo2099793752762293965at_nat )
     => ( aa_set6119337032432945050et_nat(some_set_nat,comple7399068483239264473et_nat(image_15824709712370754et_nat(F,A2))) = comple8455683388168444585et_nat(image_7383884694314771602et_nat(aTP_Lamm_vx(F),A2)) ) ) ).

% Some_SUP
tff(fact_6664_Some__SUP,axiom,
    ! [A2: set_o,F: fun_o_set_nat] :
      ( ( A2 != bot_bot_set_o )
     => ( aa_set6119337032432945050et_nat(some_set_nat,comple7399068483239264473et_nat(image_o_set_nat(F,A2))) = comple8455683388168444585et_nat(image_966425688229763753et_nat(aTP_Lamm_vy(F),A2)) ) ) ).

% Some_SUP
tff(fact_6665_Some__SUP,axiom,
    ! [A2: set_nat,F: fun_nat_set_nat] :
      ( ( A2 != bot_bot_set_nat )
     => ( aa_set6119337032432945050et_nat(some_set_nat,comple7399068483239264473et_nat(image_nat_set_nat(F,A2))) = comple8455683388168444585et_nat(image_1085372205585808685et_nat(aTP_Lamm_vv(F),A2)) ) ) ).

% Some_SUP
tff(fact_6666_Some__SUP,axiom,
    ! [A2: set_int,F: fun_int_set_nat] :
      ( ( A2 != bot_bot_set_int )
     => ( aa_set6119337032432945050et_nat(some_set_nat,comple7399068483239264473et_nat(image_int_set_nat(F,A2))) = comple8455683388168444585et_nat(image_2293489338514188681et_nat(aTP_Lamm_vz(F),A2)) ) ) ).

% Some_SUP
tff(fact_6667_Some__SUP,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,F: fun_Pr8319229360018371625t_unit] :
      ( ( A2 != bot_bo228742789529271731at_nat )
     => ( aa_Pro7616171890175246658t_unit(some_Product_unit,comple4687483117567863418t_unit(image_7082456443403096939t_unit(F,A2))) = comple7481738165189995200t_unit(image_8585598761158579761t_unit(aTP_Lamm_wa(F),A2)) ) ) ).

% Some_SUP
tff(fact_6668_Some__SUP,axiom,
    ! [A2: set_Pr1261947904930325089at_nat,F: fun_Pr2481279687482350479t_unit] :
      ( ( A2 != bot_bo2099793752762293965at_nat )
     => ( aa_Pro7616171890175246658t_unit(some_Product_unit,comple4687483117567863418t_unit(image_6169909464789311569t_unit(F,A2))) = comple7481738165189995200t_unit(image_7548311901266006551t_unit(aTP_Lamm_wb(F),A2)) ) ) ).

% Some_SUP
tff(fact_6669_Some__SUP,axiom,
    ! [A2: set_o,F: fun_o_Product_unit] :
      ( ( A2 != bot_bot_set_o )
     => ( aa_Pro7616171890175246658t_unit(some_Product_unit,comple4687483117567863418t_unit(image_o_Product_unit(F,A2))) = comple7481738165189995200t_unit(image_4415570909310888640t_unit(aTP_Lamm_wc(F),A2)) ) ) ).

% Some_SUP
tff(fact_6670_Some__SUP,axiom,
    ! [A2: set_nat,F: fun_nat_Product_unit] :
      ( ( A2 != bot_bot_set_nat )
     => ( aa_Pro7616171890175246658t_unit(some_Product_unit,comple4687483117567863418t_unit(image_8730104196221521654t_unit(F,A2))) = comple7481738165189995200t_unit(image_1497621718204147004t_unit(aTP_Lamm_wd(F),A2)) ) ) ).

% Some_SUP
tff(fact_6671_Some__SUP,axiom,
    ! [A2: set_int,F: fun_int_Product_unit] :
      ( ( A2 != bot_bot_set_int )
     => ( aa_Pro7616171890175246658t_unit(some_Product_unit,comple4687483117567863418t_unit(image_5846526143423701914t_unit(F,A2))) = comple7481738165189995200t_unit(image_1735198859854722016t_unit(aTP_Lamm_we(F),A2)) ) ) ).

% Some_SUP
tff(fact_6672_finite__range__prod,axiom,
    ! [F: fun_na1476630412504255114at_nat] :
      ( finite_finite_nat(aa_set_nat_set_nat(image_nat_nat(comp_P1955610211387027840at_nat(product_fst_nat_nat,F)),top_top_set_nat))
     => ( finite_finite_nat(aa_set_nat_set_nat(image_nat_nat(comp_P1955610211387027840at_nat(product_snd_nat_nat,F)),top_top_set_nat))
       => finite6177210948735845034at_nat(image_5846123807819985514at_nat(F,top_top_set_nat)) ) ) ).

% finite_range_prod
tff(fact_6673_finite__range__prod,axiom,
    ! [F: fun_na8209919304427304166at_int] :
      ( finite_finite_nat(aa_set_nat_set_nat(image_nat_nat(comp_P7964419862382602716at_nat(product_fst_nat_int,F)),top_top_set_nat))
     => ( finite_finite_int(image_nat_int(comp_P8963773574283657272nt_nat(product_snd_nat_int,F),top_top_set_nat))
       => finite1999359929226648326at_int(image_1668272788310788806at_int(F,top_top_set_nat)) ) ) ).

% finite_range_prod
tff(fact_6674_finite__range__prod,axiom,
    ! [F: fun_na1596024190920976919nteger] :
      ( finite_finite_nat(aa_set_nat_set_nat(image_nat_nat(comp_P9144323761349829517at_nat(produc8897218493789310642nteger,F)),top_top_set_nat))
     => ( finite6017078050557962740nteger(image_1215581382706833972nteger(comp_P5461341465284484122er_nat(produc1781891006948753140nteger,F),top_top_set_nat))
       => finite1154042800025562295nteger(image_8507997478476487799nteger(F,top_top_set_nat)) ) ) ).

% finite_range_prod
tff(fact_6675_finite__range__prod,axiom,
    ! [F: fun_na3663551987197276902nt_nat] :
      ( finite_finite_int(image_nat_int(comp_P645145991195131448nt_nat(product_fst_int_nat,F),top_top_set_nat))
     => ( finite_finite_nat(aa_set_nat_set_nat(image_nat_nat(comp_P8869164316148852700at_nat(product_snd_int_nat,F)),top_top_set_nat))
       => finite7176564660636899590nt_nat(image_6845477519721040070nt_nat(F,top_top_set_nat)) ) ) ).

% finite_range_prod
tff(fact_6676_finite__range__prod,axiom,
    ! [F: fun_na7604833841916551795nteger] :
      ( finite_finite_int(image_nat_int(comp_P59025373045620805nt_nat(produc45500017171379470nteger,F),top_top_set_nat))
     => ( finite6017078050557962740nteger(image_1215581382706833972nteger(comp_P6870028373966156406er_nat(produc2153544567185597776nteger,F),top_top_set_nat))
       => finite1525696360262406931nteger(image_8879651038713332435nteger(F,top_top_set_nat)) ) ) ).

% finite_range_prod
tff(fact_6677_finite__range__prod,axiom,
    ! [F: fun_na8176081009732395159er_nat] :
      ( finite6017078050557962740nteger(image_1215581382706833972nteger(comp_P5700178199414968986er_nat(produc8632663045010267826er_nat,F),top_top_set_nat))
     => ( finite_finite_nat(aa_set_nat_set_nat(image_nat_nat(comp_P1337767177661389325at_nat(produc1517335558169710324er_nat,F)),top_top_set_nat))
       => finite4996374594527322935er_nat(image_3126957236123472631er_nat(F,top_top_set_nat)) ) ) ).

% finite_range_prod
tff(fact_6678_finite__range__prod,axiom,
    ! [F: fun_na5685997864800668403er_int] :
      ( finite6017078050557962740nteger(image_1215581382706833972nteger(comp_P2475326853202991862er_nat(produc8630172574501217550er_int,F),top_top_set_nat))
     => ( finite_finite_int(image_nat_int(comp_P8345930540558018757nt_nat(produc1514845087660660048er_int,F),top_top_set_nat))
       => finite818523575018126227er_int(image_8172478253469051731er_int(F,top_top_set_nat)) ) ) ).

% finite_range_prod
tff(fact_6679_finite__range__prod,axiom,
    ! [F: fun_na3822476419092417572nteger] :
      ( finite6017078050557962740nteger(image_1215581382706833972nteger(comp_P3109732533133679783er_nat(produc8508995932063986495nteger,F),top_top_set_nat))
     => ( finite6017078050557962740nteger(image_1215581382706833972nteger(comp_P3109732533133679783er_nat(produc6174133586879617921nteger,F),top_top_set_nat))
       => finite2154694888287295812nteger(image_4272405876590741764nteger(F,top_top_set_nat)) ) ) ).

% finite_range_prod
tff(fact_6680_finite__range__prod,axiom,
    ! [F: fun_na1173468842265550146nt_int] :
      ( finite_finite_int(image_nat_int(comp_P6653955642190706324nt_nat(product_fst_int_int,F),top_top_set_nat))
     => ( finite_finite_int(image_nat_int(comp_P6653955642190706324nt_nat(product_snd_int_int,F),top_top_set_nat))
       => finite2998713641127702882nt_int(image_2667626500211843362nt_int(F,top_top_set_nat)) ) ) ).

% finite_range_prod
tff(fact_6681_finite__range__prod,axiom,
    ! [F: fun_Pr7036769738611282295at_nat] :
      ( finite_finite_nat(image_875570014554754200it_nat(comp_P2980510830910040157t_unit(product_fst_nat_nat,F),top_to1996260823553986621t_unit))
     => ( finite_finite_nat(image_875570014554754200it_nat(comp_P2980510830910040157t_unit(product_snd_nat_nat,F),top_to1996260823553986621t_unit))
       => finite6177210948735845034at_nat(image_7281959405765017145at_nat(F,top_to1996260823553986621t_unit)) ) ) ).

% finite_range_prod
tff(fact_6682_UN__atMost__UNIV,axiom,
    comple7399068483239264473et_nat(image_nat_set_nat(set_ord_atMost_nat,top_top_set_nat)) = top_top_set_nat ).

% UN_atMost_UNIV
tff(fact_6683_UN__lessThan__UNIV,axiom,
    comple7399068483239264473et_nat(image_nat_set_nat(set_ord_lessThan_nat,top_top_set_nat)) = top_top_set_nat ).

% UN_lessThan_UNIV
tff(fact_6684_Sup__option__def,axiom,
    ! [A2: set_option_set_nat] :
      comple8455683388168444585et_nat(A2) = $ite(
        ( ( A2 = bot_bo5650944848895983264et_nat )
        | ( A2 = insert6281397740311767046et_nat(none_set_nat,bot_bo5650944848895983264et_nat) ) ),
        none_set_nat,
        aa_set6119337032432945050et_nat(some_set_nat,comple7399068483239264473et_nat(these_set_nat(A2))) ) ).

% Sup_option_def
tff(fact_6685_Sup__option__def,axiom,
    ! [A2: set_op3165557761946182707t_unit] :
      comple7481738165189995200t_unit(A2) = $ite(
        ( ( A2 = bot_bo2792743115866486943t_unit )
        | ( A2 = insert2866144167138965411t_unit(none_Product_unit,bot_bo2792743115866486943t_unit) ) ),
        none_Product_unit,
        aa_Pro7616171890175246658t_unit(some_Product_unit,comple4687483117567863418t_unit(these_Product_unit(A2))) ) ).

% Sup_option_def
tff(fact_6686_snd__image__mp,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,B4: set_se7855581050983116737at_nat,X2: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
      ( ord_le2077887516847798113at_nat(image_7979982168039674559at_nat(produc2937545259423399429at_nat,A2),B4)
     => ( member8757157785044589968at_nat(produc2922128104949294807at_nat(X2,Y),A2)
       => member2643936169264416010at_nat(Y,B4) ) ) ).

% snd_image_mp
tff(fact_6687_snd__image__mp,axiom,
    ! [A2: set_Pr3486312109254157132nteger,B4: set_Pr4811707699266497531nteger,X2: fun_Pr5098669352780829690e_term,Y: produc8923325533196201883nteger] :
      ( ord_le3725938330318615451nteger(image_2271979006234848446nteger(produc6589491691745714842nteger,A2),B4)
     => ( member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X2),Y),A2)
       => member157494554546826820nteger(Y,B4) ) ) ).

% snd_image_mp
tff(fact_6688_snd__image__mp,axiom,
    ! [A2: set_Pr1312406793078187350et_nat,B4: set_Pr3948176798113811640et_nat,X2: fun_Pr6460944699146269935_nat_o,Y: produc3658429121746597890et_nat] :
      ( ord_le8090042543978450200et_nat(image_5643293374885392937et_nat(produc4960056325182568940et_nat,A2),B4)
     => ( member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X2),Y),A2)
       => member6260224972018164377et_nat(Y,B4) ) ) ).

% snd_image_mp
tff(fact_6689_snd__image__mp,axiom,
    ! [A2: set_Pr4040394263813967220et_nat,B4: set_Pr1312406793078187350et_nat,X2: fun_Pr6460944699146269935_nat_o,Y: produc8799533983703829792et_nat] :
      ( ord_le3919382008627836342et_nat(image_1425188809386248805et_nat(produc9081944055658670602et_nat,A2),B4)
     => ( member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X2),Y),A2)
       => member4513763875858039863et_nat(Y,B4) ) ) ).

% snd_image_mp
tff(fact_6690_snd__image__mp,axiom,
    ! [A2: set_Pr6700895561065273913nt_int,B4: set_Pr958786334691620121nt_int,X2: fun_Pr7763680713840462443e_term,Y: product_prod_int_int] :
      ( ord_le2843351958646193337nt_int(image_5003770246312495919nt_int(produc1557020426977177351nt_int,A2),B4)
     => ( member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X2),Y),A2)
       => member5262025264175285858nt_int(Y,B4) ) ) ).

% snd_image_mp
tff(fact_6691_snd__image__mp,axiom,
    ! [A2: set_Pr4166680992137330533nt_int,B4: set_Pr958786334691620121nt_int,X2: fun_in5730379987311621695e_term,Y: product_prod_int_int] :
      ( ord_le2843351958646193337nt_int(image_5733965904763621635nt_int(produc7629796867588368947nt_int,A2),B4)
     => ( member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X2),Y),A2)
       => member5262025264175285858nt_int(Y,B4) ) ) ).

% snd_image_mp
tff(fact_6692_snd__image__mp,axiom,
    ! [A2: set_Pr4811707699266497531nteger,B4: set_Code_integer,X2: code_integer,Y: code_integer] :
      ( ord_le7084787975880047091nteger(image_6316824473203919795nteger(produc6174133586879617921nteger,A2),B4)
     => ( member157494554546826820nteger(aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(X2),Y),A2)
       => member_Code_integer(Y,B4) ) ) ).

% snd_image_mp
tff(fact_6693_snd__image__mp,axiom,
    ! [A2: set_Pr958786334691620121nt_int,B4: set_int,X2: int,Y: int] :
      ( ord_less_eq_set_int(image_5042161079198086560nt_int(product_snd_int_int,A2),B4)
     => ( member5262025264175285858nt_int(aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X2),Y),A2)
       => member_int(Y,B4) ) ) ).

% snd_image_mp
tff(fact_6694_snd__image__mp,axiom,
    ! [A2: set_Pr2352657477744078772atural,B4: set_Pr7564037697178849041atural,X2: code_natural,Y: produc7822875418678951345atural] :
      ( ord_le6478268328230966961atural(image_3837677093542026988atural(produc6591912806276919810atural,A2),B4)
     => ( member2108296798382401941atural(aa_Pro7165575656943818355atural(produc6639722614265839536atural(X2),Y),A2)
       => member8280416476884352090atural(Y,B4) ) ) ).

% snd_image_mp
tff(fact_6695_snd__image__mp,axiom,
    ! [A2: set_Pr1261947904930325089at_nat,B4: set_nat,X2: nat,Y: nat] :
      ( aa_set_nat_o(ord_less_eq_set_nat(image_2486076414777270412at_nat(product_snd_nat_nat,A2)),B4)
     => ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X2),Y),A2)
       => member_nat(Y,B4) ) ) ).

% snd_image_mp
tff(fact_6696_fst__image__mp,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,B4: set_se7855581050983116737at_nat,X2: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
      ( ord_le2077887516847798113at_nat(image_7979982168039674559at_nat(produc6011863565407846595at_nat,A2),B4)
     => ( member8757157785044589968at_nat(produc2922128104949294807at_nat(X2,Y),A2)
       => member2643936169264416010at_nat(X2,B4) ) ) ).

% fst_image_mp
tff(fact_6697_fst__image__mp,axiom,
    ! [A2: set_Pr3486312109254157132nteger,B4: set_fu8280898353253485872e_term,X2: fun_Pr5098669352780829690e_term,Y: produc8923325533196201883nteger] :
      ( ord_le8538105397850660240e_term(image_5882744770105888791e_term(produc2481150572478215260nteger,A2),B4)
     => ( member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X2),Y),A2)
       => member8464590939221061905e_term(X2,B4) ) ) ).

% fst_image_mp
tff(fact_6698_fst__image__mp,axiom,
    ! [A2: set_Pr1312406793078187350et_nat,B4: set_fu3555266933746557007_nat_o,X2: fun_Pr6460944699146269935_nat_o,Y: produc3658429121746597890et_nat] :
      ( ord_le5394272759557949423_nat_o(image_4444162529858428168_nat_o(produc5325900173150335662et_nat,A2),B4)
     => ( member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X2),Y),A2)
       => member7544390268018397336_nat_o(X2,B4) ) ) ).

% fst_image_mp
tff(fact_6699_fst__image__mp,axiom,
    ! [A2: set_Pr4040394263813967220et_nat,B4: set_fu3555266933746557007_nat_o,X2: fun_Pr6460944699146269935_nat_o,Y: produc8799533983703829792et_nat] :
      ( ord_le5394272759557949423_nat_o(image_8400968272122294250_nat_o(produc4078497350495916492et_nat,A2),B4)
     => ( member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X2),Y),A2)
       => member7544390268018397336_nat_o(X2,B4) ) ) ).

% fst_image_mp
tff(fact_6700_fst__image__mp,axiom,
    ! [A2: set_Pr6700895561065273913nt_int,B4: set_fu5653557704672872225e_term,X2: fun_Pr7763680713840462443e_term,Y: product_prod_int_int] :
      ( ord_le792320400390739841e_term(image_143812984558558581e_term(produc3130796691802200265nt_int,A2),B4)
     => ( member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X2),Y),A2)
       => member1495369047980753794e_term(X2,B4) ) ) ).

% fst_image_mp
tff(fact_6701_fst__image__mp,axiom,
    ! [A2: set_Pr4166680992137330533nt_int,B4: set_fu3629540756087427317e_term,X2: fun_in5730379987311621695e_term,Y: product_prod_int_int] :
      ( ord_le2047893094613950805e_term(image_7516633138899002997e_term(produc4463008262350210037nt_int,A2),B4)
     => ( member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X2),Y),A2)
       => member4871225538671630166e_term(X2,B4) ) ) ).

% fst_image_mp
tff(fact_6702_fst__image__mp,axiom,
    ! [A2: set_Pr4811707699266497531nteger,B4: set_Code_integer,X2: code_integer,Y: code_integer] :
      ( ord_le7084787975880047091nteger(image_6316824473203919795nteger(produc8508995932063986495nteger,A2),B4)
     => ( member157494554546826820nteger(aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(X2),Y),A2)
       => member_Code_integer(X2,B4) ) ) ).

% fst_image_mp
tff(fact_6703_fst__image__mp,axiom,
    ! [A2: set_Pr958786334691620121nt_int,B4: set_int,X2: int,Y: int] :
      ( ord_less_eq_set_int(image_5042161079198086560nt_int(product_fst_int_int,A2),B4)
     => ( member5262025264175285858nt_int(aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X2),Y),A2)
       => member_int(X2,B4) ) ) ).

% fst_image_mp
tff(fact_6704_fst__image__mp,axiom,
    ! [A2: set_Pr1261947904930325089at_nat,B4: set_nat,X2: nat,Y: nat] :
      ( aa_set_nat_o(ord_less_eq_set_nat(image_2486076414777270412at_nat(product_fst_nat_nat,A2)),B4)
     => ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X2),Y),A2)
       => member_nat(X2,B4) ) ) ).

% fst_image_mp
tff(fact_6705_prod_OUnion__comp,axiom,
    ! [B4: set_set_o,G: fun_o_Code_integer] :
      ( ! [X3: set_o] :
          ( member_set_o(X3,B4)
         => finite_finite_o(X3) )
     => ( ! [A13: set_o] :
            ( member_set_o(A13,B4)
           => ! [A24: set_o] :
                ( member_set_o(A24,B4)
               => ( ( A13 != A24 )
                 => ! [X3: $o] :
                      ( member_o((X3),A13)
                     => ( member_o((X3),A24)
                       => ( aa_o_Code_integer(G,(X3)) = one_one_Code_integer ) ) ) ) ) )
       => ( aa_set3804579329223923353nteger(aa_fun2057504995935393308nteger(groups7694694392188491536nteger,G),comple90263536869209701_set_o(B4)) = aa_set5709627445990591865nteger(comp_f1748852684562694277nteger(groups8987389756002350576nteger,groups7694694392188491536nteger,G),B4) ) ) ) ).

% prod.Union_comp
tff(fact_6706_prod_OUnion__comp,axiom,
    ! [B4: set_set_int,G: fun_int_Code_integer] :
      ( ! [X3: set_int] :
          ( member_set_int(X3,B4)
         => finite_finite_int(X3) )
     => ( ! [A13: set_int] :
            ( member_set_int(A13,B4)
           => ! [A24: set_int] :
                ( member_set_int(A24,B4)
               => ( ( A13 != A24 )
                 => ! [X3: int] :
                      ( member_int(X3,A13)
                     => ( member_int(X3,A24)
                       => ( aa_int_Code_integer(G,X3) = one_one_Code_integer ) ) ) ) ) )
       => ( aa_set6880394903383512189nteger(aa_fun5294558456829105664nteger(groups3827104343326376752nteger,G),comple3221217463730067765et_int(B4)) = aa_set3853921609887811379nteger(comp_f8044896008013558041nteger(groups8770619586034088166nteger,groups3827104343326376752nteger,G),B4) ) ) ) ).

% prod.Union_comp
tff(fact_6707_prod_OUnion__comp,axiom,
    ! [B4: set_set_Code_integer,G: fun_Co8499238673658658103nteger] :
      ( ! [X3: set_Code_integer] :
          ( member1834298987299537450nteger(X3,B4)
         => finite6017078050557962740nteger(X3) )
     => ( ! [A13: set_Code_integer] :
            ( member1834298987299537450nteger(A13,B4)
           => ! [A24: set_Code_integer] :
                ( member1834298987299537450nteger(A24,B4)
               => ( ( A13 != A24 )
                 => ! [X3: code_integer] :
                      ( member_Code_integer(X3,A13)
                     => ( member_Code_integer(X3,A24)
                       => ( aa_Cod1783974652533396728nteger(G,X3) = one_one_Code_integer ) ) ) ) ) )
       => ( aa_set8546232603906849326nteger(aa_fun7145370688314743778nteger(groups3674199335183972705nteger,G),comple739944243200306918nteger(B4)) = aa_set1330082717382260836nteger(comp_f3271019896647404588nteger(groups1474571732273379991nteger,groups3674199335183972705nteger,G),B4) ) ) ) ).

% prod.Union_comp
tff(fact_6708_prod_OUnion__comp,axiom,
    ! [B4: set_set_o,G: fun_o_assn] :
      ( ! [X3: set_o] :
          ( member_set_o(X3,B4)
         => finite_finite_o(X3) )
     => ( ! [A13: set_o] :
            ( member_set_o(A13,B4)
           => ! [A24: set_o] :
                ( member_set_o(A24,B4)
               => ( ( A13 != A24 )
                 => ! [X3: $o] :
                      ( member_o((X3),A13)
                     => ( member_o((X3),A24)
                       => ( aa_o_assn(G,(X3)) = one_one_assn ) ) ) ) ) )
       => ( aa_set_o_assn(aa_fun1914167119812169564o_assn(groups5301882518646026715o_assn,G),comple90263536869209701_set_o(B4)) = aa_set_set_o_assn(comp_f4038625060515458192o_assn(groups6963733262650904763o_assn,groups5301882518646026715o_assn,G),B4) ) ) ) ).

% prod.Union_comp
tff(fact_6709_prod_OUnion__comp,axiom,
    ! [B4: set_set_int,G: fun_int_assn] :
      ( ! [X3: set_int] :
          ( member_set_int(X3,B4)
         => finite_finite_int(X3) )
     => ( ! [A13: set_int] :
            ( member_set_int(A13,B4)
           => ! [A24: set_int] :
                ( member_set_int(A24,B4)
               => ( ( A13 != A24 )
                 => ! [X3: int] :
                      ( member_int(X3,A13)
                     => ( member_int(X3,A24)
                       => ( aa_int_assn(G,X3) = one_one_assn ) ) ) ) ) )
       => ( aa_set_int_assn(aa_fun6757465843467192982t_assn(groups7882442080178216443t_assn,G),comple3221217463730067765et_int(B4)) = aa_set_set_int_assn(comp_f3572868634108735226t_assn(groups5950967880310095793t_assn,groups7882442080178216443t_assn,G),B4) ) ) ) ).

% prod.Union_comp
tff(fact_6710_prod_OUnion__comp,axiom,
    ! [B4: set_set_Code_integer,G: fun_Co4490034186337852034r_assn] :
      ( ! [X3: set_Code_integer] :
          ( member1834298987299537450nteger(X3,B4)
         => finite6017078050557962740nteger(X3) )
     => ( ! [A13: set_Code_integer] :
            ( member1834298987299537450nteger(A13,B4)
           => ! [A24: set_Code_integer] :
                ( member1834298987299537450nteger(A24,B4)
               => ( ( A13 != A24 )
                 => ! [X3: code_integer] :
                      ( member_Code_integer(X3,A13)
                     => ( member_Code_integer(X3,A24)
                       => ( aa_Code_integer_assn(G,X3) = one_one_assn ) ) ) ) ) )
       => ( aa_set7873363181767135481r_assn(aa_fun4520394192108194424r_assn(groups1304777262505850412r_assn,G),comple739944243200306918nteger(B4)) = aa_set586451247737764655r_assn(comp_f96878100917031437r_assn(groups4245288774754739042r_assn,groups1304777262505850412r_assn,G),B4) ) ) ) ).

% prod.Union_comp
tff(fact_6711_prod_OUnion__comp,axiom,
    ! [B4: set_set_o,G: fun_o_rat] :
      ( ! [X3: set_o] :
          ( member_set_o(X3,B4)
         => finite_finite_o(X3) )
     => ( ! [A13: set_o] :
            ( member_set_o(A13,B4)
           => ! [A24: set_o] :
                ( member_set_o(A24,B4)
               => ( ( A13 != A24 )
                 => ! [X3: $o] :
                      ( member_o((X3),A13)
                     => ( member_o((X3),A24)
                       => ( aa_o_rat(G,(X3)) = one_one_rat ) ) ) ) ) )
       => ( aa_set_o_rat(aa_fun7302669049306738524_o_rat(groups2869687844427037835_o_rat,G),comple90263536869209701_set_o(B4)) = aa_set_set_o_rat(comp_f1055920047293692736_o_rat(groups4233643617323539307_o_rat,groups2869687844427037835_o_rat,G),B4) ) ) ) ).

% prod.Union_comp
tff(fact_6712_prod_OUnion__comp,axiom,
    ! [B4: set_set_int,G: fun_int_rat] :
      ( ! [X3: set_int] :
          ( member_set_int(X3,B4)
         => finite_finite_int(X3) )
     => ( ! [A13: set_int] :
            ( member_set_int(A13,B4)
           => ! [A24: set_int] :
                ( member_set_int(A24,B4)
               => ( ( A13 != A24 )
                 => ! [X3: int] :
                      ( member_int(X3,A13)
                     => ( member_int(X3,A24)
                       => ( aa_int_rat(G,X3) = one_one_rat ) ) ) ) ) )
       => ( aa_set_int_rat(aa_fun991771802548846582nt_rat(groups1072433553688619179nt_rat,G),comple3221217463730067765et_int(B4)) = aa_set_set_int_rat(comp_f7120815212173581066nt_rat(groups5800339274786551393nt_rat,groups1072433553688619179nt_rat,G),B4) ) ) ) ).

% prod.Union_comp
tff(fact_6713_prod_OUnion__comp,axiom,
    ! [B4: set_set_Code_integer,G: fun_Code_integer_rat] :
      ( ! [X3: set_Code_integer] :
          ( member1834298987299537450nteger(X3,B4)
         => finite6017078050557962740nteger(X3) )
     => ( ! [A13: set_Code_integer] :
            ( member1834298987299537450nteger(A13,B4)
           => ! [A24: set_Code_integer] :
                ( member1834298987299537450nteger(A24,B4)
               => ( ( A13 != A24 )
                 => ! [X3: code_integer] :
                      ( member_Code_integer(X3,A13)
                     => ( member_Code_integer(X3,A24)
                       => ( aa_Code_integer_rat(G,X3) = one_one_rat ) ) ) ) ) )
       => ( aa_set3519029356358064041er_rat(aa_fun5443269377828775384er_rat(groups2555765274223993564er_rat,G),comple739944243200306918nteger(B4)) = aa_set4713295779865996767er_rat(comp_f227581914562382365er_rat(groups5409254039008640018er_rat,groups2555765274223993564er_rat,G),B4) ) ) ) ).

% prod.Union_comp
tff(fact_6714_prod_OUnion__comp,axiom,
    ! [B4: set_set_o,G: fun_o_nat] :
      ( ! [X3: set_o] :
          ( member_set_o(X3,B4)
         => finite_finite_o(X3) )
     => ( ! [A13: set_o] :
            ( member_set_o(A13,B4)
           => ! [A24: set_o] :
                ( member_set_o(A24,B4)
               => ( ( A13 != A24 )
                 => ! [X3: $o] :
                      ( member_o((X3),A13)
                     => ( member_o((X3),A24)
                       => ( aa_o_nat(G,(X3)) = one_one_nat ) ) ) ) ) )
       => ( aa_set_o_nat(aa_fun8470299178418016604_o_nat(groups3504817904513533571_o_nat,G),comple90263536869209701_set_o(B4)) = aa_set_set_o_nat(comp_f724240716414175032_o_nat(groups4868773677410035043_o_nat,groups3504817904513533571_o_nat,G),B4) ) ) ) ).

% prod.Union_comp
tff(fact_6715_UN__UN__finite__eq,axiom,
    ! [A2: fun_nat_set_nat] : comple7399068483239264473et_nat(image_nat_set_nat(aTP_Lamm_wf(A2),top_top_set_nat)) = comple7399068483239264473et_nat(image_nat_set_nat(A2,top_top_set_nat)) ).

% UN_UN_finite_eq
tff(fact_6716_UN__le__add__shift,axiom,
    ! [M2: fun_nat_set_nat,K: nat,N2: nat] : comple7399068483239264473et_nat(image_nat_set_nat(aa_nat1818925681583257441et_nat(aTP_Lamm_wg(M2),K),aa_nat_set_nat(set_ord_atMost_nat,N2))) = comple7399068483239264473et_nat(image_nat_set_nat(M2,aa_nat_set_nat(set_or1269000886237332187st_nat(K),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),K)))) ).

% UN_le_add_shift
tff(fact_6717_UN__le__add__shift__strict,axiom,
    ! [M2: fun_nat_set_nat,K: nat,N2: nat] : comple7399068483239264473et_nat(image_nat_set_nat(aa_nat1818925681583257441et_nat(aTP_Lamm_wg(M2),K),aa_nat_set_nat(set_ord_lessThan_nat,N2))) = comple7399068483239264473et_nat(image_nat_set_nat(M2,aa_nat_set_nat(set_or4665077453230672383an_nat(K),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N2),K)))) ).

% UN_le_add_shift_strict
tff(fact_6718_rat__sgn__code,axiom,
    ! [P2: rat] : quotient_of(aa_rat_rat(sgn_sgn_rat,P2)) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_int_int(sgn_sgn_int,aa_Pro6799258434465214121nt_int(product_fst_int_int,quotient_of(P2)))),one_one_int) ).

% rat_sgn_code
tff(fact_6719_bezw__non__0,axiom,
    ! [Y: nat,X2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),Y)
     => ( aa_nat4424723855478970923nt_int(bezw(X2),Y) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_Pro6799258434465214121nt_int(product_snd_int_int,aa_nat4424723855478970923nt_int(bezw(Y),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X2),Y)))),aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_Pro6799258434465214121nt_int(product_fst_int_int,aa_nat4424723855478970923nt_int(bezw(Y),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X2),Y)))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_Pro6799258434465214121nt_int(product_snd_int_int,aa_nat4424723855478970923nt_int(bezw(Y),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X2),Y)))),aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,X2),Y))))) ) ) ).

% bezw_non_0
tff(fact_6720_UN__finite__subset,axiom,
    ! [A2: fun_nat_set_nat,C4: set_nat] :
      ( ! [N: nat] : aa_set_nat_o(ord_less_eq_set_nat(comple7399068483239264473et_nat(image_nat_set_nat(A2,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N)))),C4)
     => aa_set_nat_o(ord_less_eq_set_nat(comple7399068483239264473et_nat(image_nat_set_nat(A2,top_top_set_nat))),C4) ) ).

% UN_finite_subset
tff(fact_6721_UN__finite2__eq,axiom,
    ! [A2: fun_nat_set_nat,B4: fun_nat_set_nat,K: nat] :
      ( ! [N: nat] : comple7399068483239264473et_nat(image_nat_set_nat(A2,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N))) = comple7399068483239264473et_nat(image_nat_set_nat(B4,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N),K))))
     => ( comple7399068483239264473et_nat(image_nat_set_nat(A2,top_top_set_nat)) = comple7399068483239264473et_nat(image_nat_set_nat(B4,top_top_set_nat)) ) ) ).

% UN_finite2_eq
tff(fact_6722_bezw_Oelims,axiom,
    ! [X2: nat,Xa: nat,Y: product_prod_int_int] :
      ( ( aa_nat4424723855478970923nt_int(bezw(X2),Xa) = Y )
     => ( Y = $ite(Xa = zero_zero_nat,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,one_one_int),zero_zero_int),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_Pro6799258434465214121nt_int(product_snd_int_int,aa_nat4424723855478970923nt_int(bezw(Xa),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X2),Xa)))),aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_Pro6799258434465214121nt_int(product_fst_int_int,aa_nat4424723855478970923nt_int(bezw(Xa),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X2),Xa)))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_Pro6799258434465214121nt_int(product_snd_int_int,aa_nat4424723855478970923nt_int(bezw(Xa),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X2),Xa)))),aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,X2),Xa)))))) ) ) ).

% bezw.elims
tff(fact_6723_bezw_Osimps,axiom,
    ! [X2: nat,Y: nat] :
      aa_nat4424723855478970923nt_int(bezw(X2),Y) = $ite(Y = zero_zero_nat,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,one_one_int),zero_zero_int),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_Pro6799258434465214121nt_int(product_snd_int_int,aa_nat4424723855478970923nt_int(bezw(Y),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X2),Y)))),aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_Pro6799258434465214121nt_int(product_fst_int_int,aa_nat4424723855478970923nt_int(bezw(Y),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X2),Y)))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_Pro6799258434465214121nt_int(product_snd_int_int,aa_nat4424723855478970923nt_int(bezw(Y),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X2),Y)))),aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,X2),Y)))))) ).

% bezw.simps
tff(fact_6724_max__ext__def,axiom,
    ! [X: set_Pr4329608150637261639at_nat] : max_ex4535816423174879388at_nat(X) = collec2601550354786890194at_nat(produc1491100424724016556_nat_o(max_ex4845989503969680116at_nat(aa_set5605188905385065315_nat_o(aTP_Lamm_bu,X)))) ).

% max_ext_def
tff(fact_6725_max__ext__def,axiom,
    ! [X: set_Pr1261947904930325089at_nat] : max_ext_nat(X) = collec6662362479098859352et_nat(produc6247414631856714078_nat_o(max_extp_nat(aa_set2634951030311766213_nat_o(aTP_Lamm_bv,X)))) ).

% max_ext_def
tff(fact_6726_max__ext__def,axiom,
    ! [X: set_Pr8693737435421807431at_nat] : max_ex8135407076693332796at_nat(X) = aa_fun1965866159956205013at_nat(collec6321179662152712658at_nat,aa_fun762164075915671590_nat_o(produc410239310623530412_nat_o,max_ex4864111882549613972at_nat(aTP_Lamm_tz(X)))) ).

% max_ext_def
tff(fact_6727_UN__finite2__subset,axiom,
    ! [A2: fun_nat_set_nat,B4: fun_nat_set_nat,K: nat] :
      ( ! [N: nat] : aa_set_nat_o(ord_less_eq_set_nat(comple7399068483239264473et_nat(image_nat_set_nat(A2,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),N)))),comple7399068483239264473et_nat(image_nat_set_nat(B4,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N),K)))))
     => aa_set_nat_o(ord_less_eq_set_nat(comple7399068483239264473et_nat(image_nat_set_nat(A2,top_top_set_nat))),comple7399068483239264473et_nat(image_nat_set_nat(B4,top_top_set_nat))) ) ).

% UN_finite2_subset
tff(fact_6728_bezw_Opelims,axiom,
    ! [X2: nat,Xa: nat,Y: product_prod_int_int] :
      ( ( aa_nat4424723855478970923nt_int(bezw(X2),Xa) = Y )
     => ( aa_Pro6150637604445964947_nat_o(accp_P4275260045618599050at_nat(bezw_rel),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X2),Xa))
       => ~ ( ( Y = $ite(Xa = zero_zero_nat,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,one_one_int),zero_zero_int),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_Pro6799258434465214121nt_int(product_snd_int_int,aa_nat4424723855478970923nt_int(bezw(Xa),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X2),Xa)))),aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_Pro6799258434465214121nt_int(product_fst_int_int,aa_nat4424723855478970923nt_int(bezw(Xa),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X2),Xa)))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_Pro6799258434465214121nt_int(product_snd_int_int,aa_nat4424723855478970923nt_int(bezw(Xa),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X2),Xa)))),aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,X2),Xa)))))) )
           => ~ aa_Pro6150637604445964947_nat_o(accp_P4275260045618599050at_nat(bezw_rel),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X2),Xa)) ) ) ) ).

% bezw.pelims
tff(fact_6729_snd__diag__id,axiom,
    ! [Z: $o] :
      ( aa_o_o(comp_P2137996956111167876_o_o_o(product_snd_o_o,aTP_Lamm_wh),(Z))
    <=> aa_o_o(id_o,(Z)) ) ).

% snd_diag_id
tff(fact_6730_snd__diag__id,axiom,
    ! [Z: nat] : aa_nat_nat(comp_P1955610211387027840at_nat(product_snd_nat_nat,aTP_Lamm_wi),Z) = aa_nat_nat(id_nat,Z) ).

% snd_diag_id
tff(fact_6731_snd__diag__id,axiom,
    ! [Z: fun_nat_o] : aa_fun5937193402907943164_nat_o(comp_P5634878600794835076_nat_o(produc3666050907618188293_nat_o,aTP_Lamm_wj),Z) = aa_fun5937193402907943164_nat_o(id_fun_nat_o,Z) ).

% snd_diag_id
tff(fact_6732_snd__diag__id,axiom,
    ! [Z: num] : aa_num_num(comp_P864883071962432936um_num(product_snd_num_num,aTP_Lamm_wk),Z) = aa_num_num(id_num,Z) ).

% snd_diag_id
tff(fact_6733_snd__diag__id,axiom,
    ! [Z: code_integer] : aa_Cod1783974652533396728nteger(comp_P7111796090210262324nteger(produc6174133586879617921nteger,aTP_Lamm_wl),Z) = aa_Cod1783974652533396728nteger(id_Code_integer,Z) ).

% snd_diag_id
tff(fact_6734_snd__diag__id,axiom,
    ! [Z: int] : aa_int_int(comp_P6651465171681656048nt_int(product_snd_int_int,aTP_Lamm_wm),Z) = aa_int_int(id_int,Z) ).

% snd_diag_id
tff(fact_6735_fst__diag__id,axiom,
    ! [Z: $o] :
      ( aa_o_o(comp_P2137996956111167876_o_o_o(product_fst_o_o,aTP_Lamm_wh),(Z))
    <=> aa_o_o(id_o,(Z)) ) ).

% fst_diag_id
tff(fact_6736_fst__diag__id,axiom,
    ! [Z: nat] : aa_nat_nat(comp_P1955610211387027840at_nat(product_fst_nat_nat,aTP_Lamm_wi),Z) = aa_nat_nat(id_nat,Z) ).

% fst_diag_id
tff(fact_6737_fst__diag__id,axiom,
    ! [Z: fun_nat_o] : aa_fun5937193402907943164_nat_o(comp_P5634878600794835076_nat_o(produc4111623175521333955_nat_o,aTP_Lamm_wj),Z) = aa_fun5937193402907943164_nat_o(id_fun_nat_o,Z) ).

% fst_diag_id
tff(fact_6738_fst__diag__id,axiom,
    ! [Z: num] : aa_num_num(comp_P864883071962432936um_num(product_fst_num_num,aTP_Lamm_wk),Z) = aa_num_num(id_num,Z) ).

% fst_diag_id
tff(fact_6739_fst__diag__id,axiom,
    ! [Z: code_integer] : aa_Cod1783974652533396728nteger(comp_P7111796090210262324nteger(produc8508995932063986495nteger,aTP_Lamm_wl),Z) = aa_Cod1783974652533396728nteger(id_Code_integer,Z) ).

% fst_diag_id
tff(fact_6740_fst__diag__id,axiom,
    ! [Z: int] : aa_int_int(comp_P6651465171681656048nt_int(product_fst_int_int,aTP_Lamm_wm),Z) = aa_int_int(id_int,Z) ).

% fst_diag_id
tff(fact_6741_size__prod__simp,axiom,
    ! [F: fun_Code_integer_nat,G: fun_Code_integer_nat,P2: produc8923325533196201883nteger] : basic_7565498685090299632nteger(F,G,P2) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_Code_integer_nat(F,aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,P2))),aa_Code_integer_nat(G,aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,P2)))),aa_nat_nat(suc,zero_zero_nat)) ).

% size_prod_simp
tff(fact_6742_size__prod__simp,axiom,
    ! [F: fun_int_nat,G: fun_int_nat,P2: product_prod_int_int] : basic_1872990034501187214nt_int(F,G,P2) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_int_nat(F,aa_Pro6799258434465214121nt_int(product_fst_int_int,P2))),aa_int_nat(G,aa_Pro6799258434465214121nt_int(product_snd_int_int,P2)))),aa_nat_nat(suc,zero_zero_nat)) ).

% size_prod_simp
tff(fact_6743_size__prod__simp,axiom,
    ! [F: fun_Code_natural_nat,G: fun_Pr2804840792690441492al_nat,P2: produc5835291356934675326atural] : basic_8185638495112405971atural(F,G,P2) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_Code_natural_nat(F,aa_Pro5806155842103967332atural(produc497848011034438852atural,P2))),aa_Pro1523461786693152325al_nat(G,aa_Pro3673693039631929973atural(produc6591912806276919810atural,P2)))),aa_nat_nat(suc,zero_zero_nat)) ).

% size_prod_simp
tff(fact_6744_fst__diag__snd,axiom,
    comp_P3428181540658402820nteger(produc8508995932063986495nteger,comp_C2277306503614464128nteger(aTP_Lamm_wl,produc6174133586879617921nteger)) = produc6174133586879617921nteger ).

% fst_diag_snd
tff(fact_6745_fst__diag__snd,axiom,
    comp_P5356232565778667509nt_int(product_fst_int_int,comp_i5941103828406351439nt_int(aTP_Lamm_wm,product_snd_int_int)) = product_snd_int_int ).

% fst_diag_snd
tff(fact_6746_fst__diag__snd,axiom,
    comp_P230220204662055659atural(produc1537665297809786051atural,comp_P4943825737035310295atural(aTP_Lamm_wn,produc6591912806276919810atural)) = produc6591912806276919810atural ).

% fst_diag_snd
tff(fact_6747_snd__diag__fst,axiom,
    comp_P3428181540658402820nteger(produc6174133586879617921nteger,comp_C2277306503614464128nteger(aTP_Lamm_wl,produc8508995932063986495nteger)) = produc8508995932063986495nteger ).

% snd_diag_fst
tff(fact_6748_snd__diag__fst,axiom,
    comp_P5356232565778667509nt_int(product_snd_int_int,comp_i5941103828406351439nt_int(aTP_Lamm_wm,product_fst_int_int)) = product_fst_int_int ).

% snd_diag_fst
tff(fact_6749_INF__Int__eq2,axiom,
    ! [S2: set_se5479201105039950375at_nat,X: set_Pr1261947904930325089at_nat,Xa3: set_Pr1261947904930325089at_nat] :
      ( aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(comple531699222623097269_nat_o(image_8577875265703384492_nat_o(aTP_Lamm_bu,S2)),X),Xa3)
    <=> member8757157785044589968at_nat(produc2922128104949294807at_nat(X,Xa3),comple6751905152567503566at_nat(S2)) ) ).

% INF_Int_eq2
tff(fact_6750_INF__Int__eq2,axiom,
    ! [S2: set_se7855581050983116737at_nat,X: nat,Xa3: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(comple6875853405106058289_nat_o(image_8883634599237391886_nat_o(aTP_Lamm_bv,S2)),X),Xa3)
    <=> member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X),Xa3),comple1930127330929219688at_nat(S2)) ) ).

% INF_Int_eq2
tff(fact_6751_INF__Int__eq2,axiom,
    ! [S2: set_se7873143835621700354nteger,X: fun_Pr5098669352780829690e_term,Xa3: produc8923325533196201883nteger] :
      ( aa_Pro4926521453222654329eger_o(aa_fun4505422719058378424eger_o(comple4186225371594386736eger_o(image_5178492454380347850eger_o(aTP_Lamm_bw,S2)),X),Xa3)
    <=> member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X),Xa3),comple323433061773777925nteger(S2)) ) ).

% INF_Int_eq2
tff(fact_6752_INF__Int__eq2,axiom,
    ! [S2: set_se3290278062343509644et_nat,X: fun_Pr6460944699146269935_nat_o,Xa3: produc3658429121746597890et_nat] :
      ( aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(comple6813979064832585404_nat_o(image_4714915674727665248_nat_o(aTP_Lamm_bx,S2)),X),Xa3)
    <=> member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X),Xa3),comple3350261554931844495et_nat(S2)) ) ).

% INF_Int_eq2
tff(fact_6753_INF__Int__eq2,axiom,
    ! [S2: set_se6059149423757001258et_nat,X: fun_Pr6460944699146269935_nat_o,Xa3: produc8799533983703829792et_nat] :
      ( aa_Pro5643009357358181178_nat_o(aa_fun912680268133416158_nat_o(comple4212820851778485918_nat_o(image_4566770532344737120_nat_o(aTP_Lamm_by,S2)),X),Xa3)
    <=> member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X),Xa3),comple1792010244656199981et_nat(S2)) ) ).

% INF_Int_eq2
tff(fact_6754_INF__Int__eq2,axiom,
    ! [S2: set_se2743246391971219311nt_int,X: fun_Pr7763680713840462443e_term,Xa3: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(aa_fun3538162476766722827_int_o(comple6728638684779775107_int_o(image_5621923772749203210_int_o(aTP_Lamm_bz,S2)),X),Xa3)
    <=> member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X),Xa3),comple4690283724815187698nt_int(S2)) ) ).

% INF_Int_eq2
tff(fact_6755_INF__Int__eq2,axiom,
    ! [S2: set_se4391686895574802075nt_int,X: fun_in5730379987311621695e_term,Xa3: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(aa_fun586359091965693151_int_o(comple6965962001593347671_int_o(image_3387664822671061514_int_o(aTP_Lamm_ca,S2)),X),Xa3)
    <=> member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X),Xa3),comple8541757751631690782nt_int(S2)) ) ).

% INF_Int_eq2
tff(fact_6756_SUP__Sup__eq2,axiom,
    ! [S2: set_se5479201105039950375at_nat,X: set_Pr1261947904930325089at_nat,Xa3: set_Pr1261947904930325089at_nat] :
      ( aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(comple5471869746640610203_nat_o(image_8577875265703384492_nat_o(aTP_Lamm_bu,S2)),X),Xa3)
    <=> member8757157785044589968at_nat(produc2922128104949294807at_nat(X,Xa3),comple4364388969068068532at_nat(S2)) ) ).

% SUP_Sup_eq2
tff(fact_6757_SUP__Sup__eq2,axiom,
    ! [S2: set_se7855581050983116737at_nat,X: nat,Xa3: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(comple5361447358958659351_nat_o(image_8883634599237391886_nat_o(aTP_Lamm_bv,S2)),X),Xa3)
    <=> member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X),Xa3),comple5685304695842803022at_nat(S2)) ) ).

% SUP_Sup_eq2
tff(fact_6758_SUP__Sup__eq2,axiom,
    ! [S2: set_se7873143835621700354nteger,X: fun_Pr5098669352780829690e_term,Xa3: produc8923325533196201883nteger] :
      ( aa_Pro4926521453222654329eger_o(aa_fun4505422719058378424eger_o(comple5202257901570954698eger_o(image_5178492454380347850eger_o(aTP_Lamm_bw,S2)),X),Xa3)
    <=> member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X),Xa3),comple7749403179893457567nteger(S2)) ) ).

% SUP_Sup_eq2
tff(fact_6759_SUP__Sup__eq2,axiom,
    ! [S2: set_se3290278062343509644et_nat,X: fun_Pr6460944699146269935_nat_o,Xa3: produc3658429121746597890et_nat] :
      ( aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(comple8308589925492879958_nat_o(image_4714915674727665248_nat_o(aTP_Lamm_bx,S2)),X),Xa3)
    <=> member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X),Xa3),comple946752071900596009et_nat(S2)) ) ).

% SUP_Sup_eq2
tff(fact_6760_SUP__Sup__eq2,axiom,
    ! [S2: set_se6059149423757001258et_nat,X: fun_Pr6460944699146269935_nat_o,Xa3: produc8799533983703829792et_nat] :
      ( aa_Pro5643009357358181178_nat_o(aa_fun912680268133416158_nat_o(comple4660109291472045368_nat_o(image_4566770532344737120_nat_o(aTP_Lamm_by,S2)),X),Xa3)
    <=> member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X),Xa3),comple828966628661558727et_nat(S2)) ) ).

% SUP_Sup_eq2
tff(fact_6761_SUP__Sup__eq2,axiom,
    ! [S2: set_se2743246391971219311nt_int,X: fun_Pr7763680713840462443e_term,Xa3: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(aa_fun3538162476766722827_int_o(comple8771317328093439261_int_o(image_5621923772749203210_int_o(aTP_Lamm_bz,S2)),X),Xa3)
    <=> member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X),Xa3),comple3054605461907987852nt_int(S2)) ) ).

% SUP_Sup_eq2
tff(fact_6762_SUP__Sup__eq2,axiom,
    ! [S2: set_se4391686895574802075nt_int,X: fun_in5730379987311621695e_term,Xa3: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(aa_fun586359091965693151_int_o(comple9222649745891163889_int_o(image_3387664822671061514_int_o(aTP_Lamm_ca,S2)),X),Xa3)
    <=> member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X),Xa3),comple7505710199608789688nt_int(S2)) ) ).

% SUP_Sup_eq2
tff(fact_6763_Inf__INT__eq2,axiom,
    ! [S2: set_fu5472951507345886094_nat_o,X: set_Pr1261947904930325089at_nat,Xa3: set_Pr1261947904930325089at_nat] :
      ( aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(comple531699222623097269_nat_o(S2),X),Xa3)
    <=> member8757157785044589968at_nat(produc2922128104949294807at_nat(X,Xa3),comple6751905152567503566at_nat(image_2888349181732859468at_nat(collec6321179662152712658at_nat,image_3264509002305780637_nat_o(produc410239310623530412_nat_o,S2)))) ) ).

% Inf_INT_eq2
tff(fact_6764_Inf__INT__eq2,axiom,
    ! [S2: set_fu7727944524835118346_nat_o,X: nat,Xa3: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(comple6875853405106058289_nat_o(S2),X),Xa3)
    <=> member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X),Xa3),comple1930127330929219688at_nat(image_19007421832380416at_nat(collec3392354462482085612at_nat,image_8786112330847644287_nat_o(produc6081775807080527818_nat_o,S2)))) ) ).

% Inf_INT_eq2
tff(fact_6765_Inf__INT__eq2,axiom,
    ! [S2: set_fu7224585531122448557eger_o,X: fun_Pr5098669352780829690e_term,Xa3: produc8923325533196201883nteger] :
      ( aa_Pro4926521453222654329eger_o(aa_fun4505422719058378424eger_o(comple4186225371594386736eger_o(S2),X),Xa3)
    <=> member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X),Xa3),comple323433061773777925nteger(image_6599205263586403426nteger(collec2950617477150063211nteger,image_6084557897575152733eger_o(produc7373287791920631523eger_o,S2)))) ) ).

% Inf_INT_eq2
tff(fact_6766_Inf__INT__eq2,axiom,
    ! [S2: set_fu3659417381080568633_nat_o,X: fun_Pr6460944699146269935_nat_o,Xa3: produc3658429121746597890et_nat] :
      ( aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(comple6813979064832585404_nat_o(S2),X),Xa3)
    <=> member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X),Xa3),comple3350261554931844495et_nat(image_7089400406489661154et_nat(collec6193113176214168693et_nat,image_6813257014334645959_nat_o(produc2915205735004773393_nat_o,S2)))) ) ).

% Inf_INT_eq2
tff(fact_6767_Inf__INT__eq2,axiom,
    ! [S2: set_fu5576194784986904859_nat_o,X: fun_Pr6460944699146269935_nat_o,Xa3: produc8799533983703829792et_nat] :
      ( aa_Pro5643009357358181178_nat_o(aa_fun912680268133416158_nat_o(comple4212820851778485918_nat_o(S2),X),Xa3)
    <=> member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X),Xa3),comple1792010244656199981et_nat(image_1768751647092834et_nat(collec5916191906451531411et_nat,image_8687135387450530375_nat_o(produc4465912260561112435_nat_o,S2)))) ) ).

% Inf_INT_eq2
tff(fact_6768_Inf__INT__eq2,axiom,
    ! [S2: set_fu1179388718870097536_int_o,X: fun_Pr7763680713840462443e_term,Xa3: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(aa_fun3538162476766722827_int_o(comple6728638684779775107_int_o(S2),X),Xa3)
    <=> member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X),Xa3),comple4690283724815187698nt_int(image_2420199643309514402nt_int(collec2586211367037964248nt_int,image_8230742269165341597_int_o(produc2207054017359051062_int_o,S2)))) ) ).

% Inf_INT_eq2
tff(fact_6769_Inf__INT__eq2,axiom,
    ! [S2: set_fu804515216739278420_int_o,X: fun_in5730379987311621695e_term,Xa3: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(aa_fun586359091965693151_int_o(comple6965962001593347671_int_o(S2),X),Xa3)
    <=> member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X),Xa3),comple8541757751631690782nt_int(image_2644176692661446050nt_int(collec8113046454796679940nt_int,image_39754620896724637_int_o(produc7271678899836001034_int_o,S2)))) ) ).

% Inf_INT_eq2
tff(fact_6770_Sup__SUP__eq2,axiom,
    ! [S2: set_fu5472951507345886094_nat_o,X: set_Pr1261947904930325089at_nat,Xa3: set_Pr1261947904930325089at_nat] :
      ( aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(comple5471869746640610203_nat_o(S2),X),Xa3)
    <=> member8757157785044589968at_nat(produc2922128104949294807at_nat(X,Xa3),comple4364388969068068532at_nat(image_2888349181732859468at_nat(collec6321179662152712658at_nat,image_3264509002305780637_nat_o(produc410239310623530412_nat_o,S2)))) ) ).

% Sup_SUP_eq2
tff(fact_6771_Sup__SUP__eq2,axiom,
    ! [S2: set_fu7727944524835118346_nat_o,X: nat,Xa3: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(comple5361447358958659351_nat_o(S2),X),Xa3)
    <=> member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X),Xa3),comple5685304695842803022at_nat(image_19007421832380416at_nat(collec3392354462482085612at_nat,image_8786112330847644287_nat_o(produc6081775807080527818_nat_o,S2)))) ) ).

% Sup_SUP_eq2
tff(fact_6772_Sup__SUP__eq2,axiom,
    ! [S2: set_fu7224585531122448557eger_o,X: fun_Pr5098669352780829690e_term,Xa3: produc8923325533196201883nteger] :
      ( aa_Pro4926521453222654329eger_o(aa_fun4505422719058378424eger_o(comple5202257901570954698eger_o(S2),X),Xa3)
    <=> member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X),Xa3),comple7749403179893457567nteger(image_6599205263586403426nteger(collec2950617477150063211nteger,image_6084557897575152733eger_o(produc7373287791920631523eger_o,S2)))) ) ).

% Sup_SUP_eq2
tff(fact_6773_Sup__SUP__eq2,axiom,
    ! [S2: set_fu3659417381080568633_nat_o,X: fun_Pr6460944699146269935_nat_o,Xa3: produc3658429121746597890et_nat] :
      ( aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(comple8308589925492879958_nat_o(S2),X),Xa3)
    <=> member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X),Xa3),comple946752071900596009et_nat(image_7089400406489661154et_nat(collec6193113176214168693et_nat,image_6813257014334645959_nat_o(produc2915205735004773393_nat_o,S2)))) ) ).

% Sup_SUP_eq2
tff(fact_6774_Sup__SUP__eq2,axiom,
    ! [S2: set_fu5576194784986904859_nat_o,X: fun_Pr6460944699146269935_nat_o,Xa3: produc8799533983703829792et_nat] :
      ( aa_Pro5643009357358181178_nat_o(aa_fun912680268133416158_nat_o(comple4660109291472045368_nat_o(S2),X),Xa3)
    <=> member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X),Xa3),comple828966628661558727et_nat(image_1768751647092834et_nat(collec5916191906451531411et_nat,image_8687135387450530375_nat_o(produc4465912260561112435_nat_o,S2)))) ) ).

% Sup_SUP_eq2
tff(fact_6775_Sup__SUP__eq2,axiom,
    ! [S2: set_fu1179388718870097536_int_o,X: fun_Pr7763680713840462443e_term,Xa3: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(aa_fun3538162476766722827_int_o(comple8771317328093439261_int_o(S2),X),Xa3)
    <=> member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X),Xa3),comple3054605461907987852nt_int(image_2420199643309514402nt_int(collec2586211367037964248nt_int,image_8230742269165341597_int_o(produc2207054017359051062_int_o,S2)))) ) ).

% Sup_SUP_eq2
tff(fact_6776_Sup__SUP__eq2,axiom,
    ! [S2: set_fu804515216739278420_int_o,X: fun_in5730379987311621695e_term,Xa3: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(aa_fun586359091965693151_int_o(comple9222649745891163889_int_o(S2),X),Xa3)
    <=> member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X),Xa3),comple7505710199608789688nt_int(image_2644176692661446050nt_int(collec8113046454796679940nt_int,image_39754620896724637_int_o(produc7271678899836001034_int_o,S2)))) ) ).

% Sup_SUP_eq2
tff(fact_6777_fst__diag__fst,axiom,
    comp_P3428181540658402820nteger(produc8508995932063986495nteger,comp_C2277306503614464128nteger(aTP_Lamm_wl,produc8508995932063986495nteger)) = produc8508995932063986495nteger ).

% fst_diag_fst
tff(fact_6778_fst__diag__fst,axiom,
    comp_P5356232565778667509nt_int(product_fst_int_int,comp_i5941103828406351439nt_int(aTP_Lamm_wm,product_fst_int_int)) = product_fst_int_int ).

% fst_diag_fst
tff(fact_6779_snd__diag__snd,axiom,
    comp_P230220204662055659atural(produc7455300194457530885atural,comp_P4943825737035310295atural(aTP_Lamm_wn,produc6591912806276919810atural)) = produc6591912806276919810atural ).

% snd_diag_snd
tff(fact_6780_snd__diag__snd,axiom,
    comp_P3428181540658402820nteger(produc6174133586879617921nteger,comp_C2277306503614464128nteger(aTP_Lamm_wl,produc6174133586879617921nteger)) = produc6174133586879617921nteger ).

% snd_diag_snd
tff(fact_6781_snd__diag__snd,axiom,
    comp_P5356232565778667509nt_int(product_snd_int_int,comp_i5941103828406351439nt_int(aTP_Lamm_wm,product_snd_int_int)) = product_snd_int_int ).

% snd_diag_snd
tff(fact_6782_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: fun_fu7695273699059480439eger_o,X2: fun_Pr5098669352780829690e_term,Y: produc8923325533196201883nteger,A: produc2453742332425399446nteger] :
      ( aa_Pro4926521453222654329eger_o(aa_fun4505422719058378424eger_o(P,X2),Y)
     => ( ( A = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X2),Y) )
       => aa_Pro4926521453222654329eger_o(aa_fun4505422719058378424eger_o(P,aa_Pro4276937008533432526e_term(produc2481150572478215260nteger,A)),aa_Pro4625778721341478855nteger(produc6589491691745714842nteger,A)) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
tff(fact_6783_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: fun_fu8419763957888848259_nat_o,X2: fun_Pr6460944699146269935_nat_o,Y: produc3658429121746597890et_nat,A: produc8799533983703829792et_nat] :
      ( aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(P,X2),Y)
     => ( ( A = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X2),Y) )
       => aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(P,aa_Pro8262445894397805713_nat_o(produc5325900173150335662et_nat,A)),aa_Pro5541488491759012064et_nat(produc4960056325182568940et_nat,A)) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
tff(fact_6784_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: fun_fu2611741329380808165_nat_o,X2: fun_Pr6460944699146269935_nat_o,Y: produc8799533983703829792et_nat,A: produc3112576180687729086et_nat] :
      ( aa_Pro5643009357358181178_nat_o(aa_fun912680268133416158_nat_o(P,X2),Y)
     => ( ( A = aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X2),Y) )
       => aa_Pro5643009357358181178_nat_o(aa_fun912680268133416158_nat_o(P,aa_Pro2837773213478468339_nat_o(produc4078497350495916492et_nat,A)),aa_Pro7798056222271281692et_nat(produc9081944055658670602et_nat,A)) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
tff(fact_6785_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: fun_fu6865642474282033866_int_o,X2: fun_Pr7763680713840462443e_term,Y: product_prod_int_int,A: produc3043004577601930755nt_int] :
      ( aa_Pro4592068669816069595_int_o(aa_fun3538162476766722827_int_o(P,X2),Y)
     => ( ( A = aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X2),Y) )
       => aa_Pro4592068669816069595_int_o(aa_fun3538162476766722827_int_o(P,aa_Pro4010435699744810540e_term(produc3130796691802200265nt_int,A)),aa_Pro2675344531184151096nt_int(produc1557020426977177351nt_int,A)) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
tff(fact_6786_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: fun_fu2978539155105838238_int_o,X2: fun_in5730379987311621695e_term,Y: product_prod_int_int,A: produc4788131091073775919nt_int] :
      ( aa_Pro4592068669816069595_int_o(aa_fun586359091965693151_int_o(P,X2),Y)
     => ( ( A = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X2),Y) )
       => aa_Pro4592068669816069595_int_o(aa_fun586359091965693151_int_o(P,aa_Pro2551989255418117932e_term(produc4463008262350210037nt_int,A)),aa_Pro4437156595432605708nt_int(produc7629796867588368947nt_int,A)) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
tff(fact_6787_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: fun_Co2081214437782444048eger_o,X2: code_integer,Y: code_integer,A: produc8923325533196201883nteger] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(P,X2),Y)
     => ( ( A = aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(X2),Y) )
       => aa_Code_integer_o(aa_Cod326357343816142457eger_o(P,aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,A)),aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,A)) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
tff(fact_6788_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: fun_int_fun_int_o,X2: int,Y: int,A: product_prod_int_int] :
      ( aa_int_o(aa_int_fun_int_o(P,X2),Y)
     => ( ( A = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X2),Y) )
       => aa_int_o(aa_int_fun_int_o(P,aa_Pro6799258434465214121nt_int(product_fst_int_int,A)),aa_Pro6799258434465214121nt_int(product_snd_int_int,A)) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
tff(fact_6789_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: fun_Co9066792663755620495ural_o,X2: code_natural,Y: produc7822875418678951345atural,A: produc5835291356934675326atural] :
      ( aa_Pro6073791466322389475ural_o(aa_Cod1393124287678120144ural_o(P,X2),Y)
     => ( ( A = aa_Pro7165575656943818355atural(produc6639722614265839536atural(X2),Y) )
       => aa_Pro6073791466322389475ural_o(aa_Cod1393124287678120144ural_o(P,aa_Pro5806155842103967332atural(produc497848011034438852atural,A)),aa_Pro3673693039631929973atural(produc6591912806276919810atural,A)) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
tff(fact_6790_normalize__def,axiom,
    ! [P2: product_prod_int_int] :
      aa_Pro6970504127699319548nt_int(normalize,P2) = $ite(
        aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),aa_Pro6799258434465214121nt_int(product_snd_int_int,P2)),
        $let(
          a2: int,
          a2:= aa_int_int(aa_int_fun_int_int(gcd_gcd_int,aa_Pro6799258434465214121nt_int(product_fst_int_int,P2)),aa_Pro6799258434465214121nt_int(product_snd_int_int,P2)),
          aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_Pro6799258434465214121nt_int(product_fst_int_int,P2)),a2)),aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_Pro6799258434465214121nt_int(product_snd_int_int,P2)),a2)) ),
        $ite(
          aa_Pro6799258434465214121nt_int(product_snd_int_int,P2) = zero_zero_int,
          aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,zero_zero_int),one_one_int),
          $let(
            a2: int,
            a2:= aa_int_int(uminus_uminus_int,aa_int_int(aa_int_fun_int_int(gcd_gcd_int,aa_Pro6799258434465214121nt_int(product_fst_int_int,P2)),aa_Pro6799258434465214121nt_int(product_snd_int_int,P2))),
            aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_Pro6799258434465214121nt_int(product_fst_int_int,P2)),a2)),aa_int_int(aa_int_fun_int_int(divide_divide_int,aa_Pro6799258434465214121nt_int(product_snd_int_int,P2)),a2)) ) ) ) ).

% normalize_def
tff(fact_6791_range__prod,axiom,
    ! [F: fun_na8176081009732395159er_nat] : ord_le3209295114279298062er_nat(image_3126957236123472631er_nat(F,top_top_set_nat),produc4260658192689636599er_nat(image_1215581382706833972nteger(comp_P5700178199414968986er_nat(produc8632663045010267826er_nat,F),top_top_set_nat),aTP_Lamm_wo(F))) ).

% range_prod
tff(fact_6792_range__prod,axiom,
    ! [F: fun_na5685997864800668403er_int] : ord_le719211969347571306er_int(image_8172478253469051731er_int(F,top_top_set_nat),produc4258167722180586323er_int(image_1215581382706833972nteger(comp_P2475326853202991862er_nat(produc8630172574501217550er_int,F),top_top_set_nat),aTP_Lamm_wp(F))) ).

% range_prod
tff(fact_6793_range__prod,axiom,
    ! [F: fun_na1596024190920976919nteger] : ord_le5852610332322655630nteger(image_8507997478476487799nteger(F,top_top_set_nat),produc4525213641468679415nteger(aa_set_nat_set_nat(image_nat_nat(comp_P9144323761349829517at_nat(produc8897218493789310642nteger,F)),top_top_set_nat),aTP_Lamm_wq(F))) ).

% range_prod
tff(fact_6794_range__prod,axiom,
    ! [F: fun_na1476630412504255114at_nat] : aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(ord_le3146513528884898305at_nat,image_5846123807819985514at_nat(F,top_top_set_nat)),produc457027306803732586at_nat(aa_set_nat_set_nat(image_nat_nat(comp_P1955610211387027840at_nat(product_fst_nat_nat,F)),top_top_set_nat),aTP_Lamm_wr(F))) ).

% range_prod
tff(fact_6795_range__prod,axiom,
    ! [F: fun_na8209919304427304166at_int] : ord_le656430383953171549at_int(image_1668272788310788806at_int(F,top_top_set_nat),produc454536836294682310at_int(aa_set_nat_set_nat(image_nat_nat(comp_P7964419862382602716at_nat(product_fst_nat_int,F)),top_top_set_nat),aTP_Lamm_ws(F))) ).

% range_prod
tff(fact_6796_range__prod,axiom,
    ! [F: fun_na7604833841916551795nteger] : ord_le2638047946463454698nteger(image_8879651038713332435nteger(F,top_top_set_nat),produc4896867201705524051nteger(image_nat_int(comp_P59025373045620805nt_nat(produc45500017171379470nteger,F),top_top_set_nat),aTP_Lamm_wt(F))) ).

% range_prod
tff(fact_6797_range__prod,axiom,
    ! [F: fun_na3663551987197276902nt_nat] : ord_le5333435103577920093nt_nat(image_6845477519721040070nt_nat(F,top_top_set_nat),produc1456381018704787142nt_nat(image_nat_int(comp_P645145991195131448nt_nat(product_fst_int_nat,F),top_top_set_nat),aTP_Lamm_wu(F))) ).

% range_prod
tff(fact_6798_range__prod,axiom,
    ! [F: fun_na3822476419092417572nteger] : ord_le3725938330318615451nteger(image_4272405876590741764nteger(F,top_top_set_nat),produc5882431272649516420nteger(image_1215581382706833972nteger(comp_P3109732533133679783er_nat(produc8508995932063986495nteger,F),top_top_set_nat),aTP_Lamm_wv(F))) ).

% range_prod
tff(fact_6799_range__prod,axiom,
    ! [F: fun_na1173468842265550146nt_int] : ord_le2843351958646193337nt_int(image_2667626500211843362nt_int(F,top_top_set_nat),produc1453890548195736866nt_int(image_nat_int(comp_P6653955642190706324nt_nat(product_fst_int_int,F),top_top_set_nat),aTP_Lamm_ww(F))) ).

% range_prod
tff(fact_6800_range__prod,axiom,
    ! [F: fun_Pr864343514034809617nteger] : ord_le3725938330318615451nteger(image_8089323762101378259nteger(F,top_to1996260823553986621t_unit),produc5882431272649516420nteger(image_3815118110082124069nteger(comp_P659088277599099894t_unit(produc8508995932063986495nteger,F),top_to1996260823553986621t_unit),aTP_Lamm_wx(F))) ).

% range_prod
tff(fact_6801_fun_Oin__rel,axiom,
    ! [R3: fun_Co2081214437782444048eger_o,A: fun_nat_Code_integer,B: fun_nat_Code_integer] :
      ( aa_fun4755383761576212144eger_o(aa_fun1781415190607348063eger_o(bNF_re1236659899165691067nteger(fequal_nat,R3),A),B)
    <=> ? [Z3: fun_na3822476419092417572nteger] :
          ( member5201028058600969421nteger(Z3,collec9032172325357639695nteger(aTP_Lamm_wy(R3)))
          & ( comp_P3109732533133679783er_nat(produc8508995932063986495nteger,Z3) = A )
          & ( comp_P3109732533133679783er_nat(produc6174133586879617921nteger,Z3) = B ) ) ) ).

% fun.in_rel
tff(fact_6802_fun_Oin__rel,axiom,
    ! [R3: fun_int_fun_int_o,A: fun_nat_int,B: fun_nat_int] :
      ( bNF_re6650684261131312217nt_int(fequal_nat,R3,A,B)
    <=> ? [Z3: fun_na1173468842265550146nt_int] :
          ( member3126637516297924075nt_int(Z3,collec470609634907078957nt_int(aTP_Lamm_wz(R3)))
          & ( comp_P6653955642190706324nt_nat(product_fst_int_int,Z3) = A )
          & ( comp_P6653955642190706324nt_nat(product_snd_int_int,Z3) = B ) ) ) ).

% fun.in_rel
tff(fact_6803_fun_Oin__rel,axiom,
    ! [R3: fun_Co2081214437782444048eger_o,A: fun_Pr1820225556744648189nteger,B: fun_Pr1820225556744648189nteger] :
      ( bNF_re8417623677625516633nteger(fequal_Product_unit,R3,A,B)
    <=> ? [Z3: fun_Pr864343514034809617nteger] :
          ( member4432617224738826152nteger(Z3,collec7092214437839010534nteger(aTP_Lamm_xa(R3)))
          & ( comp_P659088277599099894t_unit(produc8508995932063986495nteger,Z3) = A )
          & ( comp_P659088277599099894t_unit(produc6174133586879617921nteger,Z3) = B ) ) ) ).

% fun.in_rel
tff(fact_6804_fun_Oin__rel,axiom,
    ! [R3: fun_int_fun_int_o,A: fun_Product_unit_int,B: fun_Product_unit_int] :
      ( bNF_re8422471777688076791nt_int(fequal_Product_unit,R3,A,B)
    <=> ? [Z3: fun_Pr6733608168372577327nt_int] :
          ( member7232304512501848262nt_int(Z3,collec2114256676250786820nt_int(aTP_Lamm_xb(R3)))
          & ( comp_P6796073005956588617t_unit(product_fst_int_int,Z3) = A )
          & ( comp_P6796073005956588617t_unit(product_snd_int_int,Z3) = B ) ) ) ).

% fun.in_rel
tff(fact_6805_fun_Oin__rel,axiom,
    ! [R3: fun_Co2081214437782444048eger_o,A: fun_int_Code_integer,B: fun_int_Code_integer] :
      ( bNF_re1784066744496875891nteger(fequal_int,R3,A,B)
    <=> ? [Z3: fun_in4744367027289715400nteger] :
          ( member6122918666798267249nteger(Z3,collec730690896700161715nteger(aTP_Lamm_xc(R3)))
          & ( comp_P3107242062624629507er_int(produc8508995932063986495nteger,Z3) = A )
          & ( comp_P3107242062624629507er_int(produc6174133586879617921nteger,Z3) = B ) ) ) ).

% fun.in_rel
tff(fact_6806_fun_Oin__rel,axiom,
    ! [R3: fun_int_fun_int_o,A: fun_int_int,B: fun_int_int] :
      ( aa_fun_int_int_o(aa_fun2545150047610057353_int_o(bNF_re4712519889275205905nt_int(fequal_int,R3),A),B)
    <=> ? [Z3: fun_in4211310926729683942nt_int] :
          ( member6164479600762057871nt_int(Z3,collec3508451719371212753nt_int(aTP_Lamm_xd(R3)))
          & ( comp_P6651465171681656048nt_int(product_fst_int_int,Z3) = A )
          & ( comp_P6651465171681656048nt_int(product_snd_int_int,Z3) = B ) ) ) ).

% fun.in_rel
tff(fact_6807_fun_Oin__rel,axiom,
    ! [R3: fun_Co9066792663755620495ural_o,A: fun_nat_Code_natural,B: fun_na6574806417004769082atural] :
      ( bNF_re6101645755646507080atural(fequal_nat,R3,A,B)
    <=> ? [Z3: fun_na2094359461478415435atural] :
          ( member5482918008064311394atural(Z3,collec8791405069096577696atural(aTP_Lamm_xe(R3)))
          & ( comp_P5592315970379621083al_nat(produc497848011034438852atural,Z3) = A )
          & ( comp_P8477885140431536992al_nat(produc6591912806276919810atural,Z3) = B ) ) ) ).

% fun.in_rel
tff(fact_6808_fun_Oin__rel,axiom,
    ! [R3: fun_Co9066792663755620495ural_o,A: fun_Pr6278675377255837256atural,B: fun_Pr3616673511947161127atural] :
      ( bNF_re5641277236161133866atural(fequal_Product_unit,R3,A,B)
    <=> ? [Z3: fun_Pr2548841491397842206atural] :
          ( member5905631239291665351atural(Z3,collec5409277387225504521atural(aTP_Lamm_xf(R3)))
          & ( comp_P210409258367696578t_unit(produc497848011034438852atural,Z3) = A )
          & ( comp_P1945487127105810045t_unit(produc6591912806276919810atural,Z3) = B ) ) ) ).

% fun.in_rel
tff(fact_6809_fun_Oin__rel,axiom,
    ! [R3: fun_Co9066792663755620495ural_o,A: fun_int_Code_natural,B: fun_in7496697025202066910atural] :
      ( bNF_re6290619412732081552atural(fequal_int,R3,A,B)
    <=> ? [Z3: fun_in4857920871562217639atural] :
          ( member8246479418148113598atural(Z3,collec2331594442325604092atural(aTP_Lamm_xg(R3)))
          & ( comp_P5589825499870570807al_int(produc497848011034438852atural,Z3) = A )
          & ( comp_P8475394669922486716al_int(produc6591912806276919810atural,Z3) = B ) ) ) ).

% fun.in_rel
tff(fact_6810_fun_Oin__rel,axiom,
    ! [R3: fun_fu7564235448449272366at_o_o,A: fun_int_fun_nat_o,B: fun_int_fun_nat_o] :
      ( aa_fun8451603854606397830at_o_o(aa_fun527236716413744031at_o_o(bNF_re8347998229424194295_nat_o(fequal_int,R3),A),B)
    <=> ? [Z3: fun_in7664021439913478804_nat_o] :
          ( member6435579483112855485_nat_o(Z3,collec3185346009407167487_nat_o(aTP_Lamm_xh(R3)))
          & ( comp_P7610408208252206601_o_int(produc4111623175521333955_nat_o,Z3) = A )
          & ( comp_P7610408208252206601_o_int(produc3666050907618188293_nat_o,Z3) = B ) ) ) ).

% fun.in_rel
tff(fact_6811_apfst__apsnd,axiom,
    ! [F: fun_Co1966082167426949785e_term,G: fun_Co4113693717567439989nt_int,X2: produc8923325533196201883nteger] : produc4855684316150773471nt_int(F,produc3535056655957556987nteger(G,X2)) = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,aa_Cod5541156447037011290e_term(F,aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,X2))),aa_Cod6375820294346531166nt_int(G,aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,X2))) ).

% apfst_apsnd
tff(fact_6812_apfst__apsnd,axiom,
    ! [F: fun_in94812177438132456e_term,G: fun_in4211310926729683942nt_int,X2: product_prod_int_int] : produc1852316473262731728nt_int(F,produc6100211334659168315nt_int(G,X2)) = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,aa_int408404503994301353e_term(F,aa_Pro6799258434465214121nt_int(product_fst_int_int,X2))),aa_int7462565939943104719nt_int(G,aa_Pro6799258434465214121nt_int(product_snd_int_int,X2))) ).

% apfst_apsnd
tff(fact_6813_apfst__apsnd,axiom,
    ! [F: fun_Co9016714620104711083_nat_o,G: fun_Co4803750647967840348et_nat,X2: produc8923325533196201883nteger] : produc4116213131564642456et_nat(F,produc7246245855585345468nteger(G,X2)) = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,aa_Cod5288490272431355796_nat_o(F,aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,X2))),aa_Cod7444061876693584541et_nat(G,aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,X2))) ).

% apfst_apsnd
tff(fact_6814_apfst__apsnd,axiom,
    ! [F: fun_in1927439276604979228_nat_o,G: fun_in4666789911842550827et_nat,X2: product_prod_int_int] : produc2858799776146633481et_nat(F,produc9121118195053341018at_int(G,X2)) = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,aa_int7568080844962427909_nat_o(F,aa_Pro6799258434465214121nt_int(product_fst_int_int,X2))),aa_int9033694857635096172et_nat(G,aa_Pro6799258434465214121nt_int(product_snd_int_int,X2))) ).

% apfst_apsnd
tff(fact_6815_apfst__apsnd,axiom,
    ! [F: fun_Co298994598804093668e_term,G: fun_Pr5596209257725365771nt_int,X2: produc5835291356934675326atural] : produc5719200830196637908nt_int(F,produc5167862320620071534atural(G,X2)) = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,aa_Cod3874068878414155173e_term(F,aa_Pro5806155842103967332atural(produc497848011034438852atural,X2))),aa_Pro7164870388581637892nt_int(G,aa_Pro3673693039631929973atural(produc6591912806276919810atural,X2))) ).

% apfst_apsnd
tff(fact_6816_apfst__apsnd,axiom,
    ! [F: fun_Co3668495603736800980e_term,G: fun_Co6597186368970283863nteger,X2: produc8923325533196201883nteger] : produc8945651981546028870nteger(F,produc7166930624044334813nteger(G,X2)) = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,aa_Cod8918851774953611029e_term(F,aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,X2))),aa_Cod6977894654539884864nteger(G,aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,X2))) ).

% apfst_apsnd
tff(fact_6817_apfst__apsnd,axiom,
    ! [F: fun_Co4988957157240174789e_term,G: fun_Co4113693717567439989nt_int,X2: produc8923325533196201883nteger] : produc8228542470718774195nt_int(F,produc3535056655957556987nteger(G,X2)) = aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,aa_Cod5337730273189675398e_term(F,aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,X2))),aa_Cod6375820294346531166nt_int(G,aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,X2))) ).

% apfst_apsnd
tff(fact_6818_apfst__apsnd,axiom,
    ! [F: fun_in7158797356850311459e_term,G: fun_in4744367027289715400nteger,X2: product_prod_int_int] : produc8552504676914255415nteger(F,produc2935421404040714269er_int(G,X2)) = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,aa_int1137397288593391972e_term(F,aa_Pro6799258434465214121nt_int(product_fst_int_int,X2))),aa_int77912060771590321nteger(G,aa_Pro6799258434465214121nt_int(product_snd_int_int,X2))) ).

% apfst_apsnd
tff(fact_6819_apfst__apsnd,axiom,
    ! [F: fun_in237891044757944084e_term,G: fun_in4211310926729683942nt_int,X2: product_prod_int_int] : produc7648640027116863140nt_int(F,produc6100211334659168315nt_int(G,X2)) = aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,aa_int8219552307768696789e_term(F,aa_Pro6799258434465214121nt_int(product_fst_int_int,X2))),aa_int7462565939943104719nt_int(G,aa_Pro6799258434465214121nt_int(product_snd_int_int,X2))) ).

% apfst_apsnd
tff(fact_6820_apfst__apsnd,axiom,
    ! [F: fun_Co2051191115980488992_nat_o,G: fun_Pr7425815736541306438et_nat,X2: produc5835291356934675326atural] : produc7959249324659417101et_nat(F,produc1304257963789341151atural(G,X2)) = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,aa_Cod7546338805161909513_nat_o(F,aa_Pro5806155842103967332atural(produc497848011034438852atural,X2))),aa_Pro4690339539107573879et_nat(G,aa_Pro3673693039631929973atural(produc6591912806276919810atural,X2))) ).

% apfst_apsnd
tff(fact_6821_apsnd__apfst,axiom,
    ! [F: fun_Co8499238673658658103nteger,G: fun_Co8499238673658658103nteger,X2: produc8923325533196201883nteger] : aa_Pro4693618923521437820nteger(aa_fun2509385170507305080nteger(produc6499014454317279255nteger,F),aa_Pro4693618923521437820nteger(aa_fun2509385170507305080nteger(produc3195571438000033749nteger,G),X2)) = aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(aa_Cod1783974652533396728nteger(G,aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,X2))),aa_Cod1783974652533396728nteger(F,aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,X2))) ).

% apsnd_apfst
tff(fact_6822_apsnd__apfst,axiom,
    ! [F: fun_Co4113693717567439989nt_int,G: fun_Co1966082167426949785e_term,X2: produc8923325533196201883nteger] : produc6970591705382700509e_term(F,produc1373560857238714551nteger(G,X2)) = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,aa_Cod5541156447037011290e_term(G,aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,X2))),aa_Cod6375820294346531166nt_int(F,aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,X2))) ).

% apsnd_apfst
tff(fact_6823_apsnd__apfst,axiom,
    ! [F: fun_in4211310926729683942nt_int,G: fun_in94812177438132456e_term,X2: product_prod_int_int] : produc4251495004083222734e_term(F,produc6429934853825515733rm_int(G,X2)) = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,aa_int408404503994301353e_term(G,aa_Pro6799258434465214121nt_int(product_fst_int_int,X2))),aa_int7462565939943104719nt_int(F,aa_Pro6799258434465214121nt_int(product_snd_int_int,X2))) ).

% apsnd_apfst
tff(fact_6824_apsnd__apfst,axiom,
    ! [F: fun_Co4803750647967840348et_nat,G: fun_Co9016714620104711083_nat_o,X2: produc8923325533196201883nteger] : produc3435428346196091856_nat_o(F,produc8160162946510343411nteger(G,X2)) = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,aa_Cod5288490272431355796_nat_o(G,aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,X2))),aa_Cod7444061876693584541et_nat(F,aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,X2))) ).

% apsnd_apfst
tff(fact_6825_apsnd__apfst,axiom,
    ! [F: fun_in4666789911842550827et_nat,G: fun_in1927439276604979228_nat_o,X2: product_prod_int_int] : produc1318474093340237377_nat_o(F,produc2698142598960073523_o_int(G,X2)) = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,aa_int7568080844962427909_nat_o(G,aa_Pro6799258434465214121nt_int(product_fst_int_int,X2))),aa_int9033694857635096172et_nat(F,aa_Pro6799258434465214121nt_int(product_snd_int_int,X2))) ).

% apsnd_apfst
tff(fact_6826_apsnd__apfst,axiom,
    ! [F: fun_Pr5596209257725365771nt_int,G: fun_Co298994598804093668e_term,X2: produc5835291356934675326atural] : produc5989561616416747397e_term(F,produc8013365792570017484atural(G,X2)) = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,aa_Cod3874068878414155173e_term(G,aa_Pro5806155842103967332atural(produc497848011034438852atural,X2))),aa_Pro7164870388581637892nt_int(F,aa_Pro3673693039631929973atural(produc6591912806276919810atural,X2))) ).

% apsnd_apfst
tff(fact_6827_apsnd__apfst,axiom,
    ! [F: fun_Co6597186368970283863nteger,G: fun_Co3668495603736800980e_term,X2: produc8923325533196201883nteger] : produc2089341081295086202e_term(F,produc7864119354571335282nteger(G,X2)) = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,aa_Cod8918851774953611029e_term(G,aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,X2))),aa_Cod6977894654539884864nteger(F,aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,X2))) ).

% apsnd_apfst
tff(fact_6828_apsnd__apfst,axiom,
    ! [F: fun_Co4113693717567439989nt_int,G: fun_Co4988957157240174789e_term,X2: produc8923325533196201883nteger] : produc2185162023461554697e_term(F,produc444321889415134435nteger(G,X2)) = aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,aa_Cod5337730273189675398e_term(G,aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,X2))),aa_Cod6375820294346531166nt_int(F,aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,X2))) ).

% apsnd_apfst
tff(fact_6829_apsnd__apfst,axiom,
    ! [F: fun_in4744367027289715400nteger,G: fun_in7158797356850311459e_term,X2: product_prod_int_int] : produc5655117854151192939e_term(F,produc3213193131064493712rm_int(G,X2)) = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,aa_int1137397288593391972e_term(G,aa_Pro6799258434465214121nt_int(product_fst_int_int,X2))),aa_int77912060771590321nteger(F,aa_Pro6799258434465214121nt_int(product_snd_int_int,X2))) ).

% apsnd_apfst
tff(fact_6830_apsnd__apfst,axiom,
    ! [F: fun_in4211310926729683942nt_int,G: fun_in237891044757944084e_term,X2: product_prod_int_int] : produc5266752770087298298e_term(F,produc1502976015219776769rm_int(G,X2)) = aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,aa_int8219552307768696789e_term(G,aa_Pro6799258434465214121nt_int(product_fst_int_int,X2))),aa_int7462565939943104719nt_int(F,aa_Pro6799258434465214121nt_int(product_snd_int_int,X2))) ).

% apsnd_apfst
tff(fact_6831_eq__snd__iff,axiom,
    ! [B: produc8923325533196201883nteger,P2: produc2453742332425399446nteger] :
      ( ( B = aa_Pro4625778721341478855nteger(produc6589491691745714842nteger,P2) )
    <=> ? [A5: fun_Pr5098669352780829690e_term] : P2 = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A5),B) ) ).

% eq_snd_iff
tff(fact_6832_eq__snd__iff,axiom,
    ! [B: produc3658429121746597890et_nat,P2: produc8799533983703829792et_nat] :
      ( ( B = aa_Pro5541488491759012064et_nat(produc4960056325182568940et_nat,P2) )
    <=> ? [A5: fun_Pr6460944699146269935_nat_o] : P2 = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A5),B) ) ).

% eq_snd_iff
tff(fact_6833_eq__snd__iff,axiom,
    ! [B: produc8799533983703829792et_nat,P2: produc3112576180687729086et_nat] :
      ( ( B = aa_Pro7798056222271281692et_nat(produc9081944055658670602et_nat,P2) )
    <=> ? [A5: fun_Pr6460944699146269935_nat_o] : P2 = aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A5),B) ) ).

% eq_snd_iff
tff(fact_6834_eq__snd__iff,axiom,
    ! [B: product_prod_int_int,P2: produc3043004577601930755nt_int] :
      ( ( B = aa_Pro2675344531184151096nt_int(produc1557020426977177351nt_int,P2) )
    <=> ? [A5: fun_Pr7763680713840462443e_term] : P2 = aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,A5),B) ) ).

% eq_snd_iff
tff(fact_6835_eq__snd__iff,axiom,
    ! [B: product_prod_int_int,P2: produc4788131091073775919nt_int] :
      ( ( B = aa_Pro4437156595432605708nt_int(produc7629796867588368947nt_int,P2) )
    <=> ? [A5: fun_in5730379987311621695e_term] : P2 = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A5),B) ) ).

% eq_snd_iff
tff(fact_6836_eq__snd__iff,axiom,
    ! [B: code_integer,P2: produc8923325533196201883nteger] :
      ( ( B = aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,P2) )
    <=> ? [A5: code_integer] : P2 = aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(A5),B) ) ).

% eq_snd_iff
tff(fact_6837_eq__snd__iff,axiom,
    ! [B: int,P2: product_prod_int_int] :
      ( ( B = aa_Pro6799258434465214121nt_int(product_snd_int_int,P2) )
    <=> ? [A5: int] : P2 = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A5),B) ) ).

% eq_snd_iff
tff(fact_6838_eq__snd__iff,axiom,
    ! [B: produc7822875418678951345atural,P2: produc5835291356934675326atural] :
      ( ( B = aa_Pro3673693039631929973atural(produc6591912806276919810atural,P2) )
    <=> ? [A5: code_natural] : P2 = aa_Pro7165575656943818355atural(produc6639722614265839536atural(A5),B) ) ).

% eq_snd_iff
tff(fact_6839_SigmaI,axiom,
    ! [A: $o,A2: set_o,B: $o,B4: fun_o_set_o] :
      ( member_o((A),A2)
     => ( member_o((B),aa_o_set_o(B4,(A)))
       => member7466972457876170832od_o_o(product_Pair_o_o((A),(B)),product_Sigma_o_o(A2,B4)) ) ) ).

% SigmaI
tff(fact_6840_SigmaI,axiom,
    ! [A: $o,A2: set_o,B: nat,B4: fun_o_set_nat] :
      ( member_o((A),A2)
     => ( member_nat(B,aa_o_set_nat(B4,(A)))
       => member2802428098988154798_o_nat(product_Pair_o_nat((A),B),product_Sigma_o_nat(A2,B4)) ) ) ).

% SigmaI
tff(fact_6841_SigmaI,axiom,
    ! [A: $o,A2: set_o,B: int,B4: fun_o_set_int] :
      ( member_o((A),A2)
     => ( member_int(B,aa_o_set_int(B4,(A)))
       => member7847949116333733898_o_int(product_Pair_o_int((A),B),product_Sigma_o_int(A2,B4)) ) ) ).

% SigmaI
tff(fact_6842_SigmaI,axiom,
    ! [A: nat,A2: set_nat,B: $o,B4: fun_nat_set_o] :
      ( member_nat(A,A2)
     => ( member_o((B),aa_nat_set_o(B4,A))
       => member6310962623043647828_nat_o(product_Pair_nat_o(A,(B)),product_Sigma_nat_o(A2,B4)) ) ) ).

% SigmaI
tff(fact_6843_SigmaI,axiom,
    ! [A: nat,A2: set_nat,B: nat,B4: fun_nat_set_nat] :
      ( member_nat(A,A2)
     => ( member_nat(B,aa_nat_set_nat(B4,A))
       => member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B),produc457027306803732586at_nat(A2,B4)) ) ) ).

% SigmaI
tff(fact_6844_SigmaI,axiom,
    ! [A: nat,A2: set_nat,B: int,B4: fun_nat_set_int] :
      ( member_nat(A,A2)
     => ( member_int(B,aa_nat_set_int(B4,A))
       => member4262671552274231302at_int(product_Pair_nat_int(A,B),produc454536836294682310at_int(A2,B4)) ) ) ).

% SigmaI
tff(fact_6845_SigmaI,axiom,
    ! [A: int,A2: set_int,B: $o,B4: fun_int_set_o] :
      ( member_int(A,A2)
     => ( member_o((B),aa_int_set_o(B4,A))
       => member4489920277610959864_int_o(product_Pair_int_o(A,(B)),product_Sigma_int_o(A2,B4)) ) ) ).

% SigmaI
tff(fact_6846_SigmaI,axiom,
    ! [A: int,A2: set_int,B: nat,B4: fun_int_set_nat] :
      ( member_int(A,A2)
     => ( member_nat(B,aa_int_set_nat(B4,A))
       => member216504246829706758nt_nat(aa_nat8602574874988167631nt_nat(product_Pair_int_nat(A),B),produc1456381018704787142nt_nat(A2,B4)) ) ) ).

% SigmaI
tff(fact_6847_SigmaI,axiom,
    ! [A: int,A2: set_int,B: int,B4: fun_int_set_int] :
      ( member_int(A,A2)
     => ( member_int(B,aa_int_set_int(B4,A))
       => member5262025264175285858nt_int(aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A),B),produc1453890548195736866nt_int(A2,B4)) ) ) ).

% SigmaI
tff(fact_6848_SigmaI,axiom,
    ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B: $o,B4: fun_Pr8467005832278515962_set_o] :
      ( member8440522571783428010at_nat(A,A2)
     => ( member_o((B),aa_Pro5970036531051701619_set_o(B4,A))
       => member2200362271989506215_nat_o(produc855456346497908590_nat_o(A,(B)),produc203973861852599583_nat_o(A2,B4)) ) ) ).

% SigmaI
tff(fact_6849_mem__Sigma__iff,axiom,
    ! [A: $o,B: $o,A2: set_o,B4: fun_o_set_o] :
      ( member7466972457876170832od_o_o(product_Pair_o_o((A),(B)),product_Sigma_o_o(A2,B4))
    <=> ( member_o((A),A2)
        & member_o((B),aa_o_set_o(B4,(A))) ) ) ).

% mem_Sigma_iff
tff(fact_6850_mem__Sigma__iff,axiom,
    ! [A: $o,B: nat,A2: set_o,B4: fun_o_set_nat] :
      ( member2802428098988154798_o_nat(product_Pair_o_nat((A),B),product_Sigma_o_nat(A2,B4))
    <=> ( member_o((A),A2)
        & member_nat(B,aa_o_set_nat(B4,(A))) ) ) ).

% mem_Sigma_iff
tff(fact_6851_mem__Sigma__iff,axiom,
    ! [A: $o,B: int,A2: set_o,B4: fun_o_set_int] :
      ( member7847949116333733898_o_int(product_Pair_o_int((A),B),product_Sigma_o_int(A2,B4))
    <=> ( member_o((A),A2)
        & member_int(B,aa_o_set_int(B4,(A))) ) ) ).

% mem_Sigma_iff
tff(fact_6852_mem__Sigma__iff,axiom,
    ! [A: nat,B: $o,A2: set_nat,B4: fun_nat_set_o] :
      ( member6310962623043647828_nat_o(product_Pair_nat_o(A,(B)),product_Sigma_nat_o(A2,B4))
    <=> ( member_nat(A,A2)
        & member_o((B),aa_nat_set_o(B4,A)) ) ) ).

% mem_Sigma_iff
tff(fact_6853_mem__Sigma__iff,axiom,
    ! [A: nat,B: int,A2: set_nat,B4: fun_nat_set_int] :
      ( member4262671552274231302at_int(product_Pair_nat_int(A,B),produc454536836294682310at_int(A2,B4))
    <=> ( member_nat(A,A2)
        & member_int(B,aa_nat_set_int(B4,A)) ) ) ).

% mem_Sigma_iff
tff(fact_6854_mem__Sigma__iff,axiom,
    ! [A: int,B: $o,A2: set_int,B4: fun_int_set_o] :
      ( member4489920277610959864_int_o(product_Pair_int_o(A,(B)),product_Sigma_int_o(A2,B4))
    <=> ( member_int(A,A2)
        & member_o((B),aa_int_set_o(B4,A)) ) ) ).

% mem_Sigma_iff
tff(fact_6855_mem__Sigma__iff,axiom,
    ! [A: int,B: nat,A2: set_int,B4: fun_int_set_nat] :
      ( member216504246829706758nt_nat(aa_nat8602574874988167631nt_nat(product_Pair_int_nat(A),B),produc1456381018704787142nt_nat(A2,B4))
    <=> ( member_int(A,A2)
        & member_nat(B,aa_int_set_nat(B4,A)) ) ) ).

% mem_Sigma_iff
tff(fact_6856_mem__Sigma__iff,axiom,
    ! [A: int,B: int,A2: set_int,B4: fun_int_set_int] :
      ( member5262025264175285858nt_int(aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A),B),produc1453890548195736866nt_int(A2,B4))
    <=> ( member_int(A,A2)
        & member_int(B,aa_int_set_int(B4,A)) ) ) ).

% mem_Sigma_iff
tff(fact_6857_mem__Sigma__iff,axiom,
    ! [A: nat,B: nat,A2: set_nat,B4: fun_nat_set_nat] :
      ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B),produc457027306803732586at_nat(A2,B4))
    <=> ( member_nat(A,A2)
        & member_nat(B,aa_nat_set_nat(B4,A)) ) ) ).

% mem_Sigma_iff
tff(fact_6858_mem__Sigma__iff,axiom,
    ! [A: product_prod_nat_nat,B: $o,A2: set_Pr1261947904930325089at_nat,B4: fun_Pr8467005832278515962_set_o] :
      ( member2200362271989506215_nat_o(produc855456346497908590_nat_o(A,(B)),produc203973861852599583_nat_o(A2,B4))
    <=> ( member8440522571783428010at_nat(A,A2)
        & member_o((B),aa_Pro5970036531051701619_set_o(B4,A)) ) ) ).

% mem_Sigma_iff
tff(fact_6859_gcd__add1,axiom,
    ! [M: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(gcd_gcd_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)),N2) = aa_nat_nat(aa_nat_fun_nat_nat(gcd_gcd_nat,M),N2) ).

% gcd_add1
tff(fact_6860_gcd__add1,axiom,
    ! [M: int,N2: int] : aa_int_int(aa_int_fun_int_int(gcd_gcd_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,M),N2)),N2) = aa_int_int(aa_int_fun_int_int(gcd_gcd_int,M),N2) ).

% gcd_add1
tff(fact_6861_gcd__add2,axiom,
    ! [M: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(gcd_gcd_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)) = aa_nat_nat(aa_nat_fun_nat_nat(gcd_gcd_nat,M),N2) ).

% gcd_add2
tff(fact_6862_gcd__add2,axiom,
    ! [M: int,N2: int] : aa_int_int(aa_int_fun_int_int(gcd_gcd_int,M),aa_int_int(aa_int_fun_int_int(plus_plus_int,M),N2)) = aa_int_int(aa_int_fun_int_int(gcd_gcd_int,M),N2) ).

% gcd_add2
tff(fact_6863_gcd_Obottom__left__bottom,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(gcd_gcd_nat,one_one_nat),A) = one_one_nat ).

% gcd.bottom_left_bottom
tff(fact_6864_gcd_Obottom__left__bottom,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(gcd_gcd_int,one_one_int),A) = one_one_int ).

% gcd.bottom_left_bottom
tff(fact_6865_gcd_Obottom__right__bottom,axiom,
    ! [A: nat] : aa_nat_nat(aa_nat_fun_nat_nat(gcd_gcd_nat,A),one_one_nat) = one_one_nat ).

% gcd.bottom_right_bottom
tff(fact_6866_gcd_Obottom__right__bottom,axiom,
    ! [A: int] : aa_int_int(aa_int_fun_int_int(gcd_gcd_int,A),one_one_int) = one_one_int ).

% gcd.bottom_right_bottom
tff(fact_6867_apfst__conv,axiom,
    ! [F: fun_fu2505754153367914865e_term,X2: fun_Pr5098669352780829690e_term,Y: produc8923325533196201883nteger] : produc183566614307960809nteger(F,aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X2),Y)) = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,aa_fun1248587000295462322e_term(F,X2)),Y) ).

% apfst_conv
tff(fact_6868_apfst__conv,axiom,
    ! [F: fun_fu8419763957888848259_nat_o,X2: fun_Pr6460944699146269935_nat_o,Y: produc3658429121746597890et_nat] : aa_Pro5931322043027775230et_nat(produc1926458052860118910et_nat(F),aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X2),Y)) = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,aa_fun2638059832795814268_nat_o(F,X2)),Y) ).

% apfst_conv
tff(fact_6869_apfst__conv,axiom,
    ! [F: fun_fu8419763957888848259_nat_o,X2: fun_Pr6460944699146269935_nat_o,Y: produc8799533983703829792et_nat] : produc7064264152226348700et_nat(F,aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X2),Y)) = aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,aa_fun2638059832795814268_nat_o(F,X2)),Y) ).

% apfst_conv
tff(fact_6870_apfst__conv,axiom,
    ! [F: fun_fu836511555612062035e_term,X2: fun_Pr7763680713840462443e_term,Y: product_prod_int_int] : produc7857123342865048869nt_int(F,aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X2),Y)) = aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,aa_fun49903357033182740e_term(F,X2)),Y) ).

% apfst_conv
tff(fact_6871_apfst__conv,axiom,
    ! [F: fun_fu4835546211937200935e_term,X2: fun_Pr7763680713840462443e_term,Y: product_prod_int_int] : produc7965835600623382609nt_int(F,aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X2),Y)) = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,aa_fun3544567364070095336e_term(F,X2)),Y) ).

% apfst_conv
tff(fact_6872_apfst__conv,axiom,
    ! [F: fun_fu1176768540439120679e_term,X2: fun_in5730379987311621695e_term,Y: product_prod_int_int] : produc479425830829021777nt_int(F,aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X2),Y)) = aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,aa_fun1932935823081541608e_term(F,X2)),Y) ).

% apfst_conv
tff(fact_6873_apfst__conv,axiom,
    ! [F: fun_fu4810317505167811835e_term,X2: fun_in5730379987311621695e_term,Y: product_prod_int_int] : produc5901819666759714173nt_int(F,aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X2),Y)) = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,aa_fun5947755341433680828e_term(F,X2)),Y) ).

% apfst_conv
tff(fact_6874_fst__apfst,axiom,
    ! [F: fun_Co8499238673658658103nteger,X2: produc8923325533196201883nteger] : aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,aa_Pro4693618923521437820nteger(aa_fun2509385170507305080nteger(produc3195571438000033749nteger,F),X2)) = aa_Cod1783974652533396728nteger(F,aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,X2)) ).

% fst_apfst
tff(fact_6875_fst__apfst,axiom,
    ! [F: fun_int_int,X2: product_prod_int_int] : aa_Pro6799258434465214121nt_int(product_fst_int_int,aa_Pro6970504127699319548nt_int(produc2355237562570658114nt_int(F),X2)) = aa_int_int(F,aa_Pro6799258434465214121nt_int(product_fst_int_int,X2)) ).

% fst_apfst
tff(fact_6876_snd__apfst,axiom,
    ! [F: fun_Co8499238673658658103nteger,X2: produc8923325533196201883nteger] : aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,aa_Pro4693618923521437820nteger(aa_fun2509385170507305080nteger(produc3195571438000033749nteger,F),X2)) = aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,X2) ).

% snd_apfst
tff(fact_6877_snd__apfst,axiom,
    ! [F: fun_int_int,X2: product_prod_int_int] : aa_Pro6799258434465214121nt_int(product_snd_int_int,aa_Pro6970504127699319548nt_int(produc2355237562570658114nt_int(F),X2)) = aa_Pro6799258434465214121nt_int(product_snd_int_int,X2) ).

% snd_apfst
tff(fact_6878_snd__apfst,axiom,
    ! [F: fun_Co7398788559141407565atural,X2: produc5835291356934675326atural] : aa_Pro3673693039631929973atural(produc6591912806276919810atural,aa_Pro4026365172444991930atural(produc4623092060929046819atural(F),X2)) = aa_Pro3673693039631929973atural(produc6591912806276919810atural,X2) ).

% snd_apfst
tff(fact_6879_Collect__case__prod,axiom,
    ! [P: fun_nat_o,Q: fun_nat_o] : aa_fun7046812543386002057at_nat(collec3392354462482085612at_nat,aa_fun7564604662015400456_nat_o(produc6081775807080527818_nat_o,aa_fun5001253801653566085_nat_o(aTP_Lamm_xi(P),Q))) = produc457027306803732586at_nat(collect_nat(P),aTP_Lamm_xj(Q)) ).

% Collect_case_prod
tff(fact_6880_Collect__case__prod,axiom,
    ! [P: fun_nat_o,Q: fun_list_nat_o] : collec1907656820224499068st_nat(produc5265810065896090426_nat_o(aa_fun6290253675283700613_nat_o(aTP_Lamm_xk(P),Q))) = produc5227933103413159546st_nat(collect_nat(P),aTP_Lamm_xl(Q)) ).

% Collect_case_prod
tff(fact_6881_Collect__case__prod,axiom,
    ! [P: fun_list_nat_o,Q: fun_nat_o] : collec8096645339561496572at_nat(produc7308574044827705018_nat_o(aa_fun823229757805912181_nat_o(aTP_Lamm_xm(P),Q))) = produc7466890150575444730at_nat(collect_list_nat(P),aTP_Lamm_xn(Q)) ).

% Collect_case_prod
tff(fact_6882_Collect__case__prod,axiom,
    ! [P: fun_list_nat_o,Q: fun_list_nat_o] : collec1570431334306492044st_nat(produc6382697403170970154_nat_o(aa_fun3567724338799755637_nat_o(aTP_Lamm_xo(P),Q))) = produc6850429418872557834st_nat(collect_list_nat(P),aTP_Lamm_xp(Q)) ).

% Collect_case_prod
tff(fact_6883_is__unit__gcd__iff,axiom,
    ! [A: nat,B: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,aa_nat_nat(aa_nat_fun_nat_nat(gcd_gcd_nat,A),B)),one_one_nat)
    <=> ( aa_nat_nat(aa_nat_fun_nat_nat(gcd_gcd_nat,A),B) = one_one_nat ) ) ).

% is_unit_gcd_iff
tff(fact_6884_is__unit__gcd__iff,axiom,
    ! [A: int,B: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,aa_int_int(aa_int_fun_int_int(gcd_gcd_int,A),B)),one_one_int)
    <=> ( aa_int_int(aa_int_fun_int_int(gcd_gcd_int,A),B) = one_one_int ) ) ).

% is_unit_gcd_iff
tff(fact_6885_Sigma__empty1,axiom,
    ! [B4: fun_se953073389798102371at_nat] : produc7726050920695093128at_nat(bot_bo3083307316010499117at_nat,B4) = bot_bo228742789529271731at_nat ).

% Sigma_empty1
tff(fact_6886_Sigma__empty1,axiom,
    ! [B4: fun_nat_set_nat] : produc457027306803732586at_nat(bot_bot_set_nat,B4) = bot_bo2099793752762293965at_nat ).

% Sigma_empty1
tff(fact_6887_Sigma__empty2,axiom,
    ! [A2: set_se7855581050983116737at_nat] : produc7726050920695093128at_nat(A2,aTP_Lamm_xq) = bot_bo228742789529271731at_nat ).

% Sigma_empty2
tff(fact_6888_Sigma__empty2,axiom,
    ! [A2: set_nat] : produc457027306803732586at_nat(A2,aTP_Lamm_xr) = bot_bo2099793752762293965at_nat ).

% Sigma_empty2
tff(fact_6889_Times__empty,axiom,
    ! [A2: set_o,B4: set_o] :
      ( ( product_Sigma_o_o(A2,aTP_Lamm_xs(B4)) = bot_bo7073875226086086771od_o_o )
    <=> ( ( A2 = bot_bot_set_o )
        | ( B4 = bot_bot_set_o ) ) ) ).

% Times_empty
tff(fact_6890_Times__empty,axiom,
    ! [A2: set_o,B4: set_nat] :
      ( ( product_Sigma_o_nat(A2,aTP_Lamm_xt(B4)) = bot_bo66526543525301729_o_nat )
    <=> ( ( A2 = bot_bot_set_o )
        | ( B4 = bot_bot_set_nat ) ) ) ).

% Times_empty
tff(fact_6891_Times__empty,axiom,
    ! [A2: set_o,B4: set_int] :
      ( ( product_Sigma_o_int(A2,aTP_Lamm_xu(B4)) = bot_bo6799815435448350781_o_int )
    <=> ( ( A2 = bot_bot_set_o )
        | ( B4 = bot_bot_set_int ) ) ) ).

% Times_empty
tff(fact_6892_Times__empty,axiom,
    ! [A2: set_nat,B4: set_o] :
      ( ( product_Sigma_nat_o(A2,aTP_Lamm_xv(B4)) = bot_bo1114129665703605383_nat_o )
    <=> ( ( A2 = bot_bot_set_nat )
        | ( B4 = bot_bot_set_o ) ) ) ).

% Times_empty
tff(fact_6893_Times__empty,axiom,
    ! [A2: set_nat,B4: set_int] :
      ( ( produc454536836294682310at_int(A2,aTP_Lamm_xw(B4)) = bot_bo8833082644685343017at_int )
    <=> ( ( A2 = bot_bot_set_nat )
        | ( B4 = bot_bot_set_int ) ) ) ).

