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

% Refs     : [Des23] Desharnais (2023), Email to Geoff Sutcliffe
% Source   : [Des23]
% Names    : Fishers_Inequality/0039_Vector_Matrix_Mod/prob_00502_019973__28236892_1 [Des23]

% Status   : Theorem
% Rating   : ? v8.2.0
% Syntax   : Number of formulae    : 2211 ( 511 unt; 927 typ;   0 def)
%            Number of atoms       : 5016 (1486 equ;  38 cnn)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives : 10546 ( 121   ~;  18   |; 118   &;8914   @)
%                                         (   0 <=>;1375  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   7 avg)
%            Number of types       :   34 (  33 usr)
%            Number of type conns  : 10306 (10306   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  898 ( 894 usr;  17 con; 0-5 aty)
%            Number of variables   : 3714 (1265   ^;2354   !;  95   ?;3714   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2023-01-18 15:50:27.791
%------------------------------------------------------------------------------
% Could-be-implicit typings (33)
thf(ty_n_t__Multiset__Omultiset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    multis1329328054411135998ring_a: $tType ).

thf(ty_n_t__Multiset__Omultiset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    multis5521929256021820786ring_a: $tType ).

thf(ty_n_t__Matrix__Ovec_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    vec_ve5128822793932996635ring_a: $tType ).

thf(ty_n_t__Matrix__Ovec_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    vec_ma98051958688905615ring_a: $tType ).

thf(ty_n_t__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    set_ve6125835690772642148ring_a: $tType ).

thf(ty_n_t__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    set_ma1095064855528551128ring_a: $tType ).

thf(ty_n_t__Multiset__Omultiset_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    multis3731679216105815691ring_a: $tType ).

thf(ty_n_t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    vec_Fi4296597256376197294ring_a: $tType ).

thf(ty_n_t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    mat_Fi443519135453058082ring_a: $tType ).

thf(ty_n_t__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    set_Fi2982333969990053029ring_a: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Int__Oint_Mt__Int__Oint_J_J,type,
    set_int_int: $tType ).

thf(ty_n_t__Set__Oset_It__Matrix__Ovec_It__Int__Oint_J_J,type,
    set_vec_int: $tType ).

thf(ty_n_t__Set__Oset_It__Matrix__Omat_It__Int__Oint_J_J,type,
    set_mat_int: $tType ).

thf(ty_n_t__Matrix__Ovec_It__Set__Oset_It__Int__Oint_J_J,type,
    vec_set_int: $tType ).

thf(ty_n_t__Set__Oset_I_062_It__Int__Oint_M_Eo_J_J,type,
    set_int_o: $tType ).

thf(ty_n_t__Finite____Field__Omod____ring_Itf__a_J,type,
    finite_mod_ring_a: $tType ).

thf(ty_n_t__Multiset__Omultiset_It__Real__Oreal_J,type,
    multiset_real: $tType ).

thf(ty_n_t__Multiset__Omultiset_It__Nat__Onat_J,type,
    multiset_nat: $tType ).

thf(ty_n_t__Multiset__Omultiset_It__Int__Oint_J,type,
    multiset_int: $tType ).

thf(ty_n_t__Matrix__Ovec_It__Real__Oreal_J,type,
    vec_real: $tType ).

thf(ty_n_t__Matrix__Omat_It__Real__Oreal_J,type,
    mat_real: $tType ).

thf(ty_n_t__Matrix__Ovec_It__Nat__Onat_J,type,
    vec_nat: $tType ).

thf(ty_n_t__Matrix__Ovec_It__Int__Oint_J,type,
    vec_int: $tType ).

thf(ty_n_t__Matrix__Omat_It__Nat__Onat_J,type,
    mat_nat: $tType ).

thf(ty_n_t__Matrix__Omat_It__Int__Oint_J,type,
    mat_int: $tType ).

thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
    set_real: $tType ).

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

thf(ty_n_t__Set__Oset_It__Int__Oint_J,type,
    set_int: $tType ).

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

thf(ty_n_t__itself_Itf__a_J,type,
    itself_a: $tType ).

thf(ty_n_t__Real__Oreal,type,
    real: $tType ).

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

thf(ty_n_t__Int__Oint,type,
    int: $tType ).

% Explicit typings (894)
thf(sy_c_Archimedean__Field_Ofrac_001t__Real__Oreal,type,
    archim2898591450579166408c_real: real > real ).

thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_M_Eo_J_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_M_Eo_J,type,
    bNF_re416558257613726387nt_o_o: ( ( ( int > $o ) > $o ) > ( ( int > $o ) > $o ) > $o ) > ( ( ( int > int > $o ) > $o ) > ( ( int > int > $o ) > $o ) > $o ) > ( ( ( int > $o ) > $o ) > ( int > int > $o ) > $o ) > ( ( ( int > $o ) > $o ) > ( int > int > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J,type,
    bNF_re5116691816286752797_int_o: ( ( ( int > int ) > $o ) > ( ( int > int ) > $o ) > $o ) > ( ( ( int > int > int ) > $o ) > ( ( int > int > int ) > $o ) > $o ) > ( ( ( int > int ) > $o ) > ( int > int > int ) > $o ) > ( ( ( int > int ) > $o ) > ( int > int > int ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_I_Eo_M_062_I_Eo_M_Eo_J_J_001_062_I_Eo_M_062_I_Eo_M_Eo_J_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J_J,type,
    bNF_re3012816421615927389nt_o_o: ( ( $o > $o > $o ) > ( $o > $o > $o ) > $o ) > ( ( ( int > $o ) > ( int > $o ) > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > $o ) > ( ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ) > ( ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_I_Eo_M_062_I_Eo_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    bNF_re4473429657033765895_int_o: ( ( $o > $o > $o ) > ( int > int > $o ) > $o ) > ( ( ( int > $o ) > ( int > $o ) > $o ) > ( ( int > int ) > ( int > int ) > $o ) > $o ) > ( ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ) > ( ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_I_Eo_M_062_I_Eo_M_Eo_J_J_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_Eo_J_J,type,
    bNF_re2572702929266883447_nat_o: ( ( $o > $o > $o ) > ( nat > nat > $o ) > $o ) > ( ( ( int > $o ) > ( int > $o ) > $o ) > ( ( int > nat ) > ( int > nat ) > $o ) > $o ) > ( ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ) > ( ( nat > nat > $o ) > ( int > nat ) > ( int > nat ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_I_Eo_M_062_It__Int__Oint_M_Eo_J_J_001_062_I_Eo_M_062_It__Int__Oint_M_Eo_J_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    bNF_re9016137329058378357_int_o: ( ( $o > int > $o ) > ( $o > int > $o ) > $o ) > ( ( ( int > $o ) > ( int > int ) > $o ) > ( ( int > $o ) > ( int > int ) > $o ) > $o ) > ( ( $o > int > $o ) > ( int > $o ) > ( int > int ) > $o ) > ( ( $o > int > $o ) > ( int > $o ) > ( int > int ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_I_Eo_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_Eo_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_Eo_J_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_Eo_J_J,type,
    bNF_re1168432982574861285_nat_o: ( ( $o > nat > $o ) > ( $o > nat > $o ) > $o ) > ( ( ( int > $o ) > ( int > nat ) > $o ) > ( ( int > $o ) > ( int > nat ) > $o ) > $o ) > ( ( $o > nat > $o ) > ( int > $o ) > ( int > nat ) > $o ) > ( ( $o > nat > $o ) > ( int > $o ) > ( int > nat ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_I_Eo_M_Eo_J_001_062_I_Eo_M_Eo_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_It__Int__Oint_M_Eo_J_J,type,
    bNF_re8851674277422367093_int_o: ( ( $o > $o ) > ( $o > $o ) > $o ) > ( ( ( int > $o ) > int > $o ) > ( ( int > $o ) > int > $o ) > $o ) > ( ( $o > $o ) > ( int > $o ) > int > $o ) > ( ( $o > $o ) > ( int > $o ) > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_I_Eo_M_Eo_J_001_062_I_Eo_M_Eo_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J,type,
    bNF_re8423317060048895199nt_o_o: ( ( $o > $o ) > ( $o > $o ) > $o ) > ( ( ( int > $o ) > $o ) > ( ( int > $o ) > $o ) > $o ) > ( ( $o > $o ) > ( int > $o ) > $o ) > ( ( $o > $o ) > ( int > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_I_Eo_Mt__Int__Oint_J_001_062_I_Eo_Mt__Int__Oint_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J,type,
    bNF_re3022626809172352605nt_int: ( ( $o > int ) > ( $o > int ) > $o ) > ( ( ( int > $o ) > int > int ) > ( ( int > $o ) > int > int ) > $o ) > ( ( $o > int ) > ( int > $o ) > int > int ) > ( ( $o > int ) > ( int > $o ) > int > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_I_Eo_Mt__Int__Oint_J_001_062_I_Eo_Mt__Int__Oint_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    bNF_re443020842677779549_int_o: ( ( $o > int ) > ( $o > int ) > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( ( $o > int ) > int > $o ) > ( ( $o > int ) > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_I_Eo_Mt__Int__Oint_J_001_062_I_Eo_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
    bNF_re7329598968520275341nt_int: ( ( $o > int ) > ( $o > int ) > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( ( $o > int ) > int > int ) > ( ( $o > int ) > int > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_I_Eo_Mt__Int__Oint_J_001_062_I_Eo_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
    bNF_re6096367806326009557nt_nat: ( ( $o > int ) > ( $o > int ) > $o ) > ( ( int > nat ) > ( int > nat ) > $o ) > ( ( $o > int ) > int > nat ) > ( ( $o > int ) > int > nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_I_Eo_Mt__Nat__Onat_J_001_062_I_Eo_Mt__Nat__Onat_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_It__Int__Oint_Mt__Nat__Onat_J_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_It__Int__Oint_Mt__Nat__Onat_J_J,type,
    bNF_re8371370899516666973nt_nat: ( ( $o > nat ) > ( $o > nat ) > $o ) > ( ( ( int > $o ) > int > nat ) > ( ( int > $o ) > int > nat ) > $o ) > ( ( $o > nat ) > ( int > $o ) > int > nat ) > ( ( $o > nat ) > ( int > $o ) > int > nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_I_Eo_M_Eo_J_J_001_062_It__Int__Oint_M_062_I_Eo_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J_J,type,
    bNF_re6130303124124341793nt_o_o: ( ( int > $o > $o ) > ( int > $o > $o ) > $o ) > ( ( ( int > int ) > ( int > $o ) > $o ) > ( ( int > int ) > ( int > $o ) > $o ) > $o ) > ( ( int > $o > $o ) > ( int > int ) > ( int > $o ) > $o ) > ( ( int > $o > $o ) > ( int > int ) > ( int > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J_J_001_062_It__Set__Oset_It__Int__Oint_J_M_062_It__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_001_062_It__Set__Oset_It__Int__Oint_J_M_062_It__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J,type,
    bNF_re8072987537887292697ng_a_o: ( ( int > finite_mod_ring_a > $o ) > ( int > finite_mod_ring_a > $o ) > $o ) > ( ( set_int > set_Fi2982333969990053029ring_a > $o ) > ( set_int > set_Fi2982333969990053029ring_a > $o ) > $o ) > ( ( int > finite_mod_ring_a > $o ) > set_int > set_Fi2982333969990053029ring_a > $o ) > ( ( int > finite_mod_ring_a > $o ) > set_int > set_Fi2982333969990053029ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J_J_001_Eo_001_Eo,type,
    bNF_re3139618654209367653_o_o_o: ( ( int > finite_mod_ring_a > $o ) > ( int > finite_mod_ring_a > $o ) > $o ) > ( $o > $o > $o ) > ( ( int > finite_mod_ring_a > $o ) > $o ) > ( ( int > finite_mod_ring_a > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J_J_001_062_It__Matrix__Omat_It__Int__Oint_J_M_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_001_062_It__Set__Oset_It__Int__Oint_J_M_062_It__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_001_062_It__Set__Oset_It__Matrix__Omat_It__Int__Oint_J_J_M_062_It__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J_M_Eo_J_J,type,
    bNF_re6783927866172000641ng_a_o: ( ( int > finite_mod_ring_a > $o ) > ( mat_int > mat_Fi443519135453058082ring_a > $o ) > $o ) > ( ( set_int > set_Fi2982333969990053029ring_a > $o ) > ( set_mat_int > set_ma1095064855528551128ring_a > $o ) > $o ) > ( ( int > finite_mod_ring_a > $o ) > set_int > set_Fi2982333969990053029ring_a > $o ) > ( ( mat_int > mat_Fi443519135453058082ring_a > $o ) > set_mat_int > set_ma1095064855528551128ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J_J_001_062_It__Matrix__Ovec_It__Int__Oint_J_M_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_001_062_It__Set__Oset_It__Int__Oint_J_M_062_It__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_001_062_It__Set__Oset_It__Matrix__Ovec_It__Int__Oint_J_J_M_062_It__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J_M_Eo_J_J,type,
    bNF_re5266488448927231873ng_a_o: ( ( int > finite_mod_ring_a > $o ) > ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > $o ) > ( ( set_int > set_Fi2982333969990053029ring_a > $o ) > ( set_vec_int > set_ve6125835690772642148ring_a > $o ) > $o ) > ( ( int > finite_mod_ring_a > $o ) > set_int > set_Fi2982333969990053029ring_a > $o ) > ( ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > set_vec_int > set_ve6125835690772642148ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_I_Eo_M_062_I_Eo_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J_J,type,
    bNF_re6840425655782752307nt_o_o: ( ( int > int > $o ) > ( $o > $o > $o ) > $o ) > ( ( ( int > int ) > ( int > int ) > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > $o ) > ( ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ) > ( ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Finite____Field__Omod____ring_Itf__a_J_M_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Finite____Field__Omod____ring_Itf__a_J_M_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J_J,type,
    bNF_re561345951587129949ng_a_o: ( ( int > int > $o ) > ( finite_mod_ring_a > finite_mod_ring_a > $o ) > $o ) > ( ( int > int > $o ) > ( finite_mod_ring_a > finite_mod_ring_a > $o ) > $o ) > ( ( int > int > $o ) > int > int > $o ) > ( ( finite_mod_ring_a > finite_mod_ring_a > $o ) > finite_mod_ring_a > finite_mod_ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Finite____Field__Omod____ring_Itf__a_J_M_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J_J_001_062_It__Set__Oset_It__Int__Oint_J_M_062_It__Set__Oset_It__Int__Oint_J_M_Eo_J_J_001_062_It__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_M_062_It__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J,type,
    bNF_re2336052386105072073ng_a_o: ( ( int > int > $o ) > ( finite_mod_ring_a > finite_mod_ring_a > $o ) > $o ) > ( ( set_int > set_int > $o ) > ( set_Fi2982333969990053029ring_a > set_Fi2982333969990053029ring_a > $o ) > $o ) > ( ( int > int > $o ) > set_int > set_int > $o ) > ( ( finite_mod_ring_a > finite_mod_ring_a > $o ) > set_Fi2982333969990053029ring_a > set_Fi2982333969990053029ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Finite____Field__Omod____ring_Itf__a_J_M_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J_J_001_Eo_001_Eo,type,
    bNF_re3287324404599397085_o_o_o: ( ( int > int > $o ) > ( finite_mod_ring_a > finite_mod_ring_a > $o ) > $o ) > ( $o > $o > $o ) > ( ( int > int > $o ) > $o ) > ( ( finite_mod_ring_a > finite_mod_ring_a > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Finite____Field__Omod____ring_Itf__a_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
    bNF_re1800150913247624340_int_o: ( ( int > int > $o ) > ( finite_mod_ring_a > int > $o ) > $o ) > ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > int > $o ) > int > int > $o ) > ( ( finite_mod_ring_a > int > $o ) > int > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Finite____Field__Omod____ring_Itf__a_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Set__Oset_It__Int__Oint_J_M_062_It__Set__Oset_It__Int__Oint_J_M_Eo_J_J_001_062_It__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_M_062_It__Set__Oset_It__Int__Oint_J_M_Eo_J_J,type,
    bNF_re4468130210263503771_int_o: ( ( int > int > $o ) > ( finite_mod_ring_a > int > $o ) > $o ) > ( ( set_int > set_int > $o ) > ( set_Fi2982333969990053029ring_a > set_int > $o ) > $o ) > ( ( int > int > $o ) > set_int > set_int > $o ) > ( ( finite_mod_ring_a > int > $o ) > set_Fi2982333969990053029ring_a > set_int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Finite____Field__Omod____ring_Itf__a_J_M_062_It__Int__Oint_M_Eo_J_J_001_Eo_001_Eo,type,
    bNF_re5891132441370877716_o_o_o: ( ( int > int > $o ) > ( finite_mod_ring_a > int > $o ) > $o ) > ( $o > $o > $o ) > ( ( int > int > $o ) > $o ) > ( ( finite_mod_ring_a > int > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J_J_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_J_001_062_I_062_It__Finite____Field__Omod____ring_Itf__a_J_M_062_It__Int__Oint_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_J,type,
    bNF_re5072219456266741671_int_o: ( ( int > int > $o ) > ( int > finite_mod_ring_a > $o ) > $o ) > ( ( ( int > int > $o ) > int > int > $o ) > ( ( finite_mod_ring_a > int > $o ) > int > int > $o ) > $o ) > ( ( int > int > $o ) > ( int > int > $o ) > int > int > $o ) > ( ( int > finite_mod_ring_a > $o ) > ( finite_mod_ring_a > int > $o ) > int > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    bNF_re2917227035190921876_int_o: ( ( int > int > $o ) > ( int > finite_mod_ring_a > $o ) > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( ( int > int > $o ) > int > $o ) > ( ( int > finite_mod_ring_a > $o ) > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_J_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_J,type,
    bNF_re7404067519983032617_int_o: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( ( int > int > $o ) > int > int > $o ) > ( ( int > int > $o ) > int > int > $o ) > $o ) > ( ( int > int > $o ) > ( int > int > $o ) > int > int > $o ) > ( ( int > int > $o ) > ( int > int > $o ) > int > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J_001_062_I_062_It__Finite____Field__Omod____ring_Itf__a_J_Mt__Int__Oint_J_M_062_I_062_It__Finite____Field__Omod____ring_Itf__a_J_Mt__Int__Oint_J_M_Eo_J_J,type,
    bNF_re7930886852997362739_int_o: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( ( int > int ) > ( int > int ) > $o ) > ( ( finite_mod_ring_a > int ) > ( finite_mod_ring_a > int ) > $o ) > $o ) > ( ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ) > ( ( int > int > $o ) > ( finite_mod_ring_a > int ) > ( finite_mod_ring_a > int ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    bNF_re4490276714116616413_int_o: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( ( int > int ) > ( int > int ) > $o ) > ( ( int > int ) > ( int > int ) > $o ) > $o ) > ( ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ) > ( ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_I_062_It__Int__Oint_M_Eo_J_M_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_J_J_001_062_It__Int__Oint_M_062_I_062_It__Int__Oint_M_Eo_J_M_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_J_J,type,
    bNF_re428690454916900693_int_o: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > ( int > $o ) > int > int > $o ) > ( int > ( int > $o ) > int > int > $o ) > $o ) > ( ( int > int > $o ) > int > ( int > $o ) > int > int > $o ) > ( ( int > int > $o ) > int > ( int > $o ) > int > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
    bNF_re8651060166502312541_int_o: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > int > $o ) > int > int > $o ) > ( ( int > int > $o ) > int > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    bNF_re2642688597062869533_int_o: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( ( int > int > $o ) > int > $o ) > ( ( int > int > $o ) > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Set__Oset_It__Int__Oint_J_M_062_It__Set__Oset_It__Int__Oint_J_M_Eo_J_J_001_062_It__Set__Oset_It__Int__Oint_J_M_062_It__Set__Oset_It__Int__Oint_J_M_Eo_J_J,type,
    bNF_re4478252629936865629_int_o: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( set_int > set_int > $o ) > ( set_int > set_int > $o ) > $o ) > ( ( int > int > $o ) > set_int > set_int > $o ) > ( ( int > int > $o ) > set_int > set_int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Set__Oset_It__Int__Oint_J_Mt__Set__Oset_I_062_It__Int__Oint_M_Eo_J_J_J_001_062_It__Set__Oset_It__Int__Oint_J_Mt__Set__Oset_I_062_It__Int__Oint_M_Eo_J_J_J,type,
    bNF_re497851078371813853_int_o: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( set_int > set_int_o ) > ( set_int > set_int_o ) > $o ) > ( ( int > int > $o ) > set_int > set_int_o ) > ( ( int > int > $o ) > set_int > set_int_o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_Eo_001_Eo,type,
    bNF_re5869992600382051037_o_o_o: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( $o > $o > $o ) > ( ( int > int > $o ) > $o ) > ( ( int > int > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_Eo_J_J,type,
    bNF_re1378104478368373837_nat_o: ( ( int > int > $o ) > ( nat > nat > $o ) > $o ) > ( ( ( int > int ) > ( int > int ) > $o ) > ( ( int > nat ) > ( int > nat ) > $o ) > $o ) > ( ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ) > ( ( nat > nat > $o ) > ( int > nat ) > ( int > nat ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Finite____Field__Omod____ring_Itf__a_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Set__Oset_It__Int__Oint_J_M_062_It__Int__Oint_M_Eo_J_J_J_001_062_It__Int__Oint_M_062_It__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_M_062_It__Int__Oint_M_Eo_J_J_J,type,
    bNF_re1539142895448806181_int_o: ( ( int > int > int ) > ( finite_mod_ring_a > int > int ) > $o ) > ( ( int > set_int > int > $o ) > ( int > set_Fi2982333969990053029ring_a > int > $o ) > $o ) > ( ( int > int > int ) > int > set_int > int > $o ) > ( ( finite_mod_ring_a > int > int ) > int > set_Fi2982333969990053029ring_a > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Finite____Field__Omod____ring_Itf__a_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Set__Oset_It__Int__Oint_J_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_Mt__Int__Oint_J_J,type,
    bNF_re8979805298816042759_a_int: ( ( int > int > int ) > ( finite_mod_ring_a > int > int ) > $o ) > ( ( int > set_int > int ) > ( int > set_Fi2982333969990053029ring_a > int ) > $o ) > ( ( int > int > int ) > int > set_int > int ) > ( ( finite_mod_ring_a > int > int ) > int > set_Fi2982333969990053029ring_a > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_J_J_001_062_It__Int__Oint_M_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
    bNF_re5888381405672822827nt_int: ( ( int > int > int ) > ( int > int > int ) > $o ) > ( ( int > ( int > int ) > int > int > int ) > ( int > ( int > int ) > int > int > int ) > $o ) > ( ( int > int > int ) > int > ( int > int ) > int > int > int ) > ( ( int > int > int ) > int > ( int > int ) > int > int > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Set__Oset_It__Int__Oint_J_M_062_It__Int__Oint_M_Eo_J_J_J_001_062_It__Int__Oint_M_062_It__Set__Oset_It__Int__Oint_J_M_062_It__Int__Oint_M_Eo_J_J_J,type,
    bNF_re7307145319025026467_int_o: ( ( int > int > int ) > ( int > int > int ) > $o ) > ( ( int > set_int > int > $o ) > ( int > set_int > int > $o ) > $o ) > ( ( int > int > int ) > int > set_int > int > $o ) > ( ( int > int > int ) > int > set_int > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Set__Oset_It__Int__Oint_J_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Set__Oset_It__Int__Oint_J_Mt__Int__Oint_J_J,type,
    bNF_re6640931632208380629nt_int: ( ( int > int > int ) > ( int > int > int ) > $o ) > ( ( int > set_int > int ) > ( int > set_int > int ) > $o ) > ( ( int > int > int ) > int > set_int > int ) > ( ( int > int > int ) > int > set_int > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
    bNF_re3333031753742804947nt_int: ( ( int > int > int ) > ( int > int > int ) > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( ( int > int > int ) > int > int ) > ( ( int > int > int ) > int > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Set__Oset_It__Int__Oint_J_Mt__Set__Oset_I_062_It__Int__Oint_Mt__Int__Oint_J_J_J_001_062_It__Set__Oset_It__Int__Oint_J_Mt__Set__Oset_I_062_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    bNF_re4460442335046654529nt_int: ( ( int > int > int ) > ( int > int > int ) > $o ) > ( ( set_int > set_int_int ) > ( set_int > set_int_int ) > $o ) > ( ( int > int > int ) > set_int > set_int_int ) > ( ( int > int > int ) > set_int > set_int_int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_Eo_001_Eo,type,
    bNF_re6987580103263796323nt_o_o: ( ( int > int > int ) > ( int > int > int ) > $o ) > ( $o > $o > $o ) > ( ( int > int > int ) > $o ) > ( ( int > int > int ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Matrix__Omat_It__Int__Oint_J_M_Eo_J_J_001_062_It__Finite____Field__Omod____ring_Itf__a_J_M_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_001_Eo_001_Eo,type,
    bNF_re3176011413720292303_o_o_o: ( ( int > mat_int > $o ) > ( finite_mod_ring_a > mat_Fi443519135453058082ring_a > $o ) > $o ) > ( $o > $o > $o ) > ( ( int > mat_int > $o ) > $o ) > ( ( finite_mod_ring_a > mat_Fi443519135453058082ring_a > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Matrix__Omat_It__Int__Oint_J_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_001_062_I_062_It__Matrix__Omat_It__Int__Oint_J_M_062_It__Int__Oint_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_J_001_062_I_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_062_It__Int__Oint_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_J,type,
    bNF_re7916767694611508199_int_o: ( ( int > mat_int > $o ) > ( int > mat_Fi443519135453058082ring_a > $o ) > $o ) > ( ( ( mat_int > int > $o ) > int > int > $o ) > ( ( mat_Fi443519135453058082ring_a > int > $o ) > int > int > $o ) > $o ) > ( ( int > mat_int > $o ) > ( mat_int > int > $o ) > int > int > $o ) > ( ( int > mat_Fi443519135453058082ring_a > $o ) > ( mat_Fi443519135453058082ring_a > int > $o ) > int > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Matrix__Omat_It__Int__Oint_J_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    bNF_re6408424020554474550_int_o: ( ( int > mat_int > $o ) > ( int > mat_Fi443519135453058082ring_a > $o ) > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( ( int > mat_int > $o ) > int > $o ) > ( ( int > mat_Fi443519135453058082ring_a > $o ) > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Matrix__Ovec_It__Int__Oint_J_M_Eo_J_J_001_062_It__Finite____Field__Omod____ring_Itf__a_J_M_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_001_Eo_001_Eo,type,
    bNF_re8023572202256978639_o_o_o: ( ( int > vec_int > $o ) > ( finite_mod_ring_a > vec_Fi4296597256376197294ring_a > $o ) > $o ) > ( $o > $o > $o ) > ( ( int > vec_int > $o ) > $o ) > ( ( finite_mod_ring_a > vec_Fi4296597256376197294ring_a > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Matrix__Ovec_It__Int__Oint_J_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_001_062_I_062_It__Matrix__Ovec_It__Int__Oint_J_M_062_It__Int__Oint_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_J_001_062_I_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_062_It__Int__Oint_M_Eo_J_J_M_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_J,type,
    bNF_re8684700889500088319_int_o: ( ( int > vec_int > $o ) > ( int > vec_Fi4296597256376197294ring_a > $o ) > $o ) > ( ( ( vec_int > int > $o ) > int > int > $o ) > ( ( vec_Fi4296597256376197294ring_a > int > $o ) > int > int > $o ) > $o ) > ( ( int > vec_int > $o ) > ( vec_int > int > $o ) > int > int > $o ) > ( ( int > vec_Fi4296597256376197294ring_a > $o ) > ( vec_Fi4296597256376197294ring_a > int > $o ) > int > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Matrix__Ovec_It__Int__Oint_J_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    bNF_re131580980352085790_int_o: ( ( int > vec_int > $o ) > ( int > vec_Fi4296597256376197294ring_a > $o ) > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( ( int > vec_int > $o ) > int > $o ) > ( ( int > vec_Fi4296597256376197294ring_a > $o ) > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_Eo_J_J,type,
    bNF_re1274416395763232477_nat_o: ( ( int > nat > $o ) > ( int > nat > $o ) > $o ) > ( ( ( int > int ) > ( int > nat ) > $o ) > ( ( int > int ) > ( int > nat ) > $o ) > $o ) > ( ( int > nat > $o ) > ( int > int ) > ( int > nat ) > $o ) > ( ( int > nat > $o ) > ( int > int ) > ( int > nat ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_Eo_J_001_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J_001_Eo_001_Eo,type,
    bNF_re8869226137141724030_o_o_o: ( ( int > $o ) > ( finite_mod_ring_a > $o ) > $o ) > ( $o > $o > $o ) > ( ( int > $o ) > $o ) > ( ( finite_mod_ring_a > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_Eo_J_001_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bNF_re1547907014084023747ring_a: ( ( int > $o ) > ( finite_mod_ring_a > $o ) > $o ) > ( set_int > set_Fi2982333969990053029ring_a > $o ) > ( ( int > $o ) > set_int ) > ( ( finite_mod_ring_a > $o ) > set_Fi2982333969990053029ring_a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001_062_I_062_I_Eo_Mt__Int__Oint_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_I_062_I_Eo_Mt__Int__Oint_J_M_062_It__Int__Oint_M_Eo_J_J,type,
    bNF_re6844020233948794949_int_o: ( ( int > $o ) > ( int > $o ) > $o ) > ( ( ( $o > int ) > int > $o ) > ( ( $o > int ) > int > $o ) > $o ) > ( ( int > $o ) > ( $o > int ) > int > $o ) > ( ( int > $o ) > ( $o > int ) > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_I_062_I_Eo_Mt__Int__Oint_J_M_062_It__Int__Oint_M_Eo_J_J_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_I_062_I_Eo_Mt__Int__Oint_J_M_062_It__Int__Oint_M_Eo_J_J_J,type,