% Times_empty
tff(fact_6894_Times__empty,axiom,
    ! [A2: set_int,B4: set_o] :
      ( ( product_Sigma_int_o(A2,aTP_Lamm_xx(B4)) = bot_bo8092356734887935275_int_o )
    <=> ( ( A2 = bot_bot_set_int )
        | ( B4 = bot_bot_set_o ) ) ) ).

% Times_empty
tff(fact_6895_Times__empty,axiom,
    ! [A2: set_int,B4: set_nat] :
      ( ( produc1456381018704787142nt_nat(A2,aTP_Lamm_xy(B4)) = bot_bo4286715327455315753nt_nat )
    <=> ( ( A2 = bot_bot_set_int )
        | ( B4 = bot_bot_set_nat ) ) ) ).

% Times_empty
tff(fact_6896_Times__empty,axiom,
    ! [A2: set_int,B4: set_int] :
      ( ( produc1453890548195736866nt_int(A2,aTP_Lamm_xz(B4)) = bot_bo1796632182523588997nt_int )
    <=> ( ( A2 = bot_bot_set_int )
        | ( B4 = bot_bot_set_int ) ) ) ).

% Times_empty
tff(fact_6897_Times__empty,axiom,
    ! [A2: set_nat,B4: set_nat] :
      ( ( produc457027306803732586at_nat(A2,aTP_Lamm_ya(B4)) = bot_bo2099793752762293965at_nat )
    <=> ( ( A2 = bot_bot_set_nat )
        | ( B4 = bot_bot_set_nat ) ) ) ).

% Times_empty
tff(fact_6898_Times__empty,axiom,
    ! [A2: set_Pr1261947904930325089at_nat,B4: set_o] :
      ( ( produc203973861852599583_nat_o(A2,aTP_Lamm_yb(B4)) = bot_bo5454027612061941066_nat_o )
    <=> ( ( A2 = bot_bo2099793752762293965at_nat )
        | ( B4 = bot_bot_set_o ) ) ) ).

% Times_empty
tff(fact_6899_Sigma__UNIV__cancel,axiom,
    ! [A2: set_se7855581050983116737at_nat,X7: set_se7855581050983116737at_nat] : minus_3314409938677909166at_nat(produc7726050920695093128at_nat(A2,aTP_Lamm_yc(X7)),produc7726050920695093128at_nat(A2,aTP_Lamm_yd)) = bot_bo228742789529271731at_nat ).

% Sigma_UNIV_cancel
tff(fact_6900_Sigma__UNIV__cancel,axiom,
    ! [A2: set_nat,X7: set_nat] : aa_set8868280134176360700at_nat(minus_1356011639430497352at_nat(produc457027306803732586at_nat(A2,aTP_Lamm_ya(X7))),produc457027306803732586at_nat(A2,aTP_Lamm_ye)) = bot_bo2099793752762293965at_nat ).

% Sigma_UNIV_cancel
tff(fact_6901_snd__comp__apfst,axiom,
    ! [F: fun_Co8499238673658658103nteger] : comp_P3428181540658402820nteger(produc6174133586879617921nteger,aa_fun2509385170507305080nteger(produc3195571438000033749nteger,F)) = produc6174133586879617921nteger ).

% snd_comp_apfst
tff(fact_6902_snd__comp__apfst,axiom,
    ! [F: fun_int_int] : comp_P5356232565778667509nt_int(product_snd_int_int,produc2355237562570658114nt_int(F)) = product_snd_int_int ).

% snd_comp_apfst
tff(fact_6903_snd__comp__apfst,axiom,
    ! [F: fun_Co7398788559141407565atural] : comp_P7610810914149544718atural(produc6591912806276919810atural,produc4623092060929046819atural(F)) = produc6591912806276919810atural ).

% snd_comp_apfst
tff(fact_6904_UNIV__Times__UNIV,axiom,
    produc457027306803732586at_nat(top_top_set_nat,aTP_Lamm_ye) = top_to4669805908274784177at_nat ).

% UNIV_Times_UNIV
tff(fact_6905_UNIV__Times__UNIV,axiom,
    produc5506539147108004339t_unit(top_top_set_nat,aTP_Lamm_yf) = top_to8544742955230171288t_unit ).

% UNIV_Times_UNIV
tff(fact_6906_UNIV__Times__UNIV,axiom,
    produc454536836294682310at_int(top_top_set_nat,aTP_Lamm_yg) = top_to2179722763343057421at_int ).

% UNIV_Times_UNIV
tff(fact_6907_UNIV__Times__UNIV,axiom,
    produc6875377002296012693it_nat(top_to1996260823553986621t_unit,aTP_Lamm_yh) = top_to5974110478112770290it_nat ).

% UNIV_Times_UNIV
tff(fact_6908_UNIV__Times__UNIV,axiom,
    produc6121607364029222536t_unit(top_to1996260823553986621t_unit,aTP_Lamm_yi) = top_to1835807148980544151t_unit ).

% UNIV_Times_UNIV
tff(fact_6909_UNIV__Times__UNIV,axiom,
    produc6872886531786962417it_int(top_to1996260823553986621t_unit,aTP_Lamm_yj) = top_to3484027333181043534it_int ).

% UNIV_Times_UNIV
tff(fact_6910_UNIV__Times__UNIV,axiom,
    produc1456381018704787142nt_nat(top_top_set_int,aTP_Lamm_yk) = top_to6856727482967805965nt_nat ).

% UNIV_Times_UNIV
tff(fact_6911_UNIV__Times__UNIV,axiom,
    produc2622961094310184599t_unit(top_top_set_int,aTP_Lamm_yl) = top_to876157113852465980t_unit ).

% UNIV_Times_UNIV
tff(fact_6912_UNIV__Times__UNIV,axiom,
    produc1453890548195736866nt_int(top_top_set_int,aTP_Lamm_ym) = top_to4366644338036079209nt_int ).

% UNIV_Times_UNIV
tff(fact_6913_pairself__image__cart,axiom,
    ! [F: fun_nat_Code_integer,A2: set_nat,B4: set_nat] : image_5669961043262023647nteger(pairse4825235148789309005nteger(F),produc457027306803732586at_nat(A2,aTP_Lamm_ya(B4))) = produc5882431272649516420nteger(image_1215581382706833972nteger(F,A2),aa_set1342327774797759281nteger(aTP_Lamm_yn(F),B4)) ).

% pairself_image_cart
tff(fact_6914_pairself__image__cart,axiom,
    ! [F: fun_nat_set_nat,A2: set_nat,B4: set_nat] : image_4566292076127975857et_nat(pairself_nat_set_nat(F),produc457027306803732586at_nat(A2,aTP_Lamm_ya(B4))) = produc105401717395143638et_nat(image_nat_set_nat(F,A2),aa_set3960572117082860675et_nat(aTP_Lamm_yo(F),B4)) ).

% pairself_image_cart
tff(fact_6915_pairself__image__cart,axiom,
    ! [F: fun_nat_nat,A2: set_nat,B4: set_nat] : aa_set8868280134176360700at_nat(image_5168914502847457605at_nat(pairself_nat_nat(F)),produc457027306803732586at_nat(A2,aTP_Lamm_ya(B4))) = produc457027306803732586at_nat(aa_set_nat_set_nat(image_nat_nat(F),A2),aa_set562305657478724375et_nat(aTP_Lamm_yp(F),B4)) ).

% pairself_image_cart
tff(fact_6916_pairself__image__cart,axiom,
    ! [F: fun_nat_int,A2: set_nat,B4: set_nat] : image_1990417195239315453nt_int(pairself_nat_int(F),produc457027306803732586at_nat(A2,aTP_Lamm_ya(B4))) = produc1453890548195736866nt_int(image_nat_int(F,A2),aa_set7667248109638618063et_int(aTP_Lamm_yq(F),B4)) ).

% pairself_image_cart
tff(fact_6917_pairself__image__cart,axiom,
    ! [F: fun_int_int,A2: set_int,B4: set_int] : image_2653370878348428101nt_int(pairself_int_int(F),produc1453890548195736866nt_int(A2,aTP_Lamm_xz(B4))) = produc1453890548195736866nt_int(aa_set_int_set_int(image_int_int(F),A2),aa_set2836339071814736939et_int(aTP_Lamm_yr(F),B4)) ).

% pairself_image_cart
tff(fact_6918_fst__image__times,axiom,
    ! [A2: set_Code_integer,B4: set_Code_integer] :
      image_6316824473203919795nteger(produc8508995932063986495nteger,produc5882431272649516420nteger(A2,aTP_Lamm_ys(B4))) = $ite(B4 = bot_bo3990330152332043303nteger,bot_bo3990330152332043303nteger,A2) ).

% fst_image_times
tff(fact_6919_fst__image__times,axiom,
    ! [A2: set_o,B4: set_o] :
      image_7896445794123959606_o_o_o(product_fst_o_o,product_Sigma_o_o(A2,aTP_Lamm_xs(B4))) = $ite(B4 = bot_bot_set_o,bot_bot_set_o,A2) ).

% fst_image_times
tff(fact_6920_fst__image__times,axiom,
    ! [A2: set_nat,B4: set_o] :
      image_8629803608462650132_o_nat(product_fst_nat_o,product_Sigma_nat_o(A2,aTP_Lamm_xv(B4))) = $ite(B4 = bot_bot_set_o,bot_bot_set_nat,A2) ).

% fst_image_times
tff(fact_6921_fst__image__times,axiom,
    ! [A2: set_int,B4: set_o] :
      image_90517134139374612_o_int(product_fst_int_o,product_Sigma_int_o(A2,aTP_Lamm_xx(B4))) = $ite(B4 = bot_bot_set_o,bot_bot_set_int,A2) ).

% fst_image_times
tff(fact_6922_fst__image__times,axiom,
    ! [A2: set_o,B4: set_nat] :
      image_8105710389281276538_nat_o(product_fst_o_nat,product_Sigma_o_nat(A2,aTP_Lamm_xt(B4))) = $ite(B4 = bot_bot_set_nat,bot_bot_set_o,A2) ).

% fst_image_times
tff(fact_6923_fst__image__times,axiom,
    ! [A2: set_nat,B4: set_nat] :
      image_2486076414777270412at_nat(product_fst_nat_nat,produc457027306803732586at_nat(A2,aTP_Lamm_ya(B4))) = $ite(B4 = bot_bot_set_nat,bot_bot_set_nat,A2) ).

% fst_image_times
tff(fact_6924_fst__image__times,axiom,
    ! [A2: set_int,B4: set_nat] :
      image_2855239504505064772at_int(product_fst_int_nat,produc1456381018704787142nt_nat(A2,aTP_Lamm_xy(B4))) = $ite(B4 = bot_bot_set_nat,bot_bot_set_int,A2) ).

% fst_image_times
tff(fact_6925_fst__image__times,axiom,
    ! [A2: set_o,B4: set_int] :
      image_5860565421610830622_int_o(product_fst_o_int,product_Sigma_o_int(A2,aTP_Lamm_xu(B4))) = $ite(B4 = bot_bot_set_int,bot_bot_set_o,A2) ).

% fst_image_times
tff(fact_6926_fst__image__times,axiom,
    ! [A2: set_nat,B4: set_int] :
      image_4672997989470292200nt_nat(product_fst_nat_int,produc454536836294682310at_int(A2,aTP_Lamm_xw(B4))) = $ite(B4 = bot_bot_set_int,bot_bot_set_nat,A2) ).

% fst_image_times
tff(fact_6927_fst__image__times,axiom,
    ! [A2: set_int,B4: set_int] :
      image_5042161079198086560nt_int(product_fst_int_int,produc1453890548195736866nt_int(A2,aTP_Lamm_xz(B4))) = $ite(B4 = bot_bot_set_int,bot_bot_set_int,A2) ).

% fst_image_times
tff(fact_6928_snd__image__times,axiom,
    ! [A2: set_Code_integer,B4: set_Code_integer] :
      image_6316824473203919795nteger(produc6174133586879617921nteger,produc5882431272649516420nteger(A2,aTP_Lamm_ys(B4))) = $ite(A2 = bot_bo3990330152332043303nteger,bot_bo3990330152332043303nteger,B4) ).

% snd_image_times
tff(fact_6929_snd__image__times,axiom,
    ! [A2: set_o,B4: set_o] :
      image_7896445794123959606_o_o_o(product_snd_o_o,product_Sigma_o_o(A2,aTP_Lamm_xs(B4))) = $ite(A2 = bot_bot_set_o,bot_bot_set_o,B4) ).

% snd_image_times
tff(fact_6930_snd__image__times,axiom,
    ! [A2: set_o,B4: set_nat] :
      image_4888532181312399726at_nat(product_snd_o_nat,product_Sigma_o_nat(A2,aTP_Lamm_xt(B4))) = $ite(A2 = bot_bot_set_o,bot_bot_set_nat,B4) ).

% snd_image_times
tff(fact_6931_snd__image__times,axiom,
    ! [A2: set_o,B4: set_int] :
      image_7072963285496371238nt_int(product_snd_o_int,product_Sigma_o_int(A2,aTP_Lamm_xu(B4))) = $ite(A2 = bot_bot_set_o,bot_bot_set_int,B4) ).

% snd_image_times
tff(fact_6932_snd__image__times,axiom,
    ! [A2: set_nat,B4: set_o] :
      image_7478392465989118804at_o_o(product_snd_nat_o,product_Sigma_nat_o(A2,aTP_Lamm_xv(B4))) = $ite(A2 = bot_bot_set_nat,bot_bot_set_o,B4) ).

% snd_image_times
tff(fact_6933_snd__image__times,axiom,
    ! [A2: set_nat,B4: set_nat] :
      image_2486076414777270412at_nat(product_snd_nat_nat,produc457027306803732586at_nat(A2,aTP_Lamm_ya(B4))) = $ite(A2 = bot_bot_set_nat,bot_bot_set_nat,B4) ).

% snd_image_times
tff(fact_6934_snd__image__times,axiom,
    ! [A2: set_nat,B4: set_int] :
      image_4670507518961241924nt_int(product_snd_nat_int,produc454536836294682310at_int(A2,aTP_Lamm_xw(B4))) = $ite(A2 = bot_bot_set_nat,bot_bot_set_int,B4) ).

% snd_image_times
tff(fact_6935_snd__image__times,axiom,
    ! [A2: set_int,B4: set_o] :
      image_5561579847027142576nt_o_o(product_snd_int_o,product_Sigma_int_o(A2,aTP_Lamm_xx(B4))) = $ite(A2 = bot_bot_set_int,bot_bot_set_o,B4) ).

% snd_image_times
tff(fact_6936_snd__image__times,axiom,
    ! [A2: set_int,B4: set_nat] :
      image_2857729975014115048at_nat(product_snd_int_nat,produc1456381018704787142nt_nat(A2,aTP_Lamm_xy(B4))) = $ite(A2 = bot_bot_set_int,bot_bot_set_nat,B4) ).

% snd_image_times
tff(fact_6937_snd__image__times,axiom,
    ! [A2: set_int,B4: set_int] :
      image_5042161079198086560nt_int(product_snd_int_int,produc1453890548195736866nt_int(A2,aTP_Lamm_xz(B4))) = $ite(A2 = bot_bot_set_int,bot_bot_set_int,B4) ).

% snd_image_times
tff(fact_6938_fst__comp__apfst,axiom,
    ! [F: fun_Co8499238673658658103nteger] : comp_P3428181540658402820nteger(produc8508995932063986495nteger,aa_fun2509385170507305080nteger(produc3195571438000033749nteger,F)) = comp_C1043215000170864188nteger(F,produc8508995932063986495nteger) ).

% fst_comp_apfst
tff(fact_6939_fst__comp__apfst,axiom,
    ! [F: fun_int_int] : comp_P5356232565778667509nt_int(product_fst_int_int,produc2355237562570658114nt_int(F)) = comp_i4330622015127193916nt_int(F,product_fst_int_int) ).

% fst_comp_apfst
tff(fact_6940_fun_Omap__transfer,axiom,
    ! [Rb2: fun_Co2081214437782444048eger_o,Sd: fun_Co2081214437782444048eger_o] : bNF_re6079157782214477977nteger(bNF_re1062419521925302741nteger(Rb2,Sd),bNF_re2651952162905501745nteger(bNF_re6741283560065411407nteger(fequal_num,Rb2),bNF_re6741283560065411407nteger(fequal_num,Sd)),comp_C3531382070062128313er_num,comp_C3531382070062128313er_num) ).

% fun.map_transfer
tff(fact_6941_fun_Omap__transfer,axiom,
    ! [Rb2: fun_nat_fun_nat_o,Sd: fun_num_fun_num_o] : bNF_re62826171660744097nt_num(bNF_re341483209202555957um_num(Rb2,Sd),bNF_re7119215340858952409nt_num(bNF_re3715656647883201625at_nat(fequal_int,Rb2),bNF_re7626690874201225453um_num(fequal_int,Sd)),comp_nat_num_int,comp_nat_num_int) ).

% fun.map_transfer
tff(fact_6942_fun_Omap__transfer,axiom,
    ! [Rb2: fun_int_fun_int_o,Sd: fun_fu7564235448449272366at_o_o] : bNF_re3759051196448504669_nat_o(bNF_re8347998229424194295_nat_o(Rb2,Sd),bNF_re3454423673187561737_nat_o(bNF_re4712519889275205905nt_int(fequal_int,Rb2),bNF_re8347998229424194295_nat_o(fequal_int,Sd)),comp_i4004505821124781822_o_int,comp_i4004505821124781822_o_int) ).

% fun.map_transfer
tff(fact_6943_fun_Omap__transfer,axiom,
    ! [Rb2: fun_int_fun_int_o,Sd: fun_fu6971708032831053102nt_o_o] : bNF_re1178300526625999197_int_o(bNF_re8654322613993568759_int_o(Rb2,Sd),bNF_re347998642166628361_int_o(bNF_re4712519889275205905nt_int(fequal_int,Rb2),bNF_re8654322613993568759_int_o(fequal_int,Sd)),comp_i4691081854165332386_o_int,comp_i4691081854165332386_o_int) ).

% fun.map_transfer
tff(fact_6944_fun_Omap__transfer,axiom,
    ! [Rb2: fun_int_fun_int_o,Sd: fun_fu4208408993564413984_int_o] : bNF_re7874820051692727037nt_int(bNF_re5717476210804479843nt_int(Rb2,Sd),bNF_re6139702209426042631nt_int(bNF_re4712519889275205905nt_int(fequal_int,Rb2),bNF_re5717476210804479843nt_int(fequal_int,Sd)),comp_i133330754224947090nt_int,comp_i133330754224947090nt_int) ).

% fun.map_transfer
tff(fact_6945_fun_Omap__transfer,axiom,
    ! [Rb2: fun_int_fun_int_o,Sd: fun_fu7677565902479959693_rat_o] : bNF_re424392766803272243nt_rat(bNF_re2486238095283335024nt_rat(Rb2,Sd),bNF_re8704142042620765940nt_rat(bNF_re4712519889275205905nt_int(fequal_int,Rb2),bNF_re2486238095283335024nt_rat(fequal_int,Sd)),comp_i5061236333258893123nt_int,comp_i2769097025877698878at_int) ).

% fun.map_transfer
tff(fact_6946_fun_Omap__transfer,axiom,
    ! [Rb2: fun_fu7564235448449272366at_o_o,Sd: fun_fu7564235448449272366at_o_o] : bNF_re7349396894857873645_nat_o(bNF_re7140302142790738653_nat_o(Rb2,Sd),bNF_re6445433324708692061_nat_o(bNF_re8347998229424194295_nat_o(fequal_int,Rb2),bNF_re8347998229424194295_nat_o(fequal_int,Sd)),comp_f697526850294767567_o_int,comp_f697526850294767567_o_int) ).

% fun.map_transfer
tff(fact_6947_fun_Omap__transfer,axiom,
    ! [Rb2: fun_fu7564235448449272366at_o_o,Sd: fun_fu6971708032831053102nt_o_o] : bNF_re716005714690020221_int_o(bNF_re7446626527360113117_int_o(Rb2,Sd),bNF_re3339008293687758685_int_o(bNF_re8347998229424194295_nat_o(fequal_int,Rb2),bNF_re8654322613993568759_int_o(fequal_int,Sd)),comp_f1384102883335318131_o_int,comp_f1384102883335318131_o_int) ).

% fun.map_transfer
tff(fact_6948_fun_Omap__transfer,axiom,
    ! [Rb2: fun_fu7564235448449272366at_o_o,Sd: fun_fu4208408993564413984_int_o] : bNF_re7734436216040599901nt_int(bNF_re8576606815926651977nt_int(Rb2,Sd),bNF_re2152976507081458779nt_int(bNF_re8347998229424194295_nat_o(fequal_int,Rb2),bNF_re5717476210804479843nt_int(fequal_int,Sd)),comp_f2688405924591934721nt_int,comp_f2688405924591934721nt_int) ).

% fun.map_transfer
tff(fact_6949_fun_Omap__transfer,axiom,
    ! [Rb2: fun_fu6971708032831053102nt_o_o,Sd: fun_fu7564235448449272366at_o_o] : bNF_re4285988172461392477_nat_o(bNF_re3413259116532488669_nat_o(Rb2,Sd),bNF_re2199350135795421021_nat_o(bNF_re8654322613993568759_int_o(fequal_int,Rb2),bNF_re8347998229424194295_nat_o(fequal_int,Sd)),comp_f1905643983223147563_o_int,comp_f1905643983223147563_o_int) ).

% fun.map_transfer
tff(fact_6950_comp__transfer,axiom,
    ! [B4: fun_Co2081214437782444048eger_o,C4: fun_Co2081214437782444048eger_o,A2: fun_num_fun_num_o] : bNF_re6079157782214477977nteger(bNF_re1062419521925302741nteger(B4,C4),bNF_re2651952162905501745nteger(bNF_re6741283560065411407nteger(A2,B4),bNF_re6741283560065411407nteger(A2,C4)),comp_C3531382070062128313er_num,comp_C3531382070062128313er_num) ).

% comp_transfer
tff(fact_6951_comp__transfer,axiom,
    ! [B4: fun_Co1375048237525739357_nat_o,C4: fun_Co2133228800495250323_num_o,A2: fun_num_fun_int_o] : bNF_re2315437451418592029nt_num(bNF_re1758498617148825349er_num(B4,C4),bNF_re7101714357556715909nt_num(bNF_re6324211044263125204er_nat(A2,B4),bNF_re2881542830418903838er_num(A2,C4)),comp_C3531382070062128313er_num,comp_nat_num_int) ).

% comp_transfer
tff(fact_6952_comp__transfer,axiom,
    ! [B4: fun_na6318815019539281885eger_o,C4: fun_nu5413996832991386387eger_o,A2: fun_int_fun_num_o] : bNF_re8577298986372545309nteger(bNF_re8763372240999575301nteger(B4,C4),bNF_re6745137351003365765nteger(bNF_re151304249936775380nteger(A2,B4),bNF_re7315484114762210078nteger(A2,C4)),comp_nat_num_int,comp_C3531382070062128313er_num) ).

% comp_transfer
tff(fact_6953_comp__transfer,axiom,
    ! [B4: fun_nat_fun_nat_o,C4: fun_num_fun_num_o,A2: fun_int_fun_int_o] : bNF_re62826171660744097nt_num(bNF_re341483209202555957um_num(B4,C4),bNF_re7119215340858952409nt_num(bNF_re3715656647883201625at_nat(A2,B4),bNF_re7626690874201225453um_num(A2,C4)),comp_nat_num_int,comp_nat_num_int) ).

% comp_transfer
tff(fact_6954_comp__transfer,axiom,
    ! [B4: fun_int_fun_int_o,C4: fun_fu7564235448449272366at_o_o,A2: fun_int_fun_int_o] : bNF_re3759051196448504669_nat_o(bNF_re8347998229424194295_nat_o(B4,C4),bNF_re3454423673187561737_nat_o(bNF_re4712519889275205905nt_int(A2,B4),bNF_re8347998229424194295_nat_o(A2,C4)),comp_i4004505821124781822_o_int,comp_i4004505821124781822_o_int) ).

% comp_transfer
tff(fact_6955_comp__transfer,axiom,
    ! [B4: fun_int_fun_int_o,C4: fun_fu6971708032831053102nt_o_o,A2: fun_int_fun_int_o] : bNF_re1178300526625999197_int_o(bNF_re8654322613993568759_int_o(B4,C4),bNF_re347998642166628361_int_o(bNF_re4712519889275205905nt_int(A2,B4),bNF_re8654322613993568759_int_o(A2,C4)),comp_i4691081854165332386_o_int,comp_i4691081854165332386_o_int) ).

% comp_transfer
tff(fact_6956_comp__transfer,axiom,
    ! [B4: fun_int_fun_int_o,C4: fun_fu4208408993564413984_int_o,A2: fun_int_fun_int_o] : bNF_re7874820051692727037nt_int(bNF_re5717476210804479843nt_int(B4,C4),bNF_re6139702209426042631nt_int(bNF_re4712519889275205905nt_int(A2,B4),bNF_re5717476210804479843nt_int(A2,C4)),comp_i133330754224947090nt_int,comp_i133330754224947090nt_int) ).

% comp_transfer
tff(fact_6957_comp__transfer,axiom,
    ! [B4: fun_Co2081214437782444048eger_o,C4: fun_Co2466309612238040426eger_o,A2: fun_nu5413996832991386387eger_o] : bNF_re1917959877943869547nteger(bNF_re3535719783769048059nteger(B4,C4),bNF_re6610812174003455837nteger(bNF_re5202476307641864082nteger(A2,B4),bNF_re8002177354109194296nteger(A2,C4)),comp_C3531382070062128313er_num,comp_C7848664941760151970nteger) ).

% comp_transfer
tff(fact_6958_comp__transfer,axiom,
    ! [B4: fun_Co2081214437782444048eger_o,C4: fun_fu8559083954280392170eger_o,A2: fun_Co2133228800495250323_num_o] : bNF_re1125984453589466475nteger(bNF_re8292407664666371323nteger(B4,C4),bNF_re4862162959298630877nteger(bNF_re7350422212947406738nteger(A2,B4),bNF_re1115778939589153080nteger(A2,C4)),comp_C7848664941760151970nteger,comp_C3531382070062128313er_num) ).

% comp_transfer
tff(fact_6959_comp__transfer,axiom,
    ! [B4: fun_Co1375048237525739357_nat_o,C4: fun_fu7485687605903516013_num_o,A2: fun_Co8353275306710069249_int_o] : bNF_re2788112638341148655nt_num(bNF_re6729214450274395051er_num(B4,C4),bNF_re4971494712987572401nt_num(bNF_re2891348898900095767er_nat(A2,B4),bNF_re8228350525668042759er_num(A2,C4)),comp_C7848664941760151970nteger,comp_nat_num_int) ).

% comp_transfer
tff(fact_6960_power__transfer,axiom,
    ! [R3: fun_Co2081214437782444048eger_o] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,one_one_Code_integer),one_one_Code_integer)
     => ( bNF_re9064814426586422153nteger(R3,bNF_re1062419521925302741nteger(R3,R3),times_3573771949741848930nteger,times_3573771949741848930nteger)
       => bNF_re380175692409962607nteger(R3,bNF_re1236659899165691067nteger(fequal_nat,R3),power_8256067586552552935nteger,power_8256067586552552935nteger) ) ) ).

% power_transfer
tff(fact_6961_power__transfer,axiom,
    ! [R3: fun_Co4819230592921789445assn_o] :
      ( aa_assn_o(aa_Cod8400811354895609070assn_o(R3,one_one_Code_integer),one_one_assn)
     => ( bNF_re1352478543071193706n_assn(R3,bNF_re1475883931861434731r_assn(R3,R3),times_3573771949741848930nteger,times_times_assn)
       => bNF_re6260911108158577797t_assn(R3,bNF_re2692373401909853574r_assn(fequal_nat,R3),power_8256067586552552935nteger,power_power_assn) ) ) ).

% power_transfer
tff(fact_6962_power__transfer,axiom,
    ! [R3: fun_Co625613742390903637_rat_o] :
      ( aa_rat_o(aa_Cod6561327387924323390_rat_o(R3,one_one_Code_integer),one_one_rat)
     => ( bNF_re7829844138342828666at_rat(R3,bNF_re4698098036185532619er_rat(R3,R3),times_3573771949741848930nteger,times_times_rat)
       => bNF_re419171836357356005at_rat(R3,bNF_re2882060999336173110er_rat(fequal_nat,R3),power_8256067586552552935nteger,power_power_rat) ) ) ).

% power_transfer
tff(fact_6963_power__transfer,axiom,
    ! [R3: fun_Co1375048237525739357_nat_o] :
      ( aa_nat_o(aa_Cod1075288278386115654_nat_o(R3,one_one_Code_integer),one_one_nat)
     => ( bNF_re2633667331928566882at_nat(R3,bNF_re5201166830993046715er_nat(R3,R3),times_3573771949741848930nteger,times_times_nat)
       => bNF_re1755872562029691349at_nat(R3,bNF_re3517191059422668846er_nat(fequal_nat,R3),power_8256067586552552935nteger,power_power_nat) ) ) ).

% power_transfer
tff(fact_6964_power__transfer,axiom,
    ! [R3: fun_Co8353275306710069249_int_o] :
      ( aa_int_o(aa_Cod8477617969808203498_int_o(R3,one_one_Code_integer),one_one_int)
     => ( bNF_re2755378959209877878nt_int(R3,bNF_re2888858428391045491er_int(R3,R3),times_3573771949741848930nteger,times_times_int)
       => bNF_re5458596770363244685at_int(R3,bNF_re3514700588913618570er_int(fequal_nat,R3),power_8256067586552552935nteger,power_power_int) ) ) ).

% power_transfer
tff(fact_6965_power__transfer,axiom,
    ! [R3: fun_as7521517929205406341eger_o] :
      ( aa_Code_integer_o(aa_ass2896223873163428078eger_o(R3,one_one_assn),one_one_Code_integer)
     => ( bNF_re8333148941225519722nteger(R3,bNF_re4134162077946812779nteger(R3,R3),times_times_assn,times_3573771949741848930nteger)
       => bNF_re5238271293363935365nteger(R3,bNF_re1831131418152741254nteger(fequal_nat,R3),power_power_assn,power_8256067586552552935nteger) ) ) ).

% power_transfer
tff(fact_6966_power__transfer,axiom,
    ! [R3: fun_assn_fun_assn_o] :
      ( aa_assn_o(aa_assn_fun_assn_o(R3,one_one_assn),one_one_assn)
     => ( bNF_re2386586829629292363n_assn(R3,bNF_re1143782165119297793n_assn(R3,R3),times_times_assn,times_times_assn)
       => bNF_re8039158443969940635t_assn(R3,bNF_re4051817429369991249n_assn(fequal_nat,R3),power_power_assn,power_power_assn) ) ) ).

% power_transfer
tff(fact_6967_power__transfer,axiom,
    ! [R3: fun_assn_fun_rat_o] :
      ( aa_rat_o(aa_assn_fun_rat_o(R3,one_one_assn),one_one_rat)
     => ( bNF_re2823698778247379291at_rat(R3,bNF_re9003240792272343649sn_rat(R3,R3),times_times_assn,times_times_rat)
       => bNF_re3141659225902627835at_rat(R3,bNF_re4159627890580825857sn_rat(fequal_nat,R3),power_power_assn,power_power_rat) ) ) ).

% power_transfer
tff(fact_6968_power__transfer,axiom,
    ! [R3: fun_assn_fun_nat_o] :
      ( aa_nat_o(aa_assn_fun_nat_o(R3,one_one_assn),one_one_nat)
     => ( bNF_re4476954147854580547at_nat(R3,bNF_re6742580585434904145sn_nat(R3,R3),times_times_assn,times_times_nat)
       => bNF_re8087912568774460395at_nat(R3,bNF_re4794757950667321593sn_nat(fequal_nat,R3),power_power_assn,power_power_nat) ) ) ).

% power_transfer
tff(fact_6969_power__transfer,axiom,
    ! [R3: fun_assn_fun_int_o] :
      ( aa_int_o(aa_assn_fun_int_o(R3,one_one_assn),one_one_int)
     => ( bNF_re9179032068089188439nt_int(R3,bNF_re2927800259774540553sn_int(R3,R3),times_times_assn,times_times_int)
       => bNF_re8253829423823436451at_int(R3,bNF_re4792267480158271317sn_int(fequal_nat,R3),power_power_assn,power_power_int) ) ) ).

% power_transfer
tff(fact_6970_times__integer_Orsp,axiom,
    aa_fun3498034192445020252_int_o(aa_fun3119206668089765047_int_o(bNF_re5717476210804479843nt_int(fequal_int,bNF_re4712519889275205905nt_int(fequal_int,fequal_int)),times_times_int),times_times_int) ).

% times_integer.rsp
tff(fact_6971_times__natural_Orsp,axiom,
    bNF_re5162689864697376059at_nat(fequal_nat,bNF_re5653821019739307937at_nat(fequal_nat,fequal_nat),times_times_nat,times_times_nat) ).

% times_natural.rsp
tff(fact_6972_divide__natural_Orsp,axiom,
    bNF_re5162689864697376059at_nat(fequal_nat,bNF_re5653821019739307937at_nat(fequal_nat,fequal_nat),divide_divide_nat,divide_divide_nat) ).

% divide_natural.rsp
tff(fact_6973_divide__integer_Orsp,axiom,
    aa_fun3498034192445020252_int_o(aa_fun3119206668089765047_int_o(bNF_re5717476210804479843nt_int(fequal_int,bNF_re4712519889275205905nt_int(fequal_int,fequal_int)),divide_divide_int),divide_divide_int) ).

% divide_integer.rsp
tff(fact_6974_or__natural_Orsp,axiom,
    bNF_re5162689864697376059at_nat(fequal_nat,bNF_re5653821019739307937at_nat(fequal_nat,fequal_nat),bit_se1412395901928357646or_nat,bit_se1412395901928357646or_nat) ).

% or_natural.rsp
tff(fact_6975_or__integer_Orsp,axiom,
    aa_fun3498034192445020252_int_o(aa_fun3119206668089765047_int_o(bNF_re5717476210804479843nt_int(fequal_int,bNF_re4712519889275205905nt_int(fequal_int,fequal_int)),bit_se1409905431419307370or_int),bit_se1409905431419307370or_int) ).

% or_integer.rsp
tff(fact_6976_set__bit__integer_Orsp,axiom,
    bNF_re5651586111134833323nt_int(fequal_nat,bNF_re4712519889275205905nt_int(fequal_int,fequal_int),bit_se7879613467334960850it_int,bit_se7879613467334960850it_int) ).

% set_bit_integer.rsp
tff(fact_6977_set__bit__natural_Orsp,axiom,
    bNF_re5162689864697376059at_nat(fequal_nat,bNF_re5653821019739307937at_nat(fequal_nat,fequal_nat),bit_se7882103937844011126it_nat,bit_se7882103937844011126it_nat) ).

% set_bit_natural.rsp
tff(fact_6978_xor__integer_Orsp,axiom,
    aa_fun3498034192445020252_int_o(aa_fun3119206668089765047_int_o(bNF_re5717476210804479843nt_int(fequal_int,bNF_re4712519889275205905nt_int(fequal_int,fequal_int)),bit_se6526347334894502574or_int),bit_se6526347334894502574or_int) ).

% xor_integer.rsp
tff(fact_6979_xor__natural_Orsp,axiom,
    bNF_re5162689864697376059at_nat(fequal_nat,bNF_re5653821019739307937at_nat(fequal_nat,fequal_nat),bit_se6528837805403552850or_nat,bit_se6528837805403552850or_nat) ).

% xor_natural.rsp
tff(fact_6980_and__integer_Orsp,axiom,
    aa_fun3498034192445020252_int_o(aa_fun3119206668089765047_int_o(bNF_re5717476210804479843nt_int(fequal_int,bNF_re4712519889275205905nt_int(fequal_int,fequal_int)),bit_se725231765392027082nd_int),bit_se725231765392027082nd_int) ).

% and_integer.rsp
tff(fact_6981_and__natural_Orsp,axiom,
    bNF_re5162689864697376059at_nat(fequal_nat,bNF_re5653821019739307937at_nat(fequal_nat,fequal_nat),bit_se727722235901077358nd_nat,bit_se727722235901077358nd_nat) ).

% and_natural.rsp
tff(fact_6982_modulo__integer_Orsp,axiom,
    aa_fun3498034192445020252_int_o(aa_fun3119206668089765047_int_o(bNF_re5717476210804479843nt_int(fequal_int,bNF_re4712519889275205905nt_int(fequal_int,fequal_int)),modulo_modulo_int),modulo_modulo_int) ).

% modulo_integer.rsp
tff(fact_6983_modulo__natural_Orsp,axiom,
    bNF_re5162689864697376059at_nat(fequal_nat,bNF_re5653821019739307937at_nat(fequal_nat,fequal_nat),modulo_modulo_nat,modulo_modulo_nat) ).

% modulo_natural.rsp
tff(fact_6984_less__integer_Orsp,axiom,
    aa_fun227585529652676578nt_o_o(aa_fun1090463484742261919nt_o_o(bNF_re8654322613993568759_int_o(fequal_int,bNF_re5089333283451836215nt_o_o(fequal_int,fequal_o)),ord_less_int),ord_less_int) ).

% less_integer.rsp
tff(fact_6985_less__natural_Orsp,axiom,
    bNF_re1448341924010609215_nat_o(fequal_nat,bNF_re4705727531993890431at_o_o(fequal_nat,fequal_o),ord_less_nat,ord_less_nat) ).

% less_natural.rsp
tff(fact_6986_unset__bit__integer_Orsp,axiom,
    bNF_re5651586111134833323nt_int(fequal_nat,bNF_re4712519889275205905nt_int(fequal_int,fequal_int),bit_se4203085406695923979it_int,bit_se4203085406695923979it_int) ).

% unset_bit_integer.rsp
tff(fact_6987_take__bit__integer_Orsp,axiom,
    bNF_re5651586111134833323nt_int(fequal_nat,bNF_re4712519889275205905nt_int(fequal_int,fequal_int),bit_se2923211474154528505it_int,bit_se2923211474154528505it_int) ).

% take_bit_integer.rsp
tff(fact_6988_flip__bit__integer_Orsp,axiom,
    bNF_re5651586111134833323nt_int(fequal_nat,bNF_re4712519889275205905nt_int(fequal_int,fequal_int),bit_se2159334234014336723it_int,bit_se2159334234014336723it_int) ).

% flip_bit_integer.rsp
tff(fact_6989_flip__bit__natural_Orsp,axiom,
    bNF_re5162689864697376059at_nat(fequal_nat,bNF_re5653821019739307937at_nat(fequal_nat,fequal_nat),bit_se2161824704523386999it_nat,bit_se2161824704523386999it_nat) ).

% flip_bit_natural.rsp
tff(fact_6990_push__bit__natural_Orsp,axiom,
    bNF_re5162689864697376059at_nat(fequal_nat,bNF_re5653821019739307937at_nat(fequal_nat,fequal_nat),bit_se547839408752420682it_nat,bit_se547839408752420682it_nat) ).

% push_bit_natural.rsp
tff(fact_6991_push__bit__integer_Orsp,axiom,
    bNF_re5651586111134833323nt_int(fequal_nat,bNF_re4712519889275205905nt_int(fequal_int,fequal_int),bit_se545348938243370406it_int,bit_se545348938243370406it_int) ).

% push_bit_integer.rsp
tff(fact_6992_plus__integer_Orsp,axiom,
    aa_fun3498034192445020252_int_o(aa_fun3119206668089765047_int_o(bNF_re5717476210804479843nt_int(fequal_int,bNF_re4712519889275205905nt_int(fequal_int,fequal_int)),plus_plus_int),plus_plus_int) ).

% plus_integer.rsp
tff(fact_6993_plus__natural_Orsp,axiom,
    bNF_re5162689864697376059at_nat(fequal_nat,bNF_re5653821019739307937at_nat(fequal_nat,fequal_nat),plus_plus_nat,plus_plus_nat) ).

% plus_natural.rsp
tff(fact_6994_drop__bit__integer_Orsp,axiom,
    bNF_re5651586111134833323nt_int(fequal_nat,bNF_re4712519889275205905nt_int(fequal_int,fequal_int),bit_se8568078237143864401it_int,bit_se8568078237143864401it_int) ).

% drop_bit_integer.rsp
tff(fact_6995_minus__natural_Orsp,axiom,
    bNF_re5162689864697376059at_nat(fequal_nat,bNF_re5653821019739307937at_nat(fequal_nat,fequal_nat),minus_minus_nat,minus_minus_nat) ).

% minus_natural.rsp
tff(fact_6996_minus__integer_Orsp,axiom,
    aa_fun3498034192445020252_int_o(aa_fun3119206668089765047_int_o(bNF_re5717476210804479843nt_int(fequal_int,bNF_re4712519889275205905nt_int(fequal_int,fequal_int)),minus_minus_int),minus_minus_int) ).

% minus_integer.rsp
tff(fact_6997_less__eq__integer_Orsp,axiom,
    aa_fun227585529652676578nt_o_o(aa_fun1090463484742261919nt_o_o(bNF_re8654322613993568759_int_o(fequal_int,bNF_re5089333283451836215nt_o_o(fequal_int,fequal_o)),ord_less_eq_int),ord_less_eq_int) ).

% less_eq_integer.rsp
tff(fact_6998_less__eq__natural_Orsp,axiom,
    bNF_re1448341924010609215_nat_o(fequal_nat,bNF_re4705727531993890431at_o_o(fequal_nat,fequal_o),ord_less_eq_nat,ord_less_eq_nat) ).

% less_eq_natural.rsp
tff(fact_6999_SigmaE,axiom,
    ! [C: product_prod_o_o,A2: set_o,B4: fun_o_set_o] :
      ( member7466972457876170832od_o_o(C,product_Sigma_o_o(A2,B4))
     => ~ ! [X3: $o] :
            ( member_o((X3),A2)
           => ! [Y4: $o] :
                ( member_o((Y4),aa_o_set_o(B4,(X3)))
               => ( C != product_Pair_o_o((X3),(Y4)) ) ) ) ) ).

% SigmaE
tff(fact_7000_SigmaE,axiom,
    ! [C: product_prod_o_nat,A2: set_o,B4: fun_o_set_nat] :
      ( member2802428098988154798_o_nat(C,product_Sigma_o_nat(A2,B4))
     => ~ ! [X3: $o] :
            ( member_o((X3),A2)
           => ! [Y4: nat] :
                ( member_nat(Y4,aa_o_set_nat(B4,(X3)))
               => ( C != product_Pair_o_nat((X3),Y4) ) ) ) ) ).

% SigmaE
tff(fact_7001_SigmaE,axiom,
    ! [C: product_prod_o_int,A2: set_o,B4: fun_o_set_int] :
      ( member7847949116333733898_o_int(C,product_Sigma_o_int(A2,B4))
     => ~ ! [X3: $o] :
            ( member_o((X3),A2)
           => ! [Y4: int] :
                ( member_int(Y4,aa_o_set_int(B4,(X3)))
               => ( C != product_Pair_o_int((X3),Y4) ) ) ) ) ).

% SigmaE
tff(fact_7002_SigmaE,axiom,
    ! [C: product_prod_nat_o,A2: set_nat,B4: fun_nat_set_o] :
      ( member6310962623043647828_nat_o(C,product_Sigma_nat_o(A2,B4))
     => ~ ! [X3: nat] :
            ( member_nat(X3,A2)
           => ! [Y4: $o] :
                ( member_o((Y4),aa_nat_set_o(B4,X3))
               => ( C != product_Pair_nat_o(X3,(Y4)) ) ) ) ) ).

% SigmaE
tff(fact_7003_SigmaE,axiom,
    ! [C: product_prod_nat_int,A2: set_nat,B4: fun_nat_set_int] :
      ( member4262671552274231302at_int(C,produc454536836294682310at_int(A2,B4))
     => ~ ! [X3: nat] :
            ( member_nat(X3,A2)
           => ! [Y4: int] :
                ( member_int(Y4,aa_nat_set_int(B4,X3))
               => ( C != product_Pair_nat_int(X3,Y4) ) ) ) ) ).

% SigmaE
tff(fact_7004_SigmaE,axiom,
    ! [C: product_prod_int_o,A2: set_int,B4: fun_int_set_o] :
      ( member4489920277610959864_int_o(C,product_Sigma_int_o(A2,B4))
     => ~ ! [X3: int] :
            ( member_int(X3,A2)
           => ! [Y4: $o] :
                ( member_o((Y4),aa_int_set_o(B4,X3))
               => ( C != product_Pair_int_o(X3,(Y4)) ) ) ) ) ).

% SigmaE
tff(fact_7005_SigmaE,axiom,
    ! [C: product_prod_int_nat,A2: set_int,B4: fun_int_set_nat] :
      ( member216504246829706758nt_nat(C,produc1456381018704787142nt_nat(A2,B4))
     => ~ ! [X3: int] :
            ( member_int(X3,A2)
           => ! [Y4: nat] :
                ( member_nat(Y4,aa_int_set_nat(B4,X3))
               => ( C != aa_nat8602574874988167631nt_nat(product_Pair_int_nat(X3),Y4) ) ) ) ) ).

% SigmaE
tff(fact_7006_SigmaE,axiom,
    ! [C: product_prod_int_int,A2: set_int,B4: fun_int_set_int] :
      ( member5262025264175285858nt_int(C,produc1453890548195736866nt_int(A2,B4))
     => ~ ! [X3: int] :
            ( member_int(X3,A2)
           => ! [Y4: int] :
                ( member_int(Y4,aa_int_set_int(B4,X3))
               => ( C != aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X3),Y4) ) ) ) ) ).

% SigmaE
tff(fact_7007_SigmaE,axiom,
    ! [C: product_prod_nat_nat,A2: set_nat,B4: fun_nat_set_nat] :
      ( member8440522571783428010at_nat(C,produc457027306803732586at_nat(A2,B4))
     => ~ ! [X3: nat] :
            ( member_nat(X3,A2)
           => ! [Y4: nat] :
                ( member_nat(Y4,aa_nat_set_nat(B4,X3))
               => ( C != aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),Y4) ) ) ) ) ).

% SigmaE
tff(fact_7008_SigmaE,axiom,
    ! [C: produc652263959640188542_nat_o,A2: set_Pr1261947904930325089at_nat,B4: fun_Pr8467005832278515962_set_o] :
      ( member2200362271989506215_nat_o(C,produc203973861852599583_nat_o(A2,B4))
     => ~ ! [X3: product_prod_nat_nat] :
            ( member8440522571783428010at_nat(X3,A2)
           => ! [Y4: $o] :
                ( member_o((Y4),aa_Pro5970036531051701619_set_o(B4,X3))
               => ( C != produc855456346497908590_nat_o(X3,(Y4)) ) ) ) ) ).

% SigmaE
tff(fact_7009_SigmaD1,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_se7855581050983116737at_nat,B4: fun_se953073389798102371at_nat] :
      ( member8757157785044589968at_nat(produc2922128104949294807at_nat(A,B),produc7726050920695093128at_nat(A2,B4))
     => member2643936169264416010at_nat(A,A2) ) ).

% SigmaD1
tff(fact_7010_SigmaD1,axiom,
    ! [A: nat,B: nat,A2: set_nat,B4: fun_nat_set_nat] :
      ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B),produc457027306803732586at_nat(A2,B4))
     => member_nat(A,A2) ) ).

% SigmaD1
tff(fact_7011_SigmaD1,axiom,
    ! [A: fun_Pr5098669352780829690e_term,B: produc8923325533196201883nteger,A2: set_fu8280898353253485872e_term,B4: fun_fu5971215405379524186nteger] :
      ( member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A),B),produc5453309460576862807nteger(A2,B4))
     => member8464590939221061905e_term(A,A2) ) ).

% SigmaD1
tff(fact_7012_SigmaD1,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,B: produc3658429121746597890et_nat,A2: set_fu3555266933746557007_nat_o,B4: fun_fu2890809920214373946et_nat] :
      ( member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A),B),produc6971759541029228329et_nat(A2,B4))
     => member7544390268018397336_nat_o(A,A2) ) ).

% SigmaD1
tff(fact_7013_SigmaD1,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,B: produc8799533983703829792et_nat,A2: set_fu3555266933746557007_nat_o,B4: fun_fu8357309440898100312et_nat] :
      ( member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A),B),produc5673588578087545031et_nat(A2,B4))
     => member7544390268018397336_nat_o(A,A2) ) ).

% SigmaD1
tff(fact_7014_SigmaD1,axiom,
    ! [A: fun_Pr7763680713840462443e_term,B: product_prod_int_int,A2: set_fu5653557704672872225e_term,B4: fun_fu4219362280553733319nt_int] :
      ( member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,A),B),produc3974764367135812292nt_int(A2,B4))
     => member1495369047980753794e_term(A,A2) ) ).

% SigmaD1
tff(fact_7015_SigmaD1,axiom,
    ! [A: fun_in5730379987311621695e_term,B: product_prod_int_int,A2: set_fu3629540756087427317e_term,B4: fun_fu3472058528428720115nt_int] :
      ( member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A),B),produc1533099051242823152nt_int(A2,B4))
     => member4871225538671630166e_term(A,A2) ) ).

% SigmaD1
tff(fact_7016_SigmaD2,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_se7855581050983116737at_nat,B4: fun_se953073389798102371at_nat] :
      ( member8757157785044589968at_nat(produc2922128104949294807at_nat(A,B),produc7726050920695093128at_nat(A2,B4))
     => member2643936169264416010at_nat(B,aa_set6242432332095302236at_nat(B4,A)) ) ).

% SigmaD2
tff(fact_7017_SigmaD2,axiom,
    ! [A: nat,B: nat,A2: set_nat,B4: fun_nat_set_nat] :
      ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B),produc457027306803732586at_nat(A2,B4))
     => member_nat(B,aa_nat_set_nat(B4,A)) ) ).

% SigmaD2
tff(fact_7018_SigmaD2,axiom,
    ! [A: fun_Pr5098669352780829690e_term,B: produc8923325533196201883nteger,A2: set_fu8280898353253485872e_term,B4: fun_fu5971215405379524186nteger] :
      ( member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A),B),produc5453309460576862807nteger(A2,B4))
     => member157494554546826820nteger(B,aa_fun6394921419180517443nteger(B4,A)) ) ).

% SigmaD2
tff(fact_7019_SigmaD2,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,B: produc3658429121746597890et_nat,A2: set_fu3555266933746557007_nat_o,B4: fun_fu2890809920214373946et_nat] :
      ( member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A),B),produc6971759541029228329et_nat(A2,B4))
     => member6260224972018164377et_nat(B,aa_fun786139119071955819et_nat(B4,A)) ) ).

% SigmaD2
tff(fact_7020_SigmaD2,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,B: produc8799533983703829792et_nat,A2: set_fu3555266933746557007_nat_o,B4: fun_fu8357309440898100312et_nat] :
      ( member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A),B),produc5673588578087545031et_nat(A2,B4))
     => member4513763875858039863et_nat(B,aa_fun4924015400185905801et_nat(B4,A)) ) ).

% SigmaD2
tff(fact_7021_SigmaD2,axiom,
    ! [A: fun_Pr7763680713840462443e_term,B: product_prod_int_int,A2: set_fu5653557704672872225e_term,B4: fun_fu4219362280553733319nt_int] :
      ( member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,A),B),produc3974764367135812292nt_int(A2,B4))
     => member5262025264175285858nt_int(B,aa_fun2513960992105274800nt_int(B4,A)) ) ).

% SigmaD2
tff(fact_7022_SigmaD2,axiom,
    ! [A: fun_in5730379987311621695e_term,B: product_prod_int_int,A2: set_fu3629540756087427317e_term,B4: fun_fu3472058528428720115nt_int] :
      ( member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A),B),produc1533099051242823152nt_int(A2,B4))
     => member5262025264175285858nt_int(B,aa_fun2636263158522872028nt_int(B4,A)) ) ).

% SigmaD2
tff(fact_7023_SigmaE2,axiom,
    ! [A: $o,B: $o,A2: set_o,B4: fun_o_set_o] :
      ( member7466972457876170832od_o_o(product_Pair_o_o((A),(B)),product_Sigma_o_o(A2,B4))
     => ~ ( member_o((A),A2)
         => ~ member_o((B),aa_o_set_o(B4,(A))) ) ) ).

% SigmaE2
tff(fact_7024_SigmaE2,axiom,
    ! [A: $o,B: nat,A2: set_o,B4: fun_o_set_nat] :
      ( member2802428098988154798_o_nat(product_Pair_o_nat((A),B),product_Sigma_o_nat(A2,B4))
     => ~ ( member_o((A),A2)
         => ~ member_nat(B,aa_o_set_nat(B4,(A))) ) ) ).

% SigmaE2
tff(fact_7025_SigmaE2,axiom,
    ! [A: $o,B: int,A2: set_o,B4: fun_o_set_int] :
      ( member7847949116333733898_o_int(product_Pair_o_int((A),B),product_Sigma_o_int(A2,B4))
     => ~ ( member_o((A),A2)
         => ~ member_int(B,aa_o_set_int(B4,(A))) ) ) ).

% SigmaE2
tff(fact_7026_SigmaE2,axiom,
    ! [A: nat,B: $o,A2: set_nat,B4: fun_nat_set_o] :
      ( member6310962623043647828_nat_o(product_Pair_nat_o(A,(B)),product_Sigma_nat_o(A2,B4))
     => ~ ( member_nat(A,A2)
         => ~ member_o((B),aa_nat_set_o(B4,A)) ) ) ).

% SigmaE2
tff(fact_7027_SigmaE2,axiom,
    ! [A: nat,B: int,A2: set_nat,B4: fun_nat_set_int] :
      ( member4262671552274231302at_int(product_Pair_nat_int(A,B),produc454536836294682310at_int(A2,B4))
     => ~ ( member_nat(A,A2)
         => ~ member_int(B,aa_nat_set_int(B4,A)) ) ) ).

% SigmaE2
tff(fact_7028_SigmaE2,axiom,
    ! [A: int,B: $o,A2: set_int,B4: fun_int_set_o] :
      ( member4489920277610959864_int_o(product_Pair_int_o(A,(B)),product_Sigma_int_o(A2,B4))
     => ~ ( member_int(A,A2)
         => ~ member_o((B),aa_int_set_o(B4,A)) ) ) ).

% SigmaE2
tff(fact_7029_SigmaE2,axiom,
    ! [A: int,B: nat,A2: set_int,B4: fun_int_set_nat] :
      ( member216504246829706758nt_nat(aa_nat8602574874988167631nt_nat(product_Pair_int_nat(A),B),produc1456381018704787142nt_nat(A2,B4))
     => ~ ( member_int(A,A2)
         => ~ member_nat(B,aa_int_set_nat(B4,A)) ) ) ).

% SigmaE2
tff(fact_7030_SigmaE2,axiom,
    ! [A: int,B: int,A2: set_int,B4: fun_int_set_int] :
      ( member5262025264175285858nt_int(aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A),B),produc1453890548195736866nt_int(A2,B4))
     => ~ ( member_int(A,A2)
         => ~ member_int(B,aa_int_set_int(B4,A)) ) ) ).

% SigmaE2
tff(fact_7031_SigmaE2,axiom,
    ! [A: nat,B: nat,A2: set_nat,B4: fun_nat_set_nat] :
      ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B),produc457027306803732586at_nat(A2,B4))
     => ~ ( member_nat(A,A2)
         => ~ member_nat(B,aa_nat_set_nat(B4,A)) ) ) ).

% SigmaE2
tff(fact_7032_SigmaE2,axiom,
    ! [A: product_prod_nat_nat,B: $o,A2: set_Pr1261947904930325089at_nat,B4: fun_Pr8467005832278515962_set_o] :
      ( member2200362271989506215_nat_o(produc855456346497908590_nat_o(A,(B)),produc203973861852599583_nat_o(A2,B4))
     => ~ ( member8440522571783428010at_nat(A,A2)
         => ~ member_o((B),aa_Pro5970036531051701619_set_o(B4,A)) ) ) ).

% SigmaE2
tff(fact_7033_Suc_Orsp,axiom,
    aa_fun_nat_nat_o(aa_fun2341495900663639033_nat_o(bNF_re5653821019739307937at_nat(fequal_nat,fequal_nat),suc),suc) ).

% Suc.rsp
tff(fact_7034_sub_Orsp,axiom,
    bNF_re6378542964492772123um_int(fequal_num,bNF_re1822329894187522285nt_int(fequal_num,fequal_int),aTP_Lamm_nr,aTP_Lamm_nr) ).

% sub.rsp
tff(fact_7035_transfer__rule__numeral,axiom,
    ! [R3: fun_nat_fun_nat_o] :
      ( aa_nat_o(aa_nat_fun_nat_o(R3,zero_zero_nat),zero_zero_nat)
     => ( aa_nat_o(aa_nat_fun_nat_o(R3,one_one_nat),one_one_nat)
       => ( bNF_re5162689864697376059at_nat(R3,bNF_re5653821019739307937at_nat(R3,R3),plus_plus_nat,plus_plus_nat)
         => bNF_re825466652795518005at_nat(fequal_num,R3,numeral_numeral_nat,numeral_numeral_nat) ) ) ) ).

% transfer_rule_numeral
tff(fact_7036_transfer__rule__numeral,axiom,
    ! [R3: fun_nat_fun_int_o] :
      ( aa_int_o(aa_nat_fun_int_o(R3,zero_zero_nat),zero_zero_int)
     => ( aa_int_o(aa_nat_fun_int_o(R3,one_one_nat),one_one_int)
       => ( bNF_re3392879465770906191nt_int(R3,bNF_re6022984109467102297at_int(R3,R3),plus_plus_nat,plus_plus_int)
         => bNF_re822976182286467729at_int(fequal_num,R3,numeral_numeral_nat,numeral_numeral_int) ) ) ) ).

% transfer_rule_numeral
tff(fact_7037_transfer__rule__numeral,axiom,
    ! [R3: fun_na6318815019539281885eger_o] :
      ( aa_Code_integer_o(aa_nat7420681472272698950eger_o(R3,zero_zero_nat),zero_z3403309356797280102nteger)
     => ( aa_Code_integer_o(aa_nat7420681472272698950eger_o(R3,one_one_nat),one_one_Code_integer)
       => ( bNF_re5654810952157900898nteger(R3,bNF_re1599192376174140603nteger(R3,R3),plus_plus_nat,plus_p5714425477246183910nteger)
         => bNF_re6129422230220670146nteger(fequal_num,R3,numeral_numeral_nat,numera6620942414471956472nteger) ) ) ) ).

% transfer_rule_numeral
tff(fact_7038_transfer__rule__numeral,axiom,
    ! [R3: fun_nat_fun_rat_o] :
      ( aa_rat_o(aa_nat_fun_rat_o(R3,zero_zero_nat),zero_zero_rat)
     => ( aa_rat_o(aa_nat_fun_rat_o(R3,one_one_nat),one_one_rat)
       => ( bNF_re1294886888241777491at_rat(R3,bNF_re5790763769214331825at_rat(R3,R3),plus_plus_nat,plus_plus_rat)
         => bNF_re190336592709022269at_rat(fequal_num,R3,numeral_numeral_nat,numeral_numeral_rat) ) ) ) ).

% transfer_rule_numeral
tff(fact_7039_transfer__rule__numeral,axiom,
    ! [R3: fun_na2240068485812228818ural_o] :
      ( aa_Code_natural_o(aa_nat8502700792446211003ural_o(R3,zero_zero_nat),zero_z2226904508553997617atural)
     => ( aa_Code_natural_o(aa_nat8502700792446211003ural_o(R3,one_one_nat),one_one_Code_natural)
       => ( bNF_re1400205106991740995atural(R3,bNF_re3704215830270325841atural(R3,R3),plus_plus_nat,plus_p4538020629002901425atural)
         => bNF_re4953017381977387661atural(fequal_num,R3,numeral_numeral_nat,numera5444537566228673987atural) ) ) ) ).

% transfer_rule_numeral
tff(fact_7040_transfer__rule__numeral,axiom,
    ! [R3: fun_int_fun_nat_o] :
      ( aa_nat_o(aa_int_fun_nat_o(R3,zero_zero_int),zero_zero_nat)
     => ( aa_nat_o(aa_int_fun_nat_o(R3,one_one_int),one_one_nat)
       => ( bNF_re7487286609730949711at_nat(R3,bNF_re4343356799547411545nt_nat(R3,R3),plus_plus_int,plus_plus_nat)
         => bNF_re1824820364696572561nt_nat(fequal_num,R3,numeral_numeral_int,numeral_numeral_nat) ) ) ) ).

% transfer_rule_numeral
tff(fact_7041_transfer__rule__numeral,axiom,
    ! [R3: fun_int_fun_int_o] :
      ( aa_int_o(aa_int_fun_int_o(R3,zero_zero_int),zero_zero_int)
     => ( aa_int_o(aa_int_fun_int_o(R3,one_one_int),one_one_int)
       => ( aa_fun3498034192445020252_int_o(aa_fun3119206668089765047_int_o(bNF_re5717476210804479843nt_int(R3,bNF_re4712519889275205905nt_int(R3,R3)),plus_plus_int),plus_plus_int)
         => aa_fun_num_int_o(aa_fun5980320688621196205_int_o(bNF_re1822329894187522285nt_int(fequal_num,R3),numeral_numeral_int),numeral_numeral_int) ) ) ) ).

% transfer_rule_numeral
tff(fact_7042_transfer__rule__numeral,axiom,
    ! [R3: fun_in4891666191172872833eger_o] :
      ( aa_Code_integer_o(aa_int5993532643906289898eger_o(R3,zero_zero_int),zero_z3403309356797280102nteger)
     => ( aa_Code_integer_o(aa_int5993532643906289898eger_o(R3,one_one_int),one_one_Code_integer)
       => ( bNF_re9130850084932126070nteger(R3,bNF_re3379532845092657523nteger(R3,R3),plus_plus_int,plus_p5714425477246183910nteger)
         => aa_fun5823441391821850086eger_o(aa_fun7362828224538899388eger_o(bNF_re6501075790457514782nteger(fequal_num,R3),numeral_numeral_int),numera6620942414471956472nteger) ) ) ) ).

% transfer_rule_numeral
tff(fact_7043_transfer__rule__numeral,axiom,
    ! [R3: fun_int_fun_rat_o] :
      ( aa_rat_o(aa_int_fun_rat_o(R3,zero_zero_int),zero_zero_rat)
     => ( aa_rat_o(aa_int_fun_rat_o(R3,one_one_int),one_one_rat)
       => ( bNF_re3619483633275351143at_rat(R3,bNF_re4480299549022435433nt_rat(R3,R3),plus_plus_int,plus_plus_rat)
         => bNF_re1189690304610076825nt_rat(fequal_num,R3,numeral_numeral_int,numeral_numeral_rat) ) ) ) ).

% transfer_rule_numeral
tff(fact_7044_transfer__rule__numeral,axiom,
    ! [R3: fun_in812919657445819766ural_o] :
      ( aa_Code_natural_o(aa_int7075551964079801951ural_o(R3,zero_zero_int),zero_z2226904508553997617atural)
     => ( aa_Code_natural_o(aa_int7075551964079801951ural_o(R3,one_one_int),one_one_Code_natural)
       => ( bNF_re4876244239765966167atural(R3,bNF_re5484556299188842761atural(R3,R3),plus_plus_int,plus_p4538020629002901425atural)
         => bNF_re5324670942214232297atural(fequal_num,R3,numeral_numeral_int,numera5444537566228673987atural) ) ) ) ).

% transfer_rule_numeral
tff(fact_7045_uminus__integer_Orsp,axiom,
    aa_fun_int_int_o(aa_fun2545150047610057353_int_o(bNF_re4712519889275205905nt_int(fequal_int,fequal_int),uminus_uminus_int),uminus_uminus_int) ).

% uminus_integer.rsp
tff(fact_7046_integer__of__natural_Orsp,axiom,
    bNF_re6650684261131312217nt_int(fequal_nat,fequal_int,semiri1314217659103216013at_int,semiri1314217659103216013at_int) ).

% integer_of_natural.rsp
tff(fact_7047_natural__of__integer_Orsp,axiom,
    aa_fun_int_nat_o(aa_fun7045208173470077249_nat_o(bNF_re3715656647883201625at_nat(fequal_int,fequal_nat),nat2),nat2) ).

% natural_of_integer.rsp
tff(fact_7048_abs__integer_Orsp,axiom,
    aa_fun_int_int_o(aa_fun2545150047610057353_int_o(bNF_re4712519889275205905nt_int(fequal_int,fequal_int),abs_abs_int),abs_abs_int) ).

% abs_integer.rsp
tff(fact_7049_bit__integer_Orsp,axiom,
    aa_fun8451603854606397830at_o_o(aa_fun527236716413744031at_o_o(bNF_re8347998229424194295_nat_o(fequal_int,fequal_fun_nat_o),bit_se1146084159140164899it_int),bit_se1146084159140164899it_int) ).

% bit_integer.rsp
tff(fact_7050_not__integer_Orsp,axiom,
    aa_fun_int_int_o(aa_fun2545150047610057353_int_o(bNF_re4712519889275205905nt_int(fequal_int,fequal_int),bit_ri7919022796975470100ot_int),bit_ri7919022796975470100ot_int) ).

% not_integer.rsp
tff(fact_7051_sgn__integer_Orsp,axiom,
    aa_fun_int_int_o(aa_fun2545150047610057353_int_o(bNF_re4712519889275205905nt_int(fequal_int,fequal_int),sgn_sgn_int),sgn_sgn_int) ).

% sgn_integer.rsp
tff(fact_7052_mask__integer_Orsp,axiom,
    bNF_re6650684261131312217nt_int(fequal_nat,fequal_int,bit_se2000444600071755411sk_int,bit_se2000444600071755411sk_int) ).

% mask_integer.rsp
tff(fact_7053_mask__natural_Orsp,axiom,
    aa_fun_nat_nat_o(aa_fun2341495900663639033_nat_o(bNF_re5653821019739307937at_nat(fequal_nat,fequal_nat),bit_se2002935070580805687sk_nat),bit_se2002935070580805687sk_nat) ).

% mask_natural.rsp
tff(fact_7054_transfer__rule__of__int,axiom,
    ! [R3: fun_int_fun_int_o] :
      ( aa_int_o(aa_int_fun_int_o(R3,zero_zero_int),zero_zero_int)
     => ( aa_int_o(aa_int_fun_int_o(R3,one_one_int),one_one_int)
       => ( aa_fun3498034192445020252_int_o(aa_fun3119206668089765047_int_o(bNF_re5717476210804479843nt_int(R3,bNF_re4712519889275205905nt_int(R3,R3)),plus_plus_int),plus_plus_int)
         => ( aa_fun_int_int_o(aa_fun2545150047610057353_int_o(bNF_re4712519889275205905nt_int(R3,R3),uminus_uminus_int),uminus_uminus_int)
           => aa_fun_int_int_o(aa_fun2545150047610057353_int_o(bNF_re4712519889275205905nt_int(fequal_int,R3),ring_1_of_int_int),ring_1_of_int_int) ) ) ) ) ).

% transfer_rule_of_int
tff(fact_7055_transfer__rule__of__int,axiom,
    ! [R3: fun_in4891666191172872833eger_o] :
      ( aa_Code_integer_o(aa_int5993532643906289898eger_o(R3,zero_zero_int),zero_z3403309356797280102nteger)
     => ( aa_Code_integer_o(aa_int5993532643906289898eger_o(R3,one_one_int),one_one_Code_integer)
       => ( bNF_re9130850084932126070nteger(R3,bNF_re3379532845092657523nteger(R3,R3),plus_plus_int,plus_p5714425477246183910nteger)
         => ( aa_fun774133186966548707eger_o(aa_fun6864876441520360999eger_o(bNF_re3379532845092657523nteger(R3,R3),uminus_uminus_int),uminus1351360451143612070nteger)
           => bNF_re982302072995117890nteger(fequal_int,R3,ring_1_of_int_int,ring_18347121197199848620nteger) ) ) ) ) ).

% transfer_rule_of_int
tff(fact_7056_transfer__rule__of__int,axiom,
    ! [R3: fun_int_fun_rat_o] :
      ( aa_rat_o(aa_int_fun_rat_o(R3,zero_zero_int),zero_zero_rat)
     => ( aa_rat_o(aa_int_fun_rat_o(R3,one_one_int),one_one_rat)
       => ( bNF_re3619483633275351143at_rat(R3,bNF_re4480299549022435433nt_rat(R3,R3),plus_plus_int,plus_plus_rat)
         => ( aa_fun_rat_rat_o(aa_fun5612491703237866289_rat_o(bNF_re4480299549022435433nt_rat(R3,R3),uminus_uminus_int),uminus_uminus_rat)
           => bNF_re4079880299697760445nt_rat(fequal_int,R3,ring_1_of_int_int,ring_1_of_int_rat) ) ) ) ) ).

% transfer_rule_of_int
tff(fact_7057_transfer__rule__of__int,axiom,
    ! [R3: fun_Co8353275306710069249_int_o] :
      ( aa_int_o(aa_Cod8477617969808203498_int_o(R3,zero_z3403309356797280102nteger),zero_zero_int)
     => ( aa_int_o(aa_Cod8477617969808203498_int_o(R3,one_one_Code_integer),one_one_int)
       => ( bNF_re2755378959209877878nt_int(R3,bNF_re2888858428391045491er_int(R3,R3),plus_p5714425477246183910nteger,plus_plus_int)
         => ( aa_fun_int_int_o(aa_fun4591545111762374183_int_o(bNF_re2888858428391045491er_int(R3,R3),uminus1351360451143612070nteger),uminus_uminus_int)
           => bNF_re343602593470180162er_int(fequal_int,R3,ring_18347121197199848620nteger,ring_1_of_int_int) ) ) ) ) ).

% transfer_rule_of_int
tff(fact_7058_transfer__rule__of__int,axiom,
    ! [R3: fun_Co2081214437782444048eger_o] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,zero_z3403309356797280102nteger),zero_z3403309356797280102nteger)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(R3,one_one_Code_integer),one_one_Code_integer)
       => ( bNF_re9064814426586422153nteger(R3,bNF_re1062419521925302741nteger(R3,R3),plus_p5714425477246183910nteger,plus_p5714425477246183910nteger)
         => ( aa_fun774133186966548707eger_o(aa_fun8448071180471187909eger_o(bNF_re1062419521925302741nteger(R3,R3),uminus1351360451143612070nteger),uminus1351360451143612070nteger)
           => bNF_re1784066744496875891nteger(fequal_int,R3,ring_18347121197199848620nteger,ring_18347121197199848620nteger) ) ) ) ) ).

% transfer_rule_of_int
tff(fact_7059_transfer__rule__of__int,axiom,
    ! [R3: fun_Co625613742390903637_rat_o] :
      ( aa_rat_o(aa_Cod6561327387924323390_rat_o(R3,zero_z3403309356797280102nteger),zero_zero_rat)
     => ( aa_rat_o(aa_Cod6561327387924323390_rat_o(R3,one_one_Code_integer),one_one_rat)
       => ( bNF_re7829844138342828666at_rat(R3,bNF_re4698098036185532619er_rat(R3,R3),plus_p5714425477246183910nteger,plus_plus_rat)
         => ( aa_fun_rat_rat_o(aa_fun7658886767390183119_rat_o(bNF_re4698098036185532619er_rat(R3,R3),uminus1351360451143612070nteger),uminus_uminus_rat)
           => bNF_re8934335040747510510er_rat(fequal_int,R3,ring_18347121197199848620nteger,ring_1_of_int_rat) ) ) ) ) ).

% transfer_rule_of_int
tff(fact_7060_transfer__rule__of__int,axiom,
    ! [R3: fun_rat_fun_int_o] :
      ( aa_int_o(aa_rat_fun_int_o(R3,zero_zero_rat),zero_zero_int)
     => ( aa_int_o(aa_rat_fun_int_o(R3,one_one_rat),one_one_int)
       => ( bNF_re8256098235694157927nt_int(R3,bNF_re5838490730811218025at_int(R3,R3),plus_plus_rat,plus_plus_int)
         => ( aa_fun_int_int_o(aa_fun8551920076545987377_int_o(bNF_re5838490730811218025at_int(R3,R3),uminus_uminus_rat),uminus_uminus_int)
           => bNF_re3396611533439285437at_int(fequal_int,R3,ring_1_of_int_rat,ring_1_of_int_int) ) ) ) ) ).

% transfer_rule_of_int
tff(fact_7061_transfer__rule__of__int,axiom,
    ! [R3: fun_ra1401953663915778005eger_o] :
      ( aa_Code_integer_o(aa_rat2503820116649195070eger_o(R3,zero_zero_rat),zero_z3403309356797280102nteger)
     => ( aa_Code_integer_o(aa_rat2503820116649195070eger_o(R3,one_one_rat),one_one_Code_integer)
       => ( bNF_re10698882459692666nteger(R3,bNF_re2328245411608324299nteger(R3,R3),plus_plus_rat,plus_p5714425477246183910nteger)
         => ( aa_fun774133186966548707eger_o(aa_fun6979613644707851983eger_o(bNF_re2328245411608324299nteger(R3,R3),uminus_uminus_rat),uminus1351360451143612070nteger)
           => bNF_re1382721322319792878nteger(fequal_int,R3,ring_1_of_int_rat,ring_18347121197199848620nteger) ) ) ) ) ).

% transfer_rule_of_int
tff(fact_7062_transfer__rule__of__int,axiom,
    ! [R3: fun_rat_fun_rat_o] :
      ( aa_rat_o(aa_rat_fun_rat_o(R3,zero_zero_rat),zero_zero_rat)
     => ( aa_rat_o(aa_rat_fun_rat_o(R3,one_one_rat),one_one_rat)
       => ( bNF_re6158105658165029227at_rat(R3,bNF_re5606270390558447553at_rat(R3,R3),plus_plus_rat,plus_plus_rat)
         => ( aa_fun_rat_rat_o(aa_fun2395889695319020505_rat_o(bNF_re5606270390558447553at_rat(R3,R3),uminus_uminus_rat),uminus_uminus_rat)
           => bNF_re2763971943861839977at_rat(fequal_int,R3,ring_1_of_int_rat,ring_1_of_int_rat) ) ) ) ) ).

% transfer_rule_of_int
tff(fact_7063_fun_Orel__map_I1_J,axiom,
    ! [Sb: fun_fu7564235448449272366at_o_o,I: fun_fu4001317426178549763_nat_o,X2: fun_int_fun_nat_o,Y: fun_int_fun_nat_o] :
      ( aa_fun8451603854606397830at_o_o(aa_fun527236716413744031at_o_o(bNF_re8347998229424194295_nat_o(fequal_int,Sb),aa_fun16395659681819580_nat_o(aa_fun483808154807695236_nat_o(comp_f697526850294767567_o_int,I),X2)),Y)
    <=> aa_fun8451603854606397830at_o_o(aa_fun527236716413744031at_o_o(bNF_re8347998229424194295_nat_o(fequal_int,aa_fun2763792489458032301at_o_o(aTP_Lamm_yt(Sb),I)),X2),Y) ) ).

% fun.rel_map(1)
tff(fact_7064_fun_Orel__map_I1_J,axiom,
    ! [Sb: fun_fu6699046866436802030_int_o,I: fun_fu3661779633992098115nt_int,X2: fun_in1696471567231710611nt_int,Y: fun_in1696471567231710611nt_int] :
      ( bNF_re4808202430149235895nt_int(fequal_int,Sb,comp_f4771325068212425615nt_int(I,X2),Y)
    <=> bNF_re4808202430149235895nt_int(fequal_int,aa_fun3789280421985926445_int_o(aTP_Lamm_yu(Sb),I),X2,Y) ) ).

% fun.rel_map(1)
tff(fact_7065_fun_Orel__map_I1_J,axiom,
    ! [Sb: fun_fu7677565902479959693_rat_o,I: fun_fu3661779633992098115nt_int,X2: fun_in1696471567231710611nt_int,Y: fun_int_fun_int_rat] :
      ( aa_fun4793272751809872304_rat_o(aa_fun3867120139247291696_rat_o(bNF_re2486238095283335024nt_rat(fequal_int,Sb),comp_f4771325068212425615nt_int(I,X2)),Y)
    <=> aa_fun4793272751809872304_rat_o(aa_fun3867120139247291696_rat_o(bNF_re2486238095283335024nt_rat(fequal_int,aa_fun2399579938715134478_rat_o(aTP_Lamm_yv(Sb),I)),X2),Y) ) ).

% fun.rel_map(1)
tff(fact_7066_fun_Orel__map_I1_J,axiom,
    ! [Sb: fun_fu6971708032831053102nt_o_o,I: fun_fu3883539188510166275_int_o,X2: fun_int_fun_int_o,Y: fun_int_fun_int_o] :
      ( aa_fun227585529652676578nt_o_o(aa_fun1090463484742261919nt_o_o(bNF_re8654322613993568759_int_o(fequal_int,Sb),aa_fun6133342665515662012_int_o(aa_fun508258970086480260_int_o(comp_f2592220016263698127_o_int,I),X2)),Y)
    <=> aa_fun227585529652676578nt_o_o(aa_fun1090463484742261919nt_o_o(bNF_re8654322613993568759_int_o(fequal_int,aa_fun7316249240758406317nt_o_o(aTP_Lamm_yw(Sb),I)),X2),Y) ) ).

% fun.rel_map(1)
tff(fact_7067_fun_Orel__map_I1_J,axiom,
    ! [Sb: fun_fu4208408993564413984_int_o,I: fun_fu1143798476471108391nt_int,X2: fun_int_fun_int_int,Y: fun_int_fun_int_int] :
      ( aa_fun3498034192445020252_int_o(aa_fun3119206668089765047_int_o(bNF_re5717476210804479843nt_int(fequal_int,Sb),comp_f8169149803026727611nt_int(I,X2)),Y)
    <=> aa_fun3498034192445020252_int_o(aa_fun3119206668089765047_int_o(bNF_re5717476210804479843nt_int(fequal_int,aa_fun6233912309721051003_int_o(aTP_Lamm_yx(Sb),I)),X2),Y) ) ).

% fun.rel_map(1)
tff(fact_7068_fun_Orel__map_I2_J,axiom,
    ! [Sa: fun_fu7564235448449272366at_o_o,X2: fun_int_fun_nat_o,G: fun_fu4001317426178549763_nat_o,Y: fun_int_fun_nat_o] :
      ( aa_fun8451603854606397830at_o_o(aa_fun527236716413744031at_o_o(bNF_re8347998229424194295_nat_o(fequal_int,Sa),X2),aa_fun16395659681819580_nat_o(aa_fun483808154807695236_nat_o(comp_f697526850294767567_o_int,G),Y))
    <=> aa_fun8451603854606397830at_o_o(aa_fun527236716413744031at_o_o(bNF_re8347998229424194295_nat_o(fequal_int,aa_fun2763792489458032301at_o_o(aTP_Lamm_yy(Sa),G)),X2),Y) ) ).

% fun.rel_map(2)
tff(fact_7069_fun_Orel__map_I2_J,axiom,
    ! [Sa: fun_fu6699046866436802030_int_o,X2: fun_in1696471567231710611nt_int,G: fun_fu3661779633992098115nt_int,Y: fun_in1696471567231710611nt_int] :
      ( bNF_re4808202430149235895nt_int(fequal_int,Sa,X2,comp_f4771325068212425615nt_int(G,Y))
    <=> bNF_re4808202430149235895nt_int(fequal_int,aa_fun3789280421985926445_int_o(aTP_Lamm_yz(Sa),G),X2,Y) ) ).

% fun.rel_map(2)
tff(fact_7070_fun_Orel__map_I2_J,axiom,
    ! [Sa: fun_fu6699046866436802030_int_o,X2: fun_in1696471567231710611nt_int,G: fun_fu4522195968571808382nt_int,Y: fun_int_fun_int_rat] :
      ( bNF_re4808202430149235895nt_int(fequal_int,Sa,X2,comp_f647079087388013614nt_int(G,Y))
    <=> aa_fun4793272751809872304_rat_o(aa_fun3867120139247291696_rat_o(bNF_re2486238095283335024nt_rat(fequal_int,aa_fun4351174416053881551_rat_o(aTP_Lamm_za(Sa),G)),X2),Y) ) ).

% fun.rel_map(2)
tff(fact_7071_fun_Orel__map_I2_J,axiom,
    ! [Sa: fun_fu7677565902479959693_rat_o,X2: fun_in1696471567231710611nt_int,G: fun_fu7460908759652350970nt_rat,Y: fun_in1696471567231710611nt_int] :
      ( aa_fun4793272751809872304_rat_o(aa_fun3867120139247291696_rat_o(bNF_re2486238095283335024nt_rat(fequal_int,Sa),X2),comp_f5638830786481540082at_int(G,Y))
    <=> bNF_re4808202430149235895nt_int(fequal_int,aa_fun8496196461586942128_int_o(aTP_Lamm_zb(Sa),G),X2,Y) ) ).

% fun.rel_map(2)
tff(fact_7072_fun_Orel__map_I2_J,axiom,
    ! [Sa: fun_fu7677565902479959693_rat_o,X2: fun_in1696471567231710611nt_int,G: fun_fu1008360527747082367nt_rat,Y: fun_int_fun_int_rat] :
      ( aa_fun4793272751809872304_rat_o(aa_fun3867120139247291696_rat_o(bNF_re2486238095283335024nt_rat(fequal_int,Sa),X2),comp_f5789916732873203219at_int(G,Y))
    <=> aa_fun4793272751809872304_rat_o(aa_fun3867120139247291696_rat_o(bNF_re2486238095283335024nt_rat(fequal_int,aa_fun8956737304536474314_rat_o(aTP_Lamm_zc(Sa),G)),X2),Y) ) ).

% fun.rel_map(2)
tff(fact_7073_fun_Orel__map_I2_J,axiom,
    ! [Sa: fun_fu6971708032831053102nt_o_o,X2: fun_int_fun_int_o,G: fun_fu3883539188510166275_int_o,Y: fun_int_fun_int_o] :
      ( aa_fun227585529652676578nt_o_o(aa_fun1090463484742261919nt_o_o(bNF_re8654322613993568759_int_o(fequal_int,Sa),X2),aa_fun6133342665515662012_int_o(aa_fun508258970086480260_int_o(comp_f2592220016263698127_o_int,G),Y))
    <=> aa_fun227585529652676578nt_o_o(aa_fun1090463484742261919nt_o_o(bNF_re8654322613993568759_int_o(fequal_int,aa_fun7316249240758406317nt_o_o(aTP_Lamm_zd(Sa),G)),X2),Y) ) ).

% fun.rel_map(2)
tff(fact_7074_fun_Orel__map_I2_J,axiom,
    ! [Sa: fun_fu4208408993564413984_int_o,X2: fun_int_fun_int_int,G: fun_fu1143798476471108391nt_int,Y: fun_int_fun_int_int] :
      ( aa_fun3498034192445020252_int_o(aa_fun3119206668089765047_int_o(bNF_re5717476210804479843nt_int(fequal_int,Sa),X2),comp_f8169149803026727611nt_int(G,Y))
    <=> aa_fun3498034192445020252_int_o(aa_fun3119206668089765047_int_o(bNF_re5717476210804479843nt_int(fequal_int,aa_fun6233912309721051003_int_o(aTP_Lamm_ze(Sa),G)),X2),Y) ) ).

% fun.rel_map(2)
tff(fact_7075_times__eq__iff,axiom,
    ! [A2: set_o,B4: set_o,C4: set_o,D3: set_o] :
      ( ( product_Sigma_o_o(A2,aTP_Lamm_xs(B4)) = product_Sigma_o_o(C4,aTP_Lamm_xs(D3)) )
    <=> ( ( ( A2 = C4 )
          & ( B4 = D3 ) )
        | ( ( ( A2 = bot_bot_set_o )
            | ( B4 = bot_bot_set_o ) )
          & ( ( C4 = bot_bot_set_o )
            | ( D3 = bot_bot_set_o ) ) ) ) ) ).

% times_eq_iff
tff(fact_7076_times__eq__iff,axiom,
    ! [A2: set_o,B4: set_nat,C4: set_o,D3: set_nat] :
      ( ( product_Sigma_o_nat(A2,aTP_Lamm_xt(B4)) = product_Sigma_o_nat(C4,aTP_Lamm_xt(D3)) )
    <=> ( ( ( A2 = C4 )
          & ( B4 = D3 ) )
        | ( ( ( A2 = bot_bot_set_o )
            | ( B4 = bot_bot_set_nat ) )
          & ( ( C4 = bot_bot_set_o )
            | ( D3 = bot_bot_set_nat ) ) ) ) ) ).

% times_eq_iff
tff(fact_7077_times__eq__iff,axiom,
    ! [A2: set_o,B4: set_int,C4: set_o,D3: set_int] :
      ( ( product_Sigma_o_int(A2,aTP_Lamm_xu(B4)) = product_Sigma_o_int(C4,aTP_Lamm_xu(D3)) )
    <=> ( ( ( A2 = C4 )
          & ( B4 = D3 ) )
        | ( ( ( A2 = bot_bot_set_o )
            | ( B4 = bot_bot_set_int ) )
          & ( ( C4 = bot_bot_set_o )
            | ( D3 = bot_bot_set_int ) ) ) ) ) ).

% times_eq_iff
tff(fact_7078_times__eq__iff,axiom,
    ! [A2: set_nat,B4: set_o,C4: set_nat,D3: set_o] :
      ( ( product_Sigma_nat_o(A2,aTP_Lamm_xv(B4)) = product_Sigma_nat_o(C4,aTP_Lamm_xv(D3)) )
    <=> ( ( ( A2 = C4 )
          & ( B4 = D3 ) )
        | ( ( ( A2 = bot_bot_set_nat )
            | ( B4 = bot_bot_set_o ) )
          & ( ( C4 = bot_bot_set_nat )
            | ( D3 = bot_bot_set_o ) ) ) ) ) ).

% times_eq_iff
tff(fact_7079_times__eq__iff,axiom,
    ! [A2: set_nat,B4: set_nat,C4: set_nat,D3: set_nat] :
      ( ( produc457027306803732586at_nat(A2,aTP_Lamm_ya(B4)) = produc457027306803732586at_nat(C4,aTP_Lamm_ya(D3)) )
    <=> ( ( ( A2 = C4 )
          & ( B4 = D3 ) )
        | ( ( ( A2 = bot_bot_set_nat )
            | ( B4 = bot_bot_set_nat ) )
          & ( ( C4 = bot_bot_set_nat )
            | ( D3 = bot_bot_set_nat ) ) ) ) ) ).

% times_eq_iff
tff(fact_7080_times__eq__iff,axiom,
    ! [A2: set_nat,B4: set_int,C4: set_nat,D3: set_int] :
      ( ( produc454536836294682310at_int(A2,aTP_Lamm_xw(B4)) = produc454536836294682310at_int(C4,aTP_Lamm_xw(D3)) )
    <=> ( ( ( A2 = C4 )
          & ( B4 = D3 ) )
        | ( ( ( A2 = bot_bot_set_nat )
            | ( B4 = bot_bot_set_int ) )
          & ( ( C4 = bot_bot_set_nat )
            | ( D3 = bot_bot_set_int ) ) ) ) ) ).

% times_eq_iff
tff(fact_7081_times__eq__iff,axiom,
    ! [A2: set_int,B4: set_o,C4: set_int,D3: set_o] :
      ( ( product_Sigma_int_o(A2,aTP_Lamm_xx(B4)) = product_Sigma_int_o(C4,aTP_Lamm_xx(D3)) )
    <=> ( ( ( A2 = C4 )
          & ( B4 = D3 ) )
        | ( ( ( A2 = bot_bot_set_int )
            | ( B4 = bot_bot_set_o ) )
          & ( ( C4 = bot_bot_set_int )
            | ( D3 = bot_bot_set_o ) ) ) ) ) ).

% times_eq_iff
tff(fact_7082_times__eq__iff,axiom,
    ! [A2: set_int,B4: set_nat,C4: set_int,D3: set_nat] :
      ( ( produc1456381018704787142nt_nat(A2,aTP_Lamm_xy(B4)) = produc1456381018704787142nt_nat(C4,aTP_Lamm_xy(D3)) )
    <=> ( ( ( A2 = C4 )
          & ( B4 = D3 ) )
        | ( ( ( A2 = bot_bot_set_int )
            | ( B4 = bot_bot_set_nat ) )
          & ( ( C4 = bot_bot_set_int )
            | ( D3 = bot_bot_set_nat ) ) ) ) ) ).

% times_eq_iff
tff(fact_7083_times__eq__iff,axiom,
    ! [A2: set_int,B4: set_int,C4: set_int,D3: set_int] :
      ( ( produc1453890548195736866nt_int(A2,aTP_Lamm_xz(B4)) = produc1453890548195736866nt_int(C4,aTP_Lamm_xz(D3)) )
    <=> ( ( ( A2 = C4 )
          & ( B4 = D3 ) )
        | ( ( ( A2 = bot_bot_set_int )
            | ( B4 = bot_bot_set_int ) )
          & ( ( C4 = bot_bot_set_int )
            | ( D3 = bot_bot_set_int ) ) ) ) ) ).

% times_eq_iff
tff(fact_7084_times__eq__iff,axiom,
    ! [A2: set_Pr1261947904930325089at_nat,B4: set_o,C4: set_Pr1261947904930325089at_nat,D3: set_o] :
      ( ( produc203973861852599583_nat_o(A2,aTP_Lamm_yb(B4)) = produc203973861852599583_nat_o(C4,aTP_Lamm_yb(D3)) )
    <=> ( ( ( A2 = C4 )
          & ( B4 = D3 ) )
        | ( ( ( A2 = bot_bo2099793752762293965at_nat )
            | ( B4 = bot_bot_set_o ) )
          & ( ( C4 = bot_bo2099793752762293965at_nat )
            | ( D3 = bot_bot_set_o ) ) ) ) ) ).

% times_eq_iff
tff(fact_7085_dup_Orsp,axiom,
    aa_fun_int_int_o(aa_fun2545150047610057353_int_o(bNF_re4712519889275205905nt_int(fequal_int,fequal_int),aTP_Lamm_ni),aTP_Lamm_ni) ).

% dup.rsp
tff(fact_7086_Collect__case__prod__Sigma,axiom,
    ! [P: fun_nat_o,Q: fun_nat_fun_nat_o] : aa_fun7046812543386002057at_nat(collec3392354462482085612at_nat,aa_fun7564604662015400456_nat_o(produc6081775807080527818_nat_o,aa_fun6699960423209655484_nat_o(aTP_Lamm_zf(P),Q))) = produc457027306803732586at_nat(collect_nat(P),aTP_Lamm_zg(Q)) ).

% Collect_case_prod_Sigma
tff(fact_7087_Collect__case__prod__Sigma,axiom,
    ! [P: fun_nat_o,Q: fun_na7234455742697417626_nat_o] : collec1907656820224499068st_nat(produc5265810065896090426_nat_o(aa_fun6745918892298368316_nat_o(aTP_Lamm_zh(P),Q))) = produc5227933103413159546st_nat(collect_nat(P),aTP_Lamm_zi(Q)) ).

% Collect_case_prod_Sigma
tff(fact_7088_Collect__case__prod__Sigma,axiom,
    ! [P: fun_list_nat_o,Q: fun_li2421049240157457050_nat_o] : collec8096645339561496572at_nat(produc7308574044827705018_nat_o(aa_fun6275404141584987452_nat_o(aTP_Lamm_zj(P),Q))) = produc7466890150575444730at_nat(collect_list_nat(P),aTP_Lamm_zk(Q)) ).

% Collect_case_prod_Sigma
tff(fact_7089_Collect__case__prod__Sigma,axiom,
    ! [P: fun_list_nat_o,Q: fun_li1025265955262268170_nat_o] : collec1570431334306492044st_nat(produc6382697403170970154_nat_o(aa_fun6462763351938039228_nat_o(aTP_Lamm_zl(P),Q))) = produc6850429418872557834st_nat(collect_list_nat(P),aTP_Lamm_zm(Q)) ).

% Collect_case_prod_Sigma
tff(fact_7090_apsnd__apfst__commute,axiom,
    ! [F: fun_Co8499238673658658103nteger,G: fun_Co8499238673658658103nteger,P2: produc8923325533196201883nteger] : aa_Pro4693618923521437820nteger(aa_fun2509385170507305080nteger(produc6499014454317279255nteger,F),aa_Pro4693618923521437820nteger(aa_fun2509385170507305080nteger(produc3195571438000033749nteger,G),P2)) = aa_Pro4693618923521437820nteger(aa_fun2509385170507305080nteger(produc3195571438000033749nteger,G),aa_Pro4693618923521437820nteger(aa_fun2509385170507305080nteger(produc6499014454317279255nteger,F),P2)) ).

% apsnd_apfst_commute
tff(fact_7091_gcd__add__mult,axiom,
    ! [M: nat,K: nat,N2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(gcd_gcd_nat,M),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,K),M)),N2)) = aa_nat_nat(aa_nat_fun_nat_nat(gcd_gcd_nat,M),N2) ).

% gcd_add_mult
tff(fact_7092_gcd__add__mult,axiom,
    ! [M: int,K: int,N2: int] : aa_int_int(aa_int_fun_int_int(gcd_gcd_int,M),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,K),M)),N2)) = aa_int_int(aa_int_fun_int_int(gcd_gcd_int,M),N2) ).

% gcd_add_mult
tff(fact_7093_Sigma__mono,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,C4: set_Pr4329608150637261639at_nat,B4: fun_Pr6764980218223570944et_nat,D3: fun_Pr6764980218223570944et_nat] :
      ( ord_le1268244103169919719at_nat(A2,C4)
     => ( ! [X3: produc3843707927480180839at_nat] :
            ( member8757157785044589968at_nat(X3,A2)
           => aa_set_nat_o(ord_less_eq_set_nat(aa_Pro1692590229789857841et_nat(B4,X3)),aa_Pro1692590229789857841et_nat(D3,X3)) )
       => ord_le2145644191787020796at_nat(produc1095920968030776047at_nat(A2,B4),produc1095920968030776047at_nat(C4,D3)) ) ) ).

% Sigma_mono
tff(fact_7094_Sigma__mono,axiom,
    ! [A2: set_Pr1261947904930325089at_nat,C4: set_Pr1261947904930325089at_nat,B4: fun_Pr9038118721296872730et_nat,D3: fun_Pr9038118721296872730et_nat] :
      ( aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(ord_le3146513528884898305at_nat,A2),C4)
     => ( ! [X3: product_prod_nat_nat] :
            ( member8440522571783428010at_nat(X3,A2)
           => aa_set_nat_o(ord_less_eq_set_nat(aa_Pro9123573313595863371et_nat(B4,X3)),aa_Pro9123573313595863371et_nat(D3,X3)) )
       => ord_le7094820750414311574at_nat(produc7672662199629908489at_nat(A2,B4),produc7672662199629908489at_nat(C4,D3)) ) ) ).

% Sigma_mono
tff(fact_7095_Sigma__mono,axiom,
    ! [A2: set_o,C4: set_o,B4: fun_o_set_nat,D3: fun_o_set_nat] :
      ( ord_less_eq_set_o(A2,C4)
     => ( ! [X3: $o] :
            ( member_o((X3),A2)
           => aa_set_nat_o(ord_less_eq_set_nat(aa_o_set_nat(B4,(X3))),aa_o_set_nat(D3,(X3))) )
       => ord_le6472378536984071597_o_nat(product_Sigma_o_nat(A2,B4),product_Sigma_o_nat(C4,D3)) ) ) ).

% Sigma_mono
tff(fact_7096_Sigma__mono,axiom,
    ! [A2: set_int,C4: set_int,B4: fun_int_set_nat,D3: fun_int_set_nat] :
      ( ord_less_eq_set_int(A2,C4)
     => ( ! [X3: int] :
            ( member_int(X3,A2)
           => aa_set_nat_o(ord_less_eq_set_nat(aa_int_set_nat(B4,X3)),aa_int_set_nat(D3,X3)) )
       => ord_le5333435103577920093nt_nat(produc1456381018704787142nt_nat(A2,B4),produc1456381018704787142nt_nat(C4,D3)) ) ) ).

% Sigma_mono
tff(fact_7097_Sigma__mono,axiom,
    ! [A2: set_nat,C4: set_nat,B4: fun_nat_set_nat,D3: fun_nat_set_nat] :
      ( aa_set_nat_o(ord_less_eq_set_nat(A2),C4)
     => ( ! [X3: nat] :
            ( member_nat(X3,A2)
           => aa_set_nat_o(ord_less_eq_set_nat(aa_nat_set_nat(B4,X3)),aa_nat_set_nat(D3,X3)) )
       => aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(ord_le3146513528884898305at_nat,produc457027306803732586at_nat(A2,B4)),produc457027306803732586at_nat(C4,D3)) ) ) ).

% Sigma_mono
tff(fact_7098_bezout__int,axiom,
    ! [X2: int,Y: int] :
    ? [U2: int,V4: int] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,U2),X2)),aa_int_int(aa_int_fun_int_int(times_times_int,V4),Y)) = aa_int_int(aa_int_fun_int_int(gcd_gcd_int,X2),Y) ).

% bezout_int
tff(fact_7099_Times__subset__cancel2,axiom,
    ! [X2: produc3843707927480180839at_nat,C4: set_Pr4329608150637261639at_nat,A2: set_nat,B4: set_nat] :
      ( member8757157785044589968at_nat(X2,C4)
     => ( ord_le3218026494883419554at_nat(produc396409126344608333at_nat(A2,aTP_Lamm_zn(C4)),produc396409126344608333at_nat(B4,aTP_Lamm_zn(C4)))
      <=> aa_set_nat_o(ord_less_eq_set_nat(A2),B4) ) ) ).

% Times_subset_cancel2
tff(fact_7100_Times__subset__cancel2,axiom,
    ! [X2: product_prod_nat_nat,C4: set_Pr1261947904930325089at_nat,A2: set_nat,B4: set_nat] :
      ( member8440522571783428010at_nat(X2,C4)
     => ( ord_le3050193496395145148at_nat(produc1809337555817847783at_nat(A2,aTP_Lamm_zo(C4)),produc1809337555817847783at_nat(B4,aTP_Lamm_zo(C4)))
      <=> aa_set_nat_o(ord_less_eq_set_nat(A2),B4) ) ) ).

% Times_subset_cancel2
tff(fact_7101_Times__subset__cancel2,axiom,
    ! [X2: $o,C4: set_o,A2: set_nat,B4: set_nat] :
      ( member_o((X2),C4)
     => ( ord_le7519981659162375251_nat_o(product_Sigma_nat_o(A2,aTP_Lamm_xv(C4)),product_Sigma_nat_o(B4,aTP_Lamm_xv(C4)))
      <=> aa_set_nat_o(ord_less_eq_set_nat(A2),B4) ) ) ).

% Times_subset_cancel2
tff(fact_7102_Times__subset__cancel2,axiom,
    ! [X2: nat,C4: set_nat,A2: set_nat,B4: set_nat] :
      ( member_nat(X2,C4)
     => ( aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(ord_le3146513528884898305at_nat,produc457027306803732586at_nat(A2,aTP_Lamm_ya(C4))),produc457027306803732586at_nat(B4,aTP_Lamm_ya(C4)))
      <=> aa_set_nat_o(ord_less_eq_set_nat(A2),B4) ) ) ).

% Times_subset_cancel2
tff(fact_7103_Times__subset__cancel2,axiom,
    ! [X2: int,C4: set_int,A2: set_nat,B4: set_nat] :
      ( member_int(X2,C4)
     => ( ord_le656430383953171549at_int(produc454536836294682310at_int(A2,aTP_Lamm_xw(C4)),produc454536836294682310at_int(B4,aTP_Lamm_xw(C4)))
      <=> aa_set_nat_o(ord_less_eq_set_nat(A2),B4) ) ) ).

% Times_subset_cancel2
tff(fact_7104_UN__Times__distrib,axiom,
    ! [E3: fun_nat_set_nat,F4: fun_nat_set_nat,A2: set_nat,B4: set_nat] : comple5685304695842803022at_nat(aa_set6242432332095302236at_nat(image_5423882813909314213at_nat(produc8197505143624133779at_nat(aa_fun2373699841287868962at_nat(aTP_Lamm_zq(E3),F4))),produc457027306803732586at_nat(A2,aTP_Lamm_ya(B4)))) = produc457027306803732586at_nat(comple7399068483239264473et_nat(image_nat_set_nat(E3,A2)),aa_set562305657478724375et_nat(aTP_Lamm_zr(F4),B4)) ).

% UN_Times_distrib
tff(fact_7105_mem__Times__iff,axiom,
    ! [X2: product_prod_o_o,A2: set_o,B4: set_o] :
      ( member7466972457876170832od_o_o(X2,product_Sigma_o_o(A2,aTP_Lamm_xs(B4)))
    <=> ( member_o(aa_Pro2802791181778974573_o_o_o(product_fst_o_o,X2),A2)
        & member_o(aa_Pro2802791181778974573_o_o_o(product_snd_o_o,X2),B4) ) ) ).

% mem_Times_iff
tff(fact_7106_mem__Times__iff,axiom,
    ! [X2: product_prod_o_nat,A2: set_o,B4: set_nat] :
      ( member2802428098988154798_o_nat(X2,product_Sigma_o_nat(A2,aTP_Lamm_xt(B4)))
    <=> ( member_o(aa_Pro5092300983057929219_nat_o(product_fst_o_nat,X2),A2)
        & member_nat(aa_Pro7345537496369368101at_nat(product_snd_o_nat,X2),B4) ) ) ).

% mem_Times_iff
tff(fact_7107_mem__Times__iff,axiom,
    ! [X2: product_prod_o_int,A2: set_o,B4: set_int] :
      ( member7847949116333733898_o_int(X2,product_Sigma_o_int(A2,aTP_Lamm_xu(B4)))
    <=> ( member_o(aa_Pro2847156015387483303_int_o(product_fst_o_int,X2),A2)
        & member_int(aa_Pro306596563698563805nt_int(product_snd_o_int,X2),B4) ) ) ).

% mem_Times_iff
tff(fact_7108_mem__Times__iff,axiom,
    ! [X2: product_prod_nat_o,A2: set_nat,B4: set_o] :
      ( member6310962623043647828_nat_o(X2,product_Sigma_nat_o(A2,aTP_Lamm_xv(B4)))
    <=> ( member_nat(aa_Pro1863436886664842699_o_nat(product_fst_nat_o,X2),A2)
        & member_o(aa_Pro4464983059765771485at_o_o(product_snd_nat_o,X2),B4) ) ) ).

% mem_Times_iff
tff(fact_7109_mem__Times__iff,axiom,
    ! [X2: product_prod_nat_int,A2: set_nat,B4: set_int] :
      ( member4262671552274231302at_int(X2,produc454536836294682310at_int(A2,aTP_Lamm_xw(B4)))
    <=> ( member_nat(aa_Pro6430095344737419761nt_nat(product_fst_nat_int,X2),A2)
        & member_int(aa_Pro6427604874228369485nt_int(product_snd_nat_int,X2),B4) ) ) ).

% mem_Times_iff
tff(fact_7110_mem__Times__iff,axiom,
    ! [X2: product_prod_int_o,A2: set_int,B4: set_o] :
      ( member4489920277610959864_int_o(X2,product_Sigma_int_o(A2,aTP_Lamm_xx(B4)))
    <=> ( member_int(aa_Pro2547522449196342987_o_int(product_fst_int_o,X2),A2)
        & member_o(aa_Pro2548170440803795257nt_o_o(product_snd_int_o,X2),B4) ) ) ).

% mem_Times_iff
tff(fact_7111_mem__Times__iff,axiom,
    ! [X2: product_prod_int_nat,A2: set_int,B4: set_nat] :
      ( member216504246829706758nt_nat(X2,produc1456381018704787142nt_nat(A2,aTP_Lamm_xy(B4)))
    <=> ( member_int(aa_Pro4612336859772192333at_int(product_fst_int_nat,X2),A2)
        & member_nat(aa_Pro4614827330281242609at_nat(product_snd_int_nat,X2),B4) ) ) ).

% mem_Times_iff
tff(fact_7112_mem__Times__iff,axiom,
    ! [X2: product_prod_nat_nat,A2: set_nat,B4: set_nat] :
      ( member8440522571783428010at_nat(X2,produc457027306803732586at_nat(A2,aTP_Lamm_ya(B4)))
    <=> ( member_nat(aa_Pro4243173770044397973at_nat(product_fst_nat_nat,X2),A2)
        & member_nat(aa_Pro4243173770044397973at_nat(product_snd_nat_nat,X2),B4) ) ) ).

% mem_Times_iff
tff(fact_7113_mem__Times__iff,axiom,
    ! [X2: produc8923325533196201883nteger,A2: set_Code_integer,B4: set_Code_integer] :
      ( member157494554546826820nteger(X2,produc5882431272649516420nteger(A2,aTP_Lamm_ys(B4)))
    <=> ( member_Code_integer(aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,X2),A2)
        & member_Code_integer(aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,X2),B4) ) ) ).

% mem_Times_iff
tff(fact_7114_mem__Times__iff,axiom,
    ! [X2: product_prod_int_int,A2: set_int,B4: set_int] :
      ( member5262025264175285858nt_int(X2,produc1453890548195736866nt_int(A2,aTP_Lamm_xz(B4)))
    <=> ( member_int(aa_Pro6799258434465214121nt_int(product_fst_int_int,X2),A2)
        & member_int(aa_Pro6799258434465214121nt_int(product_snd_int_int,X2),B4) ) ) ).

% mem_Times_iff
tff(fact_7115_in__prod__fst__sndI,axiom,
    ! [X2: product_prod_o_o,A2: set_o,B4: set_o] :
      ( member_o(aa_Pro2802791181778974573_o_o_o(product_fst_o_o,X2),A2)
     => ( member_o(aa_Pro2802791181778974573_o_o_o(product_snd_o_o,X2),B4)
       => member7466972457876170832od_o_o(X2,product_Sigma_o_o(A2,aTP_Lamm_xs(B4))) ) ) ).

% in_prod_fst_sndI
tff(fact_7116_in__prod__fst__sndI,axiom,
    ! [X2: product_prod_o_nat,A2: set_o,B4: set_nat] :
      ( member_o(aa_Pro5092300983057929219_nat_o(product_fst_o_nat,X2),A2)
     => ( member_nat(aa_Pro7345537496369368101at_nat(product_snd_o_nat,X2),B4)
       => member2802428098988154798_o_nat(X2,product_Sigma_o_nat(A2,aTP_Lamm_xt(B4))) ) ) ).

% in_prod_fst_sndI
tff(fact_7117_in__prod__fst__sndI,axiom,
    ! [X2: product_prod_o_int,A2: set_o,B4: set_int] :
      ( member_o(aa_Pro2847156015387483303_int_o(product_fst_o_int,X2),A2)
     => ( member_int(aa_Pro306596563698563805nt_int(product_snd_o_int,X2),B4)
       => member7847949116333733898_o_int(X2,product_Sigma_o_int(A2,aTP_Lamm_xu(B4))) ) ) ).

% in_prod_fst_sndI
tff(fact_7118_in__prod__fst__sndI,axiom,
    ! [X2: product_prod_nat_o,A2: set_nat,B4: set_o] :
      ( member_nat(aa_Pro1863436886664842699_o_nat(product_fst_nat_o,X2),A2)
     => ( member_o(aa_Pro4464983059765771485at_o_o(product_snd_nat_o,X2),B4)
       => member6310962623043647828_nat_o(X2,product_Sigma_nat_o(A2,aTP_Lamm_xv(B4))) ) ) ).

% in_prod_fst_sndI
tff(fact_7119_in__prod__fst__sndI,axiom,
    ! [X2: product_prod_nat_nat,A2: set_nat,B4: set_nat] :
      ( member_nat(aa_Pro4243173770044397973at_nat(product_fst_nat_nat,X2),A2)
     => ( member_nat(aa_Pro4243173770044397973at_nat(product_snd_nat_nat,X2),B4)
       => member8440522571783428010at_nat(X2,produc457027306803732586at_nat(A2,aTP_Lamm_ya(B4))) ) ) ).

% in_prod_fst_sndI
tff(fact_7120_in__prod__fst__sndI,axiom,
    ! [X2: product_prod_nat_int,A2: set_nat,B4: set_int] :
      ( member_nat(aa_Pro6430095344737419761nt_nat(product_fst_nat_int,X2),A2)
     => ( member_int(aa_Pro6427604874228369485nt_int(product_snd_nat_int,X2),B4)
       => member4262671552274231302at_int(X2,produc454536836294682310at_int(A2,aTP_Lamm_xw(B4))) ) ) ).

% in_prod_fst_sndI
tff(fact_7121_in__prod__fst__sndI,axiom,
    ! [X2: product_prod_int_o,A2: set_int,B4: set_o] :
      ( member_int(aa_Pro2547522449196342987_o_int(product_fst_int_o,X2),A2)
     => ( member_o(aa_Pro2548170440803795257nt_o_o(product_snd_int_o,X2),B4)
       => member4489920277610959864_int_o(X2,product_Sigma_int_o(A2,aTP_Lamm_xx(B4))) ) ) ).

% in_prod_fst_sndI
tff(fact_7122_in__prod__fst__sndI,axiom,
    ! [X2: product_prod_int_nat,A2: set_int,B4: set_nat] :
      ( member_int(aa_Pro4612336859772192333at_int(product_fst_int_nat,X2),A2)
     => ( member_nat(aa_Pro4614827330281242609at_nat(product_snd_int_nat,X2),B4)
       => member216504246829706758nt_nat(X2,produc1456381018704787142nt_nat(A2,aTP_Lamm_xy(B4))) ) ) ).

% in_prod_fst_sndI
tff(fact_7123_in__prod__fst__sndI,axiom,
    ! [X2: produc8923325533196201883nteger,A2: set_Code_integer,B4: set_Code_integer] :
      ( member_Code_integer(aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,X2),A2)
     => ( member_Code_integer(aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,X2),B4)
       => member157494554546826820nteger(X2,produc5882431272649516420nteger(A2,aTP_Lamm_ys(B4))) ) ) ).

% in_prod_fst_sndI
tff(fact_7124_in__prod__fst__sndI,axiom,
    ! [X2: product_prod_int_int,A2: set_int,B4: set_int] :
      ( member_int(aa_Pro6799258434465214121nt_int(product_fst_int_int,X2),A2)
     => ( member_int(aa_Pro6799258434465214121nt_int(product_snd_int_int,X2),B4)
       => member5262025264175285858nt_int(X2,produc1453890548195736866nt_int(A2,aTP_Lamm_xz(B4))) ) ) ).

% in_prod_fst_sndI
tff(fact_7125_swap__product,axiom,
    ! [A2: set_Pr4811707699266497531nteger,B4: set_fu8280898353253485872e_term] : image_3617234230432879585nteger(produc1137639668546780417nteger(aTP_Lamm_um),produc6630550384232064845e_term(A2,aTP_Lamm_zs(B4))) = produc5453309460576862807nteger(B4,aTP_Lamm_zt(A2)) ).

% swap_product
tff(fact_7126_swap__product,axiom,
    ! [A2: set_Pr3948176798113811640et_nat,B4: set_fu3555266933746557007_nat_o] : image_2538532745900505353et_nat(produc1257024432443326049et_nat(aTP_Lamm_un),produc7293743972641680163_nat_o(A2,aTP_Lamm_zu(B4))) = produc6971759541029228329et_nat(B4,aTP_Lamm_zv(A2)) ).

% swap_product
tff(fact_7127_swap__product,axiom,
    ! [A2: set_Pr1312406793078187350et_nat,B4: set_fu3555266933746557007_nat_o] : image_660286381542540297et_nat(produc5430029401411191265et_nat(aTP_Lamm_uo),produc4533482196970043141_nat_o(A2,aTP_Lamm_zw(B4))) = produc5673588578087545031et_nat(B4,aTP_Lamm_zx(A2)) ).

% swap_product
tff(fact_7128_swap__product,axiom,
    ! [A2: set_Pr958786334691620121nt_int,B4: set_fu5653557704672872225e_term] : image_3062550852079041117nt_int(produc4605791130040086525nt_int(aTP_Lamm_up),produc276578409427628764e_term(A2,aTP_Lamm_zy(B4))) = produc3974764367135812292nt_int(B4,aTP_Lamm_zz(A2)) ).

% swap_product
tff(fact_7129_swap__product,axiom,
    ! [A2: set_Pr958786334691620121nt_int,B4: set_fu3629540756087427317e_term] : image_4281971784858038109nt_int(produc8624921108698535677nt_int(aTP_Lamm_uq),produc4575053565521557168e_term(A2,aTP_Lamm_aaa(B4))) = produc1533099051242823152nt_int(B4,aTP_Lamm_aab(A2)) ).

% swap_product
tff(fact_7130_swap__product,axiom,
    ! [A2: set_int,B4: set_int] : image_2653370878348428101nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,aTP_Lamm_ut),produc1453890548195736866nt_int(A2,aTP_Lamm_xz(B4))) = produc1453890548195736866nt_int(B4,aTP_Lamm_xz(A2)) ).

% swap_product
tff(fact_7131_Sigma__empty__iff,axiom,
    ! [I4: set_se7855581050983116737at_nat,X7: fun_se953073389798102371at_nat] :
      ( ( produc7726050920695093128at_nat(I4,X7) = bot_bo228742789529271731at_nat )
    <=> ! [X4: set_Pr1261947904930325089at_nat] :
          ( member2643936169264416010at_nat(X4,I4)
         => ( aa_set6242432332095302236at_nat(X7,X4) = bot_bo3083307316010499117at_nat ) ) ) ).

% Sigma_empty_iff
tff(fact_7132_Sigma__empty__iff,axiom,
    ! [I4: set_nat,X7: fun_nat_set_nat] :
      ( ( produc457027306803732586at_nat(I4,X7) = bot_bo2099793752762293965at_nat )
    <=> ! [X4: nat] :
          ( member_nat(X4,I4)
         => ( aa_nat_set_nat(X7,X4) = bot_bot_set_nat ) ) ) ).

% Sigma_empty_iff
tff(fact_7133_gcd__mult__unit2,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),one_one_nat)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(gcd_gcd_nat,B),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,C),A)) = aa_nat_nat(aa_nat_fun_nat_nat(gcd_gcd_nat,B),C) ) ) ).

% gcd_mult_unit2
tff(fact_7134_gcd__mult__unit2,axiom,
    ! [A: int,B: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),one_one_int)
     => ( aa_int_int(aa_int_fun_int_int(gcd_gcd_int,B),aa_int_int(aa_int_fun_int_int(times_times_int,C),A)) = aa_int_int(aa_int_fun_int_int(gcd_gcd_int,B),C) ) ) ).

% gcd_mult_unit2
tff(fact_7135_gcd__mult__unit1,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),one_one_nat)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(gcd_gcd_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),A)),C) = aa_nat_nat(aa_nat_fun_nat_nat(gcd_gcd_nat,B),C) ) ) ).

% gcd_mult_unit1
tff(fact_7136_gcd__mult__unit1,axiom,
    ! [A: int,B: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),one_one_int)
     => ( aa_int_int(aa_int_fun_int_int(gcd_gcd_int,aa_int_int(aa_int_fun_int_int(times_times_int,B),A)),C) = aa_int_int(aa_int_fun_int_int(gcd_gcd_int,B),C) ) ) ).

% gcd_mult_unit1
tff(fact_7137_gcd__div__unit1,axiom,
    ! [A: int,B: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),one_one_int)
     => ( aa_int_int(aa_int_fun_int_int(gcd_gcd_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,B),A)),C) = aa_int_int(aa_int_fun_int_int(gcd_gcd_int,B),C) ) ) ).

% gcd_div_unit1
tff(fact_7138_gcd__div__unit1,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),one_one_nat)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(gcd_gcd_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,B),A)),C) = aa_nat_nat(aa_nat_fun_nat_nat(gcd_gcd_nat,B),C) ) ) ).

% gcd_div_unit1
tff(fact_7139_gcd__div__unit2,axiom,
    ! [A: int,B: int,C: int] :
      ( aa_int_o(aa_int_fun_int_o(dvd_dvd_int,A),one_one_int)
     => ( aa_int_int(aa_int_fun_int_int(gcd_gcd_int,B),aa_int_int(aa_int_fun_int_int(divide_divide_int,C),A)) = aa_int_int(aa_int_fun_int_int(gcd_gcd_int,B),C) ) ) ).

% gcd_div_unit2
tff(fact_7140_gcd__div__unit2,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,A),one_one_nat)
     => ( aa_nat_nat(aa_nat_fun_nat_nat(gcd_gcd_nat,B),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,C),A)) = aa_nat_nat(aa_nat_fun_nat_nat(gcd_gcd_nat,B),C) ) ) ).

% gcd_div_unit2
tff(fact_7141_less__int_Otransfer,axiom,
    bNF_re4195927319312321177_int_o(pcr_int,bNF_re6644619430987730960nt_o_o(pcr_int,fequal_o),aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,aTP_Lamm_fe),ord_less_int) ).

% less_int.transfer
tff(fact_7142_less__eq__int_Otransfer,axiom,
    bNF_re4195927319312321177_int_o(pcr_int,bNF_re6644619430987730960nt_o_o(pcr_int,fequal_o),aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,aTP_Lamm_fg),ord_less_eq_int) ).

% less_eq_int.transfer
tff(fact_7143_plus__int_Otransfer,axiom,
    bNF_re8869769828555196650nt_int(pcr_int,bNF_re7400052026677387805at_int(pcr_int,pcr_int),aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,aTP_Lamm_fz),plus_plus_int) ).

% plus_int.transfer
tff(fact_7144_minus__int_Otransfer,axiom,
    bNF_re8869769828555196650nt_int(pcr_int,bNF_re7400052026677387805at_int(pcr_int,pcr_int),aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,aTP_Lamm_gb),minus_minus_int) ).

% minus_int.transfer
tff(fact_7145_times__subset__iff,axiom,
    ! [A2: set_o,C4: set_o,B4: set_o,D3: set_o] :
      ( ord_le192195778054999463od_o_o(product_Sigma_o_o(A2,aTP_Lamm_xs(C4)),product_Sigma_o_o(B4,aTP_Lamm_xs(D3)))
    <=> ( ( A2 = bot_bot_set_o )
        | ( C4 = bot_bot_set_o )
        | ( ord_less_eq_set_o(A2,B4)
          & ord_less_eq_set_o(C4,D3) ) ) ) ).

% times_subset_iff
tff(fact_7146_times__subset__iff,axiom,
    ! [A2: set_o,C4: set_int,B4: set_o,D3: set_int] :
      ( ord_le3982295392052344841_o_int(product_Sigma_o_int(A2,aTP_Lamm_xu(C4)),product_Sigma_o_int(B4,aTP_Lamm_xu(D3)))
    <=> ( ( A2 = bot_bot_set_o )
        | ( C4 = bot_bot_set_int )
        | ( ord_less_eq_set_o(A2,B4)
          & ord_less_eq_set_int(C4,D3) ) ) ) ).

% times_subset_iff
tff(fact_7147_times__subset__iff,axiom,
    ! [A2: set_int,C4: set_o,B4: set_int,D3: set_o] :
      ( ord_le5274836691491929335_int_o(product_Sigma_int_o(A2,aTP_Lamm_xx(C4)),product_Sigma_int_o(B4,aTP_Lamm_xx(D3)))
    <=> ( ( A2 = bot_bot_set_int )
        | ( C4 = bot_bot_set_o )
        | ( ord_less_eq_set_int(A2,B4)
          & ord_less_eq_set_o(C4,D3) ) ) ) ).

% times_subset_iff
tff(fact_7148_times__subset__iff,axiom,
    ! [A2: set_int,C4: set_int,B4: set_int,D3: set_int] :
      ( ord_le2843351958646193337nt_int(produc1453890548195736866nt_int(A2,aTP_Lamm_xz(C4)),produc1453890548195736866nt_int(B4,aTP_Lamm_xz(D3)))
    <=> ( ( A2 = bot_bot_set_int )
        | ( C4 = bot_bot_set_int )
        | ( ord_less_eq_set_int(A2,B4)
          & ord_less_eq_set_int(C4,D3) ) ) ) ).

% times_subset_iff
tff(fact_7149_times__subset__iff,axiom,
    ! [A2: set_o,C4: set_nat,B4: set_o,D3: set_nat] :
      ( ord_le6472378536984071597_o_nat(product_Sigma_o_nat(A2,aTP_Lamm_xt(C4)),product_Sigma_o_nat(B4,aTP_Lamm_xt(D3)))
    <=> ( ( A2 = bot_bot_set_o )
        | ( C4 = bot_bot_set_nat )
        | ( ord_less_eq_set_o(A2,B4)
          & aa_set_nat_o(ord_less_eq_set_nat(C4),D3) ) ) ) ).

% times_subset_iff
tff(fact_7150_times__subset__iff,axiom,
    ! [A2: set_int,C4: set_nat,B4: set_int,D3: set_nat] :
      ( ord_le5333435103577920093nt_nat(produc1456381018704787142nt_nat(A2,aTP_Lamm_xy(C4)),produc1456381018704787142nt_nat(B4,aTP_Lamm_xy(D3)))
    <=> ( ( A2 = bot_bot_set_int )
        | ( C4 = bot_bot_set_nat )
        | ( ord_less_eq_set_int(A2,B4)
          & aa_set_nat_o(ord_less_eq_set_nat(C4),D3) ) ) ) ).

% times_subset_iff
tff(fact_7151_times__subset__iff,axiom,
    ! [A2: set_nat,C4: set_o,B4: set_nat,D3: set_o] :
      ( ord_le7519981659162375251_nat_o(product_Sigma_nat_o(A2,aTP_Lamm_xv(C4)),product_Sigma_nat_o(B4,aTP_Lamm_xv(D3)))
    <=> ( ( A2 = bot_bot_set_nat )
        | ( C4 = bot_bot_set_o )
        | ( aa_set_nat_o(ord_less_eq_set_nat(A2),B4)
          & ord_less_eq_set_o(C4,D3) ) ) ) ).

% times_subset_iff
tff(fact_7152_times__subset__iff,axiom,
    ! [A2: set_nat,C4: set_int,B4: set_nat,D3: set_int] :
      ( ord_le656430383953171549at_int(produc454536836294682310at_int(A2,aTP_Lamm_xw(C4)),produc454536836294682310at_int(B4,aTP_Lamm_xw(D3)))
    <=> ( ( A2 = bot_bot_set_nat )
        | ( C4 = bot_bot_set_int )
        | ( aa_set_nat_o(ord_less_eq_set_nat(A2),B4)
          & ord_less_eq_set_int(C4,D3) ) ) ) ).

% times_subset_iff
tff(fact_7153_times__subset__iff,axiom,
    ! [A2: set_nat,C4: set_nat,B4: set_nat,D3: set_nat] :
      ( aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(ord_le3146513528884898305at_nat,produc457027306803732586at_nat(A2,aTP_Lamm_ya(C4))),produc457027306803732586at_nat(B4,aTP_Lamm_ya(D3)))
    <=> ( ( A2 = bot_bot_set_nat )
        | ( C4 = bot_bot_set_nat )
        | ( aa_set_nat_o(ord_less_eq_set_nat(A2),B4)
          & aa_set_nat_o(ord_less_eq_set_nat(C4),D3) ) ) ) ).

% times_subset_iff
tff(fact_7154_times__subset__iff,axiom,
    ! [A2: set_Pr1261947904930325089at_nat,C4: set_o,B4: set_Pr1261947904930325089at_nat,D3: set_o] :
      ( ord_le5919393503700438654_nat_o(produc203973861852599583_nat_o(A2,aTP_Lamm_yb(C4)),produc203973861852599583_nat_o(B4,aTP_Lamm_yb(D3)))
    <=> ( ( A2 = bot_bo2099793752762293965at_nat )
        | ( C4 = bot_bot_set_o )
        | ( aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(ord_le3146513528884898305at_nat,A2),B4)
          & ord_less_eq_set_o(C4,D3) ) ) ) ).

% times_subset_iff
tff(fact_7155_image__paired__Times,axiom,
    ! [F: fun_nat_Code_integer,G: fun_nat_Code_integer,A2: set_nat,B4: set_nat] : image_5669961043262023647nteger(produc39701218431283661nteger(aa_fun7952091224041096005nteger(aTP_Lamm_aac(F),G)),produc457027306803732586at_nat(A2,aTP_Lamm_ya(B4))) = produc5882431272649516420nteger(image_1215581382706833972nteger(F,A2),aa_set1342327774797759281nteger(aTP_Lamm_yn(G),B4)) ).

% image_paired_Times
tff(fact_7156_image__paired__Times,axiom,
    ! [F: fun_nat_Code_integer,G: fun_nat_nat,A2: set_nat,B4: set_nat] : image_1372510298004463058er_nat(produc4146132627719282624er_nat(aa_fun7093963954598080645er_nat(aTP_Lamm_aad(F),G)),produc457027306803732586at_nat(A2,aTP_Lamm_ya(B4))) = produc4260658192689636599er_nat(image_1215581382706833972nteger(F,A2),aa_set3222090474234563492et_nat(aTP_Lamm_aae(G),B4)) ).

% image_paired_Times
tff(fact_7157_image__paired__Times,axiom,
    ! [F: fun_nat_Code_integer,G: fun_nat_int,A2: set_nat,B4: set_nat] : image_6418031315350042158er_int(produc9191653645064861724er_int(aa_fun8714824397388734853er_int(aTP_Lamm_aaf(F),G)),produc457027306803732586at_nat(A2,aTP_Lamm_ya(B4))) = produc4258167722180586323er_int(image_1215581382706833972nteger(F,A2),aa_set732007329302836736et_int(aTP_Lamm_aag(G),B4)) ).

% image_paired_Times
tff(fact_7158_image__paired__Times,axiom,
    ! [F: fun_nat_Code_integer,G: fun_int_int,A2: set_nat,B4: set_int] : image_202211252889950930er_int(produc1728318271963197120er_int(aa_fun3338573009006755021er_int(aTP_Lamm_aah(F),G)),produc454536836294682310at_int(A2,aTP_Lamm_xw(B4))) = produc4258167722180586323er_int(image_1215581382706833972nteger(F,A2),aa_set8360975810291373660et_int(aTP_Lamm_aai(G),B4)) ).

% image_paired_Times
tff(fact_7159_image__paired__Times,axiom,
    ! [F: fun_nat_nat,G: fun_nat_Code_integer,A2: set_nat,B4: set_nat] : image_6753550540357478226nteger(produc303800833217521984nteger(aa_fun8323025376520073144nteger(aTP_Lamm_aaj(F),G)),produc457027306803732586at_nat(A2,aTP_Lamm_ya(B4))) = produc4525213641468679415nteger(aa_set_nat_set_nat(image_nat_nat(F),A2),aa_set4032875478442387108nteger(aTP_Lamm_aak(G),B4)) ).

% image_paired_Times
tff(fact_7160_image__paired__Times,axiom,
    ! [F: fun_nat_nat,G: fun_nat_nat,A2: set_nat,B4: set_nat] : aa_set8868280134176360700at_nat(image_5168914502847457605at_nat(produc2626176000494625587at_nat(aa_fun4348998216881757432at_nat(aTP_Lamm_aal(F),G))),produc457027306803732586at_nat(A2,aTP_Lamm_ya(B4))) = produc457027306803732586at_nat(aa_set_nat_set_nat(image_nat_nat(F),A2),aa_set562305657478724375et_nat(aTP_Lamm_yp(G),B4)) ).

% image_paired_Times
tff(fact_7161_image__paired__Times,axiom,
    ! [F: fun_nat_nat,G: fun_nat_int,A2: set_nat,B4: set_nat] : image_991063483338260897at_int(produc7671697017840204687at_int(aa_fun2313822316067610104at_int(aTP_Lamm_aam(F),G)),produc457027306803732586at_nat(A2,aTP_Lamm_ya(B4))) = produc454536836294682310at_int(aa_set_nat_set_nat(image_nat_nat(F),A2),aa_set7295594549401773427et_int(aTP_Lamm_aan(G),B4)) ).

% image_paired_Times
tff(fact_7162_image__paired__Times,axiom,
    ! [F: fun_nat_nat,G: fun_int_int,A2: set_nat,B4: set_int] : image_9117352539549038149at_int(produc1486167065449562675at_int(aa_fun566144318431074624at_int(aTP_Lamm_aao(F),G)),produc454536836294682310at_int(A2,aTP_Lamm_xw(B4))) = produc454536836294682310at_int(aa_set_nat_set_nat(image_nat_nat(F),A2),aa_set2464685511577892303et_int(aTP_Lamm_aap(G),B4)) ).

% image_paired_Times
tff(fact_7163_image__paired__Times,axiom,
    ! [F: fun_nat_int,G: fun_nat_Code_integer,A2: set_nat,B4: set_nat] : image_7125204100594322862nteger(produc675454393454366620nteger(aa_fun947730671064037908nteger(aTP_Lamm_aaq(F),G)),produc457027306803732586at_nat(A2,aTP_Lamm_ya(B4))) = produc4896867201705524051nteger(image_nat_int(F,A2),aa_set1723057546349436160nteger(aTP_Lamm_aar(G),B4)) ).

% image_paired_Times
tff(fact_7164_image__paired__Times,axiom,
    ! [F: fun_nat_int,G: fun_nat_nat,A2: set_nat,B4: set_nat] : image_6168268214748512161nt_nat(produc3625529712395680143nt_nat(aa_fun7567701811046127444nt_nat(aTP_Lamm_aas(F),G)),produc457027306803732586at_nat(A2,aTP_Lamm_ya(B4))) = produc1456381018704787142nt_nat(image_nat_int(F,A2),aa_set933959217715569011et_nat(aTP_Lamm_aat(G),B4)) ).

% image_paired_Times
tff(fact_7165_fst__image__Sigma,axiom,
    ! [A2: set_Code_integer,B4: fun_Co744628173305925485nteger] : image_6316824473203919795nteger(produc8508995932063986495nteger,produc5882431272649516420nteger(A2,B4)) = collect_Code_integer(aa_fun7245632122240156009eger_o(aTP_Lamm_aau(A2),B4)) ).

% fst_image_Sigma
tff(fact_7166_fst__image__Sigma,axiom,
    ! [A2: set_o,B4: fun_o_set_o] : image_7896445794123959606_o_o_o(product_fst_o_o,product_Sigma_o_o(A2,B4)) = collect_o(aa_fun4619127644298054564un_o_o(aTP_Lamm_aav(A2),B4)) ).

% fst_image_Sigma
tff(fact_7167_fst__image__Sigma,axiom,
    ! [A2: set_int,B4: fun_int_set_o] : image_90517134139374612_o_int(product_fst_int_o,product_Sigma_int_o(A2,B4)) = collect_int(aa_fun4291261932532047132_int_o(aTP_Lamm_aaw(A2),B4)) ).

% fst_image_Sigma
tff(fact_7168_fst__image__Sigma,axiom,
    ! [A2: set_nat,B4: fun_nat_set_o] : image_8629803608462650132_o_nat(product_fst_nat_o,product_Sigma_nat_o(A2,B4)) = collect_nat(aa_fun4904187145036355100_nat_o(aTP_Lamm_aax(A2),B4)) ).

% fst_image_Sigma
tff(fact_7169_fst__image__Sigma,axiom,
    ! [A2: set_o,B4: fun_o_set_nat] : image_8105710389281276538_nat_o(product_fst_o_nat,product_Sigma_o_nat(A2,B4)) = collect_o(aa_fun8423158570077026744un_o_o(aTP_Lamm_aay(A2),B4)) ).

% fst_image_Sigma
tff(fact_7170_fst__image__Sigma,axiom,
    ! [A2: set_int,B4: fun_int_set_nat] : image_2855239504505064772at_int(product_fst_int_nat,produc1456381018704787142nt_nat(A2,B4)) = collect_int(aa_fun1965424933913381656_int_o(aTP_Lamm_aaz(A2),B4)) ).

% fst_image_Sigma
tff(fact_7171_fst__image__Sigma,axiom,
    ! [A2: set_nat,B4: fun_nat_set_nat] : image_2486076414777270412at_nat(product_fst_nat_nat,produc457027306803732586at_nat(A2,B4)) = collect_nat(aa_fun2108954047564320208_nat_o(aTP_Lamm_aba(A2),B4)) ).

% fst_image_Sigma
tff(fact_7172_fst__image__Sigma,axiom,
    ! [A2: set_o,B4: fun_o_set_int] : image_5860565421610830622_int_o(product_fst_o_int,product_Sigma_o_int(A2,B4)) = collect_o(aa_fun3615580826569402900un_o_o(aTP_Lamm_abb(A2),B4)) ).

% fst_image_Sigma
tff(fact_7173_fst__image__Sigma,axiom,
    ! [A2: set_nat,B4: fun_nat_set_int] : image_4672997989470292200nt_nat(product_fst_nat_int,produc454536836294682310at_int(A2,B4)) = collect_nat(aa_fun3985882680581680244_nat_o(aTP_Lamm_abc(A2),B4)) ).

% fst_image_Sigma
tff(fact_7174_fst__image__Sigma,axiom,
    ! [A2: set_int,B4: fun_int_set_int] : image_5042161079198086560nt_int(product_fst_int_int,produc1453890548195736866nt_int(A2,B4)) = collect_int(aa_fun3842353566930741692_int_o(aTP_Lamm_abd(A2),B4)) ).

% fst_image_Sigma
tff(fact_7175_Sigma__def,axiom,
    ! [A2: set_fu8280898353253485872e_term,B4: fun_fu5971215405379524186nteger] : produc5453309460576862807nteger(A2,B4) = comple7749403179893457567nteger(image_5753923617458574413nteger(aTP_Lamm_abf(B4),A2)) ).

% Sigma_def
tff(fact_7176_Sigma__def,axiom,
    ! [A2: set_fu3555266933746557007_nat_o,B4: fun_fu2890809920214373946et_nat] : produc6971759541029228329et_nat(A2,B4) = comple946752071900596009et_nat(image_1549266068120649472et_nat(aTP_Lamm_abh(B4),A2)) ).

% Sigma_def
tff(fact_7177_Sigma__def,axiom,
    ! [A2: set_fu3555266933746557007_nat_o,B4: fun_fu8357309440898100312et_nat] : produc5673588578087545031et_nat(A2,B4) = comple828966628661558727et_nat(image_67816568901280286et_nat(aTP_Lamm_abj(B4),A2)) ).

% Sigma_def
tff(fact_7178_Sigma__def,axiom,
    ! [A2: set_fu5653557704672872225e_term,B4: fun_fu4219362280553733319nt_int] : produc3974764367135812292nt_int(A2,B4) = comple3054605461907987852nt_int(image_7441934579048575915nt_int(aTP_Lamm_abl(B4),A2)) ).

% Sigma_def
tff(fact_7179_Sigma__def,axiom,
    ! [A2: set_fu3629540756087427317e_term,B4: fun_fu3472058528428720115nt_int] : produc1533099051242823152nt_int(A2,B4) = comple7505710199608789688nt_int(image_3787029643364842667nt_int(aTP_Lamm_abn(B4),A2)) ).

% Sigma_def
tff(fact_7180_Sigma__def,axiom,
    ! [A2: set_se7855581050983116737at_nat,B4: fun_se953073389798102371at_nat] : produc7726050920695093128at_nat(A2,B4) = comple4364388969068068532at_nat(image_6898982319499645995at_nat(aTP_Lamm_abp(B4),A2)) ).

% Sigma_def
tff(fact_7181_Sigma__def,axiom,
    ! [A2: set_nat,B4: fun_nat_set_nat] : produc457027306803732586at_nat(A2,B4) = comple5685304695842803022at_nat(image_7178329752028323786at_nat(aTP_Lamm_abr(B4),A2)) ).

% Sigma_def
tff(fact_7182_times__int_Otransfer,axiom,
    bNF_re8869769828555196650nt_int(pcr_int,bNF_re7400052026677387805at_int(pcr_int,pcr_int),aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,aTP_Lamm_gd),times_times_int) ).

% times_int.transfer
tff(fact_7183_num__of__integer_Orsp,axiom,
    aa_fun_int_num_o(aa_fun7722276931801436589_num_o(bNF_re7626690874201225453um_num(fequal_int,fequal_num),aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,num_of_nat),nat2)),aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,num_of_nat),nat2)) ).

% num_of_integer.rsp
tff(fact_7184_snd__image__Sigma,axiom,
    ! [A2: set_Code_integer,B4: fun_Co744628173305925485nteger] : image_6316824473203919795nteger(produc6174133586879617921nteger,produc5882431272649516420nteger(A2,B4)) = comple739944243200306918nteger(image_2291390168754192375nteger(B4,A2)) ).

% snd_image_Sigma
tff(fact_7185_snd__image__Sigma,axiom,
    ! [A2: set_int,B4: fun_int_set_int] : image_5042161079198086560nt_int(product_snd_int_int,produc1453890548195736866nt_int(A2,B4)) = comple3221217463730067765et_int(image_int_set_int(B4,A2)) ).

% snd_image_Sigma
tff(fact_7186_snd__image__Sigma,axiom,
    ! [A2: set_Code_natural,B4: fun_Co2944084857415636034atural] : image_3837677093542026988atural(produc6591912806276919810atural,produc6231535905537262655atural(A2,B4)) = comple4956303571586142718atural(image_3530315724569248802atural(B4,A2)) ).

% snd_image_Sigma
tff(fact_7187_snd__image__Sigma,axiom,
    ! [A2: set_nat,B4: fun_nat_set_nat] : image_2486076414777270412at_nat(product_snd_nat_nat,produc457027306803732586at_nat(A2,B4)) = comple7399068483239264473et_nat(image_nat_set_nat(B4,A2)) ).

% snd_image_Sigma
tff(fact_7188_subset__fst__snd,axiom,
    ! [A2: set_Pr4811707699266497531nteger] : ord_le3725938330318615451nteger(A2,produc5882431272649516420nteger(image_6316824473203919795nteger(produc8508995932063986495nteger,A2),aTP_Lamm_abs(A2))) ).

% subset_fst_snd
tff(fact_7189_subset__fst__snd,axiom,
    ! [A2: set_Pr958786334691620121nt_int] : ord_le2843351958646193337nt_int(A2,produc1453890548195736866nt_int(image_5042161079198086560nt_int(product_fst_int_int,A2),aTP_Lamm_abt(A2))) ).

% subset_fst_snd
tff(fact_7190_subset__fst__snd,axiom,
    ! [A2: set_Pr2352657477744078772atural] : ord_le2202040463148982292atural(A2,produc6231535905537262655atural(image_8194678751871465133atural(produc497848011034438852atural,A2),aTP_Lamm_abu(A2))) ).

% subset_fst_snd
tff(fact_7191_int__transfer,axiom,
    bNF_re6830278522597306478at_int(fequal_nat,pcr_int,aTP_Lamm_abv,semiri1314217659103216013at_int) ).

% int_transfer
tff(fact_7192_uminus__int_Otransfer,axiom,
    aa_fun_int_int_o(aa_fun856177901615811547_int_o(bNF_re7400052026677387805at_int(pcr_int,pcr_int),produc2626176000494625587at_nat(aTP_Lamm_dg)),uminus_uminus_int) ).

% uminus_int.transfer
tff(fact_7193_eq__fst__iff,axiom,
    ! [A: fun_Pr5098669352780829690e_term,P2: produc2453742332425399446nteger] :
      ( ( A = aa_Pro4276937008533432526e_term(produc2481150572478215260nteger,P2) )
    <=> ? [B6: produc8923325533196201883nteger] : P2 = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,A),B6) ) ).

% eq_fst_iff
tff(fact_7194_eq__fst__iff,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,P2: produc8799533983703829792et_nat] :
      ( ( A = aa_Pro8262445894397805713_nat_o(produc5325900173150335662et_nat,P2) )
    <=> ? [B6: produc3658429121746597890et_nat] : P2 = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,A),B6) ) ).

% eq_fst_iff
tff(fact_7195_eq__fst__iff,axiom,
    ! [A: fun_Pr6460944699146269935_nat_o,P2: produc3112576180687729086et_nat] :
      ( ( A = aa_Pro2837773213478468339_nat_o(produc4078497350495916492et_nat,P2) )
    <=> ? [B6: produc8799533983703829792et_nat] : P2 = aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,A),B6) ) ).

% eq_fst_iff
tff(fact_7196_eq__fst__iff,axiom,
    ! [A: fun_Pr7763680713840462443e_term,P2: produc3043004577601930755nt_int] :
      ( ( A = aa_Pro4010435699744810540e_term(produc3130796691802200265nt_int,P2) )
    <=> ? [B6: product_prod_int_int] : P2 = aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,A),B6) ) ).

% eq_fst_iff
tff(fact_7197_eq__fst__iff,axiom,
    ! [A: fun_in5730379987311621695e_term,P2: produc4788131091073775919nt_int] :
      ( ( A = aa_Pro2551989255418117932e_term(produc4463008262350210037nt_int,P2) )
    <=> ? [B6: product_prod_int_int] : P2 = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,A),B6) ) ).

% eq_fst_iff
tff(fact_7198_eq__fst__iff,axiom,
    ! [A: code_integer,P2: produc8923325533196201883nteger] :
      ( ( A = aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,P2) )
    <=> ? [B6: code_integer] : P2 = aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(A),B6) ) ).

% eq_fst_iff
tff(fact_7199_eq__fst__iff,axiom,
    ! [A: int,P2: product_prod_int_int] :
      ( ( A = aa_Pro6799258434465214121nt_int(product_fst_int_int,P2) )
    <=> ? [B6: int] : P2 = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A),B6) ) ).

% eq_fst_iff
tff(fact_7200_transfer__rule__of__nat,axiom,
    ! [R3: fun_rat_fun_rat_o] :
      ( aa_rat_o(aa_rat_fun_rat_o(R3,zero_zero_rat),zero_zero_rat)
     => ( aa_rat_o(aa_rat_fun_rat_o(R3,one_one_rat),one_one_rat)
       => ( bNF_re6158105658165029227at_rat(R3,bNF_re5606270390558447553at_rat(R3,R3),plus_plus_rat,plus_plus_rat)
         => bNF_re4702136315717946289at_rat(fequal_nat,R3,semiri681578069525770553at_rat,semiri681578069525770553at_rat) ) ) ) ).

% transfer_rule_of_nat
tff(fact_7201_transfer__rule__of__nat,axiom,
    ! [R3: fun_rat_fun_int_o] :
      ( aa_int_o(aa_rat_fun_int_o(R3,zero_zero_rat),zero_zero_int)
     => ( aa_int_o(aa_rat_fun_int_o(R3,one_one_rat),one_one_int)
       => ( bNF_re8256098235694157927nt_int(R3,bNF_re5838490730811218025at_int(R3,R3),plus_plus_rat,plus_plus_int)
         => bNF_re5334775905295391749at_int(fequal_nat,R3,semiri681578069525770553at_rat,semiri1314217659103216013at_int) ) ) ) ).

% transfer_rule_of_nat
tff(fact_7202_transfer__rule__of__nat,axiom,
    ! [R3: fun_rat_fun_nat_o] :
      ( aa_nat_o(aa_rat_fun_nat_o(R3,zero_zero_rat),zero_zero_nat)
     => ( aa_nat_o(aa_rat_fun_nat_o(R3,one_one_rat),one_one_nat)
       => ( bNF_re802536597765851987at_nat(R3,bNF_re5469327641083423665at_nat(R3,R3),plus_plus_rat,plus_plus_nat)
         => bNF_re5337266375804442025at_nat(fequal_nat,R3,semiri681578069525770553at_rat,semiri1316708129612266289at_nat) ) ) ) ).

% transfer_rule_of_nat
tff(fact_7203_transfer__rule__of__nat,axiom,
    ! [R3: fun_ra1401953663915778005eger_o] :
      ( aa_Code_integer_o(aa_rat2503820116649195070eger_o(R3,zero_zero_rat),zero_z3403309356797280102nteger)
     => ( aa_Code_integer_o(aa_rat2503820116649195070eger_o(R3,one_one_rat),one_one_Code_integer)
       => ( bNF_re10698882459692666nteger(R3,bNF_re2328245411608324299nteger(R3,R3),plus_plus_rat,plus_p5714425477246183910nteger)
         => bNF_re4553819317763231286nteger(fequal_nat,R3,semiri681578069525770553at_rat,semiri4939895301339042750nteger) ) ) ) ).

% transfer_rule_of_nat
tff(fact_7204_transfer__rule__of__nat,axiom,
    ! [R3: fun_ra6546579167043500746ural_o] :
      ( aa_Code_natural_o(aa_rat3585839436822707123ural_o(R3,zero_zero_rat),zero_z2226904508553997617atural)
     => ( aa_Code_natural_o(aa_rat3585839436822707123ural_o(R3,one_one_rat),one_one_Code_natural)
       => ( bNF_re4979465074148308571atural(R3,bNF_re4433268865704509537atural(R3,R3),plus_plus_rat,plus_p4538020629002901425atural)
         => bNF_re3377414469519948801atural(fequal_nat,R3,semiri681578069525770553at_rat,semiri3763490453095760265atural) ) ) ) ).

% transfer_rule_of_nat
tff(fact_7205_transfer__rule__of__nat,axiom,
    ! [R3: fun_int_fun_rat_o] :
      ( aa_rat_o(aa_int_fun_rat_o(R3,zero_zero_int),zero_zero_rat)
     => ( aa_rat_o(aa_int_fun_rat_o(R3,one_one_int),one_one_rat)
       => ( bNF_re3619483633275351143at_rat(R3,bNF_re4480299549022435433nt_rat(R3,R3),plus_plus_int,plus_plus_rat)
         => bNF_re6018044671553866757nt_rat(fequal_nat,R3,semiri1314217659103216013at_int,semiri681578069525770553at_rat) ) ) ) ).

% transfer_rule_of_nat
tff(fact_7206_transfer__rule__of__nat,axiom,
    ! [R3: fun_int_fun_int_o] :
      ( aa_int_o(aa_int_fun_int_o(R3,zero_zero_int),zero_zero_int)
     => ( aa_int_o(aa_int_fun_int_o(R3,one_one_int),one_one_int)
       => ( aa_fun3498034192445020252_int_o(aa_fun3119206668089765047_int_o(bNF_re5717476210804479843nt_int(R3,bNF_re4712519889275205905nt_int(R3,R3)),plus_plus_int),plus_plus_int)
         => bNF_re6650684261131312217nt_int(fequal_nat,R3,semiri1314217659103216013at_int,semiri1314217659103216013at_int) ) ) ) ).

% transfer_rule_of_nat
tff(fact_7207_transfer__rule__of__nat,axiom,
    ! [R3: fun_int_fun_nat_o] :
      ( aa_nat_o(aa_int_fun_nat_o(R3,zero_zero_int),zero_zero_nat)
     => ( aa_nat_o(aa_int_fun_nat_o(R3,one_one_int),one_one_nat)
       => ( bNF_re7487286609730949711at_nat(R3,bNF_re4343356799547411545nt_nat(R3,R3),plus_plus_int,plus_plus_nat)
         => bNF_re6653174731640362493nt_nat(fequal_nat,R3,semiri1314217659103216013at_int,semiri1316708129612266289at_nat) ) ) ) ).

% transfer_rule_of_nat
tff(fact_7208_transfer__rule__of__nat,axiom,
    ! [R3: fun_in4891666191172872833eger_o] :
      ( aa_Code_integer_o(aa_int5993532643906289898eger_o(R3,zero_zero_int),zero_z3403309356797280102nteger)
     => ( aa_Code_integer_o(aa_int5993532643906289898eger_o(R3,one_one_int),one_one_Code_integer)
       => ( bNF_re9130850084932126070nteger(R3,bNF_re3379532845092657523nteger(R3,R3),plus_plus_int,plus_p5714425477246183910nteger)
         => bNF_re4153400068438556298nteger(fequal_nat,R3,semiri1314217659103216013at_int,semiri4939895301339042750nteger) ) ) ) ).

% transfer_rule_of_nat
tff(fact_7209_transfer__rule__of__nat,axiom,
    ! [R3: fun_in812919657445819766ural_o] :
      ( aa_Code_natural_o(aa_int7075551964079801951ural_o(R3,zero_zero_int),zero_z2226904508553997617atural)
     => ( aa_Code_natural_o(aa_int7075551964079801951ural_o(R3,one_one_int),one_one_Code_natural)
       => ( bNF_re4876244239765966167atural(R3,bNF_re5484556299188842761atural(R3,R3),plus_plus_int,plus_p4538020629002901425atural)
         => bNF_re2976995220195273813atural(fequal_nat,R3,semiri1314217659103216013at_int,semiri3763490453095760265atural) ) ) ) ).

% transfer_rule_of_nat
tff(fact_7210_transfer__rule__of__bool,axiom,
    ! [R3: fun_rat_fun_rat_o] :
      ( aa_rat_o(aa_rat_fun_rat_o(R3,zero_zero_rat),zero_zero_rat)
     => ( aa_rat_o(aa_rat_fun_rat_o(R3,one_one_rat),one_one_rat)
       => bNF_re8824113547921424783at_rat(fequal_o,R3,zero_n2052037380579107095ol_rat,zero_n2052037380579107095ol_rat) ) ) ).

% transfer_rule_of_bool
tff(fact_7211_transfer__rule__of__bool,axiom,
    ! [R3: fun_rat_fun_nat_o] :
      ( aa_nat_o(aa_rat_fun_nat_o(R3,zero_zero_rat),zero_zero_nat)
     => ( aa_nat_o(aa_rat_fun_nat_o(R3,one_one_rat),one_one_nat)
       => bNF_re235871571153144711at_nat(fequal_o,R3,zero_n2052037380579107095ol_rat,zero_n2687167440665602831ol_nat) ) ) ).

% transfer_rule_of_bool
tff(fact_7212_transfer__rule__of__bool,axiom,
    ! [R3: fun_rat_fun_int_o] :
      ( aa_int_o(aa_rat_fun_int_o(R3,zero_zero_rat),zero_zero_int)
     => ( aa_int_o(aa_rat_fun_int_o(R3,one_one_rat),one_one_int)
       => bNF_re233381100644094435at_int(fequal_o,R3,zero_n2052037380579107095ol_rat,zero_n2684676970156552555ol_int) ) ) ).

% transfer_rule_of_bool
tff(fact_7213_transfer__rule__of__bool,axiom,
    ! [R3: fun_ra1401953663915778005eger_o] :
      ( aa_Code_integer_o(aa_rat2503820116649195070eger_o(R3,zero_zero_rat),zero_z3403309356797280102nteger)
     => ( aa_Code_integer_o(aa_rat2503820116649195070eger_o(R3,one_one_rat),one_one_Code_integer)
       => bNF_re5635613845597506580nteger(fequal_o,R3,zero_n2052037380579107095ol_rat,zero_n356916108424825756nteger) ) ) ).

% transfer_rule_of_bool
tff(fact_7214_transfer__rule__of__bool,axiom,
    ! [R3: fun_nat_fun_rat_o] :
      ( aa_rat_o(aa_nat_fun_rat_o(R3,zero_zero_nat),zero_zero_rat)
     => ( aa_rat_o(aa_nat_fun_rat_o(R3,one_one_nat),one_one_rat)
       => bNF_re9140668191856290695at_rat(fequal_o,R3,zero_n2687167440665602831ol_nat,zero_n2052037380579107095ol_rat) ) ) ).

% transfer_rule_of_bool
tff(fact_7215_transfer__rule__of__bool,axiom,
    ! [R3: fun_nat_fun_nat_o] :
      ( aa_nat_o(aa_nat_fun_nat_o(R3,zero_zero_nat),zero_zero_nat)
     => ( aa_nat_o(aa_nat_fun_nat_o(R3,one_one_nat),one_one_nat)
       => bNF_re552426215088010623at_nat(fequal_o,R3,zero_n2687167440665602831ol_nat,zero_n2687167440665602831ol_nat) ) ) ).

% transfer_rule_of_bool
tff(fact_7216_transfer__rule__of__bool,axiom,
    ! [R3: fun_nat_fun_int_o] :
      ( aa_int_o(aa_nat_fun_int_o(R3,zero_zero_nat),zero_zero_int)
     => ( aa_int_o(aa_nat_fun_int_o(R3,one_one_nat),one_one_int)
       => bNF_re549935744578960347at_int(fequal_o,R3,zero_n2687167440665602831ol_nat,zero_n2684676970156552555ol_int) ) ) ).

% transfer_rule_of_bool
tff(fact_7217_transfer__rule__of__bool,axiom,
    ! [R3: fun_na6318815019539281885eger_o] :
      ( aa_Code_integer_o(aa_nat7420681472272698950eger_o(R3,zero_zero_nat),zero_z3403309356797280102nteger)
     => ( aa_Code_integer_o(aa_nat7420681472272698950eger_o(R3,one_one_nat),one_one_Code_integer)
       => bNF_re4863541036035986956nteger(fequal_o,R3,zero_n2687167440665602831ol_nat,zero_n356916108424825756nteger) ) ) ).

% transfer_rule_of_bool
tff(fact_7218_transfer__rule__of__bool,axiom,
    ! [R3: fun_int_fun_rat_o] :
      ( aa_rat_o(aa_int_fun_rat_o(R3,zero_zero_int),zero_zero_rat)
     => ( aa_rat_o(aa_int_fun_rat_o(R3,one_one_int),one_one_rat)
       => bNF_re916649866902569443nt_rat(fequal_o,R3,zero_n2684676970156552555ol_int,zero_n2052037380579107095ol_rat) ) ) ).

% transfer_rule_of_bool
tff(fact_7219_transfer__rule__of__bool,axiom,
    ! [R3: fun_int_fun_nat_o] :
      ( aa_nat_o(aa_int_fun_nat_o(R3,zero_zero_int),zero_zero_nat)
     => ( aa_nat_o(aa_int_fun_nat_o(R3,one_one_int),one_one_nat)
       => bNF_re1551779926989065179nt_nat(fequal_o,R3,zero_n2684676970156552555ol_int,zero_n2687167440665602831ol_nat) ) ) ).

% transfer_rule_of_bool
tff(fact_7220_plus__rat_Otransfer,axiom,
    bNF_re6323452265856231590at_rat(pcr_rat,bNF_re8279943556446156061nt_rat(pcr_rat,pcr_rat),aTP_Lamm_abw,plus_plus_rat) ).

% plus_rat.transfer
tff(fact_7221_inverse__rat_Otransfer,axiom,
    aa_fun_rat_rat_o(aa_fun382765352565706371_rat_o(bNF_re8279943556446156061nt_rat(pcr_rat,pcr_rat),aTP_Lamm_abx),inverse_inverse_rat) ).

% inverse_rat.transfer
tff(fact_7222_Id__on__def,axiom,
    ! [A2: set_se7855581050983116737at_nat] : id_on_6713504163309144702at_nat(A2) = comple4364388969068068532at_nat(image_6898982319499645995at_nat(aTP_Lamm_aby,A2)) ).

% Id_on_def
tff(fact_7223_Id__on__def,axiom,
    ! [A2: set_nat] : id_on_nat(A2) = comple5685304695842803022at_nat(image_7178329752028323786at_nat(aTP_Lamm_abz,A2)) ).

% Id_on_def
tff(fact_7224_times__rat_Otransfer,axiom,
    bNF_re6323452265856231590at_rat(pcr_rat,bNF_re8279943556446156061nt_rat(pcr_rat,pcr_rat),aTP_Lamm_aca,times_times_rat) ).

% times_rat.transfer
tff(fact_7225_gcd__1__nat,axiom,
    ! [M: nat] : aa_nat_nat(aa_nat_fun_nat_nat(gcd_gcd_nat,M),one_one_nat) = one_one_nat ).

% gcd_1_nat
tff(fact_7226_Id__onI,axiom,
    ! [A: set_Pr1261947904930325089at_nat,A2: set_se7855581050983116737at_nat] :
      ( member2643936169264416010at_nat(A,A2)
     => member8757157785044589968at_nat(produc2922128104949294807at_nat(A,A),id_on_6713504163309144702at_nat(A2)) ) ).

% Id_onI
tff(fact_7227_Id__onI,axiom,
    ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
      ( member8757157785044589968at_nat(A,A2)
     => member6009668390874684176at_nat(produc2335810615602371415at_nat(A,A),id_on_7869290023980668164at_nat(A2)) ) ).

% Id_onI
tff(fact_7228_Id__onI,axiom,
    ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
      ( member8440522571783428010at_nat(A,A2)
     => member8206827879206165904at_nat(produc6161850002892822231at_nat(A,A),id_on_2554058798563519774at_nat(A2)) ) ).

% Id_onI
tff(fact_7229_Id__onI,axiom,
    ! [A: $o,A2: set_o] :
      ( member_o((A),A2)
     => member7466972457876170832od_o_o(product_Pair_o_o((A),(A)),id_on_o(A2)) ) ).

% Id_onI
tff(fact_7230_Id__onI,axiom,
    ! [A: nat,A2: set_nat] :
      ( member_nat(A,A2)
     => member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),A),id_on_nat(A2)) ) ).

% Id_onI
tff(fact_7231_Id__onI,axiom,
    ! [A: int,A2: set_int] :
      ( member_int(A,A2)
     => member5262025264175285858nt_int(aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A),A),id_on_int(A2)) ) ).

% Id_onI
tff(fact_7232_unset__bit__natural_Orsp,axiom,
    bNF_re5162689864697376059at_nat(fequal_nat,bNF_re5653821019739307937at_nat(fequal_nat,fequal_nat),bit_se4205575877204974255it_nat,bit_se4205575877204974255it_nat) ).

% unset_bit_natural.rsp
tff(fact_7233_take__bit__natural_Orsp,axiom,
    bNF_re5162689864697376059at_nat(fequal_nat,bNF_re5653821019739307937at_nat(fequal_nat,fequal_nat),bit_se2925701944663578781it_nat,bit_se2925701944663578781it_nat) ).

% take_bit_natural.rsp
tff(fact_7234_bit__natural_Orsp,axiom,
    bNF_re1448341924010609215_nat_o(fequal_nat,fequal_fun_nat_o,bit_se1148574629649215175it_nat,bit_se1148574629649215175it_nat) ).

% bit_natural.rsp
tff(fact_7235_drop__bit__natural_Orsp,axiom,
    bNF_re5162689864697376059at_nat(fequal_nat,bNF_re5653821019739307937at_nat(fequal_nat,fequal_nat),bit_se8570568707652914677it_nat,bit_se8570568707652914677it_nat) ).

% drop_bit_natural.rsp
tff(fact_7236_Id__on__iff,axiom,
    ! [X2: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
      ( member6009668390874684176at_nat(produc2335810615602371415at_nat(X2,Y),id_on_7869290023980668164at_nat(A2))
    <=> ( ( X2 = Y )
        & member8757157785044589968at_nat(X2,A2) ) ) ).

% Id_on_iff
tff(fact_7237_Id__on__iff,axiom,
    ! [X2: product_prod_nat_nat,Y: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
      ( member8206827879206165904at_nat(produc6161850002892822231at_nat(X2,Y),id_on_2554058798563519774at_nat(A2))
    <=> ( ( X2 = Y )
        & member8440522571783428010at_nat(X2,A2) ) ) ).

% Id_on_iff
tff(fact_7238_Id__on__iff,axiom,
    ! [X2: $o,Y: $o,A2: set_o] :
      ( member7466972457876170832od_o_o(product_Pair_o_o((X2),(Y)),id_on_o(A2))
    <=> ( ( (X2)
        <=> (Y) )
        & member_o((X2),A2) ) ) ).

% Id_on_iff
tff(fact_7239_Id__on__iff,axiom,
    ! [X2: int,Y: int,A2: set_int] :
      ( member5262025264175285858nt_int(aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X2),Y),id_on_int(A2))
    <=> ( ( X2 = Y )
        & member_int(X2,A2) ) ) ).

% Id_on_iff
tff(fact_7240_Id__on__iff,axiom,
    ! [X2: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,A2: set_se7855581050983116737at_nat] :
      ( member8757157785044589968at_nat(produc2922128104949294807at_nat(X2,Y),id_on_6713504163309144702at_nat(A2))
    <=> ( ( X2 = Y )
        & member2643936169264416010at_nat(X2,A2) ) ) ).

% Id_on_iff
tff(fact_7241_Id__on__iff,axiom,
    ! [X2: nat,Y: nat,A2: set_nat] :
      ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X2),Y),id_on_nat(A2))
    <=> ( ( X2 = Y )
        & member_nat(X2,A2) ) ) ).

% Id_on_iff
tff(fact_7242_Id__on__eqI,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_se7855581050983116737at_nat] :
      ( ( A = B )
     => ( member2643936169264416010at_nat(A,A2)
       => member8757157785044589968at_nat(produc2922128104949294807at_nat(A,B),id_on_6713504163309144702at_nat(A2)) ) ) ).

% Id_on_eqI
tff(fact_7243_Id__on__eqI,axiom,
    ! [A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
      ( ( A = B )
     => ( member8757157785044589968at_nat(A,A2)
       => member6009668390874684176at_nat(produc2335810615602371415at_nat(A,B),id_on_7869290023980668164at_nat(A2)) ) ) ).

% Id_on_eqI
tff(fact_7244_Id__on__eqI,axiom,
    ! [A: product_prod_nat_nat,B: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
      ( ( A = B )
     => ( member8440522571783428010at_nat(A,A2)
       => member8206827879206165904at_nat(produc6161850002892822231at_nat(A,B),id_on_2554058798563519774at_nat(A2)) ) ) ).

% Id_on_eqI
tff(fact_7245_Id__on__eqI,axiom,
    ! [A: $o,B: $o,A2: set_o] :
      ( ( (A)
      <=> (B) )
     => ( member_o((A),A2)
       => member7466972457876170832od_o_o(product_Pair_o_o((A),(B)),id_on_o(A2)) ) ) ).

% Id_on_eqI
tff(fact_7246_Id__on__eqI,axiom,
    ! [A: nat,B: nat,A2: set_nat] :
      ( ( A = B )
     => ( member_nat(A,A2)
       => member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B),id_on_nat(A2)) ) ) ).

% Id_on_eqI
tff(fact_7247_Id__on__eqI,axiom,
    ! [A: int,B: int,A2: set_int] :
      ( ( A = B )
     => ( member_int(A,A2)
       => member5262025264175285858nt_int(aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A),B),id_on_int(A2)) ) ) ).

% Id_on_eqI
tff(fact_7248_Id__onE,axiom,
    ! [C: produc1906917888121415911at_nat,A2: set_Pr4329608150637261639at_nat] :
      ( member6009668390874684176at_nat(C,id_on_7869290023980668164at_nat(A2))
     => ~ ! [X3: produc3843707927480180839at_nat] :
            ( member8757157785044589968at_nat(X3,A2)
           => ( C != produc2335810615602371415at_nat(X3,X3) ) ) ) ).

% Id_onE
tff(fact_7249_Id__onE,axiom,
    ! [C: produc859450856879609959at_nat,A2: set_Pr1261947904930325089at_nat] :
      ( member8206827879206165904at_nat(C,id_on_2554058798563519774at_nat(A2))
     => ~ ! [X3: product_prod_nat_nat] :
            ( member8440522571783428010at_nat(X3,A2)
           => ( C != produc6161850002892822231at_nat(X3,X3) ) ) ) ).

% Id_onE
tff(fact_7250_Id__onE,axiom,
    ! [C: product_prod_o_o,A2: set_o] :
      ( member7466972457876170832od_o_o(C,id_on_o(A2))
     => ~ ! [X3: $o] :
            ( member_o((X3),A2)
           => ( C != product_Pair_o_o((X3),(X3)) ) ) ) ).

% Id_onE
tff(fact_7251_Id__onE,axiom,
    ! [C: product_prod_int_int,A2: set_int] :
      ( member5262025264175285858nt_int(C,id_on_int(A2))
     => ~ ! [X3: int] :
            ( member_int(X3,A2)
           => ( C != aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X3),X3) ) ) ) ).

% Id_onE
tff(fact_7252_Id__onE,axiom,
    ! [C: produc3843707927480180839at_nat,A2: set_se7855581050983116737at_nat] :
      ( member8757157785044589968at_nat(C,id_on_6713504163309144702at_nat(A2))
     => ~ ! [X3: set_Pr1261947904930325089at_nat] :
            ( member2643936169264416010at_nat(X3,A2)
           => ( C != produc2922128104949294807at_nat(X3,X3) ) ) ) ).

% Id_onE
tff(fact_7253_Id__onE,axiom,
    ! [C: product_prod_nat_nat,A2: set_nat] :
      ( member8440522571783428010at_nat(C,id_on_nat(A2))
     => ~ ! [X3: nat] :
            ( member_nat(X3,A2)
           => ( C != aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),X3) ) ) ) ).

% Id_onE
tff(fact_7254_bezout__nat,axiom,
    ! [A: nat,B: nat] :
      ( ( A != zero_zero_nat )
     => ? [X3: nat,Y4: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,A),X3) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,B),Y4)),aa_nat_nat(aa_nat_fun_nat_nat(gcd_gcd_nat,A),B)) ) ).

% bezout_nat
tff(fact_7255_one__rat_Otransfer,axiom,
    aa_rat_o(aa_Pro2298929076809959388_rat_o(pcr_rat,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,one_one_int),one_one_int)),one_one_rat) ).

% one_rat.transfer
tff(fact_7256_zero__rat_Otransfer,axiom,
    aa_rat_o(aa_Pro2298929076809959388_rat_o(pcr_rat,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,zero_zero_int),one_one_int)),zero_zero_rat) ).

% zero_rat.transfer
tff(fact_7257_bezw__aux,axiom,
    ! [X2: nat,Y: nat] : aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(aa_nat_fun_nat_nat(gcd_gcd_nat,X2),Y)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_Pro6799258434465214121nt_int(product_fst_int_int,aa_nat4424723855478970923nt_int(bezw(X2),Y))),aa_nat_int(semiri1314217659103216013at_int,X2))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_Pro6799258434465214121nt_int(product_snd_int_int,aa_nat4424723855478970923nt_int(bezw(X2),Y))),aa_nat_int(semiri1314217659103216013at_int,Y))) ).

% bezw_aux
tff(fact_7258_uminus__rat_Otransfer,axiom,
    aa_fun_rat_rat_o(aa_fun382765352565706371_rat_o(bNF_re8279943556446156061nt_rat(pcr_rat,pcr_rat),aTP_Lamm_acb),uminus_uminus_rat) ).

% uminus_rat.transfer
tff(fact_7259_gcd__nat_Opelims,axiom,
    ! [X2: nat,Xa: nat,Y: nat] :
      ( ( aa_nat_nat(aa_nat_fun_nat_nat(gcd_gcd_nat,X2),Xa) = Y )
     => ( aa_Pro6150637604445964947_nat_o(accp_P4275260045618599050at_nat(gcd_nat_rel),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X2),Xa))
       => ~ ( ( Y = $ite(Xa = zero_zero_nat,X2,aa_nat_nat(aa_nat_fun_nat_nat(gcd_gcd_nat,Xa),aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X2),Xa))) )
           => ~ aa_Pro6150637604445964947_nat_o(accp_P4275260045618599050at_nat(gcd_nat_rel),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X2),Xa)) ) ) ) ).

% gcd_nat.pelims
tff(fact_7260_o__rsp_I1_J,axiom,
    ! [R23: fun_Co2081214437782444048eger_o,R32: fun_Co2081214437782444048eger_o,R12: fun_num_fun_num_o] : bNF_re6079157782214477977nteger(bNF_re1062419521925302741nteger(R23,R32),bNF_re2651952162905501745nteger(bNF_re6741283560065411407nteger(R12,R23),bNF_re6741283560065411407nteger(R12,R32)),comp_C3531382070062128313er_num,comp_C3531382070062128313er_num) ).

% o_rsp(1)
tff(fact_7261_o__rsp_I1_J,axiom,
    ! [R23: fun_Co1375048237525739357_nat_o,R32: fun_Co2133228800495250323_num_o,R12: fun_num_fun_int_o] : bNF_re2315437451418592029nt_num(bNF_re1758498617148825349er_num(R23,R32),bNF_re7101714357556715909nt_num(bNF_re6324211044263125204er_nat(R12,R23),bNF_re2881542830418903838er_num(R12,R32)),comp_C3531382070062128313er_num,comp_nat_num_int) ).

% o_rsp(1)
tff(fact_7262_o__rsp_I1_J,axiom,
    ! [R23: fun_na6318815019539281885eger_o,R32: fun_nu5413996832991386387eger_o,R12: fun_int_fun_num_o] : bNF_re8577298986372545309nteger(bNF_re8763372240999575301nteger(R23,R32),bNF_re6745137351003365765nteger(bNF_re151304249936775380nteger(R12,R23),bNF_re7315484114762210078nteger(R12,R32)),comp_nat_num_int,comp_C3531382070062128313er_num) ).

% o_rsp(1)
tff(fact_7263_o__rsp_I1_J,axiom,
    ! [R23: fun_nat_fun_nat_o,R32: fun_num_fun_num_o,R12: fun_int_fun_int_o] : bNF_re62826171660744097nt_num(bNF_re341483209202555957um_num(R23,R32),bNF_re7119215340858952409nt_num(bNF_re3715656647883201625at_nat(R12,R23),bNF_re7626690874201225453um_num(R12,R32)),comp_nat_num_int,comp_nat_num_int) ).

% o_rsp(1)
tff(fact_7264_o__rsp_I1_J,axiom,
    ! [R23: fun_int_fun_int_o,R32: fun_fu7564235448449272366at_o_o,R12: fun_int_fun_int_o] : bNF_re3759051196448504669_nat_o(bNF_re8347998229424194295_nat_o(R23,R32),bNF_re3454423673187561737_nat_o(bNF_re4712519889275205905nt_int(R12,R23),bNF_re8347998229424194295_nat_o(R12,R32)),comp_i4004505821124781822_o_int,comp_i4004505821124781822_o_int) ).

% o_rsp(1)
tff(fact_7265_o__rsp_I1_J,axiom,
    ! [R23: fun_int_fun_int_o,R32: fun_fu6971708032831053102nt_o_o,R12: fun_int_fun_int_o] : bNF_re1178300526625999197_int_o(bNF_re8654322613993568759_int_o(R23,R32),bNF_re347998642166628361_int_o(bNF_re4712519889275205905nt_int(R12,R23),bNF_re8654322613993568759_int_o(R12,R32)),comp_i4691081854165332386_o_int,comp_i4691081854165332386_o_int) ).

% o_rsp(1)
tff(fact_7266_o__rsp_I1_J,axiom,
    ! [R23: fun_int_fun_int_o,R32: fun_fu4208408993564413984_int_o,R12: fun_int_fun_int_o] : bNF_re7874820051692727037nt_int(bNF_re5717476210804479843nt_int(R23,R32),bNF_re6139702209426042631nt_int(bNF_re4712519889275205905nt_int(R12,R23),bNF_re5717476210804479843nt_int(R12,R32)),comp_i133330754224947090nt_int,comp_i133330754224947090nt_int) ).

% o_rsp(1)
tff(fact_7267_o__rsp_I1_J,axiom,
    ! [R23: fun_Co2081214437782444048eger_o,R32: fun_Co2466309612238040426eger_o,R12: fun_nu5413996832991386387eger_o] : bNF_re1917959877943869547nteger(bNF_re3535719783769048059nteger(R23,R32),bNF_re6610812174003455837nteger(bNF_re5202476307641864082nteger(R12,R23),bNF_re8002177354109194296nteger(R12,R32)),comp_C3531382070062128313er_num,comp_C7848664941760151970nteger) ).

% o_rsp(1)
tff(fact_7268_o__rsp_I1_J,axiom,
    ! [R23: fun_Co2081214437782444048eger_o,R32: fun_fu8559083954280392170eger_o,R12: fun_Co2133228800495250323_num_o] : bNF_re1125984453589466475nteger(bNF_re8292407664666371323nteger(R23,R32),bNF_re4862162959298630877nteger(bNF_re7350422212947406738nteger(R12,R23),bNF_re1115778939589153080nteger(R12,R32)),comp_C7848664941760151970nteger,comp_C3531382070062128313er_num) ).

% o_rsp(1)
tff(fact_7269_o__rsp_I1_J,axiom,
    ! [R23: fun_Co1375048237525739357_nat_o,R32: fun_fu7485687605903516013_num_o,R12: fun_Co8353275306710069249_int_o] : bNF_re2788112638341148655nt_num(bNF_re6729214450274395051er_num(R23,R32),bNF_re4971494712987572401nt_num(bNF_re2891348898900095767er_nat(R12,R23),bNF_re8228350525668042759er_num(R12,R32)),comp_C7848664941760151970nteger,comp_nat_num_int) ).

% o_rsp(1)
tff(fact_7270_o__rsp_I2_J,axiom,
    ! [R12: fun_num_fun_num_o] : bNF_re6079157782214477977nteger(fequal7260506811903038370nteger,bNF_re2651952162905501745nteger(bNF_re6741283560065411407nteger(R12,fequal_Code_integer),bNF_re6741283560065411407nteger(R12,fequal_Code_integer)),comp_C3531382070062128313er_num,comp_C3531382070062128313er_num) ).

% o_rsp(2)
tff(fact_7271_o__rsp_I2_J,axiom,
    ! [R12: fun_int_fun_int_o] : bNF_re62826171660744097nt_num(fequal_fun_nat_num,bNF_re7119215340858952409nt_num(bNF_re3715656647883201625at_nat(R12,fequal_nat),bNF_re7626690874201225453um_num(R12,fequal_num)),comp_nat_num_int,comp_nat_num_int) ).

% o_rsp(2)
tff(fact_7272_o__rsp_I2_J,axiom,
    ! [R12: fun_int_fun_int_o] : bNF_re7349396894857873645_nat_o(fequal2175970220065309678_nat_o,bNF_re6445433324708692061_nat_o(bNF_re8347998229424194295_nat_o(R12,fequal_fun_nat_o),bNF_re8347998229424194295_nat_o(R12,fequal_fun_nat_o)),comp_f697526850294767567_o_int,comp_f697526850294767567_o_int) ).

% o_rsp(2)
tff(fact_7273_o__rsp_I2_J,axiom,
    ! [R12: fun_int_fun_int_o] : bNF_re716005714690020221_int_o(fequal9154197289249639570_int_o,bNF_re3339008293687758685_int_o(bNF_re8347998229424194295_nat_o(R12,fequal_fun_nat_o),bNF_re8654322613993568759_int_o(R12,fequal_fun_int_o)),comp_f1384102883335318131_o_int,comp_f1384102883335318131_o_int) ).

% o_rsp(2)
tff(fact_7274_o__rsp_I2_J,axiom,
    ! [R12: fun_int_fun_int_o] : bNF_re7734436216040599901nt_int(fequal6821775106820213214nt_int,bNF_re2152976507081458779nt_int(bNF_re8347998229424194295_nat_o(R12,fequal_fun_nat_o),bNF_re5717476210804479843nt_int(R12,fequal_fun_int_int)),comp_f2688405924591934721nt_int,comp_f2688405924591934721nt_int) ).

% o_rsp(2)
tff(fact_7275_o__rsp_I2_J,axiom,
    ! [R12: fun_int_fun_int_o] : bNF_re4285988172461392477_nat_o(fequal4303336950067372106_nat_o,bNF_re2199350135795421021_nat_o(bNF_re8654322613993568759_int_o(R12,fequal_fun_int_o),bNF_re8347998229424194295_nat_o(R12,fequal_fun_nat_o)),comp_f1905643983223147563_o_int,comp_f1905643983223147563_o_int) ).

% o_rsp(2)
tff(fact_7276_o__rsp_I2_J,axiom,
    ! [R12: fun_int_fun_int_o] : bNF_re6875969029148314861_int_o(fequal2058191982396926190_int_o,bNF_re8316297141629263453_int_o(bNF_re8654322613993568759_int_o(R12,fequal_fun_int_o),bNF_re8654322613993568759_int_o(R12,fequal_fun_int_o)),comp_f2592220016263698127_o_int,comp_f2592220016263698127_o_int) ).

% o_rsp(2)
tff(fact_7277_o__rsp_I2_J,axiom,
    ! [R12: fun_int_fun_int_o] : bNF_re9021905627891609437nt_int(fequal5394626278453804162nt_int,bNF_re1265104817942401883nt_int(bNF_re8654322613993568759_int_o(R12,fequal_fun_int_o),bNF_re5717476210804479843nt_int(R12,fequal_fun_int_int)),comp_f4365919156373684133nt_int,comp_f4365919156373684133nt_int) ).

% o_rsp(2)
tff(fact_7278_o__rsp_I2_J,axiom,
    ! [R12: fun_int_fun_int_o] : bNF_re2173054563122083805_nat_o(fequal4362665925801888570_nat_o,bNF_re7106894507765562203_nat_o(bNF_re5717476210804479843nt_int(R12,fequal_fun_int_int),bNF_re8347998229424194295_nat_o(R12,fequal_fun_nat_o)),comp_f4214646440711632789_o_int,comp_f4214646440711632789_o_int) ).

% o_rsp(2)
tff(fact_7279_o__rsp_I2_J,axiom,
    ! [R12: fun_int_fun_int_o] : bNF_re7201718523177301469_int_o(fequal2117520958131442654_int_o,bNF_re4000469476744628827_int_o(bNF_re5717476210804479843nt_int(R12,fequal_fun_int_int),bNF_re8654322613993568759_int_o(R12,fequal_fun_int_o)),comp_f4901222473752183353_o_int,comp_f4901222473752183353_o_int) ).

% o_rsp(2)
tff(fact_7280_apfst__convE,axiom,
    ! [Q3: produc2453742332425399446nteger,F: fun_fu2505754153367914865e_term,P2: produc2453742332425399446nteger] :
      ( ( Q3 = produc183566614307960809nteger(F,P2) )
     => ~ ! [X3: fun_Pr5098669352780829690e_term,Y4: produc8923325533196201883nteger] :
            ( ( P2 = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X3),Y4) )
           => ( Q3 != aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,aa_fun1248587000295462322e_term(F,X3)),Y4) ) ) ) ).

% apfst_convE
tff(fact_7281_apfst__convE,axiom,
    ! [Q3: produc8799533983703829792et_nat,F: fun_fu8419763957888848259_nat_o,P2: produc8799533983703829792et_nat] :
      ( ( Q3 = aa_Pro5931322043027775230et_nat(produc1926458052860118910et_nat(F),P2) )
     => ~ ! [X3: fun_Pr6460944699146269935_nat_o,Y4: produc3658429121746597890et_nat] :
            ( ( P2 = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X3),Y4) )
           => ( Q3 != aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,aa_fun2638059832795814268_nat_o(F,X3)),Y4) ) ) ) ).

% apfst_convE
tff(fact_7282_apfst__convE,axiom,
    ! [Q3: produc3112576180687729086et_nat,F: fun_fu8419763957888848259_nat_o,P2: produc3112576180687729086et_nat] :
      ( ( Q3 = produc7064264152226348700et_nat(F,P2) )
     => ~ ! [X3: fun_Pr6460944699146269935_nat_o,Y4: produc8799533983703829792et_nat] :
            ( ( P2 = aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X3),Y4) )
           => ( Q3 != aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,aa_fun2638059832795814268_nat_o(F,X3)),Y4) ) ) ) ).

% apfst_convE
tff(fact_7283_apfst__convE,axiom,
    ! [Q3: produc3043004577601930755nt_int,F: fun_fu836511555612062035e_term,P2: produc3043004577601930755nt_int] :
      ( ( Q3 = produc7857123342865048869nt_int(F,P2) )
     => ~ ! [X3: fun_Pr7763680713840462443e_term,Y4: product_prod_int_int] :
            ( ( P2 = aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X3),Y4) )
           => ( Q3 != aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,aa_fun49903357033182740e_term(F,X3)),Y4) ) ) ) ).

% apfst_convE
tff(fact_7284_apfst__convE,axiom,
    ! [Q3: produc4788131091073775919nt_int,F: fun_fu4835546211937200935e_term,P2: produc3043004577601930755nt_int] :
      ( ( Q3 = produc7965835600623382609nt_int(F,P2) )
     => ~ ! [X3: fun_Pr7763680713840462443e_term,Y4: product_prod_int_int] :
            ( ( P2 = aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X3),Y4) )
           => ( Q3 != aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,aa_fun3544567364070095336e_term(F,X3)),Y4) ) ) ) ).

% apfst_convE
tff(fact_7285_apfst__convE,axiom,
    ! [Q3: produc3043004577601930755nt_int,F: fun_fu1176768540439120679e_term,P2: produc4788131091073775919nt_int] :
      ( ( Q3 = produc479425830829021777nt_int(F,P2) )
     => ~ ! [X3: fun_in5730379987311621695e_term,Y4: product_prod_int_int] :
            ( ( P2 = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X3),Y4) )
           => ( Q3 != aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,aa_fun1932935823081541608e_term(F,X3)),Y4) ) ) ) ).

% apfst_convE
tff(fact_7286_apfst__convE,axiom,
    ! [Q3: produc4788131091073775919nt_int,F: fun_fu4810317505167811835e_term,P2: produc4788131091073775919nt_int] :
      ( ( Q3 = produc5901819666759714173nt_int(F,P2) )
     => ~ ! [X3: fun_in5730379987311621695e_term,Y4: product_prod_int_int] :
            ( ( P2 = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X3),Y4) )
           => ( Q3 != aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,aa_fun5947755341433680828e_term(F,X3)),Y4) ) ) ) ).

% apfst_convE
tff(fact_7287_UN__le__eq__Un0,axiom,
    ! [M2: fun_na5670658592214072528at_nat,N2: nat] : comple4364388969068068532at_nat(image_1087905878993176368at_nat(M2,aa_nat_set_nat(set_ord_atMost_nat,N2))) = sup_su5525570899277871387at_nat(comple4364388969068068532at_nat(image_1087905878993176368at_nat(M2,aa_nat_set_nat(set_or1269000886237332187st_nat(one_one_nat),N2))),aa_nat8843416860741599929at_nat(M2,zero_zero_nat)) ).

% UN_le_eq_Un0
tff(fact_7288_UN__le__eq__Un0,axiom,
    ! [M2: fun_nat_set_nat,N2: nat] : comple7399068483239264473et_nat(image_nat_set_nat(M2,aa_nat_set_nat(set_ord_atMost_nat,N2))) = sup_sup_set_nat(comple7399068483239264473et_nat(image_nat_set_nat(M2,aa_nat_set_nat(set_or1269000886237332187st_nat(one_one_nat),N2))),aa_nat_set_nat(M2,zero_zero_nat)) ).

% UN_le_eq_Un0
tff(fact_7289_times__int_Orsp,axiom,
    bNF_re6214786843070381989at_nat(intrel,bNF_re2241393799969408733at_nat(intrel,intrel),aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,aTP_Lamm_gd),aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,aTP_Lamm_gd)) ).

% times_int.rsp
tff(fact_7290_sup__Some,axiom,
    ! [X2: set_nat,Y: set_nat] : sup_su3598758113090618626et_nat(aa_set6119337032432945050et_nat(some_set_nat,X2),aa_set6119337032432945050et_nat(some_set_nat,Y)) = aa_set6119337032432945050et_nat(some_set_nat,sup_sup_set_nat(X2,Y)) ).

% sup_Some
tff(fact_7291_sup__Some,axiom,
    ! [X2: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] : sup_su2273273666271716065at_nat(some_s5890477192898017836at_nat(X2),some_s5890477192898017836at_nat(Y)) = some_s5890477192898017836at_nat(sup_su5525570899277871387at_nat(X2,Y)) ).

% sup_Some
tff(fact_7292_sup__Some,axiom,
    ! [X2: product_unit,Y: product_unit] : sup_su7717485023253700007t_unit(aa_Pro7616171890175246658t_unit(some_Product_unit,X2),aa_Pro7616171890175246658t_unit(some_Product_unit,Y)) = aa_Pro7616171890175246658t_unit(some_Product_unit,aa_Pro8294289767544744956t_unit(sup_sup_Product_unit(X2),Y)) ).

% sup_Some
tff(fact_7293_sup__Some,axiom,
    ! [X2: assn,Y: assn] : sup_sup_option_assn(some_assn(X2),some_assn(Y)) = some_assn(sup_sup_assn(X2,Y)) ).

% sup_Some
tff(fact_7294_intrel__iff,axiom,
    ! [X2: nat,Y: nat,U: nat,V: nat] :
      ( aa_Pro6150637604445964947_nat_o(aa_Pro989595756709598047_nat_o(intrel,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X2),Y)),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,U),V))
    <=> ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X2),V) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,U),Y) ) ) ).

% intrel_iff
tff(fact_7295_insert__Times__insert,axiom,
    ! [A: $o,A2: set_o,B: $o,B4: set_o] : product_Sigma_o_o(insert_o((A),A2),aa_set_o_fun_o_set_o(aTP_Lamm_acc((B)),B4)) = insert6201435330877294327od_o_o(product_Pair_o_o((A),(B)),sup_su5769328420594410459od_o_o(product_Sigma_o_o(A2,aa_set_o_fun_o_set_o(aTP_Lamm_acc((B)),B4)),product_Sigma_o_o(insert_o((A),A2),aTP_Lamm_xs(B4)))) ).

% insert_Times_insert
tff(fact_7296_insert__Times__insert,axiom,
    ! [A: $o,A2: set_o,B: nat,B4: set_nat] : product_Sigma_o_nat(insert_o((A),A2),aa_set1696117090455734765et_nat(aTP_Lamm_acd(B),B4)) = insert7948214739558299847_o_nat(product_Pair_o_nat((A),B),sup_su8679140417860611193_o_nat(product_Sigma_o_nat(A2,aa_set1696117090455734765et_nat(aTP_Lamm_acd(B),B4)),product_Sigma_o_nat(insert_o((A),A2),aTP_Lamm_xt(B4)))) ).

% insert_Times_insert
tff(fact_7297_insert__Times__insert,axiom,
    ! [A: $o,A2: set_o,B: int,B4: set_int] : product_Sigma_o_int(insert_o((A),A2),aa_set8238700067146519789et_int(aTP_Lamm_ace(B),B4)) = insert3770363720049103139_o_int(product_Pair_o_int((A),B),sup_su6189057272928884437_o_int(product_Sigma_o_int(A2,aa_set8238700067146519789et_int(aTP_Lamm_ace(B),B4)),product_Sigma_o_int(insert_o((A),A2),aTP_Lamm_xu(B4)))) ).

% insert_Times_insert
tff(fact_7298_insert__Times__insert,axiom,
    ! [A: nat,A2: set_nat,B: $o,B4: set_o] : product_Sigma_nat_o(insert_nat(A,A2),aa_set557987488673405253_set_o(aTP_Lamm_acf((B)),B4)) = insert2233377226759017069_nat_o(product_Pair_nat_o(A,(B)),sup_su503371503184139039_nat_o(product_Sigma_nat_o(A2,aa_set557987488673405253_set_o(aTP_Lamm_acf((B)),B4)),product_Sigma_nat_o(insert_nat(A,A2),aTP_Lamm_xv(B4)))) ).

% insert_Times_insert
tff(fact_7299_insert__Times__insert,axiom,
    ! [A: nat,A2: set_nat,B: nat,B4: set_nat] : produc457027306803732586at_nat(insert_nat(A,A2),aa_set562305657478724375et_nat(aTP_Lamm_acg(B),B4)) = aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B)),aa_set8868280134176360700at_nat(sup_su6327502436637775413at_nat(produc457027306803732586at_nat(A2,aa_set562305657478724375et_nat(aTP_Lamm_acg(B),B4))),produc457027306803732586at_nat(insert_nat(A,A2),aTP_Lamm_ya(B4)))) ).

% insert_Times_insert
tff(fact_7300_insert__Times__insert,axiom,
    ! [A: nat,A2: set_nat,B: int,B4: set_int] : produc454536836294682310at_int(insert_nat(A,A2),aa_set2464685511577892303et_int(aTP_Lamm_ach(B),B4)) = insert4033959196097957677at_int(product_Pair_nat_int(A,B),sup_su3837419291706048657at_int(produc454536836294682310at_int(A2,aa_set2464685511577892303et_int(aTP_Lamm_ach(B),B4)),produc454536836294682310at_int(insert_nat(A,A2),aTP_Lamm_xw(B4)))) ).

% insert_Times_insert
tff(fact_7301_insert__Times__insert,axiom,
    ! [A: int,A2: set_int,B: $o,B4: set_o] : product_Sigma_int_o(insert_int(A,A2),aa_set1244563521713955817_set_o(aTP_Lamm_aci((B)),B4)) = insert412334881326329105_int_o(product_Pair_int_o(A,(B)),sup_su7481598572368468931_int_o(product_Sigma_int_o(A2,aa_set1244563521713955817_set_o(aTP_Lamm_aci((B)),B4)),product_Sigma_int_o(insert_int(A,A2),aTP_Lamm_xx(B4)))) ).

% insert_Times_insert
tff(fact_7302_insert__Times__insert,axiom,
    ! [A: int,A2: set_int,B: nat,B4: set_nat] : produc1456381018704787142nt_nat(insert_int(A,A2),aa_set933959217715569011et_nat(aTP_Lamm_acj(B),B4)) = insert9211163927508208941nt_nat(aa_nat8602574874988167631nt_nat(product_Pair_int_nat(A),B),sup_su8514424011330797201nt_nat(produc1456381018704787142nt_nat(A2,aa_set933959217715569011et_nat(aTP_Lamm_acj(B),B4)),produc1456381018704787142nt_nat(insert_int(A,A2),aTP_Lamm_xy(B4)))) ).

% insert_Times_insert
tff(fact_7303_insert__Times__insert,axiom,
    ! [A: int,A2: set_int,B: int,B4: set_int] : produc1453890548195736866nt_int(insert_int(A,A2),aa_set2836339071814736939et_int(aTP_Lamm_ack(B),B4)) = insert5033312907999012233nt_int(aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A),B),sup_su6024340866399070445nt_int(produc1453890548195736866nt_int(A2,aa_set2836339071814736939et_int(aTP_Lamm_ack(B),B4)),produc1453890548195736866nt_int(insert_int(A,A2),aTP_Lamm_xz(B4)))) ).

% insert_Times_insert
tff(fact_7304_insert__Times__insert,axiom,
    ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B: $o,B4: set_o] : produc203973861852599583_nat_o(aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(A),A2),aa_set1227366709740544310_set_o(aTP_Lamm_acl((B)),B4)) = insert2126339615020983374_nat_o(produc855456346497908590_nat_o(A,(B)),sup_su5921324857680904370_nat_o(produc203973861852599583_nat_o(A2,aa_set1227366709740544310_set_o(aTP_Lamm_acl((B)),B4)),produc203973861852599583_nat_o(aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(A),A2),aTP_Lamm_yb(B4)))) ).

% insert_Times_insert
tff(fact_7305_Sigma__Un__distrib1,axiom,
    ! [I4: set_se7855581050983116737at_nat,J4: set_se7855581050983116737at_nat,C4: fun_se953073389798102371at_nat] : produc7726050920695093128at_nat(sup_su3642409539654194069at_nat(I4,J4),C4) = sup_su5525570899277871387at_nat(produc7726050920695093128at_nat(I4,C4),produc7726050920695093128at_nat(J4,C4)) ).

% Sigma_Un_distrib1
tff(fact_7306_Sigma__Un__distrib2,axiom,
    ! [I4: set_se7855581050983116737at_nat,A2: fun_se953073389798102371at_nat,B4: fun_se953073389798102371at_nat] : produc7726050920695093128at_nat(I4,aa_fun3786497492886271492at_nat(aTP_Lamm_acm(A2),B4)) = sup_su5525570899277871387at_nat(produc7726050920695093128at_nat(I4,A2),produc7726050920695093128at_nat(I4,B4)) ).

% Sigma_Un_distrib2
tff(fact_7307_Times__Un__distrib1,axiom,
    ! [A2: set_se7855581050983116737at_nat,B4: set_se7855581050983116737at_nat,C4: set_se7855581050983116737at_nat] : produc7726050920695093128at_nat(sup_su3642409539654194069at_nat(A2,B4),aTP_Lamm_yc(C4)) = sup_su5525570899277871387at_nat(produc7726050920695093128at_nat(A2,aTP_Lamm_yc(C4)),produc7726050920695093128at_nat(B4,aTP_Lamm_yc(C4))) ).

% Times_Un_distrib1
tff(fact_7308_set__diff__diff__left,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,B4: set_Pr4329608150637261639at_nat,C4: set_Pr4329608150637261639at_nat] : minus_3314409938677909166at_nat(minus_3314409938677909166at_nat(A2,B4),C4) = minus_3314409938677909166at_nat(A2,sup_su5525570899277871387at_nat(B4,C4)) ).

% set_diff_diff_left
tff(fact_7309_set__diff__diff__left,axiom,
    ! [A2: set_nat,B4: set_nat,C4: set_nat] : minus_minus_set_nat(minus_minus_set_nat(A2,B4),C4) = minus_minus_set_nat(A2,sup_sup_set_nat(B4,C4)) ).

% set_diff_diff_left
tff(fact_7310_sup__option__def,axiom,
    ! [X2: option_set_nat,Y: option_set_nat] : sup_su3598758113090618626et_nat(X2,Y) = case_o4054078431260844265et_nat(Y,aa_opt5648106117674462701et_nat(aTP_Lamm_aco(X2),Y),X2) ).

% sup_option_def
tff(fact_7311_sup__option__def,axiom,
    ! [X2: option1583680563626158861at_nat,Y: option1583680563626158861at_nat] : sup_su2273273666271716065at_nat(X2,Y) = case_o9080059180780454917at_nat(Y,aa_opt1027706798495913626at_nat(aTP_Lamm_acq(X2),Y),X2) ).

% sup_option_def
tff(fact_7312_sup__option__def,axiom,
    ! [X2: option_Product_unit,Y: option_Product_unit] : sup_su7717485023253700007t_unit(X2,Y) = case_o2985186191577459077t_unit(Y,aa_opt8900914514660672992t_unit(aTP_Lamm_acs(X2),Y),X2) ).

% sup_option_def
tff(fact_7313_sup__option__def,axiom,
    ! [X2: option_assn,Y: option_assn] : sup_sup_option_assn(X2,Y) = case_o4484465799723439917n_assn(Y,aa_opt1471905160178427347n_assn(aTP_Lamm_acu(X2),Y),X2) ).

% sup_option_def
tff(fact_7314_ivl__disj__un__two__touch_I4_J,axiom,
    ! [L: rat,M: rat,U: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,L),M)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,M),U)
       => ( sup_sup_set_rat(set_or633870826150836451st_rat(L,M),set_or633870826150836451st_rat(M,U)) = set_or633870826150836451st_rat(L,U) ) ) ) ).

% ivl_disj_un_two_touch(4)
tff(fact_7315_ivl__disj__un__two__touch_I4_J,axiom,
    ! [L: num,M: num,U: num] :
      ( aa_num_o(aa_num_fun_num_o(ord_less_eq_num,L),M)
     => ( aa_num_o(aa_num_fun_num_o(ord_less_eq_num,M),U)
       => ( sup_sup_set_num(set_or7049704709247886629st_num(L,M),set_or7049704709247886629st_num(M,U)) = set_or7049704709247886629st_num(L,U) ) ) ) ).

% ivl_disj_un_two_touch(4)
tff(fact_7316_ivl__disj__un__two__touch_I4_J,axiom,
    ! [L: int,M: int,U: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,L),M)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,M),U)
       => ( sup_sup_set_int(aa_int_set_int(set_or1266510415728281911st_int(L),M),aa_int_set_int(set_or1266510415728281911st_int(M),U)) = aa_int_set_int(set_or1266510415728281911st_int(L),U) ) ) ) ).

% ivl_disj_un_two_touch(4)
tff(fact_7317_ivl__disj__un__two__touch_I4_J,axiom,
    ! [L: nat,M: nat,U: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,L),M)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),U)
       => ( sup_sup_set_nat(aa_nat_set_nat(set_or1269000886237332187st_nat(L),M),aa_nat_set_nat(set_or1269000886237332187st_nat(M),U)) = aa_nat_set_nat(set_or1269000886237332187st_nat(L),U) ) ) ) ).

% ivl_disj_un_two_touch(4)
tff(fact_7318_ivl__disj__un__two__touch_I4_J,axiom,
    ! [L: code_integer,M: code_integer,U: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,L),M)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,M),U)
       => ( sup_su848401254843788991nteger(aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(L),M),aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(M),U)) = aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(L),U) ) ) ) ).

% ivl_disj_un_two_touch(4)
tff(fact_7319_ivl__disj__un__two_I3_J,axiom,
    ! [L: rat,M: rat,U: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,L),M)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,M),U)
       => ( sup_sup_set_rat(set_or4029947393144176647an_rat(L,M),set_or4029947393144176647an_rat(M,U)) = set_or4029947393144176647an_rat(L,U) ) ) ) ).

% ivl_disj_un_two(3)
tff(fact_7320_ivl__disj__un__two_I3_J,axiom,
    ! [L: num,M: num,U: num] :
      ( aa_num_o(aa_num_fun_num_o(ord_less_eq_num,L),M)
     => ( aa_num_o(aa_num_fun_num_o(ord_less_eq_num,M),U)
       => ( sup_sup_set_num(set_or1222409239386451017an_num(L,M),set_or1222409239386451017an_num(M,U)) = set_or1222409239386451017an_num(L,U) ) ) ) ).

% ivl_disj_un_two(3)
tff(fact_7321_ivl__disj__un__two_I3_J,axiom,
    ! [L: nat,M: nat,U: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,L),M)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),U)
       => ( sup_sup_set_nat(aa_nat_set_nat(set_or4665077453230672383an_nat(L),M),aa_nat_set_nat(set_or4665077453230672383an_nat(M),U)) = aa_nat_set_nat(set_or4665077453230672383an_nat(L),U) ) ) ) ).

% ivl_disj_un_two(3)
tff(fact_7322_ivl__disj__un__two_I3_J,axiom,
    ! [L: code_integer,M: code_integer,U: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,L),M)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,M),U)
       => ( sup_su848401254843788991nteger(aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(L),M),aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(M),U)) = aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(L),U) ) ) ) ).

% ivl_disj_un_two(3)
tff(fact_7323_ivl__disj__un__two_I3_J,axiom,
    ! [L: int,M: int,U: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,L),M)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,M),U)
       => ( sup_sup_set_int(aa_int_set_int(set_or4662586982721622107an_int(L),M),aa_int_set_int(set_or4662586982721622107an_int(M),U)) = aa_int_set_int(set_or4662586982721622107an_int(L),U) ) ) ) ).

% ivl_disj_un_two(3)
tff(fact_7324_max__ext__additive,axiom,
    ! [A2: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat,R3: set_Pr8693737435421807431at_nat,C4: set_Pr1261947904930325089at_nat,D3: set_Pr1261947904930325089at_nat] :
      ( member8757157785044589968at_nat(produc2922128104949294807at_nat(A2,B4),max_ex8135407076693332796at_nat(R3))
     => ( member8757157785044589968at_nat(produc2922128104949294807at_nat(C4,D3),max_ex8135407076693332796at_nat(R3))
       => member8757157785044589968at_nat(produc2922128104949294807at_nat(aa_set8868280134176360700at_nat(sup_su6327502436637775413at_nat(A2),C4),aa_set8868280134176360700at_nat(sup_su6327502436637775413at_nat(B4),D3)),max_ex8135407076693332796at_nat(R3)) ) ) ).

% max_ext_additive
tff(fact_7325_max__ext__additive,axiom,
    ! [A2: set_nat,B4: set_nat,R3: set_Pr1261947904930325089at_nat,C4: set_nat,D3: set_nat] :
      ( member8277197624267554838et_nat(produc4532415448927165861et_nat(A2,B4),max_ext_nat(R3))
     => ( member8277197624267554838et_nat(produc4532415448927165861et_nat(C4,D3),max_ext_nat(R3))
       => member8277197624267554838et_nat(produc4532415448927165861et_nat(sup_sup_set_nat(A2,C4),sup_sup_set_nat(B4,D3)),max_ext_nat(R3)) ) ) ).

% max_ext_additive
tff(fact_7326_max__ext__additive,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,B4: set_Pr4329608150637261639at_nat,R3: set_Pr5564308138774400199at_nat,C4: set_Pr4329608150637261639at_nat,D3: set_Pr4329608150637261639at_nat] :
      ( member1466754251312161552at_nat(produc9060074326276436823at_nat(A2,B4),max_ex8833738776070432290at_nat(R3))
     => ( member1466754251312161552at_nat(produc9060074326276436823at_nat(C4,D3),max_ex8833738776070432290at_nat(R3))
       => member1466754251312161552at_nat(produc9060074326276436823at_nat(sup_su5525570899277871387at_nat(A2,C4),sup_su5525570899277871387at_nat(B4,D3)),max_ex8833738776070432290at_nat(R3)) ) ) ).

% max_ext_additive
tff(fact_7327_zero__int_Orsp,axiom,
    aa_Pro6150637604445964947_nat_o(aa_Pro989595756709598047_nat_o(intrel,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,zero_zero_nat),zero_zero_nat)),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,zero_zero_nat),zero_zero_nat)) ).

% zero_int.rsp
tff(fact_7328_ivl__disj__un__two_I7_J,axiom,
    ! [L: rat,M: rat,U: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,L),M)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,M),U)
       => ( sup_sup_set_rat(set_or4029947393144176647an_rat(L,M),set_or633870826150836451st_rat(M,U)) = set_or633870826150836451st_rat(L,U) ) ) ) ).

% ivl_disj_un_two(7)
tff(fact_7329_ivl__disj__un__two_I7_J,axiom,
    ! [L: num,M: num,U: num] :
      ( aa_num_o(aa_num_fun_num_o(ord_less_eq_num,L),M)
     => ( aa_num_o(aa_num_fun_num_o(ord_less_eq_num,M),U)
       => ( sup_sup_set_num(set_or1222409239386451017an_num(L,M),set_or7049704709247886629st_num(M,U)) = set_or7049704709247886629st_num(L,U) ) ) ) ).

% ivl_disj_un_two(7)
tff(fact_7330_ivl__disj__un__two_I7_J,axiom,
    ! [L: nat,M: nat,U: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,L),M)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),U)
       => ( sup_sup_set_nat(aa_nat_set_nat(set_or4665077453230672383an_nat(L),M),aa_nat_set_nat(set_or1269000886237332187st_nat(M),U)) = aa_nat_set_nat(set_or1269000886237332187st_nat(L),U) ) ) ) ).

% ivl_disj_un_two(7)
tff(fact_7331_ivl__disj__un__two_I7_J,axiom,
    ! [L: code_integer,M: code_integer,U: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,L),M)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,M),U)
       => ( sup_su848401254843788991nteger(aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(L),M),aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(M),U)) = aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(L),U) ) ) ) ).

% ivl_disj_un_two(7)
tff(fact_7332_ivl__disj__un__two_I7_J,axiom,
    ! [L: int,M: int,U: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,L),M)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,M),U)
       => ( sup_sup_set_int(aa_int_set_int(set_or4662586982721622107an_int(L),M),aa_int_set_int(set_or1266510415728281911st_int(M),U)) = aa_int_set_int(set_or1266510415728281911st_int(L),U) ) ) ) ).

% ivl_disj_un_two(7)
tff(fact_7333_card__Un__le,axiom,
    ! [A2: set_int,B4: set_int] : aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite_card_int(sup_sup_set_int(A2,B4))),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,finite_card_int(A2)),finite_card_int(B4))) ).

% card_Un_le
tff(fact_7334_card__Un__le,axiom,
    ! [A2: set_Product_unit,B4: set_Product_unit] : aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite410649719033368117t_unit(sup_su793286257634532545t_unit(A2,B4))),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,finite410649719033368117t_unit(A2)),finite410649719033368117t_unit(B4))) ).

% card_Un_le
tff(fact_7335_card__Un__le,axiom,
    ! [A2: set_list_nat,B4: set_list_nat] : aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite_card_list_nat(sup_sup_set_list_nat(A2,B4))),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,finite_card_list_nat(A2)),finite_card_list_nat(B4))) ).

% card_Un_le
tff(fact_7336_card__Un__le,axiom,
    ! [A2: set_nat,B4: set_nat] : aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_set_nat_nat(finite_card_nat,sup_sup_set_nat(A2,B4))),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_set_nat_nat(finite_card_nat,A2)),aa_set_nat_nat(finite_card_nat,B4))) ).

% card_Un_le
tff(fact_7337_card__Un__le,axiom,
    ! [A2: set_Pr4329608150637261639at_nat,B4: set_Pr4329608150637261639at_nat] : aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,finite3771342082235030671at_nat(sup_su5525570899277871387at_nat(A2,B4))),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,finite3771342082235030671at_nat(A2)),finite3771342082235030671at_nat(B4))) ).

% card_Un_le
tff(fact_7338_ivl__disj__un__one_I2_J,axiom,
    ! [L: rat,U: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,L),U)
     => ( sup_sup_set_rat(set_ord_lessThan_rat(L),set_or4029947393144176647an_rat(L,U)) = set_ord_lessThan_rat(U) ) ) ).

% ivl_disj_un_one(2)
tff(fact_7339_ivl__disj__un__one_I2_J,axiom,
    ! [L: num,U: num] :
      ( aa_num_o(aa_num_fun_num_o(ord_less_eq_num,L),U)
     => ( sup_sup_set_num(set_ord_lessThan_num(L),set_or1222409239386451017an_num(L,U)) = set_ord_lessThan_num(U) ) ) ).

% ivl_disj_un_one(2)
tff(fact_7340_ivl__disj__un__one_I2_J,axiom,
    ! [L: nat,U: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,L),U)
     => ( sup_sup_set_nat(aa_nat_set_nat(set_ord_lessThan_nat,L),aa_nat_set_nat(set_or4665077453230672383an_nat(L),U)) = aa_nat_set_nat(set_ord_lessThan_nat,U) ) ) ).

% ivl_disj_un_one(2)
tff(fact_7341_ivl__disj__un__one_I2_J,axiom,
    ! [L: code_integer,U: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,L),U)
     => ( sup_su848401254843788991nteger(aa_Cod2813182003028390446nteger(set_or5754767410780653050nteger,L),aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(L),U)) = aa_Cod2813182003028390446nteger(set_or5754767410780653050nteger,U) ) ) ).

% ivl_disj_un_one(2)
tff(fact_7342_ivl__disj__un__one_I2_J,axiom,
    ! [L: int,U: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,L),U)
     => ( sup_sup_set_int(aa_int_set_int(set_ord_lessThan_int,L),aa_int_set_int(set_or4662586982721622107an_int(L),U)) = aa_int_set_int(set_ord_lessThan_int,U) ) ) ).

% ivl_disj_un_one(2)
tff(fact_7343_atLeastLessThan__add__Un,axiom,
    ! [I: nat,J: nat,K: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,I),J)
     => ( aa_nat_set_nat(set_or4665077453230672383an_nat(I),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),K)) = sup_sup_set_nat(aa_nat_set_nat(set_or4665077453230672383an_nat(I),J),aa_nat_set_nat(set_or4665077453230672383an_nat(J),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),K))) ) ) ).

% atLeastLessThan_add_Un
tff(fact_7344_uminus__int_Orsp,axiom,
    aa_fun3538214411680374423_nat_o(aa_fun6920661532540581549_nat_o(bNF_re2241393799969408733at_nat(intrel,intrel),produc2626176000494625587at_nat(aTP_Lamm_dg)),produc2626176000494625587at_nat(aTP_Lamm_dg)) ).

% uminus_int.rsp
tff(fact_7345_one__int_Orsp,axiom,
    aa_Pro6150637604445964947_nat_o(aa_Pro989595756709598047_nat_o(intrel,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,one_one_nat),zero_zero_nat)),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,one_one_nat),zero_zero_nat)) ).

% one_int.rsp
tff(fact_7346_ivl__disj__un__two__touch_I2_J,axiom,
    ! [L: rat,M: rat,U: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,L),M)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,M),U)
       => ( sup_sup_set_rat(set_or633870826150836451st_rat(L,M),set_or4029947393144176647an_rat(M,U)) = set_or4029947393144176647an_rat(L,U) ) ) ) ).

% ivl_disj_un_two_touch(2)
tff(fact_7347_ivl__disj__un__two__touch_I2_J,axiom,
    ! [L: num,M: num,U: num] :
      ( aa_num_o(aa_num_fun_num_o(ord_less_eq_num,L),M)
     => ( aa_num_o(aa_num_fun_num_o(ord_less_num,M),U)
       => ( sup_sup_set_num(set_or7049704709247886629st_num(L,M),set_or1222409239386451017an_num(M,U)) = set_or1222409239386451017an_num(L,U) ) ) ) ).

% ivl_disj_un_two_touch(2)
tff(fact_7348_ivl__disj__un__two__touch_I2_J,axiom,
    ! [L: nat,M: nat,U: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,L),M)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M),U)
       => ( sup_sup_set_nat(aa_nat_set_nat(set_or1269000886237332187st_nat(L),M),aa_nat_set_nat(set_or4665077453230672383an_nat(M),U)) = aa_nat_set_nat(set_or4665077453230672383an_nat(L),U) ) ) ) ).

% ivl_disj_un_two_touch(2)
tff(fact_7349_ivl__disj__un__two__touch_I2_J,axiom,
    ! [L: code_integer,M: code_integer,U: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,L),M)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,M),U)
       => ( sup_su848401254843788991nteger(aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(L),M),aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(M),U)) = aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(L),U) ) ) ) ).

% ivl_disj_un_two_touch(2)
tff(fact_7350_ivl__disj__un__two__touch_I2_J,axiom,
    ! [L: int,M: int,U: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,L),M)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,M),U)
       => ( sup_sup_set_int(aa_int_set_int(set_or1266510415728281911st_int(L),M),aa_int_set_int(set_or4662586982721622107an_int(M),U)) = aa_int_set_int(set_or4662586982721622107an_int(L),U) ) ) ) ).

% ivl_disj_un_two_touch(2)
tff(fact_7351_ivl__disj__un__two_I1_J,axiom,
    ! [L: rat,M: rat,U: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,L),M)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,M),U)
       => ( sup_sup_set_rat(set_or5199638295745620268an_rat(L,M),set_or4029947393144176647an_rat(M,U)) = set_or5199638295745620268an_rat(L,U) ) ) ) ).

% ivl_disj_un_two(1)
tff(fact_7352_ivl__disj__un__two_I1_J,axiom,
    ! [L: num,M: num,U: num] :
      ( aa_num_o(aa_num_fun_num_o(ord_less_num,L),M)
     => ( aa_num_o(aa_num_fun_num_o(ord_less_eq_num,M),U)
       => ( sup_sup_set_num(set_or2392100141987894638an_num(L,M),set_or1222409239386451017an_num(M,U)) = set_or2392100141987894638an_num(L,U) ) ) ) ).

% ivl_disj_un_two(1)
tff(fact_7353_ivl__disj__un__two_I1_J,axiom,
    ! [L: int,M: int,U: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,L),M)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,M),U)
       => ( sup_sup_set_int(aa_int_set_int(set_or5832277885323065728an_int(L),M),aa_int_set_int(set_or4662586982721622107an_int(M),U)) = aa_int_set_int(set_or5832277885323065728an_int(L),U) ) ) ) ).

% ivl_disj_un_two(1)
tff(fact_7354_ivl__disj__un__two_I1_J,axiom,
    ! [L: nat,M: nat,U: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,L),M)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),U)
       => ( sup_sup_set_nat(aa_nat_set_nat(set_or5834768355832116004an_nat(L),M),aa_nat_set_nat(set_or4665077453230672383an_nat(M),U)) = aa_nat_set_nat(set_or5834768355832116004an_nat(L),U) ) ) ) ).

% ivl_disj_un_two(1)
tff(fact_7355_ivl__disj__un__two_I1_J,axiom,
    ! [L: code_integer,M: code_integer,U: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,L),M)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,M),U)
       => ( sup_su848401254843788991nteger(aa_Cod2813182003028390446nteger(set_or4266950643985792945nteger(L),M),aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(M),U)) = aa_Cod2813182003028390446nteger(set_or4266950643985792945nteger(L),U) ) ) ) ).

% ivl_disj_un_two(1)
tff(fact_7356_ivl__disj__un__singleton_I2_J,axiom,
    ! [U: $o] : sup_sup_set_o(aa_o_set_o(set_ord_lessThan_o,(U)),insert_o((U),bot_bot_set_o)) = aa_o_set_o(set_ord_atMost_o,(U)) ).

% ivl_disj_un_singleton(2)
tff(fact_7357_ivl__disj__un__singleton_I2_J,axiom,
    ! [U: int] : sup_sup_set_int(aa_int_set_int(set_ord_lessThan_int,U),insert_int(U,bot_bot_set_int)) = aa_int_set_int(set_ord_atMost_int,U) ).

% ivl_disj_un_singleton(2)
tff(fact_7358_ivl__disj__un__singleton_I2_J,axiom,
    ! [U: nat] : sup_sup_set_nat(aa_nat_set_nat(set_ord_lessThan_nat,U),insert_nat(U,bot_bot_set_nat)) = aa_nat_set_nat(set_ord_atMost_nat,U) ).

% ivl_disj_un_singleton(2)
tff(fact_7359_ivl__disj__un__one_I4_J,axiom,
    ! [L: rat,U: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,L),U)
     => ( sup_sup_set_rat(set_ord_lessThan_rat(L),set_or633870826150836451st_rat(L,U)) = set_ord_atMost_rat(U) ) ) ).

% ivl_disj_un_one(4)
tff(fact_7360_ivl__disj__un__one_I4_J,axiom,
    ! [L: num,U: num] :
      ( aa_num_o(aa_num_fun_num_o(ord_less_eq_num,L),U)
     => ( sup_sup_set_num(set_ord_lessThan_num(L),set_or7049704709247886629st_num(L,U)) = set_ord_atMost_num(U) ) ) ).

% ivl_disj_un_one(4)
tff(fact_7361_ivl__disj__un__one_I4_J,axiom,
    ! [L: int,U: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,L),U)
     => ( sup_sup_set_int(aa_int_set_int(set_ord_lessThan_int,L),aa_int_set_int(set_or1266510415728281911st_int(L),U)) = aa_int_set_int(set_ord_atMost_int,U) ) ) ).

% ivl_disj_un_one(4)
tff(fact_7362_ivl__disj__un__one_I4_J,axiom,
    ! [L: nat,U: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,L),U)
     => ( sup_sup_set_nat(aa_nat_set_nat(set_ord_lessThan_nat,L),aa_nat_set_nat(set_or1269000886237332187st_nat(L),U)) = aa_nat_set_nat(set_ord_atMost_nat,U) ) ) ).

% ivl_disj_un_one(4)
tff(fact_7363_ivl__disj__un__one_I4_J,axiom,
    ! [L: code_integer,U: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,L),U)
     => ( sup_su848401254843788991nteger(aa_Cod2813182003028390446nteger(set_or5754767410780653050nteger,L),aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(L),U)) = aa_Cod2813182003028390446nteger(set_or9101266186257409494nteger,U) ) ) ).

% ivl_disj_un_one(4)
tff(fact_7364_ivl__disj__un__one_I1_J,axiom,
    ! [L: rat,U: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,L),U)
     => ( sup_sup_set_rat(set_ord_atMost_rat(L),set_or5199638295745620268an_rat(L,U)) = set_ord_lessThan_rat(U) ) ) ).

% ivl_disj_un_one(1)
tff(fact_7365_ivl__disj__un__one_I1_J,axiom,
    ! [L: num,U: num] :
      ( aa_num_o(aa_num_fun_num_o(ord_less_num,L),U)
     => ( sup_sup_set_num(set_ord_atMost_num(L),set_or2392100141987894638an_num(L,U)) = set_ord_lessThan_num(U) ) ) ).

% ivl_disj_un_one(1)
tff(fact_7366_ivl__disj__un__one_I1_J,axiom,
    ! [L: int,U: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,L),U)
     => ( sup_sup_set_int(aa_int_set_int(set_ord_atMost_int,L),aa_int_set_int(set_or5832277885323065728an_int(L),U)) = aa_int_set_int(set_ord_lessThan_int,U) ) ) ).

% ivl_disj_un_one(1)
tff(fact_7367_ivl__disj__un__one_I1_J,axiom,
    ! [L: nat,U: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,L),U)
     => ( sup_sup_set_nat(aa_nat_set_nat(set_ord_atMost_nat,L),aa_nat_set_nat(set_or5834768355832116004an_nat(L),U)) = aa_nat_set_nat(set_ord_lessThan_nat,U) ) ) ).

% ivl_disj_un_one(1)
tff(fact_7368_ivl__disj__un__one_I1_J,axiom,
    ! [L: code_integer,U: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,L),U)
     => ( sup_su848401254843788991nteger(aa_Cod2813182003028390446nteger(set_or9101266186257409494nteger,L),aa_Cod2813182003028390446nteger(set_or4266950643985792945nteger(L),U)) = aa_Cod2813182003028390446nteger(set_or5754767410780653050nteger,U) ) ) ).

% ivl_disj_un_one(1)
tff(fact_7369_intrel__def,axiom,
    intrel = aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,aTP_Lamm_acw) ).

% intrel_def
tff(fact_7370_ivl__disj__un__singleton_I6_J,axiom,
    ! [L: $o,U: $o] :
      ( aa_o_o(aa_o_fun_o_o(ord_less_eq_o,(L)),(U))
     => ( sup_sup_set_o(aa_o_set_o(set_or7139685690850216873Than_o((L)),(U)),insert_o((U),bot_bot_set_o)) = aa_o_set_o(set_or8904488021354931149Most_o((L)),(U)) ) ) ).

% ivl_disj_un_singleton(6)
tff(fact_7371_ivl__disj__un__singleton_I6_J,axiom,
    ! [L: rat,U: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,L),U)
     => ( sup_sup_set_rat(set_or4029947393144176647an_rat(L,U),insert_rat(U,bot_bot_set_rat)) = set_or633870826150836451st_rat(L,U) ) ) ).

% ivl_disj_un_singleton(6)
tff(fact_7372_ivl__disj__un__singleton_I6_J,axiom,
    ! [L: num,U: num] :
      ( aa_num_o(aa_num_fun_num_o(ord_less_eq_num,L),U)
     => ( sup_sup_set_num(set_or1222409239386451017an_num(L,U),insert_num(U,bot_bot_set_num)) = set_or7049704709247886629st_num(L,U) ) ) ).

% ivl_disj_un_singleton(6)
tff(fact_7373_ivl__disj__un__singleton_I6_J,axiom,
    ! [L: nat,U: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,L),U)
     => ( sup_sup_set_nat(aa_nat_set_nat(set_or4665077453230672383an_nat(L),U),insert_nat(U,bot_bot_set_nat)) = aa_nat_set_nat(set_or1269000886237332187st_nat(L),U) ) ) ).

% ivl_disj_un_singleton(6)
tff(fact_7374_ivl__disj__un__singleton_I6_J,axiom,
    ! [L: code_integer,U: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,L),U)
     => ( sup_su848401254843788991nteger(aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(L),U),insert_Code_integer(U,bot_bo3990330152332043303nteger)) = aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(L),U) ) ) ).

% ivl_disj_un_singleton(6)
tff(fact_7375_ivl__disj__un__singleton_I6_J,axiom,
    ! [L: int,U: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,L),U)
     => ( sup_sup_set_int(aa_int_set_int(set_or4662586982721622107an_int(L),U),insert_int(U,bot_bot_set_int)) = aa_int_set_int(set_or1266510415728281911st_int(L),U) ) ) ).

% ivl_disj_un_singleton(6)
tff(fact_7376_ivl__disj__un__singleton_I3_J,axiom,
    ! [L: $o,U: $o] :
      ( aa_o_o(aa_o_fun_o_o(ord_less_o,(L)),(U))
     => ( sup_sup_set_o(insert_o((L),bot_bot_set_o),aa_o_set_o(set_or1716231572884733764Than_o((L)),(U))) = aa_o_set_o(set_or7139685690850216873Than_o((L)),(U)) ) ) ).

% ivl_disj_un_singleton(3)
tff(fact_7377_ivl__disj__un__singleton_I3_J,axiom,
    ! [L: rat,U: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,L),U)
     => ( sup_sup_set_rat(insert_rat(L,bot_bot_set_rat),set_or5199638295745620268an_rat(L,U)) = set_or4029947393144176647an_rat(L,U) ) ) ).