    bNF_re785544210196170973_int_o: ( ( int > $o ) > ( int > $o ) > $o ) > ( ( ( int > $o ) > ( $o > int ) > int > $o ) > ( ( int > $o ) > ( $o > int ) > int > $o ) > $o ) > ( ( int > $o ) > ( int > $o ) > ( $o > int ) > int > $o ) > ( ( int > $o ) > ( int > $o ) > ( $o > int ) > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J,type,
    bNF_re513079643185015507nt_o_o: ( ( int > $o ) > ( int > $o ) > $o ) > ( ( ( int > $o ) > $o ) > ( ( int > $o ) > $o ) > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_I_062_I_Eo_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_I_062_I_Eo_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    bNF_re1144695058418211421nt_int: ( ( int > $o ) > ( int > $o ) > $o ) > ( ( ( int > int ) > ( $o > int ) > int > int ) > ( ( int > int ) > ( $o > int ) > int > int ) > $o ) > ( ( int > $o ) > ( int > int ) > ( $o > int ) > int > int ) > ( ( int > $o ) > ( int > int ) > ( $o > int ) > int > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
    bNF_re6571774352052816285_int_o: ( ( int > $o ) > ( int > $o ) > $o ) > ( ( ( int > int ) > $o ) > ( ( int > int ) > $o ) > $o ) > ( ( int > $o ) > ( int > int ) > $o ) > ( ( int > $o ) > ( int > int ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_I_062_I_Eo_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Nat__Onat_J_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_I_062_I_Eo_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Nat__Onat_J_J_J,type,
    bNF_re8143304301122804317nt_nat: ( ( int > $o ) > ( int > $o ) > $o ) > ( ( ( int > nat ) > ( $o > int ) > int > nat ) > ( ( int > nat ) > ( $o > int ) > int > nat ) > $o ) > ( ( int > $o ) > ( int > nat ) > ( $o > int ) > int > nat ) > ( ( int > $o ) > ( int > nat ) > ( $o > int ) > int > nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_Eo_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_Eo_J,type,
    bNF_re366876804441710237_nat_o: ( ( int > $o ) > ( int > $o ) > $o ) > ( ( ( int > nat ) > $o ) > ( ( int > nat ) > $o ) > $o ) > ( ( int > $o ) > ( int > nat ) > $o ) > ( ( int > $o ) > ( int > nat ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001_062_I_062_It__Nat__Onat_Mt__Int__Oint_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_I_062_It__Nat__Onat_Mt__Int__Oint_J_M_062_It__Int__Oint_M_Eo_J_J,type,
    bNF_re8874617004901089501_int_o: ( ( int > $o ) > ( int > $o ) > $o ) > ( ( ( nat > int ) > int > $o ) > ( ( nat > int ) > int > $o ) > $o ) > ( ( int > $o ) > ( nat > int ) > int > $o ) > ( ( int > $o ) > ( nat > int ) > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_062_I_Eo_M_062_It__Int__Oint_M_Eo_J_J_J_001_062_It__Int__Oint_M_062_I_Eo_M_062_It__Int__Oint_M_Eo_J_J_J,type,
    bNF_re6967601477061121941_int_o: ( ( int > $o ) > ( int > $o ) > $o ) > ( ( int > $o > int > $o ) > ( int > $o > int > $o ) > $o ) > ( ( int > $o ) > int > $o > int > $o ) > ( ( int > $o ) > int > $o > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
    bNF_re8966525682393678365_int_o: ( ( int > $o ) > ( int > $o ) > $o ) > ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > $o ) > int > int > $o ) > ( ( int > $o ) > int > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    bNF_re2562776159637780957_int_o: ( ( int > $o ) > ( int > $o ) > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( ( int > $o ) > int > $o ) > ( ( int > $o ) > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
    bNF_re1510820403721876237nt_int: ( ( int > $o ) > ( int > $o ) > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( ( int > $o ) > int > int ) > ( ( int > $o ) > int > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
    bNF_re277589241527610453nt_nat: ( ( int > $o ) > ( int > $o ) > $o ) > ( ( int > nat ) > ( int > nat ) > $o ) > ( ( int > $o ) > int > nat ) > ( ( int > $o ) > int > nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Set__Oset_It__Int__Oint_J_Mt__Set__Oset_I_Eo_J_J_001_062_It__Set__Oset_It__Int__Oint_J_Mt__Set__Oset_I_Eo_J_J,type,
    bNF_re5225647679341271645_set_o: ( ( int > $o ) > ( int > $o ) > $o ) > ( ( set_int > set_o ) > ( set_int > set_o ) > $o ) > ( ( int > $o ) > set_int > set_o ) > ( ( int > $o ) > set_int > set_o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001_Eo_001_Eo,type,
    bNF_re6378653760509651613_o_o_o: ( ( int > $o ) > ( int > $o ) > $o ) > ( $o > $o > $o ) > ( ( int > $o ) > $o ) > ( ( int > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J,type,
    bNF_re6121003078962415843et_int: ( ( int > $o ) > ( int > $o ) > $o ) > ( set_int > set_int > $o ) > ( ( int > $o ) > set_int ) > ( ( int > $o ) > set_int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
    bNF_re4810274416841960511_int_o: ( ( int > $o ) > ( int > int ) > $o ) > ( ( ( int > $o ) > $o ) > ( ( int > int ) > $o ) > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( ( int > int ) > ( int > int ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_Eo_001_Eo,type,
    bNF_re5653686079057778813nt_o_o: ( ( int > $o ) > ( int > int ) > $o ) > ( $o > $o > $o ) > ( ( int > $o ) > $o ) > ( ( int > int ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_Eo_J,type,
    bNF_re1028521115286184183_nat_o: ( ( int > $o ) > ( int > nat ) > $o ) > ( ( ( int > $o ) > $o ) > ( ( int > nat ) > $o ) > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( ( int > nat ) > ( int > nat ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
    bNF_re4654332367156724257at_o_o: ( ( int > $o ) > ( int > nat ) > $o ) > ( $o > $o > $o ) > ( ( int > $o ) > $o ) > ( ( int > nat ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Finite____Field__Omod____ring_Itf__a_J_Mt__Finite____Field__Omod____ring_Itf__a_J_J_001_062_It__Set__Oset_It__Int__Oint_J_Mt__Set__Oset_It__Int__Oint_J_J_001_062_It__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_Mt__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    bNF_re5468675425431845637ring_a: ( ( int > int ) > ( finite_mod_ring_a > finite_mod_ring_a ) > $o ) > ( ( set_int > set_int ) > ( set_Fi2982333969990053029ring_a > set_Fi2982333969990053029ring_a ) > $o ) > ( ( int > int ) > set_int > set_int ) > ( ( finite_mod_ring_a > finite_mod_ring_a ) > set_Fi2982333969990053029ring_a > set_Fi2982333969990053029ring_a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Finite____Field__Omod____ring_Itf__a_J_Mt__Int__Oint_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_001_062_I_062_It__Finite____Field__Omod____ring_Itf__a_J_Mt__Int__Oint_J_M_Eo_J,type,
    bNF_re7705526925582604071_int_o: ( ( int > int ) > ( finite_mod_ring_a > int ) > $o ) > ( ( ( int > int ) > $o ) > ( ( finite_mod_ring_a > int ) > $o ) > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( ( finite_mod_ring_a > int ) > ( finite_mod_ring_a > int ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Finite____Field__Omod____ring_Itf__a_J_Mt__Int__Oint_J_001_Eo_001_Eo,type,
    bNF_re8039882297063496332nt_o_o: ( ( int > int ) > ( finite_mod_ring_a > int ) > $o ) > ( $o > $o > $o ) > ( ( int > int ) > $o ) > ( ( finite_mod_ring_a > int ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_M_Eo_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J,type,
    bNF_re6856201910719030053nt_o_o: ( ( int > int ) > ( int > $o ) > $o ) > ( ( ( int > int ) > $o ) > ( ( int > $o ) > $o ) > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_M_Eo_J_001_Eo_001_Eo,type,
    bNF_re2570638569070957389_o_o_o: ( ( int > int ) > ( int > $o ) > $o ) > ( $o > $o > $o ) > ( ( int > int ) > $o ) > ( ( int > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_I_062_I_Eo_M_Eo_J_M_062_I_062_It__Int__Oint_M_Eo_J_M_062_It__Int__Oint_M_Eo_J_J_J_001_062_I_062_I_Eo_M_Eo_J_M_062_I_062_It__Int__Oint_M_Eo_J_M_062_It__Int__Oint_M_Eo_J_J_J,type,
    bNF_re2841006154458801825_int_o: ( ( int > int ) > ( int > int ) > $o ) > ( ( ( $o > $o ) > ( int > $o ) > int > $o ) > ( ( $o > $o ) > ( int > $o ) > int > $o ) > $o ) > ( ( int > int ) > ( $o > $o ) > ( int > $o ) > int > $o ) > ( ( int > int ) > ( $o > $o ) > ( int > $o ) > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_I_062_I_Eo_Mt__Int__Oint_J_M_062_I_062_It__Int__Oint_M_Eo_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J_J_001_062_I_062_I_Eo_Mt__Int__Oint_J_M_062_I_062_It__Int__Oint_M_Eo_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    bNF_re7994082533931791685nt_int: ( ( int > int ) > ( int > int ) > $o ) > ( ( ( $o > int ) > ( int > $o ) > int > int ) > ( ( $o > int ) > ( int > $o ) > int > int ) > $o ) > ( ( int > int ) > ( $o > int ) > ( int > $o ) > int > int ) > ( ( int > int ) > ( $o > int ) > ( int > $o ) > int > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_I_062_I_Eo_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_I_062_I_Eo_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J,type,
    bNF_re4856174267440235917nt_int: ( ( int > int ) > ( int > int ) > $o ) > ( ( ( $o > int ) > int > int ) > ( ( $o > int ) > int > int ) > $o ) > ( ( int > int ) > ( $o > int ) > int > int ) > ( ( int > int ) > ( $o > int ) > int > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_I_062_I_Eo_Mt__Nat__Onat_J_M_062_I_062_It__Int__Oint_M_Eo_J_M_062_It__Int__Oint_Mt__Nat__Onat_J_J_J_001_062_I_062_I_Eo_Mt__Nat__Onat_J_M_062_I_062_It__Int__Oint_M_Eo_J_M_062_It__Int__Oint_Mt__Nat__Onat_J_J_J,type,
    bNF_re3201000475353829189nt_nat: ( ( int > int ) > ( int > int ) > $o ) > ( ( ( $o > nat ) > ( int > $o ) > int > nat ) > ( ( $o > nat ) > ( int > $o ) > int > nat ) > $o ) > ( ( int > int ) > ( $o > nat ) > ( int > $o ) > int > nat ) > ( ( int > int ) > ( $o > nat ) > ( int > $o ) > int > nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J,type,
    bNF_re6961808529855443971nt_o_o: ( ( int > int ) > ( int > int ) > $o ) > ( ( ( int > $o ) > $o ) > ( ( int > $o ) > $o ) > $o ) > ( ( int > int ) > ( int > $o ) > $o ) > ( ( int > int ) > ( int > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
    bNF_re619888514246228685_int_o: ( ( int > int ) > ( int > int ) > $o ) > ( ( ( int > int ) > $o ) > ( ( int > int ) > $o ) > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( ( int > int ) > ( int > int ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_Eo_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_Eo_J,type,
    bNF_re3638363003489898445_nat_o: ( ( int > int ) > ( int > int ) > $o ) > ( ( ( int > nat ) > $o ) > ( ( int > nat ) > $o ) > $o ) > ( ( int > int ) > ( int > nat ) > $o ) > ( ( int > int ) > ( int > nat ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_I_062_It__Nat__Onat_M_Eo_J_M_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_M_Eo_J_J_J_001_062_I_062_It__Nat__Onat_M_Eo_J_M_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_M_Eo_J_J_J,type,
    bNF_re2389797945169007513_int_o: ( ( int > int ) > ( int > int ) > $o ) > ( ( ( nat > $o ) > ( int > nat ) > int > $o ) > ( ( nat > $o ) > ( int > nat ) > int > $o ) > $o ) > ( ( int > int ) > ( nat > $o ) > ( int > nat ) > int > $o ) > ( ( int > int ) > ( nat > $o ) > ( int > nat ) > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_I_062_It__Nat__Onat_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_I_062_It__Nat__Onat_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J,type,
    bNF_re421952579363528881nt_int: ( ( int > int ) > ( int > int ) > $o ) > ( ( ( nat > int ) > int > int ) > ( ( nat > int ) > int > int ) > $o ) > ( ( int > int ) > ( nat > int ) > int > int ) > ( ( int > int ) > ( nat > int ) > int > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    bNF_re8280112600883147625nt_int: ( ( int > int ) > ( int > int ) > $o ) > ( ( int > int > int > int ) > ( int > int > int > int ) > $o ) > ( ( int > int ) > int > int > int > int ) > ( ( int > int ) > int > int > int > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J,type,
    bNF_re724639330072410579nt_int: ( ( int > int ) > ( int > int ) > $o ) > ( ( int > int > int ) > ( int > int > int ) > $o ) > ( ( int > int ) > int > int > int ) > ( ( int > int ) > int > int > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Set__Oset_It__Int__Oint_J_Mt__Set__Oset_It__Int__Oint_J_J_001_062_It__Set__Oset_It__Int__Oint_J_Mt__Set__Oset_It__Int__Oint_J_J,type,
    bNF_re4448180118338355989et_int: ( ( int > int ) > ( int > int ) > $o ) > ( ( set_int > set_int ) > ( set_int > set_int ) > $o ) > ( ( int > int ) > set_int > set_int ) > ( ( int > int ) > set_int > set_int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_Eo_001_Eo,type,
    bNF_re1277823837431233485nt_o_o: ( ( int > int ) > ( int > int ) > $o ) > ( $o > $o > $o ) > ( ( int > int ) > $o ) > ( ( int > int ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint_001t__Int__Oint,type,
    bNF_re8159601828672395943nt_int: ( ( int > int ) > ( int > int ) > $o ) > ( int > int > $o ) > ( ( int > int ) > int ) > ( ( int > int ) > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_Eo_J,type,
    bNF_re6215008164563829709_nat_o: ( ( int > int ) > ( int > nat ) > $o ) > ( ( ( int > int ) > $o ) > ( ( int > nat ) > $o ) > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( ( int > nat ) > ( int > nat ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
    bNF_re278470125530178929at_o_o: ( ( int > int ) > ( int > nat ) > $o ) > ( $o > $o > $o ) > ( ( int > int ) > $o ) > ( ( int > nat ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Set__Oset_It__Int__Oint_J_Mt__Set__Oset_It__Int__Oint_J_J_001_062_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    bNF_re8645648040046385573et_nat: ( ( int > int ) > ( nat > nat ) > $o ) > ( ( set_int > set_int ) > ( set_nat > set_nat ) > $o ) > ( ( int > int ) > set_int > set_int ) > ( ( nat > nat ) > set_nat > set_nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_M_Eo_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_Eo_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J,type,
    bNF_re8458729935450468901nt_o_o: ( ( int > nat ) > ( int > $o ) > $o ) > ( ( ( int > nat ) > $o ) > ( ( int > $o ) > $o ) > $o ) > ( ( int > nat ) > ( int > nat ) > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_M_Eo_J_001_Eo_001_Eo,type,
    bNF_re7959771505041706665_o_o_o: ( ( int > nat ) > ( int > $o ) > $o ) > ( $o > $o > $o ) > ( ( int > nat ) > $o ) > ( ( int > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_Eo_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
    bNF_re3282862283220456469_int_o: ( ( int > nat ) > ( int > int ) > $o ) > ( ( ( int > nat ) > $o ) > ( ( int > int ) > $o ) > $o ) > ( ( int > nat ) > ( int > nat ) > $o ) > ( ( int > int ) > ( int > int ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_Eo_001_Eo,type,
    bNF_re69706704502853489nt_o_o: ( ( int > nat ) > ( int > int ) > $o ) > ( $o > $o > $o ) > ( ( int > nat ) > $o ) > ( ( int > int ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_I_062_I_Eo_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Nat__Onat_J_J_001_062_I_062_I_Eo_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Nat__Onat_J_J,type,
    bNF_re3015352480858811349nt_nat: ( ( int > nat ) > ( int > nat ) > $o ) > ( ( ( $o > int ) > int > nat ) > ( ( $o > int ) > int > nat ) > $o ) > ( ( int > nat ) > ( $o > int ) > int > nat ) > ( ( int > nat ) > ( $o > int ) > int > nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_I_062_It__Nat__Onat_Mt__Int__Oint_J_M_062_It__Int__Oint_M_Eo_J_J_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_I_062_It__Nat__Onat_Mt__Int__Oint_J_M_062_It__Int__Oint_M_Eo_J_J_J,type,
    bNF_re8957533069481939353_int_o: ( ( int > nat ) > ( int > nat ) > $o ) > ( ( ( int > $o ) > ( nat > int ) > int > $o ) > ( ( int > $o ) > ( nat > int ) > int > $o ) > $o ) > ( ( int > nat ) > ( int > $o ) > ( nat > int ) > int > $o ) > ( ( int > nat ) > ( int > $o ) > ( nat > int ) > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J,type,
    bNF_re7816892618387588427nt_o_o: ( ( int > nat ) > ( int > nat ) > $o ) > ( ( ( int > $o ) > $o ) > ( ( int > $o ) > $o ) > $o ) > ( ( int > nat ) > ( int > $o ) > $o ) > ( ( int > nat ) > ( int > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_I_062_It__Nat__Onat_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_I_062_It__Nat__Onat_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    bNF_re1675945521237804325nt_int: ( ( int > nat ) > ( int > nat ) > $o ) > ( ( ( int > int ) > ( nat > int ) > int > int ) > ( ( int > int ) > ( nat > int ) > int > int ) > $o ) > ( ( int > nat ) > ( int > int ) > ( nat > int ) > int > int ) > ( ( int > nat ) > ( int > int ) > ( nat > int ) > int > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
    bNF_re5859507444294387733_int_o: ( ( int > nat ) > ( int > nat ) > $o ) > ( ( ( int > int ) > $o ) > ( ( int > int ) > $o ) > $o ) > ( ( int > nat ) > ( int > int ) > $o ) > ( ( int > nat ) > ( int > int ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_I_062_It__Nat__Onat_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Nat__Onat_J_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_I_062_It__Nat__Onat_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Nat__Onat_J_J_J,type,
    bNF_re8516618236367403957nt_nat: ( ( int > nat ) > ( int > nat ) > $o ) > ( ( ( int > nat ) > ( nat > int ) > int > nat ) > ( ( int > nat ) > ( nat > int ) > int > nat ) > $o ) > ( ( int > nat ) > ( int > nat ) > ( nat > int ) > int > nat ) > ( ( int > nat ) > ( int > nat ) > ( nat > int ) > int > nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_Eo_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_Eo_J,type,
    bNF_re8877981933538057493_nat_o: ( ( int > nat ) > ( int > nat ) > $o ) > ( ( ( int > nat ) > $o ) > ( ( int > nat ) > $o ) > $o ) > ( ( int > nat ) > ( int > nat ) > $o ) > ( ( int > nat ) > ( int > nat ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_I_062_It__Nat__Onat_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Nat__Onat_J_J_001_062_I_062_It__Nat__Onat_Mt__Int__Oint_J_M_062_It__Int__Oint_Mt__Nat__Onat_J_J,type,
    bNF_re6913270855792892737nt_nat: ( ( int > nat ) > ( int > nat ) > $o ) > ( ( ( nat > int ) > int > nat ) > ( ( nat > int ) > int > nat ) > $o ) > ( ( int > nat ) > ( nat > int ) > int > nat ) > ( ( int > nat ) > ( nat > int ) > int > nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_062_It__Int__Oint_Mt__Nat__Onat_J_J_J_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_062_It__Int__Oint_Mt__Nat__Onat_J_J_J,type,
    bNF_re4228487696381020993nt_nat: ( ( int > nat ) > ( int > nat ) > $o ) > ( ( int > nat > int > nat ) > ( int > nat > int > nat ) > $o ) > ( ( int > nat ) > int > nat > int > nat ) > ( ( int > nat ) > int > nat > int > nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    bNF_re6080477866362396757_int_o: ( ( int > nat ) > ( int > nat ) > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( ( int > nat ) > int > $o ) > ( ( int > nat ) > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Set__Oset_It__Int__Oint_J_Mt__Set__Oset_It__Nat__Onat_J_J_001_062_It__Set__Oset_It__Int__Oint_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    bNF_re1462970895668484517et_nat: ( ( int > nat ) > ( int > nat ) > $o ) > ( ( set_int > set_nat ) > ( set_int > set_nat ) > $o ) > ( ( int > nat ) > set_int > set_nat ) > ( ( int > nat ) > set_int > set_nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
    bNF_re8293725029456574741at_o_o: ( ( int > nat ) > ( int > nat ) > $o ) > ( $o > $o > $o ) > ( ( int > nat ) > $o ) > ( ( int > nat ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_re1996201511620343607at_nat: ( ( int > nat ) > ( int > nat ) > $o ) > ( nat > nat > $o ) > ( ( int > nat ) > nat ) > ( ( int > nat ) > nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Matrix__Omat_It__Int__Oint_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J_J_001_Eo_001_Eo,type,
    bNF_re9174360872848916795_o_o_o: ( ( mat_int > int > $o ) > ( mat_Fi443519135453058082ring_a > finite_mod_ring_a > $o ) > $o ) > ( $o > $o > $o ) > ( ( mat_int > int > $o ) > $o ) > ( ( mat_Fi443519135453058082ring_a > finite_mod_ring_a > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Matrix__Omat_It__Int__Oint_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
    bNF_re6198949750846496950_int_o: ( ( mat_int > int > $o ) > ( mat_Fi443519135453058082ring_a > int > $o ) > $o ) > ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( mat_int > int > $o ) > int > int > $o ) > ( ( mat_Fi443519135453058082ring_a > int > $o ) > int > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Matrix__Omat_It__Int__Oint_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Set__Oset_It__Matrix__Omat_It__Int__Oint_J_J_M_062_It__Set__Oset_It__Int__Oint_J_M_Eo_J_J_001_062_It__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J_M_062_It__Set__Oset_It__Int__Oint_J_M_Eo_J_J,type,
    bNF_re7208957339489685447_int_o: ( ( mat_int > int > $o ) > ( mat_Fi443519135453058082ring_a > int > $o ) > $o ) > ( ( set_mat_int > set_int > $o ) > ( set_ma1095064855528551128ring_a > set_int > $o ) > $o ) > ( ( mat_int > int > $o ) > set_mat_int > set_int > $o ) > ( ( mat_Fi443519135453058082ring_a > int > $o ) > set_ma1095064855528551128ring_a > set_int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Matrix__Omat_It__Int__Oint_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_062_It__Int__Oint_M_Eo_J_J_001_Eo_001_Eo,type,
    bNF_re2185885084462657334_o_o_o: ( ( mat_int > int > $o ) > ( mat_Fi443519135453058082ring_a > int > $o ) > $o ) > ( $o > $o > $o ) > ( ( mat_int > int > $o ) > $o ) > ( ( mat_Fi443519135453058082ring_a > int > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Matrix__Omat_It__Int__Oint_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Set__Oset_It__Matrix__Omat_It__Int__Oint_J_J_M_062_It__Int__Oint_M_Eo_J_J_J_001_062_It__Int__Oint_M_062_It__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J_M_062_It__Int__Oint_M_Eo_J_J_J,type,
    bNF_re5968936872641161301_int_o: ( ( mat_int > int > int ) > ( mat_Fi443519135453058082ring_a > int > int ) > $o ) > ( ( int > set_mat_int > int > $o ) > ( int > set_ma1095064855528551128ring_a > int > $o ) > $o ) > ( ( mat_int > int > int ) > int > set_mat_int > int > $o ) > ( ( mat_Fi443519135453058082ring_a > int > int ) > int > set_ma1095064855528551128ring_a > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Matrix__Omat_It__Int__Oint_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Set__Oset_It__Matrix__Omat_It__Int__Oint_J_J_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J_Mt__Int__Oint_J_J,type,
    bNF_re5718981180934321651_a_int: ( ( mat_int > int > int ) > ( mat_Fi443519135453058082ring_a > int > int ) > $o ) > ( ( int > set_mat_int > int ) > ( int > set_ma1095064855528551128ring_a > int ) > $o ) > ( ( mat_int > int > int ) > int > set_mat_int > int ) > ( ( mat_Fi443519135453058082ring_a > int > int ) > int > set_ma1095064855528551128ring_a > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Matrix__Omat_It__Int__Oint_J_M_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J_J_001_062_It__Set__Oset_It__Matrix__Omat_It__Int__Oint_J_J_M_062_It__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J_M_Eo_J_J_001_062_It__Set__Oset_It__Int__Oint_J_M_062_It__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J,type,
    bNF_re746635091991164545ng_a_o: ( ( mat_int > mat_Fi443519135453058082ring_a > $o ) > ( int > finite_mod_ring_a > $o ) > $o ) > ( ( set_mat_int > set_ma1095064855528551128ring_a > $o ) > ( set_int > set_Fi2982333969990053029ring_a > $o ) > $o ) > ( ( mat_int > mat_Fi443519135453058082ring_a > $o ) > set_mat_int > set_ma1095064855528551128ring_a > $o ) > ( ( int > finite_mod_ring_a > $o ) > set_int > set_Fi2982333969990053029ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Matrix__Omat_It__Int__Oint_J_M_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_001_062_It__Matrix__Omat_It__Int__Oint_J_M_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_001_062_It__Matrix__Omat_It__Int__Oint_J_M_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_001_062_It__Matrix__Omat_It__Int__Oint_J_M_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J,type,
    bNF_re9109869686183513365ng_a_o: ( ( mat_int > mat_Fi443519135453058082ring_a > $o ) > ( mat_int > mat_Fi443519135453058082ring_a > $o ) > $o ) > ( ( mat_int > mat_Fi443519135453058082ring_a > $o ) > ( mat_int > mat_Fi443519135453058082ring_a > $o ) > $o ) > ( ( mat_int > mat_Fi443519135453058082ring_a > $o ) > mat_int > mat_Fi443519135453058082ring_a > $o ) > ( ( mat_int > mat_Fi443519135453058082ring_a > $o ) > mat_int > mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Matrix__Omat_It__Int__Oint_J_M_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_001_062_It__Matrix__Omat_It__Int__Oint_J_M_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_001_062_It__Matrix__Omat_It__Int__Oint_J_M_Eo_J_001_062_It__Matrix__Omat_It__Int__Oint_J_M_Eo_J,type,