% ivl_disj_un_singleton(3)
tff(fact_7378_ivl__disj__un__singleton_I3_J,axiom,
    ! [L: num,U: num] :
      ( aa_num_o(aa_num_fun_num_o(ord_less_num,L),U)
     => ( sup_sup_set_num(insert_num(L,bot_bot_set_num),set_or2392100141987894638an_num(L,U)) = set_or1222409239386451017an_num(L,U) ) ) ).

% ivl_disj_un_singleton(3)
tff(fact_7379_ivl__disj__un__singleton_I3_J,axiom,
    ! [L: int,U: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,L),U)
     => ( sup_sup_set_int(insert_int(L,bot_bot_set_int),aa_int_set_int(set_or5832277885323065728an_int(L),U)) = aa_int_set_int(set_or4662586982721622107an_int(L),U) ) ) ).

% ivl_disj_un_singleton(3)
tff(fact_7380_ivl__disj__un__singleton_I3_J,axiom,
    ! [L: nat,U: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,L),U)
     => ( sup_sup_set_nat(insert_nat(L,bot_bot_set_nat),aa_nat_set_nat(set_or5834768355832116004an_nat(L),U)) = aa_nat_set_nat(set_or4665077453230672383an_nat(L),U) ) ) ).

% ivl_disj_un_singleton(3)
tff(fact_7381_ivl__disj__un__singleton_I3_J,axiom,
    ! [L: code_integer,U: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,L),U)
     => ( sup_su848401254843788991nteger(insert_Code_integer(L,bot_bo3990330152332043303nteger),aa_Cod2813182003028390446nteger(set_or4266950643985792945nteger(L),U)) = aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(L),U) ) ) ).

% ivl_disj_un_singleton(3)
tff(fact_7382_ivl__disj__un__two_I4_J,axiom,
    ! [L: rat,M: rat,U: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,L),M)
     => ( aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,M),U)
       => ( sup_sup_set_rat(set_or633870826150836451st_rat(L,M),set_or5199638295745620268an_rat(M,U)) = set_or4029947393144176647an_rat(L,U) ) ) ) ).

% ivl_disj_un_two(4)
tff(fact_7383_ivl__disj__un__two_I4_J,axiom,
    ! [L: num,M: num,U: num] :
      ( aa_num_o(aa_num_fun_num_o(ord_less_eq_num,L),M)
     => ( aa_num_o(aa_num_fun_num_o(ord_less_num,M),U)
       => ( sup_sup_set_num(set_or7049704709247886629st_num(L,M),set_or2392100141987894638an_num(M,U)) = set_or1222409239386451017an_num(L,U) ) ) ) ).

% ivl_disj_un_two(4)
tff(fact_7384_ivl__disj__un__two_I4_J,axiom,
    ! [L: int,M: int,U: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,L),M)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_int,M),U)
       => ( sup_sup_set_int(aa_int_set_int(set_or1266510415728281911st_int(L),M),aa_int_set_int(set_or5832277885323065728an_int(M),U)) = aa_int_set_int(set_or4662586982721622107an_int(L),U) ) ) ) ).

% ivl_disj_un_two(4)
tff(fact_7385_ivl__disj__un__two_I4_J,axiom,
    ! [L: nat,M: nat,U: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,L),M)
     => ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M),U)
       => ( sup_sup_set_nat(aa_nat_set_nat(set_or1269000886237332187st_nat(L),M),aa_nat_set_nat(set_or5834768355832116004an_nat(M),U)) = aa_nat_set_nat(set_or4665077453230672383an_nat(L),U) ) ) ) ).

% ivl_disj_un_two(4)
tff(fact_7386_ivl__disj__un__two_I4_J,axiom,
    ! [L: code_integer,M: code_integer,U: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,L),M)
     => ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,M),U)
       => ( sup_su848401254843788991nteger(aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(L),M),aa_Cod2813182003028390446nteger(set_or4266950643985792945nteger(M),U)) = aa_Cod2813182003028390446nteger(set_or8404916559141939852nteger(L),U) ) ) ) ).

% ivl_disj_un_two(4)
tff(fact_7387_less__int_Orsp,axiom,
    bNF_re4103222659376994899_nat_o(intrel,bNF_re3666534408544137501at_o_o(intrel,fequal_o),aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,aTP_Lamm_fe),aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,aTP_Lamm_fe)) ).

% less_int.rsp
tff(fact_7388_less__eq__int_Orsp,axiom,
    bNF_re4103222659376994899_nat_o(intrel,bNF_re3666534408544137501at_o_o(intrel,fequal_o),aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,aTP_Lamm_fg),aa_fun5912894404062470332_nat_o(produc6395135316500328296_nat_o,aTP_Lamm_fg)) ).

% less_eq_int.rsp
tff(fact_7389_plus__int_Orsp,axiom,
    bNF_re6214786843070381989at_nat(intrel,bNF_re2241393799969408733at_nat(intrel,intrel),aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,aTP_Lamm_fz),aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,aTP_Lamm_fz)) ).

% plus_int.rsp
tff(fact_7390_minus__int_Orsp,axiom,
    bNF_re6214786843070381989at_nat(intrel,bNF_re2241393799969408733at_nat(intrel,intrel),aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,aTP_Lamm_gb),aa_fun6875833325056119164at_nat(produc4528391901023682385at_nat,aTP_Lamm_gb)) ).

% minus_int.rsp
tff(fact_7391_max__weak__def,axiom,
    fun_max_weak = sup_su5525570899277871387at_nat(max_ex8135407076693332796at_nat(fun_pair_leq),aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(produc2922128104949294807at_nat(bot_bo2099793752762293965at_nat,bot_bo2099793752762293965at_nat)),bot_bo228742789529271731at_nat)) ).

% max_weak_def
tff(fact_7392_min__weak__def,axiom,
    fun_min_weak = sup_su5525570899277871387at_nat(min_ex6901939911449802026at_nat(fun_pair_leq),aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(produc2922128104949294807at_nat(bot_bo2099793752762293965at_nat,bot_bo2099793752762293965at_nat)),bot_bo228742789529271731at_nat)) ).

% min_weak_def
tff(fact_7393_fold__union__pair,axiom,
    ! [B4: set_Pr4811707699266497531nteger,X2: fun_Pr5098669352780829690e_term,A2: set_Pr3486312109254157132nteger] :
      ( finite2154694888287295812nteger(B4)
     => ( sup_su4503389074446631032nteger(comple7749403179893457567nteger(image_1718222391602322082nteger(aTP_Lamm_abe(X2),B4)),A2) = finite5714315773265140383nteger(aTP_Lamm_acx(X2),A2,B4) ) ) ).

% fold_union_pair
tff(fact_7394_fold__union__pair,axiom,
    ! [B4: set_Pr3948176798113811640et_nat,X2: fun_Pr6460944699146269935_nat_o,A2: set_Pr1312406793078187350et_nat] :
      ( finite2970523954037356441et_nat(B4)
     => ( sup_su2387659076810923138et_nat(comple946752071900596009et_nat(image_7009121673873379551et_nat(aTP_Lamm_abg(X2),B4)),A2) = finite2242536663760659874et_nat(aTP_Lamm_acy(X2),A2,B4) ) ) ).

% fold_union_pair
tff(fact_7395_fold__union__pair,axiom,
    ! [B4: set_Pr1312406793078187350et_nat,X2: fun_Pr6460944699146269935_nat_o,A2: set_Pr4040394263813967220et_nat] :
      ( finite2753043699534600503et_nat(B4)
     => ( sup_su5858552540197408416et_nat(comple828966628661558727et_nat(image_3818865380660343963et_nat(aTP_Lamm_abi(X2),B4)),A2) = finite7678581116841817694et_nat(aTP_Lamm_acz(X2),A2,B4) ) ) ).

% fold_union_pair
tff(fact_7396_fold__union__pair,axiom,
    ! [B4: set_Pr958786334691620121nt_int,X2: fun_Pr7763680713840462443e_term,A2: set_Pr6700895561065273913nt_int] :
      ( finite2998713641127702882nt_int(B4)
     => ( sup_su2017857570560100197nt_int(comple3054605461907987852nt_int(image_6157797188692319661nt_int(aTP_Lamm_abk(X2),B4)),A2) = finite5989910380944892330nt_int(aTP_Lamm_ada(X2),A2,B4) ) ) ).

% fold_union_pair
tff(fact_7397_fold__union__pair,axiom,
    ! [B4: set_Pr958786334691620121nt_int,X2: fun_in5730379987311621695e_term,A2: set_Pr4166680992137330533nt_int] :
      ( finite2998713641127702882nt_int(B4)
     => ( sup_su7513280395484302481nt_int(comple7505710199608789688nt_int(image_2686860183053050585nt_int(aTP_Lamm_abm(X2),B4)),A2) = finite5328971291029987030nt_int(aTP_Lamm_adb(X2),A2,B4) ) ) ).

% fold_union_pair
tff(fact_7398_fold__union__pair,axiom,
    ! [B4: set_se7855581050983116737at_nat,X2: set_Pr1261947904930325089at_nat,A2: set_Pr4329608150637261639at_nat] :
      ( finite9047747110432174090at_nat(B4)
     => ( sup_su5525570899277871387at_nat(comple4364388969068068532at_nat(image_6898982319499645995at_nat(aTP_Lamm_abo(X2),B4)),A2) = finite3179781904389220718at_nat(aTP_Lamm_adc(X2),A2,B4) ) ) ).

% fold_union_pair
tff(fact_7399_fold__union__pair,axiom,
    ! [B4: set_nat,X2: nat,A2: set_Pr1261947904930325089at_nat] :
      ( finite_finite_nat(B4)
     => ( aa_set8868280134176360700at_nat(sup_su6327502436637775413at_nat(comple5685304695842803022at_nat(image_7178329752028323786at_nat(aTP_Lamm_abq(X2),B4))),A2) = finite3745491028973389255at_nat(aTP_Lamm_add(X2),A2,B4) ) ) ).

% fold_union_pair
tff(fact_7400_Field__insert,axiom,
    ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,R2: set_Pr4329608150637261639at_nat] : field_3145993188331922222at_nat(aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(produc2922128104949294807at_nat(A,B)),R2)) = sup_su3642409539654194069at_nat(insert9200635055090092081at_nat(A,insert9200635055090092081at_nat(B,bot_bo3083307316010499117at_nat)),field_3145993188331922222at_nat(R2)) ).

% Field_insert
tff(fact_7401_Field__insert,axiom,
    ! [A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat,R2: set_Pr5564308138774400199at_nat] : field_2862844103579723188at_nat(insert398606708087465655at_nat(produc2335810615602371415at_nat(A,B),R2)) = sup_su5525570899277871387at_nat(aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(A),aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(B),bot_bo228742789529271731at_nat)),field_2862844103579723188at_nat(R2)) ).

% Field_insert
tff(fact_7402_Field__insert,axiom,
    ! [A: product_prod_nat_nat,B: product_prod_nat_nat,R2: set_Pr8693737435421807431at_nat] : field_4706345496283612622at_nat(insert5050368324300391991at_nat(produc6161850002892822231at_nat(A,B),R2)) = aa_set8868280134176360700at_nat(sup_su6327502436637775413at_nat(aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(A),aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(B),bot_bo2099793752762293965at_nat))),field_4706345496283612622at_nat(R2)) ).

% Field_insert
tff(fact_7403_Field__insert,axiom,
    ! [A: $o,B: $o,R2: set_Product_prod_o_o] : field_o(insert6201435330877294327od_o_o(product_Pair_o_o((A),(B)),R2)) = sup_sup_set_o(insert_o((A),insert_o((B),bot_bot_set_o)),field_o(R2)) ).

% Field_insert
tff(fact_7404_Field__insert,axiom,
    ! [A: nat,B: nat,R2: set_Pr1261947904930325089at_nat] : field_nat(aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,A),B)),R2)) = sup_sup_set_nat(insert_nat(A,insert_nat(B,bot_bot_set_nat)),field_nat(R2)) ).

% Field_insert
tff(fact_7405_Field__insert,axiom,
    ! [A: int,B: int,R2: set_Pr958786334691620121nt_int] : field_int(insert5033312907999012233nt_int(aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A),B),R2)) = sup_sup_set_int(insert_int(A,insert_int(B,bot_bot_set_int)),field_int(R2)) ).

% Field_insert
tff(fact_7406_set__to__map__insert,axiom,
    ! [Kv: product_prod_nat_nat,S2: set_Pr1261947904930325089at_nat] :
      ( ~ member_nat(aa_Pro4243173770044397973at_nat(product_fst_nat_nat,Kv),image_2486076414777270412at_nat(product_fst_nat_nat,S2))
     => ( set_to_map_nat_nat(aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(Kv),S2)) = fun_up1493157387958331631on_nat(set_to_map_nat_nat(S2),aa_Pro4243173770044397973at_nat(product_fst_nat_nat,Kv),aa_nat_option_nat(some_nat,aa_Pro4243173770044397973at_nat(product_snd_nat_nat,Kv))) ) ) ).

% set_to_map_insert
tff(fact_7407_set__to__map__insert,axiom,
    ! [Kv: product_prod_o_num,S2: set_Pr7040061329075590551_o_num] :
      ( ~ member_o(aa_Pro5850481546027440185_num_o(product_fst_o_num,Kv),image_8863890952250787504_num_o(product_fst_o_num,S2))
     => ( set_to_map_o_num(insert8656458676507137553_o_num(Kv,S2)) = fun_upd_o_option_num(set_to_map_o_num(S2),aa_Pro5850481546027440185_num_o(product_fst_o_num,Kv),aa_num_option_num(some_num,product_snd_o_num(Kv))) ) ) ).

% set_to_map_insert
tff(fact_7408_set__to__map__insert,axiom,
    ! [Kv: product_prod_nat_num,S2: set_Pr6200539531224447659at_num] :
      ( ~ member_nat(aa_Pro6261568864010571487um_nat(product_fst_nat_num,Kv),image_4504471508743443926um_nat(product_fst_nat_num,S2))
     => ( set_to_map_nat_num(insert8920054152555992091at_num(Kv,S2)) = fun_up2201401324907169337on_num(set_to_map_nat_num(S2),aa_Pro6261568864010571487um_nat(product_fst_nat_num,Kv),aa_num_option_num(some_num,product_snd_nat_num(Kv))) ) ) ).

% set_to_map_insert
tff(fact_7409_set__to__map__insert,axiom,
    ! [Kv: product_prod_int_num,S2: set_Pr8387461105917469447nt_num] :
      ( ~ member_int(aa_Pro6630731953738365847um_int(product_fst_int_num,Kv),image_4873634598471238286um_int(product_fst_int_num,S2))
     => ( set_to_map_int_num(insert696035827602270839nt_num(Kv,S2)) = fun_up4328768054909231765on_num(set_to_map_int_num(S2),aa_Pro6630731953738365847um_int(product_fst_int_num,Kv),aa_num_option_num(some_num,product_snd_int_num(Kv))) ) ) ).

% set_to_map_insert
tff(fact_7410_set__to__map__insert,axiom,
    ! [Kv: produc8923325533196201883nteger,S2: set_Pr4811707699266497531nteger] :
      ( ~ member_Code_integer(aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,Kv),image_6316824473203919795nteger(produc8508995932063986495nteger,S2))
     => ( set_to6264436334439079987nteger(insert4913895101485356395nteger(Kv,S2)) = fun_up6566892301432185865nteger(set_to6264436334439079987nteger(S2),aa_Pro5245656335456409788nteger(produc8508995932063986495nteger,Kv),aa_Cod5017737808611256136nteger(some_Code_integer,aa_Pro5245656335456409788nteger(produc6174133586879617921nteger,Kv))) ) ) ).

% set_to_map_insert
tff(fact_7411_set__to__map__insert,axiom,
    ! [Kv: product_prod_int_int,S2: set_Pr958786334691620121nt_int] :
      ( ~ member_int(aa_Pro6799258434465214121nt_int(product_fst_int_int,Kv),image_5042161079198086560nt_int(product_fst_int_int,S2))
     => ( set_to_map_int_int(insert5033312907999012233nt_int(Kv,S2)) = fun_up8666045135305973159on_int(set_to_map_int_int(S2),aa_Pro6799258434465214121nt_int(product_fst_int_int,Kv),aa_int_option_int(some_int,aa_Pro6799258434465214121nt_int(product_snd_int_int,Kv))) ) ) ).

% set_to_map_insert
tff(fact_7412_set__to__map__insert,axiom,
    ! [Kv: produc9082142974458947146at_num,S2: set_Pr7477759153910077568at_num] :
      ( ~ member8440522571783428010at_nat(aa_Pro8934633562067165177at_nat(produc1179527155093393624at_num,Kv),image_7418169580930627696at_nat(produc1179527155093393624at_num,S2))
     => ( set_to5081529003106763492at_num(insert2790150385885543546at_num(Kv,S2)) = fun_up8025039454679724718on_num(set_to5081529003106763492at_num(S2),aa_Pro8934633562067165177at_nat(produc1179527155093393624at_num,Kv),aa_num_option_num(some_num,produc8847702614181477910at_num(Kv))) ) ) ).

% set_to_map_insert
tff(fact_7413_set__to__map__insert,axiom,
    ! [Kv: produc5835291356934675326atural,S2: set_Pr2352657477744078772atural] :
      ( ~ member_Code_natural(aa_Pro5806155842103967332atural(produc497848011034438852atural,Kv),image_8194678751871465133atural(produc497848011034438852atural,S2))
     => ( set_to6039658477269176016atural(insert6505218763252461998atural(Kv,S2)) = fun_up2923169431403285008atural(set_to6039658477269176016atural(S2),aa_Pro5806155842103967332atural(produc497848011034438852atural,Kv),some_P5671840033927537686atural(aa_Pro3673693039631929973atural(produc6591912806276919810atural,Kv))) ) ) ).

% set_to_map_insert
tff(fact_7414_set__to__map__insert,axiom,
    ! [Kv: produc2900562427881843919it_nat,S2: set_Pr6777250647868329861it_nat] :
      ( ~ member_o(aa_Pro2750588290097631179_nat_o(produc1440270732834495325it_nat,Kv),image_5849890305759347266_nat_o(produc1440270732834495325it_nat,S2))
     => ( set_to3023635543527487849it_nat(insert6915099157023601407it_nat(Kv,S2)) = fun_up1288979561775348147it_nat(set_to3023635543527487849it_nat(S2),aa_Pro2750588290097631179_nat_o(produc1440270732834495325it_nat,Kv),aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc5978051280710547099it_nat(Kv))) ) ) ).

% set_to_map_insert
tff(fact_7415_set__to__map__insert,axiom,
    ! [Kv: produc3839731585411834681it_nat,S2: set_Pr633603713510679705it_nat] :
      ( ~ member_nat(aa_Pro8662700311855308749at_nat(produc5854401122675660893it_nat,Kv),image_5261730836495542980at_nat(produc5854401122675660893it_nat,S2))
     => ( set_to785951348762482001it_nat(insert2528233410557839625it_nat(Kv,S2)) = fun_up4116053422210368295it_nat(set_to785951348762482001it_nat(S2),aa_Pro8662700311855308749at_nat(produc5854401122675660893it_nat,Kv),aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc8417671938598930591it_nat(Kv))) ) ) ).

% set_to_map_insert
tff(fact_7416_plus__rat_Orsp,axiom,
    bNF_re4734134812813710757nt_int(ratrel,bNF_re7145576690424134365nt_int(ratrel,ratrel),aTP_Lamm_abw,aTP_Lamm_abw) ).

% plus_rat.rsp
tff(fact_7417_inverse__rat_Orsp,axiom,
    aa_fun2650603632653508759_int_o(aa_fun3734617511155415725_int_o(bNF_re7145576690424134365nt_int(ratrel,ratrel),aTP_Lamm_abx),aTP_Lamm_abx) ).

% inverse_rat.rsp
tff(fact_7418_image__update,axiom,
    ! [X2: nat,A2: set_nat,F: fun_nat_Code_integer,N2: code_integer] :
      ( ~ member_nat(X2,A2)
     => ( image_1215581382706833972nteger(fun_up3904115110581602988nteger(F,X2,N2),A2) = image_1215581382706833972nteger(F,A2) ) ) ).

% image_update
tff(fact_7419_image__update,axiom,
    ! [X2: nat,A2: set_nat,F: fun_nat_set_nat,N2: set_nat] :
      ( ~ member_nat(X2,A2)
     => ( image_nat_set_nat(fun_upd_nat_set_nat(F,X2,N2),A2) = image_nat_set_nat(F,A2) ) ) ).

% image_update
tff(fact_7420_image__update,axiom,
    ! [X2: nat,A2: set_nat,F: fun_nat_nat,N2: nat] :
      ( ~ member_nat(X2,A2)
     => ( aa_set_nat_set_nat(image_nat_nat(aa_nat_fun_nat_nat(fun_upd_nat_nat(F,X2),N2)),A2) = aa_set_nat_set_nat(image_nat_nat(F),A2) ) ) ).

% image_update
tff(fact_7421_image__update,axiom,
    ! [X2: nat,A2: set_nat,F: fun_nat_int,N2: int] :
      ( ~ member_nat(X2,A2)
     => ( image_nat_int(fun_upd_nat_int(F,X2,N2),A2) = image_nat_int(F,A2) ) ) ).

% image_update
tff(fact_7422_image__update,axiom,
    ! [X2: int,A2: set_int,F: fun_int_int,N2: int] :
      ( ~ member_int(X2,A2)
     => ( aa_set_int_set_int(image_int_int(aa_int_fun_int_int(fun_upd_int_int(F,X2),N2)),A2) = aa_set_int_set_int(image_int_int(F),A2) ) ) ).

% image_update
tff(fact_7423_finite__Field__eq__finite,axiom,
    ! [R3: set_Product_prod_o_o] :
      ( finite_finite_o(field_o(R3))
    <=> finite6120865539452801872od_o_o(R3) ) ).

% finite_Field_eq_finite
tff(fact_7424_finite__Field__eq__finite,axiom,
    ! [R3: set_Pr1261947904930325089at_nat] :
      ( finite_finite_nat(field_nat(R3))
    <=> finite6177210948735845034at_nat(R3) ) ).

% finite_Field_eq_finite
tff(fact_7425_finite__Field__eq__finite,axiom,
    ! [R3: set_Pr958786334691620121nt_int] :
      ( finite_finite_int(field_int(R3))
    <=> finite2998713641127702882nt_int(R3) ) ).

% finite_Field_eq_finite
tff(fact_7426_finite__Field__eq__finite,axiom,
    ! [R3: set_Pr4811707699266497531nteger] :
      ( finite6017078050557962740nteger(field_Code_integer(R3))
    <=> finite2154694888287295812nteger(R3) ) ).

% finite_Field_eq_finite
tff(fact_7427_finite__Field__eq__finite,axiom,
    ! [R3: set_Pr8693737435421807431at_nat] :
      ( finite6177210948735845034at_nat(field_4706345496283612622at_nat(R3))
    <=> finite4392333629123659920at_nat(R3) ) ).

% finite_Field_eq_finite
tff(fact_7428_image__map__upd,axiom,
    ! [X2: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,M: fun_Pr6553355248451873380on_num,Y: num] :
      ( ~ member8757157785044589968at_nat(X2,A2)
     => ( image_8464016542990802060on_num(fun_up3286109336741039636on_num(M,X2,aa_num_option_num(some_num,Y)),A2) = image_8464016542990802060on_num(M,A2) ) ) ).

% image_map_upd
tff(fact_7429_image__map__upd,axiom,
    ! [X2: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,M: fun_Pr7397166214287566974on_num,Y: num] :
      ( ~ member8440522571783428010at_nat(X2,A2)
     => ( image_1023191801488348454on_num(fun_up8025039454679724718on_num(M,X2,aa_num_option_num(some_num,Y)),A2) = image_1023191801488348454on_num(M,A2) ) ) ).

% image_map_upd
tff(fact_7430_image__map__upd,axiom,
    ! [X2: $o,A2: set_o,M: fun_o_option_num,Y: num] :
      ( ~ member_o((X2),A2)
     => ( image_o_option_num(fun_upd_o_option_num(M,(X2),aa_num_option_num(some_num,Y)),A2) = image_o_option_num(M,A2) ) ) ).

% image_map_upd
tff(fact_7431_image__map__upd,axiom,
    ! [X2: nat,A2: set_nat,M: fun_nat_option_num,Y: num] :
      ( ~ member_nat(X2,A2)
     => ( image_nat_option_num(fun_up2201401324907169337on_num(M,X2,aa_num_option_num(some_num,Y)),A2) = image_nat_option_num(M,A2) ) ) ).

% image_map_upd
tff(fact_7432_image__map__upd,axiom,
    ! [X2: int,A2: set_int,M: fun_int_option_num,Y: num] :
      ( ~ member_int(X2,A2)
     => ( image_int_option_num(fun_up4328768054909231765on_num(M,X2,aa_num_option_num(some_num,Y)),A2) = image_int_option_num(M,A2) ) ) ).

% image_map_upd
tff(fact_7433_image__map__upd,axiom,
    ! [X2: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,M: fun_Pr6865292569827446866it_nat,Y: produc8664842809031399944it_nat] :
      ( ~ member8757157785044589968at_nat(X2,A2)
     => ( image_140351626946063738it_nat(fun_up5549328659429834498it_nat(M,X2,aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,Y)),A2) = image_140351626946063738it_nat(M,A2) ) ) ).

% image_map_upd
tff(fact_7434_image__map__upd,axiom,
    ! [X2: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,M: fun_Pr6624299372562097772it_nat,Y: produc8664842809031399944it_nat] :
      ( ~ member8440522571783428010at_nat(X2,A2)
     => ( image_5755308894823448084it_nat(fun_up3996838528606387100it_nat(M,X2,aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,Y)),A2) = image_5755308894823448084it_nat(M,A2) ) ) ).

% image_map_upd
tff(fact_7435_image__map__upd,axiom,
    ! [X2: $o,A2: set_o,M: fun_o_7229649064035662211it_nat,Y: produc8664842809031399944it_nat] :
      ( ~ member_o((X2),A2)
     => ( image_5849929686412825643it_nat(fun_up1288979561775348147it_nat(M,(X2),aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,Y)),A2) = image_5849929686412825643it_nat(M,A2) ) ) ).

% image_map_upd
tff(fact_7436_image__map__upd,axiom,
    ! [X2: nat,A2: set_nat,M: fun_na5667031169817407269it_nat,Y: produc8664842809031399944it_nat] :
      ( ~ member_nat(X2,A2)
     => ( image_5028743614110135983it_nat(fun_up4116053422210368295it_nat(M,X2,aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,Y)),A2) = image_5028743614110135983it_nat(M,A2) ) ) ).

% image_map_upd
tff(fact_7437_image__map__upd,axiom,
    ! [X2: int,A2: set_int,M: fun_in8543325783774419841it_nat,Y: produc8664842809031399944it_nat] :
      ( ~ member_int(X2,A2)
     => ( image_7905038228067148555it_nat(fun_up6992348036167380867it_nat(M,X2,aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,Y)),A2) = image_7905038228067148555it_nat(M,A2) ) ) ).

% image_map_upd
tff(fact_7438_FieldI2,axiom,
    ! [I: produc3843707927480180839at_nat,J: produc3843707927480180839at_nat,R3: set_Pr5564308138774400199at_nat] :
      ( member6009668390874684176at_nat(produc2335810615602371415at_nat(I,J),R3)
     => member8757157785044589968at_nat(J,field_2862844103579723188at_nat(R3)) ) ).

% FieldI2
tff(fact_7439_FieldI2,axiom,
    ! [I: product_prod_nat_nat,J: product_prod_nat_nat,R3: set_Pr8693737435421807431at_nat] :
      ( member8206827879206165904at_nat(produc6161850002892822231at_nat(I,J),R3)
     => member8440522571783428010at_nat(J,field_4706345496283612622at_nat(R3)) ) ).

% FieldI2
tff(fact_7440_FieldI2,axiom,
    ! [I: int,J: int,R3: set_Pr958786334691620121nt_int] :
      ( member5262025264175285858nt_int(aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,I),J),R3)
     => member_int(J,field_int(R3)) ) ).

% FieldI2
tff(fact_7441_FieldI2,axiom,
    ! [I: set_Pr1261947904930325089at_nat,J: set_Pr1261947904930325089at_nat,R3: set_Pr4329608150637261639at_nat] :
      ( member8757157785044589968at_nat(produc2922128104949294807at_nat(I,J),R3)
     => member2643936169264416010at_nat(J,field_3145993188331922222at_nat(R3)) ) ).

% FieldI2
tff(fact_7442_FieldI2,axiom,
    ! [I: nat,J: nat,R3: set_Pr1261947904930325089at_nat] :
      ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,I),J),R3)
     => member_nat(J,field_nat(R3)) ) ).

% FieldI2
tff(fact_7443_FieldI2,axiom,
    ! [I: $o,J: $o,R3: set_Product_prod_o_o] :
      ( member7466972457876170832od_o_o(product_Pair_o_o((I),(J)),R3)
     => member_o((J),field_o(R3)) ) ).

% FieldI2
tff(fact_7444_FieldI1,axiom,
    ! [I: produc3843707927480180839at_nat,J: produc3843707927480180839at_nat,R3: set_Pr5564308138774400199at_nat] :
      ( member6009668390874684176at_nat(produc2335810615602371415at_nat(I,J),R3)
     => member8757157785044589968at_nat(I,field_2862844103579723188at_nat(R3)) ) ).

% FieldI1
tff(fact_7445_FieldI1,axiom,
    ! [I: product_prod_nat_nat,J: product_prod_nat_nat,R3: set_Pr8693737435421807431at_nat] :
      ( member8206827879206165904at_nat(produc6161850002892822231at_nat(I,J),R3)
     => member8440522571783428010at_nat(I,field_4706345496283612622at_nat(R3)) ) ).

% FieldI1
tff(fact_7446_FieldI1,axiom,
    ! [I: int,J: int,R3: set_Pr958786334691620121nt_int] :
      ( member5262025264175285858nt_int(aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,I),J),R3)
     => member_int(I,field_int(R3)) ) ).

% FieldI1
tff(fact_7447_FieldI1,axiom,
    ! [I: set_Pr1261947904930325089at_nat,J: set_Pr1261947904930325089at_nat,R3: set_Pr4329608150637261639at_nat] :
      ( member8757157785044589968at_nat(produc2922128104949294807at_nat(I,J),R3)
     => member2643936169264416010at_nat(I,field_3145993188331922222at_nat(R3)) ) ).

% FieldI1
tff(fact_7448_FieldI1,axiom,
    ! [I: nat,J: nat,R3: set_Pr1261947904930325089at_nat] :
      ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,I),J),R3)
     => member_nat(I,field_nat(R3)) ) ).

% FieldI1
tff(fact_7449_FieldI1,axiom,
    ! [I: $o,J: $o,R3: set_Product_prod_o_o] :
      ( member7466972457876170832od_o_o(product_Pair_o_o((I),(J)),R3)
     => member_o((I),field_o(R3)) ) ).

% FieldI1
tff(fact_7450_sup__Un__eq2,axiom,
    ! [R3: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat,X: nat,Xa3: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(sup_su8083968640029086462_nat_o(aa_set2634951030311766213_nat_o(aTP_Lamm_bv,R3),aa_set2634951030311766213_nat_o(aTP_Lamm_bv,S2)),X),Xa3)
    <=> member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X),Xa3),aa_set8868280134176360700at_nat(sup_su6327502436637775413at_nat(R3),S2)) ) ).

% sup_Un_eq2
tff(fact_7451_sup__Un__eq2,axiom,
    ! [R3: set_Pr3486312109254157132nteger,S2: set_Pr3486312109254157132nteger,X: fun_Pr5098669352780829690e_term,Xa3: produc8923325533196201883nteger] :
      ( aa_Pro4926521453222654329eger_o(aa_fun4505422719058378424eger_o(sup_su8446958762992054435eger_o(aa_set282680696547864321eger_o(aTP_Lamm_bw,R3),aa_set282680696547864321eger_o(aTP_Lamm_bw,S2)),X),Xa3)
    <=> member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,X),Xa3),sup_su4503389074446631032nteger(R3,S2)) ) ).

% sup_Un_eq2
tff(fact_7452_sup__Un__eq2,axiom,
    ! [R3: set_Pr1312406793078187350et_nat,S2: set_Pr1312406793078187350et_nat,X: fun_Pr6460944699146269935_nat_o,Xa3: produc3658429121746597890et_nat] :
      ( aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(sup_su4970993554803434671_nat_o(aa_set6295625606485646487_nat_o(aTP_Lamm_bx,R3),aa_set6295625606485646487_nat_o(aTP_Lamm_bx,S2)),X),Xa3)
    <=> member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,X),Xa3),sup_su2387659076810923138et_nat(R3,S2)) ) ).

% sup_Un_eq2
tff(fact_7453_sup__Un__eq2,axiom,
    ! [R3: set_Pr4040394263813967220et_nat,S2: set_Pr4040394263813967220et_nat,X: fun_Pr6460944699146269935_nat_o,Xa3: produc8799533983703829792et_nat] :
      ( aa_Pro5643009357358181178_nat_o(aa_fun912680268133416158_nat_o(sup_su6780828561269846801_nat_o(aa_set2269662337286943895_nat_o(aTP_Lamm_by,R3),aa_set2269662337286943895_nat_o(aTP_Lamm_by,S2)),X),Xa3)
    <=> member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X),Xa3),sup_su5858552540197408416et_nat(R3,S2)) ) ).

% sup_Un_eq2
tff(fact_7454_sup__Un__eq2,axiom,
    ! [R3: set_Pr6700895561065273913nt_int,S2: set_Pr6700895561065273913nt_int,X: fun_Pr7763680713840462443e_term,Xa3: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(aa_fun3538162476766722827_int_o(sup_su2175524065394371574_int_o(aa_set8857007276572228673_int_o(aTP_Lamm_bz,R3),aa_set8857007276572228673_int_o(aTP_Lamm_bz,S2)),X),Xa3)
    <=> member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,X),Xa3),sup_su2017857570560100197nt_int(R3,S2)) ) ).

% sup_Un_eq2
tff(fact_7455_sup__Un__eq2,axiom,
    ! [R3: set_Pr4166680992137330533nt_int,S2: set_Pr4166680992137330533nt_int,X: fun_in5730379987311621695e_term,Xa3: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(aa_fun586359091965693151_int_o(sup_su7230269426179251658_int_o(aa_set6932945912113297217_int_o(aTP_Lamm_ca,R3),aa_set6932945912113297217_int_o(aTP_Lamm_ca,S2)),X),Xa3)
    <=> member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,X),Xa3),sup_su7513280395484302481nt_int(R3,S2)) ) ).

% sup_Un_eq2
tff(fact_7456_sup__Un__eq2,axiom,
    ! [R3: set_Pr4329608150637261639at_nat,S2: set_Pr4329608150637261639at_nat,X: set_Pr1261947904930325089at_nat,Xa3: set_Pr1261947904930325089at_nat] :
      ( aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(sup_su5424986631308460290_nat_o(aa_set5605188905385065315_nat_o(aTP_Lamm_bu,R3),aa_set5605188905385065315_nat_o(aTP_Lamm_bu,S2)),X),Xa3)
    <=> member8757157785044589968at_nat(produc2922128104949294807at_nat(X,Xa3),sup_su5525570899277871387at_nat(R3,S2)) ) ).

% sup_Un_eq2
tff(fact_7457_fun__upd__comp,axiom,
    ! [F: fun_Co8499238673658658103nteger,G: fun_num_Code_integer,X2: num,Y: code_integer] : aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),fun_up1844922938552261878nteger(G,X2,Y)) = fun_up1844922938552261878nteger(aa_fun8039327588056924198nteger(aa_fun2129879960000001626nteger(comp_C3531382070062128313er_num,F),G),X2,aa_Cod1783974652533396728nteger(F,Y)) ).

% fun_upd_comp
tff(fact_7458_fun__upd__comp,axiom,
    ! [F: fun_Co1561183069634336733nteger,G: fun_Co8499238673658658103nteger,X2: code_integer,Y: code_integer] : aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),aa_Cod4161879620478718930nteger(fun_up8355007323143964473nteger(G,X2),Y)) = fun_up1280136195588363103nteger(aa_fun4856328718102079442nteger(aa_fun1515160681128992300nteger(comp_C7848664941760151970nteger,F),G),X2,aa_Cod1978467581589928094nteger(F,Y)) ).

% fun_upd_comp
tff(fact_7459_fun__upd__comp,axiom,
    ! [F: fun_fu4800041728187187127nteger,G: fun_Co1981900195452921617nteger,X2: code_integer,Y: fun_Co8499238673658658103nteger] : comp_f6739083541385432444nteger(F,fun_up7364656672652868627nteger(G,X2,Y)) = fun_up1280136195588363103nteger(comp_f6739083541385432444nteger(F,G),X2,aa_fun2509385170507305080nteger(F,Y)) ).

% fun_upd_comp
tff(fact_7460_fun__upd__comp,axiom,
    ! [F: fun_nat_num,G: fun_int_nat,X2: int,Y: nat] : aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),fun_upd_int_nat(G,X2,Y)) = fun_upd_int_num(aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,F),G),X2,aa_nat_num(F,Y)) ).

% fun_upd_comp
tff(fact_7461_one__rat_Orsp,axiom,
    aa_Pro4592068669816069595_int_o(aa_Pro3952998155787061599_int_o(ratrel,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,one_one_int),one_one_int)),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,one_one_int),one_one_int)) ).

% one_rat.rsp
tff(fact_7462_R__subset__Field,axiom,
    ! [R3: set_Pr1261947904930325089at_nat] : aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(ord_le3146513528884898305at_nat,R3),produc457027306803732586at_nat(field_nat(R3),aTP_Lamm_ade(R3))) ).

% R_subset_Field
tff(fact_7463_R__subset__Field,axiom,
    ! [R3: set_Product_prod_o_o] : ord_le192195778054999463od_o_o(R3,product_Sigma_o_o(field_o(R3),aTP_Lamm_adf(R3))) ).

% R_subset_Field
tff(fact_7464_fst__in__Field,axiom,
    ! [R3: set_Product_prod_o_o] : ord_less_eq_set_o(image_7896445794123959606_o_o_o(product_fst_o_o,R3),field_o(R3)) ).

% fst_in_Field
tff(fact_7465_fst__in__Field,axiom,
    ! [R3: set_Pr4811707699266497531nteger] : ord_le7084787975880047091nteger(image_6316824473203919795nteger(produc8508995932063986495nteger,R3),field_Code_integer(R3)) ).

% fst_in_Field
tff(fact_7466_fst__in__Field,axiom,
    ! [R3: set_Pr958786334691620121nt_int] : ord_less_eq_set_int(image_5042161079198086560nt_int(product_fst_int_int,R3),field_int(R3)) ).

% fst_in_Field
tff(fact_7467_fst__in__Field,axiom,
    ! [R3: set_Pr1261947904930325089at_nat] : aa_set_nat_o(ord_less_eq_set_nat(image_2486076414777270412at_nat(product_fst_nat_nat,R3)),field_nat(R3)) ).

% fst_in_Field
tff(fact_7468_snd__in__Field,axiom,
    ! [R3: set_Product_prod_o_o] : ord_less_eq_set_o(image_7896445794123959606_o_o_o(product_snd_o_o,R3),field_o(R3)) ).

% snd_in_Field
tff(fact_7469_snd__in__Field,axiom,
    ! [R3: set_Pr4811707699266497531nteger] : ord_le7084787975880047091nteger(image_6316824473203919795nteger(produc6174133586879617921nteger,R3),field_Code_integer(R3)) ).

% snd_in_Field
tff(fact_7470_snd__in__Field,axiom,
    ! [R3: set_Pr958786334691620121nt_int] : ord_less_eq_set_int(image_5042161079198086560nt_int(product_snd_int_int,R3),field_int(R3)) ).

% snd_in_Field
tff(fact_7471_snd__in__Field,axiom,
    ! [R3: set_Pr1261947904930325089at_nat] : aa_set_nat_o(ord_less_eq_set_nat(image_2486076414777270412at_nat(product_snd_nat_nat,R3)),field_nat(R3)) ).

% snd_in_Field
tff(fact_7472_zero__rat_Orsp,axiom,
    aa_Pro4592068669816069595_int_o(aa_Pro3952998155787061599_int_o(ratrel,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,zero_zero_int),one_one_int)),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,zero_zero_int),one_one_int)) ).

% zero_rat.rsp
tff(fact_7473_Fract_Orsp,axiom,
    bNF_re4808202430149235895nt_int(fequal_int,bNF_re6250860962936578807nt_int(fequal_int,ratrel),aTP_Lamm_adg,aTP_Lamm_adg) ).

% Fract.rsp
tff(fact_7474_sum_Oeq__fold,axiom,
    ! [G: fun_nat_nat,A2: set_nat] : aa_set_nat_nat(groups3542108847815614940at_nat(G),A2) = aa_set_nat_nat(finite_fold_nat_nat(comp_n7084669201029016610at_nat(plus_plus_nat,G),zero_zero_nat),A2) ).

% sum.eq_fold
tff(fact_7475_sum_Oeq__fold,axiom,
    ! [G: fun_int_int,A2: set_int] : aa_set_int_int(groups4538972089207619220nt_int(G),A2) = aa_set_int_int(finite_fold_int_int(aa_fun5911324870756489105nt_int(aa_fun5609932731973438348nt_int(comp_i133330754224947090nt_int,plus_plus_int),G),zero_zero_int),A2) ).

% sum.eq_fold
tff(fact_7476_prod_Oeq__fold,axiom,
    ! [G: fun_nat_nat,A2: set_nat] : aa_set_nat_nat(groups708209901874060359at_nat(G),A2) = aa_set_nat_nat(finite_fold_nat_nat(comp_n7084669201029016610at_nat(times_times_nat,G),one_one_nat),A2) ).

% prod.eq_fold
tff(fact_7477_prod_Oeq__fold,axiom,
    ! [G: fun_nat_int,A2: set_nat] : groups705719431365010083at_int(G,A2) = finite_fold_nat_int(comp_i135821224733997366nt_nat(times_times_int,G),one_one_int,A2) ).

% prod.eq_fold
tff(fact_7478_prod_Oeq__fold,axiom,
    ! [G: fun_int_int,A2: set_int] : aa_set_int_int(groups1705073143266064639nt_int(G),A2) = aa_set_int_int(finite_fold_int_int(aa_fun5911324870756489105nt_int(aa_fun5609932731973438348nt_int(comp_i133330754224947090nt_int,times_times_int),G),one_one_int),A2) ).

% prod.eq_fold
tff(fact_7479_finite__range__updI,axiom,
    ! [F: fun_nat_option_num,A: nat,B: num] :
      ( finite6231397076622260609on_num(image_nat_option_num(F,top_top_set_nat))
     => finite6231397076622260609on_num(image_nat_option_num(fun_up2201401324907169337on_num(F,A,aa_num_option_num(some_num,B)),top_top_set_nat)) ) ).

% finite_range_updI
tff(fact_7480_finite__range__updI,axiom,
    ! [F: fun_na5667031169817407269it_nat,A: nat,B: produc8664842809031399944it_nat] :
      ( finite6292238467249657455it_nat(image_5028743614110135983it_nat(F,top_top_set_nat))
     => finite6292238467249657455it_nat(image_5028743614110135983it_nat(fun_up4116053422210368295it_nat(F,A,aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,B)),top_top_set_nat)) ) ).

% finite_range_updI
tff(fact_7481_finite__range__updI,axiom,
    ! [F: fun_Pr792663941044724234on_num,A: product_unit,B: num] :
      ( finite6231397076622260609on_num(image_5965367930834091826on_num(F,top_to1996260823553986621t_unit))
     => finite6231397076622260609on_num(image_5965367930834091826on_num(fun_up4695802795598371002on_num(F,A,aa_num_option_num(some_num,B)),top_to1996260823553986621t_unit)) ) ).

% finite_range_updI
tff(fact_7482_finite__range__updI,axiom,
    ! [F: fun_Pr6171258863536582648it_nat,A: product_unit,B: produc8664842809031399944it_nat] :
      ( finite6292238467249657455it_nat(image_5022536681399171104it_nat(F,top_to1996260823553986621t_unit))
     => finite6292238467249657455it_nat(image_5022536681399171104it_nat(fun_up1973317344121680296it_nat(F,A,aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,B)),top_to1996260823553986621t_unit)) ) ).

% finite_range_updI
tff(fact_7483_finite__range__updI,axiom,
    ! [F: fun_int_option_num,A: int,B: num] :
      ( finite6231397076622260609on_num(image_int_option_num(F,top_top_set_int))
     => finite6231397076622260609on_num(image_int_option_num(fun_up4328768054909231765on_num(F,A,aa_num_option_num(some_num,B)),top_top_set_int)) ) ).

% finite_range_updI
tff(fact_7484_finite__range__updI,axiom,
    ! [F: fun_in8543325783774419841it_nat,A: int,B: produc8664842809031399944it_nat] :
      ( finite6292238467249657455it_nat(image_7905038228067148555it_nat(F,top_top_set_int))
     => finite6292238467249657455it_nat(image_7905038228067148555it_nat(fun_up6992348036167380867it_nat(F,A,aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,B)),top_top_set_int)) ) ).

% finite_range_updI
tff(fact_7485_fun__upd__image,axiom,
    ! [F: fun_o_o,X2: $o,Y: $o,A2: set_o] :
      aa_set_o_set_o(image_o_o(aa_o_fun_o_o(fun_upd_o_o(F,(X2)),(Y))),A2) = $ite(member_o((X2),A2),insert_o((Y),aa_set_o_set_o(image_o_o(F),minus_minus_set_o(A2,insert_o((X2),bot_bot_set_o)))),aa_set_o_set_o(image_o_o(F),A2)) ).

% fun_upd_image
tff(fact_7486_fun__upd__image,axiom,
    ! [F: fun_o_nat,X2: $o,Y: nat,A2: set_o] :
      image_o_nat(fun_upd_o_nat(F,(X2),Y),A2) = $ite(member_o((X2),A2),insert_nat(Y,image_o_nat(F,minus_minus_set_o(A2,insert_o((X2),bot_bot_set_o)))),image_o_nat(F,A2)) ).

% fun_upd_image
tff(fact_7487_fun__upd__image,axiom,
    ! [F: fun_o_int,X2: $o,Y: int,A2: set_o] :
      image_o_int(fun_upd_o_int(F,(X2),Y),A2) = $ite(member_o((X2),A2),insert_int(Y,image_o_int(F,minus_minus_set_o(A2,insert_o((X2),bot_bot_set_o)))),image_o_int(F,A2)) ).

% fun_upd_image
tff(fact_7488_fun__upd__image,axiom,
    ! [F: fun_int_o,X2: int,Y: $o,A2: set_int] :
      image_int_o(fun_upd_int_o(F,X2,(Y)),A2) = $ite(member_int(X2,A2),insert_o((Y),image_int_o(F,minus_minus_set_int(A2,insert_int(X2,bot_bot_set_int)))),image_int_o(F,A2)) ).

% fun_upd_image
tff(fact_7489_fun__upd__image,axiom,
    ! [F: fun_int_nat,X2: int,Y: nat,A2: set_int] :
      image_int_nat(fun_upd_int_nat(F,X2,Y),A2) = $ite(member_int(X2,A2),insert_nat(Y,image_int_nat(F,minus_minus_set_int(A2,insert_int(X2,bot_bot_set_int)))),image_int_nat(F,A2)) ).

% fun_upd_image
tff(fact_7490_fun__upd__image,axiom,
    ! [F: fun_int_int,X2: int,Y: int,A2: set_int] :
      aa_set_int_set_int(image_int_int(aa_int_fun_int_int(fun_upd_int_int(F,X2),Y)),A2) = $ite(member_int(X2,A2),insert_int(Y,aa_set_int_set_int(image_int_int(F),minus_minus_set_int(A2,insert_int(X2,bot_bot_set_int)))),aa_set_int_set_int(image_int_int(F),A2)) ).

% fun_upd_image
tff(fact_7491_fun__upd__image,axiom,
    ! [F: fun_nat_Code_integer,X2: nat,Y: code_integer,A2: set_nat] :
      image_1215581382706833972nteger(fun_up3904115110581602988nteger(F,X2,Y),A2) = $ite(member_nat(X2,A2),insert_Code_integer(Y,image_1215581382706833972nteger(F,minus_minus_set_nat(A2,insert_nat(X2,bot_bot_set_nat)))),image_1215581382706833972nteger(F,A2)) ).

% fun_upd_image
tff(fact_7492_fun__upd__image,axiom,
    ! [F: fun_nat_o,X2: nat,Y: $o,A2: set_nat] :
      image_nat_o(aa_o_fun_nat_o(fun_upd_nat_o(F,X2),(Y)),A2) = $ite(member_nat(X2,A2),insert_o((Y),image_nat_o(F,minus_minus_set_nat(A2,insert_nat(X2,bot_bot_set_nat)))),image_nat_o(F,A2)) ).

% fun_upd_image
tff(fact_7493_fun__upd__image,axiom,
    ! [F: fun_nat_nat,X2: nat,Y: nat,A2: set_nat] :
      aa_set_nat_set_nat(image_nat_nat(aa_nat_fun_nat_nat(fun_upd_nat_nat(F,X2),Y)),A2) = $ite(member_nat(X2,A2),insert_nat(Y,aa_set_nat_set_nat(image_nat_nat(F),minus_minus_set_nat(A2,insert_nat(X2,bot_bot_set_nat)))),aa_set_nat_set_nat(image_nat_nat(F),A2)) ).

% fun_upd_image
tff(fact_7494_fun__upd__image,axiom,
    ! [F: fun_nat_int,X2: nat,Y: int,A2: set_nat] :
      image_nat_int(fun_upd_nat_int(F,X2,Y),A2) = $ite(member_nat(X2,A2),insert_int(Y,image_nat_int(F,minus_minus_set_nat(A2,insert_nat(X2,bot_bot_set_nat)))),image_nat_int(F,A2)) ).

% fun_upd_image
tff(fact_7495_times__rat_Orsp,axiom,
    bNF_re4734134812813710757nt_int(ratrel,bNF_re7145576690424134365nt_int(ratrel,ratrel),aTP_Lamm_aca,aTP_Lamm_aca) ).

% times_rat.rsp
tff(fact_7496_uminus__rat_Orsp,axiom,
    aa_fun2650603632653508759_int_o(aa_fun3734617511155415725_int_o(bNF_re7145576690424134365nt_int(ratrel,ratrel),aTP_Lamm_acb),aTP_Lamm_acb) ).

% uminus_rat.rsp
tff(fact_7497_plus__rat_Oabs__eq,axiom,
    ! [Xa: product_prod_int_int,X2: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(aa_Pro3952998155787061599_int_o(ratrel,Xa),Xa)
     => ( aa_Pro4592068669816069595_int_o(aa_Pro3952998155787061599_int_o(ratrel,X2),X2)
       => ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_Pro6166618844887768661nt_rat(abs_Rat,Xa)),aa_Pro6166618844887768661nt_rat(abs_Rat,X2)) = aa_Pro6166618844887768661nt_rat(abs_Rat,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_Pro6799258434465214121nt_int(product_fst_int_int,Xa)),aa_Pro6799258434465214121nt_int(product_snd_int_int,X2))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_Pro6799258434465214121nt_int(product_fst_int_int,X2)),aa_Pro6799258434465214121nt_int(product_snd_int_int,Xa)))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_Pro6799258434465214121nt_int(product_snd_int_int,Xa)),aa_Pro6799258434465214121nt_int(product_snd_int_int,X2)))) ) ) ) ).

% plus_rat.abs_eq
tff(fact_7498_inverse__rat_Oabs__eq,axiom,
    ! [X2: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(aa_Pro3952998155787061599_int_o(ratrel,X2),X2)
     => ( aa_rat_rat(inverse_inverse_rat,aa_Pro6166618844887768661nt_rat(abs_Rat,X2)) = aa_Pro6166618844887768661nt_rat(abs_Rat,
            $ite(aa_Pro6799258434465214121nt_int(product_fst_int_int,X2) = zero_zero_int,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,zero_zero_int),one_one_int),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_Pro6799258434465214121nt_int(product_snd_int_int,X2)),aa_Pro6799258434465214121nt_int(product_fst_int_int,X2)))) ) ) ).

% inverse_rat.abs_eq
tff(fact_7499_times__rat_Oabs__eq,axiom,
    ! [Xa: product_prod_int_int,X2: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(aa_Pro3952998155787061599_int_o(ratrel,Xa),Xa)
     => ( aa_Pro4592068669816069595_int_o(aa_Pro3952998155787061599_int_o(ratrel,X2),X2)
       => ( aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_Pro6166618844887768661nt_rat(abs_Rat,Xa)),aa_Pro6166618844887768661nt_rat(abs_Rat,X2)) = aa_Pro6166618844887768661nt_rat(abs_Rat,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_Pro6799258434465214121nt_int(product_fst_int_int,Xa)),aa_Pro6799258434465214121nt_int(product_fst_int_int,X2))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_Pro6799258434465214121nt_int(product_snd_int_int,Xa)),aa_Pro6799258434465214121nt_int(product_snd_int_int,X2)))) ) ) ) ).

% times_rat.abs_eq
tff(fact_7500_uminus__rat_Oabs__eq,axiom,
    ! [X2: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(aa_Pro3952998155787061599_int_o(ratrel,X2),X2)
     => ( aa_rat_rat(uminus_uminus_rat,aa_Pro6166618844887768661nt_rat(abs_Rat,X2)) = aa_Pro6166618844887768661nt_rat(abs_Rat,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_int_int(uminus_uminus_int,aa_Pro6799258434465214121nt_int(product_fst_int_int,X2))),aa_Pro6799258434465214121nt_int(product_snd_int_int,X2))) ) ) ).

% uminus_rat.abs_eq
tff(fact_7501_one__rat__def,axiom,
    one_one_rat = aa_Pro6166618844887768661nt_rat(abs_Rat,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,one_one_int),one_one_int)) ).

% one_rat_def
tff(fact_7502_zero__rat__def,axiom,
    zero_zero_rat = aa_Pro6166618844887768661nt_rat(abs_Rat,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,zero_zero_int),one_one_int)) ).

% zero_rat_def
tff(fact_7503_plus__rat__def,axiom,
    plus_plus_rat = map_fu5968964422797239547at_rat(rep_Rat,map_fu5673905371560938248nt_rat(rep_Rat,abs_Rat),aTP_Lamm_abw) ).

% plus_rat_def
tff(fact_7504_inverse__rat__def,axiom,
    inverse_inverse_rat = aa_fun7041730090766645614at_rat(map_fu5673905371560938248nt_rat(rep_Rat,abs_Rat),aTP_Lamm_abx) ).

% inverse_rat_def
tff(fact_7505_times__rat__def,axiom,
    times_times_rat = map_fu5968964422797239547at_rat(rep_Rat,map_fu5673905371560938248nt_rat(rep_Rat,abs_Rat),aTP_Lamm_aca) ).

% times_rat_def
tff(fact_7506_uminus__rat__def,axiom,
    uminus_uminus_rat = aa_fun7041730090766645614at_rat(map_fu5673905371560938248nt_rat(rep_Rat,abs_Rat),aTP_Lamm_acb) ).

% uminus_rat_def
tff(fact_7507_card__le__Suc__Max,axiom,
    ! [S2: set_nat] :
      ( finite_finite_nat(S2)
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_set_nat_nat(finite_card_nat,S2)),aa_nat_nat(suc,aa_set_nat_nat(lattic8265883725875713057ax_nat,S2))) ) ).

% card_le_Suc_Max
tff(fact_7508_greaterThan__Suc,axiom,
    ! [K: nat] : aa_nat_set_nat(set_or1210151606488870762an_nat,aa_nat_nat(suc,K)) = minus_minus_set_nat(aa_nat_set_nat(set_or1210151606488870762an_nat,K),insert_nat(aa_nat_nat(suc,K),bot_bot_set_nat)) ).

% greaterThan_Suc
tff(fact_7509_INT__greaterThan__UNIV,axiom,
    comple7806235888213564991et_nat(image_nat_set_nat(set_or1210151606488870762an_nat,top_top_set_nat)) = bot_bot_set_nat ).

% INT_greaterThan_UNIV
tff(fact_7510_greaterThan__0,axiom,
    aa_nat_set_nat(set_or1210151606488870762an_nat,zero_zero_nat) = aa_set_nat_set_nat(image_nat_nat(suc),top_top_set_nat) ).

% greaterThan_0
tff(fact_7511_euclidean__size__integer_Orep__eq,axiom,
    ! [X2: code_integer] : aa_Code_integer_nat(euclid6377331345833325938nteger,X2) = aa_int_nat(euclid4774559944035922753ze_int,aa_Code_integer_int(code_int_of_integer,X2)) ).

% euclidean_size_integer.rep_eq
tff(fact_7512_euclidean__size__integer_Oabs__eq,axiom,
    ! [X2: int] : aa_Code_integer_nat(euclid6377331345833325938nteger,aa_int_Code_integer(code_integer_of_int,X2)) = aa_int_nat(euclid4774559944035922753ze_int,X2) ).

% euclidean_size_integer.abs_eq
tff(fact_7513_euclidean__size__natural_Orsp,axiom,
    aa_fun_nat_nat_o(aa_fun2341495900663639033_nat_o(bNF_re5653821019739307937at_nat(fequal_nat,fequal_nat),euclid4777050414544973029ze_nat),euclid4777050414544973029ze_nat) ).

% euclidean_size_natural.rsp
tff(fact_7514_euclidean__size__integer__def,axiom,
    euclid6377331345833325938nteger = map_fu6539832666145259331at_nat(code_int_of_integer,id_nat,euclid4774559944035922753ze_int) ).

% euclidean_size_integer_def
tff(fact_7515_euclidean__size__integer_Orsp,axiom,
    aa_fun_int_nat_o(aa_fun7045208173470077249_nat_o(bNF_re3715656647883201625at_nat(fequal_int,fequal_nat),euclid4774559944035922753ze_int),euclid4774559944035922753ze_int) ).

% euclidean_size_integer.rsp
tff(fact_7516_division__segment__integer_Orep__eq,axiom,
    ! [X2: code_integer] : aa_Code_integer_int(code_int_of_integer,aa_Cod1783974652533396728nteger(euclid6289375185220004616nteger,X2)) = aa_int_int(euclid3395696857347342551nt_int,aa_Code_integer_int(code_int_of_integer,X2)) ).

% division_segment_integer.rep_eq
tff(fact_7517_division__segment__integer_Oabs__eq,axiom,
    ! [X2: int] : aa_Cod1783974652533396728nteger(euclid6289375185220004616nteger,aa_int_Code_integer(code_integer_of_int,X2)) = aa_int_Code_integer(code_integer_of_int,aa_int_int(euclid3395696857347342551nt_int,X2)) ).

% division_segment_integer.abs_eq
tff(fact_7518_division__segment__nat__def,axiom,
    ! [N2: nat] : aa_nat_nat(euclid3398187327856392827nt_nat,N2) = one_one_nat ).

% division_segment_nat_def
tff(fact_7519_division__segment__integer_Orsp,axiom,
    aa_fun_int_int_o(aa_fun2545150047610057353_int_o(bNF_re4712519889275205905nt_int(fequal_int,fequal_int),euclid3395696857347342551nt_int),euclid3395696857347342551nt_int) ).

% division_segment_integer.rsp
tff(fact_7520_division__segment__natural_Orsp,axiom,
    aa_fun_nat_nat_o(aa_fun2341495900663639033_nat_o(bNF_re5653821019739307937at_nat(fequal_nat,fequal_nat),euclid3398187327856392827nt_nat),euclid3398187327856392827nt_nat) ).

% division_segment_natural.rsp
tff(fact_7521_division__segment__integer__def,axiom,
    euclid6289375185220004616nteger = aa_fun8964553180794676938nteger(map_fu2599414010547811884nteger(code_int_of_integer,code_integer_of_int),euclid3395696857347342551nt_int) ).

% division_segment_integer_def
tff(fact_7522_finite__greaterThanAtMost,axiom,
    ! [L: nat,U: nat] : finite_finite_nat(aa_nat_set_nat(set_or6659071591806873216st_nat(L),U)) ).

% finite_greaterThanAtMost
tff(fact_7523_finite__greaterThanAtMost__int,axiom,
    ! [L: int,U: int] : finite_finite_int(aa_int_set_int(set_or6656581121297822940st_int(L),U)) ).

% finite_greaterThanAtMost_int
tff(fact_7524_finite__greaterThanAtMost__integer,axiom,
    ! [L: code_integer,U: code_integer] : finite6017078050557962740nteger(aa_Cod2813182003028390446nteger(set_or2715278749043346189nteger(L),U)) ).

% finite_greaterThanAtMost_integer
tff(fact_7525_card__greaterThanAtMost,axiom,
    ! [L: nat,U: nat] : aa_set_nat_nat(finite_card_nat,aa_nat_set_nat(set_or6659071591806873216st_nat(L),U)) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,U),L) ).

% card_greaterThanAtMost
tff(fact_7526_card__greaterThanAtMost__int,axiom,
    ! [L: int,U: int] : finite_card_int(aa_int_set_int(set_or6656581121297822940st_int(L),U)) = aa_int_nat(nat2,aa_int_int(aa_int_fun_int_int(minus_minus_int,U),L)) ).

% card_greaterThanAtMost_int
tff(fact_7527_atLeastSucAtMost__greaterThanAtMost,axiom,
    ! [L: nat,U: nat] : aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,L)),U) = aa_nat_set_nat(set_or6659071591806873216st_nat(L),U) ).

% atLeastSucAtMost_greaterThanAtMost
tff(fact_7528_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
    ! [L: int,U: int] : aa_int_set_int(set_or1266510415728281911st_int(aa_int_int(aa_int_fun_int_int(plus_plus_int,L),one_one_int)),U) = aa_int_set_int(set_or6656581121297822940st_int(L),U) ).

% atLeastPlusOneAtMost_greaterThanAtMost_int
tff(fact_7529_atLeastPlusOneAtMost__greaterThanAtMost__integer,axiom,
    ! [L: code_integer,U: code_integer] : aa_Cod2813182003028390446nteger(set_or189985376899183464nteger(aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,L),one_one_Code_integer)),U) = aa_Cod2813182003028390446nteger(set_or2715278749043346189nteger(L),U) ).

% atLeastPlusOneAtMost_greaterThanAtMost_integer
tff(fact_7530_UN__atLeast__UNIV,axiom,
    comple7399068483239264473et_nat(image_nat_set_nat(set_ord_atLeast_nat,top_top_set_nat)) = top_top_set_nat ).

% UN_atLeast_UNIV
tff(fact_7531_atLeast__0,axiom,
    aa_nat_set_nat(set_ord_atLeast_nat,zero_zero_nat) = top_top_set_nat ).

% atLeast_0
tff(fact_7532_Inf__unit__def,axiom,
    ! [Uu: set_Product_unit] : comple2584293577114468500t_unit(Uu) = product_Unity ).

% Inf_unit_def
tff(fact_7533_Sup__unit__def,axiom,
    ! [Uu: set_Product_unit] : comple4687483117567863418t_unit(Uu) = product_Unity ).

% Sup_unit_def
tff(fact_7534_old_Ounit_Oexhaust,axiom,
    ! [Y: product_unit] : Y = product_Unity ).

% old.unit.exhaust
tff(fact_7535_top__unit__def,axiom,
    top_top_Product_unit = product_Unity ).

% top_unit_def
tff(fact_7536_uminus__unit__def,axiom,
    ! [Uu: product_unit] : aa_Pro8294289767544744956t_unit(uminus2952777764628376836t_unit,Uu) = product_Unity ).

% uminus_unit_def
tff(fact_7537_bot__unit__def,axiom,
    bot_bot_Product_unit = product_Unity ).

% bot_unit_def
tff(fact_7538_sup__unit__def,axiom,
    ! [Uu: product_unit,Uv: product_unit] : aa_Pro8294289767544744956t_unit(sup_sup_Product_unit(Uu),Uv) = product_Unity ).

% sup_unit_def
tff(fact_7539_UNIV__unit,axiom,
    top_to1996260823553986621t_unit = insert_Product_unit(product_Unity,bot_bo3957492148770167129t_unit) ).

% UNIV_unit
tff(fact_7540_atLeast__Suc__greaterThan,axiom,
    ! [K: nat] : aa_nat_set_nat(set_ord_atLeast_nat,aa_nat_nat(suc,K)) = aa_nat_set_nat(set_or1210151606488870762an_nat,K) ).

% atLeast_Suc_greaterThan
tff(fact_7541_wait__def,axiom,
    ! [N2: nat] : heap_Time_wait(N2) = heap_T6183433275982383450t_unit(aTP_Lamm_adh(N2)) ).

% wait_def
tff(fact_7542_execute__assert_H,axiom,
    ! [P: $o,Ha: heap_e7401611519738050253t_unit] :
      aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(refine_Imp_assert((P))),Ha) = $ite((P),aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(product_Unity,produc584006145561248582it_nat(Ha,zero_zero_nat))),none_P9117596204409417319it_nat) ).

% execute_assert'
tff(fact_7543_atLeast__Suc,axiom,
    ! [K: nat] : aa_nat_set_nat(set_ord_atLeast_nat,aa_nat_nat(suc,K)) = minus_minus_set_nat(aa_nat_set_nat(set_ord_atLeast_nat,K),insert_nat(K,bot_bot_set_nat)) ).

% atLeast_Suc
tff(fact_7544_default__unit__def,axiom,
    defaul566961228789861419t_unit = product_Unity ).

% default_unit_def
tff(fact_7545_inf__unit__def,axiom,
    ! [Uu: product_unit,Uv: product_unit] : aa_Pro8294289767544744956t_unit(inf_inf_Product_unit(Uu),Uv) = product_Unity ).

% inf_unit_def
tff(fact_7546_floor__rat__def,axiom,
    ! [X2: rat] : archim3151403230148437115or_rat(X2) = the_int(aa_rat_fun_int_o(aTP_Lamm_adi,X2)) ).

% floor_rat_def
tff(fact_7547_rat__floor__lemma,axiom,
    ! [A: int,B: int] :
      ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_int_rat(ring_1_of_int_rat,aa_int_int(aa_int_fun_int_int(divide_divide_int,A),B))),aa_int_rat(aa_int_fun_int_rat(fract,A),B))
      & aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,aa_int_rat(aa_int_fun_int_rat(fract,A),B)),aa_int_rat(ring_1_of_int_rat,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(divide_divide_int,A),B)),one_one_int))) ) ).

% rat_floor_lemma
tff(fact_7548_num__of__integer_Otransfer,axiom,
    bNF_re6718328864250387230um_num(code_pcr_integer,fequal_num,aa_fun7214996087693374330nt_num(aa_fun6849364718390456542nt_num(comp_nat_num_int,num_of_nat),nat2),code_num_of_integer) ).

% num_of_integer.transfer
tff(fact_7549_prod__decode__triangle__add,axiom,
    ! [K: nat,M: nat] : aa_nat7603221163087113075at_nat(nat_prod_decode,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(nat_triangle,K)),M)) = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(nat_prod_decode_aux,K),M) ).

% prod_decode_triangle_add
tff(fact_7550_add__rat,axiom,
    ! [B: int,D2: int,A: int,C: int] :
      ( ( B != zero_zero_int )
     => ( ( D2 != zero_zero_int )
       => ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_int_rat(aa_int_fun_int_rat(fract,A),B)),aa_int_rat(aa_int_fun_int_rat(fract,C),D2)) = aa_int_rat(aa_int_fun_int_rat(fract,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,A),D2)),aa_int_int(aa_int_fun_int_int(times_times_int,C),B))),aa_int_int(aa_int_fun_int_int(times_times_int,B),D2)) ) ) ) ).

% add_rat
tff(fact_7551_integer_Orep__transfer,axiom,
    bNF_re3804157879324367682nt_int(code_pcr_integer,fequal_int,aTP_Lamm_cp,code_int_of_integer) ).

% integer.rep_transfer
tff(fact_7552_integer_Oid__abs__transfer,axiom,
    bNF_re982302072995117890nteger(fequal_int,code_pcr_integer,aTP_Lamm_cp,code_integer_of_int) ).

% integer.id_abs_transfer
tff(fact_7553_zero__integer_Otransfer,axiom,
    aa_Code_integer_o(aa_int5993532643906289898eger_o(code_pcr_integer,zero_zero_int),zero_z3403309356797280102nteger) ).

% zero_integer.transfer
tff(fact_7554_plus__integer_Otransfer,axiom,
    bNF_re9130850084932126070nteger(code_pcr_integer,bNF_re3379532845092657523nteger(code_pcr_integer,code_pcr_integer),plus_plus_int,plus_p5714425477246183910nteger) ).

% plus_integer.transfer
tff(fact_7555_quotient__of__eq,axiom,
    ! [A: int,B: int,P2: int,Q3: int] :
      ( ( quotient_of(aa_int_rat(aa_int_fun_int_rat(fract,A),B)) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,P2),Q3) )
     => ( aa_int_rat(aa_int_fun_int_rat(fract,P2),Q3) = aa_int_rat(aa_int_fun_int_rat(fract,A),B) ) ) ).

% quotient_of_eq
tff(fact_7556_less__integer_Otransfer,axiom,
    bNF_re5122946609719563319eger_o(code_pcr_integer,bNF_re6574881592172037608er_o_o(code_pcr_integer,fequal_o),ord_less_int,ord_le6747313008572928689nteger) ).

% less_integer.transfer
tff(fact_7557_one__integer_Otransfer,axiom,
    aa_Code_integer_o(aa_int5993532643906289898eger_o(code_pcr_integer,one_one_int),one_one_Code_integer) ).

% one_integer.transfer
tff(fact_7558_less__eq__integer_Otransfer,axiom,
    bNF_re5122946609719563319eger_o(code_pcr_integer,bNF_re6574881592172037608er_o_o(code_pcr_integer,fequal_o),ord_less_eq_int,ord_le3102999989581377725nteger) ).

% less_eq_integer.transfer
tff(fact_7559_uminus__integer_Otransfer,axiom,
    aa_fun774133186966548707eger_o(aa_fun6864876441520360999eger_o(bNF_re3379532845092657523nteger(code_pcr_integer,code_pcr_integer),uminus_uminus_int),uminus1351360451143612070nteger) ).

% uminus_integer.transfer
tff(fact_7560_times__integer_Otransfer,axiom,
    bNF_re9130850084932126070nteger(code_pcr_integer,bNF_re3379532845092657523nteger(code_pcr_integer,code_pcr_integer),times_times_int,times_3573771949741848930nteger) ).

% times_integer.transfer
tff(fact_7561_minus__integer_Otransfer,axiom,
    bNF_re9130850084932126070nteger(code_pcr_integer,bNF_re3379532845092657523nteger(code_pcr_integer,code_pcr_integer),minus_minus_int,minus_8373710615458151222nteger) ).

% minus_integer.transfer
tff(fact_7562_abs__integer_Otransfer,axiom,
    aa_fun774133186966548707eger_o(aa_fun6864876441520360999eger_o(bNF_re3379532845092657523nteger(code_pcr_integer,code_pcr_integer),abs_abs_int),abs_abs_Code_integer) ).

% abs_integer.transfer
tff(fact_7563_nat__of__integer_Otransfer,axiom,
    bNF_re2807294637932363402at_nat(code_pcr_integer,fequal_nat,nat2,code_nat_of_integer) ).

% nat_of_integer.transfer
tff(fact_7564_normalize__eq,axiom,
    ! [A: int,B: int,P2: int,Q3: int] :
      ( ( aa_Pro6970504127699319548nt_int(normalize,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A),B)) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,P2),Q3) )
     => ( aa_int_rat(aa_int_fun_int_rat(fract,P2),Q3) = aa_int_rat(aa_int_fun_int_rat(fract,A),B) ) ) ).

% normalize_eq
tff(fact_7565_integer__of__nat_Otransfer,axiom,
    bNF_re4153400068438556298nteger(fequal_nat,code_pcr_integer,semiri1314217659103216013at_int,code_integer_of_nat) ).

% integer_of_nat.transfer
tff(fact_7566_divide__integer_Otransfer,axiom,
    bNF_re9130850084932126070nteger(code_pcr_integer,bNF_re3379532845092657523nteger(code_pcr_integer,code_pcr_integer),divide_divide_int,divide6298287555418463151nteger) ).

% divide_integer.transfer
tff(fact_7567_modulo__integer_Otransfer,axiom,
    bNF_re9130850084932126070nteger(code_pcr_integer,bNF_re3379532845092657523nteger(code_pcr_integer,code_pcr_integer),modulo_modulo_int,modulo364778990260209775nteger) ).

% modulo_integer.transfer
tff(fact_7568_sgn__integer_Otransfer,axiom,
    aa_fun774133186966548707eger_o(aa_fun6864876441520360999eger_o(bNF_re3379532845092657523nteger(code_pcr_integer,code_pcr_integer),sgn_sgn_int),sgn_sgn_Code_integer) ).

% sgn_integer.transfer
tff(fact_7569_dup_Otransfer,axiom,
    aa_fun774133186966548707eger_o(aa_fun6864876441520360999eger_o(bNF_re3379532845092657523nteger(code_pcr_integer,code_pcr_integer),aTP_Lamm_ni),code_dup) ).

% dup.transfer
tff(fact_7570_take__bit__integer_Otransfer,axiom,
    bNF_re4578097776928471693nteger(fequal_nat,bNF_re3379532845092657523nteger(code_pcr_integer,code_pcr_integer),bit_se2923211474154528505it_int,bit_se1745604003318907178nteger) ).

% take_bit_integer.transfer
tff(fact_7571_not__integer_Otransfer,axiom,
    aa_fun774133186966548707eger_o(aa_fun6864876441520360999eger_o(bNF_re3379532845092657523nteger(code_pcr_integer,code_pcr_integer),bit_ri7919022796975470100ot_int),bit_ri7632146776885996613nteger) ).

% not_integer.transfer
tff(fact_7572_and__integer_Otransfer,axiom,
    bNF_re9130850084932126070nteger(code_pcr_integer,bNF_re3379532845092657523nteger(code_pcr_integer,code_pcr_integer),bit_se725231765392027082nd_int,bit_se3949692690581998587nteger) ).

% and_integer.transfer
tff(fact_7573_bit__integer_Otransfer,axiom,
    bNF_re6821560923358799272_nat_o(code_pcr_integer,fequal_fun_nat_o,bit_se1146084159140164899it_int,bit_se9216721137139052372nteger) ).

% bit_integer.transfer
tff(fact_7574_or__integer_Otransfer,axiom,
    bNF_re9130850084932126070nteger(code_pcr_integer,bNF_re3379532845092657523nteger(code_pcr_integer,code_pcr_integer),bit_se1409905431419307370or_int,bit_se1080825931792720795nteger) ).

% or_integer.transfer
tff(fact_7575_xor__integer_Otransfer,axiom,
    bNF_re9130850084932126070nteger(code_pcr_integer,bNF_re3379532845092657523nteger(code_pcr_integer,code_pcr_integer),bit_se6526347334894502574or_int,bit_se3222712562003087583nteger) ).

% xor_integer.transfer
tff(fact_7576_drop__bit__integer_Otransfer,axiom,
    bNF_re4578097776928471693nteger(fequal_nat,bNF_re3379532845092657523nteger(code_pcr_integer,code_pcr_integer),bit_se8568078237143864401it_int,bit_se3928097537394005634nteger) ).

% drop_bit_integer.transfer
tff(fact_7577_push__bit__integer_Otransfer,axiom,
    bNF_re4578097776928471693nteger(fequal_nat,bNF_re3379532845092657523nteger(code_pcr_integer,code_pcr_integer),bit_se545348938243370406it_int,bit_se7788150548672797655nteger) ).

% push_bit_integer.transfer
tff(fact_7578_mask__integer_Otransfer,axiom,
    bNF_re4153400068438556298nteger(fequal_nat,code_pcr_integer,bit_se2000444600071755411sk_int,bit_se2119862282449309892nteger) ).

% mask_integer.transfer
tff(fact_7579_unset__bit__integer_Otransfer,axiom,
    bNF_re4578097776928471693nteger(fequal_nat,bNF_re3379532845092657523nteger(code_pcr_integer,code_pcr_integer),bit_se4203085406695923979it_int,bit_se8260200283734997820nteger) ).

% unset_bit_integer.transfer
tff(fact_7580_set__bit__integer_Otransfer,axiom,
    bNF_re4578097776928471693nteger(fequal_nat,bNF_re3379532845092657523nteger(code_pcr_integer,code_pcr_integer),bit_se7879613467334960850it_int,bit_se2793503036327961859nteger) ).

% set_bit_integer.transfer
tff(fact_7581_division__segment__integer_Otransfer,axiom,
    aa_fun774133186966548707eger_o(aa_fun6864876441520360999eger_o(bNF_re3379532845092657523nteger(code_pcr_integer,code_pcr_integer),euclid3395696857347342551nt_int),euclid6289375185220004616nteger) ).

% division_segment_integer.transfer
tff(fact_7582_flip__bit__integer_Otransfer,axiom,
    bNF_re4578097776928471693nteger(fequal_nat,bNF_re3379532845092657523nteger(code_pcr_integer,code_pcr_integer),bit_se2159334234014336723it_int,bit_se1345352211410354436nteger) ).

% flip_bit_integer.transfer
tff(fact_7583_euclidean__size__integer_Otransfer,axiom,
    bNF_re2807294637932363402at_nat(code_pcr_integer,fequal_nat,euclid4774559944035922753ze_int,euclid6377331345833325938nteger) ).

% euclidean_size_integer.transfer
tff(fact_7584_quotient__of__Fract,axiom,
    ! [A: int,B: int] : quotient_of(aa_int_rat(aa_int_fun_int_rat(fract,A),B)) = aa_Pro6970504127699319548nt_int(normalize,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,A),B)) ).

% quotient_of_Fract
tff(fact_7585_sub_Otransfer,axiom,
    bNF_re4520166952630509772nteger(fequal_num,bNF_re6501075790457514782nteger(fequal_num,code_pcr_integer),aTP_Lamm_nr,code_sub) ).

% sub.transfer
tff(fact_7586_Fract_Oabs__eq,axiom,
    ! [Xa: int,X2: int] :
      aa_int_rat(aa_int_fun_int_rat(fract,Xa),X2) = aa_Pro6166618844887768661nt_rat(abs_Rat,
        $ite(X2 = zero_zero_int,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,zero_zero_int),one_one_int),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Xa),X2))) ).

% Fract.abs_eq
tff(fact_7587_Fract_Otransfer,axiom,
    aa_fun4793272751809872304_rat_o(aa_fun3867120139247291696_rat_o(bNF_re2486238095283335024nt_rat(fequal_int,bNF_re2214769303045360666nt_rat(fequal_int,pcr_rat)),aTP_Lamm_adg),fract) ).

% Fract.transfer
tff(fact_7588_Fract__add__one,axiom,
    ! [N2: int,M: int] :
      ( ( N2 != zero_zero_int )
     => ( aa_int_rat(aa_int_fun_int_rat(fract,aa_int_int(aa_int_fun_int_int(plus_plus_int,M),N2)),N2) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_int_rat(aa_int_fun_int_rat(fract,M),N2)),one_one_rat) ) ) ).

% Fract_add_one
tff(fact_7589_Fract__def,axiom,
    fract = map_fu7945985449245211511nt_rat(id_int,map_fu3424225382358772769nt_rat(id_int,abs_Rat),aTP_Lamm_adg) ).

% Fract_def
tff(fact_7590_list__decode_Opinduct,axiom,
    ! [A0: nat,P: fun_nat_o] :
      ( aa_nat_o(accp_nat(nat_list_decode_rel),A0)
     => ( ( aa_nat_o(accp_nat(nat_list_decode_rel),zero_zero_nat)
         => aa_nat_o(P,zero_zero_nat) )
       => ( ! [N: nat] :
              ( aa_nat_o(accp_nat(nat_list_decode_rel),aa_nat_nat(suc,N))
             => ( ! [X: nat,Y5: nat] :
                    ( ( aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X),Y5) = aa_nat7603221163087113075at_nat(nat_prod_decode,N) )
                   => aa_nat_o(P,Y5) )
               => aa_nat_o(P,aa_nat_nat(suc,N)) ) )
         => aa_nat_o(P,A0) ) ) ) ).

% list_decode.pinduct
tff(fact_7591_type__definition__integer,axiom,
    type_d8366093980585677751er_int(code_int_of_integer,code_integer_of_int,top_top_set_int) ).

% type_definition_integer
tff(fact_7592_pred__nat__trancl__eq__le,axiom,
    ! [M: nat,N2: nat] :
      ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,M),N2),aa_set8868280134176360700at_nat(transi2905341329935302413cl_nat,pred_nat))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,M),N2) ) ).

% pred_nat_trancl_eq_le
tff(fact_7593_less__eq,axiom,
    ! [M: nat,N2: nat] :
      ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,M),N2),aa_set8868280134176360700at_nat(transi6264000038957366511cl_nat,pred_nat))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,M),N2) ) ).

% less_eq
tff(fact_7594_upt__0__eq__Nil__conv,axiom,
    ! [J: nat] :
      ( ( upt(zero_zero_nat,J) = nil_nat )
    <=> ( J = zero_zero_nat ) ) ).

% upt_0_eq_Nil_conv
tff(fact_7595_map__add__upt_H,axiom,
    ! [Ofs: nat,A: nat,B: nat] : map_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_mr,Ofs),upt(A,B)) = upt(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,A),Ofs),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,B),Ofs)) ).

% map_add_upt'
tff(fact_7596_map__add__upt,axiom,
    ! [N2: nat,M: nat] : map_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_mr,N2),upt(zero_zero_nat,M)) = upt(N2,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,M),N2)) ).

% map_add_upt
tff(fact_7597_upt__filter__extend,axiom,
    ! [U: nat,U3: nat,P: fun_nat_o] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,U),U3)
     => ( ! [I2: nat] :
            ( ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,U),I2)
              & aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,I2),U3) )
           => ~ aa_nat_o(P,I2) )
       => ( filter_nat(P,upt(zero_zero_nat,U)) = filter_nat(P,upt(zero_zero_nat,U3)) ) ) ) ).

% upt_filter_extend
tff(fact_7598_nth__upt,axiom,
    ! [I: nat,K: nat,J: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K)),J)
     => ( aa_nat_nat(nth_nat(upt(I,J)),K) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),K) ) ) ).

% nth_upt
tff(fact_7599_upt__eq__Cons__conv,axiom,
    ! [I: nat,J: nat,X2: nat,Xsa: list_nat] :
      ( ( upt(I,J) = cons_nat(X2,Xsa) )
    <=> ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,I),J)
        & ( I = X2 )
        & ( upt(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),one_one_nat),J) = Xsa ) ) ) ).

% upt_eq_Cons_conv
tff(fact_7600_list__decode_Opelims,axiom,
    ! [X2: nat,Y: list_nat] :
      ( ( nat_list_decode(X2) = Y )
     => ( aa_nat_o(accp_nat(nat_list_decode_rel),X2)
       => ( ( ( X2 = zero_zero_nat )
           => ( ( Y = nil_nat )
             => ~ aa_nat_o(accp_nat(nat_list_decode_rel),zero_zero_nat) ) )
         => ~ ! [N: nat] :
                ( ( X2 = aa_nat_nat(suc,N) )
               => ( ( Y = produc2761476792215241774st_nat(aTP_Lamm_adj,aa_nat7603221163087113075at_nat(nat_prod_decode,N)) )
                 => ~ aa_nat_o(accp_nat(nat_list_decode_rel),aa_nat_nat(suc,N)) ) ) ) ) ) ).

% list_decode.pelims
tff(fact_7601_drop__upt,axiom,
    ! [M: nat,I: nat,J: nat] : drop_nat(M,upt(I,J)) = upt(aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),M),J) ).

% drop_upt
tff(fact_7602_natural__zero__minus__one,axiom,
    aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(minus_7197305767214868737atural,zero_z2226904508553997617atural),one_one_Code_natural) = zero_z2226904508553997617atural ).

% natural_zero_minus_one
tff(fact_7603_list__decode_Opsimps_I1_J,axiom,
    ( aa_nat_o(accp_nat(nat_list_decode_rel),zero_zero_nat)
   => ( nat_list_decode(zero_zero_nat) = nil_nat ) ) ).

% list_decode.psimps(1)
tff(fact_7604_list__decode_Opsimps_I2_J,axiom,
    ! [N2: nat] :
      ( aa_nat_o(accp_nat(nat_list_decode_rel),aa_nat_nat(suc,N2))
     => ( nat_list_decode(aa_nat_nat(suc,N2)) = produc2761476792215241774st_nat(aTP_Lamm_adj,aa_nat7603221163087113075at_nat(nat_prod_decode,N2)) ) ) ).

% list_decode.psimps(2)
tff(fact_7605_list__encode_Oelims,axiom,
    ! [X2: list_nat,Y: nat] :
      ( ( aa_list_nat_nat(nat_list_encode,X2) = Y )
     => ( ( ( X2 = nil_nat )
         => ( Y != zero_zero_nat ) )
       => ~ ! [X3: nat,Xs: list_nat] :
              ( ( X2 = cons_nat(X3,Xs) )
             => ( Y != aa_nat_nat(suc,aa_Pro4243173770044397973at_nat(nat_prod_encode,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),aa_list_nat_nat(nat_list_encode,Xs)))) ) ) ) ) ).

% list_encode.elims
tff(fact_7606_upt__merge,axiom,
    ! [I: nat,J: nat,K: nat] :
      ( ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,I),J)
        & aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,J),K) )
     => ( append_nat(upt(I,J),upt(J,K)) = upt(I,K) ) ) ).

% upt_merge
tff(fact_7607_upt__eq__append__conv,axiom,
    ! [I: nat,J: nat,Xsa: list_nat,Ys: list_nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,I),J)
     => ( ( upt(I,J) = append_nat(Xsa,Ys) )
      <=> ? [K4: nat] :
            ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,I),K4)
            & aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,K4),J)
            & ( upt(I,K4) = Xsa )
            & ( upt(K4,J) = Ys ) ) ) ) ).

% upt_eq_append_conv
tff(fact_7608_upt__append,axiom,
    ! [I: nat,J: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,I),J)
     => ( append_nat(upt(zero_zero_nat,I),upt(I,J)) = upt(zero_zero_nat,J) ) ) ).

% upt_append
tff(fact_7609_upt__add__eq__append,axiom,
    ! [I: nat,J: nat,K: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,I),J)
     => ( upt(I,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),K)) = append_nat(upt(I,J),upt(J,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,J),K))) ) ) ).

% upt_add_eq_append
tff(fact_7610_upt__eq__lel__conv,axiom,
    ! [L: nat,Ha: nat,Is1: list_nat,I: nat,Is2: list_nat] :
      ( ( upt(L,Ha) = append_nat(Is1,cons_nat(I,Is2)) )
    <=> ( ( Is1 = upt(L,I) )
        & ( Is2 = upt(aa_nat_nat(suc,I),Ha) )
        & aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,L),I)
        & aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,I),Ha) ) ) ).

% upt_eq_lel_conv
tff(fact_7611_list__encode_Osimps_I2_J,axiom,
    ! [X2: nat,Xsa: list_nat] : aa_list_nat_nat(nat_list_encode,cons_nat(X2,Xsa)) = aa_nat_nat(suc,aa_Pro4243173770044397973at_nat(nat_prod_encode,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X2),aa_list_nat_nat(nat_list_encode,Xsa)))) ).

% list_encode.simps(2)
tff(fact_7612_list__encode_Opelims,axiom,
    ! [X2: list_nat,Y: nat] :
      ( ( aa_list_nat_nat(nat_list_encode,X2) = Y )
     => ( aa_list_nat_o(accp_list_nat(nat_list_encode_rel),X2)
       => ( ( ( X2 = nil_nat )
           => ( ( Y = zero_zero_nat )
             => ~ aa_list_nat_o(accp_list_nat(nat_list_encode_rel),nil_nat) ) )
         => ~ ! [X3: nat,Xs: list_nat] :
                ( ( X2 = cons_nat(X3,Xs) )
               => ( ( Y = aa_nat_nat(suc,aa_Pro4243173770044397973at_nat(nat_prod_encode,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X3),aa_list_nat_nat(nat_list_encode,Xs)))) )
                 => ~ aa_list_nat_o(accp_list_nat(nat_list_encode_rel),cons_nat(X3,Xs)) ) ) ) ) ) ).

% list_encode.pelims
tff(fact_7613_last__upt,axiom,
    ! [I: nat,J: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,I),J)
     => ( aa_list_nat_nat(last_nat,upt(I,J)) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,J),one_one_nat) ) ) ).

% last_upt
tff(fact_7614_nth__sorted__list__of__set__greaterThanLessThan,axiom,
    ! [N2: nat,J: nat,I: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,J),aa_nat_nat(suc,I)))
     => ( aa_nat_nat(nth_nat(linord2614967742042102400et_nat(aa_nat_set_nat(set_or5834768355832116004an_nat(I),J))),N2) = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),N2)) ) ) ).

% nth_sorted_list_of_set_greaterThanLessThan
tff(fact_7615_nth__sorted__list__of__set__greaterThanAtMost,axiom,
    ! [N2: nat,J: nat,I: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,J),I))
     => ( aa_nat_nat(nth_nat(linord2614967742042102400et_nat(aa_nat_set_nat(set_or6659071591806873216st_nat(I),J))),N2) = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),N2)) ) ) ).

% nth_sorted_list_of_set_greaterThanAtMost
tff(fact_7616_upto_Opelims,axiom,
    ! [X2: int,Xa: int,Y: list_int] :
      ( ( upto(X2,Xa) = Y )
     => ( aa_Pro4592068669816069595_int_o(accp_P1096762738010456898nt_int(upto_rel),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X2),Xa))
       => ~ ( ( Y = $ite(aa_int_o(aa_int_fun_int_o(ord_less_eq_int,X2),Xa),cons_int(X2,upto(aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),one_one_int),Xa)),nil_int) )
           => ~ aa_Pro4592068669816069595_int_o(accp_P1096762738010456898nt_int(upto_rel),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,X2),Xa)) ) ) ) ).

% upto.pelims
tff(fact_7617_upto_Opsimps,axiom,
    ! [I: int,J: int] :
      ( aa_Pro4592068669816069595_int_o(accp_P1096762738010456898nt_int(upto_rel),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,I),J))
     => ( upto(I,J) = $ite(aa_int_o(aa_int_fun_int_o(ord_less_eq_int,I),J),cons_int(I,upto(aa_int_int(aa_int_fun_int_int(plus_plus_int,I),one_one_int),J)),nil_int) ) ) ).

% upto.psimps
tff(fact_7618_nth__upto,axiom,
    ! [I: int,K: nat,J: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,I),aa_nat_int(semiri1314217659103216013at_int,K))),J)
     => ( aa_nat_int(nth_int(upto(I,J)),K) = aa_int_int(aa_int_fun_int_int(plus_plus_int,I),aa_nat_int(semiri1314217659103216013at_int,K)) ) ) ).

% nth_upto
tff(fact_7619_length__upto,axiom,
    ! [I: int,J: int] : size_size_list_int(upto(I,J)) = aa_int_nat(nat2,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,J),I)),one_one_int)) ).

% length_upto
tff(fact_7620_upto__rec__numeral_I1_J,axiom,
    ! [M: num,N2: num] :
      upto(aa_num_int(numeral_numeral_int,M),aa_num_int(numeral_numeral_int,N2)) = $ite(aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_num_int(numeral_numeral_int,M)),aa_num_int(numeral_numeral_int,N2)),cons_int(aa_num_int(numeral_numeral_int,M),upto(aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_num_int(numeral_numeral_int,M)),one_one_int),aa_num_int(numeral_numeral_int,N2))),nil_int) ).

% upto_rec_numeral(1)
tff(fact_7621_upto__rec__numeral_I2_J,axiom,
    ! [M: num,N2: num] :
      upto(aa_num_int(numeral_numeral_int,M),aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,N2))) = $ite(aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_num_int(numeral_numeral_int,M)),aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,N2))),cons_int(aa_num_int(numeral_numeral_int,M),upto(aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_num_int(numeral_numeral_int,M)),one_one_int),aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,N2)))),nil_int) ).

% upto_rec_numeral(2)
tff(fact_7622_upto__rec__numeral_I3_J,axiom,
    ! [M: num,N2: num] :
      upto(aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,M)),aa_num_int(numeral_numeral_int,N2)) = $ite(aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,M))),aa_num_int(numeral_numeral_int,N2)),cons_int(aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,M)),upto(aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,M))),one_one_int),aa_num_int(numeral_numeral_int,N2))),nil_int) ).

% upto_rec_numeral(3)
tff(fact_7623_upto__rec__numeral_I4_J,axiom,
    ! [M: num,N2: num] :
      upto(aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,M)),aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,N2))) = $ite(aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,M))),aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,N2))),cons_int(aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,M)),upto(aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,M))),one_one_int),aa_int_int(uminus_uminus_int,aa_num_int(numeral_numeral_int,N2)))),nil_int) ).

% upto_rec_numeral(4)
tff(fact_7624_upto__split2,axiom,
    ! [I: int,J: int,K: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,I),J)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,J),K)
       => ( upto(I,K) = append_int(upto(I,J),upto(aa_int_int(aa_int_fun_int_int(plus_plus_int,J),one_one_int),K)) ) ) ) ).

% upto_split2
tff(fact_7625_upto__rec1,axiom,
    ! [I: int,J: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,I),J)
     => ( upto(I,J) = cons_int(I,upto(aa_int_int(aa_int_fun_int_int(plus_plus_int,I),one_one_int),J)) ) ) ).

% upto_rec1
tff(fact_7626_upto_Osimps,axiom,
    ! [I: int,J: int] :
      upto(I,J) = $ite(aa_int_o(aa_int_fun_int_o(ord_less_eq_int,I),J),cons_int(I,upto(aa_int_int(aa_int_fun_int_int(plus_plus_int,I),one_one_int),J)),nil_int) ).

% upto.simps
tff(fact_7627_upto_Oelims,axiom,
    ! [X2: int,Xa: int,Y: list_int] :
      ( ( upto(X2,Xa) = Y )
     => ( Y = $ite(aa_int_o(aa_int_fun_int_o(ord_less_eq_int,X2),Xa),cons_int(X2,upto(aa_int_int(aa_int_fun_int_int(plus_plus_int,X2),one_one_int),Xa)),nil_int) ) ) ).

% upto.elims
tff(fact_7628_greaterThanAtMost__upto,axiom,
    ! [I: int,J: int] : aa_int_set_int(set_or6656581121297822940st_int(I),J) = set_int2(upto(aa_int_int(aa_int_fun_int_int(plus_plus_int,I),one_one_int),J)) ).

% greaterThanAtMost_upto
tff(fact_7629_upto__split3,axiom,
    ! [I: int,J: int,K: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,I),J)
     => ( aa_int_o(aa_int_fun_int_o(ord_less_eq_int,J),K)
       => ( upto(I,K) = append_int(upto(I,aa_int_int(aa_int_fun_int_int(minus_minus_int,J),one_one_int)),cons_int(J,upto(aa_int_int(aa_int_fun_int_int(plus_plus_int,J),one_one_int),K))) ) ) ) ).

% upto_split3
tff(fact_7630_greaterThanLessThan__upto,axiom,
    ! [I: int,J: int] : aa_int_set_int(set_or5832277885323065728an_int(I),J) = set_int2(upto(aa_int_int(aa_int_fun_int_int(plus_plus_int,I),one_one_int),aa_int_int(aa_int_fun_int_int(minus_minus_int,J),one_one_int))) ).

% greaterThanLessThan_upto
tff(fact_7631_take__upt,axiom,
    ! [I: nat,M: nat,N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),M)),N2)
     => ( take_nat(M,upt(I,N2)) = upt(I,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,I),M)) ) ) ).

% take_upt
tff(fact_7632_butlast__upt,axiom,
    ! [M: nat,N2: nat] : butlast_nat(upt(M,N2)) = upt(M,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)) ).

% butlast_upt
tff(fact_7633_next_Osimps,axiom,
    ! [V: code_natural,W: code_natural] :
      aa_Pro7165575656943818355atural(next,produc3574140220909816553atural(V,W)) = $let(
        v: code_natural,
        v:= aa_Cod4272041906116450446atural(minus_shift(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,one))))))))))))))))))))))))))))))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,V),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one)))))))))))))))))),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit0,one)))))))))))))))))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,V),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,one)))))))))))))))))),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit0,one)))))))))))))))),
        $let(
          w: code_natural,
          w:= aa_Cod4272041906116450446atural(minus_shift(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,one))))))))))))))))))))))))))))))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,W),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit1,one)))))))))))))))))),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit0,one)))))))))))))))))),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,W),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit1,one)))))))))))))))))),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit1,one)))))))))))))),
          aa_Pro7165575656943818355atural(produc6639722614265839536atural(aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_Cod4272041906116450446atural(minus_shift(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,one))))))))))))))))))))))))))))))),v),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,w),one_one_Code_natural))),one_one_Code_natural)),produc3574140220909816553atural(v,w)) ) ) ).

% next.simps
tff(fact_7634_full__exhaustive__natural_H_Ocases,axiom,
    ! [X2: produc9140211490168418807atural] :
      ~ ! [F2: fun_Pr285225112257423215e_term,D: code_natural,I2: code_natural] : X2 != produc3399137497101226409atural(F2,produc3574140220909816553atural(D,I2)) ).

% full_exhaustive_natural'.cases
tff(fact_7635_exhaustive__natural_H_Ocases,axiom,
    ! [X2: produc7476732711998919211atural] :
      ~ ! [F2: fun_Co6386927884524458043e_term,D: code_natural,I2: code_natural] : X2 != produc3379161622255323613atural(F2,produc3574140220909816553atural(D,I2)) ).

% exhaustive_natural'.cases
tff(fact_7636_log_Ocases,axiom,
    ! [X2: produc7822875418678951345atural] :
      ~ ! [B2: code_natural,I2: code_natural] : X2 != produc3574140220909816553atural(B2,I2) ).

% log.cases
tff(fact_7637_minus__shift__def,axiom,
    ! [R2: code_natural,K: code_natural,L: code_natural] :
      aa_Cod4272041906116450446atural(minus_shift(R2,K),L) = $ite(aa_Code_natural_o(aa_Cod1485054954640246627ural_o(ord_le5570908160329646204atural,K),L),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(minus_7197305767214868737atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,R2),K)),L),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(minus_7197305767214868737atural,K),L)) ).

% minus_shift_def
tff(fact_7638_split__seed__def,axiom,
    ! [S: produc7822875418678951345atural] : split_seed(S) = produc8282080750456430313atural(aTP_Lamm_adl(S),S) ).

% split_seed_def
tff(fact_7639_log_Osimps,axiom,
    ! [B: code_natural,I: code_natural] :
      aa_Cod4272041906116450446atural(log(B),I) = $ite(
        ( aa_Code_natural_o(aa_Cod1485054954640246627ural_o(ord_le1926595141338095240atural,B),one_one_Code_natural)
        | aa_Code_natural_o(aa_Cod1485054954640246627ural_o(ord_le5570908160329646204atural,I),B) ),
        one_one_Code_natural,
        aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,one_one_Code_natural),aa_Cod4272041906116450446atural(log(B),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,I),B))) ) ).

% log.simps
tff(fact_7640_log_Oelims,axiom,
    ! [X2: code_natural,Xa: code_natural,Y: code_natural] :
      ( ( aa_Cod4272041906116450446atural(log(X2),Xa) = Y )
     => ( Y = $ite(
            ( aa_Code_natural_o(aa_Cod1485054954640246627ural_o(ord_le1926595141338095240atural,X2),one_one_Code_natural)
            | aa_Code_natural_o(aa_Cod1485054954640246627ural_o(ord_le5570908160329646204atural,Xa),X2) ),
            one_one_Code_natural,
            aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,one_one_Code_natural),aa_Cod4272041906116450446atural(log(X2),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,Xa),X2))) ) ) ) ).

% log.elims
tff(fact_7641_inc__shift__def,axiom,
    ! [V: code_natural,K: code_natural] :
      aa_Cod4272041906116450446atural(inc_shift(V),K) = $ite(V = K,one_one_Code_natural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,K),one_one_Code_natural)) ).

% inc_shift_def
tff(fact_7642_log_Opelims,axiom,
    ! [X2: code_natural,Xa: code_natural,Y: code_natural] :
      ( ( aa_Cod4272041906116450446atural(log(X2),Xa) = Y )
     => ( aa_Pro6073791466322389475ural_o(accp_P8126237942716283194atural(log_rel),produc3574140220909816553atural(X2,Xa))
       => ~ ( ( Y = $ite(
                  ( aa_Code_natural_o(aa_Cod1485054954640246627ural_o(ord_le1926595141338095240atural,X2),one_one_Code_natural)
                  | aa_Code_natural_o(aa_Cod1485054954640246627ural_o(ord_le5570908160329646204atural,Xa),X2) ),
                  one_one_Code_natural,
                  aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,one_one_Code_natural),aa_Cod4272041906116450446atural(log(X2),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,Xa),X2))) ) )
           => ~ aa_Pro6073791466322389475ural_o(accp_P8126237942716283194atural(log_rel),produc3574140220909816553atural(X2,Xa)) ) ) ) ).

% log.pelims
tff(fact_7643_Random_Orange__def,axiom,
    ! [K: code_natural] : range(K) = produc5538323210962509403atural(iterat8892046348760725948atural(aa_Cod4272041906116450446atural(log(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,one)))))))))))))))))))))))))))))))),K),aTP_Lamm_adn,one_one_Code_natural),aTP_Lamm_ado(K)) ).

% Random.range_def
tff(fact_7644_wmsI,axiom,
    ! [A2: multis2468970476368604999at_nat,B4: multis2468970476368604999at_nat,Z6: multis2468970476368604999at_nat] :
      ( ( member8757157785044589968at_nat(produc2922128104949294807at_nat(set_ms8126754132646256062at_nat(A2),set_ms8126754132646256062at_nat(B4)),fun_max_strict)
        | ( ( A2 = zero_z1048942125864253310at_nat )
          & ( B4 = zero_z1048942125864253310at_nat ) ) )
     => member6689249552917799696at_nat(produc4348348721325984599at_nat(aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(Z6),A2),aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(Z6),B4)),ms_weak) ) ).

% wmsI
tff(fact_7645_smsI,axiom,
    ! [A2: multis2468970476368604999at_nat,B4: multis2468970476368604999at_nat,Z6: multis2468970476368604999at_nat] :
      ( member8757157785044589968at_nat(produc2922128104949294807at_nat(set_ms8126754132646256062at_nat(A2),set_ms8126754132646256062at_nat(B4)),fun_max_strict)
     => member6689249552917799696at_nat(produc4348348721325984599at_nat(aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(Z6),A2),aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(Z6),B4)),ms_strict) ) ).

% smsI
tff(fact_7646_ms__reduction__pair,axiom,
    fun_re7357418987779152907at_nat(produc5245064249948416855at_nat(ms_strict,ms_weak)) ).

% ms_reduction_pair
tff(fact_7647_ms__strictI,axiom,
    ! [Z6: multis2468970476368604999at_nat,Z7: multis2468970476368604999at_nat,A2: multis2468970476368604999at_nat,B4: multis2468970476368604999at_nat] :
      ( pw_leq(Z6,Z7)
     => ( member8757157785044589968at_nat(produc2922128104949294807at_nat(set_ms8126754132646256062at_nat(A2),set_ms8126754132646256062at_nat(B4)),fun_max_strict)
       => member6689249552917799696at_nat(produc4348348721325984599at_nat(aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(Z6),A2),aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(Z7),B4)),ms_strict) ) ) ).

% ms_strictI
tff(fact_7648_ms__weakI1,axiom,
    ! [Z6: multis2468970476368604999at_nat,Z7: multis2468970476368604999at_nat,A2: multis2468970476368604999at_nat,B4: multis2468970476368604999at_nat] :
      ( pw_leq(Z6,Z7)
     => ( member8757157785044589968at_nat(produc2922128104949294807at_nat(set_ms8126754132646256062at_nat(A2),set_ms8126754132646256062at_nat(B4)),fun_max_strict)
       => member6689249552917799696at_nat(produc4348348721325984599at_nat(aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(Z6),A2),aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(Z7),B4)),ms_weak) ) ) ).

% ms_weakI1
tff(fact_7649_pw__leq__split,axiom,
    ! [X7: multis2468970476368604999at_nat,Y7: multis2468970476368604999at_nat] :
      ( pw_leq(X7,Y7)
     => ? [A6: multis2468970476368604999at_nat,B7: multis2468970476368604999at_nat,Z8: multis2468970476368604999at_nat] :
          ( ( X7 = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(A6),Z8) )
          & ( Y7 = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(B7),Z8) )
          & ( member8757157785044589968at_nat(produc2922128104949294807at_nat(set_ms8126754132646256062at_nat(A6),set_ms8126754132646256062at_nat(B7)),fun_max_strict)
            | ( ( B7 = zero_z1048942125864253310at_nat )
              & ( A6 = zero_z1048942125864253310at_nat ) ) ) ) ) ).

% pw_leq_split
tff(fact_7650_ms__weakI2,axiom,
    ! [Z6: multis2468970476368604999at_nat,Z7: multis2468970476368604999at_nat] :
      ( pw_leq(Z6,Z7)
     => member6689249552917799696at_nat(produc4348348721325984599at_nat(aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(Z6),zero_z1048942125864253310at_nat),aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(Z7),zero_z1048942125864253310at_nat)),ms_weak) ) ).

% ms_weakI2
tff(fact_7651_pw__leq__lstep,axiom,
    ! [X2: product_prod_nat_nat,Y: product_prod_nat_nat] :
      ( member8206827879206165904at_nat(produc6161850002892822231at_nat(X2,Y),fun_pair_leq)
     => pw_leq(add_ms2612439473150266591at_nat(X2,zero_z1048942125864253310at_nat),add_ms2612439473150266591at_nat(Y,zero_z1048942125864253310at_nat)) ) ).

% pw_leq_lstep
tff(fact_7652_pw__leq__step,axiom,
    ! [X2: product_prod_nat_nat,Y: product_prod_nat_nat,X7: multis2468970476368604999at_nat,Y7: multis2468970476368604999at_nat] :
      ( member8206827879206165904at_nat(produc6161850002892822231at_nat(X2,Y),fun_pair_leq)
     => ( pw_leq(X7,Y7)
       => pw_leq(aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(add_ms2612439473150266591at_nat(X2,zero_z1048942125864253310at_nat)),X7),aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(add_ms2612439473150266591at_nat(Y,zero_z1048942125864253310at_nat)),Y7)) ) ) ).

% pw_leq_step
tff(fact_7653_pw__leq_Osimps,axiom,
    ! [A1: multis2468970476368604999at_nat,A22: multis2468970476368604999at_nat] :
      ( pw_leq(A1,A22)
    <=> ( ( ( A1 = zero_z1048942125864253310at_nat )
          & ( A22 = zero_z1048942125864253310at_nat ) )
        | ? [X4: product_prod_nat_nat,Y3: product_prod_nat_nat,X8: multis2468970476368604999at_nat,Y8: multis2468970476368604999at_nat] :
            ( ( A1 = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(add_ms2612439473150266591at_nat(X4,zero_z1048942125864253310at_nat)),X8) )
            & ( A22 = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(add_ms2612439473150266591at_nat(Y3,zero_z1048942125864253310at_nat)),Y8) )
            & member8206827879206165904at_nat(produc6161850002892822231at_nat(X4,Y3),fun_pair_leq)
            & pw_leq(X8,Y8) ) ) ) ).

% pw_leq.simps
tff(fact_7654_pw__leq_Ocases,axiom,
    ! [A1: multis2468970476368604999at_nat,A22: multis2468970476368604999at_nat] :
      ( pw_leq(A1,A22)
     => ( ( ( A1 = zero_z1048942125864253310at_nat )
         => ( A22 != zero_z1048942125864253310at_nat ) )
       => ~ ! [X3: product_prod_nat_nat,Y4: product_prod_nat_nat,X9: multis2468970476368604999at_nat] :
              ( ( A1 = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(add_ms2612439473150266591at_nat(X3,zero_z1048942125864253310at_nat)),X9) )
             => ! [Y9: multis2468970476368604999at_nat] :
                  ( ( A22 = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(add_ms2612439473150266591at_nat(Y4,zero_z1048942125864253310at_nat)),Y9) )
                 => ( member8206827879206165904at_nat(produc6161850002892822231at_nat(X3,Y4),fun_pair_leq)
                   => ~ pw_leq(X9,Y9) ) ) ) ) ) ).

% pw_leq.cases
tff(fact_7655_Code__Numeral_Osub__code_I4_J,axiom,
    ! [N2: num] : aa_num_Code_integer(aa_num5808785979904431436nteger(code_sub,one),aa_num_num(bit0,N2)) = aa_num_Code_integer(code_Neg,aa_num_num(bitM,N2)) ).

% Code_Numeral.sub_code(4)
tff(fact_7656_Code__Numeral_Odup__code_I3_J,axiom,
    ! [N2: num] : aa_Cod1783974652533396728nteger(code_dup,aa_num_Code_integer(code_Neg,N2)) = aa_num_Code_integer(code_Neg,aa_num_num(bit0,N2)) ).

% Code_Numeral.dup_code(3)
tff(fact_7657_less__integer__code_I3_J,axiom,
    ! [L: num] : ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),aa_num_Code_integer(code_Neg,L)) ).

% less_integer_code(3)
tff(fact_7658_less__integer__code_I7_J,axiom,
    ! [K: num] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_num_Code_integer(code_Neg,K)),zero_z3403309356797280102nteger) ).

% less_integer_code(7)
tff(fact_7659_plus__integer__code_I6_J,axiom,
    ! [M: num,N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_num_Code_integer(code_Neg,M)),aa_num_Code_integer(code_Neg,N2)) = aa_num_Code_integer(code_Neg,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2)) ).

% plus_integer_code(6)
tff(fact_7660_less__eq__integer__code_I7_J,axiom,
    ! [K: num] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_num_Code_integer(code_Neg,K)),zero_z3403309356797280102nteger) ).

% less_eq_integer_code(7)
tff(fact_7661_less__eq__integer__code_I3_J,axiom,
    ! [L: num] : ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_num_Code_integer(code_Neg,L)) ).

% less_eq_integer_code(3)
tff(fact_7662_less__integer__code_I9_J,axiom,
    ! [K: num,L: num] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_num_Code_integer(code_Neg,K)),aa_num_Code_integer(code_Neg,L))
    <=> aa_num_o(aa_num_fun_num_o(ord_less_num,L),K) ) ).

% less_integer_code(9)
tff(fact_7663_less__eq__integer__code_I9_J,axiom,
    ! [K: num,L: num] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_num_Code_integer(code_Neg,K)),aa_num_Code_integer(code_Neg,L))
    <=> aa_num_o(aa_num_fun_num_o(ord_less_eq_num,L),K) ) ).

% less_eq_integer_code(9)
tff(fact_7664_minus__integer__code_I6_J,axiom,
    ! [M: num,N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_num_Code_integer(code_Neg,M)),aa_num_Code_integer(code_Neg,N2)) = aa_num_Code_integer(aa_num5808785979904431436nteger(code_sub,N2),M) ).

% minus_integer_code(6)
tff(fact_7665_divmod__abs__code_I2_J,axiom,
    ! [K: num,L: num] : aa_Cod6977894654539884864nteger(code_divmod_abs(aa_num_Code_integer(code_Neg,K)),aa_num_Code_integer(code_Neg,L)) = unique3479559517661332726nteger(K,L) ).

% divmod_abs_code(2)
tff(fact_7666_Code__Numeral_Osub__code_I5_J,axiom,
    ! [N2: num] : aa_num_Code_integer(aa_num5808785979904431436nteger(code_sub,one),aa_num_num(bit1,N2)) = aa_num_Code_integer(code_Neg,aa_num_num(bit0,N2)) ).

% Code_Numeral.sub_code(5)
tff(fact_7667_card__length__sum__list__rec,axiom,
    ! [M: nat,N5: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,one_one_nat),M)
     => ( finite_card_list_nat(collect_list_nat(aa_nat5883842100386203267_nat_o(aTP_Lamm_adp(M),N5))) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,finite_card_list_nat(collect_list_nat(aa_nat5883842100386203267_nat_o(aTP_Lamm_adq(M),N5)))),finite_card_list_nat(collect_list_nat(aa_nat5883842100386203267_nat_o(aTP_Lamm_adr(M),N5)))) ) ) ).

% card_length_sum_list_rec
tff(fact_7668_card__length__sum__list,axiom,
    ! [M: nat,N5: nat] : finite_card_list_nat(collect_list_nat(aa_nat5883842100386203267_nat_o(aTP_Lamm_adp(M),N5))) = aa_nat_nat(aa_nat_fun_nat_nat(binomial,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,N5),M)),one_one_nat)),N5) ).

% card_length_sum_list
tff(fact_7669_natural__of__nat__of__nat,axiom,
    code_natural_of_nat = semiri3763490453095760265atural ).

% natural_of_nat_of_nat
tff(fact_7670_division__segment__natural_Oabs__eq,axiom,
    ! [X2: nat] : aa_Cod4272041906116450446atural(euclid5112970336976722131atural,aa_nat_Code_natural(code_natural_of_nat,X2)) = aa_nat_Code_natural(code_natural_of_nat,aa_nat_nat(euclid3398187327856392827nt_nat,X2)) ).

% division_segment_natural.abs_eq
tff(fact_7671_set__bit__natural_Oabs__eq,axiom,
    ! [Xa: nat,X2: nat] : aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se1617098188084679374atural,Xa),aa_nat_Code_natural(code_natural_of_nat,X2)) = aa_nat_Code_natural(code_natural_of_nat,aa_nat_nat(aa_nat_fun_nat_nat(bit_se7882103937844011126it_nat,Xa),X2)) ).

% set_bit_natural.abs_eq
tff(fact_7672_flip__bit__natural_Oabs__eq,axiom,
    ! [Xa: nat,X2: nat] : aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se168947363167071951atural,Xa),aa_nat_Code_natural(code_natural_of_nat,X2)) = aa_nat_Code_natural(code_natural_of_nat,aa_nat_nat(aa_nat_fun_nat_nat(bit_se2161824704523386999it_nat,Xa),X2)) ).

% flip_bit_natural.abs_eq
tff(fact_7673_unset__bit__natural_Oabs__eq,axiom,
    ! [Xa: nat,X2: nat] : aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se7083795435491715335atural,Xa),aa_nat_Code_natural(code_natural_of_nat,X2)) = aa_nat_Code_natural(code_natural_of_nat,aa_nat_nat(aa_nat_fun_nat_nat(bit_se4205575877204974255it_nat,Xa),X2)) ).

% unset_bit_natural.abs_eq
tff(fact_7674_euclidean__size__natural_Oabs__eq,axiom,
    ! [X2: nat] : aa_Code_natural_nat(euclid5200926497590043453atural,aa_nat_Code_natural(code_natural_of_nat,X2)) = aa_nat_nat(euclid4777050414544973029ze_nat,X2) ).

% euclidean_size_natural.abs_eq
tff(fact_7675_bit__natural_Oabs__eq,axiom,
    ! [X2: nat] : aa_Cod9120328075896114107_nat_o(bit_se8040316288895769887atural,aa_nat_Code_natural(code_natural_of_nat,X2)) = aa_nat_fun_nat_o(bit_se1148574629649215175it_nat,X2) ).

% bit_natural.abs_eq
tff(fact_7676_natural__of__nat__cases,axiom,
    ! [X2: code_natural] :
      ~ ! [Y4: nat] :
          ( ( X2 = aa_nat_Code_natural(code_natural_of_nat,Y4) )
         => ~ member_nat(Y4,top_top_set_nat) ) ).

% natural_of_nat_cases
tff(fact_7677_natural__of__nat__induct,axiom,
    ! [P: fun_Code_natural_o,X2: code_natural] :
      ( ! [Y4: nat] :
          ( member_nat(Y4,top_top_set_nat)
         => aa_Code_natural_o(P,aa_nat_Code_natural(code_natural_of_nat,Y4)) )
     => aa_Code_natural_o(P,X2) ) ).

% natural_of_nat_induct
tff(fact_7678_natural__of__nat__inject,axiom,
    ! [X2: nat,Y: nat] :
      ( member_nat(X2,top_top_set_nat)
     => ( member_nat(Y,top_top_set_nat)
       => ( ( aa_nat_Code_natural(code_natural_of_nat,X2) = aa_nat_Code_natural(code_natural_of_nat,Y) )
        <=> ( X2 = Y ) ) ) ) ).

% natural_of_nat_inject
tff(fact_7679_take__bit__natural_Oabs__eq,axiom,
    ! [Xa: nat,X2: nat] : aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se569199155075624693atural,Xa),aa_nat_Code_natural(code_natural_of_nat,X2)) = aa_nat_Code_natural(code_natural_of_nat,aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,Xa),X2)) ).

% take_bit_natural.abs_eq
tff(fact_7680_and__natural_Oabs__eq,axiom,
    ! [Xa: nat,X2: nat] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se2773287842338716102atural,aa_nat_Code_natural(code_natural_of_nat,Xa)),aa_nat_Code_natural(code_natural_of_nat,X2)) = aa_nat_Code_natural(code_natural_of_nat,aa_nat_nat(aa_nat_fun_nat_nat(bit_se727722235901077358nd_nat,Xa),X2)) ).

% and_natural.abs_eq
tff(fact_7681_xor__natural_Oabs__eq,axiom,
    ! [Xa: nat,X2: nat] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se2046307713759805098atural,aa_nat_Code_natural(code_natural_of_nat,Xa)),aa_nat_Code_natural(code_natural_of_nat,X2)) = aa_nat_Code_natural(code_natural_of_nat,aa_nat_nat(aa_nat_fun_nat_nat(bit_se6528837805403552850or_nat,Xa),X2)) ).

% xor_natural.abs_eq
tff(fact_7682_or__natural_Oabs__eq,axiom,
    ! [Xa: nat,X2: nat] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se9127793120404214118atural,aa_nat_Code_natural(code_natural_of_nat,Xa)),aa_nat_Code_natural(code_natural_of_nat,X2)) = aa_nat_Code_natural(code_natural_of_nat,aa_nat_nat(aa_nat_fun_nat_nat(bit_se1412395901928357646or_nat,Xa),X2)) ).

% or_natural.abs_eq
tff(fact_7683_mask__natural_Oabs__eq,axiom,
    ! [X2: nat] : aa_nat_Code_natural(bit_se943457434206027407atural,X2) = aa_nat_Code_natural(code_natural_of_nat,aa_nat_nat(bit_se2002935070580805687sk_nat,X2)) ).

% mask_natural.abs_eq
tff(fact_7684_push__bit__natural_Oabs__eq,axiom,
    ! [Xa: nat,X2: nat] : aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se6611745700429515170atural,Xa),aa_nat_Code_natural(code_natural_of_nat,X2)) = aa_nat_Code_natural(code_natural_of_nat,aa_nat_nat(aa_nat_fun_nat_nat(bit_se547839408752420682it_nat,Xa),X2)) ).

% push_bit_natural.abs_eq
tff(fact_7685_drop__bit__natural_Oabs__eq,axiom,
    ! [Xa: nat,X2: nat] : aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se2751692689150723149atural,Xa),aa_nat_Code_natural(code_natural_of_nat,X2)) = aa_nat_Code_natural(code_natural_of_nat,aa_nat_nat(aa_nat_fun_nat_nat(bit_se8570568707652914677it_nat,Xa),X2)) ).

% drop_bit_natural.abs_eq
tff(fact_7686_zero__natural__def,axiom,
    zero_z2226904508553997617atural = aa_nat_Code_natural(code_natural_of_nat,zero_zero_nat) ).

% zero_natural_def
tff(fact_7687_one__natural__def,axiom,
    one_one_Code_natural = aa_nat_Code_natural(code_natural_of_nat,one_one_nat) ).

% one_natural_def
tff(fact_7688_less__natural_Oabs__eq,axiom,
    ! [Xa: nat,X2: nat] :
      ( aa_Code_natural_o(aa_Cod1485054954640246627ural_o(ord_le5570908160329646204atural,aa_nat_Code_natural(code_natural_of_nat,Xa)),aa_nat_Code_natural(code_natural_of_nat,X2))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,Xa),X2) ) ).

% less_natural.abs_eq
tff(fact_7689_plus__natural_Oabs__eq,axiom,
    ! [Xa: nat,X2: nat] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,aa_nat_Code_natural(code_natural_of_nat,Xa)),aa_nat_Code_natural(code_natural_of_nat,X2)) = aa_nat_Code_natural(code_natural_of_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Xa),X2)) ).

% plus_natural.abs_eq
tff(fact_7690_minus__natural_Oabs__eq,axiom,
    ! [Xa: nat,X2: nat] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(minus_7197305767214868737atural,aa_nat_Code_natural(code_natural_of_nat,Xa)),aa_nat_Code_natural(code_natural_of_nat,X2)) = aa_nat_Code_natural(code_natural_of_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Xa),X2)) ).

% minus_natural.abs_eq
tff(fact_7691_less__eq__natural_Oabs__eq,axiom,
    ! [Xa: nat,X2: nat] :
      ( aa_Code_natural_o(aa_Cod1485054954640246627ural_o(ord_le1926595141338095240atural,aa_nat_Code_natural(code_natural_of_nat,Xa)),aa_nat_Code_natural(code_natural_of_nat,X2))
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,Xa),X2) ) ).

% less_eq_natural.abs_eq
tff(fact_7692_times__natural_Oabs__eq,axiom,
    ! [Xa: nat,X2: nat] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_nat_Code_natural(code_natural_of_nat,Xa)),aa_nat_Code_natural(code_natural_of_nat,X2)) = aa_nat_Code_natural(code_natural_of_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,Xa),X2)) ).

% times_natural.abs_eq
tff(fact_7693_divide__natural_Oabs__eq,axiom,
    ! [Xa: nat,X2: nat] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,aa_nat_Code_natural(code_natural_of_nat,Xa)),aa_nat_Code_natural(code_natural_of_nat,X2)) = aa_nat_Code_natural(code_natural_of_nat,aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,Xa),X2)) ).

% divide_natural.abs_eq
tff(fact_7694_mask__natural__def,axiom,
    bit_se943457434206027407atural = map_fu4742413587575543474atural(id_nat,code_natural_of_nat,bit_se2002935070580805687sk_nat) ).

% mask_natural_def
tff(fact_7695_modulo__natural_Oabs__eq,axiom,
    ! [Xa: nat,X2: nat] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,aa_nat_Code_natural(code_natural_of_nat,Xa)),aa_nat_Code_natural(code_natural_of_nat,X2)) = aa_nat_Code_natural(code_natural_of_nat,aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,Xa),X2)) ).

% modulo_natural.abs_eq
tff(fact_7696_Nat_Oabs__eq,axiom,
    ! [X2: int] : aa_Cod607569804290114243atural(code_Nat,aa_int_Code_integer(code_integer_of_int,X2)) = aa_nat_Code_natural(code_natural_of_nat,aa_int_nat(nat2,X2)) ).

% Nat.abs_eq
tff(fact_7697_Nat__def,axiom,
    code_Nat = map_fu1051355602067684763atural(code_int_of_integer,code_natural_of_nat,nat2) ).

% Nat_def
tff(fact_7698_natural__of__integer_Oabs__eq,axiom,
    ! [X2: int] : aa_Cod607569804290114243atural(code_n4118661773612635043nteger,aa_int_Code_integer(code_integer_of_int,X2)) = aa_nat_Code_natural(code_natural_of_nat,aa_int_nat(nat2,X2)) ).

% natural_of_integer.abs_eq
tff(fact_7699_natural__of__nat__of__natural__inverse,axiom,
    ! [N2: code_natural] : aa_nat_Code_natural(code_natural_of_nat,aa_Code_natural_nat(code_nat_of_natural,N2)) = N2 ).

% natural_of_nat_of_natural_inverse
tff(fact_7700_nat__of__natural__of__nat__inverse,axiom,
    ! [N2: nat] : aa_Code_natural_nat(code_nat_of_natural,aa_nat_Code_natural(code_natural_of_nat,N2)) = N2 ).

% nat_of_natural_of_nat_inverse
tff(fact_7701_nat__of__natural__inverse,axiom,
    ! [X2: code_natural] : aa_nat_Code_natural(code_natural_of_nat,aa_Code_natural_nat(code_nat_of_natural,X2)) = X2 ).

% nat_of_natural_inverse
tff(fact_7702_nat__of__natural__min,axiom,
    ! [K: code_natural,L: code_natural] : aa_Code_natural_nat(code_nat_of_natural,aa_Cod4272041906116450446atural(ord_min_Code_natural(K),L)) = aa_nat_nat(aa_nat_fun_nat_nat(ord_min_nat,aa_Code_natural_nat(code_nat_of_natural,K)),aa_Code_natural_nat(code_nat_of_natural,L)) ).

% nat_of_natural_min
tff(fact_7703_nat__of__natural__max,axiom,
    ! [K: code_natural,L: code_natural] : aa_Code_natural_nat(code_nat_of_natural,aa_Cod4272041906116450446atural(ord_max_Code_natural(K),L)) = aa_nat_nat(aa_nat_fun_nat_nat(ord_max_nat,aa_Code_natural_nat(code_nat_of_natural,K)),aa_Code_natural_nat(code_nat_of_natural,L)) ).

% nat_of_natural_max
tff(fact_7704_of__nat__of__natural,axiom,
    ! [N2: code_natural] : aa_nat_Code_natural(semiri3763490453095760265atural,aa_Code_natural_nat(code_nat_of_natural,N2)) = N2 ).

% of_nat_of_natural
tff(fact_7705_nat__of__natural__of__nat,axiom,
    ! [N2: nat] : aa_Code_natural_nat(code_nat_of_natural,aa_nat_Code_natural(semiri3763490453095760265atural,N2)) = N2 ).

% nat_of_natural_of_nat
tff(fact_7706_zero__natural_Orep__eq,axiom,
    aa_Code_natural_nat(code_nat_of_natural,zero_z2226904508553997617atural) = zero_zero_nat ).

% zero_natural.rep_eq
tff(fact_7707_one__natural_Orep__eq,axiom,
    aa_Code_natural_nat(code_nat_of_natural,one_one_Code_natural) = one_one_nat ).

% one_natural.rep_eq
tff(fact_7708_plus__natural_Orep__eq,axiom,
    ! [X2: code_natural,Xa: code_natural] : aa_Code_natural_nat(code_nat_of_natural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,X2),Xa)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_Code_natural_nat(code_nat_of_natural,X2)),aa_Code_natural_nat(code_nat_of_natural,Xa)) ).

% plus_natural.rep_eq
tff(fact_7709_minus__natural_Orep__eq,axiom,
    ! [X2: code_natural,Xa: code_natural] : aa_Code_natural_nat(code_nat_of_natural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(minus_7197305767214868737atural,X2),Xa)) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_Code_natural_nat(code_nat_of_natural,X2)),aa_Code_natural_nat(code_nat_of_natural,Xa)) ).

% minus_natural.rep_eq
tff(fact_7710_nat__of__natural__numeral,axiom,
    ! [K: num] : aa_Code_natural_nat(code_nat_of_natural,aa_num_Code_natural(numera5444537566228673987atural,K)) = aa_num_nat(numeral_numeral_nat,K) ).

% nat_of_natural_numeral
tff(fact_7711_times__natural_Orep__eq,axiom,
    ! [X2: code_natural,Xa: code_natural] : aa_Code_natural_nat(code_nat_of_natural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,X2),Xa)) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_Code_natural_nat(code_nat_of_natural,X2)),aa_Code_natural_nat(code_nat_of_natural,Xa)) ).

% times_natural.rep_eq
tff(fact_7712_divide__natural_Orep__eq,axiom,
    ! [X2: code_natural,Xa: code_natural] : aa_Code_natural_nat(code_nat_of_natural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(divide5121882707175180666atural,X2),Xa)) = aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,aa_Code_natural_nat(code_nat_of_natural,X2)),aa_Code_natural_nat(code_nat_of_natural,Xa)) ).

% divide_natural.rep_eq
tff(fact_7713_modulo__natural_Orep__eq,axiom,
    ! [X2: code_natural,Xa: code_natural] : aa_Code_natural_nat(code_nat_of_natural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,X2),Xa)) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,aa_Code_natural_nat(code_nat_of_natural,X2)),aa_Code_natural_nat(code_nat_of_natural,Xa)) ).

% modulo_natural.rep_eq
tff(fact_7714_division__segment__natural_Orep__eq,axiom,
    ! [X2: code_natural] : aa_Code_natural_nat(code_nat_of_natural,aa_Cod4272041906116450446atural(euclid5112970336976722131atural,X2)) = aa_nat_nat(euclid3398187327856392827nt_nat,aa_Code_natural_nat(code_nat_of_natural,X2)) ).

% division_segment_natural.rep_eq
tff(fact_7715_euclidean__size__natural_Orep__eq,axiom,
    ! [X2: code_natural] : aa_Code_natural_nat(euclid5200926497590043453atural,X2) = aa_nat_nat(euclid4777050414544973029ze_nat,aa_Code_natural_nat(code_nat_of_natural,X2)) ).

% euclidean_size_natural.rep_eq
tff(fact_7716_unset__bit__natural_Orep__eq,axiom,
    ! [X2: nat,Xa: code_natural] : aa_Code_natural_nat(code_nat_of_natural,aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se7083795435491715335atural,X2),Xa)) = aa_nat_nat(aa_nat_fun_nat_nat(bit_se4205575877204974255it_nat,X2),aa_Code_natural_nat(code_nat_of_natural,Xa)) ).

% unset_bit_natural.rep_eq
tff(fact_7717_flip__bit__natural_Orep__eq,axiom,
    ! [X2: nat,Xa: code_natural] : aa_Code_natural_nat(code_nat_of_natural,aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se168947363167071951atural,X2),Xa)) = aa_nat_nat(aa_nat_fun_nat_nat(bit_se2161824704523386999it_nat,X2),aa_Code_natural_nat(code_nat_of_natural,Xa)) ).

% flip_bit_natural.rep_eq
tff(fact_7718_set__bit__natural_Orep__eq,axiom,
    ! [X2: nat,Xa: code_natural] : aa_Code_natural_nat(code_nat_of_natural,aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se1617098188084679374atural,X2),Xa)) = aa_nat_nat(aa_nat_fun_nat_nat(bit_se7882103937844011126it_nat,X2),aa_Code_natural_nat(code_nat_of_natural,Xa)) ).

% set_bit_natural.rep_eq
tff(fact_7719_Nat_Orep__eq,axiom,
    ! [X2: code_integer] : aa_Code_natural_nat(code_nat_of_natural,aa_Cod607569804290114243atural(code_Nat,X2)) = aa_int_nat(nat2,aa_Code_integer_int(code_int_of_integer,X2)) ).

% Nat.rep_eq
tff(fact_7720_push__bit__natural_Orep__eq,axiom,
    ! [X2: nat,Xa: code_natural] : aa_Code_natural_nat(code_nat_of_natural,aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se6611745700429515170atural,X2),Xa)) = aa_nat_nat(aa_nat_fun_nat_nat(bit_se547839408752420682it_nat,X2),aa_Code_natural_nat(code_nat_of_natural,Xa)) ).

% push_bit_natural.rep_eq
tff(fact_7721_mask__natural_Orep__eq,axiom,
    ! [X2: nat] : aa_Code_natural_nat(code_nat_of_natural,aa_nat_Code_natural(bit_se943457434206027407atural,X2)) = aa_nat_nat(bit_se2002935070580805687sk_nat,X2) ).

% mask_natural.rep_eq
tff(fact_7722_and__natural_Orep__eq,axiom,
    ! [X2: code_natural,Xa: code_natural] : aa_Code_natural_nat(code_nat_of_natural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se2773287842338716102atural,X2),Xa)) = aa_nat_nat(aa_nat_fun_nat_nat(bit_se727722235901077358nd_nat,aa_Code_natural_nat(code_nat_of_natural,X2)),aa_Code_natural_nat(code_nat_of_natural,Xa)) ).

% and_natural.rep_eq
tff(fact_7723_bit__natural_Orep__eq,axiom,
    ! [X2: code_natural] : aa_Cod9120328075896114107_nat_o(bit_se8040316288895769887atural,X2) = aa_nat_fun_nat_o(bit_se1148574629649215175it_nat,aa_Code_natural_nat(code_nat_of_natural,X2)) ).

% bit_natural.rep_eq
tff(fact_7724_nat__of__natural__inject,axiom,
    ! [X2: code_natural,Y: code_natural] :
      ( ( aa_Code_natural_nat(code_nat_of_natural,X2) = aa_Code_natural_nat(code_nat_of_natural,Y) )
    <=> ( X2 = Y ) ) ).

% nat_of_natural_inject
tff(fact_7725_natural__eqI,axiom,
    ! [M: code_natural,N2: code_natural] :
      ( ( aa_Code_natural_nat(code_nat_of_natural,M) = aa_Code_natural_nat(code_nat_of_natural,N2) )
     => ( M = N2 ) ) ).

% natural_eqI
tff(fact_7726_natural__eq__iff,axiom,
    ! [M: code_natural,N2: code_natural] :
      ( ( M = N2 )
    <=> ( aa_Code_natural_nat(code_nat_of_natural,M) = aa_Code_natural_nat(code_nat_of_natural,N2) ) ) ).

% natural_eq_iff
tff(fact_7727_natural__cases,axiom,
    ! [M: code_natural] :
      ~ ! [N: nat] : M != aa_nat_Code_natural(semiri3763490453095760265atural,N) ).

% natural_cases
tff(fact_7728_nat__of__natural,axiom,
    ! [X2: code_natural] : member_nat(aa_Code_natural_nat(code_nat_of_natural,X2),top_top_set_nat) ).

% nat_of_natural
tff(fact_7729_nat__of__natural__cases,axiom,
    ! [Y: nat] :
      ( member_nat(Y,top_top_set_nat)
     => ~ ! [X3: code_natural] : Y != aa_Code_natural_nat(code_nat_of_natural,X3) ) ).

% nat_of_natural_cases
tff(fact_7730_nat__of__natural__induct,axiom,
    ! [Y: nat,P: fun_nat_o] :
      ( member_nat(Y,top_top_set_nat)
     => ( ! [X3: code_natural] : aa_nat_o(P,aa_Code_natural_nat(code_nat_of_natural,X3))
       => aa_nat_o(P,Y) ) ) ).

% nat_of_natural_induct
tff(fact_7731_take__bit__natural_Orep__eq,axiom,
    ! [X2: nat,Xa: code_natural] : aa_Code_natural_nat(code_nat_of_natural,aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se569199155075624693atural,X2),Xa)) = aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,X2),aa_Code_natural_nat(code_nat_of_natural,Xa)) ).

% take_bit_natural.rep_eq
tff(fact_7732_or__natural_Orep__eq,axiom,
    ! [X2: code_natural,Xa: code_natural] : aa_Code_natural_nat(code_nat_of_natural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se9127793120404214118atural,X2),Xa)) = aa_nat_nat(aa_nat_fun_nat_nat(bit_se1412395901928357646or_nat,aa_Code_natural_nat(code_nat_of_natural,X2)),aa_Code_natural_nat(code_nat_of_natural,Xa)) ).

% or_natural.rep_eq
tff(fact_7733_xor__natural_Orep__eq,axiom,
    ! [X2: code_natural,Xa: code_natural] : aa_Code_natural_nat(code_nat_of_natural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(bit_se2046307713759805098atural,X2),Xa)) = aa_nat_nat(aa_nat_fun_nat_nat(bit_se6528837805403552850or_nat,aa_Code_natural_nat(code_nat_of_natural,X2)),aa_Code_natural_nat(code_nat_of_natural,Xa)) ).

% xor_natural.rep_eq
tff(fact_7734_drop__bit__natural_Orep__eq,axiom,
    ! [X2: nat,Xa: code_natural] : aa_Code_natural_nat(code_nat_of_natural,aa_Cod4272041906116450446atural(aa_nat5282697797315388251atural(bit_se2751692689150723149atural,X2),Xa)) = aa_nat_nat(aa_nat_fun_nat_nat(bit_se8570568707652914677it_nat,X2),aa_Code_natural_nat(code_nat_of_natural,Xa)) ).

% drop_bit_natural.rep_eq
tff(fact_7735_natural__of__integer_Orep__eq,axiom,
    ! [X2: code_integer] : aa_Code_natural_nat(code_nat_of_natural,aa_Cod607569804290114243atural(code_n4118661773612635043nteger,X2)) = aa_int_nat(nat2,aa_Code_integer_int(code_int_of_integer,X2)) ).

% natural_of_integer.rep_eq
tff(fact_7736_less__natural_Orep__eq,axiom,
    ! [X2: code_natural,Xa: code_natural] :
      ( aa_Code_natural_o(aa_Cod1485054954640246627ural_o(ord_le5570908160329646204atural,X2),Xa)
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_Code_natural_nat(code_nat_of_natural,X2)),aa_Code_natural_nat(code_nat_of_natural,Xa)) ) ).

% less_natural.rep_eq
tff(fact_7737_natural__of__nat__inverse,axiom,
    ! [Y: nat] :
      ( member_nat(Y,top_top_set_nat)
     => ( aa_Code_natural_nat(code_nat_of_natural,aa_nat_Code_natural(code_natural_of_nat,Y)) = Y ) ) ).

% natural_of_nat_inverse
tff(fact_7738_type__definition__natural,axiom,
    type_d4410041424927559462al_nat(code_nat_of_natural,code_natural_of_nat,top_top_set_nat) ).

% type_definition_natural
tff(fact_7739_or__natural__def,axiom,
    bit_se9127793120404214118atural = map_fu7613509917203888380atural(code_nat_of_natural,map_fu1239815594074539274atural(code_nat_of_natural,code_natural_of_nat),bit_se1412395901928357646or_nat) ).

% or_natural_def
tff(fact_7740_xor__natural__def,axiom,
    bit_se2046307713759805098atural = map_fu7613509917203888380atural(code_nat_of_natural,map_fu1239815594074539274atural(code_nat_of_natural,code_natural_of_nat),bit_se6528837805403552850or_nat) ).

% xor_natural_def
tff(fact_7741_and__natural__def,axiom,
    bit_se2773287842338716102atural = map_fu7613509917203888380atural(code_nat_of_natural,map_fu1239815594074539274atural(code_nat_of_natural,code_natural_of_nat),bit_se727722235901077358nd_nat) ).

% and_natural_def
tff(fact_7742_less__eq__natural_Orep__eq,axiom,
    ! [X2: code_natural,Xa: code_natural] :
      ( aa_Code_natural_o(aa_Cod1485054954640246627ural_o(ord_le1926595141338095240atural,X2),Xa)
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_Code_natural_nat(code_nat_of_natural,X2)),aa_Code_natural_nat(code_nat_of_natural,Xa)) ) ).

% less_eq_natural.rep_eq
tff(fact_7743_division__segment__natural__def,axiom,
    euclid5112970336976722131atural = aa_fun5114738747585492520atural(map_fu1239815594074539274atural(code_nat_of_natural,code_natural_of_nat),euclid3398187327856392827nt_nat) ).

% division_segment_natural_def
tff(fact_7744_euclidean__size__natural__def,axiom,
    euclid5200926497590043453atural = map_fu226235371393106610at_nat(code_nat_of_natural,id_nat,euclid4777050414544973029ze_nat) ).

% euclidean_size_natural_def
tff(fact_7745_plus__natural__def,axiom,
    plus_p4538020629002901425atural = map_fu7613509917203888380atural(code_nat_of_natural,map_fu1239815594074539274atural(code_nat_of_natural,code_natural_of_nat),plus_plus_nat) ).

% plus_natural_def
tff(fact_7746_minus__natural__def,axiom,
    minus_7197305767214868737atural = map_fu7613509917203888380atural(code_nat_of_natural,map_fu1239815594074539274atural(code_nat_of_natural,code_natural_of_nat),minus_minus_nat) ).

% minus_natural_def
tff(fact_7747_bit__natural__def,axiom,
    bit_se8040316288895769887atural = map_fu820683741283188176_nat_o(code_nat_of_natural,id_fun_nat_o,bit_se1148574629649215175it_nat) ).

% bit_natural_def
tff(fact_7748_less__natural__def,axiom,
    ord_le5570908160329646204atural = map_fu2458051687388636536ural_o(code_nat_of_natural,map_fu4892316939951275536at_o_o(code_nat_of_natural,id_o),ord_less_nat) ).

% less_natural_def
tff(fact_7749_times__natural__def,axiom,
    times_2397367101498566445atural = map_fu7613509917203888380atural(code_nat_of_natural,map_fu1239815594074539274atural(code_nat_of_natural,code_natural_of_nat),times_times_nat) ).

% times_natural_def
tff(fact_7750_divide__natural__def,axiom,
    divide5121882707175180666atural = map_fu7613509917203888380atural(code_nat_of_natural,map_fu1239815594074539274atural(code_nat_of_natural,code_natural_of_nat),divide_divide_nat) ).

% divide_natural_def
tff(fact_7751_take__bit__natural__def,axiom,
    bit_se569199155075624693atural = map_fu5588224966615042724atural(id_nat,map_fu1239815594074539274atural(code_nat_of_natural,code_natural_of_nat),bit_se2925701944663578781it_nat) ).

% take_bit_natural_def
tff(fact_7752_push__bit__natural__def,axiom,
    bit_se6611745700429515170atural = map_fu5588224966615042724atural(id_nat,map_fu1239815594074539274atural(code_nat_of_natural,code_natural_of_nat),bit_se547839408752420682it_nat) ).

% push_bit_natural_def
tff(fact_7753_less__eq__natural__def,axiom,
    ord_le1926595141338095240atural = map_fu2458051687388636536ural_o(code_nat_of_natural,map_fu4892316939951275536at_o_o(code_nat_of_natural,id_o),ord_less_eq_nat) ).

% less_eq_natural_def
tff(fact_7754_modulo__natural__def,axiom,
    modulo8411746178871703098atural = map_fu7613509917203888380atural(code_nat_of_natural,map_fu1239815594074539274atural(code_nat_of_natural,code_natural_of_nat),modulo_modulo_nat) ).

% modulo_natural_def
tff(fact_7755_drop__bit__natural__def,axiom,
    bit_se2751692689150723149atural = map_fu5588224966615042724atural(id_nat,map_fu1239815594074539274atural(code_nat_of_natural,code_natural_of_nat),bit_se8570568707652914677it_nat) ).

% drop_bit_natural_def
tff(fact_7756_unset__bit__natural__def,axiom,
    bit_se7083795435491715335atural = map_fu5588224966615042724atural(id_nat,map_fu1239815594074539274atural(code_nat_of_natural,code_natural_of_nat),bit_se4205575877204974255it_nat) ).

% unset_bit_natural_def
tff(fact_7757_flip__bit__natural__def,axiom,
    bit_se168947363167071951atural = map_fu5588224966615042724atural(id_nat,map_fu1239815594074539274atural(code_nat_of_natural,code_natural_of_nat),bit_se2161824704523386999it_nat) ).

% flip_bit_natural_def
tff(fact_7758_set__bit__natural__def,axiom,
    bit_se1617098188084679374atural = map_fu5588224966615042724atural(id_nat,map_fu1239815594074539274atural(code_nat_of_natural,code_natural_of_nat),bit_se7882103937844011126it_nat) ).

% set_bit_natural_def
tff(fact_7759_natural__decr,axiom,
    ! [N2: code_natural] :
      ( ( N2 != zero_z2226904508553997617atural )
     => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_Code_natural_nat(code_nat_of_natural,N2)),aa_nat_nat(suc,zero_zero_nat))),aa_Code_natural_nat(code_nat_of_natural,N2)) ) ).

% natural_decr
tff(fact_7760_natural__of__integer__def,axiom,
    code_n4118661773612635043nteger = map_fu1051355602067684763atural(code_int_of_integer,code_natural_of_nat,nat2) ).

% natural_of_integer_def
tff(fact_7761_integer__of__natural__of__integer,axiom,
    ! [K: code_integer] : aa_Cod5448446754359732931nteger(code_i5400310926305786745atural,aa_Cod607569804290114243atural(code_n4118661773612635043nteger,K)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(ord_max_Code_integer,zero_z3403309356797280102nteger),K) ).

% integer_of_natural_of_integer
tff(fact_7762_integer__of__natural_Orep__eq,axiom,
    ! [X2: code_natural] : aa_Code_integer_int(code_int_of_integer,aa_Cod5448446754359732931nteger(code_i5400310926305786745atural,X2)) = aa_nat_int(semiri1314217659103216013at_int,aa_Code_natural_nat(code_nat_of_natural,X2)) ).

% integer_of_natural.rep_eq
tff(fact_7763_int__of__integer__of__natural,axiom,
    ! [N2: code_natural] : aa_Code_integer_int(code_int_of_integer,aa_Cod5448446754359732931nteger(code_i5400310926305786745atural,N2)) = aa_nat_int(semiri1314217659103216013at_int,aa_Code_natural_nat(code_nat_of_natural,N2)) ).

% int_of_integer_of_natural
tff(fact_7764_integer__of__natural__of__nat,axiom,
    ! [N2: nat] : aa_Cod5448446754359732931nteger(code_i5400310926305786745atural,aa_nat_Code_natural(semiri3763490453095760265atural,N2)) = aa_nat_Code_integer(semiri4939895301339042750nteger,N2) ).

% integer_of_natural_of_nat
tff(fact_7765_natural__of__integer__of__natural,axiom,
    ! [N2: code_natural] : aa_Cod607569804290114243atural(code_n4118661773612635043nteger,aa_Cod5448446754359732931nteger(code_i5400310926305786745atural,N2)) = N2 ).

% natural_of_integer_of_natural
tff(fact_7766_integer__of__natural__def,axiom,
    code_i5400310926305786745atural = map_fu2787874002554666395nteger(code_nat_of_natural,code_integer_of_int,semiri1314217659103216013at_int) ).

% integer_of_natural_def
tff(fact_7767_integer__of__natural_Oabs__eq,axiom,
    ! [X2: nat] : aa_Cod5448446754359732931nteger(code_i5400310926305786745atural,aa_nat_Code_natural(code_natural_of_nat,X2)) = aa_int_Code_integer(code_integer_of_int,aa_nat_int(semiri1314217659103216013at_int,X2)) ).

% integer_of_natural.abs_eq
tff(fact_7768_Code__Numeral_Osize__nat__def,axiom,
    code_size_nat = code_nat_of_natural ).

% Code_Numeral.size_nat_def
tff(fact_7769_Code__Numeral_OSuc__def,axiom,
    code_Suc = aa_fun5114738747585492520atural(map_fu1239815594074539274atural(code_nat_of_natural,code_natural_of_nat),suc) ).

% Code_Numeral.Suc_def
tff(fact_7770_natural_Oinject,axiom,
    ! [Natural: code_natural,Natural2: code_natural] :
      ( ( aa_Cod4272041906116450446atural(code_Suc,Natural) = aa_Cod4272041906116450446atural(code_Suc,Natural2) )
    <=> ( Natural = Natural2 ) ) ).

% natural.inject
tff(fact_7771_Suc_Orep__eq,axiom,
    ! [X2: code_natural] : aa_Code_natural_nat(code_nat_of_natural,aa_Cod4272041906116450446atural(code_Suc,X2)) = aa_nat_nat(suc,aa_Code_natural_nat(code_nat_of_natural,X2)) ).

% Suc.rep_eq
tff(fact_7772_natural_Oexhaust,axiom,
    ! [Y: code_natural] :
      ( ( Y != zero_z2226904508553997617atural )
     => ~ ! [Natural3: code_natural] : Y != aa_Cod4272041906116450446atural(code_Suc,Natural3) ) ).

% natural.exhaust
tff(fact_7773_natural_Odistinct_I1_J,axiom,
    ! [Natural2: code_natural] : zero_z2226904508553997617atural != aa_Cod4272041906116450446atural(code_Suc,Natural2) ).

% natural.distinct(1)
tff(fact_7774_natural_Odistinct_I2_J,axiom,
    ! [Natural2: code_natural] : aa_Cod4272041906116450446atural(code_Suc,Natural2) != zero_z2226904508553997617atural ).

% natural.distinct(2)
tff(fact_7775_Suc_Oabs__eq,axiom,
    ! [X2: nat] : aa_Cod4272041906116450446atural(code_Suc,aa_nat_Code_natural(code_natural_of_nat,X2)) = aa_nat_Code_natural(code_natural_of_nat,aa_nat_nat(suc,X2)) ).

% Suc.abs_eq
tff(fact_7776_Suc__natural__minus__one,axiom,
    ! [N2: code_natural] : aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(minus_7197305767214868737atural,aa_Cod4272041906116450446atural(code_Suc,N2)),one_one_Code_natural) = N2 ).

% Suc_natural_minus_one
tff(fact_7777_random__aux__set_Ocases,axiom,
    ! [X2: produc7822875418678951345atural] :
      ( ! [J3: code_natural] : X2 != produc3574140220909816553atural(zero_z2226904508553997617atural,J3)
     => ~ ! [I2: code_natural,J3: code_natural] : X2 != produc3574140220909816553atural(aa_Cod4272041906116450446atural(code_Suc,I2),J3) ) ).

% random_aux_set.cases
tff(fact_7778_Code__Numeral_Osub__code_I2_J,axiom,
    ! [M: num] : aa_num_Code_integer(aa_num5808785979904431436nteger(code_sub,aa_num_num(bit0,M)),one) = aa_num_Code_integer(code_Pos,aa_num_num(bitM,M)) ).

% Code_Numeral.sub_code(2)
tff(fact_7779_Code__Numeral_OPos__def,axiom,
    code_Pos = numera6620942414471956472nteger ).

% Code_Numeral.Pos_def
tff(fact_7780_Pos__fold_I2_J,axiom,
    ! [K: num] : aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,K)) = aa_num_Code_integer(code_Pos,aa_num_num(bit0,K)) ).

% Pos_fold(2)
tff(fact_7781_Pos__fold_I1_J,axiom,
    aa_num_Code_integer(numera6620942414471956472nteger,one) = aa_num_Code_integer(code_Pos,one) ).

% Pos_fold(1)
tff(fact_7782_Pos__fold_I3_J,axiom,
    ! [K: num] : aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit1,K)) = aa_num_Code_integer(code_Pos,aa_num_num(bit1,K)) ).

% Pos_fold(3)
tff(fact_7783_one__integer__code,axiom,
    one_one_Code_integer = aa_num_Code_integer(code_Pos,one) ).

% one_integer_code
tff(fact_7784_Code__Numeral_Odup__code_I2_J,axiom,
    ! [N2: num] : aa_Cod1783974652533396728nteger(code_dup,aa_num_Code_integer(code_Pos,N2)) = aa_num_Code_integer(code_Pos,aa_num_num(bit0,N2)) ).

% Code_Numeral.dup_code(2)
tff(fact_7785_less__integer__code_I4_J,axiom,
    ! [K: num] : ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_num_Code_integer(code_Pos,K)),zero_z3403309356797280102nteger) ).

% less_integer_code(4)
tff(fact_7786_less__integer__code_I2_J,axiom,
    ! [L: num] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),aa_num_Code_integer(code_Pos,L)) ).

% less_integer_code(2)
tff(fact_7787_plus__integer__code_I3_J,axiom,
    ! [M: num,N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_num_Code_integer(code_Pos,M)),aa_num_Code_integer(code_Pos,N2)) = aa_num_Code_integer(code_Pos,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2)) ).

% plus_integer_code(3)
tff(fact_7788_less__eq__integer__code_I2_J,axiom,
    ! [L: num] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,zero_z3403309356797280102nteger),aa_num_Code_integer(code_Pos,L)) ).

% less_eq_integer_code(2)
tff(fact_7789_less__eq__integer__code_I4_J,axiom,
    ! [K: num] : ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_num_Code_integer(code_Pos,K)),zero_z3403309356797280102nteger) ).

% less_eq_integer_code(4)
tff(fact_7790_less__integer__code_I8_J,axiom,
    ! [K: num,L: num] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_num_Code_integer(code_Neg,K)),aa_num_Code_integer(code_Pos,L)) ).

% less_integer_code(8)
tff(fact_7791_less__integer__code_I6_J,axiom,
    ! [K: num,L: num] : ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_num_Code_integer(code_Pos,K)),aa_num_Code_integer(code_Neg,L)) ).

% less_integer_code(6)
tff(fact_7792_uminus__integer__code_I3_J,axiom,
    ! [M: num] : aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(code_Neg,M)) = aa_num_Code_integer(code_Pos,M) ).

% uminus_integer_code(3)
tff(fact_7793_uminus__integer__code_I2_J,axiom,
    ! [M: num] : aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(code_Pos,M)) = aa_num_Code_integer(code_Neg,M) ).

% uminus_integer_code(2)
tff(fact_7794_Code__Numeral_ONeg__def,axiom,
    ! [N2: num] : aa_num_Code_integer(code_Neg,N2) = aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,aa_num_Code_integer(code_Pos,N2)) ).

% Code_Numeral.Neg_def
tff(fact_7795_less__eq__integer__code_I8_J,axiom,
    ! [K: num,L: num] : aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_num_Code_integer(code_Neg,K)),aa_num_Code_integer(code_Pos,L)) ).

% less_eq_integer_code(8)
tff(fact_7796_less__eq__integer__code_I6_J,axiom,
    ! [K: num,L: num] : ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_num_Code_integer(code_Pos,K)),aa_num_Code_integer(code_Neg,L)) ).

% less_eq_integer_code(6)
tff(fact_7797_times__integer__code_I3_J,axiom,
    ! [M: num,N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(code_Pos,M)),aa_num_Code_integer(code_Pos,N2)) = aa_num_Code_integer(code_Pos,aa_num_num(aa_num_fun_num_num(times_times_num,M),N2)) ).

% times_integer_code(3)
tff(fact_7798_less__integer__code_I5_J,axiom,
    ! [K: num,L: num] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,aa_num_Code_integer(code_Pos,K)),aa_num_Code_integer(code_Pos,L))
    <=> aa_num_o(aa_num_fun_num_o(ord_less_num,K),L) ) ).

% less_integer_code(5)
tff(fact_7799_less__eq__integer__code_I5_J,axiom,
    ! [K: num,L: num] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_num_Code_integer(code_Pos,K)),aa_num_Code_integer(code_Pos,L))
    <=> aa_num_o(aa_num_fun_num_o(ord_less_eq_num,K),L) ) ).

% less_eq_integer_code(5)
tff(fact_7800_minus__integer__code_I3_J,axiom,
    ! [M: num,N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_num_Code_integer(code_Pos,M)),aa_num_Code_integer(code_Pos,N2)) = aa_num_Code_integer(aa_num5808785979904431436nteger(code_sub,M),N2) ).

% minus_integer_code(3)
tff(fact_7801_divmod__abs__code_I1_J,axiom,
    ! [K: num,L: num] : aa_Cod6977894654539884864nteger(code_divmod_abs(aa_num_Code_integer(code_Pos,K)),aa_num_Code_integer(code_Pos,L)) = unique3479559517661332726nteger(K,L) ).

% divmod_abs_code(1)
tff(fact_7802_minus__integer__code_I4_J,axiom,
    ! [M: num,N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_num_Code_integer(code_Pos,M)),aa_num_Code_integer(code_Neg,N2)) = aa_num_Code_integer(code_Pos,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2)) ).

% minus_integer_code(4)
tff(fact_7803_minus__integer__code_I5_J,axiom,
    ! [M: num,N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_num_Code_integer(code_Neg,M)),aa_num_Code_integer(code_Pos,N2)) = aa_num_Code_integer(code_Neg,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2)) ).

% minus_integer_code(5)
tff(fact_7804_times__integer__code_I4_J,axiom,
    ! [M: num,N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(code_Pos,M)),aa_num_Code_integer(code_Neg,N2)) = aa_num_Code_integer(code_Neg,aa_num_num(aa_num_fun_num_num(times_times_num,M),N2)) ).

% times_integer_code(4)
tff(fact_7805_times__integer__code_I5_J,axiom,
    ! [M: num,N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(code_Neg,M)),aa_num_Code_integer(code_Pos,N2)) = aa_num_Code_integer(code_Neg,aa_num_num(aa_num_fun_num_num(times_times_num,M),N2)) ).

% times_integer_code(5)
tff(fact_7806_times__integer__code_I6_J,axiom,
    ! [M: num,N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(code_Neg,M)),aa_num_Code_integer(code_Neg,N2)) = aa_num_Code_integer(code_Pos,aa_num_num(aa_num_fun_num_num(times_times_num,M),N2)) ).

% times_integer_code(6)
tff(fact_7807_plus__integer__code_I4_J,axiom,
    ! [M: num,N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_num_Code_integer(code_Pos,M)),aa_num_Code_integer(code_Neg,N2)) = aa_num_Code_integer(aa_num5808785979904431436nteger(code_sub,M),N2) ).

% plus_integer_code(4)
tff(fact_7808_plus__integer__code_I5_J,axiom,
    ! [M: num,N2: num] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_num_Code_integer(code_Neg,M)),aa_num_Code_integer(code_Pos,N2)) = aa_num_Code_integer(aa_num5808785979904431436nteger(code_sub,N2),M) ).

% plus_integer_code(5)
tff(fact_7809_divmod__abs__code_I3_J,axiom,
    ! [K: num,L: num] : aa_Cod6977894654539884864nteger(code_divmod_abs(aa_num_Code_integer(code_Neg,K)),aa_num_Code_integer(code_Pos,L)) = unique3479559517661332726nteger(K,L) ).

% divmod_abs_code(3)
tff(fact_7810_divmod__abs__code_I4_J,axiom,
    ! [K: num,L: num] : aa_Cod6977894654539884864nteger(code_divmod_abs(aa_num_Code_integer(code_Pos,K)),aa_num_Code_integer(code_Neg,L)) = unique3479559517661332726nteger(K,L) ).

% divmod_abs_code(4)
tff(fact_7811_Code__Numeral_Osub__code_I3_J,axiom,
    ! [M: num] : aa_num_Code_integer(aa_num5808785979904431436nteger(code_sub,aa_num_num(bit1,M)),one) = aa_num_Code_integer(code_Pos,aa_num_num(bit0,M)) ).

% Code_Numeral.sub_code(3)
tff(fact_7812_normalize__stable,axiom,
    ! [Q3: int,P2: int] :
      ( aa_int_o(aa_int_fun_int_o(ord_less_int,zero_zero_int),Q3)
     => ( aa_int_o(aa_int_fun_int_o(algebr932160517623751201me_int,P2),Q3)
       => ( aa_Pro6970504127699319548nt_int(normalize,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,P2),Q3)) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,P2),Q3) ) ) ) ).

% normalize_stable
tff(fact_7813_quotient__of__coprime,axiom,
    ! [R2: rat,P2: int,Q3: int] :
      ( ( quotient_of(R2) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,P2),Q3) )
     => aa_int_o(aa_int_fun_int_o(algebr932160517623751201me_int,P2),Q3) ) ).

% quotient_of_coprime
tff(fact_7814_normalize__coprime,axiom,
    ! [R2: product_prod_int_int,P2: int,Q3: int] :
      ( ( aa_Pro6970504127699319548nt_int(normalize,R2) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,P2),Q3) )
     => aa_int_o(aa_int_fun_int_o(algebr932160517623751201me_int,P2),Q3) ) ).

% normalize_coprime
tff(fact_7815_coprime__common__divisor__nat,axiom,
    ! [A: nat,B: nat,X2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(algebr934650988132801477me_nat,A),B)
     => ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,X2),A)
       => ( aa_nat_o(aa_nat_fun_nat_o(dvd_dvd_nat,X2),B)
         => ( X2 = one_one_nat ) ) ) ) ).

% coprime_common_divisor_nat
tff(fact_7816_coprime__diff__one__right__nat,axiom,
    ! [N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => aa_nat_o(aa_nat_fun_nat_o(algebr934650988132801477me_nat,N2),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)) ) ).

% coprime_diff_one_right_nat
tff(fact_7817_coprime__diff__one__left__nat,axiom,
    ! [N2: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,zero_zero_nat),N2)
     => aa_nat_o(aa_nat_fun_nat_o(algebr934650988132801477me_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,N2),one_one_nat)),N2) ) ).

% coprime_diff_one_left_nat
tff(fact_7818_integer__of__char__code,axiom,
    ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] : integer_of_char(char2((B0),(B1),(B22),(B32),(B42),(B52),(B62),(B72))) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_o_Code_integer(zero_n356916108424825756nteger,(B72))),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)))),aa_o_Code_integer(zero_n356916108424825756nteger,(B62)))),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)))),aa_o_Code_integer(zero_n356916108424825756nteger,(B52)))),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)))),aa_o_Code_integer(zero_n356916108424825756nteger,(B42)))),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)))),aa_o_Code_integer(zero_n356916108424825756nteger,(B32)))),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)))),aa_o_Code_integer(zero_n356916108424825756nteger,(B22)))),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)))),aa_o_Code_integer(zero_n356916108424825756nteger,(B1)))),aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one)))),aa_o_Code_integer(zero_n356916108424825756nteger,(B0))) ).

% integer_of_char_code
tff(fact_7819_Suc__funpow,axiom,
    ! [N2: nat] : compow_fun_nat_nat(N2,suc) = aa_nat_fun_nat_nat(plus_plus_nat,N2) ).

% Suc_funpow
tff(fact_7820_or__not__num__neg_Opelims,axiom,
    ! [X2: num,Xa: num,Y: num] :
      ( ( aa_num_num(aa_num_fun_num_num(bit_or_not_num_neg,X2),Xa) = Y )
     => ( accp_P3113834385874906142um_num(bit_or3848514188828904588eg_rel,product_Pair_num_num(X2,Xa))
       => ( ( ( X2 = one )
           => ( ( Xa = one )
             => ( ( Y = one )
               => ~ accp_P3113834385874906142um_num(bit_or3848514188828904588eg_rel,product_Pair_num_num(one,one)) ) ) )
         => ( ( ( X2 = one )
             => ! [M4: num] :
                  ( ( Xa = aa_num_num(bit0,M4) )
                 => ( ( Y = aa_num_num(bit1,M4) )
                   => ~ accp_P3113834385874906142um_num(bit_or3848514188828904588eg_rel,product_Pair_num_num(one,aa_num_num(bit0,M4))) ) ) )
           => ( ( ( X2 = one )
               => ! [M4: num] :
                    ( ( Xa = aa_num_num(bit1,M4) )
                   => ( ( Y = aa_num_num(bit1,M4) )
                     => ~ accp_P3113834385874906142um_num(bit_or3848514188828904588eg_rel,product_Pair_num_num(one,aa_num_num(bit1,M4))) ) ) )
             => ( ! [N: num] :
                    ( ( X2 = aa_num_num(bit0,N) )
                   => ( ( Xa = one )
                     => ( ( Y = aa_num_num(bit0,one) )
                       => ~ accp_P3113834385874906142um_num(bit_or3848514188828904588eg_rel,product_Pair_num_num(aa_num_num(bit0,N),one)) ) ) )
               => ( ! [N: num] :
                      ( ( X2 = aa_num_num(bit0,N) )
                     => ! [M4: num] :
                          ( ( Xa = aa_num_num(bit0,M4) )
                         => ( ( Y = aa_num_num(bitM,aa_num_num(aa_num_fun_num_num(bit_or_not_num_neg,N),M4)) )
                           => ~ accp_P3113834385874906142um_num(bit_or3848514188828904588eg_rel,product_Pair_num_num(aa_num_num(bit0,N),aa_num_num(bit0,M4))) ) ) )
                 => ( ! [N: num] :
                        ( ( X2 = aa_num_num(bit0,N) )
                       => ! [M4: num] :
                            ( ( Xa = aa_num_num(bit1,M4) )
                           => ( ( Y = aa_num_num(bit0,aa_num_num(aa_num_fun_num_num(bit_or_not_num_neg,N),M4)) )
                             => ~ accp_P3113834385874906142um_num(bit_or3848514188828904588eg_rel,product_Pair_num_num(aa_num_num(bit0,N),aa_num_num(bit1,M4))) ) ) )
                   => ( ! [N: num] :
                          ( ( X2 = aa_num_num(bit1,N) )
                         => ( ( Xa = one )
                           => ( ( Y = one )
                             => ~ accp_P3113834385874906142um_num(bit_or3848514188828904588eg_rel,product_Pair_num_num(aa_num_num(bit1,N),one)) ) ) )
                     => ( ! [N: num] :
                            ( ( X2 = aa_num_num(bit1,N) )
                           => ! [M4: num] :
                                ( ( Xa = aa_num_num(bit0,M4) )
                               => ( ( Y = aa_num_num(bitM,aa_num_num(aa_num_fun_num_num(bit_or_not_num_neg,N),M4)) )
                                 => ~ accp_P3113834385874906142um_num(bit_or3848514188828904588eg_rel,product_Pair_num_num(aa_num_num(bit1,N),aa_num_num(bit0,M4))) ) ) )
                       => ~ ! [N: num] :
                              ( ( X2 = aa_num_num(bit1,N) )
                             => ! [M4: num] :
                                  ( ( Xa = aa_num_num(bit1,M4) )
                                 => ( ( Y = aa_num_num(bitM,aa_num_num(aa_num_fun_num_num(bit_or_not_num_neg,N),M4)) )
                                   => ~ accp_P3113834385874906142um_num(bit_or3848514188828904588eg_rel,product_Pair_num_num(aa_num_num(bit1,N),aa_num_num(bit1,M4))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% or_not_num_neg.pelims
tff(fact_7821_cr__natural__def,axiom,
    ! [X: nat,Xa3: code_natural] :
      ( aa_Code_natural_o(aa_nat8502700792446211003ural_o(code_cr_natural,X),Xa3)
    <=> ( X = aa_Code_natural_nat(code_nat_of_natural,Xa3) ) ) ).

% cr_natural_def
tff(fact_7822_cr__integer__def,axiom,
    ! [X: int,Xa3: code_integer] :
      ( aa_Code_integer_o(aa_int5993532643906289898eger_o(code_cr_integer,X),Xa3)
    <=> ( X = aa_Code_integer_int(code_int_of_integer,Xa3) ) ) ).

% cr_integer_def
tff(fact_7823_integer_Opcr__cr__eq,axiom,
    code_pcr_integer = code_cr_integer ).

% integer.pcr_cr_eq
tff(fact_7824_unit__factor__simps_I2_J,axiom,
    ! [N2: nat] : aa_nat_nat(unit_f2748546683901255202or_nat,aa_nat_nat(suc,N2)) = one_one_nat ).

% unit_factor_simps(2)
tff(fact_7825_unit__factor__nat__def,axiom,
    ! [N2: nat] :
      aa_nat_nat(unit_f2748546683901255202or_nat,N2) = $ite(N2 = zero_zero_nat,zero_zero_nat,one_one_nat) ).

% unit_factor_nat_def
tff(fact_7826_Nat_Otransfer,axiom,
    bNF_re1831474436612530402atural(code_pcr_integer,code_pcr_natural,nat2,code_Nat) ).

% Nat.transfer
tff(fact_7827_pcr__natural__def,axiom,
    code_pcr_natural = relcom1729257228895983867atural(fequal_nat,code_cr_natural) ).

% pcr_natural_def
tff(fact_7828_natural_Orep__transfer,axiom,
    bNF_re7333046803109187065at_nat(code_pcr_natural,fequal_nat,aTP_Lamm_co,code_nat_of_natural) ).

% natural.rep_transfer
tff(fact_7829_natural_Oid__abs__transfer,axiom,
    bNF_re2605341659958429177atural(fequal_nat,code_pcr_natural,aTP_Lamm_co,code_natural_of_nat) ).

% natural.id_abs_transfer
tff(fact_7830_natural_Opcr__cr__eq,axiom,
    code_pcr_natural = code_cr_natural ).

% natural.pcr_cr_eq
tff(fact_7831_zero__natural_Otransfer,axiom,
    aa_Code_natural_o(aa_nat8502700792446211003ural_o(code_pcr_natural,zero_zero_nat),zero_z2226904508553997617atural) ).

% zero_natural.transfer
tff(fact_7832_one__natural_Otransfer,axiom,
    aa_Code_natural_o(aa_nat8502700792446211003ural_o(code_pcr_natural,one_one_nat),one_one_Code_natural) ).

% one_natural.transfer
tff(fact_7833_less__natural_Otransfer,axiom,
    bNF_re701982943866114111ural_o(code_pcr_natural,bNF_re2785088596696291543al_o_o(code_pcr_natural,fequal_o),ord_less_nat,ord_le5570908160329646204atural) ).

% less_natural.transfer
tff(fact_7834_plus__natural_Otransfer,axiom,
    bNF_re1400205106991740995atural(code_pcr_natural,bNF_re3704215830270325841atural(code_pcr_natural,code_pcr_natural),plus_plus_nat,plus_p4538020629002901425atural) ).

% plus_natural.transfer
tff(fact_7835_Suc_Otransfer,axiom,
    aa_fun1921403200066283853ural_o(aa_fun7534057414028546889ural_o(bNF_re3704215830270325841atural(code_pcr_natural,code_pcr_natural),suc),code_Suc) ).

% Suc.transfer
tff(fact_7836_minus__natural_Otransfer,axiom,
    bNF_re1400205106991740995atural(code_pcr_natural,bNF_re3704215830270325841atural(code_pcr_natural,code_pcr_natural),minus_minus_nat,minus_7197305767214868737atural) ).

% minus_natural.transfer
tff(fact_7837_pcr__integer__def,axiom,
    code_pcr_integer = relcom967497705283160040nteger(fequal_int,code_cr_integer) ).

% pcr_integer_def
tff(fact_7838_less__eq__natural_Otransfer,axiom,
    bNF_re701982943866114111ural_o(code_pcr_natural,bNF_re2785088596696291543al_o_o(code_pcr_natural,fequal_o),ord_less_eq_nat,ord_le1926595141338095240atural) ).

% less_eq_natural.transfer
tff(fact_7839_times__natural_Otransfer,axiom,
    bNF_re1400205106991740995atural(code_pcr_natural,bNF_re3704215830270325841atural(code_pcr_natural,code_pcr_natural),times_times_nat,times_2397367101498566445atural) ).

% times_natural.transfer
tff(fact_7840_divide__natural_Otransfer,axiom,
    bNF_re1400205106991740995atural(code_pcr_natural,bNF_re3704215830270325841atural(code_pcr_natural,code_pcr_natural),divide_divide_nat,divide5121882707175180666atural) ).

% divide_natural.transfer
tff(fact_7841_modulo__natural_Otransfer,axiom,
    bNF_re1400205106991740995atural(code_pcr_natural,bNF_re3704215830270325841atural(code_pcr_natural,code_pcr_natural),modulo_modulo_nat,modulo8411746178871703098atural) ).

% modulo_natural.transfer
tff(fact_7842_take__bit__natural_Otransfer,axiom,
    bNF_re728283343719287275atural(fequal_nat,bNF_re3704215830270325841atural(code_pcr_natural,code_pcr_natural),bit_se2925701944663578781it_nat,bit_se569199155075624693atural) ).

% take_bit_natural.transfer
tff(fact_7843_xor__natural_Otransfer,axiom,
    bNF_re1400205106991740995atural(code_pcr_natural,bNF_re3704215830270325841atural(code_pcr_natural,code_pcr_natural),bit_se6528837805403552850or_nat,bit_se2046307713759805098atural) ).

% xor_natural.transfer
tff(fact_7844_or__natural_Otransfer,axiom,
    bNF_re1400205106991740995atural(code_pcr_natural,bNF_re3704215830270325841atural(code_pcr_natural,code_pcr_natural),bit_se1412395901928357646or_nat,bit_se9127793120404214118atural) ).

% or_natural.transfer
tff(fact_7845_and__natural_Otransfer,axiom,
    bNF_re1400205106991740995atural(code_pcr_natural,bNF_re3704215830270325841atural(code_pcr_natural,code_pcr_natural),bit_se727722235901077358nd_nat,bit_se2773287842338716102atural) ).

% and_natural.transfer
tff(fact_7846_bit__natural_Otransfer,axiom,
    bNF_re2187160483004581015_nat_o(code_pcr_natural,fequal_fun_nat_o,bit_se1148574629649215175it_nat,bit_se8040316288895769887atural) ).

% bit_natural.transfer
tff(fact_7847_push__bit__natural_Otransfer,axiom,
    bNF_re728283343719287275atural(fequal_nat,bNF_re3704215830270325841atural(code_pcr_natural,code_pcr_natural),bit_se547839408752420682it_nat,bit_se6611745700429515170atural) ).

% push_bit_natural.transfer
tff(fact_7848_mask__natural_Otransfer,axiom,
    bNF_re2605341659958429177atural(fequal_nat,code_pcr_natural,bit_se2002935070580805687sk_nat,bit_se943457434206027407atural) ).

% mask_natural.transfer
tff(fact_7849_drop__bit__natural_Otransfer,axiom,
    bNF_re728283343719287275atural(fequal_nat,bNF_re3704215830270325841atural(code_pcr_natural,code_pcr_natural),bit_se8570568707652914677it_nat,bit_se2751692689150723149atural) ).

% drop_bit_natural.transfer
tff(fact_7850_division__segment__natural_Otransfer,axiom,
    aa_fun1921403200066283853ural_o(aa_fun7534057414028546889ural_o(bNF_re3704215830270325841atural(code_pcr_natural,code_pcr_natural),euclid3398187327856392827nt_nat),euclid5112970336976722131atural) ).

% division_segment_natural.transfer
tff(fact_7851_flip__bit__natural_Otransfer,axiom,
    bNF_re728283343719287275atural(fequal_nat,bNF_re3704215830270325841atural(code_pcr_natural,code_pcr_natural),bit_se2161824704523386999it_nat,bit_se168947363167071951atural) ).

% flip_bit_natural.transfer
tff(fact_7852_set__bit__natural_Otransfer,axiom,
    bNF_re728283343719287275atural(fequal_nat,bNF_re3704215830270325841atural(code_pcr_natural,code_pcr_natural),bit_se7882103937844011126it_nat,bit_se1617098188084679374atural) ).

% set_bit_natural.transfer
tff(fact_7853_unset__bit__natural_Otransfer,axiom,
    bNF_re728283343719287275atural(fequal_nat,bNF_re3704215830270325841atural(code_pcr_natural,code_pcr_natural),bit_se4205575877204974255it_nat,bit_se7083795435491715335atural) ).

% unset_bit_natural.transfer
tff(fact_7854_euclidean__size__natural_Otransfer,axiom,
    bNF_re7333046803109187065at_nat(code_pcr_natural,fequal_nat,euclid4777050414544973029ze_nat,euclid5200926497590043453atural) ).

% euclidean_size_natural.transfer
tff(fact_7855_integer__of__natural_Otransfer,axiom,
    bNF_re5252274238750452962nteger(code_pcr_natural,code_pcr_integer,semiri1314217659103216013at_int,code_i5400310926305786745atural) ).

% integer_of_natural.transfer
tff(fact_7856_natural__of__integer_Otransfer,axiom,
    bNF_re1831474436612530402atural(code_pcr_integer,code_pcr_natural,nat2,code_n4118661773612635043nteger) ).

% natural_of_integer.transfer
tff(fact_7857_plus__num__def,axiom,
    ! [M: num,N2: num] : aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2) = aa_nat_num(num_of_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(nat_of_num,M)),aa_num_nat(nat_of_num,N2))) ).

% plus_num_def
tff(fact_7858_Lcm__nat__empty,axiom,
    aa_set_nat_nat(gcd_Lcm_nat,bot_bot_set_nat) = one_one_nat ).

% Lcm_nat_empty
tff(fact_7859_nat__of__num_Osimps_I2_J,axiom,
    ! [X2: num] : aa_num_nat(nat_of_num,aa_num_num(bit0,X2)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(nat_of_num,X2)),aa_num_nat(nat_of_num,X2)) ).

% nat_of_num.simps(2)
tff(fact_7860_nat__of__num__code_I1_J,axiom,
    aa_num_nat(nat_of_num,one) = one_one_nat ).

% nat_of_num_code(1)
tff(fact_7861_nat__of__num__add,axiom,
    ! [X2: num,Y: num] : aa_num_nat(nat_of_num,aa_num_num(aa_num_fun_num_num(plus_plus_num,X2),Y)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(nat_of_num,X2)),aa_num_nat(nat_of_num,Y)) ).

% nat_of_num_add
tff(fact_7862_nat__of__num__code_I2_J,axiom,
    ! [N2: num] :
      aa_num_nat(nat_of_num,aa_num_num(bit0,N2)) = $let(
        m: nat,
        m:= aa_num_nat(nat_of_num,N2),
        aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,m),m) ) ).

% nat_of_num_code(2)
tff(fact_7863_nat__of__num_Osimps_I3_J,axiom,
    ! [X2: num] : aa_num_nat(nat_of_num,aa_num_num(bit1,X2)) = aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_num_nat(nat_of_num,X2)),aa_num_nat(nat_of_num,X2))) ).

% nat_of_num.simps(3)
tff(fact_7864_nat__of__num__code_I3_J,axiom,
    ! [N2: num] :
      aa_num_nat(nat_of_num,aa_num_num(bit1,N2)) = $let(
        m: nat,
        m:= aa_num_nat(nat_of_num,N2),
        aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,m),m)) ) ).

% nat_of_num_code(3)
tff(fact_7865_Gcd__nat__eq__one,axiom,
    ! [N5: set_nat] :
      ( member_nat(one_one_nat,N5)
     => ( aa_set_nat_nat(gcd_Gcd_nat,N5) = one_one_nat ) ) ).

% Gcd_nat_eq_one
tff(fact_7866_card__of__Field__natLeq,axiom,
    member8757157785044589968at_nat(produc2922128104949294807at_nat(bNF_Ca3793111618940312692of_nat(field_nat(bNF_Ca8665028551170535155natLeq)),bNF_Ca8665028551170535155natLeq),bNF_We5258908940166488438at_nat) ).

% card_of_Field_natLeq
tff(fact_7867_card__of__nat,axiom,
    member8757157785044589968at_nat(produc2922128104949294807at_nat(bNF_Ca3793111618940312692of_nat(top_top_set_nat),bNF_Ca8665028551170535155natLeq),bNF_We5258908940166488438at_nat) ).

% card_of_nat
tff(fact_7868_ctwo__Cnotzero,axiom,
    ( ~ member444158400953824016od_o_o(produc763777882069021527od_o_o(bNF_Cardinal_ctwo,bNF_Cardinal_czero_o),bNF_We2654380646378065620so_o_o)
    & bNF_Ca8331644756375544342r_on_o(field_o(bNF_Cardinal_ctwo),bNF_Cardinal_ctwo) ) ).

% ctwo_Cnotzero
tff(fact_7869_ctwo__ordLess__natLeq,axiom,
    member4095101504841534314at_nat(produc8517790099723286449at_nat(bNF_Cardinal_ctwo,bNF_Ca8665028551170535155natLeq),bNF_We8182288985678559134_o_nat) ).

% ctwo_ordLess_natLeq
tff(fact_7870_or__num_Opelims,axiom,
    ! [X2: num,Xa: num,Y: num] :
      ( ( aa_num_num(aa_num_fun_num_num(bit_un6697907153464112080or_num,X2),Xa) = Y )
     => ( accp_P3113834385874906142um_num(bit_un4773296044027857193um_rel,product_Pair_num_num(X2,Xa))
       => ( ( ( X2 = one )
           => ( ( Xa = one )
             => ( ( Y = one )
               => ~ accp_P3113834385874906142um_num(bit_un4773296044027857193um_rel,product_Pair_num_num(one,one)) ) ) )
         => ( ( ( X2 = one )
             => ! [N: num] :
                  ( ( Xa = aa_num_num(bit0,N) )
                 => ( ( Y = aa_num_num(bit1,N) )
                   => ~ accp_P3113834385874906142um_num(bit_un4773296044027857193um_rel,product_Pair_num_num(one,aa_num_num(bit0,N))) ) ) )
           => ( ( ( X2 = one )
               => ! [N: num] :
                    ( ( Xa = aa_num_num(bit1,N) )
                   => ( ( Y = aa_num_num(bit1,N) )
                     => ~ accp_P3113834385874906142um_num(bit_un4773296044027857193um_rel,product_Pair_num_num(one,aa_num_num(bit1,N))) ) ) )
             => ( ! [M4: num] :
                    ( ( X2 = aa_num_num(bit0,M4) )
                   => ( ( Xa = one )
                     => ( ( Y = aa_num_num(bit1,M4) )
                       => ~ accp_P3113834385874906142um_num(bit_un4773296044027857193um_rel,product_Pair_num_num(aa_num_num(bit0,M4),one)) ) ) )
               => ( ! [M4: num] :
                      ( ( X2 = aa_num_num(bit0,M4) )
                     => ! [N: num] :
                          ( ( Xa = aa_num_num(bit0,N) )
                         => ( ( Y = aa_num_num(bit0,aa_num_num(aa_num_fun_num_num(bit_un6697907153464112080or_num,M4),N)) )
                           => ~ accp_P3113834385874906142um_num(bit_un4773296044027857193um_rel,product_Pair_num_num(aa_num_num(bit0,M4),aa_num_num(bit0,N))) ) ) )
                 => ( ! [M4: num] :
                        ( ( X2 = aa_num_num(bit0,M4) )
                       => ! [N: num] :
                            ( ( Xa = aa_num_num(bit1,N) )
                           => ( ( Y = aa_num_num(bit1,aa_num_num(aa_num_fun_num_num(bit_un6697907153464112080or_num,M4),N)) )
                             => ~ accp_P3113834385874906142um_num(bit_un4773296044027857193um_rel,product_Pair_num_num(aa_num_num(bit0,M4),aa_num_num(bit1,N))) ) ) )
                   => ( ! [M4: num] :
                          ( ( X2 = aa_num_num(bit1,M4) )
                         => ( ( Xa = one )
                           => ( ( Y = aa_num_num(bit1,M4) )
                             => ~ accp_P3113834385874906142um_num(bit_un4773296044027857193um_rel,product_Pair_num_num(aa_num_num(bit1,M4),one)) ) ) )
                     => ( ! [M4: num] :
                            ( ( X2 = aa_num_num(bit1,M4) )
                           => ! [N: num] :
                                ( ( Xa = aa_num_num(bit0,N) )
                               => ( ( Y = aa_num_num(bit1,aa_num_num(aa_num_fun_num_num(bit_un6697907153464112080or_num,M4),N)) )
                                 => ~ accp_P3113834385874906142um_num(bit_un4773296044027857193um_rel,product_Pair_num_num(aa_num_num(bit1,M4),aa_num_num(bit0,N))) ) ) )
                       => ~ ! [M4: num] :
                              ( ( X2 = aa_num_num(bit1,M4) )
                             => ! [N: num] :
                                  ( ( Xa = aa_num_num(bit1,N) )
                                 => ( ( Y = aa_num_num(bit1,aa_num_num(aa_num_fun_num_num(bit_un6697907153464112080or_num,M4),N)) )
                                   => ~ accp_P3113834385874906142um_num(bit_un4773296044027857193um_rel,product_Pair_num_num(aa_num_num(bit1,M4),aa_num_num(bit1,N))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% or_num.pelims
tff(fact_7871_Quotient__natural,axiom,
    quotie743640454666494480atural(fequal_nat,code_natural_of_nat,code_nat_of_natural,code_cr_natural) ).

% Quotient_natural
tff(fact_7872_Quotient__integer,axiom,
    quotie2291698863146621601nteger(fequal_int,code_integer_of_int,code_int_of_integer,code_cr_integer) ).

% Quotient_integer
tff(fact_7873_Lcm__nat__def,axiom,
    ! [M2: set_nat] :
      aa_set_nat_nat(gcd_Lcm_nat,M2) = $ite(finite_finite_nat(M2),aa_set_nat_nat(lattic7826324295020591184_F_nat(gcd_lcm_nat,one_one_nat),M2),zero_zero_nat) ).

% Lcm_nat_def
tff(fact_7874_Lcm__nat__set__eq__fold,axiom,
    ! [Xsa: list_nat] : aa_set_nat_nat(gcd_Lcm_nat,set_nat2(Xsa)) = aa_nat_nat(fold_nat_nat(gcd_lcm_nat,Xsa),one_one_nat) ).

% Lcm_nat_set_eq_fold
tff(fact_7875_mod__h__bot__iff_I7_J,axiom,
    ! [P: assn,Q: assn,Ha: heap_e7401611519738050253t_unit] :
      ( aa_Pro653082453696054616_nat_o(rep_assn(sup_sup_assn(P,Q)),produc7507926704131184380et_nat(Ha,bot_bot_set_nat))
    <=> ( aa_Pro653082453696054616_nat_o(rep_assn(P),produc7507926704131184380et_nat(Ha,bot_bot_set_nat))
        | aa_Pro653082453696054616_nat_o(rep_assn(Q),produc7507926704131184380et_nat(Ha,bot_bot_set_nat)) ) ) ).

% mod_h_bot_iff(7)
tff(fact_7876_mod__h__bot__iff_I5_J,axiom,
    ! [P: assn,Q: assn,Ha: heap_e7401611519738050253t_unit] :
      ( aa_Pro653082453696054616_nat_o(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(Ha,bot_bot_set_nat))
    <=> ( aa_Pro653082453696054616_nat_o(rep_assn(P),produc7507926704131184380et_nat(Ha,bot_bot_set_nat))
        & aa_Pro653082453696054616_nat_o(rep_assn(Q),produc7507926704131184380et_nat(Ha,bot_bot_set_nat)) ) ) ).

% mod_h_bot_iff(5)
tff(fact_7877_mod__h__bot__iff_I6_J,axiom,
    ! [P: assn,Q: assn,Ha: heap_e7401611519738050253t_unit] :
      ( aa_Pro653082453696054616_nat_o(rep_assn(inf_inf_assn(P,Q)),produc7507926704131184380et_nat(Ha,bot_bot_set_nat))
    <=> ( aa_Pro653082453696054616_nat_o(rep_assn(P),produc7507926704131184380et_nat(Ha,bot_bot_set_nat))
        & aa_Pro653082453696054616_nat_o(rep_assn(Q),produc7507926704131184380et_nat(Ha,bot_bot_set_nat)) ) ) ).

% mod_h_bot_iff(6)
tff(fact_7878_mod__h__bot__iff_I2_J,axiom,
    ! [Ha: heap_e7401611519738050253t_unit] : aa_Pro653082453696054616_nat_o(rep_assn(top_top_assn),produc7507926704131184380et_nat(Ha,bot_bot_set_nat)) ).

% mod_h_bot_iff(2)
tff(fact_7879_times__assn__raw_Ocases,axiom,
    ! [X2: produc3112576180687729086et_nat] :
      ~ ! [P4: fun_Pr6460944699146269935_nat_o,Q6: fun_Pr6460944699146269935_nat_o,H: heap_e7401611519738050253t_unit,As: set_nat] : X2 != aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,P4),aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,Q6),produc7507926704131184380et_nat(H,As))) ).

% times_assn_raw.cases
tff(fact_7880_one__assn__raw_Ocases,axiom,
    ! [X2: produc3658429121746597890et_nat] :
      ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] : X2 != produc7507926704131184380et_nat(H,As) ).

% one_assn_raw.cases
tff(fact_7881_mod__star__conv,axiom,
    ! [A2: assn,B4: assn,Ha: produc3658429121746597890et_nat] :
      ( aa_Pro653082453696054616_nat_o(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,A2),B4)),Ha)
    <=> ? [Hr: heap_e7401611519738050253t_unit,As1: set_nat,As2: set_nat] :
          ( ( Ha = produc7507926704131184380et_nat(Hr,sup_sup_set_nat(As1,As2)) )
          & ( inf_inf_set_nat(As1,As2) = bot_bot_set_nat )
          & aa_Pro653082453696054616_nat_o(rep_assn(A2),produc7507926704131184380et_nat(Hr,As1))
          & aa_Pro653082453696054616_nat_o(rep_assn(B4),produc7507926704131184380et_nat(Hr,As2)) ) ) ).

% mod_star_conv
tff(fact_7882_star__assnI,axiom,
    ! [P: assn,Ha: heap_e7401611519738050253t_unit,As3: set_nat,Q: assn,As4: set_nat] :
      ( aa_Pro653082453696054616_nat_o(rep_assn(P),produc7507926704131184380et_nat(Ha,As3))
     => ( aa_Pro653082453696054616_nat_o(rep_assn(Q),produc7507926704131184380et_nat(Ha,As4))
       => ( ( inf_inf_set_nat(As3,As4) = bot_bot_set_nat )
         => aa_Pro653082453696054616_nat_o(rep_assn(aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,P),Q)),produc7507926704131184380et_nat(Ha,sup_sup_set_nat(As3,As4))) ) ) ) ).

% star_assnI
tff(fact_7883_mod__emp__simp,axiom,
    ! [Ha: heap_e7401611519738050253t_unit] : aa_Pro653082453696054616_nat_o(rep_assn(one_one_assn),produc7507926704131184380et_nat(Ha,bot_bot_set_nat)) ).

% mod_emp_simp
tff(fact_7884_mod__h__bot__indep,axiom,
    ! [P: assn,Ha: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit] :
      ( aa_Pro653082453696054616_nat_o(rep_assn(P),produc7507926704131184380et_nat(Ha,bot_bot_set_nat))
    <=> aa_Pro653082453696054616_nat_o(rep_assn(P),produc7507926704131184380et_nat(H3,bot_bot_set_nat)) ) ).

% mod_h_bot_indep
tff(fact_7885_times__assn__raw_Osimps,axiom,
    ! [P: fun_Pr6460944699146269935_nat_o,Q: fun_Pr6460944699146269935_nat_o,Ha: heap_e7401611519738050253t_unit,As3: set_nat] :
      ( aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(times_assn_raw(P),Q),produc7507926704131184380et_nat(Ha,As3))
    <=> ? [As1: set_nat,As2: set_nat] :
          ( ( As3 = sup_sup_set_nat(As1,As2) )
          & ( inf_inf_set_nat(As1,As2) = bot_bot_set_nat )
          & aa_Pro653082453696054616_nat_o(P,produc7507926704131184380et_nat(Ha,As1))
          & aa_Pro653082453696054616_nat_o(Q,produc7507926704131184380et_nat(Ha,As2)) ) ) ).

% times_assn_raw.simps
tff(fact_7886_times__assn__raw_Oelims_I3_J,axiom,
    ! [X2: fun_Pr6460944699146269935_nat_o,Xa: fun_Pr6460944699146269935_nat_o,Xb: produc3658429121746597890et_nat] :
      ( ~ aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(times_assn_raw(X2),Xa),Xb)
     => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
            ( ( Xb = produc7507926704131184380et_nat(H,As) )
           => ? [As12: set_nat,As22: set_nat] :
                ( ( As = sup_sup_set_nat(As12,As22) )
                & ( inf_inf_set_nat(As12,As22) = bot_bot_set_nat )
                & aa_Pro653082453696054616_nat_o(X2,produc7507926704131184380et_nat(H,As12))
                & aa_Pro653082453696054616_nat_o(Xa,produc7507926704131184380et_nat(H,As22)) ) ) ) ).

% times_assn_raw.elims(3)
tff(fact_7887_times__assn__raw_Oelims_I2_J,axiom,
    ! [X2: fun_Pr6460944699146269935_nat_o,Xa: fun_Pr6460944699146269935_nat_o,Xb: produc3658429121746597890et_nat] :
      ( aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(times_assn_raw(X2),Xa),Xb)
     => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
            ( ( Xb = produc7507926704131184380et_nat(H,As) )
           => ~ ? [As13: set_nat,As23: set_nat] :
                  ( ( As = sup_sup_set_nat(As13,As23) )
                  & ( inf_inf_set_nat(As13,As23) = bot_bot_set_nat )
                  & aa_Pro653082453696054616_nat_o(X2,produc7507926704131184380et_nat(H,As13))
                  & aa_Pro653082453696054616_nat_o(Xa,produc7507926704131184380et_nat(H,As23)) ) ) ) ).

% times_assn_raw.elims(2)
tff(fact_7888_times__assn__raw_Oelims_I1_J,axiom,
    ! [X2: fun_Pr6460944699146269935_nat_o,Xa: fun_Pr6460944699146269935_nat_o,Xb: produc3658429121746597890et_nat,Y: $o] :
      ( ( aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(times_assn_raw(X2),Xa),Xb)
      <=> (Y) )
     => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
            ( ( Xb = produc7507926704131184380et_nat(H,As) )
           => ( (Y)
            <=> ~ ? [As1: set_nat,As2: set_nat] :
                    ( ( As = sup_sup_set_nat(As1,As2) )
                    & ( inf_inf_set_nat(As1,As2) = bot_bot_set_nat )
                    & aa_Pro653082453696054616_nat_o(X2,produc7507926704131184380et_nat(H,As1))
                    & aa_Pro653082453696054616_nat_o(Xa,produc7507926704131184380et_nat(H,As2)) ) ) ) ) ).

% times_assn_raw.elims(1)
tff(fact_7889_times__assn__raw_Opelims_I1_J,axiom,
    ! [X2: fun_Pr6460944699146269935_nat_o,Xa: fun_Pr6460944699146269935_nat_o,Xb: produc3658429121746597890et_nat,Y: $o] :
      ( ( aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(times_assn_raw(X2),Xa),Xb)
      <=> (Y) )
     => ( aa_Pro2671238023309943196_nat_o(accp_P1394777952347926645et_nat(times_assn_raw_rel),aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X2),aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,Xa),Xb)))
       => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
              ( ( Xb = produc7507926704131184380et_nat(H,As) )
             => ( ( (Y)
                <=> ? [As1: set_nat,As2: set_nat] :
                      ( ( As = sup_sup_set_nat(As1,As2) )
                      & ( inf_inf_set_nat(As1,As2) = bot_bot_set_nat )
                      & aa_Pro653082453696054616_nat_o(X2,produc7507926704131184380et_nat(H,As1))
                      & aa_Pro653082453696054616_nat_o(Xa,produc7507926704131184380et_nat(H,As2)) ) )
               => ~ aa_Pro2671238023309943196_nat_o(accp_P1394777952347926645et_nat(times_assn_raw_rel),aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X2),aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,Xa),produc7507926704131184380et_nat(H,As)))) ) ) ) ) ).

% times_assn_raw.pelims(1)
tff(fact_7890_times__assn__raw_Opelims_I2_J,axiom,
    ! [X2: fun_Pr6460944699146269935_nat_o,Xa: fun_Pr6460944699146269935_nat_o,Xb: produc3658429121746597890et_nat] :
      ( aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(times_assn_raw(X2),Xa),Xb)
     => ( aa_Pro2671238023309943196_nat_o(accp_P1394777952347926645et_nat(times_assn_raw_rel),aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X2),aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,Xa),Xb)))
       => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
              ( ( Xb = produc7507926704131184380et_nat(H,As) )
             => ( aa_Pro2671238023309943196_nat_o(accp_P1394777952347926645et_nat(times_assn_raw_rel),aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X2),aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,Xa),produc7507926704131184380et_nat(H,As))))
               => ~ ? [As13: set_nat,As23: set_nat] :
                      ( ( As = sup_sup_set_nat(As13,As23) )
                      & ( inf_inf_set_nat(As13,As23) = bot_bot_set_nat )
                      & aa_Pro653082453696054616_nat_o(X2,produc7507926704131184380et_nat(H,As13))
                      & aa_Pro653082453696054616_nat_o(Xa,produc7507926704131184380et_nat(H,As23)) ) ) ) ) ) ).

% times_assn_raw.pelims(2)
tff(fact_7891_times__assn__raw_Opelims_I3_J,axiom,
    ! [X2: fun_Pr6460944699146269935_nat_o,Xa: fun_Pr6460944699146269935_nat_o,Xb: produc3658429121746597890et_nat] :
      ( ~ aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(times_assn_raw(X2),Xa),Xb)
     => ( aa_Pro2671238023309943196_nat_o(accp_P1394777952347926645et_nat(times_assn_raw_rel),aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X2),aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,Xa),Xb)))
       => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
              ( ( Xb = produc7507926704131184380et_nat(H,As) )
             => ( aa_Pro2671238023309943196_nat_o(accp_P1394777952347926645et_nat(times_assn_raw_rel),aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X2),aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,Xa),produc7507926704131184380et_nat(H,As))))
               => ? [As12: set_nat,As22: set_nat] :
                    ( ( As = sup_sup_set_nat(As12,As22) )
                    & ( inf_inf_set_nat(As12,As22) = bot_bot_set_nat )
                    & aa_Pro653082453696054616_nat_o(X2,produc7507926704131184380et_nat(H,As12))
                    & aa_Pro653082453696054616_nat_o(Xa,produc7507926704131184380et_nat(H,As22)) ) ) ) ) ) ).

% times_assn_raw.pelims(3)
tff(fact_7892_mod__h__bot__iff_I1_J,axiom,
    ! [B: $o,Ha: heap_e7401611519738050253t_unit] :
      ( aa_Pro653082453696054616_nat_o(rep_assn(aa_o_assn(pure_assn,(B))),produc7507926704131184380et_nat(Ha,bot_bot_set_nat))
    <=> (B) ) ).

% mod_h_bot_iff(1)
tff(fact_7893_mod__relH,axiom,
    ! [As3: set_nat,Ha: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit,P: assn] :
      ( aa_hea7994211679605476167unit_o(relH(As3,Ha),H3)
     => ( aa_Pro653082453696054616_nat_o(rep_assn(P),produc7507926704131184380et_nat(Ha,As3))
      <=> aa_Pro653082453696054616_nat_o(rep_assn(P),produc7507926704131184380et_nat(H3,As3)) ) ) ).

% mod_relH
tff(fact_7894_in__range__empty,axiom,
    ! [Ha: heap_e7401611519738050253t_unit] : aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(Ha,bot_bot_set_nat)) ).

% in_range_empty
tff(fact_7895_in__range__dist__union,axiom,
    ! [Ha: heap_e7401611519738050253t_unit,As3: set_nat,As4: set_nat] :
      ( aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(Ha,sup_sup_set_nat(As3,As4)))
    <=> ( aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(Ha,As3))
        & aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(Ha,As4)) ) ) ).

% in_range_dist_union
tff(fact_7896_relH__refl,axiom,
    ! [Ha: heap_e7401611519738050253t_unit,As3: set_nat] :
      ( aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(Ha,As3))
     => aa_hea7994211679605476167unit_o(relH(As3,Ha),Ha) ) ).

% relH_refl
tff(fact_7897_relH__in__rangeI_I1_J,axiom,
    ! [As3: set_nat,Ha: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit] :
      ( aa_hea7994211679605476167unit_o(relH(As3,Ha),H3)
     => aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(Ha,As3)) ) ).

% relH_in_rangeI(1)
tff(fact_7898_relH__in__rangeI_I2_J,axiom,
    ! [As3: set_nat,Ha: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit] :
      ( aa_hea7994211679605476167unit_o(relH(As3,Ha),H3)
     => aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(H3,As3)) ) ).

% relH_in_rangeI(2)
tff(fact_7899_in__range__subset,axiom,
    ! [As3: set_nat,As4: set_nat,Ha: heap_e7401611519738050253t_unit] :
      ( aa_set_nat_o(ord_less_eq_set_nat(As3),As4)
     => ( aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(Ha,As4))
       => aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(Ha,As3)) ) ) ).

% in_range_subset
tff(fact_7900_in__range_Oelims_I3_J,axiom,
    ! [X2: produc3658429121746597890et_nat] :
      ( ~ aa_Pro653082453696054616_nat_o(in_range,X2)
     => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
            ( ( X2 = produc7507926704131184380et_nat(H,As) )
           => ! [X3: nat] :
                ( member_nat(X3,As)
               => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,X3),lim_Product_unit(H)) ) ) ) ).

% in_range.elims(3)
tff(fact_7901_in__range_Oelims_I2_J,axiom,
    ! [X2: produc3658429121746597890et_nat] :
      ( aa_Pro653082453696054616_nat_o(in_range,X2)
     => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
            ( ( X2 = produc7507926704131184380et_nat(H,As) )
           => ~ ! [X: nat] :
                  ( member_nat(X,As)
                 => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,X),lim_Product_unit(H)) ) ) ) ).

% in_range.elims(2)
tff(fact_7902_in__range_Oelims_I1_J,axiom,
    ! [X2: produc3658429121746597890et_nat,Y: $o] :
      ( ( aa_Pro653082453696054616_nat_o(in_range,X2)
      <=> (Y) )
     => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
            ( ( X2 = produc7507926704131184380et_nat(H,As) )
           => ( (Y)
            <=> ~ ! [X4: nat] :
                    ( member_nat(X4,As)
                   => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,X4),lim_Product_unit(H)) ) ) ) ) ).

% in_range.elims(1)
tff(fact_7903_in__range_Osimps,axiom,
    ! [Ha: heap_e7401611519738050253t_unit,As3: set_nat] :
      ( aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(Ha,As3))
    <=> ! [X4: nat] :
          ( member_nat(X4,As3)
         => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,X4),lim_Product_unit(Ha)) ) ) ).

% in_range.simps
tff(fact_7904_wand__assnI,axiom,
    ! [Ha: heap_e7401611519738050253t_unit,As3: set_nat,Q: assn,R3: assn] :
      ( aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(Ha,As3))
     => ( ! [H2: heap_e7401611519738050253t_unit,As5: set_nat] :
            ( ( inf_inf_set_nat(As3,As5) = bot_bot_set_nat )
           => ( aa_hea7994211679605476167unit_o(relH(As3,Ha),H2)
             => ( aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(H2,As3))
               => ( aa_Pro653082453696054616_nat_o(rep_assn(Q),produc7507926704131184380et_nat(H2,As5))
                 => aa_Pro653082453696054616_nat_o(rep_assn(R3),produc7507926704131184380et_nat(H2,sup_sup_set_nat(As3,As5))) ) ) ) )
       => aa_Pro653082453696054616_nat_o(rep_assn(wand_assn(Q,R3)),produc7507926704131184380et_nat(Ha,As3)) ) ) ).

% wand_assnI
tff(fact_7905_wand__raw_Osimps,axiom,
    ! [P: fun_Pr6460944699146269935_nat_o,Q: fun_Pr6460944699146269935_nat_o,Ha: heap_e7401611519738050253t_unit,As3: set_nat] :
      ( aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(wand_raw(P),Q),produc7507926704131184380et_nat(Ha,As3))
    <=> ( aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(Ha,As3))
        & ! [H5: heap_e7401611519738050253t_unit,As6: set_nat] :
            ( ( ( inf_inf_set_nat(As3,As6) = bot_bot_set_nat )
              & aa_hea7994211679605476167unit_o(relH(As3,Ha),H5)
              & aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(H5,As3))
              & aa_Pro653082453696054616_nat_o(P,produc7507926704131184380et_nat(H5,As6)) )
           => aa_Pro653082453696054616_nat_o(Q,produc7507926704131184380et_nat(H5,sup_sup_set_nat(As3,As6))) ) ) ) ).

% wand_raw.simps
tff(fact_7906_wand__raw_Oelims_I1_J,axiom,
    ! [X2: fun_Pr6460944699146269935_nat_o,Xa: fun_Pr6460944699146269935_nat_o,Xb: produc3658429121746597890et_nat,Y: $o] :
      ( ( aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(wand_raw(X2),Xa),Xb)
      <=> (Y) )
     => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
            ( ( Xb = produc7507926704131184380et_nat(H,As) )
           => ( (Y)
            <=> ~ ( aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(H,As))
                  & ! [H5: heap_e7401611519738050253t_unit,As6: set_nat] :
                      ( ( ( inf_inf_set_nat(As,As6) = bot_bot_set_nat )
                        & aa_hea7994211679605476167unit_o(relH(As,H),H5)
                        & aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(H5,As))
                        & aa_Pro653082453696054616_nat_o(X2,produc7507926704131184380et_nat(H5,As6)) )
                     => aa_Pro653082453696054616_nat_o(Xa,produc7507926704131184380et_nat(H5,sup_sup_set_nat(As,As6))) ) ) ) ) ) ).

% wand_raw.elims(1)
tff(fact_7907_wand__raw_Oelims_I3_J,axiom,
    ! [X2: fun_Pr6460944699146269935_nat_o,Xa: fun_Pr6460944699146269935_nat_o,Xb: produc3658429121746597890et_nat] :
      ( ~ aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(wand_raw(X2),Xa),Xb)
     => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
            ( ( Xb = produc7507926704131184380et_nat(H,As) )
           => ( aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(H,As))
              & ! [H2: heap_e7401611519738050253t_unit,As5: set_nat] :
                  ( ( ( inf_inf_set_nat(As,As5) = bot_bot_set_nat )
                    & aa_hea7994211679605476167unit_o(relH(As,H),H2)
                    & aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(H2,As))
                    & aa_Pro653082453696054616_nat_o(X2,produc7507926704131184380et_nat(H2,As5)) )
                 => aa_Pro653082453696054616_nat_o(Xa,produc7507926704131184380et_nat(H2,sup_sup_set_nat(As,As5))) ) ) ) ) ).

% wand_raw.elims(3)
tff(fact_7908_wand__raw_Oelims_I2_J,axiom,
    ! [X2: fun_Pr6460944699146269935_nat_o,Xa: fun_Pr6460944699146269935_nat_o,Xb: produc3658429121746597890et_nat] :
      ( aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(wand_raw(X2),Xa),Xb)
     => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
            ( ( Xb = produc7507926704131184380et_nat(H,As) )
           => ~ ( aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(H,As))
                & ! [H6: heap_e7401611519738050253t_unit,As7: set_nat] :
                    ( ( ( inf_inf_set_nat(As,As7) = bot_bot_set_nat )
                      & aa_hea7994211679605476167unit_o(relH(As,H),H6)
                      & aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(H6,As))
                      & aa_Pro653082453696054616_nat_o(X2,produc7507926704131184380et_nat(H6,As7)) )
                   => aa_Pro653082453696054616_nat_o(Xa,produc7507926704131184380et_nat(H6,sup_sup_set_nat(As,As7))) ) ) ) ) ).

% wand_raw.elims(2)
tff(fact_7909_wand__raw_Opelims_I3_J,axiom,
    ! [X2: fun_Pr6460944699146269935_nat_o,Xa: fun_Pr6460944699146269935_nat_o,Xb: produc3658429121746597890et_nat] :
      ( ~ aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(wand_raw(X2),Xa),Xb)
     => ( aa_Pro2671238023309943196_nat_o(accp_P1394777952347926645et_nat(wand_raw_rel),aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X2),aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,Xa),Xb)))
       => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
              ( ( Xb = produc7507926704131184380et_nat(H,As) )
             => ( aa_Pro2671238023309943196_nat_o(accp_P1394777952347926645et_nat(wand_raw_rel),aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X2),aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,Xa),produc7507926704131184380et_nat(H,As))))
               => ( aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(H,As))
                  & ! [H2: heap_e7401611519738050253t_unit,As5: set_nat] :
                      ( ( ( inf_inf_set_nat(As,As5) = bot_bot_set_nat )
                        & aa_hea7994211679605476167unit_o(relH(As,H),H2)
                        & aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(H2,As))
                        & aa_Pro653082453696054616_nat_o(X2,produc7507926704131184380et_nat(H2,As5)) )
                     => aa_Pro653082453696054616_nat_o(Xa,produc7507926704131184380et_nat(H2,sup_sup_set_nat(As,As5))) ) ) ) ) ) ) ).

% wand_raw.pelims(3)
tff(fact_7910_wand__raw_Opelims_I2_J,axiom,
    ! [X2: fun_Pr6460944699146269935_nat_o,Xa: fun_Pr6460944699146269935_nat_o,Xb: produc3658429121746597890et_nat] :
      ( aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(wand_raw(X2),Xa),Xb)
     => ( aa_Pro2671238023309943196_nat_o(accp_P1394777952347926645et_nat(wand_raw_rel),aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X2),aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,Xa),Xb)))
       => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
              ( ( Xb = produc7507926704131184380et_nat(H,As) )
             => ( aa_Pro2671238023309943196_nat_o(accp_P1394777952347926645et_nat(wand_raw_rel),aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X2),aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,Xa),produc7507926704131184380et_nat(H,As))))
               => ~ ( aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(H,As))
                    & ! [H6: heap_e7401611519738050253t_unit,As7: set_nat] :
                        ( ( ( inf_inf_set_nat(As,As7) = bot_bot_set_nat )
                          & aa_hea7994211679605476167unit_o(relH(As,H),H6)
                          & aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(H6,As))
                          & aa_Pro653082453696054616_nat_o(X2,produc7507926704131184380et_nat(H6,As7)) )
                       => aa_Pro653082453696054616_nat_o(Xa,produc7507926704131184380et_nat(H6,sup_sup_set_nat(As,As7))) ) ) ) ) ) ) ).

% wand_raw.pelims(2)
tff(fact_7911_wand__raw_Opelims_I1_J,axiom,
    ! [X2: fun_Pr6460944699146269935_nat_o,Xa: fun_Pr6460944699146269935_nat_o,Xb: produc3658429121746597890et_nat,Y: $o] :
      ( ( aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(wand_raw(X2),Xa),Xb)
      <=> (Y) )
     => ( aa_Pro2671238023309943196_nat_o(accp_P1394777952347926645et_nat(wand_raw_rel),aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X2),aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,Xa),Xb)))
       => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
              ( ( Xb = produc7507926704131184380et_nat(H,As) )
             => ( ( (Y)
                <=> ( aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(H,As))
                    & ! [H5: heap_e7401611519738050253t_unit,As6: set_nat] :
                        ( ( ( inf_inf_set_nat(As,As6) = bot_bot_set_nat )
                          & aa_hea7994211679605476167unit_o(relH(As,H),H5)
                          & aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(H5,As))
                          & aa_Pro653082453696054616_nat_o(X2,produc7507926704131184380et_nat(H5,As6)) )
                       => aa_Pro653082453696054616_nat_o(Xa,produc7507926704131184380et_nat(H5,sup_sup_set_nat(As,As6))) ) ) )
               => ~ aa_Pro2671238023309943196_nat_o(accp_P1394777952347926645et_nat(wand_raw_rel),aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,X2),aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,Xa),produc7507926704131184380et_nat(H,As)))) ) ) ) ) ).

% wand_raw.pelims(1)
tff(fact_7912_in__range_Opelims_I3_J,axiom,
    ! [X2: produc3658429121746597890et_nat] :
      ( ~ aa_Pro653082453696054616_nat_o(in_range,X2)
     => ( aa_Pro653082453696054616_nat_o(accp_P5801069581201407417et_nat(in_range_rel),X2)
       => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
              ( ( X2 = produc7507926704131184380et_nat(H,As) )
             => ( aa_Pro653082453696054616_nat_o(accp_P5801069581201407417et_nat(in_range_rel),produc7507926704131184380et_nat(H,As))
               => ! [X3: nat] :
                    ( member_nat(X3,As)
                   => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,X3),lim_Product_unit(H)) ) ) ) ) ) ).

% in_range.pelims(3)
tff(fact_7913_in__range_Opelims_I2_J,axiom,
    ! [X2: produc3658429121746597890et_nat] :
      ( aa_Pro653082453696054616_nat_o(in_range,X2)
     => ( aa_Pro653082453696054616_nat_o(accp_P5801069581201407417et_nat(in_range_rel),X2)
       => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
              ( ( X2 = produc7507926704131184380et_nat(H,As) )
             => ( aa_Pro653082453696054616_nat_o(accp_P5801069581201407417et_nat(in_range_rel),produc7507926704131184380et_nat(H,As))
               => ~ ! [X: nat] :
                      ( member_nat(X,As)
                     => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,X),lim_Product_unit(H)) ) ) ) ) ) ).

% in_range.pelims(2)
tff(fact_7914_in__range_Opelims_I1_J,axiom,
    ! [X2: produc3658429121746597890et_nat,Y: $o] :
      ( ( aa_Pro653082453696054616_nat_o(in_range,X2)
      <=> (Y) )
     => ( aa_Pro653082453696054616_nat_o(accp_P5801069581201407417et_nat(in_range_rel),X2)
       => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
              ( ( X2 = produc7507926704131184380et_nat(H,As) )
             => ( ( (Y)
                <=> ! [X4: nat] :
                      ( member_nat(X4,As)
                     => aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,X4),lim_Product_unit(H)) ) )
               => ~ aa_Pro653082453696054616_nat_o(accp_P5801069581201407417et_nat(in_range_rel),produc7507926704131184380et_nat(H,As)) ) ) ) ) ).

% in_range.pelims(1)
tff(fact_7915_one__assn__raw_Oelims_I3_J,axiom,
    ! [X2: produc3658429121746597890et_nat] :
      ( ~ aa_Pro653082453696054616_nat_o(one_assn_raw,X2)
     => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
            ( ( X2 = produc7507926704131184380et_nat(H,As) )
           => ( As = bot_bot_set_nat ) ) ) ).

% one_assn_raw.elims(3)
tff(fact_7916_one__assn__raw_Oelims_I2_J,axiom,
    ! [X2: produc3658429121746597890et_nat] :
      ( aa_Pro653082453696054616_nat_o(one_assn_raw,X2)
     => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
            ( ( X2 = produc7507926704131184380et_nat(H,As) )
           => ( As != bot_bot_set_nat ) ) ) ).

% one_assn_raw.elims(2)
tff(fact_7917_one__assn__raw_Oelims_I1_J,axiom,
    ! [X2: produc3658429121746597890et_nat,Y: $o] :
      ( ( aa_Pro653082453696054616_nat_o(one_assn_raw,X2)
      <=> (Y) )
     => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
            ( ( X2 = produc7507926704131184380et_nat(H,As) )
           => ( (Y)
            <=> ( As != bot_bot_set_nat ) ) ) ) ).

% one_assn_raw.elims(1)
tff(fact_7918_one__assn__raw_Osimps,axiom,
    ! [Ha: heap_e7401611519738050253t_unit,As3: set_nat] :
      ( aa_Pro653082453696054616_nat_o(one_assn_raw,produc7507926704131184380et_nat(Ha,As3))
    <=> ( As3 = bot_bot_set_nat ) ) ).

% one_assn_raw.simps
tff(fact_7919_one__assn__raw_Opelims_I3_J,axiom,
    ! [X2: produc3658429121746597890et_nat] :
      ( ~ aa_Pro653082453696054616_nat_o(one_assn_raw,X2)
     => ( aa_Pro653082453696054616_nat_o(accp_P5801069581201407417et_nat(one_assn_raw_rel),X2)
       => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
              ( ( X2 = produc7507926704131184380et_nat(H,As) )
             => ( aa_Pro653082453696054616_nat_o(accp_P5801069581201407417et_nat(one_assn_raw_rel),produc7507926704131184380et_nat(H,As))
               => ( As = bot_bot_set_nat ) ) ) ) ) ).

% one_assn_raw.pelims(3)
tff(fact_7920_one__assn__raw_Opelims_I2_J,axiom,
    ! [X2: produc3658429121746597890et_nat] :
      ( aa_Pro653082453696054616_nat_o(one_assn_raw,X2)
     => ( aa_Pro653082453696054616_nat_o(accp_P5801069581201407417et_nat(one_assn_raw_rel),X2)
       => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
              ( ( X2 = produc7507926704131184380et_nat(H,As) )
             => ( aa_Pro653082453696054616_nat_o(accp_P5801069581201407417et_nat(one_assn_raw_rel),produc7507926704131184380et_nat(H,As))
               => ( As != bot_bot_set_nat ) ) ) ) ) ).

% one_assn_raw.pelims(2)
tff(fact_7921_one__assn__raw_Opelims_I1_J,axiom,
    ! [X2: produc3658429121746597890et_nat,Y: $o] :
      ( ( aa_Pro653082453696054616_nat_o(one_assn_raw,X2)
      <=> (Y) )
     => ( aa_Pro653082453696054616_nat_o(accp_P5801069581201407417et_nat(one_assn_raw_rel),X2)
       => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
              ( ( X2 = produc7507926704131184380et_nat(H,As) )
             => ( ( (Y)
                <=> ( As = bot_bot_set_nat ) )
               => ~ aa_Pro653082453696054616_nat_o(accp_P5801069581201407417et_nat(one_assn_raw_rel),produc7507926704131184380et_nat(H,As)) ) ) ) ) ).

% one_assn_raw.pelims(1)
tff(fact_7922_proper__iff,axiom,
    ! [P: fun_Pr6460944699146269935_nat_o,As3: set_nat,Ha: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit] :
      ( aa_fun1675921005893230629at_o_o(proper,P)
     => ( aa_hea7994211679605476167unit_o(relH(As3,Ha),H3)
       => ( aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(H3,As3))
         => ( aa_Pro653082453696054616_nat_o(P,produc7507926704131184380et_nat(Ha,As3))
          <=> aa_Pro653082453696054616_nat_o(P,produc7507926704131184380et_nat(H3,As3)) ) ) ) ) ).

% proper_iff
tff(fact_7923_proper__def,axiom,
    ! [P: fun_Pr6460944699146269935_nat_o] :
      ( aa_fun1675921005893230629at_o_o(proper,P)
    <=> ! [H7: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,As8: set_nat] :
          ( ( aa_Pro653082453696054616_nat_o(P,produc7507926704131184380et_nat(H7,As8))
           => aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(H7,As8)) )
          & ( ( aa_Pro653082453696054616_nat_o(P,produc7507926704131184380et_nat(H7,As8))
              & aa_hea7994211679605476167unit_o(relH(As8,H7),H5)
              & aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(H5,As8)) )
           => aa_Pro653082453696054616_nat_o(P,produc7507926704131184380et_nat(H5,As8)) ) ) ) ).

% proper_def
tff(fact_7924_properD2,axiom,
    ! [P: fun_Pr6460944699146269935_nat_o,Ha: heap_e7401611519738050253t_unit,As3: set_nat,H3: heap_e7401611519738050253t_unit] :
      ( aa_fun1675921005893230629at_o_o(proper,P)
     => ( aa_Pro653082453696054616_nat_o(P,produc7507926704131184380et_nat(Ha,As3))
       => ( aa_hea7994211679605476167unit_o(relH(As3,Ha),H3)
         => ( aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(H3,As3))
           => aa_Pro653082453696054616_nat_o(P,produc7507926704131184380et_nat(H3,As3)) ) ) ) ) ).

% properD2
tff(fact_7925_properD1,axiom,
    ! [P: fun_Pr6460944699146269935_nat_o,Ha: heap_e7401611519738050253t_unit,As3: set_nat] :
      ( aa_fun1675921005893230629at_o_o(proper,P)
     => ( aa_Pro653082453696054616_nat_o(P,produc7507926704131184380et_nat(Ha,As3))
       => aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(Ha,As3)) ) ) ).

% properD1
tff(fact_7926_properI,axiom,
    ! [P: fun_Pr6460944699146269935_nat_o] :
      ( ! [As: set_nat,H: heap_e7401611519738050253t_unit] :
          ( aa_Pro653082453696054616_nat_o(P,produc7507926704131184380et_nat(H,As))
         => aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(H,As)) )
     => ( ! [As: set_nat,H: heap_e7401611519738050253t_unit,H2: heap_e7401611519738050253t_unit] :
            ( aa_Pro653082453696054616_nat_o(P,produc7507926704131184380et_nat(H,As))
           => ( aa_hea7994211679605476167unit_o(relH(As,H),H2)
             => ( aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(H2,As))
               => aa_Pro653082453696054616_nat_o(P,produc7507926704131184380et_nat(H2,As)) ) ) )
       => aa_fun1675921005893230629at_o_o(proper,P) ) ) ).

% properI
tff(fact_7927_Int_Osub__code_I8_J,axiom,
    ! [M: num,N2: num] : aa_num_int(sub(aa_num_num(bit1,M)),aa_num_num(bit0,N2)) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(dup,aa_num_int(sub(M),N2))),one_one_int) ).

% Int.sub_code(8)
tff(fact_7928_Int_Odup__def,axiom,
    ! [K: int] : aa_int_int(dup,K) = aa_int_int(aa_int_fun_int_int(plus_plus_int,K),K) ).

% Int.dup_def
tff(fact_7929_relH__def,axiom,
    ! [As3: set_nat,Ha: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit] :
      ( aa_hea7994211679605476167unit_o(relH(As3,Ha),H3)
    <=> ( aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(Ha,As3))
        & aa_Pro653082453696054616_nat_o(in_range,produc7507926704131184380et_nat(H3,As3))
        & ! [T5: typerep,X4: nat] :
            ( member_nat(X4,As3)
           => ( ( aa_nat_nat(refs_Product_unit(Ha,T5),X4) = aa_nat_nat(refs_Product_unit(H3,T5),X4) )
              & ( arrays_Product_unit(Ha,T5,X4) = arrays_Product_unit(H3,T5,X4) ) ) ) ) ) ).