    bNF_re1419448087627042795_int_o: ( ( mat_int > mat_Fi443519135453058082ring_a > $o ) > ( mat_int > mat_Fi443519135453058082ring_a > $o ) > $o ) > ( ( mat_int > $o ) > ( mat_int > $o ) > $o ) > ( ( mat_int > mat_Fi443519135453058082ring_a > $o ) > mat_int > $o ) > ( ( mat_int > mat_Fi443519135453058082ring_a > $o ) > mat_int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Matrix__Omat_It__Int__Oint_J_M_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_001_062_It__Matrix__Ovec_It__Int__Oint_J_M_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_001_062_It__Matrix__Omat_It__Int__Oint_J_M_Eo_J_001_062_It__Matrix__Ovec_It__Int__Oint_J_M_Eo_J,type,
    bNF_re6999084953581488503_int_o: ( ( mat_int > mat_Fi443519135453058082ring_a > $o ) > ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > $o ) > ( ( mat_int > $o ) > ( vec_int > $o ) > $o ) > ( ( mat_int > mat_Fi443519135453058082ring_a > $o ) > mat_int > $o ) > ( ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > vec_int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Matrix__Omat_It__Int__Oint_J_M_062_It__Matrix__Omat_It__Int__Oint_J_M_Eo_J_J_001_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_001_062_It__Matrix__Omat_It__Int__Oint_J_M_062_It__Matrix__Omat_It__Int__Oint_J_M_Eo_J_J_001_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J,type,
    bNF_re7693591110265091205ng_a_o: ( ( mat_int > mat_int > $o ) > ( mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a > $o ) > $o ) > ( ( mat_int > mat_int > $o ) > ( mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a > $o ) > $o ) > ( ( mat_int > mat_int > $o ) > mat_int > mat_int > $o ) > ( ( mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a > $o ) > mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Matrix__Omat_It__Int__Oint_J_M_062_It__Matrix__Omat_It__Int__Oint_J_M_Eo_J_J_001_062_It__Matrix__Omat_It__Int__Oint_J_M_062_It__Matrix__Omat_It__Int__Oint_J_M_Eo_J_J_001_062_I_062_It__Matrix__Omat_It__Int__Oint_J_M_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_M_062_It__Matrix__Omat_It__Int__Oint_J_M_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_J_001_062_I_062_It__Matrix__Omat_It__Int__Oint_J_M_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_M_062_It__Matrix__Omat_It__Int__Oint_J_M_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_J,type,
    bNF_re849768681852557265ng_a_o: ( ( mat_int > mat_int > $o ) > ( mat_int > mat_int > $o ) > $o ) > ( ( ( mat_int > mat_Fi443519135453058082ring_a > $o ) > mat_int > mat_Fi443519135453058082ring_a > $o ) > ( ( mat_int > mat_Fi443519135453058082ring_a > $o ) > mat_int > mat_Fi443519135453058082ring_a > $o ) > $o ) > ( ( mat_int > mat_int > $o ) > ( mat_int > mat_Fi443519135453058082ring_a > $o ) > mat_int > mat_Fi443519135453058082ring_a > $o ) > ( ( mat_int > mat_int > $o ) > ( mat_int > mat_Fi443519135453058082ring_a > $o ) > mat_int > mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Matrix__Omat_It__Int__Oint_J_M_Eo_J_001_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_001_Eo_001_Eo,type,
    bNF_re3523364678894640886_o_o_o: ( ( mat_int > $o ) > ( mat_Fi443519135453058082ring_a > $o ) > $o ) > ( $o > $o > $o ) > ( ( mat_int > $o ) > $o ) > ( ( mat_Fi443519135453058082ring_a > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Matrix__Omat_It__Int__Oint_J_M_Eo_J_001_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_001t__Set__Oset_It__Matrix__Omat_It__Int__Oint_J_J_001t__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    bNF_re6509371104199398375ring_a: ( ( mat_int > $o ) > ( mat_Fi443519135453058082ring_a > $o ) > $o ) > ( set_mat_int > set_ma1095064855528551128ring_a > $o ) > ( ( mat_int > $o ) > set_mat_int ) > ( ( mat_Fi443519135453058082ring_a > $o ) > set_ma1095064855528551128ring_a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Matrix__Ovec_It__Int__Oint_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J_J_001_Eo_001_Eo,type,
    bNF_re7402094339212515411_o_o_o: ( ( vec_int > int > $o ) > ( vec_Fi4296597256376197294ring_a > finite_mod_ring_a > $o ) > $o ) > ( $o > $o > $o ) > ( ( vec_int > int > $o ) > $o ) > ( ( vec_Fi4296597256376197294ring_a > finite_mod_ring_a > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Matrix__Ovec_It__Int__Oint_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
    bNF_re1812577071873895326_int_o: ( ( vec_int > int > $o ) > ( vec_Fi4296597256376197294ring_a > int > $o ) > $o ) > ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( vec_int > int > $o ) > int > int > $o ) > ( ( vec_Fi4296597256376197294ring_a > int > $o ) > int > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Matrix__Ovec_It__Int__Oint_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Set__Oset_It__Matrix__Ovec_It__Int__Oint_J_J_M_062_It__Set__Oset_It__Int__Oint_J_M_Eo_J_J_001_062_It__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J_M_062_It__Set__Oset_It__Int__Oint_J_M_Eo_J_J,type,
    bNF_re5672091554521441735_int_o: ( ( vec_int > int > $o ) > ( vec_Fi4296597256376197294ring_a > int > $o ) > $o ) > ( ( set_vec_int > set_int > $o ) > ( set_ve6125835690772642148ring_a > set_int > $o ) > $o ) > ( ( vec_int > int > $o ) > set_vec_int > set_int > $o ) > ( ( vec_Fi4296597256376197294ring_a > int > $o ) > set_ve6125835690772642148ring_a > set_int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Matrix__Ovec_It__Int__Oint_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_062_It__Int__Oint_M_Eo_J_J_001_Eo_001_Eo,type,
    bNF_re3166440945848855070_o_o_o: ( ( vec_int > int > $o ) > ( vec_Fi4296597256376197294ring_a > int > $o ) > $o ) > ( $o > $o > $o ) > ( ( vec_int > int > $o ) > $o ) > ( ( vec_Fi4296597256376197294ring_a > int > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Matrix__Ovec_It__Int__Oint_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Set__Oset_It__Matrix__Ovec_It__Int__Oint_J_J_M_062_It__Int__Oint_M_Eo_J_J_J_001_062_It__Int__Oint_M_062_It__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J_M_062_It__Int__Oint_M_Eo_J_J_J,type,
    bNF_re9120361678303120445_int_o: ( ( vec_int > int > int ) > ( vec_Fi4296597256376197294ring_a > int > int ) > $o ) > ( ( int > set_vec_int > int > $o ) > ( int > set_ve6125835690772642148ring_a > int > $o ) > $o ) > ( ( vec_int > int > int ) > int > set_vec_int > int > $o ) > ( ( vec_Fi4296597256376197294ring_a > int > int ) > int > set_ve6125835690772642148ring_a > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Matrix__Ovec_It__Int__Oint_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Set__Oset_It__Matrix__Ovec_It__Int__Oint_J_J_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J_Mt__Int__Oint_J_J,type,
    bNF_re1176066524844287475_a_int: ( ( vec_int > int > int ) > ( vec_Fi4296597256376197294ring_a > int > int ) > $o ) > ( ( int > set_vec_int > int ) > ( int > set_ve6125835690772642148ring_a > int ) > $o ) > ( ( vec_int > int > int ) > int > set_vec_int > int ) > ( ( vec_Fi4296597256376197294ring_a > int > int ) > int > set_ve6125835690772642148ring_a > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Matrix__Ovec_It__Int__Oint_J_M_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J_J_001_062_It__Set__Oset_It__Matrix__Ovec_It__Int__Oint_J_J_M_062_It__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J_M_Eo_J_J_001_062_It__Set__Oset_It__Int__Oint_J_M_062_It__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J,type,
    bNF_re7025310947142835329ng_a_o: ( ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > ( int > finite_mod_ring_a > $o ) > $o ) > ( ( set_vec_int > set_ve6125835690772642148ring_a > $o ) > ( set_int > set_Fi2982333969990053029ring_a > $o ) > $o ) > ( ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > set_vec_int > set_ve6125835690772642148ring_a > $o ) > ( ( int > finite_mod_ring_a > $o ) > set_int > set_Fi2982333969990053029ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Matrix__Ovec_It__Int__Oint_J_M_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_001_062_It__Matrix__Omat_It__Int__Oint_J_M_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_001_062_It__Matrix__Ovec_It__Int__Oint_J_M_Eo_J_001_062_It__Matrix__Omat_It__Int__Oint_J_M_Eo_J,type,
    bNF_re2243167975609497975_int_o: ( ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > ( mat_int > mat_Fi443519135453058082ring_a > $o ) > $o ) > ( ( vec_int > $o ) > ( mat_int > $o ) > $o ) > ( ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > vec_int > $o ) > ( ( mat_int > mat_Fi443519135453058082ring_a > $o ) > mat_int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Matrix__Ovec_It__Int__Oint_J_M_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_001_062_It__Matrix__Ovec_It__Int__Oint_J_M_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_001_062_It__Matrix__Ovec_It__Int__Oint_J_M_Eo_J_001_062_It__Matrix__Ovec_It__Int__Oint_J_M_Eo_J,type,
    bNF_re7822804841563943683_int_o: ( ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > $o ) > ( ( vec_int > $o ) > ( vec_int > $o ) > $o ) > ( ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > vec_int > $o ) > ( ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > vec_int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Matrix__Ovec_It__Int__Oint_J_M_062_It__Matrix__Ovec_It__Int__Oint_J_M_Eo_J_J_001_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_001_062_It__Matrix__Ovec_It__Int__Oint_J_M_062_It__Matrix__Ovec_It__Int__Oint_J_M_Eo_J_J_001_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J,type,
    bNF_re531798068885152853ng_a_o: ( ( vec_int > vec_int > $o ) > ( vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a > $o ) > $o ) > ( ( vec_int > vec_int > $o ) > ( vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a > $o ) > $o ) > ( ( vec_int > vec_int > $o ) > vec_int > vec_int > $o ) > ( ( vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a > $o ) > vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Matrix__Ovec_It__Int__Oint_J_M_062_It__Matrix__Ovec_It__Int__Oint_J_M_Eo_J_J_001_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J_001_Eo_001_Eo,type,
    bNF_re1256193828122302425_o_o_o: ( ( vec_int > vec_int > $o ) > ( vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a > $o ) > $o ) > ( $o > $o > $o ) > ( ( vec_int > vec_int > $o ) > $o ) > ( ( vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Matrix__Ovec_It__Int__Oint_J_M_Eo_J_001_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_001_Eo_001_Eo,type,
    bNF_re3034707934920152030_o_o_o: ( ( vec_int > $o ) > ( vec_Fi4296597256376197294ring_a > $o ) > $o ) > ( $o > $o > $o ) > ( ( vec_int > $o ) > $o ) > ( ( vec_Fi4296597256376197294ring_a > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Matrix__Ovec_It__Int__Oint_J_M_Eo_J_001_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_001t__Set__Oset_It__Matrix__Ovec_It__Int__Oint_J_J_001t__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    bNF_re8209676071344003583ring_a: ( ( vec_int > $o ) > ( vec_Fi4296597256376197294ring_a > $o ) > $o ) > ( set_vec_int > set_ve6125835690772642148ring_a > $o ) > ( ( vec_int > $o ) > set_vec_int ) > ( ( vec_Fi4296597256376197294ring_a > $o ) > set_ve6125835690772642148ring_a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Matrix__Ovec_It__Int__Oint_J_Mt__Int__Oint_J_001_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_Mt__Finite____Field__Omod____ring_Itf__a_J_J_001_062_It__Set__Oset_It__Matrix__Ovec_It__Int__Oint_J_J_Mt__Set__Oset_It__Int__Oint_J_J_001_062_It__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J_Mt__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    bNF_re7161980590383822241ring_a: ( ( vec_int > int ) > ( vec_Fi4296597256376197294ring_a > finite_mod_ring_a ) > $o ) > ( ( set_vec_int > set_int ) > ( set_ve6125835690772642148ring_a > set_Fi2982333969990053029ring_a ) > $o ) > ( ( vec_int > int ) > set_vec_int > set_int ) > ( ( vec_Fi4296597256376197294ring_a > finite_mod_ring_a ) > set_ve6125835690772642148ring_a > set_Fi2982333969990053029ring_a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_M_062_I_Eo_M_Eo_J_J_001_062_It__Nat__Onat_M_062_I_Eo_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J_J,type,
    bNF_re4138666560314401969nt_o_o: ( ( nat > $o > $o ) > ( nat > $o > $o ) > $o ) > ( ( ( int > nat ) > ( int > $o ) > $o ) > ( ( int > nat ) > ( int > $o ) > $o ) > $o ) > ( ( nat > $o > $o ) > ( int > nat ) > ( int > $o ) > $o ) > ( ( nat > $o > $o ) > ( int > nat ) > ( int > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Nat__Onat_M_062_It__Int__Oint_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    bNF_re9128218472039263965_int_o: ( ( nat > int > $o ) > ( nat > int > $o ) > $o ) > ( ( ( int > nat ) > ( int > int ) > $o ) > ( ( int > nat ) > ( int > int ) > $o ) > $o ) > ( ( nat > int > $o ) > ( int > nat ) > ( int > int ) > $o ) > ( ( nat > int > $o ) > ( int > nat ) > ( int > int ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_Eo_M_062_I_Eo_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_Eo_J_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J_J,type,
    bNF_re4194204844150045891nt_o_o: ( ( nat > nat > $o ) > ( $o > $o > $o ) > $o ) > ( ( ( int > nat ) > ( int > nat ) > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > $o ) > ( ( nat > nat > $o ) > ( int > nat ) > ( int > nat ) > $o ) > ( ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    bNF_re9024530389434122605_int_o: ( ( nat > nat > $o ) > ( int > int > $o ) > $o ) > ( ( ( int > nat ) > ( int > nat ) > $o ) > ( ( int > int ) > ( int > int ) > $o ) > $o ) > ( ( nat > nat > $o ) > ( int > nat ) > ( int > nat ) > $o ) > ( ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_Eo_J_J,type,
    bNF_re5912358153685880029_nat_o: ( ( nat > nat > $o ) > ( nat > nat > $o ) > $o ) > ( ( ( int > nat ) > ( int > nat ) > $o ) > ( ( int > nat ) > ( int > nat ) > $o ) > $o ) > ( ( nat > nat > $o ) > ( int > nat ) > ( int > nat ) > $o ) > ( ( nat > nat > $o ) > ( int > nat ) > ( int > nat ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_It__Int__Oint_M_Eo_J_J,type,
    bNF_re302001808991886301_int_o: ( ( nat > $o ) > ( nat > $o ) > $o ) > ( ( ( int > nat ) > int > $o ) > ( ( int > nat ) > int > $o ) > $o ) > ( ( nat > $o ) > ( int > nat ) > int > $o ) > ( ( nat > $o ) > ( int > nat ) > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_Eo_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_Eo_J,type,
    bNF_re1475021005839661469_nat_o: ( ( nat > $o ) > ( nat > $o ) > $o ) > ( ( ( int > nat ) > $o ) > ( ( int > nat ) > $o ) > $o ) > ( ( nat > $o ) > ( int > nat ) > $o ) > ( ( nat > $o ) > ( int > nat ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Int__Oint_J_001_062_It__Nat__Onat_Mt__Int__Oint_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    bNF_re5424208017755137109_int_o: ( ( nat > int ) > ( nat > int ) > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( ( nat > int ) > int > $o ) > ( ( nat > int ) > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Int__Oint_J_001_062_It__Nat__Onat_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
    bNF_re102136085403910533nt_int: ( ( nat > int ) > ( nat > int ) > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( ( nat > int ) > int > int ) > ( ( nat > int ) > int > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Int__Oint_J_001_062_It__Nat__Onat_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
    bNF_re8092276960064420557nt_nat: ( ( nat > int ) > ( nat > int ) > $o ) > ( ( int > nat ) > ( int > nat ) > $o ) > ( ( nat > int ) > int > nat ) > ( ( nat > int ) > int > nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Nat__Onat_J_J_001_062_It__Set__Oset_It__Int__Oint_J_Mt__Set__Oset_It__Int__Oint_J_J,type,
    bNF_re1078555597002162597et_int: ( ( nat > nat ) > ( int > int ) > $o ) > ( ( set_nat > set_nat ) > ( set_int > set_int ) > $o ) > ( ( nat > nat ) > set_nat > set_nat ) > ( ( int > int ) > set_int > set_int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Nat__Onat_J_J_001_062_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
    bNF_re5276023518710192181et_nat: ( ( nat > nat ) > ( nat > nat ) > $o ) > ( ( set_nat > set_nat ) > ( set_nat > set_nat ) > $o ) > ( ( nat > nat ) > set_nat > set_nat ) > ( ( nat > nat ) > set_nat > set_nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_I_Eo_M_Eo_J_001_062_I_Eo_M_Eo_J,type,
    bNF_re6472675536664000681_o_o_o: ( $o > $o > $o ) > ( ( $o > $o ) > ( $o > $o ) > $o ) > ( $o > $o > $o ) > ( $o > $o > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J,type,
    bNF_re6420062293230768483nt_int: ( $o > $o > $o ) > ( ( int > int > int ) > ( int > int > int ) > $o ) > ( $o > int > int > int ) > ( $o > int > int > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    bNF_re3817415506245077661_int_o: ( $o > $o > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( $o > int > $o ) > ( $o > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
    bNF_re3790380520279025053_nat_o: ( $o > $o > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( $o > nat > $o ) > ( $o > nat > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_Eo_001_Eo,type,
    bNF_rel_fun_o_o_o_o: ( $o > $o > $o ) > ( $o > $o > $o ) > ( $o > $o ) > ( $o > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Int__Oint_001t__Int__Oint,type,
    bNF_re1549289456480014903nt_int: ( $o > $o > $o ) > ( int > int > $o ) > ( $o > int ) > ( $o > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_re552426215088010623at_nat: ( $o > $o > $o ) > ( nat > nat > $o ) > ( $o > nat ) > ( $o > nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_Eo_001t__Int__Oint_001_062_I_Eo_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    bNF_re5432788727719671445_int_o: ( $o > int > $o ) > ( ( $o > $o ) > ( int > $o ) > $o ) > ( $o > $o > $o ) > ( int > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_Eo_001t__Int__Oint_001_Eo_001_Eo,type,
    bNF_re5301841019279710247nt_o_o: ( $o > int > $o ) > ( $o > $o > $o ) > ( $o > $o ) > ( int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_Eo_001t__Nat__Onat_001_062_I_Eo_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
    bNF_re7444536988384623437_nat_o: ( $o > nat > $o ) > ( ( $o > $o ) > ( nat > $o ) > $o ) > ( $o > $o > $o ) > ( nat > nat > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001_Eo_001t__Nat__Onat_001_Eo_001_Eo,type,
    bNF_re7218653638241686475at_o_o: ( $o > nat > $o ) > ( $o > $o > $o ) > ( $o > $o ) > ( nat > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Finite____Field__Omod____ring_Itf__a_J_001_Eo_001_Eo,type,
    bNF_re5912972185147205917_a_o_o: ( finite_mod_ring_a > finite_mod_ring_a > $o ) > ( $o > $o > $o ) > ( finite_mod_ring_a > $o ) > ( finite_mod_ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Int__Oint_001t__Int__Oint,type,
    bNF_re1123535563933081591nt_int: ( finite_mod_ring_a > finite_mod_ring_a > $o ) > ( int > int > $o ) > ( finite_mod_ring_a > int ) > ( finite_mod_ring_a > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bNF_re7588912355631532003ring_a: ( finite_mod_ring_a > finite_mod_ring_a > $o ) > ( mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a > $o ) > ( finite_mod_ring_a > mat_Fi443519135453058082ring_a ) > ( finite_mod_ring_a > mat_Fi443519135453058082ring_a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bNF_re529297735971823867ring_a: ( finite_mod_ring_a > finite_mod_ring_a > $o ) > ( vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a > $o ) > ( finite_mod_ring_a > vec_Fi4296597256376197294ring_a ) > ( finite_mod_ring_a > vec_Fi4296597256376197294ring_a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_re126672322541077311at_nat: ( finite_mod_ring_a > finite_mod_ring_a > $o ) > ( nat > nat > $o ) > ( finite_mod_ring_a > nat ) > ( finite_mod_ring_a > nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001_Eo_001_Eo,type,
    bNF_re5352847140489197770_a_o_o: ( finite_mod_ring_a > mat_Fi443519135453058082ring_a > $o ) > ( $o > $o > $o ) > ( finite_mod_ring_a > $o ) > ( mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001_Eo_001_Eo,type,
    bNF_re3816977551999327062_a_o_o: ( finite_mod_ring_a > vec_Fi4296597256376197294ring_a > $o ) > ( $o > $o > $o ) > ( finite_mod_ring_a > $o ) > ( vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001_Eo_001_062_It__Int__Oint_M_Eo_J_001_062_I_Eo_M_Eo_J,type,
    bNF_re8893569941355005307_o_o_o: ( int > $o > $o ) > ( ( int > $o ) > ( $o > $o ) > $o ) > ( int > int > $o ) > ( $o > $o > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001_Eo_001_Eo_001_Eo,type,
    bNF_re4469125395230562381_o_o_o: ( int > $o > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( $o > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J,type,
    bNF_re1743884151495963297ng_a_o: ( int > finite_mod_ring_a > $o ) > ( ( int > $o ) > ( finite_mod_ring_a > $o ) > $o ) > ( int > int > $o ) > ( finite_mod_ring_a > finite_mod_ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    bNF_re3873409527727426490_int_o: ( int > finite_mod_ring_a > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( int > int > $o ) > ( finite_mod_ring_a > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
    bNF_re6585011533847851626nt_int: ( int > finite_mod_ring_a > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( int > int > int ) > ( finite_mod_ring_a > int > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J_001_062_It__Matrix__Omat_It__Int__Oint_J_M_Eo_J_001_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J,type,
    bNF_re4973150902881326489ng_a_o: ( int > finite_mod_ring_a > $o ) > ( ( mat_int > $o ) > ( mat_Fi443519135453058082ring_a > $o ) > $o ) > ( int > mat_int > $o ) > ( finite_mod_ring_a > mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J_001_062_It__Matrix__Ovec_It__Int__Oint_J_M_Eo_J_001_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J,type,
    bNF_re4244150877105976961ng_a_o: ( int > finite_mod_ring_a > $o ) > ( ( vec_int > $o ) > ( vec_Fi4296597256376197294ring_a > $o ) > $o ) > ( int > vec_int > $o ) > ( finite_mod_ring_a > vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J_001_062_It__Set__Oset_It__Int__Oint_J_M_Eo_J_001_062_It__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J,type,
    bNF_re1630919894521622923ng_a_o: ( int > finite_mod_ring_a > $o ) > ( ( set_int > $o ) > ( set_Fi2982333969990053029ring_a > $o ) > $o ) > ( int > set_int > $o ) > ( finite_mod_ring_a > set_Fi2982333969990053029ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J_001_Eo_001_Eo,type,
    bNF_re8290846538823883642_a_o_o: ( int > finite_mod_ring_a > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( finite_mod_ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    bNF_re4694112744541868061ring_a: ( int > finite_mod_ring_a > $o ) > ( int > finite_mod_ring_a > $o ) > ( int > int ) > ( finite_mod_ring_a > finite_mod_ring_a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Int__Oint_001t__Int__Oint,type,
    bNF_re8614909862389055444nt_int: ( int > finite_mod_ring_a > $o ) > ( int > int > $o ) > ( int > int ) > ( finite_mod_ring_a > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bNF_re5430594279747096653ring_a: ( int > finite_mod_ring_a > $o ) > ( mat_int > mat_Fi443519135453058082ring_a > $o ) > ( int > mat_int ) > ( finite_mod_ring_a > mat_Fi443519135453058082ring_a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bNF_re6498750967587248461ring_a: ( int > finite_mod_ring_a > $o ) > ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > ( int > vec_int ) > ( finite_mod_ring_a > vec_Fi4296597256376197294ring_a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_M_062_It__Int__Oint_M_Eo_J_J,type,
    bNF_re1806261209056574701_int_o: ( int > int > $o ) > ( ( ( int > int > $o ) > int > $o ) > ( ( int > int > $o ) > int > $o ) > $o ) > ( int > ( int > int > $o ) > int > $o ) > ( int > ( int > int > $o ) > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_M_062_It__Int__Oint_Mt__Int__Oint_J_J,type,
    bNF_re776728095411994473nt_int: ( int > int > $o ) > ( ( ( int > int > int ) > int > int ) > ( ( int > int > int ) > int > int ) > $o ) > ( int > ( int > int > int ) > int > int ) > ( int > ( int > int > int ) > int > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_J,type,
    bNF_re2903057588882071961_int_o: ( int > int > $o ) > ( ( ( int > $o ) > int > int > $o ) > ( ( int > $o ) > int > int > $o ) > $o ) > ( int > ( int > $o ) > int > int > $o ) > ( int > ( int > $o ) > int > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J,type,
    bNF_re1280668699144990829nt_o_o: ( int > int > $o ) > ( ( ( int > $o ) > $o ) > ( ( int > $o ) > $o ) > $o ) > ( int > ( int > $o ) > $o ) > ( int > ( int > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
    bNF_re3338030124694030697nt_int: ( int > int > $o ) > ( ( ( int > int ) > int > int > int ) > ( ( int > int ) > int > int > int ) > $o ) > ( int > ( int > int ) > int > int > int ) > ( int > ( int > int ) > int > int > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_Mt__Int__Oint_J_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_Mt__Int__Oint_J,type,
    bNF_re8360549327529751101nt_int: ( int > int > $o ) > ( ( ( int > int ) > int ) > ( ( int > int ) > int ) > $o ) > ( int > ( int > int ) > int ) > ( int > ( int > int ) > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_Mt__Nat__Onat_J_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_Mt__Nat__Onat_J,type,
    bNF_re3451822466932340941at_nat: ( int > int > $o ) > ( ( ( int > nat ) > nat ) > ( ( int > nat ) > nat ) > $o ) > ( int > ( int > nat ) > nat ) > ( int > ( int > nat ) > nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_I_Eo_M_062_It__Int__Oint_M_Eo_J_J_001_062_I_Eo_M_062_It__Int__Oint_M_Eo_J_J,type,
    bNF_re2682350871644790041_int_o: ( int > int > $o ) > ( ( $o > int > $o ) > ( $o > int > $o ) > $o ) > ( int > $o > int > $o ) > ( int > $o > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_I_Eo_M_Eo_J_001_062_I_Eo_M_Eo_J,type,
    bNF_re2126651504659934083_o_o_o: ( int > int > $o ) > ( ( $o > $o ) > ( $o > $o ) > $o ) > ( int > $o > $o ) > ( int > $o > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J_001_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J,type,
    bNF_re6948380915580796713ng_a_o: ( int > int > $o ) > ( ( finite_mod_ring_a > $o ) > ( finite_mod_ring_a > $o ) > $o ) > ( int > finite_mod_ring_a > $o ) > ( int > finite_mod_ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J,type,
    bNF_re6390757846875798589nt_int: ( int > int > $o ) > ( ( int > int > int ) > ( int > int > int ) > $o ) > ( int > int > int > int ) > ( int > int > int > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_M_Eo_J_001_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J,type,
    bNF_re1393113005842329636ng_a_o: ( int > int > $o ) > ( ( int > $o ) > ( finite_mod_ring_a > $o ) > $o ) > ( int > int > $o ) > ( int > finite_mod_ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    bNF_re3403563459893282935_int_o: ( int > int > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( int > int > $o ) > ( int > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
    bNF_re711492959462206631nt_int: ( int > int > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( int > int > int ) > ( int > int > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Matrix__Omat_It__Int__Oint_J_M_Eo_J_001_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J,type,
    bNF_re4404534803379308188ng_a_o: ( int > int > $o ) > ( ( mat_int > $o ) > ( mat_Fi443519135453058082ring_a > $o ) > $o ) > ( int > mat_int > $o ) > ( int > mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Matrix__Ovec_It__Int__Oint_J_M_Eo_J_001_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J,type,
    bNF_re3675534777603958660ng_a_o: ( int > int > $o ) > ( ( vec_int > $o ) > ( vec_Fi4296597256376197294ring_a > $o ) > $o ) > ( int > vec_int > $o ) > ( int > vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Nat__Onat_M_062_It__Int__Oint_Mt__Nat__Onat_J_J_001_062_It__Nat__Onat_M_062_It__Int__Oint_Mt__Nat__Onat_J_J,type,
    bNF_re5791889273166771917nt_nat: ( int > int > $o ) > ( ( nat > int > nat ) > ( nat > int > nat ) > $o ) > ( int > nat > int > nat ) > ( int > nat > int > nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
    bNF_re3376528473927230327_nat_o: ( int > int > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( int > nat > $o ) > ( int > nat > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Set__Oset_It__Int__Oint_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_M_062_It__Int__Oint_M_Eo_J_J,type,
    bNF_re6175638012571284388_int_o: ( int > int > $o ) > ( ( set_int > int > $o ) > ( set_Fi2982333969990053029ring_a > int > $o ) > $o ) > ( int > set_int > int > $o ) > ( int > set_Fi2982333969990053029ring_a > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Set__Oset_It__Int__Oint_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Set__Oset_It__Int__Oint_J_M_062_It__Int__Oint_M_Eo_J_J,type,
    bNF_re2819329681884988983_int_o: ( int > int > $o ) > ( ( set_int > int > $o ) > ( set_int > int > $o ) > $o ) > ( int > set_int > int > $o ) > ( int > set_int > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Set__Oset_It__Int__Oint_J_M_Eo_J_001_062_It__Set__Oset_It__Int__Oint_J_M_Eo_J,type,
    bNF_re8356144997044566263_int_o: ( int > int > $o ) > ( ( set_int > $o ) > ( set_int > $o ) > $o ) > ( int > set_int > $o ) > ( int > set_int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Set__Oset_It__Int__Oint_J_Mt__Int__Oint_J_001_062_It__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_Mt__Int__Oint_J,type,
    bNF_re8097885208332794076_a_int: ( int > int > $o ) > ( ( set_int > int ) > ( set_Fi2982333969990053029ring_a > int ) > $o ) > ( int > set_int > int ) > ( int > set_Fi2982333969990053029ring_a > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Set__Oset_It__Int__Oint_J_Mt__Int__Oint_J_001_062_It__Set__Oset_It__Int__Oint_J_Mt__Int__Oint_J,type,
    bNF_re8906821383403939603nt_int: ( int > int > $o ) > ( ( set_int > int ) > ( set_int > int ) > $o ) > ( int > set_int > int ) > ( int > set_int > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Set__Oset_It__Matrix__Omat_It__Int__Oint_J_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J_M_062_It__Int__Oint_M_Eo_J_J,type,
    bNF_re4547852988781568774_int_o: ( int > int > $o ) > ( ( set_mat_int > int > $o ) > ( set_ma1095064855528551128ring_a > int > $o ) > $o ) > ( int > set_mat_int > int > $o ) > ( int > set_ma1095064855528551128ring_a > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Set__Oset_It__Matrix__Omat_It__Int__Oint_J_J_Mt__Int__Oint_J_001_062_It__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J_Mt__Int__Oint_J,type,
    bNF_re7619386655275720398_a_int: ( int > int > $o ) > ( ( set_mat_int > int ) > ( set_ma1095064855528551128ring_a > int ) > $o ) > ( int > set_mat_int > int ) > ( int > set_ma1095064855528551128ring_a > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Set__Oset_It__Matrix__Ovec_It__Int__Oint_J_J_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J_M_062_It__Int__Oint_M_Eo_J_J,type,
    bNF_re5257061086073980398_int_o: ( int > int > $o ) > ( ( set_vec_int > int > $o ) > ( set_ve6125835690772642148ring_a > int > $o ) > $o ) > ( int > set_vec_int > int > $o ) > ( int > set_ve6125835690772642148ring_a > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Set__Oset_It__Matrix__Ovec_It__Int__Oint_J_J_Mt__Int__Oint_J_001_062_It__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J_Mt__Int__Oint_J,type,
    bNF_re1694616526693603790_a_int: ( int > int > $o ) > ( ( set_vec_int > int ) > ( set_ve6125835690772642148ring_a > int ) > $o ) > ( int > set_vec_int > int ) > ( int > set_ve6125835690772642148ring_a > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_Eo_001_Eo,type,
    bNF_re5089333283451836215nt_o_o: ( int > int > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_Eo_001t__Int__Oint,type,
    bNF_re2495491232194430029_o_int: ( int > int > $o ) > ( $o > int > $o ) > ( int > $o ) > ( int > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_Eo_001t__Nat__Onat,type,
    bNF_re2497981702703480305_o_nat: ( int > int > $o ) > ( $o > nat > $o ) > ( int > $o ) > ( int > nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
    bNF_re3779610718378977651_int_o: ( int > int > $o ) > ( int > $o > $o ) > ( int > int ) > ( int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
    bNF_re4712519889275205905nt_int: ( int > int > $o ) > ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat,type,
    bNF_re4715010359784256181nt_nat: ( int > int > $o ) > ( int > nat > $o ) > ( int > int ) > ( int > nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001_Eo,type,
    bNF_re5600653063811665615_nat_o: ( int > int > $o ) > ( nat > $o > $o ) > ( int > nat ) > ( int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
    bNF_re3713166177374151349at_int: ( int > int > $o ) > ( nat > int > $o ) > ( int > nat ) > ( int > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_re3715656647883201625at_nat: ( int > int > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( int > nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001_062_It__Set__Oset_It__Int__Oint_J_M_Eo_J_001_062_It__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J_M_Eo_J,type,
    bNF_re3611541376831158135ng_a_o: ( int > mat_Fi443519135453058082ring_a > $o ) > ( ( set_int > $o ) > ( set_ma1095064855528551128ring_a > $o ) > $o ) > ( int > set_int > $o ) > ( mat_Fi443519135453058082ring_a > set_ma1095064855528551128ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Matrix__Omat_It__Int__Oint_J_001_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J_001_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J,type,
    bNF_re4810065245219074393ng_a_o: ( int > mat_int > $o ) > ( ( finite_mod_ring_a > $o ) > ( mat_Fi443519135453058082ring_a > $o ) > $o ) > ( int > finite_mod_ring_a > $o ) > ( mat_int > mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001_062_It__Set__Oset_It__Int__Oint_J_M_Eo_J_001_062_It__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J_M_Eo_J,type,
    bNF_re3464415642011276407ng_a_o: ( int > vec_Fi4296597256376197294ring_a > $o ) > ( ( set_int > $o ) > ( set_ve6125835690772642148ring_a > $o ) > $o ) > ( int > set_int > $o ) > ( vec_Fi4296597256376197294ring_a > set_ve6125835690772642148ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Matrix__Ovec_It__Int__Oint_J_001_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J_001_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J,type,
    bNF_re7899986136908408921ng_a_o: ( int > vec_int > $o ) > ( ( finite_mod_ring_a > $o ) > ( vec_Fi4296597256376197294ring_a > $o ) > $o ) > ( int > finite_mod_ring_a > $o ) > ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Nat__Onat_001_062_It__Int__Oint_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
    bNF_re832142806295076215_nat_o: ( int > nat > $o ) > ( ( int > $o ) > ( nat > $o ) > $o ) > ( int > int > $o ) > ( nat > nat > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Nat__Onat_001_062_It__Set__Oset_It__Int__Oint_J_M_Eo_J_001_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J,type,
    bNF_re4553266823265959927_nat_o: ( int > nat > $o ) > ( ( set_int > $o ) > ( set_nat > $o ) > $o ) > ( int > set_int > $o ) > ( nat > set_nat > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Nat__Onat_001_Eo_001_Eo,type,
    bNF_re7006145902413812443at_o_o: ( int > nat > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( nat > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat,type,
    bNF_re4343356799547411545nt_nat: ( int > nat > $o ) > ( int > nat > $o ) > ( int > int ) > ( nat > nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Finite____Field__Omod____ring_Itf__a_J_001_Eo_001_Eo,type,
    bNF_re8373915239858509316_a_o_o: ( mat_Fi443519135453058082ring_a > finite_mod_ring_a > $o ) > ( $o > $o > $o ) > ( mat_Fi443519135453058082ring_a > $o ) > ( finite_mod_ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Int__Oint_001_062_It__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J_M_Eo_J_001_062_It__Set__Oset_It__Int__Oint_J_M_Eo_J,type,
    bNF_re3297285065332102371_int_o: ( mat_Fi443519135453058082ring_a > int > $o ) > ( ( set_ma1095064855528551128ring_a > $o ) > ( set_int > $o ) > $o ) > ( mat_Fi443519135453058082ring_a > set_ma1095064855528551128ring_a > $o ) > ( int > set_int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001_Eo_001_Eo,type,
    bNF_re3698012824587224355_a_o_o: ( mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a > $o ) > ( $o > $o > $o ) > ( mat_Fi443519135453058082ring_a > $o ) > ( mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001_Eo_001_Eo,type,
    bNF_re2162143236097353647_a_o_o: ( mat_Fi443519135453058082ring_a > vec_Fi4296597256376197294ring_a > $o ) > ( $o > $o > $o ) > ( mat_Fi443519135453058082ring_a > $o ) > ( vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Omat_It__Int__Oint_J_001t__Int__Oint_001_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_001_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J,type,
    bNF_re5662754106317279473ng_a_o: ( mat_int > int > $o ) > ( ( mat_Fi443519135453058082ring_a > $o ) > ( finite_mod_ring_a > $o ) > $o ) > ( mat_int > mat_Fi443519135453058082ring_a > $o ) > ( int > finite_mod_ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J,type,
    bNF_re8055952673531087345ng_a_o: ( mat_int > mat_Fi443519135453058082ring_a > $o ) > ( ( int > $o ) > ( finite_mod_ring_a > $o ) > $o ) > ( mat_int > int > $o ) > ( mat_Fi443519135453058082ring_a > finite_mod_ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    bNF_re1270729808710627434_int_o: ( mat_int > mat_Fi443519135453058082ring_a > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( mat_int > int > $o ) > ( mat_Fi443519135453058082ring_a > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
    bNF_re2807999186244189978nt_int: ( mat_int > mat_Fi443519135453058082ring_a > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( mat_int > int > int ) > ( mat_Fi443519135453058082ring_a > int > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001_062_It__Matrix__Omat_It__Int__Oint_J_M_Eo_J_001_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J,type,
    bNF_re8187416184292455657ng_a_o: ( mat_int > mat_Fi443519135453058082ring_a > $o ) > ( ( mat_int > $o ) > ( mat_Fi443519135453058082ring_a > $o ) > $o ) > ( mat_int > mat_int > $o ) > ( mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
    bNF_re1243694822744574826_nat_o: ( mat_int > mat_Fi443519135453058082ring_a > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( mat_int > nat > $o ) > ( mat_Fi443519135453058082ring_a > nat > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001_062_It__Set__Oset_It__Matrix__Omat_It__Int__Oint_J_J_M_Eo_J_001_062_It__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J_M_Eo_J,type,
    bNF_re7855085375772821011ng_a_o: ( mat_int > mat_Fi443519135453058082ring_a > $o ) > ( ( set_mat_int > $o ) > ( set_ma1095064855528551128ring_a > $o ) > $o ) > ( mat_int > set_mat_int > $o ) > ( mat_Fi443519135453058082ring_a > set_ma1095064855528551128ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001_Eo_001_Eo,type,
    bNF_re6153771816476299306_a_o_o: ( mat_int > mat_Fi443519135453058082ring_a > $o ) > ( $o > $o > $o ) > ( mat_int > $o ) > ( mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    bNF_re2560879581620072301ring_a: ( mat_int > mat_Fi443519135453058082ring_a > $o ) > ( int > finite_mod_ring_a > $o ) > ( mat_int > int ) > ( mat_Fi443519135453058082ring_a > finite_mod_ring_a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bNF_re7267033552616699805ring_a: ( mat_int > mat_Fi443519135453058082ring_a > $o ) > ( mat_int > mat_Fi443519135453058082ring_a > $o ) > ( mat_int > mat_int ) > ( mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bNF_re8335190240456851613ring_a: ( mat_int > mat_Fi443519135453058082ring_a > $o ) > ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > ( mat_int > vec_int ) > ( mat_Fi443519135453058082ring_a > vec_Fi4296597256376197294ring_a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_re4847214273728626636at_nat: ( mat_int > mat_Fi443519135453058082ring_a > $o ) > ( nat > nat > $o ) > ( mat_int > nat ) > ( mat_Fi443519135453058082ring_a > nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Int__Oint_J_001_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_001_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J,type,
    bNF_re3207547038660532189ng_a_o: ( mat_int > mat_int > $o ) > ( ( mat_Fi443519135453058082ring_a > $o ) > ( mat_Fi443519135453058082ring_a > $o ) > $o ) > ( mat_int > mat_Fi443519135453058082ring_a > $o ) > ( mat_int > mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Int__Oint_J_001_062_It__Matrix__Omat_It__Int__Oint_J_M_Eo_J_001_062_It__Matrix__Omat_It__Int__Oint_J_M_Eo_J,type,
    bNF_re5814136157216229839_int_o: ( mat_int > mat_int > $o ) > ( ( mat_int > $o ) > ( mat_int > $o ) > $o ) > ( mat_int > mat_int > $o ) > ( mat_int > mat_int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Int__Oint_J_001_Eo_001_Eo,type,
    bNF_re5904460004506961949nt_o_o: ( mat_int > mat_int > $o ) > ( $o > $o > $o ) > ( mat_int > $o ) > ( mat_int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Int__Oint_J,type,
    bNF_re3172240519465120989at_int: ( mat_int > mat_int > $o ) > ( mat_int > mat_int > $o ) > ( mat_int > mat_int ) > ( mat_int > mat_int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Ovec_It__Int__Oint_J_001_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_001_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J,type,
    bNF_re5652364884431686341ng_a_o: ( mat_int > vec_int > $o ) > ( ( mat_Fi443519135453058082ring_a > $o ) > ( vec_Fi4296597256376197294ring_a > $o ) > $o ) > ( mat_int > mat_Fi443519135453058082ring_a > $o ) > ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Ovec_It__Int__Oint_J_001_Eo_001_Eo,type,
    bNF_re1257695248469094033nt_o_o: ( mat_int > vec_int > $o ) > ( $o > $o > $o ) > ( mat_int > $o ) > ( vec_int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Finite____Field__Omod____ring_Itf__a_J_001_Eo_001_Eo,type,
    bNF_re5329533212257213048_a_o_o: ( vec_Fi4296597256376197294ring_a > finite_mod_ring_a > $o ) > ( $o > $o > $o ) > ( vec_Fi4296597256376197294ring_a > $o ) > ( finite_mod_ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Int__Oint_001_062_It__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J_M_Eo_J_001_062_It__Set__Oset_It__Int__Oint_J_M_Eo_J,type,
    bNF_re7714729098714725883_int_o: ( vec_Fi4296597256376197294ring_a > int > $o ) > ( ( set_ve6125835690772642148ring_a > $o ) > ( set_int > $o ) > $o ) > ( vec_Fi4296597256376197294ring_a > set_ve6125835690772642148ring_a > $o ) > ( int > set_int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001_Eo_001_Eo,type,
    bNF_re8041672266701334447_a_o_o: ( vec_Fi4296597256376197294ring_a > mat_Fi443519135453058082ring_a > $o ) > ( $o > $o > $o ) > ( vec_Fi4296597256376197294ring_a > $o ) > ( mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001_Eo_001_Eo,type,
    bNF_re6505802678211463739_a_o_o: ( vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a > $o ) > ( $o > $o > $o ) > ( vec_Fi4296597256376197294ring_a > $o ) > ( vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Nat__Onat_001_062_It__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J_M_Eo_J_001_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J,type,
    bNF_re4623018748902118651_nat_o: ( vec_Fi4296597256376197294ring_a > nat > $o ) > ( ( set_ve6125835690772642148ring_a > $o ) > ( set_nat > $o ) > $o ) > ( vec_Fi4296597256376197294ring_a > set_ve6125835690772642148ring_a > $o ) > ( nat > set_nat > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Ovec_It__Int__Oint_J_001t__Int__Oint_001_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_001_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J,type,
    bNF_re6180959097202804209ng_a_o: ( vec_int > int > $o ) > ( ( vec_Fi4296597256376197294ring_a > $o ) > ( finite_mod_ring_a > $o ) > $o ) > ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > ( int > finite_mod_ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Omat_It__Int__Oint_J_001_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_001_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J,type,
    bNF_re6848855223299790069ng_a_o: ( vec_int > mat_int > $o ) > ( ( vec_Fi4296597256376197294ring_a > $o ) > ( mat_Fi443519135453058082ring_a > $o ) > $o ) > ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > ( mat_int > mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Omat_It__Int__Oint_J_001_Eo_001_Eo,type,
    bNF_re5326586026928855209nt_o_o: ( vec_int > mat_int > $o ) > ( $o > $o > $o ) > ( vec_int > $o ) > ( mat_int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J,type,
    bNF_re245202343922368753ng_a_o: ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > ( ( int > $o ) > ( finite_mod_ring_a > $o ) > $o ) > ( vec_int > int > $o ) > ( vec_Fi4296597256376197294ring_a > finite_mod_ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    bNF_re7877854262379379050_int_o: ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( vec_int > int > $o ) > ( vec_Fi4296597256376197294ring_a > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
    bNF_re6494125082490456090nt_int: ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( vec_int > int > int ) > ( vec_Fi4296597256376197294ring_a > int > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001_062_It__Matrix__Ovec_It__Int__Oint_J_M_Eo_J_001_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J,type,
    bNF_re151890839321169105ng_a_o: ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > ( ( vec_int > $o ) > ( vec_Fi4296597256376197294ring_a > $o ) > $o ) > ( vec_int > vec_int > $o ) > ( vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
    bNF_re7850819276413326442_nat_o: ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( vec_int > nat > $o ) > ( vec_Fi4296597256376197294ring_a > nat > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001_062_It__Nat__Onat_Mt__Int__Oint_J_001_062_It__Nat__Onat_Mt__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bNF_re1259227427626606373ring_a: ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > ( ( nat > int ) > ( nat > finite_mod_ring_a ) > $o ) > ( vec_int > nat > int ) > ( vec_Fi4296597256376197294ring_a > nat > finite_mod_ring_a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001_062_It__Set__Oset_It__Matrix__Ovec_It__Int__Oint_J_J_M_Eo_J_001_062_It__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J_M_Eo_J,type,
    bNF_re6884500472961882619ng_a_o: ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > ( ( set_vec_int > $o ) > ( set_ve6125835690772642148ring_a > $o ) > $o ) > ( vec_int > set_vec_int > $o ) > ( vec_Fi4296597256376197294ring_a > set_ve6125835690772642148ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001_Eo_001_Eo,type,
    bNF_re507051067509135658_a_o_o: ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > ( $o > $o > $o ) > ( vec_int > $o ) > ( vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    bNF_re5232057317656209005ring_a: ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > ( int > finite_mod_ring_a > $o ) > ( vec_int > int ) > ( vec_Fi4296597256376197294ring_a > finite_mod_ring_a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bNF_re6504867418239889053ring_a: ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > ( mat_int > mat_Fi443519135453058082ring_a > $o ) > ( vec_int > mat_int ) > ( vec_Fi4296597256376197294ring_a > mat_Fi443519135453058082ring_a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bNF_re7573024106080040861ring_a: ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > ( vec_int > vec_int ) > ( vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_re5216812267390093516at_nat: ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > ( nat > nat > $o ) > ( vec_int > nat ) > ( vec_Fi4296597256376197294ring_a > nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Int__Oint_J_001_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_001_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J,type,
    bNF_re70301032216168413ng_a_o: ( vec_int > vec_int > $o ) > ( ( vec_Fi4296597256376197294ring_a > $o ) > ( vec_Fi4296597256376197294ring_a > $o ) > $o ) > ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Int__Oint_J_001_Eo_001_Eo,type,
    bNF_re679821270890987293nt_o_o: ( vec_int > vec_int > $o ) > ( $o > $o > $o ) > ( vec_int > $o ) > ( vec_int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001_Eo_001_062_It__Nat__Onat_M_Eo_J_001_062_I_Eo_M_Eo_J,type,
    bNF_re6709961196992454779_o_o_o: ( nat > $o > $o ) > ( ( nat > $o ) > ( $o > $o ) > $o ) > ( nat > nat > $o ) > ( $o > $o > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001_Eo_001_Eo_001_Eo,type,
    bNF_re2164719486249941929_o_o_o: ( nat > $o > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( $o > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Int__Oint_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    bNF_re3149889684360781247_int_o: ( nat > int > $o ) > ( ( nat > $o ) > ( int > $o ) > $o ) > ( nat > nat > $o ) > ( int > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Int__Oint_001_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J_001_062_It__Set__Oset_It__Int__Oint_J_M_Eo_J,type,
    bNF_re6703580107126279231_int_o: ( nat > int > $o ) > ( ( set_nat > $o ) > ( set_int > $o ) > $o ) > ( nat > set_nat > $o ) > ( int > set_int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Int__Oint_001_Eo_001_Eo,type,
    bNF_re2788914913031914203nt_o_o: ( nat > int > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
    bNF_re6022984109467102297at_int: ( nat > int > $o ) > ( nat > int > $o ) > ( nat > nat ) > ( int > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_I_Eo_M_Eo_J_001_062_I_Eo_M_Eo_J,type,
    bNF_re6222992434181357259_o_o_o: ( nat > nat > $o ) > ( ( $o > $o ) > ( $o > $o ) > $o ) > ( nat > $o > $o ) > ( nat > $o > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    bNF_re605504016728627135_int_o: ( nat > nat > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( nat > int > $o ) > ( nat > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
    bNF_re3552752127234388279nt_nat: ( nat > nat > $o ) > ( ( int > nat ) > ( int > nat ) > $o ) > ( nat > int > nat ) > ( nat > int > nat ) > $o ).