% relH_def
tff(fact_7930_plus__int__code_I6_J,axiom,
    ! [M: num,N2: num] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_num_int(neg,M)),aa_num_int(neg,N2)) = aa_num_int(neg,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2)) ).

% plus_int_code(6)
tff(fact_7931_plus__int__code_I5_J,axiom,
    ! [M: num,N2: num] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_num_int(neg,M)),aa_num_int(pos,N2)) = aa_num_int(sub(N2),M) ).

% plus_int_code(5)
tff(fact_7932_plus__int__code_I4_J,axiom,
    ! [M: num,N2: num] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_num_int(pos,M)),aa_num_int(neg,N2)) = aa_num_int(sub(M),N2) ).

% plus_int_code(4)
tff(fact_7933_minus__int__code_I4_J,axiom,
    ! [M: num,N2: num] : aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_num_int(pos,M)),aa_num_int(neg,N2)) = aa_num_int(pos,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2)) ).

% minus_int_code(4)
tff(fact_7934_plus__int__code_I3_J,axiom,
    ! [M: num,N2: num] : aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_num_int(pos,M)),aa_num_int(pos,N2)) = aa_num_int(pos,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2)) ).

% plus_int_code(3)
tff(fact_7935_minus__int__code_I5_J,axiom,
    ! [M: num,N2: num] : aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_num_int(neg,M)),aa_num_int(pos,N2)) = aa_num_int(neg,aa_num_num(aa_num_fun_num_num(plus_plus_num,M),N2)) ).

% minus_int_code(5)
tff(fact_7936_Unity__def,axiom,
    product_Unity = aa_o_Product_unit(product_Abs_unit,$true) ).

% Unity_def
tff(fact_7937_Abs__unit__inject,axiom,
    ! [X2: $o,Y: $o] :
      ( member_o((X2),insert_o($true,bot_bot_set_o))
     => ( member_o((Y),insert_o($true,bot_bot_set_o))
       => ( ( aa_o_Product_unit(product_Abs_unit,(X2)) = aa_o_Product_unit(product_Abs_unit,(Y)) )
        <=> ( (X2)
          <=> (Y) ) ) ) ) ).

% Abs_unit_inject
tff(fact_7938_Abs__unit__induct,axiom,
    ! [P: fun_Product_unit_o,X2: product_unit] :
      ( ! [Y4: $o] :
          ( member_o((Y4),insert_o($true,bot_bot_set_o))
         => aa_Product_unit_o(P,aa_o_Product_unit(product_Abs_unit,(Y4))) )
     => aa_Product_unit_o(P,X2) ) ).

% Abs_unit_induct
tff(fact_7939_Abs__unit__cases,axiom,
    ! [X2: product_unit] :
      ~ ! [Y4: $o] :
          ( ( X2 = aa_o_Product_unit(product_Abs_unit,(Y4)) )
         => ~ member_o((Y4),insert_o($true,bot_bot_set_o)) ) ).

% Abs_unit_cases
tff(fact_7940_integer_Odomain,axiom,
    ! [P: fun_int_o] :
      ( ( domainp_int_int(fequal_int) = P )
     => ( domain452967906960104687nteger(code_pcr_integer) = P ) ) ).

% integer.domain
tff(fact_7941_natural_Odomain,axiom,
    ! [P: fun_nat_o] :
      ( ( domainp_nat_nat(fequal_nat) = P )
     => ( domain8128281535334753374atural(code_pcr_natural) = P ) ) ).

% natural.domain
tff(fact_7942_Abs__unit__inverse,axiom,
    ! [Y: $o] :
      ( member_o((Y),insert_o($true,bot_bot_set_o))
     => ( aa_Product_unit_o(product_Rep_unit,aa_o_Product_unit(product_Abs_unit,(Y)))
      <=> (Y) ) ) ).

% Abs_unit_inverse
tff(fact_7943_type__definition__unit,axiom,
    type_d6188575255521822967unit_o(product_Rep_unit,product_Abs_unit,insert_o($true,bot_bot_set_o)) ).

% type_definition_unit
tff(fact_7944_Rep__unit__inverse,axiom,
    ! [X2: product_unit] : aa_o_Product_unit(product_Abs_unit,aa_Product_unit_o(product_Rep_unit,X2)) = X2 ).

% Rep_unit_inverse
tff(fact_7945_Rep__unit__inject,axiom,
    ! [X2: product_unit,Y: product_unit] :
      ( ( aa_Product_unit_o(product_Rep_unit,X2)
      <=> aa_Product_unit_o(product_Rep_unit,Y) )
    <=> ( X2 = Y ) ) ).

% Rep_unit_inject
tff(fact_7946_Rep__unit,axiom,
    ! [X2: product_unit] : member_o(aa_Product_unit_o(product_Rep_unit,X2),insert_o($true,bot_bot_set_o)) ).

% Rep_unit
tff(fact_7947_Rep__unit__cases,axiom,
    ! [Y: $o] :
      ( member_o((Y),insert_o($true,bot_bot_set_o))
     => ~ ! [X3: product_unit] :
            ( (Y)
          <=> ~ aa_Product_unit_o(product_Rep_unit,X3) ) ) ).

% Rep_unit_cases
tff(fact_7948_Rep__unit__induct,axiom,
    ! [Y: $o,P: fun_o_o] :
      ( member_o((Y),insert_o($true,bot_bot_set_o))
     => ( ! [X3: product_unit] : aa_o_o(P,aa_Product_unit_o(product_Rep_unit,X3))
       => aa_o_o(P,(Y)) ) ) ).

% Rep_unit_induct
tff(fact_7949_positive__add,axiom,
    ! [X2: rat,Y: rat] :
      ( aa_rat_o(positive,X2)
     => ( aa_rat_o(positive,Y)
       => aa_rat_o(positive,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,X2),Y)) ) ) ).

% positive_add
tff(fact_7950_nth__item_Opinduct,axiom,
    ! [A0: nat,P: fun_nat_o] :
      ( aa_nat_o(accp_nat(nth_item_rel),A0)
     => ( ( aa_nat_o(accp_nat(nth_item_rel),zero_zero_nat)
         => aa_nat_o(P,zero_zero_nat) )
       => ( ! [N: nat] :
              ( aa_nat_o(accp_nat(nth_item_rel),aa_nat_nat(suc,N))
             => ( ! [A7: nat,Aa: nat] :
                    ( ( nat_sum_decode(N) = sum_Inl_nat_nat(A7) )
                   => ( ( nat_sum_decode(A7) = sum_Inl_nat_nat(Aa) )
                     => aa_nat_o(P,Aa) ) )
               => ( ! [A7: nat,B5: nat] :
                      ( ( nat_sum_decode(N) = sum_Inl_nat_nat(A7) )
                     => ( ( nat_sum_decode(A7) = sum_Inr_nat_nat(B5) )
                       => aa_nat_o(P,B5) ) )
                 => ( ! [B5: nat,Ba: nat,X: nat,Y5: nat] :
                        ( ( nat_sum_decode(N) = sum_Inr_nat_nat(B5) )
                       => ( ( nat_sum_decode(B5) = sum_Inr_nat_nat(Ba) )
                         => ( ( aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X),Y5) = aa_nat7603221163087113075at_nat(nat_prod_decode,Ba) )
                           => aa_nat_o(P,X) ) ) )
                   => ( ! [B5: nat,Ba: nat,X: nat,Y5: nat] :
                          ( ( nat_sum_decode(N) = sum_Inr_nat_nat(B5) )
                         => ( ( nat_sum_decode(B5) = sum_Inr_nat_nat(Ba) )
                           => ( ( aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,X),Y5) = aa_nat7603221163087113075at_nat(nat_prod_decode,Ba) )
                             => aa_nat_o(P,Y5) ) ) )
                     => aa_nat_o(P,aa_nat_nat(suc,N)) ) ) ) ) )
         => aa_nat_o(P,A0) ) ) ) ).

% nth_item.pinduct
tff(fact_7951_ATP_Olambda__1,axiom,
    ! [Uu: product_prod_int_int] :
      aa_Pro6970504127699319548nt_int(aTP_Lamm_abx,Uu) = $ite(aa_Pro6799258434465214121nt_int(product_fst_int_int,Uu) = zero_zero_int,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,zero_zero_int),one_one_int),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_Pro6799258434465214121nt_int(product_snd_int_int,Uu)),aa_Pro6799258434465214121nt_int(product_fst_int_int,Uu))) ).

% ATP.lambda_1
tff(fact_7952_ATP_Olambda__2,axiom,
    ! [Uu: set_set_Code_integer] : aa_set5345935369443442227er_int(aTP_Lamm_ug,Uu) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(uminus_uminus_int,one_one_int)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,finite1340570857867686763nteger(Uu)),one_one_nat))),aa_nat_int(semiri1314217659103216013at_int,finite4902975817058060853nteger(comple1256288197631046732nteger(Uu)))) ).

% ATP.lambda_2
tff(fact_7953_ATP_Olambda__3,axiom,
    ! [Uu: set_set_Product_unit] : aa_set1590017630834857277it_int(aTP_Lamm_ua,Uu) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(uminus_uminus_int,one_one_int)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,finite22775419188893461t_unit(Uu)),one_one_nat))),aa_nat_int(semiri1314217659103216013at_int,finite410649719033368117t_unit(comple7216939928495492468t_unit(Uu)))) ).

% ATP.lambda_3
tff(fact_7954_ATP_Olambda__4,axiom,
    ! [Uu: set_se7855581050983116737at_nat] : aa_set2246171803582654129at_int(aTP_Lamm_ui,Uu) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(uminus_uminus_int,one_one_int)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,finite4356350796350151305at_nat(Uu)),one_one_nat))),aa_nat_int(semiri1314217659103216013at_int,aa_set4749074711808745205at_nat(finite711546835091564841at_nat,comple1930127330929219688at_nat(Uu)))) ).

% ATP.lambda_4
tff(fact_7955_ATP_Olambda__5,axiom,
    ! [Uu: set_set_list_nat] : aa_set4520658747456594998at_int(aTP_Lamm_uc,Uu) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(uminus_uminus_int,one_one_int)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,finite2364142230527598318st_nat(Uu)),one_one_nat))),aa_nat_int(semiri1314217659103216013at_int,finite_card_list_nat(comple184543376406953807st_nat(Uu)))) ).

% ATP.lambda_5
tff(fact_7956_ATP_Olambda__6,axiom,
    ! [Uu: set_set_nat] : aa_set_set_nat_int(aTP_Lamm_uk,Uu) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(uminus_uminus_int,one_one_int)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,finite_card_set_nat(Uu)),one_one_nat))),aa_nat_int(semiri1314217659103216013at_int,aa_set_nat_nat(finite_card_nat,comple7806235888213564991et_nat(Uu)))) ).

% ATP.lambda_6
tff(fact_7957_ATP_Olambda__7,axiom,
    ! [Uu: set_set_int] : aa_set_set_int_int(aTP_Lamm_ue,Uu) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(uminus_uminus_int,one_one_int)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,finite_card_set_int(Uu)),one_one_nat))),aa_nat_int(semiri1314217659103216013at_int,finite_card_int(comple3628384868704368283et_int(Uu)))) ).

% ATP.lambda_7
tff(fact_7958_ATP_Olambda__8,axiom,
    ! [Uu: set_Pr1261947904930325089at_nat] : aa_set1427696295806717282at_nat(aTP_Lamm_aby,Uu) = aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(produc2922128104949294807at_nat(Uu,Uu)),bot_bo228742789529271731at_nat) ).

% ATP.lambda_8
tff(fact_7959_ATP_Olambda__9,axiom,
    ! [Uu: nat] : aa_nat7062706319057040595at_nat(aTP_Lamm_abz,Uu) = aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Uu),Uu)),bot_bo2099793752762293965at_nat) ).

% ATP.lambda_9
tff(fact_7960_ATP_Olambda__10,axiom,
    ! [Uu: product_prod_int_int] : aa_Pro6970504127699319548nt_int(aTP_Lamm_acb,Uu) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_int_int(uminus_uminus_int,aa_Pro6799258434465214121nt_int(product_fst_int_int,Uu))),aa_Pro6799258434465214121nt_int(product_snd_int_int,Uu)) ).

% ATP.lambda_10
tff(fact_7961_ATP_Olambda__11,axiom,
    ! [Uu: nat] : aa_nat_nat(aTP_Lamm_dx,Uu) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uu),aa_nat_nat(suc,zero_zero_nat)) ).

% ATP.lambda_11
tff(fact_7962_ATP_Olambda__12,axiom,
    ! [Uu: int] : aa_int_int(aTP_Lamm_ni,Uu) = aa_int_int(aa_int_fun_int_int(plus_plus_int,Uu),Uu) ).

% ATP.lambda_12
tff(fact_7963_ATP_Olambda__13,axiom,
    ! [Uu: code_integer] : aa_Cod6977894654539884864nteger(aTP_Lamm_wl,Uu) = aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(Uu),Uu) ).

% ATP.lambda_13
tff(fact_7964_ATP_Olambda__14,axiom,
    ! [Uu: produc7822875418678951345atural] : aa_Pro1971126414814181170atural(aTP_Lamm_wn,Uu) = produc4480994950612372183atural(Uu,Uu) ).

% ATP.lambda_14
tff(fact_7965_ATP_Olambda__15,axiom,
    ! [Uu: $o] : aa_o_P8186867570850176203od_o_o(aTP_Lamm_wh,(Uu)) = product_Pair_o_o((Uu),(Uu)) ).

% ATP.lambda_15
tff(fact_7966_ATP_Olambda__16,axiom,
    ! [Uu: num] : aa_num3156681643174609981um_num(aTP_Lamm_wk,Uu) = product_Pair_num_num(Uu,Uu) ).

% ATP.lambda_16
tff(fact_7967_ATP_Olambda__17,axiom,
    ! [Uu: nat] : aa_nat7603221163087113075at_nat(aTP_Lamm_wi,Uu) = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Uu),Uu) ).

% ATP.lambda_17
tff(fact_7968_ATP_Olambda__18,axiom,
    ! [Uu: int] : aa_int7462565939943104719nt_int(aTP_Lamm_wm,Uu) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Uu),Uu) ).

% ATP.lambda_18
tff(fact_7969_ATP_Olambda__19,axiom,
    ! [Uu: fun_nat_o] : aa_fun2081456873842488898_nat_o(aTP_Lamm_wj,Uu) = produc3725555944217366743_nat_o(Uu,Uu) ).

% ATP.lambda_19
tff(fact_7970_ATP_Olambda__20,axiom,
    ! [Uu: code_natural] : aa_Cod4272041906116450446atural(aTP_Lamm_hc,Uu) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,Uu),one_one_Code_natural) ).

% ATP.lambda_20
tff(fact_7971_ATP_Olambda__21,axiom,
    ! [Uu: code_integer] : aa_Cod1783974652533396728nteger(aTP_Lamm_hb,Uu) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,Uu),one_one_Code_integer) ).

% ATP.lambda_21
tff(fact_7972_ATP_Olambda__22,axiom,
    ! [Uu: rat] : aa_rat_rat(aTP_Lamm_gy,Uu) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,Uu),one_one_rat) ).

% ATP.lambda_22
tff(fact_7973_ATP_Olambda__23,axiom,
    ! [Uu: nat] : aa_nat_nat(aTP_Lamm_ha,Uu) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uu),one_one_nat) ).

% ATP.lambda_23
tff(fact_7974_ATP_Olambda__24,axiom,
    ! [Uu: int] : aa_int_int(aTP_Lamm_gz,Uu) = aa_int_int(aa_int_fun_int_int(plus_plus_int,Uu),one_one_int) ).

% ATP.lambda_24
tff(fact_7975_ATP_Olambda__25,axiom,
    ! [Uu: nat] : aa_nat7603221163087113075at_nat(aTP_Lamm_abv,Uu) = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Uu),zero_zero_nat) ).

% ATP.lambda_25
tff(fact_7976_ATP_Olambda__26,axiom,
    ! [Uu: code_natural] : aa_Cod6352003912080677724atural(aTP_Lamm_adn,Uu) = produc5538323210962509403atural(next,aTP_Lamm_adm(Uu)) ).

% ATP.lambda_26
tff(fact_7977_ATP_Olambda__27,axiom,
    ! [Uu: product_unit] : aa_Pro371939380295300617t_unit(aTP_Lamm_hi,Uu) = produc1863717115126956122t_unit(aTP_Lamm_hh(Uu)) ).

% ATP.lambda_27
tff(fact_7978_ATP_Olambda__28,axiom,
    ! [Uu: array_a] : aa_arr5115324663822341685rray_a(aTP_Lamm_hg,Uu) = produc2025300630104146186rray_a(aTP_Lamm_hf(Uu)) ).

% ATP.lambda_28
tff(fact_7979_ATP_Olambda__29,axiom,
    ! [Uu: num] : aa_num_option_num(aTP_Lamm_ij,Uu) = aa_num_option_num(some_num,aa_num_num(bit1,Uu)) ).

% ATP.lambda_29
tff(fact_7980_ATP_Olambda__30,axiom,
    ! [Uu: num] : aa_num_option_num(aTP_Lamm_he,Uu) = aa_num_option_num(some_num,aa_num_num(bit0,Uu)) ).

% ATP.lambda_30
tff(fact_7981_ATP_Olambda__31,axiom,
    ! [Uu: int] : aa_int2565445551602696444nt_int(aTP_Lamm_nb,Uu) = aa_int2565445551602696444nt_int(product_Pair_int_int,aa_int_int(uminus_uminus_int,Uu)) ).

% ATP.lambda_31
tff(fact_7982_ATP_Olambda__32,axiom,
    ! [Uu: int] : aa_int2565445551602696444nt_int(aTP_Lamm_nc,Uu) = aa_int2565445551602696444nt_int(product_Pair_int_int,aa_int_int(abs_abs_int,Uu)) ).

% ATP.lambda_32
tff(fact_7983_ATP_Olambda__33,axiom,
    ! [Uu: nat] : aa_nat8803788312118491388at_nat(aTP_Lamm_cq,Uu) = aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_nat_nat(suc,Uu)) ).

% ATP.lambda_33
tff(fact_7984_ATP_Olambda__34,axiom,
    ! [Uu: product_unit] : aa_Pro5533504860201378154at_nat(aTP_Lamm_ko,Uu) = produc4278983685114131267at_nat(aTP_Lamm_km) ).

% ATP.lambda_34
tff(fact_7985_ATP_Olambda__35,axiom,
    ! [Uu: array_a] : aa_arr7625186775369825262at_nat(aTP_Lamm_kn,Uu) = produc4278983685114131267at_nat(aTP_Lamm_km) ).

% ATP.lambda_35
tff(fact_7986_ATP_Olambda__36,axiom,
    ! [Uu: product_unit] : aa_Pro2296358444443531977t_unit(aTP_Lamm_ht,Uu) = produc9092781844693468442t_unit(aTP_Lamm_hr) ).

% ATP.lambda_36
tff(fact_7987_ATP_Olambda__37,axiom,
    ! [Uu: array_a] : aa_arr3387439787600506181t_unit(aTP_Lamm_hs,Uu) = produc9092781844693468442t_unit(aTP_Lamm_hr) ).

% ATP.lambda_37
tff(fact_7988_ATP_Olambda__38,axiom,
    ! [Uu: num,Uua: nat] : aa_nat_option_num(aTP_Lamm_mk(Uu),Uua) = aa_num_option_num(case_num_option_num(aa_num_option_num(some_num,one),aTP_Lamm_mi(Uua),aTP_Lamm_mj(Uua)),Uu) ).

% ATP.lambda_38
tff(fact_7989_ATP_Olambda__39,axiom,
    ! [Uu: int,Uua: int] :
      aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(aTP_Lamm_nh,Uu),Uua) = $ite(Uu = zero_zero_int,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,zero_zero_int),one_one_int),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(sgn_sgn_int,Uu)),Uua)),aa_int_int(abs_abs_int,Uu))) ).

% ATP.lambda_39
tff(fact_7990_ATP_Olambda__40,axiom,
    ! [Uu: int,Uua: int] :
      aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(aTP_Lamm_adg,Uu),Uua) = $ite(Uua = zero_zero_int,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,zero_zero_int),one_one_int),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Uu),Uua)) ).

% ATP.lambda_40
tff(fact_7991_ATP_Olambda__41,axiom,
    ! [Uu: option_int,Uua: int] :
      ( aa_int_o(aTP_Lamm_bm(Uu),Uua)
    <=> case_option_o_int($true,aa_int_fun_int_o(aTP_Lamm_bl,Uua),Uu) ) ).

% ATP.lambda_41
tff(fact_7992_ATP_Olambda__42,axiom,
    ! [Uu: option_nat,Uua: nat] :
      ( aa_nat_o(aTP_Lamm_bk(Uu),Uua)
    <=> case_option_o_nat($true,aa_nat_fun_nat_o(aTP_Lamm_bj,Uua),Uu) ) ).

% ATP.lambda_42
tff(fact_7993_ATP_Olambda__43,axiom,
    ! [Uu: option_num,Uua: num] :
      ( aa_num_o(aTP_Lamm_bi(Uu),Uua)
    <=> aa_option_num_o(case_option_o_num($true,aa_num_fun_num_o(aTP_Lamm_bh,Uua)),Uu) ) ).

% ATP.lambda_43
tff(fact_7994_ATP_Olambda__44,axiom,
    ! [Uu: option_rat,Uua: rat] :
      ( aa_rat_o(aTP_Lamm_bg(Uu),Uua)
    <=> case_option_o_rat($true,aa_rat_fun_rat_o(aTP_Lamm_bf,Uua),Uu) ) ).

% ATP.lambda_44
tff(fact_7995_ATP_Olambda__45,axiom,
    ! [Uu: option_Code_integer,Uua: code_integer] :
      ( aa_Code_integer_o(aTP_Lamm_be(Uu),Uua)
    <=> case_o43118980978444458nteger($true,aa_Cod326357343816142457eger_o(aTP_Lamm_bd,Uua),Uu) ) ).

% ATP.lambda_45
tff(fact_7996_ATP_Olambda__46,axiom,
    ! [Uu: nat,Uua: num] : aa_num_option_num(aa_nat3713591252005393295on_num(aTP_Lamm_ml,Uu),Uua) = aa_nat_option_num(case_nat_option_num(none_num,aTP_Lamm_mk(Uua)),Uu) ).

% ATP.lambda_46
tff(fact_7997_ATP_Olambda__47,axiom,
    ! [Uu: option_set_nat,Uua: set_nat] :
      ( aa_set_nat_o(aTP_Lamm_ch(Uu),Uua)
    <=> case_o4401850862724306899et_nat($false,ord_less_eq_set_nat(Uua),Uu) ) ).

% ATP.lambda_47
tff(fact_7998_ATP_Olambda__48,axiom,
    ! [Uu: option_rat,Uua: rat] :
      ( aa_rat_o(aTP_Lamm_ci(Uu),Uua)
    <=> case_option_o_rat($false,aa_rat_fun_rat_o(ord_less_eq_rat,Uua),Uu) ) ).

% ATP.lambda_48
tff(fact_7999_ATP_Olambda__49,axiom,
    ! [Uu: option_num,Uua: num] :
      ( aa_num_o(aTP_Lamm_cj(Uu),Uua)
    <=> aa_option_num_o(case_option_o_num($false,aa_num_fun_num_o(ord_less_eq_num,Uua)),Uu) ) ).

% ATP.lambda_49
tff(fact_8000_ATP_Olambda__50,axiom,
    ! [Uu: option_nat,Uua: nat] :
      ( aa_nat_o(aTP_Lamm_ck(Uu),Uua)
    <=> case_option_o_nat($false,aa_nat_fun_nat_o(ord_less_eq_nat,Uua),Uu) ) ).

% ATP.lambda_50
tff(fact_8001_ATP_Olambda__51,axiom,
    ! [Uu: option_int,Uua: int] :
      ( aa_int_o(aTP_Lamm_cl(Uu),Uua)
    <=> case_option_o_int($false,aa_int_fun_int_o(ord_less_eq_int,Uua),Uu) ) ).

% ATP.lambda_51
tff(fact_8002_ATP_Olambda__52,axiom,
    ! [Uu: nat,Uua: num] : aa_num_option_num(aTP_Lamm_mi(Uu),Uua) = aa_opt5369159329878751634on_num(case_o6005452278849405969um_num(none_num,aTP_Lamm_he),aa_num_option_num(bit_take_bit_num(Uu),Uua)) ).

% ATP.lambda_52
tff(fact_8003_ATP_Olambda__53,axiom,
    ! [Uu: fun_nat_fun_nat_int,Uua: nat] : aa_nat_int(aTP_Lamm_mo(Uu),Uua) = groups705719431365010083at_int(aa_nat_fun_nat_int(aTP_Lamm_mn(Uu),Uua),aa_nat_set_nat(set_ord_atMost_nat,Uua)) ).

% ATP.lambda_53
tff(fact_8004_ATP_Olambda__54,axiom,
    ! [Uu: fun_nat_fun_nat_nat,Uua: nat] : aa_nat_nat(aTP_Lamm_mm(Uu),Uua) = aa_set_nat_nat(groups708209901874060359at_nat(aa_nat_fun_nat_nat(aTP_Lamm_hw(Uu),Uua)),aa_nat_set_nat(set_ord_atMost_nat,Uua)) ).

% ATP.lambda_54
tff(fact_8005_ATP_Olambda__55,axiom,
    ! [Uu: fun_nat_fun_nat_nat,Uua: nat] : aa_nat_nat(aTP_Lamm_hx(Uu),Uua) = aa_set_nat_nat(groups3542108847815614940at_nat(aa_nat_fun_nat_nat(aTP_Lamm_hw(Uu),Uua)),aa_nat_set_nat(set_ord_atMost_nat,Uua)) ).

% ATP.lambda_55
tff(fact_8006_ATP_Olambda__56,axiom,
    ! [Uu: product_prod_int_int,Uua: product_prod_int_int] : aa_Pro6970504127699319548nt_int(aa_Pro4124234152028750080nt_int(aTP_Lamm_abw,Uu),Uua) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_Pro6799258434465214121nt_int(product_fst_int_int,Uu)),aa_Pro6799258434465214121nt_int(product_snd_int_int,Uua))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_Pro6799258434465214121nt_int(product_fst_int_int,Uua)),aa_Pro6799258434465214121nt_int(product_snd_int_int,Uu)))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_Pro6799258434465214121nt_int(product_snd_int_int,Uu)),aa_Pro6799258434465214121nt_int(product_snd_int_int,Uua))) ).

% ATP.lambda_56
tff(fact_8007_ATP_Olambda__57,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat_Code_integer(aTP_Lamm_jv(Uu),Uua) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),Uua)),aa_nat_Code_integer(semiri4939895301339042750nteger,Uua))),aa_nat_Code_integer(semiri4939895301339042750nteger,aa_nat_nat(aa_nat_fun_nat_nat(binomial,Uu),Uua))) ).

% ATP.lambda_57
tff(fact_8008_ATP_Olambda__58,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat_rat(aTP_Lamm_jt(Uu),Uua) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),Uua)),aa_nat_rat(semiri681578069525770553at_rat,Uua))),aa_nat_rat(semiri681578069525770553at_rat,aa_nat_nat(aa_nat_fun_nat_nat(binomial,Uu),Uua))) ).

% ATP.lambda_58
tff(fact_8009_ATP_Olambda__59,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat_int(aa_nat_fun_nat_int(aTP_Lamm_ju,Uu),Uua) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(uminus_uminus_int,one_one_int)),Uua)),aa_nat_int(semiri1314217659103216013at_int,Uua))),aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(aa_nat_fun_nat_nat(binomial,Uu),Uua))) ).

% ATP.lambda_59
tff(fact_8010_ATP_Olambda__60,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat_rat(aTP_Lamm_iq(Uu),Uua) = aa_rat_rat(divide_divide_rat(aa_nat_rat(gbinomial_rat(aa_nat_rat(semiri681578069525770553at_rat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uu),Uua))),Uua)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one))),Uua)) ).

% ATP.lambda_60
tff(fact_8011_ATP_Olambda__61,axiom,
    ! [Uu: code_integer,Uua: code_integer] :
      aa_Code_integer_int(aa_Cod1242632294114111009er_int(aTP_Lamm_kk,Uu),Uua) = $let(
        l2: int,
        l2:= aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_Code_integer_int(code_int_of_integer,Uu)),
        $ite(Uua = zero_z3403309356797280102nteger,l2,aa_int_int(aa_int_fun_int_int(plus_plus_int,l2),one_one_int)) ) ).

% ATP.lambda_61
tff(fact_8012_ATP_Olambda__62,axiom,
    ! [Uu: product_prod_int_int,Uua: product_prod_int_int] : aa_Pro6970504127699319548nt_int(aa_Pro4124234152028750080nt_int(aTP_Lamm_aca,Uu),Uua) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_Pro6799258434465214121nt_int(product_fst_int_int,Uu)),aa_Pro6799258434465214121nt_int(product_fst_int_int,Uua))),aa_int_int(aa_int_fun_int_int(times_times_int,aa_Pro6799258434465214121nt_int(product_snd_int_int,Uu)),aa_Pro6799258434465214121nt_int(product_snd_int_int,Uua))) ).

% ATP.lambda_62
tff(fact_8013_ATP_Olambda__63,axiom,
    ! [Uu: rat,Uua: int] :
      ( aa_int_o(aa_rat_fun_int_o(aTP_Lamm_adi,Uu),Uua)
    <=> ( aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,aa_int_rat(ring_1_of_int_rat,Uua)),Uu)
        & aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,Uu),aa_int_rat(ring_1_of_int_rat,aa_int_int(aa_int_fun_int_int(plus_plus_int,Uua),one_one_int))) ) ) ).

% ATP.lambda_63
tff(fact_8014_ATP_Olambda__64,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat_Code_integer(aTP_Lamm_iu(Uu),Uua) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,one_one_Code_integer)),Uua)),aa_nat_Code_integer(semiri4939895301339042750nteger,aa_nat_nat(aa_nat_fun_nat_nat(binomial,Uu),Uua))) ).

% ATP.lambda_64
tff(fact_8015_ATP_Olambda__65,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat_rat(aTP_Lamm_is(Uu),Uua) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),Uua)),aa_nat_rat(semiri681578069525770553at_rat,aa_nat_nat(aa_nat_fun_nat_nat(binomial,Uu),Uua))) ).

% ATP.lambda_65
tff(fact_8016_ATP_Olambda__66,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat_int(aa_nat_fun_nat_int(aTP_Lamm_it,Uu),Uua) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_int_int(uminus_uminus_int,one_one_int)),Uua)),aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(aa_nat_fun_nat_nat(binomial,Uu),Uua))) ).

% ATP.lambda_66
tff(fact_8017_ATP_Olambda__67,axiom,
    ! [Uu: rat,Uua: nat] : aa_nat_rat(aTP_Lamm_ik(Uu),Uua) = aa_nat_rat(gbinomial_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,Uu),aa_nat_rat(semiri681578069525770553at_rat,Uua))),Uua) ).

% ATP.lambda_67
tff(fact_8018_ATP_Olambda__68,axiom,
    ! [Uu: rat,Uua: nat] : aa_nat_rat(aTP_Lamm_ii(Uu),Uua) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(gbinomial_rat(Uu),Uua)),aa_rat_rat(minus_minus_rat(aa_rat_rat(divide_divide_rat(Uu),aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one)))),aa_nat_rat(semiri681578069525770553at_rat,Uua))) ).

% ATP.lambda_68
tff(fact_8019_ATP_Olambda__69,axiom,
    ! [Uu: rat,Uua: nat] : aa_nat_rat(aTP_Lamm_il(Uu),Uua) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(gbinomial_rat(Uu),Uua)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(uminus_uminus_rat,one_one_rat)),Uua)) ).

% ATP.lambda_69
tff(fact_8020_ATP_Olambda__70,axiom,
    ! [Uu: set_set_Code_integer,Uua: set_set_Code_integer] :
      ( aa_set6460979282782877649eger_o(aTP_Lamm_uh(Uu),Uua)
    <=> ( ord_le1914454125413604393nteger(Uua,Uu)
        & ( Uua != bot_bo9204850693367297629nteger ) ) ) ).

% ATP.lambda_70
tff(fact_8021_ATP_Olambda__71,axiom,
    ! [Uu: set_set_Product_unit,Uua: set_set_Product_unit] :
      ( aa_set1868964232251763271unit_o(aTP_Lamm_ub(Uu),Uua)
    <=> ( ord_le3674001228145610605t_unit(Uua,Uu)
        & ( Uua != bot_bo6284674557190688313t_unit ) ) ) ).

% ATP.lambda_71
tff(fact_8022_ATP_Olambda__72,axiom,
    ! [Uu: set_se7855581050983116737at_nat,Uua: set_se7855581050983116737at_nat] :
      ( aa_set5218765425691562963_nat_o(aTP_Lamm_uj(Uu),Uua)
    <=> ( ord_le2077887516847798113at_nat(Uua,Uu)
        & ( Uua != bot_bo3083307316010499117at_nat ) ) ) ).

% ATP.lambda_72
tff(fact_8023_ATP_Olambda__73,axiom,
    ! [Uu: set_set_list_nat,Uua: set_set_list_nat] :
      ( aa_set7045010141486209806_nat_o(aTP_Lamm_ud(Uu),Uua)
    <=> ( ord_le1068707526560357548st_nat(Uua,Uu)
        & ( Uua != bot_bo3886227569956363488st_nat ) ) ) ).

% ATP.lambda_73
tff(fact_8024_ATP_Olambda__74,axiom,
    ! [Uu: set_set_nat,Uua: set_set_nat] :
      ( aa_set_set_nat_o(aTP_Lamm_ul(Uu),Uua)
    <=> ( ord_le6893508408891458716et_nat(Uua,Uu)
        & ( Uua != bot_bot_set_set_nat ) ) ) ).

% ATP.lambda_74
tff(fact_8025_ATP_Olambda__75,axiom,
    ! [Uu: set_set_int,Uua: set_set_int] :
      ( aa_set_set_int_o(aTP_Lamm_uf(Uu),Uua)
    <=> ( ord_le4403425263959731960et_int(Uua,Uu)
        & ( Uua != bot_bot_set_set_int ) ) ) ).

% ATP.lambda_75
tff(fact_8026_ATP_Olambda__76,axiom,
    ! [Uu: set_op239864471688321678it_nat,Uua: option8956607266484857688it_nat] :
      ( aa_opt8360315729766332930_nat_o(aTP_Lamm_nw(Uu),Uua)
    <=> ( member5596548051065438575it_nat(Uua,Uu)
        & ( Uua != none_P9117596204409417319it_nat ) ) ) ).

% ATP.lambda_76
tff(fact_8027_ATP_Olambda__77,axiom,
    ! [Uu: set_op3940070208846178154it_nat,Uua: option3216581401566546698it_nat] :
      ( aa_opt4809530629565672394_nat_o(aTP_Lamm_nu(Uu),Uua)
    <=> ( member3517700364412436275it_nat(Uua,Uu)
        & ( Uua != none_P2587165478634041381it_nat ) ) ) ).

% ATP.lambda_77
tff(fact_8028_ATP_Olambda__78,axiom,
    ! [Uu: set_option_num,Uua: option_num] :
      ( aa_option_num_o(aTP_Lamm_nv(Uu),Uua)
    <=> ( member_option_num(Uua,Uu)
        & ( Uua != none_num ) ) ) ).

% ATP.lambda_78
tff(fact_8029_ATP_Olambda__79,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_jd,Uu),Uua) = aa_nat_nat(aa_nat_fun_nat_nat(binomial,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uu),Uua)),Uu) ).

% ATP.lambda_79
tff(fact_8030_ATP_Olambda__80,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_jc,Uu),Uua) = aa_nat_nat(aa_nat_fun_nat_nat(binomial,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uu),Uua)),Uua) ).

% ATP.lambda_80
tff(fact_8031_ATP_Olambda__81,axiom,
    ! [Uu: set_Pr1261947904930325089at_nat,Uua: set_Pr1261947904930325089at_nat] : aa_set1427696295806717282at_nat(aTP_Lamm_abo(Uu),Uua) = aa_set4883462369968598652at_nat(insert9069300056098147895at_nat(produc2922128104949294807at_nat(Uu,Uua)),bot_bo228742789529271731at_nat) ).

% ATP.lambda_81
tff(fact_8032_ATP_Olambda__82,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat7062706319057040595at_nat(aTP_Lamm_abq(Uu),Uua) = aa_set8868280134176360700at_nat(insert8211810215607154385at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Uu),Uua)),bot_bo2099793752762293965at_nat) ).

% ATP.lambda_82
tff(fact_8033_ATP_Olambda__83,axiom,
    ! [Uu: fun_Pr5098669352780829690e_term,Uua: produc8923325533196201883nteger] : aa_Pro659252730400088491nteger(aTP_Lamm_abe(Uu),Uua) = aa_set4655596970315180246nteger(insert4459515811902188230nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,Uu),Uua)),bot_bo9050247954524366304nteger) ).

% ATP.lambda_83
tff(fact_8034_ATP_Olambda__84,axiom,
    ! [Uu: fun_Pr6460944699146269935_nat_o,Uua: produc3658429121746597890et_nat] : aa_Pro3465147227354336150et_nat(aTP_Lamm_abg(Uu),Uua) = aa_set4110577973744520298et_nat(insert663245765287195472et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,Uu),Uua)),bot_bo1493351289776401898et_nat) ).

% ATP.lambda_84
tff(fact_8035_ATP_Olambda__85,axiom,
    ! [Uu: fun_Pr6460944699146269935_nat_o,Uua: produc8799533983703829792et_nat] : aa_Pro1476848909050865746et_nat(aTP_Lamm_abi(Uu),Uua) = aa_set7201747738020000294et_nat(insert727258735945777134et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,Uu),Uua)),bot_bo6121529163330120712et_nat) ).

% ATP.lambda_85
tff(fact_8036_ATP_Olambda__86,axiom,
    ! [Uu: fun_Pr7763680713840462443e_term,Uua: product_prod_int_int] : aa_Pro1072212120072018102nt_int(aTP_Lamm_abk(Uu),Uua) = aa_set3423462778074857648nt_int(insert4130518925788644403nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,Uu),Uua)),bot_bo2501116328598523085nt_int) ).

% ATP.lambda_86
tff(fact_8037_ATP_Olambda__87,axiom,
    ! [Uu: fun_in5730379987311621695e_term,Uua: product_prod_int_int] : aa_Pro3986193103337010658nt_int(aTP_Lamm_abm(Uu),Uua) = aa_set3385707584125383432nt_int(insert845627424500119391nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,Uu),Uua)),bot_bo5189594446080201209nt_int) ).

% ATP.lambda_87
tff(fact_8038_ATP_Olambda__88,axiom,
    ! [Uu: fun_Co9066792663755620495ural_o,Uua: fun_Pr2548841491397842206atural] :
      ( aa_fun3223653959534381366ural_o(aTP_Lamm_xf(Uu),Uua)
    <=> ord_le2202040463148982292atural(image_220848230107539526atural(Uua,top_to1996260823553986621t_unit),collec1991479681304692691atural(produc7358226366420480123ural_o(Uu))) ) ).

% ATP.lambda_88
tff(fact_8039_ATP_Olambda__89,axiom,
    ! [Uu: fun_Co9066792663755620495ural_o,Uua: fun_na2094359461478415435atural] :
      ( aa_fun2422601084904007759ural_o(aTP_Lamm_xe(Uu),Uua)
    <=> ord_le2202040463148982292atural(image_4072043198136622805atural(Uua,top_top_set_nat),collec1991479681304692691atural(produc7358226366420480123ural_o(Uu))) ) ).

% ATP.lambda_89
tff(fact_8040_ATP_Olambda__90,axiom,
    ! [Uu: fun_Co9066792663755620495ural_o,Uua: fun_in4857920871562217639atural] :
      ( aa_fun3094526197865446643ural_o(aTP_Lamm_xg(Uu),Uua)
    <=> ord_le2202040463148982292atural(image_6835604608220425009atural(Uua,top_top_set_int),collec1991479681304692691atural(produc7358226366420480123ural_o(Uu))) ) ).

% ATP.lambda_90
tff(fact_8041_ATP_Olambda__91,axiom,
    ! [Uu: fun_Co2081214437782444048eger_o,Uua: fun_Pr864343514034809617nteger] :
      ( aa_fun6524165814161438345eger_o(aTP_Lamm_xa(Uu),Uua)
    <=> ord_le3725938330318615451nteger(image_8089323762101378259nteger(Uua,top_to1996260823553986621t_unit),collec7766031446232907142nteger(produc2066375834425727024eger_o(Uu))) ) ).

% ATP.lambda_91
tff(fact_8042_ATP_Olambda__92,axiom,
    ! [Uu: fun_Co2081214437782444048eger_o,Uua: fun_na3822476419092417572nteger] :
      ( aa_fun4972185446673663664eger_o(aTP_Lamm_wy(Uu),Uua)
    <=> ord_le3725938330318615451nteger(image_4272405876590741764nteger(Uua,top_top_set_nat),collec7766031446232907142nteger(produc2066375834425727024eger_o(Uu))) ) ).

% ATP.lambda_92
tff(fact_8043_ATP_Olambda__93,axiom,
    ! [Uu: fun_Co2081214437782444048eger_o,Uua: fun_in4744367027289715400nteger] :
      ( aa_fun6795050498662842124eger_o(aTP_Lamm_xc(Uu),Uua)
    <=> ord_le3725938330318615451nteger(image_5194296484788039592nteger(Uua,top_top_set_int),collec7766031446232907142nteger(produc2066375834425727024eger_o(Uu))) ) ).

% ATP.lambda_93
tff(fact_8044_ATP_Olambda__94,axiom,
    ! [Uu: fun_int_fun_int_o,Uua: fun_Pr6733608168372577327nt_int] :
      ( aa_fun7140827668162456043_int_o(aTP_Lamm_xb(Uu),Uua)
    <=> ord_le2843351958646193337nt_int(image_4103462098156874993nt_int(Uua,top_to1996260823553986621t_unit),collec213857154873943460nt_int(produc4947309494688390418_int_o(Uu))) ) ).

% ATP.lambda_94
tff(fact_8045_ATP_Olambda__95,axiom,
    ! [Uu: fun_int_fun_int_o,Uua: fun_na1173468842265550146nt_int] :
      ( aa_fun6509235634262356498_int_o(aTP_Lamm_wz(Uu),Uua)
    <=> ord_le2843351958646193337nt_int(image_2667626500211843362nt_int(Uua,top_top_set_nat),collec213857154873943460nt_int(produc4947309494688390418_int_o(Uu))) ) ).

% ATP.lambda_95
tff(fact_8046_ATP_Olambda__96,axiom,
    ! [Uu: fun_int_fun_int_o,Uua: fun_in4211310926729683942nt_int] :
      ( aa_fun8476666123149806190_int_o(aTP_Lamm_xd(Uu),Uua)
    <=> ord_le2843351958646193337nt_int(image_5705468584675977158nt_int(Uua,top_top_set_int),collec213857154873943460nt_int(produc4947309494688390418_int_o(Uu))) ) ).

% ATP.lambda_96
tff(fact_8047_ATP_Olambda__97,axiom,
    ! [Uu: fun_fu7564235448449272366at_o_o,Uua: fun_in7664021439913478804_nat_o] :
      ( aa_fun5734334393156979392at_o_o(aTP_Lamm_xh(Uu),Uua)
    <=> ord_le9038753718846915815_nat_o(image_7736141092170400500_nat_o(Uua,top_top_set_int),collec8329916443099062226_nat_o(produc8121780756122614700at_o_o(Uu))) ) ).

% ATP.lambda_97
tff(fact_8048_ATP_Olambda__98,axiom,
    ! [Uu: fun_Pr864343514034809617nteger,Uua: code_integer] : aa_Cod2813182003028390446nteger(aTP_Lamm_wx(Uu),Uua) = image_3815118110082124069nteger(comp_P659088277599099894t_unit(produc6174133586879617921nteger,Uu),top_to1996260823553986621t_unit) ).

% ATP.lambda_98
tff(fact_8049_ATP_Olambda__99,axiom,
    ! [Uu: fun_na3822476419092417572nteger,Uua: code_integer] : aa_Cod2813182003028390446nteger(aTP_Lamm_wv(Uu),Uua) = image_1215581382706833972nteger(comp_P3109732533133679783er_nat(produc6174133586879617921nteger,Uu),top_top_set_nat) ).

% ATP.lambda_99
tff(fact_8050_ATP_Olambda__100,axiom,
    ! [Uu: fun_na8176081009732395159er_nat,Uua: code_integer] : aa_Cod6142706534279259169et_nat(aTP_Lamm_wo(Uu),Uua) = aa_set_nat_set_nat(image_nat_nat(comp_P1337767177661389325at_nat(produc1517335558169710324er_nat,Uu)),top_top_set_nat) ).

% ATP.lambda_100
tff(fact_8051_ATP_Olambda__101,axiom,
    ! [Uu: fun_na5685997864800668403er_int,Uua: code_integer] : aa_Cod1964855514770062461et_int(aTP_Lamm_wp(Uu),Uua) = image_nat_int(comp_P8345930540558018757nt_nat(produc1514845087660660048er_int,Uu),top_top_set_nat) ).

% ATP.lambda_101
tff(fact_8052_ATP_Olambda__102,axiom,
    ! [Uu: fun_na1596024190920976919nteger,Uua: nat] : aa_nat8922193080109606305nteger(aTP_Lamm_wq(Uu),Uua) = image_1215581382706833972nteger(comp_P5461341465284484122er_nat(produc1781891006948753140nteger,Uu),top_top_set_nat) ).

% ATP.lambda_102
tff(fact_8053_ATP_Olambda__103,axiom,
    ! [Uu: fun_na1476630412504255114at_nat,Uua: nat] : aa_nat_set_nat(aTP_Lamm_wr(Uu),Uua) = aa_set_nat_set_nat(image_nat_nat(comp_P1955610211387027840at_nat(product_snd_nat_nat,Uu)),top_top_set_nat) ).

% ATP.lambda_103
tff(fact_8054_ATP_Olambda__104,axiom,
    ! [Uu: fun_na8209919304427304166at_int,Uua: nat] : aa_nat_set_int(aTP_Lamm_ws(Uu),Uua) = image_nat_int(comp_P8963773574283657272nt_nat(product_snd_nat_int,Uu),top_top_set_nat) ).

% ATP.lambda_104
tff(fact_8055_ATP_Olambda__105,axiom,
    ! [Uu: fun_na7604833841916551795nteger,Uua: int] : aa_int6612375148016655357nteger(aTP_Lamm_wt(Uu),Uua) = image_1215581382706833972nteger(comp_P6870028373966156406er_nat(produc2153544567185597776nteger,Uu),top_top_set_nat) ).

% ATP.lambda_105
tff(fact_8056_ATP_Olambda__106,axiom,
    ! [Uu: fun_na3663551987197276902nt_nat,Uua: int] : aa_int_set_nat(aTP_Lamm_wu(Uu),Uua) = aa_set_nat_set_nat(image_nat_nat(comp_P8869164316148852700at_nat(product_snd_int_nat,Uu)),top_top_set_nat) ).

% ATP.lambda_106
tff(fact_8057_ATP_Olambda__107,axiom,
    ! [Uu: fun_na1173468842265550146nt_int,Uua: int] : aa_int_set_int(aTP_Lamm_ww(Uu),Uua) = image_nat_int(comp_P6653955642190706324nt_nat(product_snd_int_int,Uu),top_top_set_nat) ).

% ATP.lambda_107
tff(fact_8058_ATP_Olambda__108,axiom,
    ! [Uu: fun_nat_assn,Uua: nat] : aa_nat_assn(aTP_Lamm_lv(Uu),Uua) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_nat_assn(Uu,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),Uua))),aa_nat_assn(Uu,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),Uua)))) ).

% ATP.lambda_108
tff(fact_8059_ATP_Olambda__109,axiom,
    ! [Uu: fun_nat_rat,Uua: nat] : aa_nat_rat(aTP_Lamm_lw(Uu),Uua) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(Uu,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),Uua))),aa_nat_rat(Uu,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),Uua)))) ).

% ATP.lambda_109
tff(fact_8060_ATP_Olambda__110,axiom,
    ! [Uu: fun_nat_nat,Uua: nat] : aa_nat_nat(aTP_Lamm_lx(Uu),Uua) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(Uu,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),Uua))),aa_nat_nat(Uu,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),Uua)))) ).

% ATP.lambda_110
tff(fact_8061_ATP_Olambda__111,axiom,
    ! [Uu: fun_nat_int,Uua: nat] : aa_nat_int(aTP_Lamm_ly(Uu),Uua) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(Uu,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),Uua))),aa_nat_int(Uu,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),Uua)))) ).

% ATP.lambda_111
tff(fact_8062_ATP_Olambda__112,axiom,
    ! [Uu: fun_na2338080690716861136at_nat,Uua: nat] : aa_nat2240542744625857721at_nat(aTP_Lamm_ge(Uu),Uua) = aa_mul5754855110707352700at_nat(plus_p7104986032573967614at_nat(aa_nat2240542744625857721at_nat(Uu,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),Uua))),aa_nat2240542744625857721at_nat(Uu,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),Uua)))) ).

% ATP.lambda_112
tff(fact_8063_ATP_Olambda__113,axiom,
    ! [Uu: fun_nat_rat,Uua: nat] : aa_nat_rat(aTP_Lamm_gf(Uu),Uua) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(Uu,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),Uua))),aa_nat_rat(Uu,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),Uua)))) ).

% ATP.lambda_113
tff(fact_8064_ATP_Olambda__114,axiom,
    ! [Uu: fun_nat_nat,Uua: nat] : aa_nat_nat(aTP_Lamm_gh(Uu),Uua) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(Uu,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),Uua))),aa_nat_nat(Uu,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),Uua)))) ).

% ATP.lambda_114
tff(fact_8065_ATP_Olambda__115,axiom,
    ! [Uu: fun_nat_int,Uua: nat] : aa_nat_int(aTP_Lamm_gg(Uu),Uua) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(Uu,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),Uua))),aa_nat_int(Uu,aa_nat_nat(suc,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),Uua)))) ).

% ATP.lambda_115
tff(fact_8066_ATP_Olambda__116,axiom,
    ! [Uu: fun_nat_Code_integer,Uua: nat] : aa_nat_Code_integer(aTP_Lamm_ds(Uu),Uua) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_nat_Code_integer(Uu,aa_nat_nat(suc,Uua))),aa_nat_Code_integer(Uu,Uua)) ).

% ATP.lambda_116
tff(fact_8067_ATP_Olambda__117,axiom,
    ! [Uu: fun_nat_rat,Uua: nat] : aa_nat_rat(aTP_Lamm_dt(Uu),Uua) = aa_rat_rat(minus_minus_rat(aa_nat_rat(Uu,aa_nat_nat(suc,Uua))),aa_nat_rat(Uu,Uua)) ).

% ATP.lambda_117
tff(fact_8068_ATP_Olambda__118,axiom,
    ! [Uu: fun_nat_int,Uua: nat] : aa_nat_int(aTP_Lamm_du(Uu),Uua) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(Uu,aa_nat_nat(suc,Uua))),aa_nat_int(Uu,Uua)) ).

% ATP.lambda_118
tff(fact_8069_ATP_Olambda__119,axiom,
    ! [Uu: fun_nat_fun_nat_nat,Uua: nat] : aa_nat_nat(aTP_Lamm_kx(Uu),Uua) = aa_set_nat_nat(groups708209901874060359at_nat(aa_nat_fun_nat_nat(Uu,Uua)),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),Uua)) ).

% ATP.lambda_119
tff(fact_8070_ATP_Olambda__120,axiom,
    ! [Uu: fun_nat_fun_nat_int,Uua: nat] : aa_nat_int(aTP_Lamm_kz(Uu),Uua) = groups705719431365010083at_int(aa_nat_fun_nat_int(Uu,Uua),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),Uua)) ).

% ATP.lambda_120
tff(fact_8071_ATP_Olambda__121,axiom,
    ! [Uu: fun_nat_fun_nat_nat,Uua: nat] : aa_nat_nat(aTP_Lamm_kd(Uu),Uua) = aa_set_nat_nat(groups3542108847815614940at_nat(aa_nat_fun_nat_nat(Uu,Uua)),aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),Uua)) ).

% ATP.lambda_121
tff(fact_8072_ATP_Olambda__122,axiom,
    ! [Uu: fun_nat_Code_integer,Uua: nat] : aa_nat_Code_integer(aTP_Lamm_cr(Uu),Uua) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_nat_Code_integer(Uu,Uua)),aa_nat_Code_integer(Uu,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uua),one_one_nat))) ).

% ATP.lambda_122
tff(fact_8073_ATP_Olambda__123,axiom,
    ! [Uu: fun_nat_rat,Uua: nat] : aa_nat_rat(aTP_Lamm_cs(Uu),Uua) = aa_rat_rat(minus_minus_rat(aa_nat_rat(Uu,Uua)),aa_nat_rat(Uu,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uua),one_one_nat))) ).

% ATP.lambda_123
tff(fact_8074_ATP_Olambda__124,axiom,
    ! [Uu: fun_nat_int,Uua: nat] : aa_nat_int(aTP_Lamm_ct(Uu),Uua) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(Uu,Uua)),aa_nat_int(Uu,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uua),one_one_nat))) ).

% ATP.lambda_124
tff(fact_8075_ATP_Olambda__125,axiom,
    ! [Uu: fun_nat_Code_integer,Uua: nat] : aa_nat_Code_integer(aTP_Lamm_ed(Uu),Uua) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_nat_Code_integer(Uu,Uua)),aa_nat_Code_integer(Uu,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uua),one_one_nat))) ).

% ATP.lambda_125
tff(fact_8076_ATP_Olambda__126,axiom,
    ! [Uu: fun_nat_rat,Uua: nat] : aa_nat_rat(aTP_Lamm_ee(Uu),Uua) = aa_rat_rat(minus_minus_rat(aa_nat_rat(Uu,Uua)),aa_nat_rat(Uu,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uua),one_one_nat))) ).

% ATP.lambda_126
tff(fact_8077_ATP_Olambda__127,axiom,
    ! [Uu: fun_nat_int,Uua: nat] : aa_nat_int(aTP_Lamm_ef(Uu),Uua) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(Uu,Uua)),aa_nat_int(Uu,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uua),one_one_nat))) ).

% ATP.lambda_127
tff(fact_8078_ATP_Olambda__128,axiom,
    ! [Uu: fun_nat_Code_integer,Uua: nat] : aa_nat_Code_integer(aTP_Lamm_ho(Uu),Uua) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_nat_Code_integer(Uu,Uua)),aa_nat_Code_integer(Uu,aa_nat_nat(suc,Uua))) ).

% ATP.lambda_128
tff(fact_8079_ATP_Olambda__129,axiom,
    ! [Uu: fun_nat_rat,Uua: nat] : aa_nat_rat(aTP_Lamm_hp(Uu),Uua) = aa_rat_rat(minus_minus_rat(aa_nat_rat(Uu,Uua)),aa_nat_rat(Uu,aa_nat_nat(suc,Uua))) ).

% ATP.lambda_129
tff(fact_8080_ATP_Olambda__130,axiom,
    ! [Uu: fun_nat_int,Uua: nat] : aa_nat_int(aTP_Lamm_hq(Uu),Uua) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(Uu,Uua)),aa_nat_int(Uu,aa_nat_nat(suc,Uua))) ).

% ATP.lambda_130
tff(fact_8081_ATP_Olambda__131,axiom,
    ! [Uu: fun_nat_fun_nat_nat,Uua: nat] : aa_nat_nat(aTP_Lamm_le(Uu),Uua) = aa_set_nat_nat(groups708209901874060359at_nat(aa_nat_fun_nat_nat(Uu,Uua)),aa_nat_set_nat(set_ord_lessThan_nat,Uua)) ).

% ATP.lambda_131
tff(fact_8082_ATP_Olambda__132,axiom,
    ! [Uu: fun_nat_fun_nat_int,Uua: nat] : aa_nat_int(aTP_Lamm_lf(Uu),Uua) = groups705719431365010083at_int(aa_nat_fun_nat_int(Uu,Uua),aa_nat_set_nat(set_ord_lessThan_nat,Uua)) ).

% ATP.lambda_132
tff(fact_8083_ATP_Olambda__133,axiom,
    ! [Uu: fun_nat_fun_nat_nat,Uua: nat] : aa_nat_nat(aTP_Lamm_iz(Uu),Uua) = aa_set_nat_nat(groups3542108847815614940at_nat(aa_nat_fun_nat_nat(Uu,Uua)),aa_nat_set_nat(set_ord_lessThan_nat,Uua)) ).

% ATP.lambda_133
tff(fact_8084_ATP_Olambda__134,axiom,
    ! [Uu: fun_Co8499238673658658103nteger,Uua: code_integer] :
      ( aa_Code_integer_o(aTP_Lamm_rr(Uu),Uua)
    <=> ( aa_Cod1783974652533396728nteger(Uu,Uua) = one_one_Code_integer ) ) ).

% ATP.lambda_134
tff(fact_8085_ATP_Olambda__135,axiom,
    ! [Uu: fun_Co4490034186337852034r_assn,Uua: code_integer] :
      ( aa_Code_integer_o(aTP_Lamm_rt(Uu),Uua)
    <=> ( aa_Code_integer_assn(Uu,Uua) = one_one_assn ) ) ).

% ATP.lambda_135
tff(fact_8086_ATP_Olambda__136,axiom,
    ! [Uu: fun_Code_integer_rat,Uua: code_integer] :
      ( aa_Code_integer_o(aTP_Lamm_rv(Uu),Uua)
    <=> ( aa_Code_integer_rat(Uu,Uua) = one_one_rat ) ) ).

% ATP.lambda_136
tff(fact_8087_ATP_Olambda__137,axiom,
    ! [Uu: fun_Code_integer_nat,Uua: code_integer] :
      ( aa_Code_integer_o(aTP_Lamm_rx(Uu),Uua)
    <=> ( aa_Code_integer_nat(Uu,Uua) = one_one_nat ) ) ).

% ATP.lambda_137
tff(fact_8088_ATP_Olambda__138,axiom,
    ! [Uu: fun_Code_integer_int,Uua: code_integer] :
      ( aa_Code_integer_o(aTP_Lamm_ry(Uu),Uua)
    <=> ( aa_Code_integer_int(Uu,Uua) = one_one_int ) ) ).

% ATP.lambda_138
tff(fact_8089_ATP_Olambda__139,axiom,
    ! [Uu: fun_nat_Code_integer,Uua: nat] :
      ( aa_nat_o(aTP_Lamm_rz(Uu),Uua)
    <=> ( aa_nat_Code_integer(Uu,Uua) = one_one_Code_integer ) ) ).

% ATP.lambda_139
tff(fact_8090_ATP_Olambda__140,axiom,
    ! [Uu: fun_int_Code_integer,Uua: int] :
      ( aa_int_o(aTP_Lamm_rq(Uu),Uua)
    <=> ( aa_int_Code_integer(Uu,Uua) = one_one_Code_integer ) ) ).

% ATP.lambda_140
tff(fact_8091_ATP_Olambda__141,axiom,
    ! [Uu: fun_int_assn,Uua: int] :
      ( aa_int_o(aTP_Lamm_rs(Uu),Uua)
    <=> ( aa_int_assn(Uu,Uua) = one_one_assn ) ) ).

% ATP.lambda_141
tff(fact_8092_ATP_Olambda__142,axiom,
    ! [Uu: fun_int_rat,Uua: int] :
      ( aa_int_o(aTP_Lamm_ru(Uu),Uua)
    <=> ( aa_int_rat(Uu,Uua) = one_one_rat ) ) ).

% ATP.lambda_142
tff(fact_8093_ATP_Olambda__143,axiom,
    ! [Uu: fun_int_nat,Uua: int] :
      ( aa_int_o(aTP_Lamm_rw(Uu),Uua)
    <=> ( aa_int_nat(Uu,Uua) = one_one_nat ) ) ).

% ATP.lambda_143
tff(fact_8094_ATP_Olambda__144,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_ty,Uu),Uua) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(nat_triangle,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uu),Uua))),Uu) ).

% ATP.lambda_144
tff(fact_8095_ATP_Olambda__145,axiom,
    ! [Uu: num,Uua: num] : aa_num_int(aTP_Lamm_hd(Uu),Uua) = aa_int_int(aa_nat_fun_int_int(bit_se2923211474154528505it_int,aa_num_nat(numeral_numeral_nat,Uu)),aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),aa_num_nat(numeral_numeral_nat,Uu))),aa_num_int(numeral_numeral_int,Uua))) ).

% ATP.lambda_145
tff(fact_8096_ATP_Olambda__146,axiom,
    ! [Uu: num,Uua: num] : aa_num_int(aa_num_fun_num_int(aTP_Lamm_nr,Uu),Uua) = aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_num_int(numeral_numeral_int,Uu)),aa_num_int(numeral_numeral_int,Uua)) ).

% ATP.lambda_146
tff(fact_8097_ATP_Olambda__147,axiom,
    ! [Uu: code_integer,Uua: code_integer] :
      aa_Code_integer_num(aa_Cod6128727250572145423er_num(aTP_Lamm_kb,Uu),Uua) = $let(
        l2: num,
        l2:= aa_Code_integer_num(code_num_of_integer,Uu),
        $let(
          l3: num,
          l3:= aa_num_num(aa_num_fun_num_num(plus_plus_num,l2),l2),
          $ite(Uua = zero_z3403309356797280102nteger,l3,aa_num_num(aa_num_fun_num_num(plus_plus_num,l3),one)) ) ) ).

% ATP.lambda_147
tff(fact_8098_ATP_Olambda__148,axiom,
    ! [Uu: code_integer,Uua: code_integer] :
      aa_Code_integer_nat(aa_Cod5420483313623307717er_nat(aTP_Lamm_ki,Uu),Uua) = $let(
        l2: nat,
        l2:= aa_Code_integer_nat(code_nat_of_integer,Uu),
        $let(
          l3: nat,
          l3:= aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,l2),l2),
          $ite(Uua = zero_z3403309356797280102nteger,l3,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,l3),one_one_nat)) ) ) ).

% ATP.lambda_148
tff(fact_8099_ATP_Olambda__149,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat_rat(aTP_Lamm_im(Uu),Uua) = aa_nat_rat(gbinomial_rat(aa_nat_rat(semiri681578069525770553at_rat,Uua)),Uu) ).

% ATP.lambda_149
tff(fact_8100_ATP_Olambda__150,axiom,
    ! [Uu: code_integer,Uua: code_integer] : aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(aTP_Lamm_gv,Uu),Uua) = aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(Uu),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),Uua)),one_one_Code_integer)) ).

% ATP.lambda_150
tff(fact_8101_ATP_Olambda__151,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(aTP_Lamm_gx,Uu),Uua) = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Uu),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),Uua)),one_one_nat)) ).

% ATP.lambda_151
tff(fact_8102_ATP_Olambda__152,axiom,
    ! [Uu: int,Uua: int] : aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(aTP_Lamm_gw,Uu),Uua) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Uu),aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),Uua)),one_one_int)) ).

% ATP.lambda_152
tff(fact_8103_ATP_Olambda__153,axiom,
    ! [Uu: code_integer,Uua: code_integer] : aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(aTP_Lamm_gs,Uu),Uua) = aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(Uu),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),Uua)) ).

% ATP.lambda_153
tff(fact_8104_ATP_Olambda__154,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(aTP_Lamm_gu,Uu),Uua) = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Uu),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),Uua)) ).

% ATP.lambda_154
tff(fact_8105_ATP_Olambda__155,axiom,
    ! [Uu: int,Uua: int] : aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(aTP_Lamm_gt,Uu),Uua) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Uu),aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),Uua)) ).

% ATP.lambda_155
tff(fact_8106_ATP_Olambda__156,axiom,
    ! [Uu: rat,Uua: nat] : aa_nat_rat(aTP_Lamm_kj(Uu),Uua) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,Uu),aa_rat_rat(divide_divide_rat(aa_nat_rat(semiri681578069525770553at_rat,Uua)),aa_num_rat(numeral_numeral_rat,aa_num_num(bit0,one)))) ).

% ATP.lambda_156
tff(fact_8107_ATP_Olambda__157,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_iv,Uu),Uua) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,Uua),aa_nat_nat(aa_nat_fun_nat_nat(binomial,Uu),Uua)) ).

% ATP.lambda_157
tff(fact_8108_ATP_Olambda__158,axiom,
    ! [Uu: product_unit,Uua: heap_e7401611519738050253t_unit] : aa_hea256619718444519449it_nat(aTP_Lamm_bs(Uu),Uua) = produc7133225469290080770it_nat(Uu,produc584006145561248582it_nat(Uua,zero_zero_nat)) ).

% ATP.lambda_158
tff(fact_8109_ATP_Olambda__159,axiom,
    ! [Uu: array_a,Uua: heap_e7401611519738050253t_unit] : aa_hea1118439097112461811it_nat(aTP_Lamm_br(Uu),Uua) = produc1733996804261680252it_nat(Uu,produc584006145561248582it_nat(Uua,zero_zero_nat)) ).

% ATP.lambda_159
tff(fact_8110_ATP_Olambda__160,axiom,
    ! [Uu: product_unit,Uua: heap_e7401611519738050253t_unit] : aa_hea256619718444519449it_nat(aTP_Lamm_ag(Uu),Uua) = produc7133225469290080770it_nat(Uu,produc584006145561248582it_nat(Uua,one_one_nat)) ).

% ATP.lambda_160
tff(fact_8111_ATP_Olambda__161,axiom,
    ! [Uu: array_a,Uua: heap_e7401611519738050253t_unit] : aa_hea1118439097112461811it_nat(aTP_Lamm_af(Uu),Uua) = produc1733996804261680252it_nat(Uu,produc584006145561248582it_nat(Uua,one_one_nat)) ).

% ATP.lambda_161
tff(fact_8112_ATP_Olambda__162,axiom,
    ! [Uu: int,Uua: int] : aa_int_int(aa_int_fun_int_int(aTP_Lamm_hu,Uu),Uua) = aa_int_int(aa_int_fun_int_int(plus_plus_int,Uu),aa_o_int(zero_n2684676970156552555ol_int,Uua != zero_zero_int)) ).

% ATP.lambda_162
tff(fact_8113_ATP_Olambda__163,axiom,
    ! [Uu: code_natural,Uua: nat] : aa_nat_Code_natural(aTP_Lamm_ln(Uu),Uua) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,Uu),aa_nat_Code_natural(semiri3763490453095760265atural,Uua)) ).

% ATP.lambda_163
tff(fact_8114_ATP_Olambda__164,axiom,
    ! [Uu: code_integer,Uua: nat] : aa_nat_Code_integer(aTP_Lamm_lm(Uu),Uua) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,Uu),aa_nat_Code_integer(semiri4939895301339042750nteger,Uua)) ).

% ATP.lambda_164
tff(fact_8115_ATP_Olambda__165,axiom,
    ! [Uu: rat,Uua: nat] : aa_nat_rat(aTP_Lamm_ll(Uu),Uua) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,Uu),aa_nat_rat(semiri681578069525770553at_rat,Uua)) ).

% ATP.lambda_165
tff(fact_8116_ATP_Olambda__166,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_lo,Uu),Uua) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uu),aa_nat_nat(semiri1316708129612266289at_nat,Uua)) ).

% ATP.lambda_166
tff(fact_8117_ATP_Olambda__167,axiom,
    ! [Uu: int,Uua: nat] : aa_nat_int(aTP_Lamm_lp(Uu),Uua) = aa_int_int(aa_int_fun_int_int(plus_plus_int,Uu),aa_nat_int(semiri1314217659103216013at_int,Uua)) ).

% ATP.lambda_167
tff(fact_8118_ATP_Olambda__168,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat_list_nat(aa_nat6157064778417537467st_nat(aTP_Lamm_adj,Uu),Uua) = cons_nat(Uu,nat_list_decode(Uua)) ).

% ATP.lambda_168
tff(fact_8119_ATP_Olambda__169,axiom,
    ! [Uu: set_nat,Uua: set_nat] :
      ( aa_set_nat_o(aTP_Lamm_hj(Uu),Uua)
    <=> aa_set_nat_o(ord_less_eq_set_nat(Uua),Uu) ) ).

% ATP.lambda_169
tff(fact_8120_ATP_Olambda__170,axiom,
    ! [Uu: rat,Uua: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(aTP_Lamm_hk,Uu),Uua)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_eq_rat,Uua),Uu) ) ).

% ATP.lambda_170
tff(fact_8121_ATP_Olambda__171,axiom,
    ! [Uu: num,Uua: num] :
      ( aa_num_o(aa_num_fun_num_o(aTP_Lamm_hl,Uu),Uua)
    <=> aa_num_o(aa_num_fun_num_o(ord_less_eq_num,Uua),Uu) ) ).

% ATP.lambda_171
tff(fact_8122_ATP_Olambda__172,axiom,
    ! [Uu: nat,Uua: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(aTP_Lamm_hn,Uu),Uua)
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,Uua),Uu) ) ).

% ATP.lambda_172
tff(fact_8123_ATP_Olambda__173,axiom,
    ! [Uu: int,Uua: int] :
      ( aa_int_o(aa_int_fun_int_o(aTP_Lamm_hm,Uu),Uua)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_eq_int,Uua),Uu) ) ).

% ATP.lambda_173
tff(fact_8124_ATP_Olambda__174,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_nt,Uu),Uua) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,Uua),Uu) ).

% ATP.lambda_174
tff(fact_8125_ATP_Olambda__175,axiom,
    ! [Uu: rat,Uua: rat] : aa_rat_rat(aTP_Lamm_mw(Uu),Uua) = aa_rat_rat(divide_divide_rat(Uua),Uu) ).

% ATP.lambda_175
tff(fact_8126_ATP_Olambda__176,axiom,
    ! [Uu: code_integer,Uua: code_integer] :
      ( aa_Code_integer_o(aa_Cod326357343816142457eger_o(aTP_Lamm_bd,Uu),Uua)
    <=> aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,Uua),Uu) ) ).

% ATP.lambda_176
tff(fact_8127_ATP_Olambda__177,axiom,
    ! [Uu: rat,Uua: rat] :
      ( aa_rat_o(aa_rat_fun_rat_o(aTP_Lamm_bf,Uu),Uua)
    <=> aa_rat_o(aa_rat_fun_rat_o(ord_less_rat,Uua),Uu) ) ).

% ATP.lambda_177
tff(fact_8128_ATP_Olambda__178,axiom,
    ! [Uu: num,Uua: num] :
      ( aa_num_o(aa_num_fun_num_o(aTP_Lamm_bh,Uu),Uua)
    <=> aa_num_o(aa_num_fun_num_o(ord_less_num,Uua),Uu) ) ).

% ATP.lambda_178
tff(fact_8129_ATP_Olambda__179,axiom,
    ! [Uu: nat,Uua: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(aTP_Lamm_bj,Uu),Uua)
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,Uua),Uu) ) ).

% ATP.lambda_179
tff(fact_8130_ATP_Olambda__180,axiom,
    ! [Uu: int,Uua: int] :
      ( aa_int_o(aa_int_fun_int_o(aTP_Lamm_bl,Uu),Uua)
    <=> aa_int_o(aa_int_fun_int_o(ord_less_int,Uua),Uu) ) ).

% ATP.lambda_180
tff(fact_8131_ATP_Olambda__181,axiom,
    ! [Uu: rat,Uua: rat] : aa_rat_rat(aTP_Lamm_no(Uu),Uua) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,Uua),Uu) ).

% ATP.lambda_181
tff(fact_8132_ATP_Olambda__182,axiom,
    ! [Uu: code_integer,Uua: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(aTP_Lamm_mv,Uu),Uua) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,Uua),Uu) ).

% ATP.lambda_182
tff(fact_8133_ATP_Olambda__183,axiom,
    ! [Uu: rat,Uua: rat] : aa_rat_rat(aTP_Lamm_mt(Uu),Uua) = aa_rat_rat(minus_minus_rat(Uua),Uu) ).

% ATP.lambda_183
tff(fact_8134_ATP_Olambda__184,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_ns,Uu),Uua) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uua),Uu) ).

% ATP.lambda_184
tff(fact_8135_ATP_Olambda__185,axiom,
    ! [Uu: int,Uua: int] : aa_int_int(aa_int_fun_int_int(aTP_Lamm_mu,Uu),Uua) = aa_int_int(aa_int_fun_int_int(minus_minus_int,Uua),Uu) ).

% ATP.lambda_185
tff(fact_8136_ATP_Olambda__186,axiom,
    ! [Uu: code_integer,Uua: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(aTP_Lamm_ms,Uu),Uua) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,Uua),Uu) ).

% ATP.lambda_186
tff(fact_8137_ATP_Olambda__187,axiom,
    ! [Uu: rat,Uua: rat] : aa_rat_rat(aTP_Lamm_mp(Uu),Uua) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,Uua),Uu) ).

% ATP.lambda_187
tff(fact_8138_ATP_Olambda__188,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_mr,Uu),Uua) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uua),Uu) ).

% ATP.lambda_188
tff(fact_8139_ATP_Olambda__189,axiom,
    ! [Uu: int,Uua: int] : aa_int_int(aa_int_fun_int_int(aTP_Lamm_mq,Uu),Uua) = aa_int_int(aa_int_fun_int_int(plus_plus_int,Uua),Uu) ).

% ATP.lambda_189
tff(fact_8140_ATP_Olambda__190,axiom,
    ! [Uu: code_natural,Uua: produc7822875418678951345atural] : aa_Pro5311756036668752637atural(aa_Cod3489170700911977190atural(aTP_Lamm_us,Uu),Uua) = produc1272419604612767874atural(Uua,Uu) ).

% ATP.lambda_190
tff(fact_8141_ATP_Olambda__191,axiom,
    ! [Uu: code_integer,Uua: code_integer] : aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(aTP_Lamm_ur,Uu),Uua) = aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(Uua),Uu) ).

% ATP.lambda_191
tff(fact_8142_ATP_Olambda__192,axiom,
    ! [Uu: produc7822875418678951345atural,Uua: code_natural] : aa_Cod6383727878942225636atural(aa_Pro4688176541098407832atural(aTP_Lamm_uu,Uu),Uua) = aa_Pro7165575656943818355atural(produc6639722614265839536atural(Uua),Uu) ).

% ATP.lambda_192
tff(fact_8143_ATP_Olambda__193,axiom,
    ! [Uu: produc8923325533196201883nteger,Uua: fun_Pr5098669352780829690e_term] : aa_fun8425650785172306510nteger(aa_Pro5774345223241026284nteger(aTP_Lamm_um,Uu),Uua) = aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,Uua),Uu) ).

% ATP.lambda_193
tff(fact_8144_ATP_Olambda__194,axiom,
    ! [Uu: produc3658429121746597890et_nat,Uua: fun_Pr6460944699146269935_nat_o] : aa_fun179180238660531795et_nat(aa_Pro3220439978920015074et_nat(aTP_Lamm_un,Uu),Uua) = aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,Uua),Uu) ).

% ATP.lambda_194
tff(fact_8145_ATP_Olambda__195,axiom,
    ! [Uu: product_prod_int_int,Uua: fun_Pr7763680713840462443e_term] : aa_fun9040010020517048364nt_int(aa_Pro7187055436517876584nt_int(aTP_Lamm_up,Uu),Uua) = aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,Uua),Uu) ).

% ATP.lambda_195
tff(fact_8146_ATP_Olambda__196,axiom,
    ! [Uu: product_prod_int_int,Uua: fun_in5730379987311621695e_term] : aa_fun3520829229142255404nt_int(aa_Pro3263785050932909160nt_int(aTP_Lamm_uq,Uu),Uua) = aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,Uua),Uu) ).

% ATP.lambda_196
tff(fact_8147_ATP_Olambda__197,axiom,
    ! [Uu: produc8799533983703829792et_nat,Uua: fun_Pr6460944699146269935_nat_o] : aa_fun8682008811809929585et_nat(aa_Pro8681318422064110306et_nat(aTP_Lamm_uo,Uu),Uua) = aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,Uua),Uu) ).

% ATP.lambda_197
tff(fact_8148_ATP_Olambda__198,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(aTP_Lamm_dg,Uu),Uua) = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Uua),Uu) ).

% ATP.lambda_198
tff(fact_8149_ATP_Olambda__199,axiom,
    ! [Uu: int,Uua: int] : aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(aTP_Lamm_ut,Uu),Uua) = aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Uua),Uu) ).

% ATP.lambda_199
tff(fact_8150_ATP_Olambda__200,axiom,
    ! [Uu: set_Pr4329608150637261639at_nat,Uua: produc3843707927480180839at_nat] :
      ( aa_Pro5947980084102686253_nat_o(aTP_Lamm_a(Uu),Uua)
    <=> member8757157785044589968at_nat(Uua,Uu) ) ).

% ATP.lambda_200
tff(fact_8151_ATP_Olambda__201,axiom,
    ! [Uu: set_Pr1261947904930325089at_nat,Uua: product_prod_nat_nat] :
      ( aa_Pro6150637604445964947_nat_o(aTP_Lamm_aa(Uu),Uua)
    <=> member8440522571783428010at_nat(Uua,Uu) ) ).

% ATP.lambda_201
tff(fact_8152_ATP_Olambda__202,axiom,
    ! [Uu: set_list_nat,Uua: list_nat] :
      ( aa_list_nat_o(aTP_Lamm_ae(Uu),Uua)
    <=> member_list_nat(Uua,Uu) ) ).

% ATP.lambda_202
tff(fact_8153_ATP_Olambda__203,axiom,
    ! [Uu: set_o,Uua: $o] :
      ( aa_o_o(aTP_Lamm_ab(Uu),(Uua))
    <=> member_o((Uua),Uu) ) ).

% ATP.lambda_203
tff(fact_8154_ATP_Olambda__204,axiom,
    ! [Uu: set_nat,Uua: nat] :
      ( aa_nat_o(aTP_Lamm_ad(Uu),Uua)
    <=> member_nat(Uua,Uu) ) ).

% ATP.lambda_204
tff(fact_8155_ATP_Olambda__205,axiom,
    ! [Uu: set_int,Uua: int] :
      ( aa_int_o(aTP_Lamm_ac(Uu),Uua)
    <=> member_int(Uua,Uu) ) ).

% ATP.lambda_205
tff(fact_8156_ATP_Olambda__206,axiom,
    ! [Uu: produc8664842809031399944it_nat,Uua: produc8664842809031399944it_nat] :
      ( aa_Pro4744234731172327378_nat_o(aTP_Lamm_ai(Uu),Uua)
    <=> ( Uua = Uu ) ) ).

% ATP.lambda_206
tff(fact_8157_ATP_Olambda__207,axiom,
    ! [Uu: num,Uua: num] :
      ( aa_num_o(aa_num_fun_num_o(aTP_Lamm_ah,Uu),Uua)
    <=> ( Uua = Uu ) ) ).

% ATP.lambda_207
tff(fact_8158_ATP_Olambda__208,axiom,
    ! [Uu: set_Pr2352657477744078772atural,Uua: code_natural] : aa_Cod7772718489437220139atural(aTP_Lamm_abu(Uu),Uua) = image_3837677093542026988atural(produc6591912806276919810atural,Uu) ).

% ATP.lambda_208
tff(fact_8159_ATP_Olambda__209,axiom,
    ! [Uu: set_Pr4811707699266497531nteger,Uua: code_integer] : aa_Cod2813182003028390446nteger(aTP_Lamm_abs(Uu),Uua) = image_6316824473203919795nteger(produc6174133586879617921nteger,Uu) ).

% ATP.lambda_209
tff(fact_8160_ATP_Olambda__210,axiom,
    ! [Uu: set_Pr958786334691620121nt_int,Uua: int] : aa_int_set_int(aTP_Lamm_abt(Uu),Uua) = image_5042161079198086560nt_int(product_snd_int_int,Uu) ).

% ATP.lambda_210
tff(fact_8161_ATP_Olambda__211,axiom,
    ! [Uu: fun_nat_nat,Uua: product_prod_nat_nat] : aa_Pro4243173770044397973at_nat(aTP_Lamm_uv(Uu),Uua) = aa_nat_nat(Uu,aa_Pro4243173770044397973at_nat(product_snd_nat_nat,Uua)) ).

% ATP.lambda_211
tff(fact_8162_ATP_Olambda__212,axiom,
    ! [Uu: fun_na8713714802964096592at_nat,Uua: product_prod_nat_nat] : aa_Pro8023792847356852296at_nat(aTP_Lamm_ux(Uu),Uua) = aa_nat7997280740862404369at_nat(Uu,aa_Pro4243173770044397973at_nat(product_snd_nat_nat,Uua)) ).

% ATP.lambda_212
tff(fact_8163_ATP_Olambda__213,axiom,
    ! [Uu: fun_na3970208099681795815_nat_o,Uua: product_prod_nat_nat] : aa_Pro989595756709598047_nat_o(aTP_Lamm_uz(Uu),Uua) = aa_nat7695548938202568488_nat_o(Uu,aa_Pro4243173770044397973at_nat(product_snd_nat_nat,Uua)) ).

% ATP.lambda_213
tff(fact_8164_ATP_Olambda__214,axiom,
    ! [Uu: fun_in4211310926729683942nt_int,Uua: product_prod_int_int] : aa_Pro6970504127699319548nt_int(aTP_Lamm_vb(Uu),Uua) = aa_int7462565939943104719nt_int(Uu,aa_Pro6799258434465214121nt_int(product_snd_int_int,Uua)) ).

% ATP.lambda_214
tff(fact_8165_ATP_Olambda__215,axiom,
    ! [Uu: fun_int_int,Uua: product_prod_int_int] : aa_Pro6799258434465214121nt_int(aTP_Lamm_vd(Uu),Uua) = aa_int_int(Uu,aa_Pro6799258434465214121nt_int(product_snd_int_int,Uua)) ).

% ATP.lambda_215
tff(fact_8166_ATP_Olambda__216,axiom,
    ! [Uu: fun_nat_nat,Uua: product_prod_nat_nat] : aa_Pro4243173770044397973at_nat(aTP_Lamm_vj(Uu),Uua) = aa_nat_nat(Uu,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,Uua)) ).

% ATP.lambda_216
tff(fact_8167_ATP_Olambda__217,axiom,
    ! [Uu: fun_na8713714802964096592at_nat,Uua: product_prod_nat_nat] : aa_Pro8023792847356852296at_nat(aTP_Lamm_vl(Uu),Uua) = aa_nat7997280740862404369at_nat(Uu,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,Uua)) ).

% ATP.lambda_217
tff(fact_8168_ATP_Olambda__218,axiom,
    ! [Uu: fun_na3970208099681795815_nat_o,Uua: product_prod_nat_nat] : aa_Pro989595756709598047_nat_o(aTP_Lamm_vn(Uu),Uua) = aa_nat7695548938202568488_nat_o(Uu,aa_Pro4243173770044397973at_nat(product_fst_nat_nat,Uua)) ).

% ATP.lambda_218
tff(fact_8169_ATP_Olambda__219,axiom,
    ! [Uu: fun_in4211310926729683942nt_int,Uua: product_prod_int_int] : aa_Pro6970504127699319548nt_int(aTP_Lamm_vp(Uu),Uua) = aa_int7462565939943104719nt_int(Uu,aa_Pro6799258434465214121nt_int(product_fst_int_int,Uua)) ).

% ATP.lambda_219
tff(fact_8170_ATP_Olambda__220,axiom,
    ! [Uu: fun_int_int,Uua: product_prod_int_int] : aa_Pro6799258434465214121nt_int(aTP_Lamm_vr(Uu),Uua) = aa_int_int(Uu,aa_Pro6799258434465214121nt_int(product_fst_int_int,Uua)) ).

% ATP.lambda_220
tff(fact_8171_ATP_Olambda__221,axiom,
    ! [Uu: fun_na2338080690716861136at_nat,Uua: nat] : aa_nat2240542744625857721at_nat(aTP_Lamm_dp(Uu),Uua) = aa_nat2240542744625857721at_nat(Uu,aa_nat_nat(suc,Uua)) ).

% ATP.lambda_221
tff(fact_8172_ATP_Olambda__222,axiom,
    ! [Uu: fun_nat_assn,Uua: nat] : aa_nat_assn(aTP_Lamm_kv(Uu),Uua) = aa_nat_assn(Uu,aa_nat_nat(suc,Uua)) ).

% ATP.lambda_222
tff(fact_8173_ATP_Olambda__223,axiom,
    ! [Uu: fun_nat_rat,Uua: nat] : aa_nat_rat(aTP_Lamm_dq(Uu),Uua) = aa_nat_rat(Uu,aa_nat_nat(suc,Uua)) ).

% ATP.lambda_223
tff(fact_8174_ATP_Olambda__224,axiom,
    ! [Uu: fun_nat_nat,Uua: nat] : aa_nat_nat(aTP_Lamm_dh(Uu),Uua) = aa_nat_nat(Uu,aa_nat_nat(suc,Uua)) ).

% ATP.lambda_224
tff(fact_8175_ATP_Olambda__225,axiom,
    ! [Uu: fun_nat_int,Uua: nat] : aa_nat_int(aTP_Lamm_dr(Uu),Uua) = aa_nat_int(Uu,aa_nat_nat(suc,Uua)) ).

% ATP.lambda_225
tff(fact_8176_ATP_Olambda__226,axiom,
    ! [Uu: nat,Uua: num] : aa_num_option_num(aTP_Lamm_mj(Uu),Uua) = aa_num_option_num(some_num,aa_option_num_num(case_option_num_num(one,bit1),aa_num_option_num(bit_take_bit_num(Uu),Uua))) ).

% ATP.lambda_226
tff(fact_8177_ATP_Olambda__227,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat7695548938202568488_nat_o(aa_nat4259715169212259317_nat_o(aTP_Lamm_acw,Uu),Uua) = aa_fun7564604662015400456_nat_o(produc6081775807080527818_nat_o,aa_nat8314798964848609180_nat_o(aTP_Lamm_acv(Uu),Uua)) ).

% ATP.lambda_227
tff(fact_8178_ATP_Olambda__228,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat7997280740862404369at_nat(aa_nat5682243440470347102at_nat(aTP_Lamm_gd,Uu),Uua) = produc2626176000494625587at_nat(aa_nat4158579785191972357at_nat(aTP_Lamm_gc(Uu),Uua)) ).

% ATP.lambda_228
tff(fact_8179_ATP_Olambda__229,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat7997280740862404369at_nat(aa_nat5682243440470347102at_nat(aTP_Lamm_gb,Uu),Uua) = produc2626176000494625587at_nat(aa_nat4158579785191972357at_nat(aTP_Lamm_ga(Uu),Uua)) ).

% ATP.lambda_229
tff(fact_8180_ATP_Olambda__230,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat7997280740862404369at_nat(aa_nat5682243440470347102at_nat(aTP_Lamm_fz,Uu),Uua) = produc2626176000494625587at_nat(aa_nat4158579785191972357at_nat(aTP_Lamm_fy(Uu),Uua)) ).

% ATP.lambda_230
tff(fact_8181_ATP_Olambda__231,axiom,
    ! [Uu: fun_Pr292408699144966967t_unit,Uua: product_unit] : aa_Pro6627971106333230706it_nat(aTP_Lamm_fo(Uu),Uua) = produc7488178964372371019it_nat(aa_Pro5266438804776016756it_nat(aTP_Lamm_fn(Uu),Uua)) ).

% ATP.lambda_231
tff(fact_8182_ATP_Olambda__232,axiom,
    ! [Uu: fun_ar1074044450438384043t_unit,Uua: array_a] : aa_arr6895087029218458358it_nat(aTP_Lamm_fm(Uu),Uua) = produc7488178964372371019it_nat(aa_arr8018972492040254448it_nat(aTP_Lamm_fl(Uu),Uua)) ).

% ATP.lambda_232
tff(fact_8183_ATP_Olambda__233,axiom,
    ! [Uu: fun_Pr5924905948197006361rray_a,Uua: product_unit] : aa_Pro1936865637519295110it_nat(aTP_Lamm_fk(Uu),Uua) = produc921929042997482327it_nat(aa_Pro9169072840722635546it_nat(aTP_Lamm_fj(Uu),Uua)) ).

% ATP.lambda_233
tff(fact_8184_ATP_Olambda__234,axiom,
    ! [Uu: fun_ar3891948820113774757rray_a,Uua: array_a] : aa_arr7695238004252175618it_nat(aTP_Lamm_fi(Uu),Uua) = produc921929042997482327it_nat(aa_arr9035823794894939038it_nat(aTP_Lamm_fh(Uu),Uua)) ).

% ATP.lambda_234
tff(fact_8185_ATP_Olambda__235,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat7695548938202568488_nat_o(aa_nat4259715169212259317_nat_o(aTP_Lamm_fg,Uu),Uua) = aa_fun7564604662015400456_nat_o(produc6081775807080527818_nat_o,aa_nat8314798964848609180_nat_o(aTP_Lamm_ff(Uu),Uua)) ).

% ATP.lambda_235
tff(fact_8186_ATP_Olambda__236,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat7695548938202568488_nat_o(aa_nat4259715169212259317_nat_o(aTP_Lamm_fe,Uu),Uua) = aa_fun7564604662015400456_nat_o(produc6081775807080527818_nat_o,aa_nat8314798964848609180_nat_o(aTP_Lamm_fd(Uu),Uua)) ).

% ATP.lambda_236
tff(fact_8187_ATP_Olambda__237,axiom,
    ! [Uu: fun_he5123621388056232515t_unit,Uua: heap_e7401611519738050253t_unit] : aa_hea684056619475940329it_nat(aTP_Lamm_bt(Uu),Uua) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(aa_hea4146273921685161788t_unit(Uu,Uua),produc584006145561248582it_nat(Uua,one_one_nat))) ).

% ATP.lambda_237
tff(fact_8188_ATP_Olambda__238,axiom,
    ! [Uu: fun_nat_set_nat,Uua: nat] : aa_nat7062706319057040595at_nat(aTP_Lamm_abr(Uu),Uua) = comple5685304695842803022at_nat(image_7178329752028323786at_nat(aTP_Lamm_abq(Uua),aa_nat_set_nat(Uu,Uua))) ).

% ATP.lambda_238
tff(fact_8189_ATP_Olambda__239,axiom,
    ! [Uu: fun_se953073389798102371at_nat,Uua: set_Pr1261947904930325089at_nat] : aa_set1427696295806717282at_nat(aTP_Lamm_abp(Uu),Uua) = comple4364388969068068532at_nat(image_6898982319499645995at_nat(aTP_Lamm_abo(Uua),aa_set6242432332095302236at_nat(Uu,Uua))) ).

% ATP.lambda_239
tff(fact_8190_ATP_Olambda__240,axiom,
    ! [Uu: fun_fu3472058528428720115nt_int,Uua: fun_in5730379987311621695e_term] : aa_fun5435896075006949730nt_int(aTP_Lamm_abn(Uu),Uua) = comple7505710199608789688nt_int(image_2686860183053050585nt_int(aTP_Lamm_abm(Uua),aa_fun2636263158522872028nt_int(Uu,Uua))) ).

% ATP.lambda_240
tff(fact_8191_ATP_Olambda__241,axiom,
    ! [Uu: fun_fu4219362280553733319nt_int,Uua: fun_Pr7763680713840462443e_term] : aa_fun8411382924985671778nt_int(aTP_Lamm_abl(Uu),Uua) = comple3054605461907987852nt_int(image_6157797188692319661nt_int(aTP_Lamm_abk(Uua),aa_fun2513960992105274800nt_int(Uu,Uua))) ).

% ATP.lambda_241
tff(fact_8192_ATP_Olambda__242,axiom,
    ! [Uu: fun_fu8357309440898100312et_nat,Uua: fun_Pr6460944699146269935_nat_o] : aa_fun6480417777262397735et_nat(aTP_Lamm_abj(Uu),Uua) = comple828966628661558727et_nat(image_3818865380660343963et_nat(aTP_Lamm_abi(Uua),aa_fun4924015400185905801et_nat(Uu,Uua))) ).

% ATP.lambda_242
tff(fact_8193_ATP_Olambda__243,axiom,
    ! [Uu: fun_fu2890809920214373946et_nat,Uua: fun_Pr6460944699146269935_nat_o] : aa_fun4924015400185905801et_nat(aTP_Lamm_abh(Uu),Uua) = comple946752071900596009et_nat(image_7009121673873379551et_nat(aTP_Lamm_abg(Uua),aa_fun786139119071955819et_nat(Uu,Uua))) ).

% ATP.lambda_243
tff(fact_8194_ATP_Olambda__244,axiom,
    ! [Uu: fun_fu5971215405379524186nteger,Uua: fun_Pr5098669352780829690e_term] : aa_fun207332883101880580nteger(aTP_Lamm_abf(Uu),Uua) = comple7749403179893457567nteger(image_1718222391602322082nteger(aTP_Lamm_abe(Uua),aa_fun6394921419180517443nteger(Uu,Uua))) ).

% ATP.lambda_244
tff(fact_8195_ATP_Olambda__245,axiom,
    ! [Uu: code_natural,Uua: code_natural] : aa_Cod6352003912080677724atural(aTP_Lamm_adm(Uu),Uua) = produc6639722614265839536atural(aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,Uua),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,Uu),aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,one)))))))))))))))))))))))))))))))))) ).

% ATP.lambda_245
tff(fact_8196_ATP_Olambda__246,axiom,
    ! [Uu: fun_nat_set_nat,Uua: nat] : aa_nat_set_nat(aTP_Lamm_wf(Uu),Uua) = comple7399068483239264473et_nat(image_nat_set_nat(Uu,aa_nat_set_nat(set_or4665077453230672383an_nat(zero_zero_nat),Uua))) ).

% ATP.lambda_246
tff(fact_8197_ATP_Olambda__247,axiom,
    ! [Uu: rat,Uua: nat] : aa_nat_fun_rat_rat(aTP_Lamm_ir(Uu),Uua) = aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(minus_minus_rat(Uu),aa_nat_rat(semiri681578069525770553at_rat,Uua))) ).

% ATP.lambda_247
tff(fact_8198_ATP_Olambda__248,axiom,
    ! [Uu: code_natural,Uua: nat] : aa_nat5282697797315388251atural(aTP_Lamm_jz(Uu),Uua) = aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,Uu),aa_nat_Code_natural(semiri3763490453095760265atural,Uua))) ).

% ATP.lambda_248
tff(fact_8199_ATP_Olambda__249,axiom,
    ! [Uu: code_integer,Uua: nat] : aa_nat6383147911832638789nteger(aTP_Lamm_jy(Uu),Uua) = aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,Uu),aa_nat_Code_integer(semiri4939895301339042750nteger,Uua))) ).

% ATP.lambda_249
tff(fact_8200_ATP_Olambda__250,axiom,
    ! [Uu: rat,Uua: nat] : aa_nat_fun_rat_rat(aTP_Lamm_jw(Uu),Uua) = aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,Uu),aa_nat_rat(semiri681578069525770553at_rat,Uua))) ).

% ATP.lambda_250
tff(fact_8201_ATP_Olambda__251,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat_fun_nat_nat(aTP_Lamm_ka(Uu),Uua) = aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uu),aa_nat_nat(semiri1316708129612266289at_nat,Uua))) ).

% ATP.lambda_251
tff(fact_8202_ATP_Olambda__252,axiom,
    ! [Uu: int,Uua: nat] : aa_nat_fun_int_int(aTP_Lamm_jx(Uu),Uua) = aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,Uu),aa_nat_int(semiri1314217659103216013at_int,Uua))) ).

% ATP.lambda_252
tff(fact_8203_ATP_Olambda__253,axiom,
    ! [Uu: product_unit,Uua: product_unit] : aa_Pro7616171890175246658t_unit(aTP_Lamm_acr(Uu),Uua) = aa_Pro7616171890175246658t_unit(some_Product_unit,aa_Pro8294289767544744956t_unit(sup_sup_Product_unit(Uu),Uua)) ).

% ATP.lambda_253
tff(fact_8204_ATP_Olambda__254,axiom,
    ! [Uu: assn,Uua: assn] : aa_assn_option_assn(aTP_Lamm_act(Uu),Uua) = some_assn(sup_sup_assn(Uu,Uua)) ).

% ATP.lambda_254
tff(fact_8205_ATP_Olambda__255,axiom,
    ! [Uu: set_Pr4329608150637261639at_nat,Uua: set_Pr4329608150637261639at_nat] : aa_set7071694670514008770at_nat(aTP_Lamm_acp(Uu),Uua) = some_s5890477192898017836at_nat(sup_su5525570899277871387at_nat(Uu,Uua)) ).

% ATP.lambda_255
tff(fact_8206_ATP_Olambda__256,axiom,
    ! [Uu: set_nat,Uua: set_nat] : aa_set6119337032432945050et_nat(aTP_Lamm_acn(Uu),Uua) = aa_set6119337032432945050et_nat(some_set_nat,sup_sup_set_nat(Uu,Uua)) ).

% ATP.lambda_256
tff(fact_8207_ATP_Olambda__257,axiom,
    ! [Uu: code_natural,Uua: code_natural] : aa_Cod6352003912080677724atural(aTP_Lamm_ado(Uu),Uua) = produc6639722614265839536atural(aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(modulo8411746178871703098atural,Uua),Uu)) ).

% ATP.lambda_257
tff(fact_8208_ATP_Olambda__258,axiom,
    ! [Uu: set_Pr1261947904930325089at_nat,Uua: set_Pr1261947904930325089at_nat] : aa_set7180998873066629928at_nat(aTP_Lamm_adc(Uu),Uua) = insert9069300056098147895at_nat(produc2922128104949294807at_nat(Uu,Uua)) ).

% ATP.lambda_258
tff(fact_8209_ATP_Olambda__259,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat5789291038776893201at_nat(aTP_Lamm_add(Uu),Uua) = insert8211810215607154385at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Uu),Uua)) ).

% ATP.lambda_259
tff(fact_8210_ATP_Olambda__260,axiom,
    ! [Uu: fun_Pr5098669352780829690e_term,Uua: produc8923325533196201883nteger] : aa_Pro5511408310453641204nteger(aTP_Lamm_acx(Uu),Uua) = insert4459515811902188230nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,Uu),Uua)) ).

% ATP.lambda_260
tff(fact_8211_ATP_Olambda__261,axiom,
    ! [Uu: fun_Pr6460944699146269935_nat_o,Uua: produc3658429121746597890et_nat] : aa_Pro4237038916479365225et_nat(aTP_Lamm_acy(Uu),Uua) = insert663245765287195472et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,Uu),Uua)) ).

% ATP.lambda_261
tff(fact_8212_ATP_Olambda__262,axiom,
    ! [Uu: fun_Pr6460944699146269935_nat_o,Uua: produc8799533983703829792et_nat] : aa_Pro702454294891323331et_nat(aTP_Lamm_acz(Uu),Uua) = insert727258735945777134et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,Uu),Uua)) ).

% ATP.lambda_262
tff(fact_8213_ATP_Olambda__263,axiom,
    ! [Uu: fun_Pr7763680713840462443e_term,Uua: product_prod_int_int] : aa_Pro1409070577063066988nt_int(aTP_Lamm_ada(Uu),Uua) = insert4130518925788644403nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,Uu),Uua)) ).

% ATP.lambda_263
tff(fact_8214_ATP_Olambda__264,axiom,
    ! [Uu: fun_in5730379987311621695e_term,Uua: product_prod_int_int] : aa_Pro6698456444936022468nt_int(aTP_Lamm_adb(Uu),Uua) = insert845627424500119391nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,Uu),Uua)) ).

% ATP.lambda_264
tff(fact_8215_ATP_Olambda__265,axiom,
    ! [Uu: nat,Uua: heap_e7401611519738050253t_unit] : aa_hea684056619475940329it_nat(aTP_Lamm_adh(Uu),Uua) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,produc7133225469290080770it_nat(product_Unity,produc584006145561248582it_nat(Uua,Uu))) ).

% ATP.lambda_265
tff(fact_8216_ATP_Olambda__266,axiom,
    ! [Uu: fun_nat_Code_integer,Uua: nat] : aa_nat6383147911832638789nteger(aTP_Lamm_lg(Uu),Uua) = aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(Uu,Uua)) ).

% ATP.lambda_266
tff(fact_8217_ATP_Olambda__267,axiom,
    ! [Uu: fun_nat_assn,Uua: nat] : aa_nat_fun_assn_assn(aTP_Lamm_lh(Uu),Uua) = aa_ass954072293579886259n_assn(times_times_assn,aa_nat_assn(Uu,Uua)) ).

% ATP.lambda_267
tff(fact_8218_ATP_Olambda__268,axiom,
    ! [Uu: fun_nat_rat,Uua: nat] : aa_nat_fun_rat_rat(aTP_Lamm_li(Uu),Uua) = aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(Uu,Uua)) ).

% ATP.lambda_268
tff(fact_8219_ATP_Olambda__269,axiom,
    ! [Uu: fun_nat_nat,Uua: nat] : aa_nat_fun_nat_nat(aTP_Lamm_lj(Uu),Uua) = aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(Uu,Uua)) ).

% ATP.lambda_269
tff(fact_8220_ATP_Olambda__270,axiom,
    ! [Uu: fun_nat_int,Uua: nat] : aa_nat_fun_int_int(aTP_Lamm_lk(Uu),Uua) = aa_int_fun_int_int(times_times_int,aa_nat_int(Uu,Uua)) ).

% ATP.lambda_270
tff(fact_8221_ATP_Olambda__271,axiom,
    ! [Uu: fun_nat_Code_integer,Uua: nat] : aa_nat6383147911832638789nteger(aTP_Lamm_dy(Uu),Uua) = aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_nat_Code_integer(Uu,Uua)) ).

% ATP.lambda_271
tff(fact_8222_ATP_Olambda__272,axiom,
    ! [Uu: fun_na2338080690716861136at_nat,Uua: nat] : aa_nat1862996181841379217at_nat(aTP_Lamm_dz(Uu),Uua) = plus_p7104986032573967614at_nat(aa_nat2240542744625857721at_nat(Uu,Uua)) ).

% ATP.lambda_272
tff(fact_8223_ATP_Olambda__273,axiom,
    ! [Uu: fun_nat_rat,Uua: nat] : aa_nat_fun_rat_rat(aTP_Lamm_ea(Uu),Uua) = aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(Uu,Uua)) ).

% ATP.lambda_273
tff(fact_8224_ATP_Olambda__274,axiom,
    ! [Uu: fun_nat_nat,Uua: nat] : aa_nat_fun_nat_nat(aTP_Lamm_ec(Uu),Uua) = aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(Uu,Uua)) ).

% ATP.lambda_274
tff(fact_8225_ATP_Olambda__275,axiom,
    ! [Uu: fun_nat_int,Uua: nat] : aa_nat_fun_int_int(aTP_Lamm_eb(Uu),Uua) = aa_int_fun_int_int(plus_plus_int,aa_nat_int(Uu,Uua)) ).

% ATP.lambda_275
tff(fact_8226_ATP_Olambda__276,axiom,
    ! [Uu: fun_Pr8319229360018371625t_unit,Uua: produc3843707927480180839at_nat] : aa_Pro436454883488707944t_unit(aTP_Lamm_wa(Uu),Uua) = aa_Pro7616171890175246658t_unit(some_Product_unit,aa_Pro1279885795167260962t_unit(Uu,Uua)) ).

% ATP.lambda_276
tff(fact_8227_ATP_Olambda__277,axiom,
    ! [Uu: fun_Pr6764980218223570944et_nat,Uua: produc3843707927480180839at_nat] : aa_Pro708668050254188033et_nat(aTP_Lamm_vw(Uu),Uua) = aa_set6119337032432945050et_nat(some_set_nat,aa_Pro1692590229789857841et_nat(Uu,Uua)) ).

% ATP.lambda_277
tff(fact_8228_ATP_Olambda__278,axiom,
    ! [Uu: fun_Pr2481279687482350479t_unit,Uua: product_prod_nat_nat] : aa_Pro4935752218105739214t_unit(aTP_Lamm_wb(Uu),Uua) = aa_Pro7616171890175246658t_unit(some_Product_unit,aa_Pro676242055593665672t_unit(Uu,Uua)) ).

% ATP.lambda_278
tff(fact_8229_ATP_Olambda__279,axiom,
    ! [Uu: fun_Pr9038118721296872730et_nat,Uua: product_prod_nat_nat] : aa_Pro2437148896120846363et_nat(aTP_Lamm_vx(Uu),Uua) = aa_set6119337032432945050et_nat(some_set_nat,aa_Pro9123573313595863371et_nat(Uu,Uua)) ).

% ATP.lambda_279
tff(fact_8230_ATP_Olambda__280,axiom,
    ! [Uu: fun_o_Product_unit,Uua: $o] : aa_o_o3081425935505226615t_unit(aTP_Lamm_wc(Uu),(Uua)) = aa_Pro7616171890175246658t_unit(some_Product_unit,aa_o_Product_unit(Uu,(Uua))) ).

% ATP.lambda_280
tff(fact_8231_ATP_Olambda__281,axiom,
    ! [Uu: fun_o_set_nat,Uua: $o] : aa_o_option_set_nat(aTP_Lamm_vy(Uu),(Uua)) = aa_set6119337032432945050et_nat(some_set_nat,aa_o_set_nat(Uu,(Uua))) ).

% ATP.lambda_281
tff(fact_8232_ATP_Olambda__282,axiom,
    ! [Uu: fun_num_num,Uua: num] : aa_num_option_num(aTP_Lamm_cf(Uu),Uua) = aa_num_option_num(some_num,aa_num_num(Uu,Uua)) ).

% ATP.lambda_282
tff(fact_8233_ATP_Olambda__283,axiom,
    ! [Uu: fun_nat_Product_unit,Uua: nat] : aa_nat162940103065333829t_unit(aTP_Lamm_wd(Uu),Uua) = aa_Pro7616171890175246658t_unit(some_Product_unit,aa_nat_Product_unit(Uu,Uua)) ).

% ATP.lambda_283
tff(fact_8234_ATP_Olambda__284,axiom,
    ! [Uu: fun_nat_set_nat,Uua: nat] : aa_nat7838062387752323300et_nat(aTP_Lamm_vv(Uu),Uua) = aa_set6119337032432945050et_nat(some_set_nat,aa_nat_set_nat(Uu,Uua)) ).

% ATP.lambda_284
tff(fact_8235_ATP_Olambda__285,axiom,
    ! [Uu: fun_int_Product_unit,Uua: int] : aa_int400517244715908841t_unit(aTP_Lamm_we(Uu),Uua) = aa_Pro7616171890175246658t_unit(some_Product_unit,aa_int_Product_unit(Uu,Uua)) ).

% ATP.lambda_285
tff(fact_8236_ATP_Olambda__286,axiom,
    ! [Uu: fun_int_set_nat,Uua: int] : aa_int9046179520680703296et_nat(aTP_Lamm_vz(Uu),Uua) = aa_set6119337032432945050et_nat(some_set_nat,aa_int_set_nat(Uu,Uua)) ).

% ATP.lambda_286
tff(fact_8237_ATP_Olambda__287,axiom,
    ! [Uu: fun_li1025265955262268170_nat_o,Uua: list_nat] : aa_lis5329267923302741684st_nat(aTP_Lamm_zm(Uu),Uua) = collect_list_nat(aa_lis557685189327716851_nat_o(Uu,Uua)) ).

% ATP.lambda_287
tff(fact_8238_ATP_Olambda__288,axiom,
    ! [Uu: fun_li2421049240157457050_nat_o,Uua: list_nat] : aa_list_nat_set_nat(aTP_Lamm_zk(Uu),Uua) = collect_nat(aa_lis1686035672126679939_nat_o(Uu,Uua)) ).

% ATP.lambda_288
tff(fact_8239_ATP_Olambda__289,axiom,
    ! [Uu: fun_na7234455742697417626_nat_o,Uua: nat] : aa_nat_set_list_nat(aTP_Lamm_zi(Uu),Uua) = collect_list_nat(aa_nat5883842100386203267_nat_o(Uu,Uua)) ).

% ATP.lambda_289
tff(fact_8240_ATP_Olambda__290,axiom,
    ! [Uu: fun_nat_fun_nat_o,Uua: nat] : aa_nat_set_nat(aTP_Lamm_zg(Uu),Uua) = collect_nat(aa_nat_fun_nat_o(Uu,Uua)) ).

% ATP.lambda_290
tff(fact_8241_ATP_Olambda__291,axiom,
    ! [Uu: fun_Product_unit_nat,Uua: product_unit] : aa_Product_unit_nat(aTP_Lamm_rn(Uu),Uua) = aa_nat_nat(suc,aa_Product_unit_nat(Uu,Uua)) ).

% ATP.lambda_291
tff(fact_8242_ATP_Olambda__292,axiom,
    ! [Uu: fun_list_nat_nat,Uua: list_nat] : aa_list_nat_nat(aTP_Lamm_ro(Uu),Uua) = aa_nat_nat(suc,aa_list_nat_nat(Uu,Uua)) ).

% ATP.lambda_292
tff(fact_8243_ATP_Olambda__293,axiom,
    ! [Uu: fun_nat_nat,Uua: nat] : aa_nat_nat(aTP_Lamm_rp(Uu),Uua) = aa_nat_nat(suc,aa_nat_nat(Uu,Uua)) ).

% ATP.lambda_293
tff(fact_8244_ATP_Olambda__294,axiom,
    ! [Uu: fun_int_nat,Uua: int] : aa_int_nat(aTP_Lamm_rm(Uu),Uua) = aa_nat_nat(suc,aa_int_nat(Uu,Uua)) ).

% ATP.lambda_294
tff(fact_8245_ATP_Olambda__295,axiom,
    ! [Uu: set_Product_prod_o_o,Uua: $o] : aa_o_set_o(aTP_Lamm_adf(Uu),(Uua)) = field_o(Uu) ).

% ATP.lambda_295
tff(fact_8246_ATP_Olambda__296,axiom,
    ! [Uu: set_Pr1261947904930325089at_nat,Uua: nat] : aa_nat_set_nat(aTP_Lamm_ade(Uu),Uua) = field_nat(Uu) ).

% ATP.lambda_296
tff(fact_8247_ATP_Olambda__297,axiom,
    ! [Uu: fun_list_nat_o,Uua: list_nat] : aa_lis5329267923302741684st_nat(aTP_Lamm_xp(Uu),Uua) = collect_list_nat(Uu) ).

% ATP.lambda_297
tff(fact_8248_ATP_Olambda__298,axiom,
    ! [Uu: fun_list_nat_o,Uua: nat] : aa_nat_set_list_nat(aTP_Lamm_xl(Uu),Uua) = collect_list_nat(Uu) ).

% ATP.lambda_298
tff(fact_8249_ATP_Olambda__299,axiom,
    ! [Uu: fun_nat_o,Uua: list_nat] : aa_list_nat_set_nat(aTP_Lamm_xn(Uu),Uua) = collect_nat(Uu) ).

% ATP.lambda_299
tff(fact_8250_ATP_Olambda__300,axiom,
    ! [Uu: fun_nat_o,Uua: nat] : aa_nat_set_nat(aTP_Lamm_xj(Uu),Uua) = collect_nat(Uu) ).

% ATP.lambda_300
tff(fact_8251_ATP_Olambda__301,axiom,
    ! [Uu: num,Uua: code_integer,Uub: code_integer] :
      aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(aTP_Lamm_gk(Uu),Uua),Uub) = $ite(aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le3102999989581377725nteger,aa_num_Code_integer(numera6620942414471956472nteger,Uu)),Uub),aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),Uua)),one_one_Code_integer)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,Uub),aa_num_Code_integer(numera6620942414471956472nteger,Uu))),aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_num_Code_integer(numera6620942414471956472nteger,aa_num_num(bit0,one))),Uua)),Uub)) ).

% ATP.lambda_301
tff(fact_8252_ATP_Olambda__302,axiom,
    ! [Uu: num,Uua: nat,Uub: nat] :
      aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(aTP_Lamm_gi(Uu),Uua),Uub) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_num_nat(numeral_numeral_nat,Uu)),Uub),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),Uua)),one_one_nat)),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uub),aa_num_nat(numeral_numeral_nat,Uu))),aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),Uua)),Uub)) ).

% ATP.lambda_302
tff(fact_8253_ATP_Olambda__303,axiom,
    ! [Uu: num,Uua: int,Uub: int] :
      aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(aTP_Lamm_gj(Uu),Uua),Uub) = $ite(aa_int_o(aa_int_fun_int_o(ord_less_eq_int,aa_num_int(numeral_numeral_int,Uu)),Uub),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),Uua)),one_one_int)),aa_int_int(aa_int_fun_int_int(minus_minus_int,Uub),aa_num_int(numeral_numeral_int,Uu))),aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_num_int(numeral_numeral_int,aa_num_num(bit0,one))),Uua)),Uub)) ).

% ATP.lambda_303
tff(fact_8254_ATP_Olambda__304,axiom,
    ! [Uu: code_integer,Uua: fun_Co8499238673658658103nteger,Uub: code_integer] :
      aa_Cod1783974652533396728nteger(aa_fun4435975922079263404nteger(aTP_Lamm_ok(Uu),Uua),Uub) = $ite(Uu = Uub,aa_Cod1783974652533396728nteger(Uua,Uub),one_one_Code_integer) ).

% ATP.lambda_304
tff(fact_8255_ATP_Olambda__305,axiom,
    ! [Uu: code_integer,Uua: fun_Co4490034186337852034r_assn,Uub: code_integer] :
      aa_Code_integer_assn(aa_fun4119713415300323650r_assn(aTP_Lamm_oo(Uu),Uua),Uub) = $ite(Uu = Uub,aa_Code_integer_assn(Uua,Uub),one_one_assn) ).

% ATP.lambda_305
tff(fact_8256_ATP_Olambda__306,axiom,
    ! [Uu: $o,Uua: fun_o_Code_integer,Uub: $o] :
      aa_o_Code_integer(aa_fun8520278569782659900nteger(aTP_Lamm_oh((Uu)),Uua),(Uub)) = $ite((Uu) = (Uub),aa_o_Code_integer(Uua,(Uub)),one_one_Code_integer) ).

% ATP.lambda_306
tff(fact_8257_ATP_Olambda__307,axiom,
    ! [Uu: $o,Uua: fun_o_assn,Uub: $o] :
      aa_o_assn(aa_fun4536517337817438332o_assn(aTP_Lamm_ol((Uu)),Uua),(Uub)) = $ite((Uu) = (Uub),aa_o_assn(Uua,(Uub)),one_one_assn) ).

% ATP.lambda_307
tff(fact_8258_ATP_Olambda__308,axiom,
    ! [Uu: $o,Uua: fun_o_rat,Uub: $o] :
      aa_o_rat(aa_fun4336163974892599420_o_rat(aTP_Lamm_op((Uu)),Uua),(Uub)) = $ite((Uu) = (Uub),aa_o_rat(Uua,(Uub)),one_one_rat) ).

% ATP.lambda_308
tff(fact_8259_ATP_Olambda__309,axiom,
    ! [Uu: nat,Uua: fun_nat_Code_integer,Uub: nat] :
      aa_nat_Code_integer(aa_fun589076786913273746nteger(aTP_Lamm_oi(Uu),Uua),Uub) = $ite(Uu = Uub,aa_nat_Code_integer(Uua,Uub),one_one_Code_integer) ).

% ATP.lambda_309
tff(fact_8260_ATP_Olambda__310,axiom,
    ! [Uu: nat,Uua: fun_nat_assn,Uub: nat] :
      aa_nat_assn(aa_fun785744391571715112t_assn(aTP_Lamm_om(Uu),Uua),Uub) = $ite(Uu = Uub,aa_nat_assn(Uua,Uub),one_one_assn) ).

% ATP.lambda_310
tff(fact_8261_ATP_Olambda__311,axiom,
    ! [Uu: nat,Uua: fun_nat_rat,Uub: nat] :
      aa_nat_rat(aa_fun765758790203053448at_rat(aTP_Lamm_oq(Uu),Uua),Uub) = $ite(Uu = Uub,aa_nat_rat(Uua,Uub),one_one_rat) ).

% ATP.lambda_311
tff(fact_8262_ATP_Olambda__312,axiom,
    ! [Uu: int,Uua: fun_int_Code_integer,Uub: int] :
      aa_int_Code_integer(aa_fun5304498221708291146nteger(aTP_Lamm_oj(Uu),Uua),Uub) = $ite(Uu = Uub,aa_int_Code_integer(Uua,Uub),one_one_Code_integer) ).

% ATP.lambda_312
tff(fact_8263_ATP_Olambda__313,axiom,
    ! [Uu: int,Uua: fun_int_assn,Uub: int] :
      aa_int_assn(aa_fun919007281442365664t_assn(aTP_Lamm_on(Uu),Uua),Uub) = $ite(Uu = Uub,aa_int_assn(Uua,Uub),one_one_assn) ).

% ATP.lambda_313
tff(fact_8264_ATP_Olambda__314,axiom,
    ! [Uu: code_integer,Uua: fun_Co8499238673658658103nteger,Uub: code_integer] :
      aa_Cod1783974652533396728nteger(aa_fun4435975922079263404nteger(aTP_Lamm_oa(Uu),Uua),Uub) = $ite(Uub = Uu,aa_Cod1783974652533396728nteger(Uua,Uub),one_one_Code_integer) ).

% ATP.lambda_314
tff(fact_8265_ATP_Olambda__315,axiom,
    ! [Uu: code_integer,Uua: fun_Co4490034186337852034r_assn,Uub: code_integer] :
      aa_Code_integer_assn(aa_fun4119713415300323650r_assn(aTP_Lamm_oe(Uu),Uua),Uub) = $ite(Uub = Uu,aa_Code_integer_assn(Uua,Uub),one_one_assn) ).

% ATP.lambda_315
tff(fact_8266_ATP_Olambda__316,axiom,
    ! [Uu: $o,Uua: fun_o_Code_integer,Uub: $o] :
      aa_o_Code_integer(aa_fun8520278569782659900nteger(aTP_Lamm_nx((Uu)),Uua),(Uub)) = $ite((Uub) = (Uu),aa_o_Code_integer(Uua,(Uub)),one_one_Code_integer) ).

% ATP.lambda_316
tff(fact_8267_ATP_Olambda__317,axiom,
    ! [Uu: $o,Uua: fun_o_assn,Uub: $o] :
      aa_o_assn(aa_fun4536517337817438332o_assn(aTP_Lamm_ob((Uu)),Uua),(Uub)) = $ite((Uub) = (Uu),aa_o_assn(Uua,(Uub)),one_one_assn) ).

% ATP.lambda_317
tff(fact_8268_ATP_Olambda__318,axiom,
    ! [Uu: $o,Uua: fun_o_rat,Uub: $o] :
      aa_o_rat(aa_fun4336163974892599420_o_rat(aTP_Lamm_of((Uu)),Uua),(Uub)) = $ite((Uub) = (Uu),aa_o_rat(Uua,(Uub)),one_one_rat) ).

% ATP.lambda_318
tff(fact_8269_ATP_Olambda__319,axiom,
    ! [Uu: nat,Uua: fun_nat_Code_integer,Uub: nat] :
      aa_nat_Code_integer(aa_fun589076786913273746nteger(aTP_Lamm_ny(Uu),Uua),Uub) = $ite(Uub = Uu,aa_nat_Code_integer(Uua,Uub),one_one_Code_integer) ).

% ATP.lambda_319
tff(fact_8270_ATP_Olambda__320,axiom,
    ! [Uu: nat,Uua: fun_nat_assn,Uub: nat] :
      aa_nat_assn(aa_fun785744391571715112t_assn(aTP_Lamm_oc(Uu),Uua),Uub) = $ite(Uub = Uu,aa_nat_assn(Uua,Uub),one_one_assn) ).

% ATP.lambda_320
tff(fact_8271_ATP_Olambda__321,axiom,
    ! [Uu: nat,Uua: fun_nat_rat,Uub: nat] :
      aa_nat_rat(aa_fun765758790203053448at_rat(aTP_Lamm_og(Uu),Uua),Uub) = $ite(Uub = Uu,aa_nat_rat(Uua,Uub),one_one_rat) ).

% ATP.lambda_321
tff(fact_8272_ATP_Olambda__322,axiom,
    ! [Uu: int,Uua: fun_int_Code_integer,Uub: int] :
      aa_int_Code_integer(aa_fun5304498221708291146nteger(aTP_Lamm_nz(Uu),Uua),Uub) = $ite(Uub = Uu,aa_int_Code_integer(Uua,Uub),one_one_Code_integer) ).

% ATP.lambda_322
tff(fact_8273_ATP_Olambda__323,axiom,
    ! [Uu: int,Uua: fun_int_assn,Uub: int] :
      aa_int_assn(aa_fun919007281442365664t_assn(aTP_Lamm_od(Uu),Uua),Uub) = $ite(Uub = Uu,aa_int_assn(Uua,Uub),one_one_assn) ).

% ATP.lambda_323
tff(fact_8274_ATP_Olambda__324,axiom,
    ! [Uu: code_integer,Uua: code_integer,Uub: code_integer] :
      aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(aTP_Lamm_ma(Uu),Uua),Uub) = $ite(Uub = zero_z3403309356797280102nteger,aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,Uua)),zero_z3403309356797280102nteger),aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,Uua)),one_one_Code_integer)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,Uu)),Uub))) ).

% ATP.lambda_324
tff(fact_8275_ATP_Olambda__325,axiom,
    ! [Uu: code_integer,Uua: code_integer,Uub: code_integer] :
      aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(aTP_Lamm_kl(Uu),Uua),Uub) = $ite(Uub = zero_z3403309356797280102nteger,aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,Uua)),zero_z3403309356797280102nteger),aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,Uua)),one_one_Code_integer)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(abs_abs_Code_integer,Uu)),Uub))) ).

% ATP.lambda_325
tff(fact_8276_ATP_Olambda__326,axiom,
    ! [Uu: code_integer,Uua: code_integer,Uub: code_integer] :
      aa_Cod6977894654539884864nteger(aa_Cod8380929501330563836nteger(aTP_Lamm_lz(Uu),Uua),Uub) = $ite(Uub = zero_z3403309356797280102nteger,aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,Uua)),zero_z3403309356797280102nteger),aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,Uua)),one_one_Code_integer)),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,Uu),Uub))) ).

% ATP.lambda_326
tff(fact_8277_ATP_Olambda__327,axiom,
    ! [Uu: fun_Co8499238673658658103nteger,Uua: fun_Code_integer_o,Uub: code_integer] :
      aa_Cod1783974652533396728nteger(aa_fun791458909507501263nteger(aTP_Lamm_qv(Uu),Uua),Uub) = $ite(aa_Code_integer_o(Uua,Uub),aa_Cod1783974652533396728nteger(Uu,Uub),one_one_Code_integer) ).

% ATP.lambda_327
tff(fact_8278_ATP_Olambda__328,axiom,
    ! [Uu: fun_Co4490034186337852034r_assn,Uua: fun_Code_integer_o,Uub: code_integer] :
      aa_Code_integer_assn(aa_fun6392223008197429786r_assn(aTP_Lamm_qz(Uu),Uua),Uub) = $ite(aa_Code_integer_o(Uua,Uub),aa_Code_integer_assn(Uu,Uub),one_one_assn) ).

% ATP.lambda_328
tff(fact_8279_ATP_Olambda__329,axiom,
    ! [Uu: fun_o_Code_integer,Uua: fun_o_o,Uub: $o] :
      aa_o_Code_integer(aa_fun6542514109734600263nteger(aTP_Lamm_qp(Uu),Uua),(Uub)) = $ite(aa_o_o(Uua,(Uub)),aa_o_Code_integer(Uu,(Uub)),one_one_Code_integer) ).

% ATP.lambda_329
tff(fact_8280_ATP_Olambda__330,axiom,
    ! [Uu: fun_o_assn,Uua: fun_o_o,Uub: $o] :
      aa_o_assn(aa_fun8560762093604944786o_assn(aTP_Lamm_qw(Uu),Uua),(Uub)) = $ite(aa_o_o(Uua,(Uub)),aa_o_assn(Uu,(Uub)),one_one_assn) ).

% ATP.lambda_330
tff(fact_8281_ATP_Olambda__331,axiom,
    ! [Uu: fun_o_rat,Uua: fun_o_o,Uub: $o] :
      aa_o_rat(aa_fun_o_o_fun_o_rat(aTP_Lamm_ra(Uu),Uua),(Uub)) = $ite(aa_o_o(Uua,(Uub)),aa_o_rat(Uu,(Uub)),one_one_rat) ).

% ATP.lambda_331
tff(fact_8282_ATP_Olambda__332,axiom,
    ! [Uu: fun_nat_Code_integer,Uua: fun_nat_o,Uub: nat] :
      aa_nat_Code_integer(aa_fun3969837373441324047nteger(aTP_Lamm_qr(Uu),Uua),Uub) = $ite(aa_nat_o(Uua,Uub),aa_nat_Code_integer(Uu,Uub),one_one_Code_integer) ).

% ATP.lambda_332
tff(fact_8283_ATP_Olambda__333,axiom,
    ! [Uu: fun_nat_assn,Uua: fun_nat_o,Uub: nat] :
      aa_nat_assn(aa_fun3990007403578212698t_assn(aTP_Lamm_qx(Uu),Uua),Uub) = $ite(aa_nat_o(Uua,Uub),aa_nat_assn(Uu,Uub),one_one_assn) ).

% ATP.lambda_333
tff(fact_8284_ATP_Olambda__334,axiom,
    ! [Uu: fun_nat_rat,Uua: fun_nat_o,Uub: nat] :
      aa_nat_rat(aa_fun696632391729880074at_rat(aTP_Lamm_rb(Uu),Uua),Uub) = $ite(aa_nat_o(Uua,Uub),aa_nat_rat(Uu,Uub),one_one_rat) ).

% ATP.lambda_334
tff(fact_8285_ATP_Olambda__335,axiom,
    ! [Uu: fun_int_Code_integer,Uua: fun_int_o,Uub: int] :
      aa_int_Code_integer(aa_fun6019004165459918095nteger(aTP_Lamm_qt(Uu),Uua),Uub) = $ite(aa_int_o(Uua,Uub),aa_int_Code_integer(Uu,Uub),one_one_Code_integer) ).

% ATP.lambda_335
tff(fact_8286_ATP_Olambda__336,axiom,
    ! [Uu: fun_int_assn,Uua: fun_int_o,Uub: int] :
      aa_int_assn(aa_fun9028805181350005338t_assn(aTP_Lamm_qy(Uu),Uua),Uub) = $ite(aa_int_o(Uua,Uub),aa_int_assn(Uu,Uub),one_one_assn) ).

% ATP.lambda_336
tff(fact_8287_ATP_Olambda__337,axiom,
    ! [Uu: fun_he8413527710729349838unit_o,Uua: fun_he4944555133437423336it_nat,Uub: heap_e7401611519738050253t_unit] :
      aa_hea684056619475940329it_nat(aa_fun2986507860694160780it_nat(aTP_Lamm_bq(Uu),Uua),Uub) = $ite(aa_hea7994211679605476167unit_o(Uu,Uub),aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,aa_hea256619718444519449it_nat(Uua,Uub)),none_P9117596204409417319it_nat) ).

% ATP.lambda_337
tff(fact_8288_ATP_Olambda__338,axiom,
    ! [Uu: fun_he8413527710729349838unit_o,Uua: fun_he281446669002384250it_nat,Uub: heap_e7401611519738050253t_unit] :
      aa_hea5936688510613671481it_nat(aa_fun3106883476453902712it_nat(aTP_Lamm_bp(Uu),Uua),Uub) = $ite(aa_hea7994211679605476167unit_o(Uu,Uub),aa_Pro1291033051762305794it_nat(some_P6105628898608307625it_nat,aa_hea1118439097112461811it_nat(Uua,Uub)),none_P2587165478634041381it_nat) ).

% ATP.lambda_338
tff(fact_8289_ATP_Olambda__339,axiom,
    ! [Uu: fun_num_fun_num_num,Uua: option_num,Uub: num] : aa_num_option_num(aa_opt8899475237019873193on_num(aTP_Lamm_bc(Uu),Uua),Uub) = aa_opt5369159329878751634on_num(case_o6005452278849405969um_num(aa_num_option_num(some_num,Uub),aa_num6390622462783740633on_num(aTP_Lamm_bb(Uu),Uub)),Uua) ).

% ATP.lambda_339
tff(fact_8290_ATP_Olambda__340,axiom,
    ! [Uu: fun_Pr1003294667014919570it_nat,Uua: option8956607266484857688it_nat,Uub: produc8664842809031399944it_nat] : aa_Pro8996696869555642526it_nat(aa_opt7728438819757478003it_nat(aTP_Lamm_ba(Uu),Uua),Uub) = case_o2963978774867076333it_nat(aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,Uub),aa_Pro5635350972512700067it_nat(aTP_Lamm_az(Uu),Uub),Uua) ).

% ATP.lambda_340
tff(fact_8291_ATP_Olambda__341,axiom,
    ! [Uu: option_assn,Uua: option_assn,Uub: assn] : aa_assn_option_assn(aa_opt1471905160178427347n_assn(aTP_Lamm_acu(Uu),Uua),Uub) = case_o4484465799723439917n_assn(Uu,aTP_Lamm_act(Uub),Uua) ).

% ATP.lambda_341
tff(fact_8292_ATP_Olambda__342,axiom,
    ! [Uu: option_Product_unit,Uua: option_Product_unit,Uub: product_unit] : aa_Pro7616171890175246658t_unit(aa_opt8900914514660672992t_unit(aTP_Lamm_acs(Uu),Uua),Uub) = case_o2985186191577459077t_unit(Uu,aTP_Lamm_acr(Uub),Uua) ).

% ATP.lambda_342
tff(fact_8293_ATP_Olambda__343,axiom,
    ! [Uu: option1583680563626158861at_nat,Uua: option1583680563626158861at_nat,Uub: set_Pr4329608150637261639at_nat] : aa_set7071694670514008770at_nat(aa_opt1027706798495913626at_nat(aTP_Lamm_acq(Uu),Uua),Uub) = case_o9080059180780454917at_nat(Uu,aTP_Lamm_acp(Uub),Uua) ).

% ATP.lambda_343
tff(fact_8294_ATP_Olambda__344,axiom,
    ! [Uu: option_set_nat,Uua: option_set_nat,Uub: set_nat] : aa_set6119337032432945050et_nat(aa_opt5648106117674462701et_nat(aTP_Lamm_aco(Uu),Uua),Uub) = case_o4054078431260844265et_nat(Uu,aTP_Lamm_acn(Uub),Uua) ).

% ATP.lambda_344
tff(fact_8295_ATP_Olambda__345,axiom,
    ! [Uu: heap_T5738788834812785303t_unit,Uua: fun_Pr292408699144966967t_unit,Uub: heap_e7401611519738050253t_unit] : aa_hea684056619475940329it_nat(aa_fun3883837016763096701it_nat(aTP_Lamm_fs(Uu),Uua),Uub) = case_o2963978774867076333it_nat(none_P9117596204409417319it_nat,produc1230459020282432263it_nat(aTP_Lamm_fo(Uua)),aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(Uu),Uub)) ).

% ATP.lambda_345
tff(fact_8296_ATP_Olambda__346,axiom,
    ! [Uu: heap_T6362127782908069795rray_a,Uua: fun_ar1074044450438384043t_unit,Uub: heap_e7401611519738050253t_unit] : aa_hea684056619475940329it_nat(aa_fun3741944862212262031it_nat(aTP_Lamm_fr(Uu),Uua),Uub) = case_o3886096569520666655it_nat(none_P9117596204409417319it_nat,produc3495058329975564393it_nat(aTP_Lamm_fm(Uua)),aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(Uu),Uub)) ).

% ATP.lambda_346
tff(fact_8297_ATP_Olambda__347,axiom,
    ! [Uu: heap_T5738788834812785303t_unit,Uua: fun_Pr5924905948197006361rray_a,Uub: heap_e7401611519738050253t_unit] : aa_hea5936688510613671481it_nat(aa_fun6304779250881220759it_nat(aTP_Lamm_fq(Uu),Uua),Uub) = case_o5699750240967658439it_nat(none_P2587165478634041381it_nat,produc875294279294635931it_nat(aTP_Lamm_fk(Uua)),aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(Uu),Uub)) ).

% ATP.lambda_347
tff(fact_8298_ATP_Olambda__348,axiom,
    ! [Uu: heap_T6362127782908069795rray_a,Uua: fun_ar3891948820113774757rray_a,Uub: heap_e7401611519738050253t_unit] : aa_hea5936688510613671481it_nat(aa_fun8757595186270888873it_nat(aTP_Lamm_fp(Uu),Uua),Uub) = case_o8555119740594961093it_nat(none_P2587165478634041381it_nat,produc8915672860170107321it_nat(aTP_Lamm_fi(Uua)),aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(Uu),Uub)) ).

% ATP.lambda_348
tff(fact_8299_ATP_Olambda__349,axiom,
    ! [Uu: fun_nat_fun_nat_nat,Uua: nat,Uub: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_hw(Uu),Uua),Uub) = aa_nat_nat(aa_nat_fun_nat_nat(Uu,Uub),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uua),Uub)) ).

% ATP.lambda_349
tff(fact_8300_ATP_Olambda__350,axiom,
    ! [Uu: fun_nat_fun_nat_int,Uua: nat,Uub: nat] : aa_nat_int(aa_nat_fun_nat_int(aTP_Lamm_mn(Uu),Uua),Uub) = aa_nat_int(aa_nat_fun_nat_int(Uu,Uub),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uua),Uub)) ).

% ATP.lambda_350
tff(fact_8301_ATP_Olambda__351,axiom,
    ! [Uu: fun_nat_fun_nat_nat,Uua: nat,Uub: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_ja(Uu),Uua),Uub) = aa_nat_nat(aa_nat_fun_nat_nat(Uu,Uub),Uua) ).

% ATP.lambda_351
tff(fact_8302_ATP_Olambda__352,axiom,
    ! [Uu: fun_nat_fun_nat_int,Uua: nat,Uub: nat] : aa_nat_int(aa_nat_fun_nat_int(aTP_Lamm_la(Uu),Uua),Uub) = aa_nat_int(aa_nat_fun_nat_int(Uu,Uub),Uua) ).

% ATP.lambda_352
tff(fact_8303_ATP_Olambda__353,axiom,
    ! [Uu: code_integer,Uua: code_integer,Uub: code_integer] :
      aa_Cod3168588076859124107eger_o(aa_Cod1096751537565085541eger_o(aTP_Lamm_mb(Uu),Uua),Uub) = produc6677183202524767010eger_o($ite(aa_Code_integer_o(aa_Cod326357343816142457eger_o(ord_le6747313008572928689nteger,zero_z3403309356797280102nteger),Uu),Uua,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(minus_8373710615458151222nteger,aa_Cod1783974652533396728nteger(uminus1351360451143612070nteger,Uua)),Uub)),Uub = one_one_Code_integer) ).

% ATP.lambda_353
tff(fact_8304_ATP_Olambda__354,axiom,
    ! [Uu: fun_nat_fun_nat_int,Uua: nat,Uub: nat] : aa_nat_int(aa_nat_fun_nat_int(aTP_Lamm_lb(Uu),Uua),Uub) = groups705719431365010083at_int(aa_nat_fun_nat_int(aTP_Lamm_la(Uu),Uub),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,Uub)),Uua)) ).

% ATP.lambda_354
tff(fact_8305_ATP_Olambda__355,axiom,
    ! [Uu: fun_nat_fun_nat_nat,Uua: nat,Uub: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_ky(Uu),Uua),Uub) = aa_set_nat_nat(groups708209901874060359at_nat(aa_nat_fun_nat_nat(aTP_Lamm_ja(Uu),Uub)),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,Uub)),Uua)) ).

% ATP.lambda_355
tff(fact_8306_ATP_Olambda__356,axiom,
    ! [Uu: fun_nat_fun_nat_nat,Uua: nat,Uub: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_jb(Uu),Uua),Uub) = aa_set_nat_nat(groups3542108847815614940at_nat(aa_nat_fun_nat_nat(aTP_Lamm_ja(Uu),Uub)),aa_nat_set_nat(set_or1269000886237332187st_nat(aa_nat_nat(suc,Uub)),Uua)) ).

% ATP.lambda_356
tff(fact_8307_ATP_Olambda__357,axiom,
    ! [Uu: produc7822875418678951345atural,Uua: code_natural,Uub: code_natural] : aa_Cod6808739660676082561atural(aa_Cod4292056611156568242atural(aTP_Lamm_adl(Uu),Uua),Uub) = produc8282080750456430313atural(aa_Cod8811915439870959971atural(aTP_Lamm_adk(Uua),Uub),aa_Pro3673693039631929973atural(produc6591912806276919810atural,aa_Pro7165575656943818355atural(next,Uu))) ).

% ATP.lambda_357
tff(fact_8308_ATP_Olambda__358,axiom,
    ! [Uu: rat,Uua: int,Uub: int] : aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(aTP_Lamm_ng(Uu),Uua),Uub) = aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,aa_int1966403025003302569nt_int(aTP_Lamm_nf(Uua),Uub)),quotient_of(Uu)) ).

% ATP.lambda_358
tff(fact_8309_ATP_Olambda__359,axiom,
    ! [Uu: rat,Uua: int,Uub: int] : aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(aTP_Lamm_ne(Uu),Uua),Uub) = aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,aa_int1966403025003302569nt_int(aTP_Lamm_nd(Uua),Uub)),quotient_of(Uu)) ).

% ATP.lambda_359
tff(fact_8310_ATP_Olambda__360,axiom,
    ! [Uu: rat,Uua: int,Uub: int] : aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(aTP_Lamm_na(Uu),Uua),Uub) = aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,aa_int1966403025003302569nt_int(aTP_Lamm_mz(Uua),Uub)),quotient_of(Uu)) ).

% ATP.lambda_360
tff(fact_8311_ATP_Olambda__361,axiom,
    ! [Uu: rat,Uua: int,Uub: int] : aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(aTP_Lamm_my(Uu),Uua),Uub) = aa_Pro6970504127699319548nt_int(aa_fun8026974734089330650nt_int(produc4245557441103728435nt_int,aa_int1966403025003302569nt_int(aTP_Lamm_mx(Uua),Uub)),quotient_of(Uu)) ).

% ATP.lambda_361
tff(fact_8312_ATP_Olambda__362,axiom,
    ! [Uu: nat,Uua: nat,Uub: list_nat] :
      ( aa_list_nat_o(aa_nat5883842100386203267_nat_o(aTP_Lamm_adq(Uu),Uua),Uub)
    <=> ( ( aa_list_nat_nat(size_size_list_nat,Uub) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uu),one_one_nat) )
        & ( aa_list_nat_nat(groups4561878855575611511st_nat,Uub) = Uua ) ) ) ).

% ATP.lambda_362
tff(fact_8313_ATP_Olambda__363,axiom,
    ! [Uu: nat,Uua: nat,Uub: list_nat] :
      ( aa_list_nat_o(aa_nat5883842100386203267_nat_o(aTP_Lamm_adr(Uu),Uua),Uub)
    <=> ( ( aa_list_nat_nat(size_size_list_nat,Uub) = Uu )
        & ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_list_nat_nat(groups4561878855575611511st_nat,Uub)),one_one_nat) = Uua ) ) ) ).

% ATP.lambda_363
tff(fact_8314_ATP_Olambda__364,axiom,
    ! [Uu: nat,Uua: nat,Uub: list_nat] :
      ( aa_list_nat_o(aa_nat5883842100386203267_nat_o(aTP_Lamm_adp(Uu),Uua),Uub)
    <=> ( ( aa_list_nat_nat(size_size_list_nat,Uub) = Uu )
        & ( aa_list_nat_nat(groups4561878855575611511st_nat,Uub) = Uua ) ) ) ).

% ATP.lambda_364
tff(fact_8315_ATP_Olambda__365,axiom,
    ! [Uu: set_nat,Uua: nat,Uub: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(aTP_Lamm_sm(Uu),Uua),Uub)
    <=> ( member_nat(aa_nat_nat(suc,Uub),Uu)
        & aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,Uub),Uua) ) ) ).

% ATP.lambda_365
tff(fact_8316_ATP_Olambda__366,axiom,
    ! [Uu: set_nat,Uua: nat,Uub: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(aTP_Lamm_sn(Uu),Uua),Uub)
    <=> ( member_nat(Uub,Uu)
        & aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,Uub),aa_nat_nat(suc,Uua)) ) ) ).

% ATP.lambda_366
tff(fact_8317_ATP_Olambda__367,axiom,
    ! [Uu: set_Code_integer,Uua: set_Code_integer,Uub: set_Code_integer] :
      ( aa_set5643387332196575111eger_o(aa_set4044230130517860621eger_o(aTP_Lamm_os(Uu),Uua),Uub)
    <=> ( minus_2355218937544613996nteger(Uub,Uu) = minus_2355218937544613996nteger(Uua,Uu) ) ) ).

% ATP.lambda_367
tff(fact_8318_ATP_Olambda__368,axiom,
    ! [Uu: set_Pr1261947904930325089at_nat,Uua: set_Pr1261947904930325089at_nat,Uub: set_Pr1261947904930325089at_nat] :
      ( aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(aTP_Lamm_ot(Uu),Uua),Uub)
    <=> ( aa_set8868280134176360700at_nat(minus_1356011639430497352at_nat(Uub),Uu) = aa_set8868280134176360700at_nat(minus_1356011639430497352at_nat(Uua),Uu) ) ) ).

% ATP.lambda_368
tff(fact_8319_ATP_Olambda__369,axiom,
    ! [Uu: set_nat,Uua: set_nat,Uub: set_nat] :
      ( aa_set_nat_o(aa_set7861427066675100071_nat_o(aTP_Lamm_ou(Uu),Uua),Uub)
    <=> ( minus_minus_set_nat(Uub,Uu) = minus_minus_set_nat(Uua,Uu) ) ) ).

% ATP.lambda_369
tff(fact_8320_ATP_Olambda__370,axiom,
    ! [Uu: set_int,Uua: set_int,Uub: set_int] :
      ( aa_set_int_o(aa_set5425576183772390127_int_o(aTP_Lamm_or(Uu),Uua),Uub)
    <=> ( minus_minus_set_int(Uub,Uu) = minus_minus_set_int(Uua,Uu) ) ) ).

% ATP.lambda_370
tff(fact_8321_ATP_Olambda__371,axiom,
    ! [Uu: set_Code_integer,Uua: fun_Code_integer_o,Uub: code_integer] :
      ( aa_Code_integer_o(aa_fun8214818745163655228eger_o(aTP_Lamm_qu(Uu),Uua),Uub)
    <=> ( member_Code_integer(Uub,Uu)
        & aa_Code_integer_o(Uua,Uub) ) ) ).

% ATP.lambda_371
tff(fact_8322_ATP_Olambda__372,axiom,
    ! [Uu: set_o,Uua: fun_o_o,Uub: $o] :
      ( aa_o_o(aa_fun_o_o_fun_o_o(aTP_Lamm_qo(Uu),Uua),(Uub))
    <=> ( member_o((Uub),Uu)
        & aa_o_o(Uua,(Uub)) ) ) ).

% ATP.lambda_372
tff(fact_8323_ATP_Olambda__373,axiom,
    ! [Uu: set_nat,Uua: fun_nat_o,Uub: nat] :
      ( aa_nat_o(aa_fun5937193402907943164_nat_o(aTP_Lamm_qq(Uu),Uua),Uub)
    <=> ( member_nat(Uub,Uu)
        & aa_nat_o(Uua,Uub) ) ) ).

% ATP.lambda_373
tff(fact_8324_ATP_Olambda__374,axiom,
    ! [Uu: set_int,Uua: fun_int_o,Uub: int] :
      ( aa_int_o(aa_fun6243517787477317628_int_o(aTP_Lamm_qs(Uu),Uua),Uub)
    <=> ( member_int(Uub,Uu)
        & aa_int_o(Uua,Uub) ) ) ).

% ATP.lambda_374
tff(fact_8325_ATP_Olambda__375,axiom,
    ! [Uu: set_Code_integer,Uua: fun_Co744628173305925485nteger,Uub: code_integer] :
      ( aa_Code_integer_o(aa_fun7245632122240156009eger_o(aTP_Lamm_aau(Uu),Uua),Uub)
    <=> ( member_Code_integer(Uub,Uu)
        & ( aa_Cod2813182003028390446nteger(Uua,Uub) != bot_bo3990330152332043303nteger ) ) ) ).

% ATP.lambda_375
tff(fact_8326_ATP_Olambda__376,axiom,
    ! [Uu: set_o,Uua: fun_o_set_o,Uub: $o] :
      ( aa_o_o(aa_fun4619127644298054564un_o_o(aTP_Lamm_aav(Uu),Uua),(Uub))
    <=> ( member_o((Uub),Uu)
        & ( aa_o_set_o(Uua,(Uub)) != bot_bot_set_o ) ) ) ).

% ATP.lambda_376
tff(fact_8327_ATP_Olambda__377,axiom,
    ! [Uu: set_o,Uua: fun_o_set_nat,Uub: $o] :
      ( aa_o_o(aa_fun8423158570077026744un_o_o(aTP_Lamm_aay(Uu),Uua),(Uub))
    <=> ( member_o((Uub),Uu)
        & ( aa_o_set_nat(Uua,(Uub)) != bot_bot_set_nat ) ) ) ).

% ATP.lambda_377
tff(fact_8328_ATP_Olambda__378,axiom,
    ! [Uu: set_o,Uua: fun_o_set_int,Uub: $o] :
      ( aa_o_o(aa_fun3615580826569402900un_o_o(aTP_Lamm_abb(Uu),Uua),(Uub))
    <=> ( member_o((Uub),Uu)
        & ( aa_o_set_int(Uua,(Uub)) != bot_bot_set_int ) ) ) ).

% ATP.lambda_378
tff(fact_8329_ATP_Olambda__379,axiom,
    ! [Uu: set_nat,Uua: fun_nat_set_o,Uub: nat] :
      ( aa_nat_o(aa_fun4904187145036355100_nat_o(aTP_Lamm_aax(Uu),Uua),Uub)
    <=> ( member_nat(Uub,Uu)
        & ( aa_nat_set_o(Uua,Uub) != bot_bot_set_o ) ) ) ).

% ATP.lambda_379
tff(fact_8330_ATP_Olambda__380,axiom,
    ! [Uu: set_nat,Uua: fun_nat_set_nat,Uub: nat] :
      ( aa_nat_o(aa_fun2108954047564320208_nat_o(aTP_Lamm_aba(Uu),Uua),Uub)
    <=> ( member_nat(Uub,Uu)
        & ( aa_nat_set_nat(Uua,Uub) != bot_bot_set_nat ) ) ) ).

% ATP.lambda_380
tff(fact_8331_ATP_Olambda__381,axiom,
    ! [Uu: set_nat,Uua: fun_nat_set_int,Uub: nat] :
      ( aa_nat_o(aa_fun3985882680581680244_nat_o(aTP_Lamm_abc(Uu),Uua),Uub)
    <=> ( member_nat(Uub,Uu)
        & ( aa_nat_set_int(Uua,Uub) != bot_bot_set_int ) ) ) ).

% ATP.lambda_381
tff(fact_8332_ATP_Olambda__382,axiom,
    ! [Uu: set_int,Uua: fun_int_set_o,Uub: int] :
      ( aa_int_o(aa_fun4291261932532047132_int_o(aTP_Lamm_aaw(Uu),Uua),Uub)
    <=> ( member_int(Uub,Uu)
        & ( aa_int_set_o(Uua,Uub) != bot_bot_set_o ) ) ) ).

% ATP.lambda_382
tff(fact_8333_ATP_Olambda__383,axiom,
    ! [Uu: set_int,Uua: fun_int_set_nat,Uub: int] :
      ( aa_int_o(aa_fun1965424933913381656_int_o(aTP_Lamm_aaz(Uu),Uua),Uub)
    <=> ( member_int(Uub,Uu)
        & ( aa_int_set_nat(Uua,Uub) != bot_bot_set_nat ) ) ) ).

% ATP.lambda_383
tff(fact_8334_ATP_Olambda__384,axiom,
    ! [Uu: set_int,Uua: fun_int_set_int,Uub: int] :
      ( aa_int_o(aa_fun3842353566930741692_int_o(aTP_Lamm_abd(Uu),Uua),Uub)
    <=> ( member_int(Uub,Uu)
        & ( aa_int_set_int(Uua,Uub) != bot_bot_set_int ) ) ) ).

% ATP.lambda_384
tff(fact_8335_ATP_Olambda__385,axiom,
    ! [Uu: set_Code_integer,Uua: fun_Co8499238673658658103nteger,Uub: code_integer] :
      ( aa_Code_integer_o(aa_fun7159535342743012639eger_o(aTP_Lamm_pd(Uu),Uua),Uub)
    <=> ( member_Code_integer(Uub,Uu)
        & ( aa_Cod1783974652533396728nteger(Uua,Uub) != zero_z3403309356797280102nteger ) ) ) ).

% ATP.lambda_385
tff(fact_8336_ATP_Olambda__386,axiom,
    ! [Uu: set_Code_integer,Uua: fun_Code_integer_rat,Uub: code_integer] :
      ( aa_Code_integer_o(aa_fun6395433285121891940eger_o(aTP_Lamm_pl(Uu),Uua),Uub)
    <=> ( member_Code_integer(Uub,Uu)
        & ( aa_Code_integer_rat(Uua,Uub) != zero_zero_rat ) ) ) ).

% ATP.lambda_386
tff(fact_8337_ATP_Olambda__387,axiom,
    ! [Uu: set_o,Uua: fun_o_Code_integer,Uub: $o] :
      ( aa_o_o(aa_fun8192762245619933327un_o_o(aTP_Lamm_ox(Uu),Uua),(Uub))
    <=> ( member_o((Uub),Uu)
        & ( aa_o_Code_integer(Uua,(Uub)) != zero_z3403309356797280102nteger ) ) ) ).

% ATP.lambda_387
tff(fact_8338_ATP_Olambda__388,axiom,
    ! [Uu: set_o,Uua: fun_o_rat,Uub: $o] :
      ( aa_o_o(aa_fun_o_rat_fun_o_o(aTP_Lamm_pf(Uu),Uua),(Uub))
    <=> ( member_o((Uub),Uu)
        & ( aa_o_rat(Uua,(Uub)) != zero_zero_rat ) ) ) ).

% ATP.lambda_388
tff(fact_8339_ATP_Olambda__389,axiom,
    ! [Uu: set_o,Uua: fun_o_nat,Uub: $o] :
      ( aa_o_o(aa_fun_o_nat_fun_o_o(aTP_Lamm_pn(Uu),Uua),(Uub))
    <=> ( member_o((Uub),Uu)
        & ( aa_o_nat(Uua,(Uub)) != zero_zero_nat ) ) ) ).

% ATP.lambda_389
tff(fact_8340_ATP_Olambda__390,axiom,
    ! [Uu: set_nat,Uua: fun_nat_Code_integer,Uub: nat] :
      ( aa_nat_o(aa_fun3480067038916266681_nat_o(aTP_Lamm_oz(Uu),Uua),Uub)
    <=> ( member_nat(Uub,Uu)
        & ( aa_nat_Code_integer(Uua,Uub) != zero_z3403309356797280102nteger ) ) ) ).

% ATP.lambda_390
tff(fact_8341_ATP_Olambda__391,axiom,
    ! [Uu: set_nat,Uua: fun_nat_rat,Uub: nat] :
      ( aa_nat_o(aa_fun1118977351124560894_nat_o(aTP_Lamm_ph(Uu),Uua),Uub)
    <=> ( member_nat(Uub,Uu)
        & ( aa_nat_rat(Uua,Uub) != zero_zero_rat ) ) ) ).

% ATP.lambda_391
tff(fact_8342_ATP_Olambda__392,axiom,
    ! [Uu: set_nat,Uua: fun_nat_nat,Uub: nat] :
      ( aa_nat_o(aa_fun8673969331427483654_nat_o(aTP_Lamm_pp(Uu),Uua),Uub)
    <=> ( member_nat(Uub,Uu)
        & ( aa_nat_nat(Uua,Uub) != zero_zero_nat ) ) ) ).

% ATP.lambda_392
tff(fact_8343_ATP_Olambda__393,axiom,
    ! [Uu: set_int,Uua: fun_int_Code_integer,Uub: int] :
      ( aa_int_o(aa_fun3336537925265328129_int_o(aTP_Lamm_pb(Uu),Uua),Uub)
    <=> ( member_int(Uub,Uu)
        & ( aa_int_Code_integer(Uua,Uub) != zero_z3403309356797280102nteger ) ) ) ).

% ATP.lambda_393
tff(fact_8344_ATP_Olambda__394,axiom,
    ! [Uu: set_int,Uua: fun_int_rat,Uub: int] :
      ( aa_int_o(aa_fun7094158214180239686_int_o(aTP_Lamm_pj(Uu),Uua),Uub)
    <=> ( member_int(Uub,Uu)
        & ( aa_int_rat(Uua,Uub) != zero_zero_rat ) ) ) ).

% ATP.lambda_394
tff(fact_8345_ATP_Olambda__395,axiom,
    ! [Uu: set_Code_integer,Uua: fun_Co8499238673658658103nteger,Uub: code_integer] :
      ( aa_Code_integer_o(aa_fun7159535342743012639eger_o(aTP_Lamm_px(Uu),Uua),Uub)
    <=> ( member_Code_integer(Uub,Uu)
        & ( aa_Cod1783974652533396728nteger(Uua,Uub) != one_one_Code_integer ) ) ) ).

% ATP.lambda_395
tff(fact_8346_ATP_Olambda__396,axiom,
    ! [Uu: set_Code_integer,Uua: fun_Co4490034186337852034r_assn,Uub: code_integer] :
      ( aa_Code_integer_o(aa_fun6538703224075513620eger_o(aTP_Lamm_qf(Uu),Uua),Uub)
    <=> ( member_Code_integer(Uub,Uu)
        & ( aa_Code_integer_assn(Uua,Uub) != one_one_assn ) ) ) ).

% ATP.lambda_396
tff(fact_8347_ATP_Olambda__397,axiom,
    ! [Uu: set_o,Uua: fun_o_Code_integer,Uub: $o] :
      ( aa_o_o(aa_fun8192762245619933327un_o_o(aTP_Lamm_pr(Uu),Uua),(Uub))
    <=> ( member_o((Uub),Uu)
        & ( aa_o_Code_integer(Uua,(Uub)) != one_one_Code_integer ) ) ) ).

% ATP.lambda_397
tff(fact_8348_ATP_Olambda__398,axiom,
    ! [Uu: set_o,Uua: fun_o_assn,Uub: $o] :
      ( aa_o_o(aa_fun8382565201914911066un_o_o(aTP_Lamm_pz(Uu),Uua),(Uub))
    <=> ( member_o((Uub),Uu)
        & ( aa_o_assn(Uua,(Uub)) != one_one_assn ) ) ) ).

% ATP.lambda_398
tff(fact_8349_ATP_Olambda__399,axiom,
    ! [Uu: set_o,Uua: fun_o_rat,Uub: $o] :
      ( aa_o_o(aa_fun_o_rat_fun_o_o(aTP_Lamm_qh(Uu),Uua),(Uub))
    <=> ( member_o((Uub),Uu)
        & ( aa_o_rat(Uua,(Uub)) != one_one_rat ) ) ) ).

% ATP.lambda_399
tff(fact_8350_ATP_Olambda__400,axiom,
    ! [Uu: set_nat,Uua: fun_nat_Code_integer,Uub: nat] :
      ( aa_nat_o(aa_fun3480067038916266681_nat_o(aTP_Lamm_pt(Uu),Uua),Uub)
    <=> ( member_nat(Uub,Uu)
        & ( aa_nat_Code_integer(Uua,Uub) != one_one_Code_integer ) ) ) ).

% ATP.lambda_400
tff(fact_8351_ATP_Olambda__401,axiom,
    ! [Uu: set_nat,Uua: fun_nat_assn,Uub: nat] :
      ( aa_nat_o(aa_fun7183233715851567790_nat_o(aTP_Lamm_qb(Uu),Uua),Uub)
    <=> ( member_nat(Uub,Uu)
        & ( aa_nat_assn(Uua,Uub) != one_one_assn ) ) ) ).

% ATP.lambda_401
tff(fact_8352_ATP_Olambda__402,axiom,
    ! [Uu: set_nat,Uua: fun_nat_rat,Uub: nat] :
      ( aa_nat_o(aa_fun1118977351124560894_nat_o(aTP_Lamm_qj(Uu),Uua),Uub)
    <=> ( member_nat(Uub,Uu)
        & ( aa_nat_rat(Uua,Uub) != one_one_rat ) ) ) ).

% ATP.lambda_402
tff(fact_8353_ATP_Olambda__403,axiom,
    ! [Uu: set_int,Uua: fun_int_Code_integer,Uub: int] :
      ( aa_int_o(aa_fun3336537925265328129_int_o(aTP_Lamm_pv(Uu),Uua),Uub)
    <=> ( member_int(Uub,Uu)
        & ( aa_int_Code_integer(Uua,Uub) != one_one_Code_integer ) ) ) ).

% ATP.lambda_403
tff(fact_8354_ATP_Olambda__404,axiom,
    ! [Uu: set_int,Uua: fun_int_assn,Uub: int] :
      ( aa_int_o(aa_fun202081646129719286_int_o(aTP_Lamm_qd(Uu),Uua),Uub)
    <=> ( member_int(Uub,Uu)
        & ( aa_int_assn(Uua,Uub) != one_one_assn ) ) ) ).

% ATP.lambda_404
tff(fact_8355_ATP_Olambda__405,axiom,
    ! [Uu: fun_Co8499238673658658103nteger,Uua: set_Code_integer,Uub: code_integer] :
      ( aa_Code_integer_o(aa_set8032437628614644675eger_o(aTP_Lamm_ti(Uu),Uua),Uub)
    <=> ( member_Code_integer(Uub,Uua)
        & ( aa_Cod1783974652533396728nteger(Uu,Uub) != one_one_Code_integer ) ) ) ).

% ATP.lambda_405
tff(fact_8356_ATP_Olambda__406,axiom,
    ! [Uu: fun_Co4490034186337852034r_assn,Uua: set_Code_integer,Uub: code_integer] :
      ( aa_Code_integer_o(aa_set8032437628614644675eger_o(aTP_Lamm_tj(Uu),Uua),Uub)
    <=> ( member_Code_integer(Uub,Uua)
        & ( aa_Code_integer_assn(Uu,Uub) != one_one_assn ) ) ) ).

% ATP.lambda_406
tff(fact_8357_ATP_Olambda__407,axiom,
    ! [Uu: fun_o_Code_integer,Uua: set_o,Uub: $o] :
      ( aa_o_o(aa_set_o_fun_o_o(aTP_Lamm_so(Uu),Uua),(Uub))
    <=> ( member_o((Uub),Uua)
        & ( aa_o_Code_integer(Uu,(Uub)) != one_one_Code_integer ) ) ) ).

% ATP.lambda_407
tff(fact_8358_ATP_Olambda__408,axiom,
    ! [Uu: fun_o_assn,Uua: set_o,Uub: $o] :
      ( aa_o_o(aa_set_o_fun_o_o(aTP_Lamm_sr(Uu),Uua),(Uub))
    <=> ( member_o((Uub),Uua)
        & ( aa_o_assn(Uu,(Uub)) != one_one_assn ) ) ) ).

% ATP.lambda_408
tff(fact_8359_ATP_Olambda__409,axiom,
    ! [Uu: fun_o_rat,Uua: set_o,Uub: $o] :
      ( aa_o_o(aa_set_o_fun_o_o(aTP_Lamm_su(Uu),Uua),(Uub))
    <=> ( member_o((Uub),Uua)
        & ( aa_o_rat(Uu,(Uub)) != one_one_rat ) ) ) ).

% ATP.lambda_409
tff(fact_8360_ATP_Olambda__410,axiom,
    ! [Uu: fun_o_nat,Uua: set_o,Uub: $o] :
      ( aa_o_o(aa_set_o_fun_o_o(aTP_Lamm_sx(Uu),Uua),(Uub))
    <=> ( member_o((Uub),Uua)
        & ( aa_o_nat(Uu,(Uub)) != one_one_nat ) ) ) ).

% ATP.lambda_410
tff(fact_8361_ATP_Olambda__411,axiom,
    ! [Uu: fun_nat_Code_integer,Uua: set_nat,Uub: nat] :
      ( aa_nat_o(aa_set_nat_fun_nat_o(aTP_Lamm_sq(Uu),Uua),Uub)
    <=> ( member_nat(Uub,Uua)
        & ( aa_nat_Code_integer(Uu,Uub) != one_one_Code_integer ) ) ) ).

% ATP.lambda_411
tff(fact_8362_ATP_Olambda__412,axiom,
    ! [Uu: fun_nat_assn,Uua: set_nat,Uub: nat] :
      ( aa_nat_o(aa_set_nat_fun_nat_o(aTP_Lamm_st(Uu),Uua),Uub)
    <=> ( member_nat(Uub,Uua)
        & ( aa_nat_assn(Uu,Uub) != one_one_assn ) ) ) ).

% ATP.lambda_412
tff(fact_8363_ATP_Olambda__413,axiom,
    ! [Uu: fun_nat_rat,Uua: set_nat,Uub: nat] :
      ( aa_nat_o(aa_set_nat_fun_nat_o(aTP_Lamm_sw(Uu),Uua),Uub)
    <=> ( member_nat(Uub,Uua)
        & ( aa_nat_rat(Uu,Uub) != one_one_rat ) ) ) ).

% ATP.lambda_413
tff(fact_8364_ATP_Olambda__414,axiom,
    ! [Uu: fun_int_Code_integer,Uua: set_int,Uub: int] :
      ( aa_int_o(aa_set_int_fun_int_o(aTP_Lamm_sp(Uu),Uua),Uub)
    <=> ( member_int(Uub,Uua)
        & ( aa_int_Code_integer(Uu,Uub) != one_one_Code_integer ) ) ) ).

% ATP.lambda_414
tff(fact_8365_ATP_Olambda__415,axiom,
    ! [Uu: fun_int_assn,Uua: set_int,Uub: int] :
      ( aa_int_o(aa_set_int_fun_int_o(aTP_Lamm_ss(Uu),Uua),Uub)
    <=> ( member_int(Uub,Uua)
        & ( aa_int_assn(Uu,Uub) != one_one_assn ) ) ) ).

% ATP.lambda_415
tff(fact_8366_ATP_Olambda__416,axiom,
    ! [Uu: fun_int_rat,Uua: set_int,Uub: int] :
      ( aa_int_o(aa_set_int_fun_int_o(aTP_Lamm_sv(Uu),Uua),Uub)
    <=> ( member_int(Uub,Uua)
        & ( aa_int_rat(Uu,Uub) != one_one_rat ) ) ) ).

% ATP.lambda_416
tff(fact_8367_ATP_Olambda__417,axiom,
    ! [Uu: nat,Uua: nat,Uub: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(aTP_Lamm_hv(Uu),Uua),Uub)
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uua),Uub)),Uu) ) ).

% ATP.lambda_417
tff(fact_8368_ATP_Olambda__418,axiom,
    ! [Uu: nat,Uua: nat,Uub: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(aTP_Lamm_iw(Uu),Uua),Uub)
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uua),Uub)),Uu) ) ).

% ATP.lambda_418
tff(fact_8369_ATP_Olambda__419,axiom,
    ! [Uu: rat,Uua: rat,Uub: rat] : aa_rat_rat(aa_rat_fun_rat_rat(aTP_Lamm_nj(Uu),Uua),Uub) = aa_rat_rat(minus_minus_rat(aa_rat_rat(divide_divide_rat(Uub),Uu)),Uua) ).

% ATP.lambda_419
tff(fact_8370_ATP_Olambda__420,axiom,
    ! [Uu: rat,Uua: rat,Uub: rat] : aa_rat_rat(aa_rat_fun_rat_rat(aTP_Lamm_nl(Uu),Uua),Uub) = aa_rat_rat(minus_minus_rat(aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,Uu),Uub)),Uua) ).

% ATP.lambda_420
tff(fact_8371_ATP_Olambda__421,axiom,
    ! [Uu: rat,Uua: rat,Uub: rat] : aa_rat_rat(aa_rat_fun_rat_rat(aTP_Lamm_nk(Uu),Uua),Uub) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(divide_divide_rat(Uub),Uu)),Uua) ).

% ATP.lambda_421
tff(fact_8372_ATP_Olambda__422,axiom,
    ! [Uu: rat,Uua: rat,Uub: rat] : aa_rat_rat(aa_rat_fun_rat_rat(aTP_Lamm_np(Uu),Uua),Uub) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,Uu),Uub)),Uua) ).

% ATP.lambda_422
tff(fact_8373_ATP_Olambda__423,axiom,
    ! [Uu: set_Pr8693737435421807431at_nat,Uua: product_prod_nat_nat,Uub: product_prod_nat_nat] :
      ( aa_Pro6150637604445964947_nat_o(aa_Pro989595756709598047_nat_o(aTP_Lamm_tz(Uu),Uua),Uub)
    <=> member8206827879206165904at_nat(produc6161850002892822231at_nat(Uua,Uub),Uu) ) ).

% ATP.lambda_423
tff(fact_8374_ATP_Olambda__424,axiom,
    ! [Uu: set_Pr4329608150637261639at_nat,Uua: set_Pr1261947904930325089at_nat,Uub: set_Pr1261947904930325089at_nat] :
      ( aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(aa_set5605188905385065315_nat_o(aTP_Lamm_bu,Uu),Uua),Uub)
    <=> member8757157785044589968at_nat(produc2922128104949294807at_nat(Uua,Uub),Uu) ) ).

% ATP.lambda_424
tff(fact_8375_ATP_Olambda__425,axiom,
    ! [Uu: set_Pr1261947904930325089at_nat,Uua: nat,Uub: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(aa_set2634951030311766213_nat_o(aTP_Lamm_bv,Uu),Uua),Uub)
    <=> member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Uua),Uub),Uu) ) ).

% ATP.lambda_425
tff(fact_8376_ATP_Olambda__426,axiom,
    ! [Uu: set_Pr3486312109254157132nteger,Uua: fun_Pr5098669352780829690e_term,Uub: produc8923325533196201883nteger] :
      ( aa_Pro4926521453222654329eger_o(aa_fun4505422719058378424eger_o(aa_set282680696547864321eger_o(aTP_Lamm_bw,Uu),Uua),Uub)
    <=> member8978266922497061677nteger(aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,Uua),Uub),Uu) ) ).

% ATP.lambda_426
tff(fact_8377_ATP_Olambda__427,axiom,
    ! [Uu: set_Pr1312406793078187350et_nat,Uua: fun_Pr6460944699146269935_nat_o,Uub: produc3658429121746597890et_nat] :
      ( aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(aa_set6295625606485646487_nat_o(aTP_Lamm_bx,Uu),Uua),Uub)
    <=> member4513763875858039863et_nat(aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,Uua),Uub),Uu) ) ).

% ATP.lambda_427
tff(fact_8378_ATP_Olambda__428,axiom,
    ! [Uu: set_Pr4040394263813967220et_nat,Uua: fun_Pr6460944699146269935_nat_o,Uub: produc8799533983703829792et_nat] :
      ( aa_Pro5643009357358181178_nat_o(aa_fun912680268133416158_nat_o(aa_set2269662337286943895_nat_o(aTP_Lamm_by,Uu),Uua),Uub)
    <=> member9174161442226468181et_nat(aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,Uua),Uub),Uu) ) ).

% ATP.lambda_428
tff(fact_8379_ATP_Olambda__429,axiom,
    ! [Uu: set_Pr6700895561065273913nt_int,Uua: fun_Pr7763680713840462443e_term,Uub: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(aa_fun3538162476766722827_int_o(aa_set8857007276572228673_int_o(aTP_Lamm_bz,Uu),Uua),Uub)
    <=> member753276645541486746nt_int(aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,Uua),Uub),Uu) ) ).

% ATP.lambda_429
tff(fact_8380_ATP_Olambda__430,axiom,
    ! [Uu: set_Pr4166680992137330533nt_int,Uua: fun_in5730379987311621695e_term,Uub: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(aa_fun586359091965693151_int_o(aa_set6932945912113297217_int_o(aTP_Lamm_ca,Uu),Uua),Uub)
    <=> member5890090881338784710nt_int(aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,Uua),Uub),Uu) ) ).

% ATP.lambda_430
tff(fact_8381_ATP_Olambda__431,axiom,
    ! [Uu: fun_nat_o,Uua: nat,Uub: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(aTP_Lamm_ov(Uu),Uua),Uub)
    <=> ( aa_nat_o(Uu,Uub)
        & aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,Uub),Uua) ) ) ).

% ATP.lambda_431
tff(fact_8382_ATP_Olambda__432,axiom,
    ! [Uu: fun_Co8499238673658658103nteger,Uua: fun_Co8499238673658658103nteger,Uub: code_integer] : aa_Cod1783974652533396728nteger(aa_fun4435975922079263404nteger(aTP_Lamm_tb(Uu),Uua),Uub) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(Uu,Uub)),aa_Cod1783974652533396728nteger(Uua,Uub)) ).

% ATP.lambda_432
tff(fact_8383_ATP_Olambda__433,axiom,
    ! [Uu: fun_Co4490034186337852034r_assn,Uua: fun_Co4490034186337852034r_assn,Uub: code_integer] : aa_Code_integer_assn(aa_fun4119713415300323650r_assn(aTP_Lamm_tf(Uu),Uua),Uub) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_Code_integer_assn(Uu,Uub)),aa_Code_integer_assn(Uua,Uub)) ).

% ATP.lambda_433
tff(fact_8384_ATP_Olambda__434,axiom,
    ! [Uu: fun_o_Code_integer,Uua: fun_o_Code_integer,Uub: $o] : aa_o_Code_integer(aa_fun8520278569782659900nteger(aTP_Lamm_sy(Uu),Uua),(Uub)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_o_Code_integer(Uu,(Uub))),aa_o_Code_integer(Uua,(Uub))) ).

% ATP.lambda_434
tff(fact_8385_ATP_Olambda__435,axiom,
    ! [Uu: fun_o_assn,Uua: fun_o_assn,Uub: $o] : aa_o_assn(aa_fun4536517337817438332o_assn(aTP_Lamm_tc(Uu),Uua),(Uub)) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_o_assn(Uu,(Uub))),aa_o_assn(Uua,(Uub))) ).

% ATP.lambda_435
tff(fact_8386_ATP_Olambda__436,axiom,
    ! [Uu: fun_o_rat,Uua: fun_o_rat,Uub: $o] : aa_o_rat(aa_fun4336163974892599420_o_rat(aTP_Lamm_tg(Uu),Uua),(Uub)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_o_rat(Uu,(Uub))),aa_o_rat(Uua,(Uub))) ).

% ATP.lambda_436
tff(fact_8387_ATP_Olambda__437,axiom,
    ! [Uu: fun_nat_Code_integer,Uua: fun_nat_Code_integer,Uub: nat] : aa_nat_Code_integer(aa_fun589076786913273746nteger(aTP_Lamm_sz(Uu),Uua),Uub) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(Uu,Uub)),aa_nat_Code_integer(Uua,Uub)) ).

% ATP.lambda_437
tff(fact_8388_ATP_Olambda__438,axiom,
    ! [Uu: fun_nat_assn,Uua: fun_nat_assn,Uub: nat] : aa_nat_assn(aa_fun785744391571715112t_assn(aTP_Lamm_td(Uu),Uua),Uub) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_nat_assn(Uu,Uub)),aa_nat_assn(Uua,Uub)) ).

% ATP.lambda_438
tff(fact_8389_ATP_Olambda__439,axiom,
    ! [Uu: fun_nat_rat,Uua: fun_nat_rat,Uub: nat] : aa_nat_rat(aa_fun765758790203053448at_rat(aTP_Lamm_th(Uu),Uua),Uub) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(Uu,Uub)),aa_nat_rat(Uua,Uub)) ).

% ATP.lambda_439
tff(fact_8390_ATP_Olambda__440,axiom,
    ! [Uu: fun_int_Code_integer,Uua: fun_int_Code_integer,Uub: int] : aa_int_Code_integer(aa_fun5304498221708291146nteger(aTP_Lamm_ta(Uu),Uua),Uub) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_int_Code_integer(Uu,Uub)),aa_int_Code_integer(Uua,Uub)) ).

% ATP.lambda_440
tff(fact_8391_ATP_Olambda__441,axiom,
    ! [Uu: fun_int_assn,Uua: fun_int_assn,Uub: int] : aa_int_assn(aa_fun919007281442365664t_assn(aTP_Lamm_te(Uu),Uua),Uub) = aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_int_assn(Uu,Uub)),aa_int_assn(Uua,Uub)) ).

% ATP.lambda_441
tff(fact_8392_ATP_Olambda__442,axiom,
    ! [Uu: fun_Pr6026251430685297nteger,Uua: fun_Pr6026251430685297nteger,Uub: product_prod_nat_nat] : aa_Pro4764841431850000930nteger(aa_fun1555571767557915900nteger(aTP_Lamm_ep(Uu),Uua),Uub) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Pro4764841431850000930nteger(Uua,Uub)),aa_Pro4764841431850000930nteger(Uu,Uub)) ).

% ATP.lambda_442
tff(fact_8393_ATP_Olambda__443,axiom,
    ! [Uu: fun_o_Code_integer,Uua: fun_o_Code_integer,Uub: $o] : aa_o_Code_integer(aa_fun8520278569782659900nteger(aTP_Lamm_eg(Uu),Uua),(Uub)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_o_Code_integer(Uua,(Uub))),aa_o_Code_integer(Uu,(Uub))) ).

% ATP.lambda_443
tff(fact_8394_ATP_Olambda__444,axiom,
    ! [Uu: fun_o_rat,Uua: fun_o_rat,Uub: $o] : aa_o_rat(aa_fun4336163974892599420_o_rat(aTP_Lamm_ej(Uu),Uua),(Uub)) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_o_rat(Uua,(Uub))),aa_o_rat(Uu,(Uub))) ).

% ATP.lambda_444
tff(fact_8395_ATP_Olambda__445,axiom,
    ! [Uu: fun_o_int,Uua: fun_o_int,Uub: $o] : aa_o_int(aa_fun4727766026823762812_o_int(aTP_Lamm_em(Uu),Uua),(Uub)) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_o_int(Uua,(Uub))),aa_o_int(Uu,(Uub))) ).

% ATP.lambda_445
tff(fact_8396_ATP_Olambda__446,axiom,
    ! [Uu: fun_nat_Code_integer,Uua: fun_nat_Code_integer,Uub: nat] : aa_nat_Code_integer(aa_fun589076786913273746nteger(aTP_Lamm_eh(Uu),Uua),Uub) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(Uua,Uub)),aa_nat_Code_integer(Uu,Uub)) ).

% ATP.lambda_446
tff(fact_8397_ATP_Olambda__447,axiom,
    ! [Uu: fun_nat_rat,Uua: fun_nat_rat,Uub: nat] : aa_nat_rat(aa_fun765758790203053448at_rat(aTP_Lamm_ek(Uu),Uua),Uub) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(Uua,Uub)),aa_nat_rat(Uu,Uub)) ).

% ATP.lambda_447
tff(fact_8398_ATP_Olambda__448,axiom,
    ! [Uu: fun_nat_int,Uua: fun_nat_int,Uub: nat] : aa_nat_int(aa_fun5565043122120104496at_int(aTP_Lamm_en(Uu),Uua),Uub) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(Uua,Uub)),aa_nat_int(Uu,Uub)) ).

% ATP.lambda_448
tff(fact_8399_ATP_Olambda__449,axiom,
    ! [Uu: fun_int_Code_integer,Uua: fun_int_Code_integer,Uub: int] : aa_int_Code_integer(aa_fun5304498221708291146nteger(aTP_Lamm_ei(Uu),Uua),Uub) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_int_Code_integer(Uua,Uub)),aa_int_Code_integer(Uu,Uub)) ).

% ATP.lambda_449
tff(fact_8400_ATP_Olambda__450,axiom,
    ! [Uu: fun_int_rat,Uua: fun_int_rat,Uub: int] : aa_int_rat(aa_fun1481061427733998144nt_rat(aTP_Lamm_el(Uu),Uua),Uub) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_int_rat(Uua,Uub)),aa_int_rat(Uu,Uub)) ).

% ATP.lambda_450
tff(fact_8401_ATP_Olambda__451,axiom,
    ! [Uu: fun_int_int,Uua: fun_int_int,Uub: int] : aa_int_int(aa_fun6280345759651049192nt_int(aTP_Lamm_eo(Uu),Uua),Uub) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(Uua,Uub)),aa_int_int(Uu,Uub)) ).

% ATP.lambda_451
tff(fact_8402_ATP_Olambda__452,axiom,
    ! [Uu: fun_nat_nat,Uua: fun_nat_nat,Uub: nat] : aa_nat_nat(aa_fun5791449513213591928at_nat(aTP_Lamm_iy(Uu),Uua),Uub) = aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(Uua,Uub)),aa_nat_nat(Uu,Uub)) ).

% ATP.lambda_452
tff(fact_8403_ATP_Olambda__453,axiom,
    ! [Uu: fun_se953073389798102371at_nat,Uua: fun_se953073389798102371at_nat,Uub: set_Pr1261947904930325089at_nat] : aa_set6242432332095302236at_nat(aa_fun3786497492886271492at_nat(aTP_Lamm_acm(Uu),Uua),Uub) = sup_su3642409539654194069at_nat(aa_set6242432332095302236at_nat(Uu,Uub),aa_set6242432332095302236at_nat(Uua,Uub)) ).

% ATP.lambda_453
tff(fact_8404_ATP_Olambda__454,axiom,
    ! [Uu: fun_Co8499238673658658103nteger,Uua: fun_Co8499238673658658103nteger,Uub: code_integer] : aa_Cod1783974652533396728nteger(aa_fun4435975922079263404nteger(aTP_Lamm_tv(Uu),Uua),Uub) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(Uu,Uub)),aa_Cod1783974652533396728nteger(Uua,Uub)) ).

% ATP.lambda_454
tff(fact_8405_ATP_Olambda__455,axiom,
    ! [Uu: fun_Code_integer_rat,Uua: fun_Code_integer_rat,Uub: code_integer] : aa_Code_integer_rat(aa_fun8169474305930283170er_rat(aTP_Lamm_tm(Uu),Uua),Uub) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_Code_integer_rat(Uu,Uub)),aa_Code_integer_rat(Uua,Uub)) ).

% ATP.lambda_455
tff(fact_8406_ATP_Olambda__456,axiom,
    ! [Uu: fun_Code_integer_nat,Uua: fun_Code_integer_nat,Uub: code_integer] : aa_Code_integer_nat(aa_fun3076867170244285586er_nat(aTP_Lamm_to(Uu),Uua),Uub) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_Code_integer_nat(Uu,Uub)),aa_Code_integer_nat(Uua,Uub)) ).

% ATP.lambda_456
tff(fact_8407_ATP_Olambda__457,axiom,
    ! [Uu: fun_Code_integer_int,Uua: fun_Code_integer_int,Uub: code_integer] : aa_Code_integer_int(aa_fun3291479149765983562er_int(aTP_Lamm_tq(Uu),Uua),Uub) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_Code_integer_int(Uu,Uub)),aa_Code_integer_int(Uua,Uub)) ).

% ATP.lambda_457
tff(fact_8408_ATP_Olambda__458,axiom,
    ! [Uu: fun_Pr8317260874932935276at_rat,Uua: fun_Pr8317260874932935276at_rat,Uub: product_prod_nat_nat] : aa_Pro3608043709957902237at_rat(aa_fun1488288443938188604at_rat(aTP_Lamm_tr(Uu),Uua),Uub) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_Pro3608043709957902237at_rat(Uu,Uub)),aa_Pro3608043709957902237at_rat(Uua,Uub)) ).

% ATP.lambda_458
tff(fact_8409_ATP_Olambda__459,axiom,
    ! [Uu: fun_o_Code_integer,Uua: fun_o_Code_integer,Uub: $o] : aa_o_Code_integer(aa_fun8520278569782659900nteger(aTP_Lamm_ts(Uu),Uua),(Uub)) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_o_Code_integer(Uu,(Uub))),aa_o_Code_integer(Uua,(Uub))) ).

% ATP.lambda_459
tff(fact_8410_ATP_Olambda__460,axiom,
    ! [Uu: fun_o_rat,Uua: fun_o_rat,Uub: $o] : aa_o_rat(aa_fun4336163974892599420_o_rat(aTP_Lamm_tw(Uu),Uua),(Uub)) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_o_rat(Uu,(Uub))),aa_o_rat(Uua,(Uub))) ).

% ATP.lambda_460
tff(fact_8411_ATP_Olambda__461,axiom,
    ! [Uu: fun_o_nat,Uua: fun_o_nat,Uub: $o] : aa_o_nat(aa_fun6176012476734143100_o_nat(aTP_Lamm_tx(Uu),Uua),(Uub)) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_o_nat(Uu,(Uub))),aa_o_nat(Uua,(Uub))) ).

% ATP.lambda_461
tff(fact_8412_ATP_Olambda__462,axiom,
    ! [Uu: fun_nat_Code_integer,Uua: fun_nat_Code_integer,Uub: nat] : aa_nat_Code_integer(aa_fun589076786913273746nteger(aTP_Lamm_tt(Uu),Uua),Uub) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_nat_Code_integer(Uu,Uub)),aa_nat_Code_integer(Uua,Uub)) ).

% ATP.lambda_462
tff(fact_8413_ATP_Olambda__463,axiom,
    ! [Uu: fun_nat_rat,Uua: fun_nat_rat,Uub: nat] : aa_nat_rat(aa_fun765758790203053448at_rat(aTP_Lamm_tk(Uu),Uua),Uub) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(Uu,Uub)),aa_nat_rat(Uua,Uub)) ).

% ATP.lambda_463
tff(fact_8414_ATP_Olambda__464,axiom,
    ! [Uu: fun_nat_nat,Uua: fun_nat_nat,Uub: nat] : aa_nat_nat(aa_fun5791449513213591928at_nat(aTP_Lamm_er(Uu),Uua),Uub) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(Uu,Uub)),aa_nat_nat(Uua,Uub)) ).

% ATP.lambda_464
tff(fact_8415_ATP_Olambda__465,axiom,
    ! [Uu: fun_nat_int,Uua: fun_nat_int,Uub: nat] : aa_nat_int(aa_fun5565043122120104496at_int(aTP_Lamm_tp(Uu),Uua),Uub) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_nat_int(Uu,Uub)),aa_nat_int(Uua,Uub)) ).

% ATP.lambda_465
tff(fact_8416_ATP_Olambda__466,axiom,
    ! [Uu: fun_int_Code_integer,Uua: fun_int_Code_integer,Uub: int] : aa_int_Code_integer(aa_fun5304498221708291146nteger(aTP_Lamm_tu(Uu),Uua),Uub) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_int_Code_integer(Uu,Uub)),aa_int_Code_integer(Uua,Uub)) ).

% ATP.lambda_466
tff(fact_8417_ATP_Olambda__467,axiom,
    ! [Uu: fun_int_rat,Uua: fun_int_rat,Uub: int] : aa_int_rat(aa_fun1481061427733998144nt_rat(aTP_Lamm_tl(Uu),Uua),Uub) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_int_rat(Uu,Uub)),aa_int_rat(Uua,Uub)) ).

% ATP.lambda_467
tff(fact_8418_ATP_Olambda__468,axiom,
    ! [Uu: fun_int_nat,Uua: fun_int_nat,Uub: int] : aa_int_nat(aa_fun6506752150744536624nt_nat(aTP_Lamm_tn(Uu),Uua),Uub) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_int_nat(Uu,Uub)),aa_int_nat(Uua,Uub)) ).

% ATP.lambda_468
tff(fact_8419_ATP_Olambda__469,axiom,
    ! [Uu: fun_int_int,Uua: fun_int_int,Uub: int] : aa_int_int(aa_fun6280345759651049192nt_int(aTP_Lamm_es(Uu),Uua),Uub) = aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(Uu,Uub)),aa_int_int(Uua,Uub)) ).

% ATP.lambda_469
tff(fact_8420_ATP_Olambda__470,axiom,
    ! [Uu: fun_nat_nat,Uua: nat,Uub: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(aTP_Lamm_ow(Uu),Uua),Uub)
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(Uu,Uub)),Uua) ) ).

% ATP.lambda_470
tff(fact_8421_ATP_Olambda__471,axiom,
    ! [Uu: fun_nat_nat,Uua: nat,Uub: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_lc(Uu),Uua),Uub) = aa_set_nat_nat(groups708209901874060359at_nat(Uu),aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,Uub),Uua)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,Uub),Uua)),Uua))) ).

% ATP.lambda_471
tff(fact_8422_ATP_Olambda__472,axiom,
    ! [Uu: fun_nat_int,Uua: nat,Uub: nat] : aa_nat_int(aa_nat_fun_nat_int(aTP_Lamm_ld(Uu),Uua),Uub) = groups705719431365010083at_int(Uu,aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,Uub),Uua)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,Uub),Uua)),Uua))) ).

% ATP.lambda_472
tff(fact_8423_ATP_Olambda__473,axiom,
    ! [Uu: fun_nat_nat,Uua: nat,Uub: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_ke(Uu),Uua),Uub) = aa_set_nat_nat(groups3542108847815614940at_nat(Uu),aa_nat_set_nat(set_or4665077453230672383an_nat(aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,Uub),Uua)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,Uub),Uua)),Uua))) ).

% ATP.lambda_473
tff(fact_8424_ATP_Olambda__474,axiom,
    ! [Uu: code_natural,Uua: code_natural,Uub: nat] : aa_nat_Code_natural(aa_Cod5320533616963873627atural(aTP_Lamm_fw(Uu),Uua),Uub) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,Uu),aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_nat_Code_natural(semiri3763490453095760265atural,Uub)),Uua)) ).

% ATP.lambda_474
tff(fact_8425_ATP_Olambda__475,axiom,
    ! [Uu: code_integer,Uua: code_integer,Uub: nat] : aa_nat_Code_integer(aa_Cod1578151519121547077nteger(aTP_Lamm_fv(Uu),Uua),Uub) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,Uu),aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(semiri4939895301339042750nteger,Uub)),Uua)) ).

% ATP.lambda_475
tff(fact_8426_ATP_Olambda__476,axiom,
    ! [Uu: rat,Uua: rat,Uub: nat] : aa_nat_rat(aa_rat_fun_nat_rat(aTP_Lamm_ft(Uu),Uua),Uub) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,Uu),aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(semiri681578069525770553at_rat,Uub)),Uua)) ).

% ATP.lambda_476
tff(fact_8427_ATP_Olambda__477,axiom,
    ! [Uu: nat,Uua: nat,Uub: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_fx(Uu),Uua),Uub) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uu),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(semiri1316708129612266289at_nat,Uub)),Uua)) ).

% ATP.lambda_477
tff(fact_8428_ATP_Olambda__478,axiom,
    ! [Uu: int,Uua: int,Uub: nat] : aa_nat_int(aa_int_fun_nat_int(aTP_Lamm_fu(Uu),Uua),Uub) = aa_int_int(aa_int_fun_int_int(plus_plus_int,Uu),aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(semiri1314217659103216013at_int,Uub)),Uua)) ).

% ATP.lambda_478
tff(fact_8429_ATP_Olambda__479,axiom,
    ! [Uu: code_integer,Uua: nat,Uub: nat] : aa_nat_Code_integer(aa_nat2010205248571845816nteger(aTP_Lamm_jm(Uu),Uua),Uub) = aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,Uu),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uua),aa_nat_nat(suc,Uub))) ).

% ATP.lambda_479
tff(fact_8430_ATP_Olambda__480,axiom,
    ! [Uu: rat,Uua: nat,Uub: nat] : aa_nat_rat(aa_nat_fun_nat_rat(aTP_Lamm_jn(Uu),Uua),Uub) = aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,Uu),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uua),aa_nat_nat(suc,Uub))) ).

% ATP.lambda_480
tff(fact_8431_ATP_Olambda__481,axiom,
    ! [Uu: int,Uua: nat,Uub: nat] : aa_nat_int(aa_nat_fun_nat_int(aTP_Lamm_jo(Uu),Uua),Uub) = aa_nat_int(aa_int_fun_nat_int(power_power_int,Uu),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uua),aa_nat_nat(suc,Uub))) ).

% ATP.lambda_481
tff(fact_8432_ATP_Olambda__482,axiom,
    ! [Uu: rat,Uua: nat,Uub: nat] : aa_nat_rat(aa_nat_fun_nat_rat(aTP_Lamm_dv(Uu),Uua),Uub) = aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,Uu),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uua),Uub)) ).

% ATP.lambda_482
tff(fact_8433_ATP_Olambda__483,axiom,
    ! [Uu: int,Uua: nat,Uub: nat] : aa_nat_int(aa_nat_fun_nat_int(aTP_Lamm_dw(Uu),Uua),Uub) = aa_nat_int(aa_int_fun_nat_int(power_power_int,Uu),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uua),Uub)) ).

% ATP.lambda_483
tff(fact_8434_ATP_Olambda__484,axiom,
    ! [Uu: nat,Uua: nat,Uub: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_eq(Uu),Uua),Uub) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uu),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,Uub),Uua)) ).

% ATP.lambda_484
tff(fact_8435_ATP_Olambda__485,axiom,
    ! [Uu: code_natural,Uua: nat,Uub: nat] : aa_nat_Code_natural(aa_nat6468655069083034883atural(aTP_Lamm_ls(Uu),Uua),Uub) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(plus_p4538020629002901425atural,Uu),aa_nat_Code_natural(semiri3763490453095760265atural,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uua),Uub))) ).

% ATP.lambda_485
tff(fact_8436_ATP_Olambda__486,axiom,
    ! [Uu: code_integer,Uua: nat,Uub: nat] : aa_nat_Code_integer(aa_nat2010205248571845816nteger(aTP_Lamm_lr(Uu),Uua),Uub) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,Uu),aa_nat_Code_integer(semiri4939895301339042750nteger,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uua),Uub))) ).

% ATP.lambda_486
tff(fact_8437_ATP_Olambda__487,axiom,
    ! [Uu: rat,Uua: nat,Uub: nat] : aa_nat_rat(aa_nat_fun_nat_rat(aTP_Lamm_lq(Uu),Uua),Uub) = aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,Uu),aa_nat_rat(semiri681578069525770553at_rat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uua),Uub))) ).

% ATP.lambda_487
tff(fact_8438_ATP_Olambda__488,axiom,
    ! [Uu: nat,Uua: nat,Uub: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_lt(Uu),Uua),Uub) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uu),aa_nat_nat(semiri1316708129612266289at_nat,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uua),Uub))) ).

% ATP.lambda_488
tff(fact_8439_ATP_Olambda__489,axiom,
    ! [Uu: int,Uua: nat,Uub: nat] : aa_nat_int(aa_nat_fun_nat_int(aTP_Lamm_lu(Uu),Uua),Uub) = aa_int_int(aa_int_fun_int_int(plus_plus_int,Uu),aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uua),Uub))) ).

% ATP.lambda_489
tff(fact_8440_ATP_Olambda__490,axiom,
    ! [Uu: $o,Uua: set_o,Uub: product_prod_nat_nat] : aa_Pro5970036531051701619_set_o(aa_set1227366709740544310_set_o(aTP_Lamm_acl((Uu)),Uua),Uub) = insert_o((Uu),Uua) ).

% ATP.lambda_490
tff(fact_8441_ATP_Olambda__491,axiom,
    ! [Uu: $o,Uua: set_o,Uub: $o] : aa_o_set_o(aa_set_o_fun_o_set_o(aTP_Lamm_acc((Uu)),Uua),(Uub)) = insert_o((Uu),Uua) ).

% ATP.lambda_491
tff(fact_8442_ATP_Olambda__492,axiom,
    ! [Uu: $o,Uua: set_o,Uub: nat] : aa_nat_set_o(aa_set557987488673405253_set_o(aTP_Lamm_acf((Uu)),Uua),Uub) = insert_o((Uu),Uua) ).

% ATP.lambda_492
tff(fact_8443_ATP_Olambda__493,axiom,
    ! [Uu: $o,Uua: set_o,Uub: int] : aa_int_set_o(aa_set1244563521713955817_set_o(aTP_Lamm_aci((Uu)),Uua),Uub) = insert_o((Uu),Uua) ).

% ATP.lambda_493
tff(fact_8444_ATP_Olambda__494,axiom,
    ! [Uu: nat,Uua: set_nat,Uub: $o] : aa_o_set_nat(aa_set1696117090455734765et_nat(aTP_Lamm_acd(Uu),Uua),(Uub)) = insert_nat(Uu,Uua) ).

% ATP.lambda_494
tff(fact_8445_ATP_Olambda__495,axiom,
    ! [Uu: nat,Uua: set_nat,Uub: nat] : aa_nat_set_nat(aa_set562305657478724375et_nat(aTP_Lamm_acg(Uu),Uua),Uub) = insert_nat(Uu,Uua) ).

% ATP.lambda_495
tff(fact_8446_ATP_Olambda__496,axiom,
    ! [Uu: nat,Uua: set_nat,Uub: int] : aa_int_set_nat(aa_set933959217715569011et_nat(aTP_Lamm_acj(Uu),Uua),Uub) = insert_nat(Uu,Uua) ).

% ATP.lambda_496
tff(fact_8447_ATP_Olambda__497,axiom,
    ! [Uu: int,Uua: set_int,Uub: $o] : aa_o_set_int(aa_set8238700067146519789et_int(aTP_Lamm_ace(Uu),Uua),(Uub)) = insert_int(Uu,Uua) ).

% ATP.lambda_497
tff(fact_8448_ATP_Olambda__498,axiom,
    ! [Uu: int,Uua: set_int,Uub: nat] : aa_nat_set_int(aa_set2464685511577892303et_int(aTP_Lamm_ach(Uu),Uua),Uub) = insert_int(Uu,Uua) ).

% ATP.lambda_498
tff(fact_8449_ATP_Olambda__499,axiom,
    ! [Uu: int,Uua: set_int,Uub: int] : aa_int_set_int(aa_set2836339071814736939et_int(aTP_Lamm_ack(Uu),Uua),Uub) = insert_int(Uu,Uua) ).

% ATP.lambda_499
tff(fact_8450_ATP_Olambda__500,axiom,
    ! [Uu: fun_nat_Code_integer,Uua: set_nat,Uub: code_integer] : aa_Cod2813182003028390446nteger(aa_set1342327774797759281nteger(aTP_Lamm_yn(Uu),Uua),Uub) = image_1215581382706833972nteger(Uu,Uua) ).

% ATP.lambda_500
tff(fact_8451_ATP_Olambda__501,axiom,
    ! [Uu: fun_nat_Code_integer,Uua: set_nat,Uub: nat] : aa_nat8922193080109606305nteger(aa_set4032875478442387108nteger(aTP_Lamm_aak(Uu),Uua),Uub) = image_1215581382706833972nteger(Uu,Uua) ).

% ATP.lambda_501
tff(fact_8452_ATP_Olambda__502,axiom,
    ! [Uu: fun_nat_Code_integer,Uua: set_nat,Uub: int] : aa_int6612375148016655357nteger(aa_set1723057546349436160nteger(aTP_Lamm_aar(Uu),Uua),Uub) = image_1215581382706833972nteger(Uu,Uua) ).

% ATP.lambda_502
tff(fact_8453_ATP_Olambda__503,axiom,
    ! [Uu: fun_nat_set_nat,Uua: set_nat,Uub: set_nat] : aa_set7246812951530217472et_nat(aa_set3960572117082860675et_nat(aTP_Lamm_yo(Uu),Uua),Uub) = image_nat_set_nat(Uu,Uua) ).

% ATP.lambda_503
tff(fact_8454_ATP_Olambda__504,axiom,
    ! [Uu: fun_nat_nat,Uua: set_nat,Uub: code_integer] : aa_Cod6142706534279259169et_nat(aa_set3222090474234563492et_nat(aTP_Lamm_aae(Uu),Uua),Uub) = aa_set_nat_set_nat(image_nat_nat(Uu),Uua) ).

% ATP.lambda_504
tff(fact_8455_ATP_Olambda__505,axiom,
    ! [Uu: fun_nat_nat,Uua: set_nat,Uub: nat] : aa_nat_set_nat(aa_set562305657478724375et_nat(aTP_Lamm_yp(Uu),Uua),Uub) = aa_set_nat_set_nat(image_nat_nat(Uu),Uua) ).

% ATP.lambda_505
tff(fact_8456_ATP_Olambda__506,axiom,
    ! [Uu: fun_nat_nat,Uua: set_nat,Uub: int] : aa_int_set_nat(aa_set933959217715569011et_nat(aTP_Lamm_aat(Uu),Uua),Uub) = aa_set_nat_set_nat(image_nat_nat(Uu),Uua) ).

% ATP.lambda_506
tff(fact_8457_ATP_Olambda__507,axiom,
    ! [Uu: fun_nat_int,Uua: set_nat,Uub: code_integer] : aa_Cod1964855514770062461et_int(aa_set732007329302836736et_int(aTP_Lamm_aag(Uu),Uua),Uub) = image_nat_int(Uu,Uua) ).

% ATP.lambda_507
tff(fact_8458_ATP_Olambda__508,axiom,
    ! [Uu: fun_nat_int,Uua: set_nat,Uub: nat] : aa_nat_set_int(aa_set7295594549401773427et_int(aTP_Lamm_aan(Uu),Uua),Uub) = image_nat_int(Uu,Uua) ).

% ATP.lambda_508
tff(fact_8459_ATP_Olambda__509,axiom,
    ! [Uu: fun_nat_int,Uua: set_nat,Uub: int] : aa_int_set_int(aa_set7667248109638618063et_int(aTP_Lamm_yq(Uu),Uua),Uub) = image_nat_int(Uu,Uua) ).

% ATP.lambda_509
tff(fact_8460_ATP_Olambda__510,axiom,
    ! [Uu: fun_int_int,Uua: set_int,Uub: code_integer] : aa_Cod1964855514770062461et_int(aa_set8360975810291373660et_int(aTP_Lamm_aai(Uu),Uua),Uub) = aa_set_int_set_int(image_int_int(Uu),Uua) ).

% ATP.lambda_510
tff(fact_8461_ATP_Olambda__511,axiom,
    ! [Uu: fun_int_int,Uua: set_int,Uub: nat] : aa_nat_set_int(aa_set2464685511577892303et_int(aTP_Lamm_aap(Uu),Uua),Uub) = aa_set_int_set_int(image_int_int(Uu),Uua) ).

% ATP.lambda_511
tff(fact_8462_ATP_Olambda__512,axiom,
    ! [Uu: fun_int_int,Uua: set_int,Uub: int] : aa_int_set_int(aa_set2836339071814736939et_int(aTP_Lamm_yr(Uu),Uua),Uub) = aa_set_int_set_int(image_int_int(Uu),Uua) ).

% ATP.lambda_512
tff(fact_8463_ATP_Olambda__513,axiom,
    ! [Uu: fun_nat_nat,Uua: nat,Uub: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_ix(Uu),Uua),Uub) = aa_nat_nat(Uu,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uua),aa_nat_nat(suc,Uub))) ).

% ATP.lambda_513
tff(fact_8464_ATP_Olambda__514,axiom,
    ! [Uu: fun_nat_int,Uua: nat,Uub: nat] : aa_nat_int(aa_nat_fun_nat_int(aTP_Lamm_ku(Uu),Uua),Uub) = aa_nat_int(Uu,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uua),aa_nat_nat(suc,Uub))) ).

% ATP.lambda_514
tff(fact_8465_ATP_Olambda__515,axiom,
    ! [Uu: fun_nat_set_nat,Uua: nat,Uub: nat] : aa_nat_set_nat(aa_nat1818925681583257441et_nat(aTP_Lamm_wg(Uu),Uua),Uub) = aa_nat_set_nat(Uu,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uub),Uua)) ).

% ATP.lambda_515
tff(fact_8466_ATP_Olambda__516,axiom,
    ! [Uu: fun_nat_nat,Uua: nat,Uub: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_di(Uu),Uua),Uub) = aa_nat_nat(Uu,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uub),Uua)) ).

% ATP.lambda_516
tff(fact_8467_ATP_Olambda__517,axiom,
    ! [Uu: fun_nat_int,Uua: nat,Uub: nat] : aa_nat_int(aa_nat_fun_nat_int(aTP_Lamm_ks(Uu),Uua),Uub) = aa_nat_int(Uu,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uub),Uua)) ).

% ATP.lambda_517
tff(fact_8468_ATP_Olambda__518,axiom,
    ! [Uu: fun_Pr2602117396471556196at_nat,Uua: nat,Uub: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_dj(Uu),Uua),Uub) = aa_Pro4243173770044397973at_nat(Uu,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Uua),Uub)) ).

% ATP.lambda_518
tff(fact_8469_ATP_Olambda__519,axiom,
    ! [Uu: fun_Pr2477239776880934807at_nat,Uua: nat,Uub: nat] : aa_nat7997280740862404369at_nat(aa_nat5682243440470347102at_nat(aTP_Lamm_dk(Uu),Uua),Uub) = aa_Pro8023792847356852296at_nat(Uu,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Uua),Uub)) ).

% ATP.lambda_519
tff(fact_8470_ATP_Olambda__520,axiom,
    ! [Uu: fun_Pr2028404973800837934_nat_o,Uua: nat,Uub: nat] : aa_nat7695548938202568488_nat_o(aa_nat4259715169212259317_nat_o(aTP_Lamm_dl(Uu),Uua),Uub) = aa_Pro989595756709598047_nat_o(Uu,aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Uua),Uub)) ).

% ATP.lambda_520
tff(fact_8471_ATP_Olambda__521,axiom,
    ! [Uu: fun_Pr2478283820680522243nt_int,Uua: int,Uub: int] : aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(aTP_Lamm_dm(Uu),Uua),Uub) = aa_Pro6970504127699319548nt_int(Uu,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Uua),Uub)) ).

% ATP.lambda_521
tff(fact_8472_ATP_Olambda__522,axiom,
    ! [Uu: fun_Pr982841511892225912nt_int,Uua: int,Uub: int] : aa_int_int(aa_int_fun_int_int(aTP_Lamm_dn(Uu),Uua),Uub) = aa_Pro6799258434465214121nt_int(Uu,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,Uua),Uub)) ).

% ATP.lambda_522
tff(fact_8473_ATP_Olambda__523,axiom,
    ! [Uu: fun_op8989173174992673105on_num,Uua: fun_num_option_num,Uub: num] : aa_num_option_num(aa_fun3636977833914307392on_num(aTP_Lamm_au(Uu),Uua),Uub) = aa_opt5369159329878751634on_num(Uu,aa_num_option_num(Uua,Uub)) ).

% ATP.lambda_523
tff(fact_8474_ATP_Olambda__524,axiom,
    ! [Uu: fun_option_num_num,Uua: fun_num_option_num,Uub: num] : aa_num_num(aa_fun7142274290070961008um_num(aTP_Lamm_av(Uu),Uua),Uub) = aa_option_num_num(Uu,aa_num_option_num(Uua,Uub)) ).

% ATP.lambda_524
tff(fact_8475_ATP_Olambda__525,axiom,
    ! [Uu: fun_option_num_int,Uua: fun_num_option_num,Uub: num] : aa_num_int(aa_fun2256179333612926594um_int(aTP_Lamm_at(Uu),Uua),Uub) = aa_option_num_int(Uu,aa_num_option_num(Uua,Uub)) ).

% ATP.lambda_525
tff(fact_8476_ATP_Olambda__526,axiom,
    ! [Uu: fun_num_option_num,Uua: fun_num_num,Uub: num] : aa_num_option_num(aa_fun612943910911948912on_num(aTP_Lamm_ax(Uu),Uua),Uub) = aa_num_option_num(Uu,aa_num_num(Uua,Uub)) ).

% ATP.lambda_526
tff(fact_8477_ATP_Olambda__527,axiom,
    ! [Uu: fun_num_num,Uua: fun_num_num,Uub: num] : aa_num_num(aa_fun8048995283964520608um_num(aTP_Lamm_ay(Uu),Uua),Uub) = aa_num_num(Uu,aa_num_num(Uua,Uub)) ).

% ATP.lambda_527
tff(fact_8478_ATP_Olambda__528,axiom,
    ! [Uu: fun_num_int,Uua: fun_num_num,Uub: num] : aa_num_int(aa_fun3162900327506486194um_int(aTP_Lamm_aw(Uu),Uua),Uub) = aa_num_int(Uu,aa_num_num(Uua,Uub)) ).

% ATP.lambda_528
tff(fact_8479_ATP_Olambda__529,axiom,
    ! [Uu: fun_int_option_num,Uua: fun_num_int,Uub: num] : aa_num_option_num(aa_fun3858197967482829954on_num(aTP_Lamm_ar(Uu),Uua),Uub) = aa_int_option_num(Uu,aa_num_int(Uua,Uub)) ).

% ATP.lambda_529
tff(fact_8480_ATP_Olambda__530,axiom,
    ! [Uu: fun_int_num,Uua: fun_num_int,Uub: num] : aa_num_num(aa_fun5215869348392759218um_num(aTP_Lamm_as(Uu),Uua),Uub) = aa_int_num(Uu,aa_num_int(Uua,Uub)) ).

% ATP.lambda_530
tff(fact_8481_ATP_Olambda__531,axiom,
    ! [Uu: fun_int_int,Uua: fun_num_int,Uub: num] : aa_num_int(aa_fun329774391934724804um_int(aTP_Lamm_aq(Uu),Uua),Uub) = aa_int_int(Uu,aa_num_int(Uua,Uub)) ).

% ATP.lambda_531
tff(fact_8482_ATP_Olambda__532,axiom,
    ! [Uu: fun_fu7564235448449272366at_o_o,Uua: fun_fu4001317426178549763_nat_o,Uub: fun_nat_o] : aa_fun4840518763754620511at_o_o(aa_fun2763792489458032301at_o_o(aTP_Lamm_yt(Uu),Uua),Uub) = aa_fun4840518763754620511at_o_o(Uu,aa_fun5937193402907943164_nat_o(Uua,Uub)) ).

% ATP.lambda_532
tff(fact_8483_ATP_Olambda__533,axiom,
    ! [Uu: fun_fu6699046866436802030_int_o,Uua: fun_fu3661779633992098115nt_int,Uub: fun_in4211310926729683942nt_int] : aa_fun1009039980557175711_int_o(aa_fun3789280421985926445_int_o(aTP_Lamm_yu(Uu),Uua),Uub) = aa_fun1009039980557175711_int_o(Uu,aa_fun6626262031093723324nt_int(Uua,Uub)) ).

% ATP.lambda_533
tff(fact_8484_ATP_Olambda__534,axiom,
    ! [Uu: fun_fu7677565902479959693_rat_o,Uua: fun_fu3661779633992098115nt_int,Uub: fun_in4211310926729683942nt_int] : aa_fun5827461210593834758_rat_o(aa_fun2399579938715134478_rat_o(aTP_Lamm_yv(Uu),Uua),Uub) = aa_fun5827461210593834758_rat_o(Uu,aa_fun6626262031093723324nt_int(Uua,Uub)) ).

% ATP.lambda_534
tff(fact_8485_ATP_Olambda__535,axiom,
    ! [Uu: fun_fu6971708032831053102nt_o_o,Uua: fun_fu3883539188510166275_int_o,Uub: fun_int_o] : aa_fun1331825017273370463nt_o_o(aa_fun7316249240758406317nt_o_o(aTP_Lamm_yw(Uu),Uua),Uub) = aa_fun1331825017273370463nt_o_o(Uu,aa_fun6243517787477317628_int_o(Uua,Uub)) ).

% ATP.lambda_535
tff(fact_8486_ATP_Olambda__536,axiom,
    ! [Uu: fun_fu4208408993564413984_int_o,Uua: fun_fu1143798476471108391nt_int,Uub: fun_int_int] : aa_fun2545150047610057353_int_o(aa_fun6233912309721051003_int_o(aTP_Lamm_yx(Uu),Uua),Uub) = aa_fun2545150047610057353_int_o(Uu,aa_fun6280345759651049192nt_int(Uua,Uub)) ).

% ATP.lambda_536
tff(fact_8487_ATP_Olambda__537,axiom,
    ! [Uu: fun_nat_set_nat,Uua: nat,Uub: nat] : aa_nat_set_nat(aa_nat1818925681583257441et_nat(aTP_Lamm_zp(Uu),Uua),Uub) = aa_nat_set_nat(Uu,Uua) ).

% ATP.lambda_537
tff(fact_8488_ATP_Olambda__538,axiom,
    ! [Uu: fun_nat_nat,Uua: nat,Uub: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_vk(Uu),Uua),Uub) = aa_nat_nat(Uu,Uua) ).

% ATP.lambda_538
tff(fact_8489_ATP_Olambda__539,axiom,
    ! [Uu: fun_na8713714802964096592at_nat,Uua: nat,Uub: nat] : aa_nat7997280740862404369at_nat(aa_nat5682243440470347102at_nat(aTP_Lamm_vm(Uu),Uua),Uub) = aa_nat7997280740862404369at_nat(Uu,Uua) ).

% ATP.lambda_539
tff(fact_8490_ATP_Olambda__540,axiom,
    ! [Uu: fun_na3970208099681795815_nat_o,Uua: nat,Uub: nat] : aa_nat7695548938202568488_nat_o(aa_nat4259715169212259317_nat_o(aTP_Lamm_vo(Uu),Uua),Uub) = aa_nat7695548938202568488_nat_o(Uu,Uua) ).

% ATP.lambda_540
tff(fact_8491_ATP_Olambda__541,axiom,
    ! [Uu: fun_in4211310926729683942nt_int,Uua: int,Uub: int] : aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(aTP_Lamm_vq(Uu),Uua),Uub) = aa_int7462565939943104719nt_int(Uu,Uua) ).

% ATP.lambda_541
tff(fact_8492_ATP_Olambda__542,axiom,
    ! [Uu: fun_int_int,Uua: int,Uub: int] : aa_int_int(aa_int_fun_int_int(aTP_Lamm_vs(Uu),Uua),Uub) = aa_int_int(Uu,Uua) ).

% ATP.lambda_542
tff(fact_8493_ATP_Olambda__543,axiom,
    ! [Uu: fun_Pr1003294667014919570it_nat,Uua: produc8664842809031399944it_nat,Uub: produc8664842809031399944it_nat] : aa_Pro8996696869555642526it_nat(aa_Pro5635350972512700067it_nat(aTP_Lamm_az(Uu),Uua),Uub) = aa_Pro8996696869555642526it_nat(some_P1914260805536162275it_nat,aa_Pro550487673543749710it_nat(aa_Pro4096753284154920275it_nat(Uu,Uua),Uub)) ).

% ATP.lambda_543
tff(fact_8494_ATP_Olambda__544,axiom,
    ! [Uu: fun_num_fun_num_num,Uua: num,Uub: num] : aa_num_option_num(aa_num6390622462783740633on_num(aTP_Lamm_bb(Uu),Uua),Uub) = aa_num_option_num(some_num,aa_num_num(aa_num_fun_num_num(Uu,Uua),Uub)) ).

% ATP.lambda_544
tff(fact_8495_ATP_Olambda__545,axiom,
    ! [Uu: fun_nat_set_nat,Uua: set_nat,Uub: nat] : aa_nat_set_nat(aa_set562305657478724375et_nat(aTP_Lamm_zr(Uu),Uua),Uub) = comple7399068483239264473et_nat(image_nat_set_nat(Uu,Uua)) ).

% ATP.lambda_545
tff(fact_8496_ATP_Olambda__546,axiom,
    ! [Uu: fun_na1668100129766719005at_nat,Uua: product_prod_nat_nat,Uub: nat,Uuc: nat] : aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(aa_Pro6895555690143131534at_nat(aTP_Lamm_cu(Uu),Uua),Uub),Uuc) = aa_Pro262675715343573244at_nat(aa_nat7997280740862404369at_nat(aa_nat5682243440470347102at_nat(Uu,Uub),Uuc),Uua) ).

% ATP.lambda_546
tff(fact_8497_ATP_Olambda__547,axiom,
    ! [Uu: fun_na5914473681949881652_nat_o,Uua: product_prod_nat_nat,Uub: nat,Uuc: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(aa_Pro1957341097241355813_nat_o(aTP_Lamm_cv(Uu),Uua),Uub),Uuc)
    <=> aa_Pro6150637604445964947_nat_o(aa_nat7695548938202568488_nat_o(aa_nat4259715169212259317_nat_o(Uu,Uub),Uuc),Uua) ) ).

% ATP.lambda_547
tff(fact_8498_ATP_Olambda__548,axiom,
    ! [Uu: nat,Uua: fun_nat_Code_integer,Uub: fun_nat_Code_integer,Uuc: nat] :
      aa_nat_Code_integer(aa_fun589076786913273746nteger(aa_fun3918145391673965625nteger(aTP_Lamm_hy(Uu),Uua),Uub),Uuc) = $ite(
        aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,Uuc),Uu),
        aa_nat_Code_integer(Uua,Uuc),
        $ite(Uuc = Uu,zero_z3403309356797280102nteger,aa_nat_Code_integer(Uub,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uuc),aa_nat_nat(suc,zero_zero_nat)))) ) ).

% ATP.lambda_548
tff(fact_8499_ATP_Olambda__549,axiom,
    ! [Uu: nat,Uua: fun_na2338080690716861136at_nat,Uub: fun_na2338080690716861136at_nat,Uuc: nat] :
      aa_nat2240542744625857721at_nat(aa_fun4141531684813184444at_nat(aa_fun8230936523094545239at_nat(aTP_Lamm_ia(Uu),Uua),Uub),Uuc) = $ite(
        aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,Uuc),Uu),
        aa_nat2240542744625857721at_nat(Uua,Uuc),
        $ite(Uuc = Uu,zero_z1048942125864253310at_nat,aa_nat2240542744625857721at_nat(Uub,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uuc),aa_nat_nat(suc,zero_zero_nat)))) ) ).

% ATP.lambda_549
tff(fact_8500_ATP_Olambda__550,axiom,
    ! [Uu: nat,Uua: fun_nat_rat,Uub: fun_nat_rat,Uuc: nat] :
      aa_nat_rat(aa_fun765758790203053448at_rat(aa_fun3638354034882855594at_rat(aTP_Lamm_ic(Uu),Uua),Uub),Uuc) = $ite(
        aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,Uuc),Uu),
        aa_nat_rat(Uua,Uuc),
        $ite(Uuc = Uu,zero_zero_rat,aa_nat_rat(Uub,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uuc),aa_nat_nat(suc,zero_zero_nat)))) ) ).

% ATP.lambda_550
tff(fact_8501_ATP_Olambda__551,axiom,
    ! [Uu: nat,Uua: fun_nat_nat,Uub: fun_nat_nat,Uuc: nat] :
      aa_nat_nat(aa_fun5791449513213591928at_nat(aa_fun6854695580826382482at_nat(aTP_Lamm_ig(Uu),Uua),Uub),Uuc) = $ite(
        aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,Uuc),Uu),
        aa_nat_nat(Uua,Uuc),
        $ite(Uuc = Uu,zero_zero_nat,aa_nat_nat(Uub,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uuc),aa_nat_nat(suc,zero_zero_nat)))) ) ).

% ATP.lambda_551
tff(fact_8502_ATP_Olambda__552,axiom,
    ! [Uu: nat,Uua: fun_nat_int,Uub: fun_nat_int,Uuc: nat] :
      aa_nat_int(aa_fun5565043122120104496at_int(aa_fun5140708168904641446at_int(aTP_Lamm_ie(Uu),Uua),Uub),Uuc) = $ite(
        aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,Uuc),Uu),
        aa_nat_int(Uua,Uuc),
        $ite(Uuc = Uu,zero_zero_int,aa_nat_int(Uub,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uuc),aa_nat_nat(suc,zero_zero_nat)))) ) ).

% ATP.lambda_552
tff(fact_8503_ATP_Olambda__553,axiom,
    ! [Uu: nat,Uua: fun_nat_Code_integer,Uub: fun_nat_Code_integer,Uuc: nat] :
      aa_nat_Code_integer(aa_fun589076786913273746nteger(aa_fun3918145391673965625nteger(aTP_Lamm_mc(Uu),Uua),Uub),Uuc) = $ite(
        aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,Uuc),Uu),
        aa_nat_Code_integer(Uua,Uuc),
        $ite(Uuc = Uu,one_one_Code_integer,aa_nat_Code_integer(Uub,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uuc),aa_nat_nat(suc,zero_zero_nat)))) ) ).

% ATP.lambda_553
tff(fact_8504_ATP_Olambda__554,axiom,
    ! [Uu: nat,Uua: fun_nat_assn,Uub: fun_nat_assn,Uuc: nat] :
      aa_nat_assn(aa_fun785744391571715112t_assn(aa_fun6591345337174305434t_assn(aTP_Lamm_md(Uu),Uua),Uub),Uuc) = $ite(
        aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,Uuc),Uu),
        aa_nat_assn(Uua,Uuc),
        $ite(Uuc = Uu,one_one_assn,aa_nat_assn(Uub,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uuc),aa_nat_nat(suc,zero_zero_nat)))) ) ).

% ATP.lambda_554
tff(fact_8505_ATP_Olambda__555,axiom,
    ! [Uu: nat,Uua: fun_nat_rat,Uub: fun_nat_rat,Uuc: nat] :
      aa_nat_rat(aa_fun765758790203053448at_rat(aa_fun3638354034882855594at_rat(aTP_Lamm_mf(Uu),Uua),Uub),Uuc) = $ite(
        aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,Uuc),Uu),
        aa_nat_rat(Uua,Uuc),
        $ite(Uuc = Uu,one_one_rat,aa_nat_rat(Uub,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uuc),aa_nat_nat(suc,zero_zero_nat)))) ) ).

% ATP.lambda_555
tff(fact_8506_ATP_Olambda__556,axiom,
    ! [Uu: nat,Uua: fun_nat_nat,Uub: fun_nat_nat,Uuc: nat] :
      aa_nat_nat(aa_fun5791449513213591928at_nat(aa_fun6854695580826382482at_nat(aTP_Lamm_mg(Uu),Uua),Uub),Uuc) = $ite(
        aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,Uuc),Uu),
        aa_nat_nat(Uua,Uuc),
        $ite(Uuc = Uu,one_one_nat,aa_nat_nat(Uub,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uuc),aa_nat_nat(suc,zero_zero_nat)))) ) ).

% ATP.lambda_556
tff(fact_8507_ATP_Olambda__557,axiom,
    ! [Uu: nat,Uua: fun_nat_int,Uub: fun_nat_int,Uuc: nat] :
      aa_nat_int(aa_fun5565043122120104496at_int(aa_fun5140708168904641446at_int(aTP_Lamm_mh(Uu),Uua),Uub),Uuc) = $ite(
        aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,Uuc),Uu),
        aa_nat_int(Uua,Uuc),
        $ite(Uuc = Uu,one_one_int,aa_nat_int(Uub,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uuc),aa_nat_nat(suc,zero_zero_nat)))) ) ).

% ATP.lambda_557
tff(fact_8508_ATP_Olambda__558,axiom,
    ! [Uu: nat,Uua: fun_nat_Code_integer,Uub: fun_nat_Code_integer,Uuc: nat] :
      aa_nat_Code_integer(aa_fun589076786913273746nteger(aa_fun3918145391673965625nteger(aTP_Lamm_hz(Uu),Uua),Uub),Uuc) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,Uuc),Uu),aa_nat_Code_integer(Uua,Uuc),aa_nat_Code_integer(Uub,Uuc)) ).

% ATP.lambda_558
tff(fact_8509_ATP_Olambda__559,axiom,
    ! [Uu: nat,Uua: fun_na2338080690716861136at_nat,Uub: fun_na2338080690716861136at_nat,Uuc: nat] :
      aa_nat2240542744625857721at_nat(aa_fun4141531684813184444at_nat(aa_fun8230936523094545239at_nat(aTP_Lamm_ib(Uu),Uua),Uub),Uuc) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,Uuc),Uu),aa_nat2240542744625857721at_nat(Uua,Uuc),aa_nat2240542744625857721at_nat(Uub,Uuc)) ).