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

thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
    bNF_re1345281282404953727at_nat: ( nat > nat > $o ) > ( ( nat > nat ) > ( nat > nat ) > $o ) > ( nat > nat > nat ) > ( nat > nat > nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J_001_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J,type,
    bNF_re2900701933347672895_nat_o: ( nat > nat > $o ) > ( ( set_nat > $o ) > ( set_nat > $o ) > $o ) > ( nat > set_nat > $o ) > ( nat > set_nat > $o ) > $o ).

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

thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    bNF_re2201348192133994456ring_a: ( nat > nat > $o ) > ( int > finite_mod_ring_a > $o ) > ( nat > int ) > ( nat > finite_mod_ring_a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Int__Oint,type,
    bNF_re6650684261131312217nt_int: ( nat > nat > $o ) > ( int > int > $o ) > ( nat > int ) > ( nat > int ) > $o ).

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

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_001_Eo_001_Eo,type,
    bNF_re1992636659909454109_a_o_o: ( set_Fi2982333969990053029ring_a > set_Fi2982333969990053029ring_a > $o ) > ( $o > $o > $o ) > ( set_Fi2982333969990053029ring_a > $o ) > ( set_Fi2982333969990053029ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J_001_Eo_001_Eo,type,
    bNF_re294612233331293024_a_o_o: ( set_Fi2982333969990053029ring_a > set_ma1095064855528551128ring_a > $o ) > ( $o > $o > $o ) > ( set_Fi2982333969990053029ring_a > $o ) > ( set_ma1095064855528551128ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J_001_Eo_001_Eo,type,
    bNF_re1568155373528815596_a_o_o: ( set_Fi2982333969990053029ring_a > set_ve6125835690772642148ring_a > $o ) > ( $o > $o > $o ) > ( set_Fi2982333969990053029ring_a > $o ) > ( set_ve6125835690772642148ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J_001_062_I_062_It__Finite____Field__Omod____ring_Itf__a_J_M_Eo_J_M_Eo_J,type,
    bNF_re3190460641836138519_a_o_o: ( set_int > set_Fi2982333969990053029ring_a > $o ) > ( ( ( int > $o ) > $o ) > ( ( finite_mod_ring_a > $o ) > $o ) > $o ) > ( set_int > ( int > $o ) > $o ) > ( set_Fi2982333969990053029ring_a > ( finite_mod_ring_a > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    bNF_re7589090870912319844_int_o: ( set_int > set_Fi2982333969990053029ring_a > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( set_int > int > $o ) > ( set_Fi2982333969990053029ring_a > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_001_062_It__Set__Oset_It__Int__Oint_J_M_Eo_J_001_062_It__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J,type,
    bNF_re6625280399352257633ng_a_o: ( set_int > set_Fi2982333969990053029ring_a > $o ) > ( ( set_int > $o ) > ( set_Fi2982333969990053029ring_a > $o ) > $o ) > ( set_int > set_int > $o ) > ( set_Fi2982333969990053029ring_a > set_Fi2982333969990053029ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_001_062_It__Set__Oset_It__Int__Oint_J_M_Eo_J_001_062_It__Set__Oset_It__Int__Oint_J_M_Eo_J,type,
    bNF_re414048519855180260_int_o: ( set_int > set_Fi2982333969990053029ring_a > $o ) > ( ( set_int > $o ) > ( set_int > $o ) > $o ) > ( set_int > set_int > $o ) > ( set_Fi2982333969990053029ring_a > set_int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_001_Eo_001_Eo,type,
    bNF_re3268453933031481124_a_o_o: ( set_int > set_Fi2982333969990053029ring_a > $o ) > ( $o > $o > $o ) > ( set_int > $o ) > ( set_Fi2982333969990053029ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Int__Oint_001t__Int__Oint,type,
    bNF_re7749175998128367230nt_int: ( set_int > set_Fi2982333969990053029ring_a > $o ) > ( int > int > $o ) > ( set_int > int ) > ( set_Fi2982333969990053029ring_a > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bNF_re5272088291242829981ring_a: ( set_int > set_Fi2982333969990053029ring_a > $o ) > ( set_int > set_Fi2982333969990053029ring_a > $o ) > ( set_int > set_int ) > ( set_Fi2982333969990053029ring_a > set_Fi2982333969990053029ring_a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J_001_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J,type,
    bNF_re9006250432731904985nt_o_o: ( set_int > set_int > $o ) > ( ( ( int > $o ) > $o ) > ( ( int > $o ) > $o ) > $o ) > ( set_int > ( int > $o ) > $o ) > ( set_int > ( int > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    bNF_re2448385431412511203_int_o: ( set_int > set_int > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( set_int > int > $o ) > ( set_int > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J_001_062_It__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_001_062_It__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J,type,
    bNF_re5132486596981259477ng_a_o: ( set_int > set_int > $o ) > ( ( set_Fi2982333969990053029ring_a > $o ) > ( set_Fi2982333969990053029ring_a > $o ) > $o ) > ( set_int > set_Fi2982333969990053029ring_a > $o ) > ( set_int > set_Fi2982333969990053029ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J_001_062_It__Set__Oset_It__Int__Oint_J_M_Eo_J_001_062_It__Set__Oset_It__Int__Oint_J_M_Eo_J,type,
    bNF_re4815948244430201443_int_o: ( set_int > set_int > $o ) > ( ( set_int > $o ) > ( set_int > $o ) > $o ) > ( set_int > set_int > $o ) > ( set_int > set_int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J_001_Eo_001_Eo,type,
    bNF_re4540111288819221667nt_o_o: ( set_int > set_int > $o ) > ( $o > $o > $o ) > ( set_int > $o ) > ( set_int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J_001t__Int__Oint_001t__Int__Oint,type,
    bNF_re2258174677021229181nt_int: ( set_int > set_int > $o ) > ( int > int > $o ) > ( set_int > int ) > ( set_int > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_I_062_It__Int__Oint_M_Eo_J_J_001t__Set__Oset_I_062_It__Int__Oint_M_Eo_J_J,type,
    bNF_re286873704650414563_int_o: ( set_int > set_int > $o ) > ( set_int_o > set_int_o > $o ) > ( set_int > set_int_o ) > ( set_int > set_int_o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_I_062_It__Int__Oint_Mt__Int__Oint_J_J_001t__Set__Oset_I_062_It__Int__Oint_Mt__Int__Oint_J_J,type,
    bNF_re6171256825458429567nt_int: ( set_int > set_int > $o ) > ( set_int_int > set_int_int > $o ) > ( set_int > set_int_int ) > ( set_int > set_int_int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_I_Eo_J_001t__Set__Oset_I_Eo_J,type,
    bNF_re320214293493010595_set_o: ( set_int > set_int > $o ) > ( set_o > set_o > $o ) > ( set_int > set_o ) > ( set_int > set_o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J,type,
    bNF_re8781014649373390825et_int: ( set_int > set_int > $o ) > ( set_int > set_int > $o ) > ( set_int > set_int ) > ( set_int > set_int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
    bNF_re6950056017887012657et_nat: ( set_int > set_int > $o ) > ( set_nat > set_nat > $o ) > ( set_int > set_nat ) > ( set_int > set_nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J_001_Eo_001_Eo,type,
    bNF_re5110367863359280793_a_o_o: ( set_int > set_ma1095064855528551128ring_a > $o ) > ( $o > $o > $o ) > ( set_int > $o ) > ( set_ma1095064855528551128ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Matrix__Omat_It__Int__Oint_J_J_001_062_It__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_001_062_It__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J_M_Eo_J,type,
    bNF_re4794200806275638105ng_a_o: ( set_int > set_mat_int > $o ) > ( ( set_Fi2982333969990053029ring_a > $o ) > ( set_ma1095064855528551128ring_a > $o ) > $o ) > ( set_int > set_Fi2982333969990053029ring_a > $o ) > ( set_mat_int > set_ma1095064855528551128ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J_001_Eo_001_Eo,type,
    bNF_re6383911003556803365_a_o_o: ( set_int > set_ve6125835690772642148ring_a > $o ) > ( $o > $o > $o ) > ( set_int > $o ) > ( set_ve6125835690772642148ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Matrix__Ovec_It__Int__Oint_J_J_001_062_It__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_001_062_It__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J_M_Eo_J,type,
    bNF_re3244266564472207961ng_a_o: ( set_int > set_vec_int > $o ) > ( ( set_Fi2982333969990053029ring_a > $o ) > ( set_ve6125835690772642148ring_a > $o ) > $o ) > ( set_int > set_Fi2982333969990053029ring_a > $o ) > ( set_vec_int > set_ve6125835690772642148ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Nat__Onat_J_001_Eo_001_Eo,type,
    bNF_re3540757576918167111at_o_o: ( set_int > set_nat > $o ) > ( $o > $o > $o ) > ( set_int > $o ) > ( set_nat > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Nat__Onat_J,type,
    bNF_re1768063143140362033et_nat: ( set_int > set_nat > $o ) > ( set_int > set_nat > $o ) > ( set_int > set_int ) > ( set_nat > set_nat ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J_001t__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_001_Eo_001_Eo,type,
    bNF_re2262145468226031790_a_o_o: ( set_ma1095064855528551128ring_a > set_Fi2982333969990053029ring_a > $o ) > ( $o > $o > $o ) > ( set_ma1095064855528551128ring_a > $o ) > ( set_Fi2982333969990053029ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J_001t__Set__Oset_It__Int__Oint_J_001_Eo_001_Eo,type,
    bNF_re8148148883495127705nt_o_o: ( set_ma1095064855528551128ring_a > set_int > $o ) > ( $o > $o > $o ) > ( set_ma1095064855528551128ring_a > $o ) > ( set_int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Matrix__Omat_It__Int__Oint_J_J_001t__Set__Oset_It__Int__Oint_J_001_062_It__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J_M_Eo_J_001_062_It__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J,type,
    bNF_re3414458586112227909ng_a_o: ( set_mat_int > set_int > $o ) > ( ( set_ma1095064855528551128ring_a > $o ) > ( set_Fi2982333969990053029ring_a > $o ) > $o ) > ( set_mat_int > set_ma1095064855528551128ring_a > $o ) > ( set_int > set_Fi2982333969990053029ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Matrix__Omat_It__Int__Oint_J_J_001t__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J_001_062_I_062_It__Matrix__Omat_It__Int__Oint_J_M_Eo_J_M_Eo_J_001_062_I_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_M_Eo_J,type,
    bNF_re9140219897439888391_a_o_o: ( set_mat_int > set_ma1095064855528551128ring_a > $o ) > ( ( ( mat_int > $o ) > $o ) > ( ( mat_Fi443519135453058082ring_a > $o ) > $o ) > $o ) > ( set_mat_int > ( mat_int > $o ) > $o ) > ( set_ma1095064855528551128ring_a > ( mat_Fi443519135453058082ring_a > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Matrix__Omat_It__Int__Oint_J_J_001t__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    bNF_re6428356065892730240_int_o: ( set_mat_int > set_ma1095064855528551128ring_a > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( set_mat_int > int > $o ) > ( set_ma1095064855528551128ring_a > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Matrix__Omat_It__Int__Oint_J_J_001t__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J_001_062_It__Set__Oset_It__Int__Oint_J_M_Eo_J_001_062_It__Set__Oset_It__Int__Oint_J_M_Eo_J,type,
    bNF_re2751829829268647424_int_o: ( set_mat_int > set_ma1095064855528551128ring_a > $o ) > ( ( set_int > $o ) > ( set_int > $o ) > $o ) > ( set_mat_int > set_int > $o ) > ( set_ma1095064855528551128ring_a > set_int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Matrix__Omat_It__Int__Oint_J_J_001t__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J_001_062_It__Set__Oset_It__Matrix__Omat_It__Int__Oint_J_J_M_Eo_J_001_062_It__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J_M_Eo_J,type,
    bNF_re2479693389296218493ng_a_o: ( set_mat_int > set_ma1095064855528551128ring_a > $o ) > ( ( set_mat_int > $o ) > ( set_ma1095064855528551128ring_a > $o ) > $o ) > ( set_mat_int > set_mat_int > $o ) > ( set_ma1095064855528551128ring_a > set_ma1095064855528551128ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Matrix__Omat_It__Int__Oint_J_J_001t__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J_001_Eo_001_Eo,type,
    bNF_re4636312053285623616_a_o_o: ( set_mat_int > set_ma1095064855528551128ring_a > $o ) > ( $o > $o > $o ) > ( set_mat_int > $o ) > ( set_ma1095064855528551128ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Matrix__Omat_It__Int__Oint_J_J_001t__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J_001t__Int__Oint_001t__Int__Oint,type,
    bNF_re3929149045106647194nt_int: ( set_mat_int > set_ma1095064855528551128ring_a > $o ) > ( int > int > $o ) > ( set_mat_int > int ) > ( set_ma1095064855528551128ring_a > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J_001t__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_001_Eo_001_Eo,type,
    bNF_re8560914720294849314_a_o_o: ( set_ve6125835690772642148ring_a > set_Fi2982333969990053029ring_a > $o ) > ( $o > $o > $o ) > ( set_ve6125835690772642148ring_a > $o ) > ( set_Fi2982333969990053029ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J_001t__Set__Oset_It__Int__Oint_J_001_Eo_001_Eo,type,
    bNF_re6378887138790115109nt_o_o: ( set_ve6125835690772642148ring_a > set_int > $o ) > ( $o > $o > $o ) > ( set_ve6125835690772642148ring_a > $o ) > ( set_int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J_001t__Set__Oset_It__Nat__Onat_J_001_Eo_001_Eo,type,
    bNF_re5379533426889060553at_o_o: ( set_ve6125835690772642148ring_a > set_nat > $o ) > ( $o > $o > $o ) > ( set_ve6125835690772642148ring_a > $o ) > ( set_nat > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Matrix__Ovec_It__Int__Oint_J_J_001t__Set__Oset_It__Int__Oint_J_001_062_It__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J_M_Eo_J_001_062_It__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J,type,
    bNF_re8928381418866904901ng_a_o: ( set_vec_int > set_int > $o ) > ( ( set_ve6125835690772642148ring_a > $o ) > ( set_Fi2982333969990053029ring_a > $o ) > $o ) > ( set_vec_int > set_ve6125835690772642148ring_a > $o ) > ( set_int > set_Fi2982333969990053029ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Matrix__Ovec_It__Int__Oint_J_J_001t__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J_001_062_I_062_It__Matrix__Ovec_It__Int__Oint_J_M_Eo_J_M_Eo_J_001_062_I_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_M_Eo_J,type,
    bNF_re5888346141626434055_a_o_o: ( set_vec_int > set_ve6125835690772642148ring_a > $o ) > ( ( ( vec_int > $o ) > $o ) > ( ( vec_Fi4296597256376197294ring_a > $o ) > $o ) > $o ) > ( set_vec_int > ( vec_int > $o ) > $o ) > ( set_ve6125835690772642148ring_a > ( vec_Fi4296597256376197294ring_a > $o ) > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Matrix__Ovec_It__Int__Oint_J_J_001t__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    bNF_re5024843099796160128_int_o: ( set_vec_int > set_ve6125835690772642148ring_a > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( set_vec_int > int > $o ) > ( set_ve6125835690772642148ring_a > int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Matrix__Ovec_It__Int__Oint_J_J_001t__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J_001_062_It__Set__Oset_It__Int__Oint_J_M_Eo_J_001_062_It__Set__Oset_It__Int__Oint_J_M_Eo_J,type,
    bNF_re9008368033911170816_int_o: ( set_vec_int > set_ve6125835690772642148ring_a > $o ) > ( ( set_int > $o ) > ( set_int > $o ) > $o ) > ( set_vec_int > set_int > $o ) > ( set_ve6125835690772642148ring_a > set_int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Matrix__Ovec_It__Int__Oint_J_J_001t__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J_001_062_It__Set__Oset_It__Matrix__Ovec_It__Int__Oint_J_J_M_Eo_J_001_062_It__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J_M_Eo_J,type,
    bNF_re8227285363166532965ng_a_o: ( set_vec_int > set_ve6125835690772642148ring_a > $o ) > ( ( set_vec_int > $o ) > ( set_ve6125835690772642148ring_a > $o ) > $o ) > ( set_vec_int > set_vec_int > $o ) > ( set_ve6125835690772642148ring_a > set_ve6125835690772642148ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Matrix__Ovec_It__Int__Oint_J_J_001t__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J_001_Eo_001_Eo,type,
    bNF_re6384220461255839808_a_o_o: ( set_vec_int > set_ve6125835690772642148ring_a > $o ) > ( $o > $o > $o ) > ( set_vec_int > $o ) > ( set_ve6125835690772642148ring_a > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Matrix__Ovec_It__Int__Oint_J_J_001t__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J_001t__Int__Oint_001t__Int__Oint,type,
    bNF_re1646730027706931610nt_int: ( set_vec_int > set_ve6125835690772642148ring_a > $o ) > ( int > int > $o ) > ( set_vec_int > int ) > ( set_ve6125835690772642148ring_a > int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Matrix__Ovec_It__Int__Oint_J_J_001t__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bNF_re3213975434357579905ring_a: ( set_vec_int > set_ve6125835690772642148ring_a > $o ) > ( set_int > set_Fi2982333969990053029ring_a > $o ) > ( set_vec_int > set_int ) > ( set_ve6125835690772642148ring_a > set_Fi2982333969990053029ring_a ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Int__Oint_J_001_Eo_001_Eo,type,
    bNF_re6849929220912172615nt_o_o: ( set_nat > set_int > $o ) > ( $o > $o > $o ) > ( set_nat > $o ) > ( set_int > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Int__Oint_J,type,
    bNF_re949339946388637489et_int: ( set_nat > set_int > $o ) > ( set_nat > set_int > $o ) > ( set_nat > set_nat ) > ( set_int > set_int ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J_001_Eo_001_Eo,type,
    bNF_re5850575509011118059at_o_o: ( set_nat > set_nat > $o ) > ( $o > $o > $o ) > ( set_nat > $o ) > ( set_nat > $o ) > $o ).

thf(sy_c_BNF__Def_Orel__fun_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
    bNF_re3159760477010384505et_nat: ( set_nat > set_nat > $o ) > ( set_nat > set_nat > $o ) > ( set_nat > set_nat ) > ( set_nat > set_nat ) > $o ).

thf(sy_c_BNF__Def_Orel__set_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    bNF_re8564061778165475840_int_o: ( ( int > $o ) > ( int > $o ) > $o ) > set_int_o > set_int_o > $o ).

thf(sy_c_BNF__Def_Orel__set_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
    bNF_re6961201103365092784nt_int: ( ( int > int ) > ( int > int ) > $o ) > set_int_int > set_int_int > $o ).

thf(sy_c_BNF__Def_Orel__set_001_Eo_001_Eo,type,
    bNF_rel_set_o_o: ( $o > $o > $o ) > set_o > set_o > $o ).

thf(sy_c_BNF__Def_Orel__set_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    bNF_re3733049804732764288ring_a: ( finite_mod_ring_a > finite_mod_ring_a > $o ) > set_Fi2982333969990053029ring_a > set_Fi2982333969990053029ring_a > $o ).

thf(sy_c_BNF__Def_Orel__set_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Int__Oint,type,
    bNF_re1082135344409829809_a_int: ( finite_mod_ring_a > int > $o ) > set_Fi2982333969990053029ring_a > set_int > $o ).

thf(sy_c_BNF__Def_Orel__set_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bNF_re2777705279855501223ring_a: ( finite_mod_ring_a > mat_Fi443519135453058082ring_a > $o ) > set_Fi2982333969990053029ring_a > set_ma1095064855528551128ring_a > $o ).

thf(sy_c_BNF__Def_Orel__set_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bNF_re6630783400778640435ring_a: ( finite_mod_ring_a > vec_Fi4296597256376197294ring_a > $o ) > set_Fi2982333969990053029ring_a > set_ve6125835690772642148ring_a > $o ).

thf(sy_c_BNF__Def_Orel__set_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    bNF_re2658327337197749847ring_a: ( int > finite_mod_ring_a > $o ) > set_int > set_Fi2982333969990053029ring_a > $o ).

thf(sy_c_BNF__Def_Orel__set_001t__Int__Oint_001t__Int__Oint,type,
    bNF_rel_set_int_int: ( int > int > $o ) > set_int > set_int > $o ).

thf(sy_c_BNF__Def_Orel__set_001t__Int__Oint_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bNF_re356296649875183376ring_a: ( int > mat_Fi443519135453058082ring_a > $o ) > set_int > set_ma1095064855528551128ring_a > $o ).

thf(sy_c_BNF__Def_Orel__set_001t__Int__Oint_001t__Matrix__Omat_It__Int__Oint_J,type,
    bNF_re4529603996441892279at_int: ( int > mat_int > $o ) > set_int > set_mat_int > $o ).

thf(sy_c_BNF__Def_Orel__set_001t__Int__Oint_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bNF_re4209374770798322588ring_a: ( int > vec_Fi4296597256376197294ring_a > $o ) > set_int > set_ve6125835690772642148ring_a > $o ).

thf(sy_c_BNF__Def_Orel__set_001t__Int__Oint_001t__Matrix__Ovec_It__Int__Oint_J,type,
    bNF_re8016063337597145643ec_int: ( int > vec_int > $o ) > set_int > set_vec_int > $o ).

thf(sy_c_BNF__Def_Orel__set_001t__Int__Oint_001t__Nat__Onat,type,
    bNF_rel_set_int_nat: ( int > nat > $o ) > set_int > set_nat > $o ).

thf(sy_c_BNF__Def_Orel__set_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    bNF_re3095019897404434401ring_a: ( mat_Fi443519135453058082ring_a > finite_mod_ring_a > $o ) > set_ma1095064855528551128ring_a > set_Fi2982333969990053029ring_a > $o ).

thf(sy_c_BNF__Def_Orel__set_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Int__Oint,type,
    bNF_re4645510655262268176_a_int: ( mat_Fi443519135453058082ring_a > int > $o ) > set_ma1095064855528551128ring_a > set_int > $o ).

thf(sy_c_BNF__Def_Orel__set_001t__Matrix__Omat_It__Int__Oint_J_001t__Int__Oint,type,
    bNF_re3806336121531400593nt_int: ( mat_int > int > $o ) > set_mat_int > set_int > $o ).

thf(sy_c_BNF__Def_Orel__set_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bNF_re3622882117544951687ring_a: ( mat_int > mat_Fi443519135453058082ring_a > $o ) > set_mat_int > set_ma1095064855528551128ring_a > $o ).

thf(sy_c_BNF__Def_Orel__set_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    bNF_re4407951392657719893ring_a: ( vec_Fi4296597256376197294ring_a > finite_mod_ring_a > $o ) > set_ve6125835690772642148ring_a > set_Fi2982333969990053029ring_a > $o ).

thf(sy_c_BNF__Def_Orel__set_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Int__Oint,type,
    bNF_re5919053795459790748_a_int: ( vec_Fi4296597256376197294ring_a > int > $o ) > set_ve6125835690772642148ring_a > set_int > $o ).

thf(sy_c_BNF__Def_Orel__set_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Nat__Onat,type,
    bNF_re5921544265968841024_a_nat: ( vec_Fi4296597256376197294ring_a > nat > $o ) > set_ve6125835690772642148ring_a > set_nat > $o ).

thf(sy_c_BNF__Def_Orel__set_001t__Matrix__Ovec_It__Int__Oint_J_001t__Int__Oint,type,
    bNF_re2560616370357726725nt_int: ( vec_int > int > $o ) > set_vec_int > set_int > $o ).

thf(sy_c_BNF__Def_Orel__set_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bNF_re4691038805385103495ring_a: ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > set_vec_int > set_ve6125835690772642148ring_a > $o ).

thf(sy_c_BNF__Def_Orel__set_001t__Nat__Onat_001t__Int__Oint,type,
    bNF_rel_set_nat_int: ( nat > int > $o ) > set_nat > set_int > $o ).

thf(sy_c_BNF__Def_Orel__set_001t__Nat__Onat_001t__Nat__Onat,type,
    bNF_rel_set_nat_nat: ( nat > nat > $o ) > set_nat > set_nat > $o ).

thf(sy_c_Basic__BNFs_Opred__fun_001t__Int__Oint_001_062_It__Int__Oint_M_Eo_J,type,
    basic_1842322873297984402_int_o: ( int > $o ) > ( ( int > $o ) > $o ) > ( int > int > $o ) > $o ).

thf(sy_c_Basic__BNFs_Opred__fun_001t__Int__Oint_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
    basic_1535474925015357768nt_int: ( int > $o ) > ( ( int > int ) > $o ) > ( int > int > int ) > $o ).

thf(sy_c_Basic__BNFs_Opred__fun_001t__Int__Oint_001_Eo,type,
    basic_pred_fun_int_o: ( int > $o ) > ( $o > $o ) > ( int > $o ) > $o ).

thf(sy_c_Basic__BNFs_Opred__fun_001t__Int__Oint_001t__Int__Oint,type,
    basic_1840264447972274429nt_int: ( int > $o ) > ( int > $o ) > ( int > int ) > $o ).

thf(sy_c_Basic__BNFs_Opred__fun_001t__Int__Oint_001t__Nat__Onat,type,
    basic_1842754918481324705nt_nat: ( int > $o ) > ( nat > $o ) > ( int > nat ) > $o ).

thf(sy_c_Basic__BNFs_Opred__fun_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Int__Oint_J,type,
    basic_1649749791364877795at_int: ( mat_int > $o ) > ( mat_int > $o ) > ( mat_int > mat_int ) > $o ).

thf(sy_c_Basic__BNFs_Opred__fun_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Ovec_It__Int__Oint_J,type,
    basic_5136209132520131159ec_int: ( mat_int > $o ) > ( vec_int > $o ) > ( mat_int > vec_int ) > $o ).

thf(sy_c_Basic__BNFs_Opred__fun_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Omat_It__Int__Oint_J,type,
    basic_5242197913839372399at_int: ( vec_int > $o ) > ( mat_int > $o ) > ( vec_int > mat_int ) > $o ).

thf(sy_c_Basic__BNFs_Opred__fun_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Int__Oint_J,type,
    basic_8728657254994625763ec_int: ( vec_int > $o ) > ( vec_int > $o ) > ( vec_int > vec_int ) > $o ).

thf(sy_c_Finite__Field_Oof__int__mod__ring_001tf__a,type,
    finite8272632373135393572ring_a: int > finite_mod_ring_a ).

thf(sy_c_Finite__Field_Oto__int__mod__ring_001tf__a,type,
    finite1095367895020317408ring_a: finite_mod_ring_a > int ).

thf(sy_c_Finite__Set_Ofold_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Int__Oint,type,
    finite8560253868564812841_a_int: ( finite_mod_ring_a > int > int ) > int > set_Fi2982333969990053029ring_a > int ).

thf(sy_c_Finite__Set_Ofold_001t__Int__Oint_001t__Int__Oint,type,
    finite_fold_int_int: ( int > int > int ) > int > set_int > int ).

thf(sy_c_Finite__Set_Ofold_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Int__Oint,type,
    finite8667313987720946328_a_int: ( mat_Fi443519135453058082ring_a > int > int ) > int > set_ma1095064855528551128ring_a > int ).

thf(sy_c_Finite__Set_Ofold_001t__Matrix__Omat_It__Int__Oint_J_001t__Int__Oint,type,
    finite1284495836055560201nt_int: ( mat_int > int > int ) > int > set_mat_int > int ).

thf(sy_c_Finite__Set_Ofold_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Int__Oint,type,
    finite717485091063693092_a_int: ( vec_Fi4296597256376197294ring_a > int > int ) > int > set_ve6125835690772642148ring_a > int ).

thf(sy_c_Finite__Set_Ofold_001t__Matrix__Ovec_It__Int__Oint_J_001t__Int__Oint,type,
    finite38776084881886333nt_int: ( vec_int > int > int ) > int > set_vec_int > int ).

thf(sy_c_Finite__Set_Ofold__graph_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Int__Oint,type,
    finite3020906298370517803_a_int: ( finite_mod_ring_a > int > int ) > int > set_Fi2982333969990053029ring_a > int > $o ).

thf(sy_c_Finite__Set_Ofold__graph_001t__Int__Oint_001t__Int__Oint,type,
    finite2438261569651828512nt_int: ( int > int > int ) > int > set_int > int > $o ).

thf(sy_c_Finite__Set_Ofold__graph_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Int__Oint,type,
    finite4811128581409355030_a_int: ( mat_Fi443519135453058082ring_a > int > int ) > int > set_ma1095064855528551128ring_a > int > $o ).

thf(sy_c_Finite__Set_Ofold__graph_001t__Matrix__Omat_It__Int__Oint_J_001t__Int__Oint,type,
    finite970587359342566411nt_int: ( mat_int > int > int ) > int > set_mat_int > int > $o ).

thf(sy_c_Finite__Set_Ofold__graph_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Int__Oint,type,
    finite6084671721606877602_a_int: ( vec_Fi4296597256376197294ring_a > int > int ) > int > set_ve6125835690772642148ring_a > int > $o ).

thf(sy_c_Finite__Set_Ofold__graph_001t__Matrix__Ovec_It__Int__Oint_J_001t__Int__Oint,type,
    finite8948239645023668351nt_int: ( vec_int > int > int ) > int > set_vec_int > int > $o ).

thf(sy_c_Fun_Ofun__upd_001t__Int__Oint_001_062_It__Int__Oint_M_Eo_J,type,
    fun_upd_int_int_o: ( int > int > $o ) > int > ( int > $o ) > int > int > $o ).

thf(sy_c_Fun_Ofun__upd_001t__Int__Oint_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
    fun_upd_int_int_int: ( int > int > int ) > int > ( int > int ) > int > int > int ).

thf(sy_c_Fun_Ofun__upd_001t__Int__Oint_001_Eo,type,
    fun_upd_int_o: ( int > $o ) > int > $o > int > $o ).

thf(sy_c_Fun_Ofun__upd_001t__Int__Oint_001t__Int__Oint,type,
    fun_upd_int_int: ( int > int ) > int > int > int > int ).

thf(sy_c_Fun_Ofun__upd_001t__Int__Oint_001t__Nat__Onat,type,
    fun_upd_int_nat: ( int > nat ) > int > nat > int > nat ).

thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001_Eo_001t__Int__Oint_001_Eo,type,
    map_fun_int_o_int_o: ( int > $o ) > ( int > $o ) > ( $o > int ) > int > $o ).

thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001_Eo_001t__Int__Oint_001t__Int__Oint,type,
    map_fu4902815859698143790nt_int: ( int > $o ) > ( int > int ) > ( $o > int ) > int > int ).

thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001_Eo_001t__Int__Oint_001t__Nat__Onat,type,
    map_fu4905306330207194066nt_nat: ( int > $o ) > ( int > nat ) > ( $o > int ) > int > nat ).

thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Int__Oint_001_Eo_001_Eo,type,
    map_fun_int_int_o_o: ( int > int ) > ( $o > $o ) > ( int > $o ) > int > $o ).

thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Int__Oint_001_Eo_001t__Int__Oint,type,
    map_fu8246717858316148564_o_int: ( int > int ) > ( $o > int ) > ( int > $o ) > int > int ).

thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Int__Oint_001_Eo_001t__Nat__Onat,type,
    map_fu8249208328825198840_o_nat: ( int > int ) > ( $o > nat ) > ( int > $o ) > int > nat ).

thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001_Eo,type,
    map_fu2128507653078608342_nat_o: ( int > int ) > ( nat > $o ) > ( int > nat ) > int > $o ).

thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint_001_Eo,type,
    map_fu8844261311460145622_int_o: ( int > nat ) > ( int > $o ) > ( nat > int ) > int > $o ).

thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint_001t__Int__Oint,type,
    map_fu8108753754978010990nt_int: ( int > nat ) > ( int > int ) > ( nat > int ) > int > int ).

thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat,type,
    map_fu8111244225487061266nt_nat: ( int > nat ) > ( int > nat ) > ( nat > int ) > int > nat ).

thf(sy_c_Groups_Oabs__class_Oabs_001t__Int__Oint,type,
    abs_abs_int: int > int ).

thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal,type,
    abs_abs_real: real > real ).

thf(sy_c_Groups_Ominus__class_Ominus_001t__Int__Oint,type,
    minus_minus_int: int > int > int ).

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

thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal,type,
    minus_minus_real: real > real > real ).

thf(sy_c_Groups_Oone__class_Oone_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    one_on2109788427901206336ring_a: finite_mod_ring_a ).

thf(sy_c_Groups_Oone__class_Oone_001t__Int__Oint,type,
    one_one_int: int ).

thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
    one_one_nat: nat ).

thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal,type,
    one_one_real: real ).

thf(sy_c_Groups_Oplus__class_Oplus_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    plus_p6165643967897163644ring_a: finite_mod_ring_a > finite_mod_ring_a > finite_mod_ring_a ).

thf(sy_c_Groups_Oplus__class_Oplus_001t__Int__Oint,type,
    plus_plus_int: int > int > int ).

thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
    plus_plus_nat: nat > nat > nat ).

thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal,type,
    plus_plus_real: real > real > real ).

thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Int__Oint,type,
    uminus_uminus_int: int > int ).

thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Real__Oreal,type,
    uminus_uminus_real: real > real ).

thf(sy_c_Groups_Ozero__class_Ozero_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    zero_z7902377541816115708ring_a: finite_mod_ring_a ).

thf(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint,type,
    zero_zero_int: int ).

thf(sy_c_Groups_Ozero__class_Ozero_001t__Multiset__Omultiset_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    zero_z6254369252435687234ring_a: multis3731679216105815691ring_a ).

thf(sy_c_Groups_Ozero__class_Ozero_001t__Multiset__Omultiset_It__Int__Oint_J,type,
    zero_z3170743180189231877et_int: multiset_int ).

thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
    zero_zero_nat: nat ).

thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal,type,
    zero_zero_real: real ).

thf(sy_c_HOL_OEx1_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    ex1_Fi6469121982000959455ring_a: ( finite_mod_ring_a > $o ) > $o ).

thf(sy_c_HOL_OEx1_001t__Int__Oint,type,
    ex1_int: ( int > $o ) > $o ).

thf(sy_c_HOL_OEx1_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    ex1_ma5014816288738628488ring_a: ( mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_HOL_OEx1_001t__Matrix__Omat_It__Int__Oint_J,type,
    ex1_mat_int: ( mat_int > $o ) > $o ).

thf(sy_c_HOL_OEx1_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    ex1_ve8867894409661767700ring_a: ( vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_HOL_OEx1_001t__Matrix__Ovec_It__Int__Oint_J,type,
    ex1_vec_int: ( vec_int > $o ) > $o ).

thf(sy_c_If_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    if_Finite_mod_ring_a: $o > finite_mod_ring_a > finite_mod_ring_a > finite_mod_ring_a ).

thf(sy_c_If_001t__Int__Oint,type,
    if_int: $o > int > int > int ).

thf(sy_c_If_001t__Nat__Onat,type,
    if_nat: $o > nat > nat > nat ).

thf(sy_c_If_001t__Real__Oreal,type,
    if_real: $o > real > real > real ).

thf(sy_c_Int_Onat,type,
    nat2: int > nat ).

thf(sy_c_Int_Opower__int_001t__Real__Oreal,type,
    power_int_real: real > int > real ).

thf(sy_c_Int_Oring__1__class_Oof__int_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    ring_18169885480643366966ring_a: int > finite_mod_ring_a ).

thf(sy_c_Int_Oring__1__class_Oof__int_001t__Int__Oint,type,
    ring_1_of_int_int: int > int ).

thf(sy_c_Int_Oring__1__class_Oof__int_001t__Real__Oreal,type,
    ring_1_of_int_real: int > real ).

thf(sy_c_Matrix_Ocol_001t__Int__Oint,type,
    col_int: mat_int > nat > vec_int ).

thf(sy_c_Matrix_Odim__col_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    dim_co4406457559947111647ring_a: mat_Fi443519135453058082ring_a > nat ).

thf(sy_c_Matrix_Odim__col_001t__Int__Oint,type,
    dim_col_int: mat_int > nat ).

thf(sy_c_Matrix_Odim__row_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    dim_ro5001971067571046597ring_a: mat_Fi443519135453058082ring_a > nat ).

thf(sy_c_Matrix_Odim__row_001t__Int__Oint,type,
    dim_row_int: mat_int > nat ).

thf(sy_c_Matrix_Odim__vec_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    dim_ve9152325144110082507ring_a: vec_Fi4296597256376197294ring_a > nat ).

thf(sy_c_Matrix_Odim__vec_001t__Int__Oint,type,
    dim_vec_int: vec_int > nat ).

thf(sy_c_Matrix_Odim__vec_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    dim_ve3499172007441373852ring_a: vec_ma98051958688905615ring_a > nat ).

thf(sy_c_Matrix_Odim__vec_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    dim_ve7352250128364513064ring_a: vec_ve5128822793932996635ring_a > nat ).

thf(sy_c_Matrix_Odim__vec_001t__Nat__Onat,type,
    dim_vec_nat: vec_nat > nat ).

thf(sy_c_Matrix_Odim__vec_001t__Real__Oreal,type,
    dim_vec_real: vec_real > nat ).

thf(sy_c_Matrix_Odim__vec_001t__Set__Oset_It__Int__Oint_J,type,
    dim_vec_set_int: vec_set_int > nat ).

thf(sy_c_Matrix_Oelements__mat_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    elemen4395573691419627848ring_a: mat_Fi443519135453058082ring_a > set_Fi2982333969990053029ring_a ).

thf(sy_c_Matrix_Oelements__mat_001t__Int__Oint,type,
    elements_mat_int: mat_int > set_int ).

thf(sy_c_Matrix_Oelements__mat_001t__Nat__Onat,type,
    elements_mat_nat: mat_nat > set_nat ).

thf(sy_c_Matrix_Omap__mat_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Int__Oint,type,
    map_ma7999993494926133152_a_int: ( finite_mod_ring_a > int ) > mat_Fi443519135453058082ring_a > mat_int ).

thf(sy_c_Matrix_Omap__mat_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    map_ma352813450859277382ring_a: ( int > finite_mod_ring_a ) > mat_int > mat_Fi443519135453058082ring_a ).

thf(sy_c_Matrix_Omap__mat_001t__Int__Oint_001t__Int__Oint,type,
    map_mat_int_int: ( int > int ) > mat_int > mat_int ).

thf(sy_c_Matrix_Omap__mat_001t__Int__Oint_001t__Real__Oreal,type,
    map_mat_int_real: ( int > real ) > mat_int > mat_real ).

thf(sy_c_Matrix_Omap__mat_001t__Nat__Onat_001t__Nat__Onat,type,
    map_mat_nat_nat: ( nat > nat ) > mat_nat > mat_nat ).

thf(sy_c_Matrix_Omap__vec_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    map_ve1378714242357356997ring_a: ( finite_mod_ring_a > finite_mod_ring_a ) > vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a ).

thf(sy_c_Matrix_Omap__vec_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Int__Oint,type,
    map_ve50164598268879916_a_int: ( finite_mod_ring_a > int ) > vec_Fi4296597256376197294ring_a > vec_int ).

thf(sy_c_Matrix_Omap__vec_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    map_ve1626356591056799954ring_a: ( int > finite_mod_ring_a ) > vec_int > vec_Fi4296597256376197294ring_a ).

thf(sy_c_Matrix_Omap__vec_001t__Int__Oint_001t__Int__Oint,type,
    map_vec_int_int: ( int > int ) > vec_int > vec_int ).

thf(sy_c_Matrix_Omap__vec_001t__Int__Oint_001t__Nat__Onat,type,
    map_vec_int_nat: ( int > nat ) > vec_int > vec_nat ).

thf(sy_c_Matrix_Omap__vec_001t__Int__Oint_001t__Real__Oreal,type,
    map_vec_int_real: ( int > real ) > vec_int > vec_real ).

thf(sy_c_Matrix_Omap__vec_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    map_ve919107713008199260ring_a: ( mat_Fi443519135453058082ring_a > finite_mod_ring_a ) > vec_ma98051958688905615ring_a > vec_Fi4296597256376197294ring_a ).

thf(sy_c_Matrix_Omap__vec_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Int__Oint,type,
    map_ve6927845091123712213_a_int: ( mat_Fi443519135453058082ring_a > int ) > vec_ma98051958688905615ring_a > vec_int ).

thf(sy_c_Matrix_Omap__vec_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Nat__Onat,type,
    map_ve6930335561632762489_a_nat: ( mat_Fi443519135453058082ring_a > nat ) > vec_ma98051958688905615ring_a > vec_nat ).

thf(sy_c_Matrix_Omap__vec_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    map_ve2232039208261484752ring_a: ( vec_Fi4296597256376197294ring_a > finite_mod_ring_a ) > vec_ve5128822793932996635ring_a > vec_Fi4296597256376197294ring_a ).

thf(sy_c_Matrix_Omap__vec_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Int__Oint,type,
    map_ve8201388231321234785_a_int: ( vec_Fi4296597256376197294ring_a > int ) > vec_ve5128822793932996635ring_a > vec_int ).

thf(sy_c_Matrix_Omap__vec_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Nat__Onat,type,
    map_ve8203878701830285061_a_nat: ( vec_Fi4296597256376197294ring_a > nat ) > vec_ve5128822793932996635ring_a > vec_nat ).

thf(sy_c_Matrix_Omap__vec_001t__Nat__Onat_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    map_ve7015489527027549230ring_a: ( nat > finite_mod_ring_a ) > vec_nat > vec_Fi4296597256376197294ring_a ).

thf(sy_c_Matrix_Omap__vec_001t__Nat__Onat_001t__Int__Oint,type,
    map_vec_nat_int: ( nat > int ) > vec_nat > vec_int ).

thf(sy_c_Matrix_Omap__vec_001t__Nat__Onat_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    map_ve3499911149087114873ring_a: ( nat > mat_Fi443519135453058082ring_a ) > vec_nat > vec_ma98051958688905615ring_a ).

thf(sy_c_Matrix_Omap__vec_001t__Nat__Onat_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    map_ve7352989270010254085ring_a: ( nat > vec_Fi4296597256376197294ring_a ) > vec_nat > vec_ve5128822793932996635ring_a ).