% ATP.lambda_559
tff(fact_8510_ATP_Olambda__560,axiom,
    ! [Uu: nat,Uua: fun_nat_assn,Uub: fun_nat_assn,Uuc: nat] :
      aa_nat_assn(aa_fun785744391571715112t_assn(aa_fun6591345337174305434t_assn(aTP_Lamm_me(Uu),Uua),Uub),Uuc) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,Uuc),Uu),aa_nat_assn(Uua,Uuc),aa_nat_assn(Uub,Uuc)) ).

% ATP.lambda_560
tff(fact_8511_ATP_Olambda__561,axiom,
    ! [Uu: nat,Uua: fun_nat_rat,Uub: fun_nat_rat,Uuc: nat] :
      aa_nat_rat(aa_fun765758790203053448at_rat(aa_fun3638354034882855594at_rat(aTP_Lamm_id(Uu),Uua),Uub),Uuc) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,Uuc),Uu),aa_nat_rat(Uua,Uuc),aa_nat_rat(Uub,Uuc)) ).

% ATP.lambda_561
tff(fact_8512_ATP_Olambda__562,axiom,
    ! [Uu: nat,Uua: fun_nat_nat,Uub: fun_nat_nat,Uuc: nat] :
      aa_nat_nat(aa_fun5791449513213591928at_nat(aa_fun6854695580826382482at_nat(aTP_Lamm_ih(Uu),Uua),Uub),Uuc) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,Uuc),Uu),aa_nat_nat(Uua,Uuc),aa_nat_nat(Uub,Uuc)) ).

% ATP.lambda_562
tff(fact_8513_ATP_Olambda__563,axiom,
    ! [Uu: nat,Uua: fun_nat_int,Uub: fun_nat_int,Uuc: nat] :
      aa_nat_int(aa_fun5565043122120104496at_int(aa_fun5140708168904641446at_int(aTP_Lamm_if(Uu),Uua),Uub),Uuc) = $ite(aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,Uuc),Uu),aa_nat_int(Uua,Uuc),aa_nat_int(Uub,Uuc)) ).

% ATP.lambda_563
tff(fact_8514_ATP_Olambda__564,axiom,
    ! [Uu: code_integer,Uua: fun_Code_integer_rat,Uub: fun_Code_integer_rat,Uuc: code_integer] :
      aa_Code_integer_rat(aa_fun8169474305930283170er_rat(aa_fun1894662059565830609er_rat(aTP_Lamm_sa(Uu),Uua),Uub),Uuc) = $ite(Uuc = Uu,aa_Code_integer_rat(Uua,Uuc),aa_Code_integer_rat(Uub,Uuc)) ).

% ATP.lambda_564
tff(fact_8515_ATP_Olambda__565,axiom,
    ! [Uu: code_integer,Uua: fun_Code_integer_nat,Uub: fun_Code_integer_nat,Uuc: code_integer] :
      aa_Code_integer_nat(aa_fun3076867170244285586er_nat(aa_fun7635586485349294009er_nat(aTP_Lamm_sb(Uu),Uua),Uub),Uuc) = $ite(Uuc = Uu,aa_Code_integer_nat(Uua,Uuc),aa_Code_integer_nat(Uub,Uuc)) ).

% ATP.lambda_565
tff(fact_8516_ATP_Olambda__566,axiom,
    ! [Uu: code_integer,Uua: fun_Code_integer_int,Uub: fun_Code_integer_int,Uuc: code_integer] :
      aa_Code_integer_int(aa_fun3291479149765983562er_int(aa_fun4411173778969602765er_int(aTP_Lamm_sc(Uu),Uua),Uub),Uuc) = $ite(Uuc = Uu,aa_Code_integer_int(Uua,Uuc),aa_Code_integer_int(Uub,Uuc)) ).

% ATP.lambda_566
tff(fact_8517_ATP_Olambda__567,axiom,
    ! [Uu: $o,Uua: fun_o_rat,Uub: fun_o_rat,Uuc: $o] :
      aa_o_rat(aa_fun4336163974892599420_o_rat(aa_fun2919298112881465802_o_rat(aTP_Lamm_sd((Uu)),Uua),Uub),(Uuc)) = $ite((Uuc) = (Uu),aa_o_rat(Uua,(Uuc)),aa_o_rat(Uub,(Uuc))) ).

% ATP.lambda_567
tff(fact_8518_ATP_Olambda__568,axiom,
    ! [Uu: $o,Uua: fun_o_nat,Uub: fun_o_nat,Uuc: $o] :
      aa_o_nat(aa_fun6176012476734143100_o_nat(aa_fun6251207968994965954_o_nat(aTP_Lamm_se((Uu)),Uua),Uub),(Uuc)) = $ite((Uuc) = (Uu),aa_o_nat(Uua,(Uuc)),aa_o_nat(Uub,(Uuc))) ).

% ATP.lambda_568
tff(fact_8519_ATP_Olambda__569,axiom,
    ! [Uu: $o,Uua: fun_o_int,Uub: fun_o_int,Uuc: $o] :
      aa_o_int(aa_fun4727766026823762812_o_int(aa_fun5648456818326528798_o_int(aTP_Lamm_sf((Uu)),Uua),Uub),(Uuc)) = $ite((Uuc) = (Uu),aa_o_int(Uua,(Uuc)),aa_o_int(Uub,(Uuc))) ).

% ATP.lambda_569
tff(fact_8520_ATP_Olambda__570,axiom,
    ! [Uu: nat,Uua: fun_nat_rat,Uub: fun_nat_rat,Uuc: nat] :
      aa_nat_rat(aa_fun765758790203053448at_rat(aa_fun3638354034882855594at_rat(aTP_Lamm_si(Uu),Uua),Uub),Uuc) = $ite(Uuc = Uu,aa_nat_rat(Uua,Uuc),aa_nat_rat(Uub,Uuc)) ).

% ATP.lambda_570
tff(fact_8521_ATP_Olambda__571,axiom,
    ! [Uu: nat,Uua: fun_nat_int,Uub: fun_nat_int,Uuc: nat] :
      aa_nat_int(aa_fun5565043122120104496at_int(aa_fun5140708168904641446at_int(aTP_Lamm_sj(Uu),Uua),Uub),Uuc) = $ite(Uuc = Uu,aa_nat_int(Uua,Uuc),aa_nat_int(Uub,Uuc)) ).

% ATP.lambda_571
tff(fact_8522_ATP_Olambda__572,axiom,
    ! [Uu: int,Uua: fun_int_rat,Uub: fun_int_rat,Uuc: int] :
      aa_int_rat(aa_fun1481061427733998144nt_rat(aa_fun2191249852558612414nt_rat(aTP_Lamm_sg(Uu),Uua),Uub),Uuc) = $ite(Uuc = Uu,aa_int_rat(Uua,Uuc),aa_int_rat(Uub,Uuc)) ).

% ATP.lambda_572
tff(fact_8523_ATP_Olambda__573,axiom,
    ! [Uu: int,Uua: fun_int_nat,Uub: fun_int_nat,Uuc: int] :
      aa_int_nat(aa_fun6506752150744536624nt_nat(aa_fun5407591398502139302nt_nat(aTP_Lamm_sh(Uu),Uua),Uub),Uuc) = $ite(Uuc = Uu,aa_int_nat(Uua,Uuc),aa_int_nat(Uub,Uuc)) ).

% ATP.lambda_573
tff(fact_8524_ATP_Olambda__574,axiom,
    ! [Uu: code_integer,Uua: fun_Co4490034186337852034r_assn,Uub: assn,Uuc: code_integer] :
      aa_Code_integer_assn(aa_ass6027779773078136296r_assn(aa_fun5785710901775686247r_assn(aTP_Lamm_rg(Uu),Uua),Uub),Uuc) = $ite(Uuc = Uu,aa_Code_integer_assn(Uua,Uuc),Uub) ).

% ATP.lambda_574
tff(fact_8525_ATP_Olambda__575,axiom,
    ! [Uu: code_integer,Uua: fun_Code_integer_rat,Uub: rat,Uuc: code_integer] :
      aa_Code_integer_rat(aa_rat6553461586499541832er_rat(aa_fun8320714231555830903er_rat(aTP_Lamm_rl(Uu),Uua),Uub),Uuc) = $ite(Uuc = Uu,aa_Code_integer_rat(Uua,Uuc),Uub) ).

% ATP.lambda_575
tff(fact_8526_ATP_Olambda__576,axiom,
    ! [Uu: product_unit,Uua: fun_Pr6626665806141890376t_assn,Uub: assn,Uuc: product_unit] :
      aa_Product_unit_assn(aa_ass3177796706412234594t_assn(aa_fun5779862164363648365t_assn(aTP_Lamm_rd(Uu),Uua),Uub),Uuc) = $ite(Uuc = Uu,aa_Product_unit_assn(Uua,Uuc),Uub) ).

% ATP.lambda_576
tff(fact_8527_ATP_Olambda__577,axiom,
    ! [Uu: product_unit,Uua: fun_Product_unit_rat,Uub: rat,Uuc: product_unit] :
      aa_Product_unit_rat(aa_rat6507435564262174562it_rat(aa_fun5217320890768598205it_rat(aTP_Lamm_ri(Uu),Uua),Uub),Uuc) = $ite(Uuc = Uu,aa_Product_unit_rat(Uua,Uuc),Uub) ).

% ATP.lambda_577
tff(fact_8528_ATP_Olambda__578,axiom,
    ! [Uu: $o,Uua: fun_o_assn,Uub: assn,Uuc: $o] :
      aa_o_assn(aa_assn_fun_o_assn(aa_fun7777267157241973165o_assn(aTP_Lamm_rc((Uu)),Uua),Uub),(Uuc)) = $ite((Uuc) = (Uu),aa_o_assn(Uua,(Uuc)),Uub) ).

% ATP.lambda_578
tff(fact_8529_ATP_Olambda__579,axiom,
    ! [Uu: $o,Uua: fun_o_rat,Uub: rat,Uuc: $o] :
      aa_o_rat(aa_rat_fun_o_rat(aa_fun5241534567979455741_o_rat(aTP_Lamm_rh((Uu)),Uua),Uub),(Uuc)) = $ite((Uuc) = (Uu),aa_o_rat(Uua,(Uuc)),Uub) ).

% ATP.lambda_579
tff(fact_8530_ATP_Olambda__580,axiom,
    ! [Uu: nat,Uua: fun_nat_assn,Uub: assn,Uuc: nat] :
      aa_nat_assn(aa_assn_fun_nat_assn(aa_fun2404858873066863565t_assn(aTP_Lamm_re(Uu),Uua),Uub),Uuc) = $ite(Uuc = Uu,aa_nat_assn(Uua,Uuc),Uub) ).

% ATP.lambda_580
tff(fact_8531_ATP_Olambda__581,axiom,
    ! [Uu: nat,Uua: fun_nat_rat,Uub: rat,Uuc: nat] :
      aa_nat_rat(aa_rat_fun_nat_rat(aa_fun5559679822142647773at_rat(aTP_Lamm_rj(Uu),Uua),Uub),Uuc) = $ite(Uuc = Uu,aa_nat_rat(Uua,Uuc),Uub) ).

% ATP.lambda_581
tff(fact_8532_ATP_Olambda__582,axiom,
    ! [Uu: int,Uua: fun_int_assn,Uub: assn,Uuc: int] :
      aa_int_assn(aa_assn_fun_int_assn(aa_fun3470678483766860421t_assn(aTP_Lamm_rf(Uu),Uua),Uub),Uuc) = $ite(Uuc = Uu,aa_int_assn(Uua,Uuc),Uub) ).

% ATP.lambda_582
tff(fact_8533_ATP_Olambda__583,axiom,
    ! [Uu: int,Uua: fun_int_rat,Uub: rat,Uuc: int] :
      aa_int_rat(aa_rat_fun_int_rat(aa_fun9155288305517341845nt_rat(aTP_Lamm_rk(Uu),Uua),Uub),Uuc) = $ite(Uuc = Uu,aa_int_rat(Uua,Uuc),Uub) ).

% ATP.lambda_583
tff(fact_8534_ATP_Olambda__584,axiom,
    ! [Uu: fun_fu7564235448449272366at_o_o,Uua: fun_fu4001317426178549763_nat_o,Uub: fun_nat_o,Uuc: fun_nat_o] :
      ( aa_fun_nat_o_o(aa_fun4840518763754620511at_o_o(aa_fun2763792489458032301at_o_o(aTP_Lamm_yy(Uu),Uua),Uub),Uuc)
    <=> aa_fun_nat_o_o(aa_fun4840518763754620511at_o_o(Uu,Uub),aa_fun5937193402907943164_nat_o(Uua,Uuc)) ) ).

% ATP.lambda_584
tff(fact_8535_ATP_Olambda__585,axiom,
    ! [Uu: fun_fu6699046866436802030_int_o,Uua: fun_fu3661779633992098115nt_int,Uub: fun_in4211310926729683942nt_int,Uuc: fun_in4211310926729683942nt_int] :
      ( aa_fun8476666123149806190_int_o(aa_fun1009039980557175711_int_o(aa_fun3789280421985926445_int_o(aTP_Lamm_yz(Uu),Uua),Uub),Uuc)
    <=> aa_fun8476666123149806190_int_o(aa_fun1009039980557175711_int_o(Uu,Uub),aa_fun6626262031093723324nt_int(Uua,Uuc)) ) ).

% ATP.lambda_585
tff(fact_8536_ATP_Olambda__586,axiom,
    ! [Uu: fun_fu6699046866436802030_int_o,Uua: fun_fu4522195968571808382nt_int,Uub: fun_in4211310926729683942nt_int,Uuc: fun_int_rat] :
      ( aa_fun_int_rat_o(aa_fun5827461210593834758_rat_o(aa_fun4351174416053881551_rat_o(aTP_Lamm_za(Uu),Uua),Uub),Uuc)
    <=> aa_fun8476666123149806190_int_o(aa_fun1009039980557175711_int_o(Uu,Uub),aa_fun1163745293653399015nt_int(Uua,Uuc)) ) ).

% ATP.lambda_586
tff(fact_8537_ATP_Olambda__587,axiom,
    ! [Uu: fun_fu7677565902479959693_rat_o,Uua: fun_fu7460908759652350970nt_rat,Uub: fun_in4211310926729683942nt_int,Uuc: fun_in4211310926729683942nt_int] :
      ( aa_fun8476666123149806190_int_o(aa_fun1009039980557175711_int_o(aa_fun8496196461586942128_int_o(aTP_Lamm_zb(Uu),Uua),Uub),Uuc)
    <=> aa_fun_int_rat_o(aa_fun5827461210593834758_rat_o(Uu,Uub),aa_fun1809696235935464875nt_rat(Uua,Uuc)) ) ).

% ATP.lambda_587
tff(fact_8538_ATP_Olambda__588,axiom,
    ! [Uu: fun_fu7677565902479959693_rat_o,Uua: fun_fu1008360527747082367nt_rat,Uub: fun_in4211310926729683942nt_int,Uuc: fun_int_rat] :
      ( aa_fun_int_rat_o(aa_fun5827461210593834758_rat_o(aa_fun8956737304536474314_rat_o(aTP_Lamm_zc(Uu),Uua),Uub),Uuc)
    <=> aa_fun_int_rat_o(aa_fun5827461210593834758_rat_o(Uu,Uub),aa_fun1481061427733998144nt_rat(Uua,Uuc)) ) ).

% ATP.lambda_588
tff(fact_8539_ATP_Olambda__589,axiom,
    ! [Uu: fun_fu6971708032831053102nt_o_o,Uua: fun_fu3883539188510166275_int_o,Uub: fun_int_o,Uuc: fun_int_o] :
      ( aa_fun_int_o_o(aa_fun1331825017273370463nt_o_o(aa_fun7316249240758406317nt_o_o(aTP_Lamm_zd(Uu),Uua),Uub),Uuc)
    <=> aa_fun_int_o_o(aa_fun1331825017273370463nt_o_o(Uu,Uub),aa_fun6243517787477317628_int_o(Uua,Uuc)) ) ).

% ATP.lambda_589
tff(fact_8540_ATP_Olambda__590,axiom,
    ! [Uu: fun_fu4208408993564413984_int_o,Uua: fun_fu1143798476471108391nt_int,Uub: fun_int_int,Uuc: fun_int_int] :
      ( aa_fun_int_int_o(aa_fun2545150047610057353_int_o(aa_fun6233912309721051003_int_o(aTP_Lamm_ze(Uu),Uua),Uub),Uuc)
    <=> aa_fun_int_int_o(aa_fun2545150047610057353_int_o(Uu,Uub),aa_fun6280345759651049192nt_int(Uua,Uuc)) ) ).

% ATP.lambda_590
tff(fact_8541_ATP_Olambda__591,axiom,
    ! [Uu: code_natural,Uua: code_natural,Uub: code_natural,Uuc: code_natural] : aa_Cod6808739660676082561atural(aa_Cod4292056611156568242atural(aa_Cod8811915439870959971atural(aTP_Lamm_adk(Uu),Uua),Uub),Uuc) = produc4480994950612372183atural(produc3574140220909816553atural(aa_Cod4272041906116450446atural(inc_shift(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,one)))))))))))))))))))))))))))))))),Uu),Uuc),produc3574140220909816553atural(Uub,aa_Cod4272041906116450446atural(inc_shift(aa_num_Code_natural(numera5444537566228673987atural,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit0,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,aa_num_num(bit1,one)))))))))))))))))))))))))))))))),Uua))) ).

% ATP.lambda_591
tff(fact_8542_ATP_Olambda__592,axiom,
    ! [Uu: nat,Uua: nat,Uub: nat,Uuc: nat] : aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(aa_nat4158579785191972357at_nat(aTP_Lamm_gc(Uu),Uua),Uub),Uuc) = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,Uu),Uub)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,Uua),Uuc))),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,Uu),Uuc)),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,Uua),Uub))) ).

% ATP.lambda_592
tff(fact_8543_ATP_Olambda__593,axiom,
    ! [Uu: fun_se4097146774670233028at_nat,Uua: set_Pr4329608150637261639at_nat,Uub: set_Pr1261947904930325089at_nat,Uuc: set_Pr1261947904930325089at_nat] :
      ( aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(aa_set5605188905385065315_nat_o(aTP_Lamm_gl(Uu),Uua),Uub),Uuc)
    <=> ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_set4749074711808745205at_nat(Uu,Uub)),aa_set4749074711808745205at_nat(Uu,Uuc))
        | ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_set4749074711808745205at_nat(Uu,Uub)),aa_set4749074711808745205at_nat(Uu,Uuc))
          & member8757157785044589968at_nat(produc2922128104949294807at_nat(Uub,Uuc),Uua) ) ) ) ).

% ATP.lambda_593
tff(fact_8544_ATP_Olambda__594,axiom,
    ! [Uu: fun_nat_nat,Uua: set_Pr1261947904930325089at_nat,Uub: nat,Uuc: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(aa_set2634951030311766213_nat_o(aTP_Lamm_gm(Uu),Uua),Uub),Uuc)
    <=> ( aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(Uu,Uub)),aa_nat_nat(Uu,Uuc))
        | ( aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(Uu,Uub)),aa_nat_nat(Uu,Uuc))
          & member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Uub),Uuc),Uua) ) ) ) ).

% ATP.lambda_594
tff(fact_8545_ATP_Olambda__595,axiom,
    ! [Uu: fun_fu4810197545401214784nteger,Uua: fun_Pr7015759342434529115eger_o,Uub: fun_Pr5098669352780829690e_term,Uuc: produc8923325533196201883nteger] :
      ( aa_Pro4926521453222654329eger_o(aa_fun4505422719058378424eger_o(aa_fun5185621348090534806eger_o(aTP_Lamm_gn(Uu),Uua),Uub),Uuc)
    <=> ( ( aa_fun1271726682903785001nteger(Uu,Uub) = some_P6772290148444788224nteger(Uuc) )
        & aa_Pro4148064003102580676eger_o(Uua,aa_Pro4291442876242880245nteger(aa_fun8303988899834042124nteger(produc565448451787809096nteger,Uub),Uuc)) ) ) ).

% ATP.lambda_595
tff(fact_8546_ATP_Olambda__596,axiom,
    ! [Uu: fun_fu2352890940381120596et_nat,Uua: fun_Pr2620521676128474833_nat_o,Uub: fun_Pr6460944699146269935_nat_o,Uuc: produc3658429121746597890et_nat] :
      ( aa_Pro653082453696054616_nat_o(aa_fun2638059832795814268_nat_o(aa_fun1045796833200626456_nat_o(aTP_Lamm_go(Uu),Uua),Uub),Uuc)
    <=> ( ( aa_fun5824947343344787589et_nat(Uu,Uub) = some_P624177172695371229et_nat(Uuc) )
        & aa_Pro5643009357358181178_nat_o(Uua,aa_Pro434340453207536480et_nat(aa_fun3926903090414666066et_nat(produc6017135503889078682et_nat,Uub),Uuc)) ) ) ).

% ATP.lambda_596
tff(fact_8547_ATP_Olambda__597,axiom,
    ! [Uu: fun_fu1905361174868762994et_nat,Uua: fun_Pr1227177680593602867_nat_o,Uub: fun_Pr6460944699146269935_nat_o,Uuc: produc8799533983703829792et_nat] :
      ( aa_Pro5643009357358181178_nat_o(aa_fun912680268133416158_nat_o(aa_fun4422562838209026524_nat_o(aTP_Lamm_gp(Uu),Uua),Uub),Uuc)
    <=> ( ( aa_fun1716447855799474851et_nat(Uu,Uub) = some_P994283844982041979et_nat(Uuc) )
        & aa_Pro2671238023309943196_nat_o(Uua,aa_Pro1979504083478021276et_nat(aa_fun615918787490101902et_nat(produc7291855603632349880et_nat,Uub),Uuc)) ) ) ).

% ATP.lambda_597
tff(fact_8548_ATP_Olambda__598,axiom,
    ! [Uu: fun_fu4253467608928286509nt_int,Uua: fun_Pr3540825087398332590_int_o,Uub: fun_Pr7763680713840462443e_term,Uuc: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(aa_fun3538162476766722827_int_o(aa_fun1054583131507368252_int_o(aTP_Lamm_gq(Uu),Uua),Uub),Uuc)
    <=> ( ( aa_fun251074914522852630nt_int(Uu,Uub) = some_P4184893108420464158nt_int(Uuc) )
        & aa_Pro2601676399929874711_int_o(Uua,aa_Pro5748361610964203648nt_int(aa_fun3265472288063244902nt_int(produc7320969046608631221nt_int,Uub),Uuc)) ) ) ).

% ATP.lambda_598
tff(fact_8549_ATP_Olambda__599,axiom,
    ! [Uu: fun_fu5631754973857388633nt_int,Uua: fun_Pr1196100989263358594_int_o,Uub: fun_in5730379987311621695e_term,Uuc: product_prod_int_int] :
      ( aa_Pro4592068669816069595_int_o(aa_fun586359091965693151_int_o(aa_fun8601777901039773924_int_o(aTP_Lamm_gr(Uu),Uua),Uub),Uuc)
    <=> ( ( aa_fun3970441718214872642nt_int(Uu,Uub) = some_P4184893108420464158nt_int(Uuc) )
        & aa_Pro5451197003417746155_int_o(Uua,aa_Pro8800328608558162860nt_int(aa_fun260840925927807678nt_int(produc4729913460834754785nt_int,Uub),Uuc)) ) ) ).

% ATP.lambda_599
tff(fact_8550_ATP_Olambda__600,axiom,
    ! [Uu: code_integer,Uua: code_integer,Uub: nat,Uuc: nat] : aa_nat_Code_integer(aa_nat2010205248571845816nteger(aa_Cod3140087502949435154nteger(aTP_Lamm_kh(Uu),Uua),Uub),Uuc) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(semiri4939895301339042750nteger,aa_nat_nat(aa_nat_fun_nat_nat(binomial,Uub),Uuc))),aa_nat_Code_integer(comm_s8582702949713902594nteger(Uu),Uuc))),aa_nat_Code_integer(comm_s8582702949713902594nteger(Uua),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uub),Uuc))) ).

% ATP.lambda_600
tff(fact_8551_ATP_Olambda__601,axiom,
    ! [Uu: rat,Uua: rat,Uub: nat,Uuc: nat] : aa_nat_rat(aa_nat_fun_nat_rat(aa_rat250263598611652360at_rat(aTP_Lamm_kf(Uu),Uua),Uub),Uuc) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(semiri681578069525770553at_rat,aa_nat_nat(aa_nat_fun_nat_nat(binomial,Uub),Uuc))),aa_nat_rat(comm_s4028243227959126397er_rat(Uu),Uuc))),aa_nat_rat(comm_s4028243227959126397er_rat(Uua),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uub),Uuc))) ).

% ATP.lambda_601
tff(fact_8552_ATP_Olambda__602,axiom,
    ! [Uu: int,Uua: int,Uub: nat,Uuc: nat] : aa_nat_int(aa_nat_fun_nat_int(aa_int431785320988601264at_int(aTP_Lamm_kg(Uu),Uua),Uub),Uuc) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(aa_nat_fun_nat_nat(binomial,Uub),Uuc))),aa_nat_int(comm_s4660882817536571857er_int(Uu),Uuc))),aa_nat_int(comm_s4660882817536571857er_int(Uua),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uub),Uuc))) ).

% ATP.lambda_602
tff(fact_8553_ATP_Olambda__603,axiom,
    ! [Uu: code_natural,Uua: code_natural,Uub: nat,Uuc: nat] : aa_nat_Code_natural(aa_nat6468655069083034883atural(aa_Cod217761371205376936atural(aTP_Lamm_js(Uu),Uua),Uub),Uuc) = aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_Cod4272041906116450446atural(aa_Cod5141017464274028979atural(times_2397367101498566445atural,aa_nat_Code_natural(semiri3763490453095760265atural,aa_nat_nat(aa_nat_fun_nat_nat(binomial,Uub),Uuc))),aa_nat_Code_natural(power_7079662738309270450atural(Uu),Uuc))),aa_nat_Code_natural(power_7079662738309270450atural(Uua),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uub),Uuc))) ).

% ATP.lambda_603
tff(fact_8554_ATP_Olambda__604,axiom,
    ! [Uu: code_integer,Uua: code_integer,Uub: nat,Uuc: nat] : aa_nat_Code_integer(aa_nat2010205248571845816nteger(aa_Cod3140087502949435154nteger(aTP_Lamm_jr(Uu),Uua),Uub),Uuc) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(semiri4939895301339042750nteger,aa_nat_nat(aa_nat_fun_nat_nat(binomial,Uub),Uuc))),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,Uu),Uuc))),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,Uua),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uub),Uuc))) ).

% ATP.lambda_604
tff(fact_8555_ATP_Olambda__605,axiom,
    ! [Uu: rat,Uua: rat,Uub: nat,Uuc: nat] : aa_nat_rat(aa_nat_fun_nat_rat(aa_rat250263598611652360at_rat(aTP_Lamm_jp(Uu),Uua),Uub),Uuc) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(semiri681578069525770553at_rat,aa_nat_nat(aa_nat_fun_nat_nat(binomial,Uub),Uuc))),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,Uu),Uuc))),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,Uua),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uub),Uuc))) ).

% ATP.lambda_605
tff(fact_8556_ATP_Olambda__606,axiom,
    ! [Uu: nat,Uua: nat,Uub: nat,Uuc: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aa_nat3783148529270815480at_nat(aTP_Lamm_jl(Uu),Uua),Uub),Uuc) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(semiri1316708129612266289at_nat,aa_nat_nat(aa_nat_fun_nat_nat(binomial,Uub),Uuc))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,Uu),Uuc))),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,Uua),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uub),Uuc))) ).

% ATP.lambda_606
tff(fact_8557_ATP_Olambda__607,axiom,
    ! [Uu: int,Uua: int,Uub: nat,Uuc: nat] : aa_nat_int(aa_nat_fun_nat_int(aa_int431785320988601264at_int(aTP_Lamm_jq(Uu),Uua),Uub),Uuc) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(semiri1314217659103216013at_int,aa_nat_nat(aa_nat_fun_nat_nat(binomial,Uub),Uuc))),aa_nat_int(aa_int_fun_nat_int(power_power_int,Uu),Uuc))),aa_nat_int(aa_int_fun_nat_int(power_power_int,Uua),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uub),Uuc))) ).

% ATP.lambda_607
tff(fact_8558_ATP_Olambda__608,axiom,
    ! [Uu: code_integer,Uua: nat,Uub: code_integer,Uuc: nat] : aa_nat_Code_integer(aa_Cod1578151519121547077nteger(aa_nat2351529209232473362nteger(aTP_Lamm_jf(Uu),Uua),Uub),Uuc) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,Uub),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uua),aa_nat_nat(suc,Uuc)))),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,Uu),Uuc)) ).

% ATP.lambda_608
tff(fact_8559_ATP_Olambda__609,axiom,
    ! [Uu: rat,Uua: nat,Uub: rat,Uuc: nat] : aa_nat_rat(aa_rat_fun_nat_rat(aa_nat298952458717073160at_rat(aTP_Lamm_jg(Uu),Uua),Uub),Uuc) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,Uub),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uua),aa_nat_nat(suc,Uuc)))),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,Uu),Uuc)) ).

% ATP.lambda_609
tff(fact_8560_ATP_Olambda__610,axiom,
    ! [Uu: int,Uua: nat,Uub: int,Uuc: nat] : aa_nat_int(aa_int_fun_nat_int(aa_nat6704147566042551216at_int(aTP_Lamm_jh(Uu),Uua),Uub),Uuc) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,Uub),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uua),aa_nat_nat(suc,Uuc)))),aa_nat_int(aa_int_fun_nat_int(power_power_int,Uu),Uuc)) ).

% ATP.lambda_610
tff(fact_8561_ATP_Olambda__611,axiom,
    ! [Uu: code_integer,Uua: nat,Uub: code_integer,Uuc: nat] : aa_nat_Code_integer(aa_Cod1578151519121547077nteger(aa_nat2351529209232473362nteger(aTP_Lamm_ji(Uu),Uua),Uub),Uuc) = aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,Uu),Uuc)),aa_nat_Code_integer(aa_Cod1578151519121547077nteger(power_8256067586552552935nteger,Uub),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uua),Uuc))) ).

% ATP.lambda_611
tff(fact_8562_ATP_Olambda__612,axiom,
    ! [Uu: rat,Uua: nat,Uub: rat,Uuc: nat] : aa_nat_rat(aa_rat_fun_nat_rat(aa_nat298952458717073160at_rat(aTP_Lamm_jj(Uu),Uua),Uub),Uuc) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,Uu),Uuc)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,Uub),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uua),Uuc))) ).

% ATP.lambda_612
tff(fact_8563_ATP_Olambda__613,axiom,
    ! [Uu: int,Uua: nat,Uub: int,Uuc: nat] : aa_nat_int(aa_int_fun_nat_int(aa_nat6704147566042551216at_int(aTP_Lamm_jk(Uu),Uua),Uub),Uuc) = aa_int_int(aa_int_fun_int_int(times_times_int,aa_nat_int(aa_int_fun_nat_int(power_power_int,Uu),Uuc)),aa_nat_int(aa_int_fun_nat_int(power_power_int,Uub),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uua),Uuc))) ).

% ATP.lambda_613
tff(fact_8564_ATP_Olambda__614,axiom,
    ! [Uu: nat,Uua: nat,Uub: nat,Uuc: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aa_nat3783148529270815480at_nat(aTP_Lamm_je(Uu),Uua),Uub),Uuc) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(binomial,Uu),Uuc)),aa_nat_nat(aa_nat_fun_nat_nat(binomial,Uua),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uub),Uuc))) ).

% ATP.lambda_614
tff(fact_8565_ATP_Olambda__615,axiom,
    ! [Uu: nat,Uua: nat,Uub: nat,Uuc: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(aa_nat8314798964848609180_nat_o(aTP_Lamm_ff(Uu),Uua),Uub),Uuc)
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uu),Uuc)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uub),Uua)) ) ).

% ATP.lambda_615
tff(fact_8566_ATP_Olambda__616,axiom,
    ! [Uu: nat,Uua: nat,Uub: nat,Uuc: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(aa_nat8314798964848609180_nat_o(aTP_Lamm_fd(Uu),Uua),Uub),Uuc)
    <=> aa_nat_o(aa_nat_fun_nat_o(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uu),Uuc)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uub),Uua)) ) ).

% ATP.lambda_616
tff(fact_8567_ATP_Olambda__617,axiom,
    ! [Uu: nat,Uua: nat,Uub: nat,Uuc: nat] : aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(aa_nat4158579785191972357at_nat(aTP_Lamm_fy(Uu),Uua),Uub),Uuc) = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uu),Uub)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uua),Uuc)) ).

% ATP.lambda_617
tff(fact_8568_ATP_Olambda__618,axiom,
    ! [Uu: nat,Uua: nat,Uub: nat,Uuc: nat] : aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(aa_nat4158579785191972357at_nat(aTP_Lamm_ga(Uu),Uua),Uub),Uuc) = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uu),Uuc)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uua),Uub)) ).

% ATP.lambda_618
tff(fact_8569_ATP_Olambda__619,axiom,
    ! [Uu: nat,Uua: nat,Uub: nat,Uuc: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(aa_nat8314798964848609180_nat_o(aTP_Lamm_acv(Uu),Uua),Uub),Uuc)
    <=> ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uu),Uuc) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uub),Uua) ) ) ).

% ATP.lambda_619
tff(fact_8570_ATP_Olambda__620,axiom,
    ! [Uu: set_Code_integer,Uua: fun_Co8499238673658658103nteger,Uub: fun_Co8499238673658658103nteger,Uuc: code_integer] :
      ( aa_Code_integer_o(aa_fun7159535342743012639eger_o(aa_fun5296778454019918337eger_o(aTP_Lamm_py(Uu),Uua),Uub),Uuc)
    <=> ( member_Code_integer(Uuc,Uu)
        & ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_Cod1783974652533396728nteger(Uua,Uuc)),aa_Cod1783974652533396728nteger(Uub,Uuc)) != one_one_Code_integer ) ) ) ).

% ATP.lambda_620
tff(fact_8571_ATP_Olambda__621,axiom,
    ! [Uu: set_Code_integer,Uua: fun_Co4490034186337852034r_assn,Uub: fun_Co4490034186337852034r_assn,Uuc: code_integer] :
      ( aa_Code_integer_o(aa_fun6538703224075513620eger_o(aa_fun4422309413433313771eger_o(aTP_Lamm_qg(Uu),Uua),Uub),Uuc)
    <=> ( member_Code_integer(Uuc,Uu)
        & ( aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_Code_integer_assn(Uua,Uuc)),aa_Code_integer_assn(Uub,Uuc)) != one_one_assn ) ) ) ).

% ATP.lambda_621
tff(fact_8572_ATP_Olambda__622,axiom,
    ! [Uu: set_o,Uua: fun_o_Code_integer,Uub: fun_o_Code_integer,Uuc: $o] :
      ( aa_o_o(aa_fun8192762245619933327un_o_o(aa_fun1865401534164435218un_o_o(aTP_Lamm_ps(Uu),Uua),Uub),(Uuc))
    <=> ( member_o((Uuc),Uu)
        & ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_o_Code_integer(Uua,(Uuc))),aa_o_Code_integer(Uub,(Uuc))) != one_one_Code_integer ) ) ) ).

% ATP.lambda_622
tff(fact_8573_ATP_Olambda__623,axiom,
    ! [Uu: set_o,Uua: fun_o_assn,Uub: fun_o_assn,Uuc: $o] :
      ( aa_o_o(aa_fun8382565201914911066un_o_o(aa_fun5794833117214906962un_o_o(aTP_Lamm_qa(Uu),Uua),Uub),(Uuc))
    <=> ( member_o((Uuc),Uu)
        & ( aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_o_assn(Uua,(Uuc))),aa_o_assn(Uub,(Uuc))) != one_one_assn ) ) ) ).

% ATP.lambda_623
tff(fact_8574_ATP_Olambda__624,axiom,
    ! [Uu: set_o,Uua: fun_o_rat,Uub: fun_o_rat,Uuc: $o] :
      ( aa_o_o(aa_fun_o_rat_fun_o_o(aa_fun5510981055783399506un_o_o(aTP_Lamm_qi(Uu),Uua),Uub),(Uuc))
    <=> ( member_o((Uuc),Uu)
        & ( aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_o_rat(Uua,(Uuc))),aa_o_rat(Uub,(Uuc))) != one_one_rat ) ) ) ).

% ATP.lambda_624
tff(fact_8575_ATP_Olambda__625,axiom,
    ! [Uu: set_nat,Uua: fun_nat_Code_integer,Uub: fun_nat_Code_integer,Uuc: nat] :
      ( aa_nat_o(aa_fun3480067038916266681_nat_o(aa_fun2745573882733218024_nat_o(aTP_Lamm_pu(Uu),Uua),Uub),Uuc)
    <=> ( member_nat(Uuc,Uu)
        & ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_nat_Code_integer(Uua,Uuc)),aa_nat_Code_integer(Uub,Uuc)) != one_one_Code_integer ) ) ) ).

% ATP.lambda_625
tff(fact_8576_ATP_Olambda__626,axiom,
    ! [Uu: set_nat,Uua: fun_nat_assn,Uub: fun_nat_assn,Uuc: nat] :
      ( aa_nat_o(aa_fun7183233715851567790_nat_o(aa_fun8595640264602358482_nat_o(aTP_Lamm_qc(Uu),Uua),Uub),Uuc)
    <=> ( member_nat(Uuc,Uu)
        & ( aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_nat_assn(Uua,Uuc)),aa_nat_assn(Uub,Uuc)) != one_one_assn ) ) ) ).

% ATP.lambda_626
tff(fact_8577_ATP_Olambda__627,axiom,
    ! [Uu: set_nat,Uua: fun_nat_rat,Uub: fun_nat_rat,Uuc: nat] :
      ( aa_nat_o(aa_fun1118977351124560894_nat_o(aa_fun8314661095172591474_nat_o(aTP_Lamm_qk(Uu),Uua),Uub),Uuc)
    <=> ( member_nat(Uuc,Uu)
        & ( aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(Uua,Uuc)),aa_nat_rat(Uub,Uuc)) != one_one_rat ) ) ) ).

% ATP.lambda_627
tff(fact_8578_ATP_Olambda__628,axiom,
    ! [Uu: set_int,Uua: fun_int_Code_integer,Uub: fun_int_Code_integer,Uuc: int] :
      ( aa_int_o(aa_fun3336537925265328129_int_o(aa_fun8818272713621706452_int_o(aTP_Lamm_pw(Uu),Uua),Uub),Uuc)
    <=> ( member_int(Uuc,Uu)
        & ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(times_3573771949741848930nteger,aa_int_Code_integer(Uua,Uuc)),aa_int_Code_integer(Uub,Uuc)) != one_one_Code_integer ) ) ) ).

% ATP.lambda_628
tff(fact_8579_ATP_Olambda__629,axiom,
    ! [Uu: set_int,Uua: fun_int_assn,Uub: fun_int_assn,Uuc: int] :
      ( aa_int_o(aa_fun202081646129719286_int_o(aa_fun871127997271750846_int_o(aTP_Lamm_qe(Uu),Uua),Uub),Uuc)
    <=> ( member_int(Uuc,Uu)
        & ( aa_assn_assn(aa_ass954072293579886259n_assn(times_times_assn,aa_int_assn(Uua,Uuc)),aa_int_assn(Uub,Uuc)) != one_one_assn ) ) ) ).

% ATP.lambda_629
tff(fact_8580_ATP_Olambda__630,axiom,
    ! [Uu: set_Code_integer,Uua: fun_Co8499238673658658103nteger,Uub: fun_Co8499238673658658103nteger,Uuc: code_integer] :
      ( aa_Code_integer_o(aa_fun7159535342743012639eger_o(aa_fun5296778454019918337eger_o(aTP_Lamm_pe(Uu),Uua),Uub),Uuc)
    <=> ( member_Code_integer(Uuc,Uu)
        & ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_Cod1783974652533396728nteger(Uua,Uuc)),aa_Cod1783974652533396728nteger(Uub,Uuc)) != zero_z3403309356797280102nteger ) ) ) ).

% ATP.lambda_630
tff(fact_8581_ATP_Olambda__631,axiom,
    ! [Uu: set_Code_integer,Uua: fun_Code_integer_rat,Uub: fun_Code_integer_rat,Uuc: code_integer] :
      ( aa_Code_integer_o(aa_fun6395433285121891940eger_o(aa_fun4095556841599367307eger_o(aTP_Lamm_pm(Uu),Uua),Uub),Uuc)
    <=> ( member_Code_integer(Uuc,Uu)
        & ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_Code_integer_rat(Uua,Uuc)),aa_Code_integer_rat(Uub,Uuc)) != zero_zero_rat ) ) ) ).

% ATP.lambda_631
tff(fact_8582_ATP_Olambda__632,axiom,
    ! [Uu: set_o,Uua: fun_o_Code_integer,Uub: fun_o_Code_integer,Uuc: $o] :
      ( aa_o_o(aa_fun8192762245619933327un_o_o(aa_fun1865401534164435218un_o_o(aTP_Lamm_oy(Uu),Uua),Uub),(Uuc))
    <=> ( member_o((Uuc),Uu)
        & ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_o_Code_integer(Uua,(Uuc))),aa_o_Code_integer(Uub,(Uuc))) != zero_z3403309356797280102nteger ) ) ) ).

% ATP.lambda_632
tff(fact_8583_ATP_Olambda__633,axiom,
    ! [Uu: set_o,Uua: fun_o_rat,Uub: fun_o_rat,Uuc: $o] :
      ( aa_o_o(aa_fun_o_rat_fun_o_o(aa_fun5510981055783399506un_o_o(aTP_Lamm_pg(Uu),Uua),Uub),(Uuc))
    <=> ( member_o((Uuc),Uu)
        & ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_o_rat(Uua,(Uuc))),aa_o_rat(Uub,(Uuc))) != zero_zero_rat ) ) ) ).

% ATP.lambda_633
tff(fact_8584_ATP_Olambda__634,axiom,
    ! [Uu: set_o,Uua: fun_o_nat,Uub: fun_o_nat,Uuc: $o] :
      ( aa_o_o(aa_fun_o_nat_fun_o_o(aa_fun5833554292436378194un_o_o(aTP_Lamm_po(Uu),Uua),Uub),(Uuc))
    <=> ( member_o((Uuc),Uu)
        & ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_o_nat(Uua,(Uuc))),aa_o_nat(Uub,(Uuc))) != zero_zero_nat ) ) ) ).

% ATP.lambda_634
tff(fact_8585_ATP_Olambda__635,axiom,
    ! [Uu: set_nat,Uua: fun_nat_Code_integer,Uub: fun_nat_Code_integer,Uuc: nat] :
      ( aa_nat_o(aa_fun3480067038916266681_nat_o(aa_fun2745573882733218024_nat_o(aTP_Lamm_pa(Uu),Uua),Uub),Uuc)
    <=> ( member_nat(Uuc,Uu)
        & ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_nat_Code_integer(Uua,Uuc)),aa_nat_Code_integer(Uub,Uuc)) != zero_z3403309356797280102nteger ) ) ) ).

% ATP.lambda_635
tff(fact_8586_ATP_Olambda__636,axiom,
    ! [Uu: set_nat,Uua: fun_nat_rat,Uub: fun_nat_rat,Uuc: nat] :
      ( aa_nat_o(aa_fun1118977351124560894_nat_o(aa_fun8314661095172591474_nat_o(aTP_Lamm_pi(Uu),Uua),Uub),Uuc)
    <=> ( member_nat(Uuc,Uu)
        & ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(Uua,Uuc)),aa_nat_rat(Uub,Uuc)) != zero_zero_rat ) ) ) ).

% ATP.lambda_636
tff(fact_8587_ATP_Olambda__637,axiom,
    ! [Uu: set_nat,Uua: fun_nat_nat,Uub: fun_nat_nat,Uuc: nat] :
      ( aa_nat_o(aa_fun8673969331427483654_nat_o(aa_fun6348600740168882050_nat_o(aTP_Lamm_pq(Uu),Uua),Uub),Uuc)
    <=> ( member_nat(Uuc,Uu)
        & ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(Uua,Uuc)),aa_nat_nat(Uub,Uuc)) != zero_zero_nat ) ) ) ).

% ATP.lambda_637
tff(fact_8588_ATP_Olambda__638,axiom,
    ! [Uu: set_int,Uua: fun_int_Code_integer,Uub: fun_int_Code_integer,Uuc: int] :
      ( aa_int_o(aa_fun3336537925265328129_int_o(aa_fun8818272713621706452_int_o(aTP_Lamm_pc(Uu),Uua),Uub),Uuc)
    <=> ( member_int(Uuc,Uu)
        & ( aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(plus_p5714425477246183910nteger,aa_int_Code_integer(Uua,Uuc)),aa_int_Code_integer(Uub,Uuc)) != zero_z3403309356797280102nteger ) ) ) ).

% ATP.lambda_638
tff(fact_8589_ATP_Olambda__639,axiom,
    ! [Uu: set_int,Uua: fun_int_rat,Uub: fun_int_rat,Uuc: int] :
      ( aa_int_o(aa_fun7094158214180239686_int_o(aa_fun1445893531507182942_int_o(aTP_Lamm_pk(Uu),Uua),Uub),Uuc)
    <=> ( member_int(Uuc,Uu)
        & ( aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_int_rat(Uua,Uuc)),aa_int_rat(Uub,Uuc)) != zero_zero_rat ) ) ) ).

% ATP.lambda_639
tff(fact_8590_ATP_Olambda__640,axiom,
    ! [Uu: fun_list_nat_o,Uua: fun_li1025265955262268170_nat_o,Uub: list_nat,Uuc: list_nat] :
      ( aa_list_nat_o(aa_lis557685189327716851_nat_o(aa_fun6462763351938039228_nat_o(aTP_Lamm_zl(Uu),Uua),Uub),Uuc)
    <=> ( aa_list_nat_o(Uu,Uub)
        & aa_list_nat_o(aa_lis557685189327716851_nat_o(Uua,Uub),Uuc) ) ) ).

% ATP.lambda_640
tff(fact_8591_ATP_Olambda__641,axiom,
    ! [Uu: fun_list_nat_o,Uua: fun_li2421049240157457050_nat_o,Uub: list_nat,Uuc: nat] :
      ( aa_nat_o(aa_lis1686035672126679939_nat_o(aa_fun6275404141584987452_nat_o(aTP_Lamm_zj(Uu),Uua),Uub),Uuc)
    <=> ( aa_list_nat_o(Uu,Uub)
        & aa_nat_o(aa_lis1686035672126679939_nat_o(Uua,Uub),Uuc) ) ) ).

% ATP.lambda_641
tff(fact_8592_ATP_Olambda__642,axiom,
    ! [Uu: fun_nat_o,Uua: fun_na7234455742697417626_nat_o,Uub: nat,Uuc: list_nat] :
      ( aa_list_nat_o(aa_nat5883842100386203267_nat_o(aa_fun6745918892298368316_nat_o(aTP_Lamm_zh(Uu),Uua),Uub),Uuc)
    <=> ( aa_nat_o(Uu,Uub)
        & aa_list_nat_o(aa_nat5883842100386203267_nat_o(Uua,Uub),Uuc) ) ) ).

% ATP.lambda_642
tff(fact_8593_ATP_Olambda__643,axiom,
    ! [Uu: fun_nat_o,Uua: fun_nat_fun_nat_o,Uub: nat,Uuc: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(aa_fun6699960423209655484_nat_o(aTP_Lamm_zf(Uu),Uua),Uub),Uuc)
    <=> ( aa_nat_o(Uu,Uub)
        & aa_nat_o(aa_nat_fun_nat_o(Uua,Uub),Uuc) ) ) ).

% ATP.lambda_643
tff(fact_8594_ATP_Olambda__644,axiom,
    ! [Uu: fun_nat_set_nat,Uua: fun_nat_set_nat,Uub: nat,Uuc: nat] : aa_nat7062706319057040595at_nat(aa_nat7495903657192774236at_nat(aa_fun2373699841287868962at_nat(aTP_Lamm_zq(Uu),Uua),Uub),Uuc) = produc457027306803732586at_nat(aa_nat_set_nat(Uu,Uub),aa_nat1818925681583257441et_nat(aTP_Lamm_zp(Uua),Uuc)) ).

% ATP.lambda_644
tff(fact_8595_ATP_Olambda__645,axiom,
    ! [Uu: fun_nat_Code_integer,Uua: fun_nat_Code_integer,Uub: nat,Uuc: nat] : aa_nat8379393489429068301nteger(aa_nat4718444463496506006nteger(aa_fun7952091224041096005nteger(aTP_Lamm_aac(Uu),Uua),Uub),Uuc) = aa_Cod6977894654539884864nteger(produc1086072967326762835nteger(aa_nat_Code_integer(Uu,Uub)),aa_nat_Code_integer(Uua,Uuc)) ).

% ATP.lambda_645
tff(fact_8596_ATP_Olambda__646,axiom,
    ! [Uu: fun_nat_Code_integer,Uua: fun_nat_nat,Uub: nat,Uuc: nat] : aa_nat3011333803152189440er_nat(aa_nat8627311254624274185er_nat(aa_fun7093963954598080645er_nat(aTP_Lamm_aad(Uu),Uua),Uub),Uuc) = aa_nat3011333803152189440er_nat(produc8807591364040884934er_nat(aa_nat_Code_integer(Uu,Uub)),aa_nat_nat(Uua,Uuc)) ).

% ATP.lambda_646
tff(fact_8597_ATP_Olambda__647,axiom,
    ! [Uu: fun_nat_Code_integer,Uua: fun_nat_int,Uub: nat,Uuc: nat] : aa_nat8056854820497768540er_int(aa_nat6137228109692547429er_int(aa_fun8714824397388734853er_int(aTP_Lamm_aaf(Uu),Uua),Uub),Uuc) = produc8805100893531834658er_int(aa_nat_Code_integer(Uu,Uub),aa_nat_int(Uua,Uuc)) ).

% ATP.lambda_647
tff(fact_8598_ATP_Olambda__648,axiom,
    ! [Uu: fun_nat_Code_integer,Uua: fun_int_int,Uub: nat,Uuc: int] : aa_int593519447396103936er_int(aa_nat7897264773445658633er_int(aa_fun3338573009006755021er_int(aTP_Lamm_aah(Uu),Uua),Uub),Uuc) = produc8805100893531834658er_int(aa_nat_Code_integer(Uu,Uub),aa_int_int(Uua,Uuc)) ).

% ATP.lambda_648
tff(fact_8599_ATP_Olambda__649,axiom,
    ! [Uu: fun_nat_nat,Uua: fun_nat_Code_integer,Uub: nat,Uuc: nat] : aa_nat8392374045505204608nteger(aa_nat2047254435812855945nteger(aa_fun8323025376520073144nteger(aTP_Lamm_aaj(Uu),Uua),Uub),Uuc) = produc9072146812819927750nteger(aa_nat_nat(Uu,Uub),aa_nat_Code_integer(Uua,Uuc)) ).

% ATP.lambda_649
tff(fact_8600_ATP_Olambda__650,axiom,
    ! [Uu: fun_nat_nat,Uua: fun_nat_nat,Uub: nat,Uuc: nat] : aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(aa_fun4348998216881757432at_nat(aTP_Lamm_aal(Uu),Uua),Uub),Uuc) = aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,aa_nat_nat(Uu,Uub)),aa_nat_nat(Uua,Uuc)) ).

% ATP.lambda_650
tff(fact_8601_ATP_Olambda__651,axiom,
    ! [Uu: fun_nat_nat,Uua: fun_nat_int,Uub: nat,Uuc: nat] : aa_nat3425370143577916367at_int(aa_nat6313705167186764632at_int(aa_fun2313822316067610104at_int(aTP_Lamm_aam(Uu),Uua),Uub),Uuc) = product_Pair_nat_int(aa_nat_nat(Uu,Uub),aa_nat_int(Uua,Uuc)) ).

% ATP.lambda_651
tff(fact_8602_ATP_Olambda__652,axiom,
    ! [Uu: fun_nat_nat,Uua: fun_int_int,Uub: nat,Uuc: int] : aa_int6463212228042050163at_int(aa_nat128175214796122620at_int(aa_fun566144318431074624at_int(aTP_Lamm_aao(Uu),Uua),Uub),Uuc) = product_Pair_nat_int(aa_nat_nat(Uu,Uub),aa_int_int(Uua,Uuc)) ).

% ATP.lambda_652
tff(fact_8603_ATP_Olambda__653,axiom,
    ! [Uu: fun_nat_int,Uua: fun_nat_Code_integer,Uub: nat,Uuc: nat] : aa_nat8764027605742049244nteger(aa_nat8056064086808430821nteger(aa_fun947730671064037908nteger(aTP_Lamm_aaq(Uu),Uua),Uub),Uuc) = produc220428336201996578nteger(aa_nat_int(Uu,Uub),aa_nat_Code_integer(Uua,Uuc)) ).

% ATP.lambda_653
tff(fact_8604_ATP_Olambda__654,axiom,
    ! [Uu: fun_nat_int,Uua: fun_nat_nat,Uub: nat,Uuc: nat] : aa_nat8602574874988167631nt_nat(aa_nat1767337849956737368nt_nat(aa_fun7567701811046127444nt_nat(aTP_Lamm_aas(Uu),Uua),Uub),Uuc) = aa_nat8602574874988167631nt_nat(product_Pair_int_nat(aa_nat_int(Uu,Uub)),aa_nat_nat(Uua,Uuc)) ).

% ATP.lambda_654
tff(fact_8605_ATP_Olambda__655,axiom,
    ! [Uu: fun_list_nat_o,Uua: fun_list_nat_o,Uub: list_nat,Uuc: list_nat] :
      ( aa_list_nat_o(aa_lis557685189327716851_nat_o(aa_fun3567724338799755637_nat_o(aTP_Lamm_xo(Uu),Uua),Uub),Uuc)
    <=> ( aa_list_nat_o(Uu,Uub)
        & aa_list_nat_o(Uua,Uuc) ) ) ).

% ATP.lambda_655
tff(fact_8606_ATP_Olambda__656,axiom,
    ! [Uu: fun_list_nat_o,Uua: fun_nat_o,Uub: list_nat,Uuc: nat] :
      ( aa_nat_o(aa_lis1686035672126679939_nat_o(aa_fun823229757805912181_nat_o(aTP_Lamm_xm(Uu),Uua),Uub),Uuc)
    <=> ( aa_list_nat_o(Uu,Uub)
        & aa_nat_o(Uua,Uuc) ) ) ).

% ATP.lambda_656
tff(fact_8607_ATP_Olambda__657,axiom,
    ! [Uu: fun_nat_o,Uua: fun_list_nat_o,Uub: nat,Uuc: list_nat] :
      ( aa_list_nat_o(aa_nat5883842100386203267_nat_o(aa_fun6290253675283700613_nat_o(aTP_Lamm_xk(Uu),Uua),Uub),Uuc)
    <=> ( aa_nat_o(Uu,Uub)
        & aa_list_nat_o(Uua,Uuc) ) ) ).

% ATP.lambda_657
tff(fact_8608_ATP_Olambda__658,axiom,
    ! [Uu: fun_nat_o,Uua: fun_nat_o,Uub: nat,Uuc: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(aa_fun5001253801653566085_nat_o(aTP_Lamm_xi(Uu),Uua),Uub),Uuc)
    <=> ( aa_nat_o(Uu,Uub)
        & aa_nat_o(Uua,Uuc) ) ) ).

% ATP.lambda_658
tff(fact_8609_ATP_Olambda__659,axiom,
    ! [Uu: fun_Pr292408699144966967t_unit,Uua: product_unit,Uub: heap_e7401611519738050253t_unit,Uuc: nat] : aa_nat3804989708481012326it_nat(aa_hea5083147195637387702it_nat(aa_Pro5266438804776016756it_nat(aTP_Lamm_fn(Uu),Uua),Uub),Uuc) = heap_T3616969660504097270t_unit(Uuc,aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(aa_Pro1108561329362217960t_unit(Uu,Uua)),Uub)) ).

% ATP.lambda_659
tff(fact_8610_ATP_Olambda__660,axiom,
    ! [Uu: fun_Pr5924905948197006361rray_a,Uua: product_unit,Uub: heap_e7401611519738050253t_unit,Uuc: nat] : aa_nat5919723204993609852it_nat(aa_hea7328941321439323714it_nat(aa_Pro9169072840722635546it_nat(aTP_Lamm_fj(Uu),Uua),Uub),Uuc) = heap_T531568236820715630rray_a(Uuc,aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(aa_Pro755961224256580114rray_a(Uu,Uua)),Uub)) ).

% ATP.lambda_660
tff(fact_8611_ATP_Olambda__661,axiom,
    ! [Uu: fun_ar1074044450438384043t_unit,Uua: array_a,Uub: heap_e7401611519738050253t_unit,Uuc: nat] : aa_nat3804989708481012326it_nat(aa_hea5083147195637387702it_nat(aa_arr8018972492040254448it_nat(aTP_Lamm_fl(Uu),Uua),Uub),Uuc) = heap_T3616969660504097270t_unit(Uuc,aa_hea684056619475940329it_nat(heap_T875086893843062177t_unit(aa_arr7999650297717212780t_unit(Uu,Uua)),Uub)) ).

% ATP.lambda_661
tff(fact_8612_ATP_Olambda__662,axiom,
    ! [Uu: fun_ar3891948820113774757rray_a,Uua: array_a,Uub: heap_e7401611519738050253t_unit,Uuc: nat] : aa_nat5919723204993609852it_nat(aa_hea7328941321439323714it_nat(aa_arr9035823794894939038it_nat(aTP_Lamm_fh(Uu),Uua),Uub),Uuc) = heap_T531568236820715630rray_a(Uuc,aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(aa_arr1142863274018860686rray_a(Uu,Uua)),Uub)) ).

% ATP.lambda_662
tff(fact_8613_ATP_Olambda__663,axiom,
    ! [Uu: fun_Pr2478283820680522243nt_int,Uua: fun_in1696471567231710611nt_int,Uub: int,Uuc: int] : aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(aa_fun4152872853588681340nt_int(aTP_Lamm_dc(Uu),Uua),Uub),Uuc) = aa_Pro6970504127699319548nt_int(Uu,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(Uua,Uub),Uuc)) ).

% ATP.lambda_663
tff(fact_8614_ATP_Olambda__664,axiom,
    ! [Uu: fun_Pr982841511892225912nt_int,Uua: fun_in1696471567231710611nt_int,Uub: int,Uuc: int] : aa_int_int(aa_int_fun_int_int(aa_fun7461304428735181397nt_int(aTP_Lamm_cy(Uu),Uua),Uub),Uuc) = aa_Pro6799258434465214121nt_int(Uu,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(Uua,Uub),Uuc)) ).

% ATP.lambda_664
tff(fact_8615_ATP_Olambda__665,axiom,
    ! [Uu: fun_nat_nat,Uua: fun_nat_fun_nat_nat,Uub: nat,Uuc: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aa_fun7716529229553496594at_nat(aTP_Lamm_cw(Uu),Uua),Uub),Uuc) = aa_nat_nat(Uu,aa_nat_nat(aa_nat_fun_nat_nat(Uua,Uub),Uuc)) ).

% ATP.lambda_665
tff(fact_8616_ATP_Olambda__666,axiom,
    ! [Uu: fun_na8713714802964096592at_nat,Uua: fun_nat_fun_nat_nat,Uub: nat,Uuc: nat] : aa_nat7997280740862404369at_nat(aa_nat5682243440470347102at_nat(aa_fun2484538639213223237at_nat(aTP_Lamm_dd(Uu),Uua),Uub),Uuc) = aa_nat7997280740862404369at_nat(Uu,aa_nat_nat(aa_nat_fun_nat_nat(Uua,Uub),Uuc)) ).

% ATP.lambda_666
tff(fact_8617_ATP_Olambda__667,axiom,
    ! [Uu: fun_na3970208099681795815_nat_o,Uua: fun_nat_fun_nat_nat,Uub: nat,Uuc: nat] : aa_nat7695548938202568488_nat_o(aa_nat4259715169212259317_nat_o(aa_fun2100511394839469148_nat_o(aTP_Lamm_da(Uu),Uua),Uub),Uuc) = aa_nat7695548938202568488_nat_o(Uu,aa_nat_nat(aa_nat_fun_nat_nat(Uua,Uub),Uuc)) ).

% ATP.lambda_667
tff(fact_8618_ATP_Olambda__668,axiom,
    ! [Uu: fun_in4211310926729683942nt_int,Uua: fun_int_fun_int_int,Uub: int,Uuc: int] : aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(aa_fun1034830265760468567nt_int(aTP_Lamm_cz(Uu),Uua),Uub),Uuc) = aa_int7462565939943104719nt_int(Uu,aa_int_int(aa_int_fun_int_int(Uua,Uub),Uuc)) ).

% ATP.lambda_668
tff(fact_8619_ATP_Olambda__669,axiom,
    ! [Uu: fun_int_int,Uua: fun_int_fun_int_int,Uub: int,Uuc: int] : aa_int_int(aa_int_fun_int_int(aa_fun6119123525526402106nt_int(aTP_Lamm_cx(Uu),Uua),Uub),Uuc) = aa_int_int(Uu,aa_int_int(aa_int_fun_int_int(Uua,Uub),Uuc)) ).

% ATP.lambda_669
tff(fact_8620_ATP_Olambda__670,axiom,
    ! [Uu: fun_fu1413608398870722896at_nat,Uua: fun_na1668100129766719005at_nat,Uub: nat,Uuc: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aa_fun8817627472026143685at_nat(aTP_Lamm_de(Uu),Uua),Uub),Uuc) = aa_fun7582795104022253201at_nat(Uu,aa_nat7997280740862404369at_nat(aa_nat5682243440470347102at_nat(Uua,Uub),Uuc)) ).

% ATP.lambda_670
tff(fact_8621_ATP_Olambda__671,axiom,
    ! [Uu: fun_fu1115759055147092071_o_nat,Uua: fun_na5914473681949881652_nat_o,Uub: nat,Uuc: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aa_fun3680403850923830236at_nat(aTP_Lamm_db(Uu),Uua),Uub),Uuc) = aa_fun1432809138467554728_o_nat(Uu,aa_nat7695548938202568488_nat_o(aa_nat4259715169212259317_nat_o(Uua,Uub),Uuc)) ).

% ATP.lambda_671
tff(fact_8622_ATP_Olambda__672,axiom,
    ! [Uu: fun_fu3275390434952296369_nat_o,Uua: fun_na5914473681949881652_nat_o,Uub: nat,Uuc: nat] : aa_nat7695548938202568488_nat_o(aa_nat4259715169212259317_nat_o(aa_fun824319262034445606_nat_o(aTP_Lamm_df(Uu),Uua),Uub),Uuc) = aa_fun359341089595923442_nat_o(Uu,aa_nat7695548938202568488_nat_o(aa_nat4259715169212259317_nat_o(Uua,Uub),Uuc)) ).

% ATP.lambda_672
tff(fact_8623_ATP_Olambda__673,axiom,
    ! [Uu: fun_nat_nat,Uua: nat,Uub: nat,Uuc: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aa_nat3783148529270815480at_nat(aTP_Lamm_kc(Uu),Uua),Uub),Uuc) = aa_nat_nat(Uu,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uub),Uua)),aa_nat_nat(suc,Uuc))) ).

% ATP.lambda_673
tff(fact_8624_ATP_Olambda__674,axiom,
    ! [Uu: fun_nat_int,Uua: nat,Uub: nat,Uuc: nat] : aa_nat_int(aa_nat_fun_nat_int(aa_nat1293065384339088724at_int(aTP_Lamm_kw(Uu),Uua),Uub),Uuc) = aa_nat_int(Uu,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uub),Uua)),aa_nat_nat(suc,Uuc))) ).

% ATP.lambda_674
tff(fact_8625_ATP_Olambda__675,axiom,
    ! [Uu: fun_nat_nat,Uua: nat,Uub: nat,Uuc: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aa_nat3783148529270815480at_nat(aTP_Lamm_do(Uu),Uua),Uub),Uuc) = aa_nat_nat(Uu,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uub),Uua)),Uuc)) ).

% ATP.lambda_675
tff(fact_8626_ATP_Olambda__676,axiom,
    ! [Uu: fun_nat_int,Uua: nat,Uub: nat,Uuc: nat] : aa_nat_int(aa_nat_fun_nat_int(aa_nat1293065384339088724at_int(aTP_Lamm_kt(Uu),Uua),Uub),Uuc) = aa_nat_int(Uu,aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,Uub),Uua)),Uuc)) ).

% ATP.lambda_676
tff(fact_8627_ATP_Olambda__677,axiom,
    ! [Uu: fun_nat_o,Uua: fun_na7044673412300895210at_nat,Uub: nat,Uuc: nat] : aa_nat7695548938202568488_nat_o(aa_nat4259715169212259317_nat_o(aa_fun1888629816020924642_nat_o(aTP_Lamm_fc(Uu),Uua),Uub),Uuc) = aa_fun7564604662015400456_nat_o(produc6081775807080527818_nat_o,aa_nat8314798964848609180_nat_o(aa_nat7293937527460703909_nat_o(aa_fun5017297687458839182_nat_o(aTP_Lamm_fb(Uu),Uua),Uub),Uuc)) ).

% ATP.lambda_677
tff(fact_8628_ATP_Olambda__678,axiom,
    ! [Uu: set_Pr1261947904930325089at_nat,Uua: set_Pr1261947904930325089at_nat,Uub: nat,Uuc: nat] : aa_nat7695548938202568488_nat_o(aa_nat4259715169212259317_nat_o(aa_set1501693898512841689_nat_o(aTP_Lamm_fa(Uu),Uua),Uub),Uuc) = aa_fun7564604662015400456_nat_o(produc6081775807080527818_nat_o,aa_nat8314798964848609180_nat_o(aa_nat7293937527460703909_nat_o(aa_set1591873763996598871_nat_o(aTP_Lamm_ez(Uu),Uua),Uub),Uuc)) ).

% ATP.lambda_678
tff(fact_8629_ATP_Olambda__679,axiom,
    ! [Uu: set_Pr1261947904930325089at_nat,Uua: set_Pr4329608150637261639at_nat,Uub: nat,Uuc: set_Pr1261947904930325089at_nat] : aa_set4888932223548040198_nat_o(aa_nat2460170648439927835_nat_o(aa_set2321460896359935973_nat_o(aTP_Lamm_ey(Uu),Uua),Uub),Uuc) = produc7997411485876045171_nat_o(aa_set4096294849986607660_nat_o(aa_nat8542548088120273133_nat_o(aa_set1734484532169114937_nat_o(aTP_Lamm_ex(Uu),Uua),Uub),Uuc)) ).

% ATP.lambda_679
tff(fact_8630_ATP_Olambda__680,axiom,
    ! [Uu: set_Pr4329608150637261639at_nat,Uua: set_Pr1261947904930325089at_nat,Uub: set_Pr1261947904930325089at_nat,Uuc: nat] : aa_nat6907252128894768643_nat_o(aa_set7004941124559686709_nat_o(aa_set5873268817925218273_nat_o(aTP_Lamm_ew(Uu),Uua),Uub),Uuc) = produc3595121349294487249_nat_o(aa_nat3868275710975325009_nat_o(aa_set6059588303149383989_nat_o(aa_set4461581360499344159_nat_o(aTP_Lamm_ev(Uu),Uua),Uub),Uuc)) ).

% ATP.lambda_680
tff(fact_8631_ATP_Olambda__681,axiom,
    ! [Uu: set_Pr4329608150637261639at_nat,Uua: set_Pr4329608150637261639at_nat,Uub: set_Pr1261947904930325089at_nat,Uuc: set_Pr1261947904930325089at_nat] : aa_set5283925091486981337_nat_o(aa_set3180801629657254467_nat_o(aa_set2810100084588730581_nat_o(aTP_Lamm_eu(Uu),Uua),Uub),Uuc) = aa_fun762164075915671590_nat_o(produc410239310623530412_nat_o,aa_set8959908230745118793_nat_o(aa_set5113931935655255541_nat_o(aa_set2536000832573987193_nat_o(aTP_Lamm_et(Uu),Uua),Uub),Uuc)) ).

% ATP.lambda_681
tff(fact_8632_ATP_Olambda__682,axiom,
    ! [Uu: int,Uua: int,Uub: int,Uuc: int] : aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(aa_int1966403025003302569nt_int(aTP_Lamm_mx(Uu),Uua),Uub),Uuc) = aa_Pro6970504127699319548nt_int(normalize,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_int_int(aa_int_fun_int_int(minus_minus_int,aa_int_int(aa_int_fun_int_int(times_times_int,Uu),Uuc)),aa_int_int(aa_int_fun_int_int(times_times_int,Uub),Uua))),aa_int_int(aa_int_fun_int_int(times_times_int,Uua),Uuc))) ).

% ATP.lambda_682
tff(fact_8633_ATP_Olambda__683,axiom,
    ! [Uu: int,Uua: int,Uub: int,Uuc: int] : aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(aa_int1966403025003302569nt_int(aTP_Lamm_mz(Uu),Uua),Uub),Uuc) = aa_Pro6970504127699319548nt_int(normalize,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_int_int(aa_int_fun_int_int(plus_plus_int,aa_int_int(aa_int_fun_int_int(times_times_int,Uu),Uuc)),aa_int_int(aa_int_fun_int_int(times_times_int,Uub),Uua))),aa_int_int(aa_int_fun_int_int(times_times_int,Uua),Uuc))) ).

% ATP.lambda_683
tff(fact_8634_ATP_Olambda__684,axiom,
    ! [Uu: int,Uua: int,Uub: int,Uuc: int] : aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(aa_int1966403025003302569nt_int(aTP_Lamm_nd(Uu),Uua),Uub),Uuc) = aa_Pro6970504127699319548nt_int(normalize,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_int_int(aa_int_fun_int_int(times_times_int,Uu),Uub)),aa_int_int(aa_int_fun_int_int(times_times_int,Uua),Uuc))) ).

% ATP.lambda_684
tff(fact_8635_ATP_Olambda__685,axiom,
    ! [Uu: int,Uua: int,Uub: int,Uuc: int] : aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(aa_int1966403025003302569nt_int(aTP_Lamm_nf(Uu),Uua),Uub),Uuc) = aa_Pro6970504127699319548nt_int(normalize,aa_int7462565939943104719nt_int(aa_int2565445551602696444nt_int(product_Pair_int_int,aa_int_int(aa_int_fun_int_int(times_times_int,Uu),Uuc)),aa_int_int(aa_int_fun_int_int(times_times_int,Uua),Uub))) ).

% ATP.lambda_685
tff(fact_8636_ATP_Olambda__686,axiom,
    ! [Uu: nat,Uua: rat,Uub: rat,Uuc: rat,Uud: nat] : aa_nat_rat(aa_rat_fun_nat_rat(aa_rat3146053865535587600at_rat(aa_rat7467449789483521253at_rat(aTP_Lamm_ip(Uu),Uua),Uub),Uuc),Uud) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(gbinomial_rat(aa_rat_rat(minus_minus_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(semiri681578069525770553at_rat,Uud)),Uua)),one_one_rat)),Uud)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,Uub),Uud))),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,Uub),Uuc)),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uu),Uud))) ).

% ATP.lambda_686
tff(fact_8637_ATP_Olambda__687,axiom,
    ! [Uu: nat,Uua: rat,Uub: rat,Uuc: rat,Uud: nat] : aa_nat_rat(aa_rat_fun_nat_rat(aa_rat3146053865535587600at_rat(aa_rat7467449789483521253at_rat(aTP_Lamm_in(Uu),Uua),Uub),Uuc),Uud) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(gbinomial_rat(aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,aa_nat_rat(semiri681578069525770553at_rat,Uu)),Uua)),Uud)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,Uub),Uud))),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,Uuc),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uu),Uud))) ).

% ATP.lambda_687
tff(fact_8638_ATP_Olambda__688,axiom,
    ! [Uu: nat,Uua: rat,Uub: rat,Uuc: rat,Uud: nat] : aa_nat_rat(aa_rat_fun_nat_rat(aa_rat3146053865535587600at_rat(aa_rat7467449789483521253at_rat(aTP_Lamm_io(Uu),Uua),Uub),Uuc),Uud) = aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_rat_rat(aa_rat_fun_rat_rat(times_times_rat,aa_nat_rat(gbinomial_rat(aa_rat_rat(uminus_uminus_rat,Uua)),Uud)),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(uminus_uminus_rat,Uub)),Uud))),aa_nat_rat(aa_rat_fun_nat_rat(power_power_rat,aa_rat_rat(aa_rat_fun_rat_rat(plus_plus_rat,Uub),Uuc)),aa_nat_nat(aa_nat_fun_nat_nat(minus_minus_nat,Uu),Uud))) ).

% ATP.lambda_688
tff(fact_8639_ATP_Olambda__689,axiom,
    ! [Uu: set_Pr4329608150637261639at_nat,Uua: set_Pr4329608150637261639at_nat,Uub: set_Pr1261947904930325089at_nat,Uuc: set_Pr1261947904930325089at_nat,Uud: set_Pr1261947904930325089at_nat,Uue: set_Pr1261947904930325089at_nat] :
      ( aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(aa_set8959908230745118793_nat_o(aa_set5113931935655255541_nat_o(aa_set2536000832573987193_nat_o(aTP_Lamm_et(Uu),Uua),Uub),Uuc),Uud),Uue)
    <=> ( member8757157785044589968at_nat(produc2922128104949294807at_nat(Uub,Uud),Uu)
        | ( ( Uub = Uud )
          & member8757157785044589968at_nat(produc2922128104949294807at_nat(Uuc,Uue),Uua) ) ) ) ).

% ATP.lambda_689
tff(fact_8640_ATP_Olambda__690,axiom,
    ! [Uu: set_Pr4329608150637261639at_nat,Uua: set_Pr1261947904930325089at_nat,Uub: set_Pr1261947904930325089at_nat,Uuc: nat,Uud: set_Pr1261947904930325089at_nat,Uue: nat] :
      ( aa_nat_o(aa_set5175029118278479676_nat_o(aa_nat3868275710975325009_nat_o(aa_set6059588303149383989_nat_o(aa_set4461581360499344159_nat_o(aTP_Lamm_ev(Uu),Uua),Uub),Uuc),Uud),Uue)
    <=> ( member8757157785044589968at_nat(produc2922128104949294807at_nat(Uub,Uud),Uu)
        | ( ( Uub = Uud )
          & member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Uuc),Uue),Uua) ) ) ) ).

% ATP.lambda_690
tff(fact_8641_ATP_Olambda__691,axiom,
    ! [Uu: set_Pr1261947904930325089at_nat,Uua: set_Pr4329608150637261639at_nat,Uub: nat,Uuc: set_Pr1261947904930325089at_nat,Uud: nat,Uue: set_Pr1261947904930325089at_nat] :
      ( aa_set3702741264012733747_nat_o(aa_nat1727191234135941576_nat_o(aa_set4096294849986607660_nat_o(aa_nat8542548088120273133_nat_o(aa_set1734484532169114937_nat_o(aTP_Lamm_ex(Uu),Uua),Uub),Uuc),Uud),Uue)
    <=> ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Uub),Uud),Uu)
        | ( ( Uub = Uud )
          & member8757157785044589968at_nat(produc2922128104949294807at_nat(Uuc,Uue),Uua) ) ) ) ).

% ATP.lambda_691
tff(fact_8642_ATP_Olambda__692,axiom,
    ! [Uu: set_Pr1261947904930325089at_nat,Uua: set_Pr1261947904930325089at_nat,Uub: nat,Uuc: nat,Uud: nat,Uue: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(aa_nat8314798964848609180_nat_o(aa_nat7293937527460703909_nat_o(aa_set1591873763996598871_nat_o(aTP_Lamm_ez(Uu),Uua),Uub),Uuc),Uud),Uue)
    <=> ( member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Uub),Uud),Uu)
        | ( ( Uub = Uud )
          & member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Uuc),Uue),Uua) ) ) ) ).

% ATP.lambda_692
tff(fact_8643_ATP_Olambda__693,axiom,
    ! [Uu: fun_nat_o,Uua: fun_na7044673412300895210at_nat,Uub: nat,Uuc: nat,Uud: nat,Uue: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(aa_nat8314798964848609180_nat_o(aa_nat7293937527460703909_nat_o(aa_fun5017297687458839182_nat_o(aTP_Lamm_fb(Uu),Uua),Uub),Uuc),Uud),Uue)
    <=> ( ( Uub = Uud )
        & aa_nat_o(Uu,Uud)
        & member8440522571783428010at_nat(aa_nat7603221163087113075at_nat(aa_nat8803788312118491388at_nat(product_Pair_nat_nat,Uuc),Uue),aa_nat7062706319057040595at_nat(Uua,Uud)) ) ) ).

% ATP.lambda_693
tff(fact_8644_ATP_Olambda__694,axiom,
    ! [Uu: product_unit,Uua: heap_e7401611519738050253t_unit,Uub: nat] : aa_nat_Product_unit(aa_hea3828351310419263941t_unit(aTP_Lamm_hh(Uu),Uua),Uub) = Uu ).

% ATP.lambda_694
tff(fact_8645_ATP_Olambda__695,axiom,
    ! [Uu: array_a,Uua: heap_e7401611519738050253t_unit,Uub: nat] : aa_nat_array_a(aa_hea2549104158996286709rray_a(aTP_Lamm_hf(Uu),Uua),Uub) = Uu ).

% ATP.lambda_695
tff(fact_8646_ATP_Olambda__696,axiom,
    ! [Uu: $o,Uua: set_Pr1261947904930325089at_nat,Uub: set_Pr1261947904930325089at_nat] :
      ( aa_set3702741264012733747_nat_o(aa_set7675215768510388063_nat_o(aTP_Lamm_sk((Uu)),Uua),Uub)
    <=> (Uu) ) ).

% ATP.lambda_696
tff(fact_8647_ATP_Olambda__697,axiom,
    ! [Uu: $o,Uua: nat,Uub: nat] :
      ( aa_nat_o(aa_nat_fun_nat_o(aTP_Lamm_sl((Uu)),Uua),Uub)
    <=> (Uu) ) ).

% ATP.lambda_697
tff(fact_8648_ATP_Olambda__698,axiom,
    ! [Uu: code_integer,Uua: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(aTP_Lamm_cb,Uu),Uua) = Uu ).

% ATP.lambda_698
tff(fact_8649_ATP_Olambda__699,axiom,
    ! [Uu: heap_e7401611519738050253t_unit,Uua: nat] : aa_nat4191430056936421439t_unit(aa_hea3178159646823327365t_unit(aTP_Lamm_hr,Uu),Uua) = Uu ).

% ATP.lambda_699
tff(fact_8650_ATP_Olambda__700,axiom,
    ! [Uu: set_Code_integer,Uua: code_integer] : aa_Cod2813182003028390446nteger(aTP_Lamm_ys(Uu),Uua) = Uu ).

% ATP.lambda_700
tff(fact_8651_ATP_Olambda__701,axiom,
    ! [Uu: set_Pr4811707699266497531nteger,Uua: fun_Pr5098669352780829690e_term] : aa_fun6394921419180517443nteger(aTP_Lamm_zt(Uu),Uua) = Uu ).

% ATP.lambda_701
tff(fact_8652_ATP_Olambda__702,axiom,
    ! [Uu: set_Pr3948176798113811640et_nat,Uua: fun_Pr6460944699146269935_nat_o] : aa_fun786139119071955819et_nat(aTP_Lamm_zv(Uu),Uua) = Uu ).

% ATP.lambda_702
tff(fact_8653_ATP_Olambda__703,axiom,
    ! [Uu: set_Pr4329608150637261639at_nat,Uua: nat] : aa_nat8843416860741599929at_nat(aTP_Lamm_zn(Uu),Uua) = Uu ).

% ATP.lambda_703
tff(fact_8654_ATP_Olambda__704,axiom,
    ! [Uu: set_Pr1261947904930325089at_nat,Uua: nat] : aa_nat7062706319057040595at_nat(aTP_Lamm_zo(Uu),Uua) = Uu ).

% ATP.lambda_704
tff(fact_8655_ATP_Olambda__705,axiom,
    ! [Uu: set_Pr958786334691620121nt_int,Uua: fun_Pr7763680713840462443e_term] : aa_fun2513960992105274800nt_int(aTP_Lamm_zz(Uu),Uua) = Uu ).

% ATP.lambda_705
tff(fact_8656_ATP_Olambda__706,axiom,
    ! [Uu: set_Pr958786334691620121nt_int,Uua: fun_in5730379987311621695e_term] : aa_fun2636263158522872028nt_int(aTP_Lamm_aab(Uu),Uua) = Uu ).

% ATP.lambda_706
tff(fact_8657_ATP_Olambda__707,axiom,
    ! [Uu: set_Pr1312406793078187350et_nat,Uua: fun_Pr6460944699146269935_nat_o] : aa_fun4924015400185905801et_nat(aTP_Lamm_zx(Uu),Uua) = Uu ).

% ATP.lambda_707
tff(fact_8658_ATP_Olambda__708,axiom,
    ! [Uu: set_o,Uua: product_prod_nat_nat] : aa_Pro5970036531051701619_set_o(aTP_Lamm_yb(Uu),Uua) = Uu ).

% ATP.lambda_708
tff(fact_8659_ATP_Olambda__709,axiom,
    ! [Uu: set_o,Uua: $o] : aa_o_set_o(aTP_Lamm_xs(Uu),(Uua)) = Uu ).

% ATP.lambda_709
tff(fact_8660_ATP_Olambda__710,axiom,
    ! [Uu: set_o,Uua: nat] : aa_nat_set_o(aTP_Lamm_xv(Uu),Uua) = Uu ).

% ATP.lambda_710
tff(fact_8661_ATP_Olambda__711,axiom,
    ! [Uu: set_o,Uua: int] : aa_int_set_o(aTP_Lamm_xx(Uu),Uua) = Uu ).

% ATP.lambda_711
tff(fact_8662_ATP_Olambda__712,axiom,
    ! [Uu: set_se7855581050983116737at_nat,Uua: set_Pr1261947904930325089at_nat] : aa_set6242432332095302236at_nat(aTP_Lamm_yc(Uu),Uua) = Uu ).

% ATP.lambda_712
tff(fact_8663_ATP_Olambda__713,axiom,
    ! [Uu: set_nat,Uua: $o] : aa_o_set_nat(aTP_Lamm_xt(Uu),(Uua)) = Uu ).

% ATP.lambda_713
tff(fact_8664_ATP_Olambda__714,axiom,
    ! [Uu: set_nat,Uua: nat] : aa_nat_set_nat(aTP_Lamm_ya(Uu),Uua) = Uu ).

% ATP.lambda_714
tff(fact_8665_ATP_Olambda__715,axiom,
    ! [Uu: set_nat,Uua: int] : aa_int_set_nat(aTP_Lamm_xy(Uu),Uua) = Uu ).

% ATP.lambda_715
tff(fact_8666_ATP_Olambda__716,axiom,
    ! [Uu: set_int,Uua: $o] : aa_o_set_int(aTP_Lamm_xu(Uu),(Uua)) = Uu ).

% ATP.lambda_716
tff(fact_8667_ATP_Olambda__717,axiom,
    ! [Uu: set_int,Uua: nat] : aa_nat_set_int(aTP_Lamm_xw(Uu),Uua) = Uu ).

% ATP.lambda_717
tff(fact_8668_ATP_Olambda__718,axiom,
    ! [Uu: set_int,Uua: int] : aa_int_set_int(aTP_Lamm_xz(Uu),Uua) = Uu ).

% ATP.lambda_718
tff(fact_8669_ATP_Olambda__719,axiom,
    ! [Uu: set_fu8280898353253485872e_term,Uua: produc8923325533196201883nteger] : aa_Pro3049322369718103567e_term(aTP_Lamm_zs(Uu),Uua) = Uu ).

% ATP.lambda_719
tff(fact_8670_ATP_Olambda__720,axiom,
    ! [Uu: set_fu3555266933746557007_nat_o,Uua: produc3658429121746597890et_nat] : aa_Pro7009299959260105231_nat_o(aTP_Lamm_zu(Uu),Uua) = Uu ).

% ATP.lambda_720
tff(fact_8671_ATP_Olambda__721,axiom,
    ! [Uu: set_fu3555266933746557007_nat_o,Uua: produc8799533983703829792et_nat] : aa_Pro1505388192238479345_nat_o(aTP_Lamm_zw(Uu),Uua) = Uu ).

% ATP.lambda_721
tff(fact_8672_ATP_Olambda__722,axiom,
    ! [Uu: set_fu5653557704672872225e_term,Uua: product_prod_int_int] : aa_Pro5850374426668061982e_term(aTP_Lamm_zy(Uu),Uua) = Uu ).

% ATP.lambda_722
tff(fact_8673_ATP_Olambda__723,axiom,
    ! [Uu: set_fu3629540756087427317e_term,Uua: product_prod_int_int] : aa_Pro1848062444984653554e_term(aTP_Lamm_aaa(Uu),Uua) = Uu ).

% ATP.lambda_723
tff(fact_8674_ATP_Olambda__724,axiom,
    ! [Uu: num,Uua: nat] : aa_nat_num(aTP_Lamm_ce(Uu),Uua) = Uu ).

% ATP.lambda_724
tff(fact_8675_ATP_Olambda__725,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_vt,Uu),Uua) = Uu ).

% ATP.lambda_725
tff(fact_8676_ATP_Olambda__726,axiom,
    ! [Uu: int,Uua: int] : aa_int_int(aa_int_fun_int_int(aTP_Lamm_vu,Uu),Uua) = Uu ).

% ATP.lambda_726
tff(fact_8677_ATP_Olambda__727,axiom,
    ! [Uu: fun_Pr5876161306168176259nteger,Uua: code_integer] : aa_Cod1978467581589928094nteger(aTP_Lamm_cc(Uu),Uua) = Uu ).

% ATP.lambda_727
tff(fact_8678_ATP_Olambda__728,axiom,
    ! [Uu: fun_Pr5876161306168176259nteger,Uua: fun_Co8499238673658658103nteger] : aa_fun2509385170507305080nteger(aTP_Lamm_cd(Uu),Uua) = Uu ).

% ATP.lambda_728
tff(fact_8679_ATP_Olambda__729,axiom,
    ! [Uu: fun_nat_nat,Uua: nat] : aa_nat_fun_nat_nat(aTP_Lamm_uw(Uu),Uua) = Uu ).

% ATP.lambda_729
tff(fact_8680_ATP_Olambda__730,axiom,
    ! [Uu: fun_na8713714802964096592at_nat,Uua: nat] : aa_nat5682243440470347102at_nat(aTP_Lamm_uy(Uu),Uua) = Uu ).

% ATP.lambda_730
tff(fact_8681_ATP_Olambda__731,axiom,
    ! [Uu: fun_na3970208099681795815_nat_o,Uua: nat] : aa_nat4259715169212259317_nat_o(aTP_Lamm_va(Uu),Uua) = Uu ).

% ATP.lambda_731
tff(fact_8682_ATP_Olambda__732,axiom,
    ! [Uu: fun_in4211310926729683942nt_int,Uua: int] : aa_int2565445551602696444nt_int(aTP_Lamm_vc(Uu),Uua) = Uu ).

% ATP.lambda_732
tff(fact_8683_ATP_Olambda__733,axiom,
    ! [Uu: fun_int_int,Uua: int] : aa_int_fun_int_int(aTP_Lamm_ve(Uu),Uua) = Uu ).

% ATP.lambda_733
tff(fact_8684_ATP_Olambda__734,axiom,
    ! [Uu: code_natural,Uua: produc7822875418678951345atural] : aa_Pro4262726347734369532atural(aa_Cod1269109650860651881atural(aTP_Lamm_vg,Uu),Uua) = Uua ).

% ATP.lambda_734
tff(fact_8685_ATP_Olambda__735,axiom,
    ! [Uu: code_integer,Uua: code_integer] : aa_Cod1783974652533396728nteger(aa_Cod4161879620478718930nteger(aTP_Lamm_vf,Uu),Uua) = Uua ).

% ATP.lambda_735
tff(fact_8686_ATP_Olambda__736,axiom,
    ! [Uu: heap_e7401611519738050253t_unit,Uua: nat] : aa_nat_nat(aa_hea461265506217620142at_nat(aTP_Lamm_km,Uu),Uua) = Uua ).

% ATP.lambda_736
tff(fact_8687_ATP_Olambda__737,axiom,
    ! [Uu: nat,Uua: nat] : aa_nat_nat(aa_nat_fun_nat_nat(aTP_Lamm_vh,Uu),Uua) = Uua ).

% ATP.lambda_737
tff(fact_8688_ATP_Olambda__738,axiom,
    ! [Uu: int,Uua: int] : aa_int_int(aa_int_fun_int_int(aTP_Lamm_vi,Uu),Uua) = Uua ).

% ATP.lambda_738
tff(fact_8689_ATP_Olambda__739,axiom,
    ! [Uu: code_integer] : aa_Cod1783974652533396728nteger(aTP_Lamm_am,Uu) = Uu ).

% ATP.lambda_739
tff(fact_8690_ATP_Olambda__740,axiom,
    ! [Uu: assn] : aa_assn_assn(aTP_Lamm_cm,Uu) = Uu ).

% ATP.lambda_740
tff(fact_8691_ATP_Olambda__741,axiom,
    ! [Uu: $o] :
      ( aa_o_o(aTP_Lamm_nq,(Uu))
    <=> (Uu) ) ).

% ATP.lambda_741
tff(fact_8692_ATP_Olambda__742,axiom,
    ! [Uu: rat] : aa_rat_rat(aTP_Lamm_cn,Uu) = Uu ).

% ATP.lambda_742
tff(fact_8693_ATP_Olambda__743,axiom,
    ! [Uu: num] : aa_num_num(aTP_Lamm_cg,Uu) = Uu ).

% ATP.lambda_743
tff(fact_8694_ATP_Olambda__744,axiom,
    ! [Uu: nat] : aa_nat_nat(aTP_Lamm_co,Uu) = Uu ).

% ATP.lambda_744
tff(fact_8695_ATP_Olambda__745,axiom,
    ! [Uu: int] : aa_int_int(aTP_Lamm_cp,Uu) = Uu ).

% ATP.lambda_745
tff(fact_8696_ATP_Olambda__746,axiom,
    ! [Uu: product_unit] : aa_Pro234974305641502940t_unit(aTP_Lamm_yi,Uu) = top_to1996260823553986621t_unit ).

% ATP.lambda_746
tff(fact_8697_ATP_Olambda__747,axiom,
    ! [Uu: product_unit] : aa_Pro6064029160526250199et_nat(aTP_Lamm_yh,Uu) = top_top_set_nat ).

% ATP.lambda_747
tff(fact_8698_ATP_Olambda__748,axiom,
    ! [Uu: product_unit] : aa_Pro1886178141017053491et_int(aTP_Lamm_yj,Uu) = top_top_set_int ).

% ATP.lambda_748
tff(fact_8699_ATP_Olambda__749,axiom,
    ! [Uu: set_Pr1261947904930325089at_nat] : aa_set6242432332095302236at_nat(aTP_Lamm_yd,Uu) = top_to7629004291339433233at_nat ).

% ATP.lambda_749
tff(fact_8700_ATP_Olambda__750,axiom,
    ! [Uu: nat] : aa_nat2714212862977473631t_unit(aTP_Lamm_yf,Uu) = top_to1996260823553986621t_unit ).

% ATP.lambda_750
tff(fact_8701_ATP_Olambda__751,axiom,
    ! [Uu: nat] : aa_nat_set_nat(aTP_Lamm_ye,Uu) = top_top_set_nat ).

% ATP.lambda_751
tff(fact_8702_ATP_Olambda__752,axiom,
    ! [Uu: nat] : aa_nat_set_int(aTP_Lamm_yg,Uu) = top_top_set_int ).

% ATP.lambda_752
tff(fact_8703_ATP_Olambda__753,axiom,
    ! [Uu: int] : aa_int6548451963861500163t_unit(aTP_Lamm_yl,Uu) = top_to1996260823553986621t_unit ).

% ATP.lambda_753
tff(fact_8704_ATP_Olambda__754,axiom,
    ! [Uu: int] : aa_int_set_nat(aTP_Lamm_yk,Uu) = top_top_set_nat ).

% ATP.lambda_754
tff(fact_8705_ATP_Olambda__755,axiom,
    ! [Uu: int] : aa_int_set_int(aTP_Lamm_ym,Uu) = top_top_set_int ).

% ATP.lambda_755
tff(fact_8706_ATP_Olambda__756,axiom,
    ! [Uu: set_Pr1261947904930325089at_nat] : aa_set6242432332095302236at_nat(aTP_Lamm_xq,Uu) = bot_bo3083307316010499117at_nat ).

% ATP.lambda_756
tff(fact_8707_ATP_Olambda__757,axiom,
    ! [Uu: nat] : aa_nat_set_nat(aTP_Lamm_xr,Uu) = bot_bot_set_nat ).

% ATP.lambda_757
tff(fact_8708_ATP_Olambda__758,axiom,
    ! [Uu: product_unit] : aa_Product_unit_nat(aTP_Lamm_qm,Uu) = one_one_nat ).

% ATP.lambda_758
tff(fact_8709_ATP_Olambda__759,axiom,
    ! [Uu: list_nat] : aa_list_nat_nat(aTP_Lamm_qn,Uu) = one_one_nat ).

% ATP.lambda_759
tff(fact_8710_ATP_Olambda__760,axiom,
    ! [Uu: nat] : aa_nat_nat(aTP_Lamm_kp,Uu) = one_one_nat ).

% ATP.lambda_760
tff(fact_8711_ATP_Olambda__761,axiom,
    ! [Uu: nat] : aa_nat_int(aTP_Lamm_kq,Uu) = one_one_int ).

% ATP.lambda_761
tff(fact_8712_ATP_Olambda__762,axiom,
    ! [Uu: int] : aa_int_nat(aTP_Lamm_ql,Uu) = one_one_nat ).

% ATP.lambda_762
tff(fact_8713_ATP_Olambda__763,axiom,
    ! [Uu: int] : aa_int_int(aTP_Lamm_kr,Uu) = one_one_int ).

% ATP.lambda_763
tff(fact_8714_ATP_Olambda__764,axiom,
    ! [Uu: heap_e7401611519738050253t_unit] : aa_hea684056619475940329it_nat(aTP_Lamm_bo,Uu) = none_P9117596204409417319it_nat ).

% ATP.lambda_764
tff(fact_8715_ATP_Olambda__765,axiom,
    ! [Uu: heap_e7401611519738050253t_unit] : aa_hea5936688510613671481it_nat(aTP_Lamm_bn,Uu) = none_P2587165478634041381it_nat ).

% ATP.lambda_765
tff(fact_8716_ATP_Olambda__766,axiom,
    ! [Uu: set_Pr1261947904930325089at_nat] : aa_set2934564513904597954at_nat(aTP_Lamm_nm,Uu) = none_s625347054029921090at_nat ).

% ATP.lambda_766
tff(fact_8717_ATP_Olambda__767,axiom,
    ! [Uu: nat] : aa_nat_option_nat(aTP_Lamm_nn,Uu) = none_nat ).

% ATP.lambda_767
tff(fact_8718_ATP_Olambda__768,axiom,
    ! [Uu: produc8664842809031399944it_nat] :
      ( aa_Pro4744234731172327378_nat_o(aTP_Lamm_al,Uu)
    <=> $false ) ).

% ATP.lambda_768
tff(fact_8719_ATP_Olambda__769,axiom,
    ! [Uu: produc6714399278180371524it_nat] :
      ( aa_Pro7528120012624322448_nat_o(aTP_Lamm_aj,Uu)
    <=> $false ) ).

% ATP.lambda_769
tff(fact_8720_ATP_Olambda__770,axiom,
    ! [Uu: num] :
      ( aa_num_o(aTP_Lamm_ak,Uu)
    <=> $false ) ).

% ATP.lambda_770
tff(fact_8721_ATP_Olambda__771,axiom,
    ! [Uu: produc8664842809031399944it_nat] :
      ( aa_Pro4744234731172327378_nat_o(aTP_Lamm_ap,Uu)
    <=> $true ) ).

% ATP.lambda_771
tff(fact_8722_ATP_Olambda__772,axiom,
    ! [Uu: produc6714399278180371524it_nat] :
      ( aa_Pro7528120012624322448_nat_o(aTP_Lamm_an,Uu)
    <=> $true ) ).

% ATP.lambda_772
tff(fact_8723_ATP_Olambda__773,axiom,
    ! [Uu: num] :
      ( aa_num_o(aTP_Lamm_ao,Uu)
    <=> $true ) ).

% ATP.lambda_773

% Helper facts (40)
tff(help_fequal_2_1_fequal_001_Eo_T,axiom,
    ! [X2: $o,Y: $o] :
      ( ( (X2) != (Y) )
      | aa_o_o(aa_o_fun_o_o(fequal_o,(X2)),(Y)) ) ).

tff(help_fequal_1_1_fequal_001_Eo_T,axiom,
    ! [X2: $o,Y: $o] :
      ( ~ aa_o_o(aa_o_fun_o_o(fequal_o,(X2)),(Y))
      | ( (X2) = (Y) ) ) ).

tff(help_fequal_2_1_fequal_001t__Int__Oint_T,axiom,
    ! [X2: int,Y: int] :
      ( ( X2 != Y )
      | aa_int_o(aa_int_fun_int_o(fequal_int,X2),Y) ) ).

tff(help_fequal_1_1_fequal_001t__Int__Oint_T,axiom,
    ! [X2: int,Y: int] :
      ( ~ aa_int_o(aa_int_fun_int_o(fequal_int,X2),Y)
      | ( X2 = Y ) ) ).

tff(help_fequal_2_1_fequal_001t__Nat__Onat_T,axiom,
    ! [X2: nat,Y: nat] :
      ( ( X2 != Y )
      | aa_nat_o(aa_nat_fun_nat_o(fequal_nat,X2),Y) ) ).

tff(help_fequal_1_1_fequal_001t__Nat__Onat_T,axiom,
    ! [X2: nat,Y: nat] :
      ( ~ aa_nat_o(aa_nat_fun_nat_o(fequal_nat,X2),Y)
      | ( X2 = Y ) ) ).

tff(help_fequal_2_1_fequal_001t__Num__Onum_T,axiom,
    ! [X2: num,Y: num] :
      ( ( X2 != Y )
      | aa_num_o(aa_num_fun_num_o(fequal_num,X2),Y) ) ).

tff(help_fequal_1_1_fequal_001t__Num__Onum_T,axiom,
    ! [X2: num,Y: num] :
      ( ~ aa_num_o(aa_num_fun_num_o(fequal_num,X2),Y)
      | ( X2 = Y ) ) ).

tff(help_fequal_2_1_fequal_001t__Product____Type__Ounit_T,axiom,
    ! [X2: product_unit,Y: product_unit] :
      ( ( X2 != Y )
      | aa_Product_unit_o(aa_Pro4895447120693452255unit_o(fequal_Product_unit,X2),Y) ) ).

tff(help_fequal_1_1_fequal_001t__Product____Type__Ounit_T,axiom,
    ! [X2: product_unit,Y: product_unit] :
      ( ~ aa_Product_unit_o(aa_Pro4895447120693452255unit_o(fequal_Product_unit,X2),Y)
      | ( X2 = Y ) ) ).

tff(help_fequal_2_1_fequal_001t__fun_It__Int__Oint_M_Eo_J_T,axiom,
    ! [X2: fun_int_o,Y: fun_int_o] :
      ( ( X2 != Y )
      | aa_fun_int_o_o(aa_fun1331825017273370463nt_o_o(fequal_fun_int_o,X2),Y) ) ).

tff(help_fequal_1_1_fequal_001t__fun_It__Int__Oint_M_Eo_J_T,axiom,
    ! [X2: fun_int_o,Y: fun_int_o] :
      ( ~ aa_fun_int_o_o(aa_fun1331825017273370463nt_o_o(fequal_fun_int_o,X2),Y)
      | ( X2 = Y ) ) ).

tff(help_fequal_2_1_fequal_001t__fun_It__Nat__Onat_M_Eo_J_T,axiom,
    ! [X2: fun_nat_o,Y: fun_nat_o] :
      ( ( X2 != Y )
      | aa_fun_nat_o_o(aa_fun4840518763754620511at_o_o(fequal_fun_nat_o,X2),Y) ) ).

tff(help_fequal_1_1_fequal_001t__fun_It__Nat__Onat_M_Eo_J_T,axiom,
    ! [X2: fun_nat_o,Y: fun_nat_o] :
      ( ~ aa_fun_nat_o_o(aa_fun4840518763754620511at_o_o(fequal_fun_nat_o,X2),Y)
      | ( X2 = Y ) ) ).

tff(help_fequal_2_1_fequal_001t__Code____Numeral__Ointeger_T,axiom,
    ! [X2: code_integer,Y: code_integer] :
      ( ( X2 != Y )
      | aa_Code_integer_o(aa_Cod326357343816142457eger_o(fequal_Code_integer,X2),Y) ) ).

tff(help_fequal_1_1_fequal_001t__Code____Numeral__Ointeger_T,axiom,
    ! [X2: code_integer,Y: code_integer] :
      ( ~ aa_Code_integer_o(aa_Cod326357343816142457eger_o(fequal_Code_integer,X2),Y)
      | ( X2 = Y ) ) ).

tff(help_fequal_2_1_fequal_001t__fun_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
    ! [X2: fun_int_int,Y: fun_int_int] :
      ( ( X2 != Y )
      | aa_fun_int_int_o(aa_fun2545150047610057353_int_o(fequal_fun_int_int,X2),Y) ) ).

tff(help_fequal_1_1_fequal_001t__fun_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
    ! [X2: fun_int_int,Y: fun_int_int] :
      ( ~ aa_fun_int_int_o(aa_fun2545150047610057353_int_o(fequal_fun_int_int,X2),Y)
      | ( X2 = Y ) ) ).

tff(help_fequal_2_1_fequal_001t__fun_It__Nat__Onat_Mt__Num__Onum_J_T,axiom,
    ! [X2: fun_nat_num,Y: fun_nat_num] :
      ( ( X2 != Y )
      | aa_fun_nat_num_o(aa_fun3018564658994998373_num_o(fequal_fun_nat_num,X2),Y) ) ).

tff(help_fequal_1_1_fequal_001t__fun_It__Nat__Onat_Mt__Num__Onum_J_T,axiom,
    ! [X2: fun_nat_num,Y: fun_nat_num] :
      ( ~ aa_fun_nat_num_o(aa_fun3018564658994998373_num_o(fequal_fun_nat_num,X2),Y)
      | ( X2 = Y ) ) ).

tff(help_fequal_2_1_fequal_001t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J_T,axiom,
    ! [X2: fun_fu3883539188510166275_int_o,Y: fun_fu3883539188510166275_int_o] :
      ( ( X2 != Y )
      | aa_fun201744096300836759nt_o_o(aa_fun5360630777332656813nt_o_o(fequal2058191982396926190_int_o,X2),Y) ) ).

tff(help_fequal_1_1_fequal_001t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J_T,axiom,
    ! [X2: fun_fu3883539188510166275_int_o,Y: fun_fu3883539188510166275_int_o] :
      ( ~ aa_fun201744096300836759nt_o_o(aa_fun5360630777332656813nt_o_o(fequal2058191982396926190_int_o,X2),Y)
      | ( X2 = Y ) ) ).

tff(help_fequal_2_1_fequal_001t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_T,axiom,
    ! [X2: fun_fu6128684156180612191_nat_o,Y: fun_fu6128684156180612191_nat_o] :
      ( ( X2 != Y )
      | aa_fun8425762421254558011at_o_o(aa_fun7789069918375247861at_o_o(fequal4303336950067372106_nat_o,X2),Y) ) ).

tff(help_fequal_1_1_fequal_001t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_T,axiom,
    ! [X2: fun_fu6128684156180612191_nat_o,Y: fun_fu6128684156180612191_nat_o] :
      ( ~ aa_fun8425762421254558011at_o_o(aa_fun7789069918375247861at_o_o(fequal4303336950067372106_nat_o,X2),Y)
      | ( X2 = Y ) ) ).

tff(help_fequal_2_1_fequal_001t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J_T,axiom,
    ! [X2: fun_fu1756172458508103847_int_o,Y: fun_fu1756172458508103847_int_o] :
      ( ( X2 != Y )
      | aa_fun5590877032271586035nt_o_o(aa_fun2176986693441167205nt_o_o(fequal9154197289249639570_int_o,X2),Y) ) ).

tff(help_fequal_1_1_fequal_001t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Int__Oint_M_Eo_J_J_T,axiom,
    ! [X2: fun_fu1756172458508103847_int_o,Y: fun_fu1756172458508103847_int_o] :
      ( ~ aa_fun5590877032271586035nt_o_o(aa_fun2176986693441167205nt_o_o(fequal9154197289249639570_int_o,X2),Y)
      | ( X2 = Y ) ) ).

tff(help_fequal_2_1_fequal_001t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_T,axiom,
    ! [X2: fun_fu4001317426178549763_nat_o,Y: fun_fu4001317426178549763_nat_o] :
      ( ( X2 != Y )
      | aa_fun4591523320370531479at_o_o(aa_fun4605425834483758253at_o_o(fequal2175970220065309678_nat_o,X2),Y) ) ).

tff(help_fequal_1_1_fequal_001t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_T,axiom,
    ! [X2: fun_fu4001317426178549763_nat_o,Y: fun_fu4001317426178549763_nat_o] :
      ( ~ aa_fun4591523320370531479at_o_o(aa_fun4605425834483758253at_o_o(fequal2175970220065309678_nat_o,X2),Y)
      | ( X2 = Y ) ) ).

tff(help_fequal_2_1_fequal_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
    ! [X2: fun_Co8499238673658658103nteger,Y: fun_Co8499238673658658103nteger] :
      ( ( X2 != Y )
      | aa_fun774133186966548707eger_o(aa_fun8448071180471187909eger_o(fequal7260506811903038370nteger,X2),Y) ) ).

tff(help_fequal_1_1_fequal_001t__fun_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
    ! [X2: fun_Co8499238673658658103nteger,Y: fun_Co8499238673658658103nteger] :
      ( ~ aa_fun774133186966548707eger_o(aa_fun8448071180471187909eger_o(fequal7260506811903038370nteger,X2),Y)
      | ( X2 = Y ) ) ).

tff(help_fequal_2_1_fequal_001t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
    ! [X2: fun_fu7811933856372049837nt_int,Y: fun_fu7811933856372049837nt_int] :
      ( ( X2 != Y )
      | aa_fun5704287868122599399_int_o(aa_fun9002780452483867999_int_o(fequal5394626278453804162nt_int,X2),Y) ) ).

tff(help_fequal_1_1_fequal_001t__fun_It__fun_It__Int__Oint_M_Eo_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
    ! [X2: fun_fu7811933856372049837nt_int,Y: fun_fu7811933856372049837nt_int] :
      ( ~ aa_fun5704287868122599399_int_o(aa_fun9002780452483867999_int_o(fequal5394626278453804162nt_int,X2),Y)
      | ( X2 = Y ) ) ).

tff(help_fequal_2_1_fequal_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_M_Eo_J_J_T,axiom,
    ! [X2: fun_fu4534828536049688329_int_o,Y: fun_fu4534828536049688329_int_o] :
      ( ( X2 != Y )
      | aa_fun9191990550722779531nt_o_o(aa_fun6205200682927395935nt_o_o(fequal2117520958131442654_int_o,X2),Y) ) ).

tff(help_fequal_1_1_fequal_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Int__Oint_M_Eo_J_J_T,axiom,
    ! [X2: fun_fu4534828536049688329_int_o,Y: fun_fu4534828536049688329_int_o] :
      ( ~ aa_fun9191990550722779531nt_o_o(aa_fun6205200682927395935nt_o_o(fequal2117520958131442654_int_o,X2),Y)
      | ( X2 = Y ) ) ).

tff(help_fequal_2_1_fequal_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_T,axiom,
    ! [X2: fun_fu6779973503720134245_nat_o,Y: fun_fu6779973503720134245_nat_o] :
      ( ( X2 != Y )
      | aa_fun8192636838821724975at_o_o(aa_fun4700854480566125407at_o_o(fequal4362665925801888570_nat_o,X2),Y) ) ).

tff(help_fequal_1_1_fequal_001t__fun_It__fun_It__Int__Oint_Mt__Int__Oint_J_Mt__fun_It__Nat__Onat_M_Eo_J_J_T,axiom,
    ! [X2: fun_fu6779973503720134245_nat_o,Y: fun_fu6779973503720134245_nat_o] :
      ( ~ aa_fun8192636838821724975at_o_o(aa_fun4700854480566125407at_o_o(fequal4362665925801888570_nat_o,X2),Y)
      | ( X2 = Y ) ) ).

tff(help_fequal_2_1_fequal_001t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
    ! [X2: fun_fu15710647883683081nt_int,Y: fun_fu15710647883683081nt_int] :
      ( ( X2 != Y )
      | aa_fun4496170735194219403_int_o(aa_fun6780808746871264351_int_o(fequal6821775106820213214nt_int,X2),Y) ) ).

tff(help_fequal_1_1_fequal_001t__fun_It__fun_It__Nat__Onat_M_Eo_J_Mt__fun_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
    ! [X2: fun_fu15710647883683081nt_int,Y: fun_fu15710647883683081nt_int] :
      ( ~ aa_fun4496170735194219403_int_o(aa_fun6780808746871264351_int_o(fequal6821775106820213214nt_int,X2),Y)
      | ( X2 = Y ) ) ).

tff(help_fequal_2_1_fequal_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_T,axiom,
    ! [X2: produc8664842809031399944it_nat,Y: produc8664842809031399944it_nat] :
      ( ( X2 != Y )
      | aa_Pro4744234731172327378_nat_o(fequal1407654770548522611it_nat(X2),Y) ) ).

tff(help_fequal_1_1_fequal_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_T,axiom,
    ! [X2: produc8664842809031399944it_nat,Y: produc8664842809031399944it_nat] :
      ( ~ aa_Pro4744234731172327378_nat_o(fequal1407654770548522611it_nat(X2),Y)
      | ( X2 = Y ) ) ).

% Conjectures (1)
tff(conj_0,conjecture,
    aa_hea5936688510613671481it_nat(heap_T5591663578999710211rray_a(array_of_list_a(xs)),h) != none_P2587165478634041381it_nat ).

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