thf(sy_c_Matrix_Omap__vec_001t__Nat__Onat_001t__Nat__Onat,type,
    map_vec_nat_nat: ( nat > nat ) > vec_nat > vec_nat ).

thf(sy_c_Matrix_Orow_001t__Int__Oint,type,
    row_int: mat_int > nat > vec_int ).

thf(sy_c_Matrix_Osmult__vec_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    smult_3577053051497313766ring_a: finite_mod_ring_a > vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a ).

thf(sy_c_Matrix_Osmult__vec_001t__Int__Oint,type,
    smult_vec_int: int > vec_int > vec_int ).

thf(sy_c_Matrix_Osmult__vec_001t__Nat__Onat,type,
    smult_vec_nat: nat > vec_nat > vec_nat ).

thf(sy_c_Matrix_Osmult__vec_001t__Real__Oreal,type,
    smult_vec_real: real > vec_real > vec_real ).

thf(sy_c_Matrix_Ounit__vec_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    unit_v6648808783362777473ring_a: nat > nat > vec_Fi4296597256376197294ring_a ).

thf(sy_c_Matrix_Ounit__vec_001t__Int__Oint,type,
    unit_vec_int: nat > nat > vec_int ).

thf(sy_c_Matrix_Ounit__vec_001t__Nat__Onat,type,
    unit_vec_nat: nat > nat > vec_nat ).

thf(sy_c_Matrix_Ounit__vec_001t__Real__Oreal,type,
    unit_vec_real: nat > nat > vec_real ).

thf(sy_c_Matrix_Oupdate__vec_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    update7295115471411923750ring_a: vec_Fi4296597256376197294ring_a > nat > finite_mod_ring_a > vec_Fi4296597256376197294ring_a ).

thf(sy_c_Matrix_Oupdate__vec_001t__Int__Oint,type,
    update_vec_int: vec_int > nat > int > vec_int ).

thf(sy_c_Matrix_Ovec__first_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    vec_fi8778413887660436251ring_a: vec_Fi4296597256376197294ring_a > nat > vec_Fi4296597256376197294ring_a ).

thf(sy_c_Matrix_Ovec__first_001t__Int__Oint,type,
    vec_first_int: vec_int > nat > vec_int ).

thf(sy_c_Matrix_Ovec__index_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    vec_in8573817152773094745ring_a: vec_Fi4296597256376197294ring_a > nat > finite_mod_ring_a ).

thf(sy_c_Matrix_Ovec__index_001t__Int__Oint,type,
    vec_index_int: vec_int > nat > int ).

thf(sy_c_Matrix_Ovec__index_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    vec_in2877697550313818510ring_a: vec_ma98051958688905615ring_a > nat > mat_Fi443519135453058082ring_a ).

thf(sy_c_Matrix_Ovec__index_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    vec_in6730775671236957722ring_a: vec_ve5128822793932996635ring_a > nat > vec_Fi4296597256376197294ring_a ).

thf(sy_c_Matrix_Ovec__index_001t__Nat__Onat,type,
    vec_index_nat: vec_nat > nat > nat ).

thf(sy_c_Matrix_Ovec__index_001t__Real__Oreal,type,
    vec_index_real: vec_real > nat > real ).

thf(sy_c_Matrix_Ovec__index_001t__Set__Oset_It__Int__Oint_J,type,
    vec_index_set_int: vec_set_int > nat > set_int ).

thf(sy_c_Matrix_Ovec__last_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    vec_la2893097508259760455ring_a: vec_Fi4296597256376197294ring_a > nat > vec_Fi4296597256376197294ring_a ).

thf(sy_c_Matrix_Ovec__last_001t__Int__Oint,type,
    vec_last_int: vec_int > nat > vec_int ).

thf(sy_c_Matrix_Ovec__set_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    vec_se7251946917745546697ring_a: vec_Fi4296597256376197294ring_a > set_Fi2982333969990053029ring_a ).

thf(sy_c_Matrix_Ovec__set_001t__Int__Oint,type,
    vec_set_int2: vec_int > set_int ).

thf(sy_c_Matrix_Ovec__set_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    vec_se8646415410842387742ring_a: vec_ma98051958688905615ring_a > set_ma1095064855528551128ring_a ).

thf(sy_c_Matrix_Ovec__set_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    vec_se3276121494910751146ring_a: vec_ve5128822793932996635ring_a > set_ve6125835690772642148ring_a ).

thf(sy_c_Matrix_Ovec__set_001t__Nat__Onat,type,
    vec_set_nat: vec_nat > set_nat ).

thf(sy_c_Matrix_Ovec__set_001t__Real__Oreal,type,
    vec_set_real: vec_real > set_real ).

thf(sy_c_Matrix_Ozero__vec_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    zero_v1122566495420860901ring_a: nat > vec_Fi4296597256376197294ring_a ).

thf(sy_c_Matrix_Ozero__vec_001t__Int__Oint,type,
    zero_vec_int: nat > vec_int ).

thf(sy_c_Matrix_Ozero__vec_001t__Nat__Onat,type,
    zero_vec_nat: nat > vec_nat ).

thf(sy_c_Matrix_Ozero__vec_001t__Real__Oreal,type,
    zero_vec_real: nat > vec_real ).

thf(sy_c_Matrix__Vector__Extras_Oall__ones__vec_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    matrix705363690926585579ring_a: nat > vec_Fi4296597256376197294ring_a ).

thf(sy_c_Matrix__Vector__Extras_Oall__ones__vec_001t__Int__Oint,type,
    matrix2748772424961467270ec_int: nat > vec_int ).

thf(sy_c_Matrix__Vector__Extras_Oall__ones__vec_001t__Nat__Onat,type,
    matrix2751262895470517546ec_nat: nat > vec_nat ).

thf(sy_c_Matrix__Vector__Extras_Oall__ones__vec_001t__Real__Oreal,type,
    matrix5166576126360777478c_real: nat > vec_real ).

thf(sy_c_Matrix__Vector__Extras_Oinjective__lim_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    matrix2095080385522958492ring_a: set_Fi2982333969990053029ring_a > ( finite_mod_ring_a > finite_mod_ring_a ) > $o ).

thf(sy_c_Matrix__Vector__Extras_Oinjective__lim_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Int__Oint,type,
    matrix1747488316349179541_a_int: set_Fi2982333969990053029ring_a > ( finite_mod_ring_a > int ) > $o ).

thf(sy_c_Matrix__Vector__Extras_Oinjective__lim_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    matrix3323680309137099579ring_a: set_int > ( int > finite_mod_ring_a ) > $o ).

thf(sy_c_Matrix__Vector__Extras_Oinjective__lim_001t__Int__Oint_001t__Int__Oint,type,
    matrix310325924459760438nt_int: set_int > ( int > int ) > $o ).

thf(sy_c_Matrix__Vector__Extras_Oinjective__lim_001t__Int__Oint_001t__Real__Oreal,type,
    matrix274465127151157942t_real: set_int > ( int > real ) > $o ).

thf(sy_c_Matrix__Vector__Extras_Oinjective__lim_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    matrix9152092669702307013ring_a: set_ma1095064855528551128ring_a > ( mat_Fi443519135453058082ring_a > finite_mod_ring_a ) > $o ).

thf(sy_c_Matrix__Vector__Extras_Oinjective__lim_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Int__Oint,type,
    matrix4639392970243543340_a_int: set_ma1095064855528551128ring_a > ( mat_Fi443519135453058082ring_a > int ) > $o ).

thf(sy_c_Matrix__Vector__Extras_Oinjective__lim_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    matrix1241652128100816697ring_a: set_ve6125835690772642148ring_a > ( vec_Fi4296597256376197294ring_a > finite_mod_ring_a ) > $o ).

thf(sy_c_Matrix__Vector__Extras_Oinjective__lim_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Int__Oint,type,
    matrix5912936110441065912_a_int: set_ve6125835690772642148ring_a > ( vec_Fi4296597256376197294ring_a > int ) > $o ).

thf(sy_c_Matrix__Vector__Extras_Oinjective__lim_001t__Nat__Onat_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    matrix8712813245107848855ring_a: set_nat > ( nat > finite_mod_ring_a ) > $o ).

thf(sy_c_Matrix__Vector__Extras_Oinjective__lim_001t__Nat__Onat_001t__Int__Oint,type,
    matrix8534344249413481690at_int: set_nat > ( nat > int ) > $o ).

thf(sy_c_Matrix__Vector__Extras_Olift__01__vec_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    matrix7517040601615355893ring_a: vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a ).

thf(sy_c_Matrix__Vector__Extras_Olift__01__vec_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Int__Oint,type,
    matrix8742746829526049276_a_int: vec_Fi4296597256376197294ring_a > vec_int ).

thf(sy_c_Matrix__Vector__Extras_Olift__01__vec_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    matrix1095566785459193506ring_a: vec_int > vec_Fi4296597256376197294ring_a ).

thf(sy_c_Matrix__Vector__Extras_Olift__01__vec_001t__Int__Oint_001t__Int__Oint,type,
    matrix8301520909418075407nt_int: vec_int > vec_int ).

thf(sy_c_Matrix__Vector__Extras_Ovec__mset_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    matrix5859482775909362318ring_a: vec_Fi4296597256376197294ring_a > multis3731679216105815691ring_a ).

thf(sy_c_Matrix__Vector__Extras_Ovec__mset_001t__Int__Oint,type,
    matrix7410472831921750563et_int: vec_int > multiset_int ).

thf(sy_c_Matrix__Vector__Extras_Ovec__mset_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    matrix8566872218577070105ring_a: vec_ma98051958688905615ring_a > multis5521929256021820786ring_a ).

thf(sy_c_Matrix__Vector__Extras_Ovec__mset_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    matrix3196578302645433509ring_a: vec_ve5128822793932996635ring_a > multis1329328054411135998ring_a ).

thf(sy_c_Matrix__Vector__Extras_Ovec__mset_001t__Nat__Onat,type,
    matrix7412963302430800839et_nat: vec_nat > multiset_nat ).

thf(sy_c_Matrix__Vector__Extras_Ovec__mset_001t__Real__Oreal,type,
    matrix1887623593855636259t_real: vec_real > multiset_real ).

thf(sy_c_Matrix__Vector__Extras_Ozero__neq__one__class_Oof__zero__neq__one_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    matrix6721843712216650060ring_a: finite_mod_ring_a > finite_mod_ring_a ).

thf(sy_c_Matrix__Vector__Extras_Ozero__neq__one__class_Oof__zero__neq__one_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Int__Oint,type,
    matrix2011149211968969189_a_int: finite_mod_ring_a > int ).

thf(sy_c_Matrix__Vector__Extras_Ozero__neq__one__class_Oof__zero__neq__one_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    matrix3587341204756889227ring_a: int > finite_mod_ring_a ).

thf(sy_c_Matrix__Vector__Extras_Ozero__neq__one__class_Oof__zero__neq__one_001t__Int__Oint_001t__Int__Oint,type,
    matrix1697308990001484774nt_int: int > int ).

thf(sy_c_Matrix__Vector__Extras_Ozero__neq__one__class_Oof__zero__neq__one_001t__Int__Oint_001t__Nat__Onat,type,
    matrix1699799460510535050nt_nat: int > nat ).

thf(sy_c_Matrix__Vector__Extras_Ozero__neq__one__class_Oof__zero__neq__one_001t__Int__Oint_001t__Real__Oreal,type,
    matrix1706393078865277798t_real: int > real ).

thf(sy_c_Matrix__Vector__Extras_Ozero__neq__one__class_Oof__zero__neq__one_001t__Nat__Onat_001t__Int__Oint,type,
    matrix697955278100430218at_int: nat > int ).

thf(sy_c_Matrix__Vector__Extras_Ozero__neq__one__class_Oof__zero__neq__one_001t__Nat__Onat_001t__Nat__Onat,type,
    matrix700445748609480494at_nat: nat > nat ).

thf(sy_c_Matrix__Vector__Extras_Ozero__neq__one__class_Oof__zero__neq__one_001t__Nat__Onat_001t__Real__Oreal,type,
    matrix8742843541027031818t_real: nat > real ).

thf(sy_c_Matrix__Vector__Extras_Ozero__neq__one__class_Oof__zero__neq__one_001t__Real__Oreal_001t__Int__Oint,type,
    matrix4084289606792104422al_int: real > int ).

thf(sy_c_Matrix__Vector__Extras_Ozero__neq__one__class_Oof__zero__neq__one_001t__Real__Oreal_001t__Nat__Onat,type,
    matrix4086780077301154698al_nat: real > nat ).

thf(sy_c_Matrix__Vector__Extras_Ozero__neq__one__class_Oof__zero__neq__one_001t__Real__Oreal_001t__Real__Oreal,type,
    matrix3070681271257819494l_real: real > real ).

thf(sy_c_Multiset_Oimage__mset_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    image_1006302053847055227ring_a: ( finite_mod_ring_a > finite_mod_ring_a ) > multis3731679216105815691ring_a > multis3731679216105815691ring_a ).

thf(sy_c_Multiset_Oimage__mset_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Int__Oint,type,
    image_7357852445201009398_a_int: ( finite_mod_ring_a > int ) > multis3731679216105815691ring_a > multiset_int ).

thf(sy_c_Multiset_Oimage__mset_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    image_8934044437988929436ring_a: ( int > finite_mod_ring_a ) > multiset_int > multis3731679216105815691ring_a ).

thf(sy_c_Multiset_Oimage__mset_001t__Int__Oint_001t__Int__Oint,type,
    image_mset_int_int: ( int > int ) > multiset_int > multiset_int ).

thf(sy_c_Multiset_Oimage__mset_001t__Int__Oint_001t__Real__Oreal,type,
    image_mset_int_real: ( int > real ) > multiset_int > multiset_real ).

thf(sy_c_Multiset_Omultiset_Ocount_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    count_7654011124160779523ring_a: multis3731679216105815691ring_a > finite_mod_ring_a > nat ).

thf(sy_c_Multiset_Omultiset_Ocount_001t__Int__Oint,type,
    count_int: multiset_int > int > nat ).

thf(sy_c_Multiset_Omultiset_Ocount_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    count_1800083599996238180ring_a: multis5521929256021820786ring_a > mat_Fi443519135453058082ring_a > nat ).

thf(sy_c_Multiset_Omultiset_Ocount_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    count_5653161720919377392ring_a: multis1329328054411135998ring_a > vec_Fi4296597256376197294ring_a > nat ).

thf(sy_c_Multiset_Omultiset_Ocount_001t__Nat__Onat,type,
    count_nat: multiset_nat > nat > nat ).

thf(sy_c_Multiset_Omultiset_Ocount_001t__Real__Oreal,type,
    count_real: multiset_real > real > nat ).

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

thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    neg_nu5901776551076858996ring_a: finite_mod_ring_a > finite_mod_ring_a ).

thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
    neg_nu5851722552734809277nc_int: int > int ).

thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
    neg_nu8295874005876285629c_real: real > real ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
    ord_less_int: int > int > $o ).

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

thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal,type,
    ord_less_real: real > real > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    ord_le826492772435143505ring_a: set_Fi2982333969990053029ring_a > set_Fi2982333969990053029ring_a > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Int__Oint_J,type,
    ord_less_set_int: set_int > set_int > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    ord_le8584791374048814380ring_a: set_ma1095064855528551128ring_a > set_ma1095064855528551128ring_a > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Matrix__Omat_It__Int__Oint_J_J,type,
    ord_less_set_mat_int: set_mat_int > set_mat_int > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    ord_le4392190172438129592ring_a: set_ve6125835690772642148ring_a > set_ve6125835690772642148ring_a > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Matrix__Ovec_It__Int__Oint_J_J,type,
    ord_less_set_vec_int: set_vec_int > set_vec_int > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_M_062_I_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_M_Eo_J_J,type,
    ord_le8512398041180637710nt_o_o: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > int > $o ) > ( int > int > $o ) > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_M_062_I_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J_J,type,
    ord_le25265541537557922_int_o: ( ( int > int > int ) > ( int > int > int ) > $o ) > ( ( int > int > int ) > ( int > int > int ) > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_062_It__Int__Oint_M_Eo_J_M_062_I_062_It__Int__Oint_M_Eo_J_M_Eo_J_J,type,
    ord_le9100565418538218190nt_o_o: ( ( int > $o ) > ( int > $o ) > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_I_062_It__Finite____Field__Omod____ring_Itf__a_J_Mt__Finite____Field__Omod____ring_Itf__a_J_J_M_Eo_J_J,type,
    ord_le4353216327012020490ng_a_o: ( ( int > int ) > ( finite_mod_ring_a > finite_mod_ring_a ) > $o ) > ( ( int > int ) > ( finite_mod_ring_a > finite_mod_ring_a ) > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_062_I_062_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
    ord_le5837993363827774264_int_o: ( ( int > int ) > ( int > int ) > $o ) > ( ( int > int ) > ( int > int ) > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_062_I_062_It__Int__Oint_Mt__Nat__Onat_J_M_Eo_J_J,type,
    ord_le7357923999124086768_nat_o: ( ( int > nat ) > ( int > nat ) > $o ) > ( ( int > nat ) > ( int > nat ) > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_062_It__Matrix__Omat_It__Int__Oint_J_Mt__Matrix__Omat_It__Int__Oint_J_J_M_062_I_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_Mt__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J_M_Eo_J_J,type,
    ord_le3697366711325567390ng_a_o: ( ( mat_int > mat_int ) > ( mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a ) > $o ) > ( ( mat_int > mat_int ) > ( mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a ) > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_M_062_I_Eo_M_Eo_J_J,type,
    ord_less_eq_o_o_o: ( $o > $o > $o ) > ( $o > $o > $o ) > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
    ord_le6741204236512500942_int_o: ( int > int > $o ) > ( int > int > $o ) > $o ).

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

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Int__Oint,type,
    ord_less_eq_int: int > int > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Matrix__Ovec_It__Int__Oint_J,type,
    ord_less_eq_vec_int: vec_int > vec_int > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Matrix__Ovec_It__Nat__Onat_J,type,
    ord_less_eq_vec_nat: vec_nat > vec_nat > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Matrix__Ovec_It__Real__Oreal_J,type,
    ord_less_eq_vec_real: vec_real > vec_real > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Matrix__Ovec_It__Set__Oset_It__Int__Oint_J_J,type,
    ord_le264858229241918703et_int: vec_set_int > vec_set_int > $o ).

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

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal,type,
    ord_less_eq_real: real > real > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    ord_le3976570047013626949ring_a: set_Fi2982333969990053029ring_a > set_Fi2982333969990053029ring_a > $o ).

thf(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 ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    ord_le9104675595724731192ring_a: set_ma1095064855528551128ring_a > set_ma1095064855528551128ring_a > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Matrix__Omat_It__Int__Oint_J_J,type,
    ord_le5299038897506728741at_int: set_mat_int > set_mat_int > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    ord_le4912074394114046404ring_a: set_ve6125835690772642148ring_a > set_ve6125835690772642148ring_a > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Matrix__Ovec_It__Int__Oint_J_J,type,
    ord_le5046699514128596377ec_int: set_vec_int > set_vec_int > $o ).

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

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    top_to2069866484006881781ring_a: set_Fi2982333969990053029ring_a ).

thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Int__Oint_J,type,
    top_top_set_int: set_int ).

thf(sy_c_Partial__Function_Ofun__ord_001_Eo_001_Eo_001t__Int__Oint,type,
    partia913349131986167100_o_int: ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ).

thf(sy_c_Partial__Function_Ofun__ord_001_Eo_001t__Int__Oint_001t__Int__Oint,type,
    partia5540654559940588002nt_int: ( $o > int > $o ) > ( int > $o ) > ( int > int ) > $o ).

thf(sy_c_Partial__Function_Ofun__ord_001_Eo_001t__Nat__Onat_001t__Int__Oint,type,
    partia4541300848039533446at_int: ( $o > nat > $o ) > ( int > $o ) > ( int > nat ) > $o ).

thf(sy_c_Partial__Function_Ofun__ord_001t__Int__Oint_001_Eo_001t__Int__Oint,type,
    partia8884556558558592776_o_int: ( int > $o > $o ) > ( int > int ) > ( int > $o ) > $o ).

thf(sy_c_Partial__Function_Ofun__ord_001t__Int__Oint_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    partia1478704387905588059ring_a: ( int > int > $o ) > ( finite_mod_ring_a > int ) > ( finite_mod_ring_a > int ) > $o ).

thf(sy_c_Partial__Function_Ofun__ord_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
    partia4528494827531477782nt_int: ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ).

thf(sy_c_Partial__Function_Ofun__ord_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
    partia3529141115630423226at_int: ( int > nat > $o ) > ( int > int ) > ( int > nat ) > $o ).

thf(sy_c_Partial__Function_Ofun__ord_001t__Nat__Onat_001_Eo_001t__Int__Oint,type,
    partia8197980525518042212_o_int: ( nat > $o > $o ) > ( int > nat ) > ( int > $o ) > $o ).

thf(sy_c_Partial__Function_Ofun__ord_001t__Nat__Onat_001t__Int__Oint_001t__Int__Oint,type,
    partia4156841267294633146nt_int: ( nat > int > $o ) > ( int > nat ) > ( int > int ) > $o ).

thf(sy_c_Partial__Function_Ofun__ord_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint,type,
    partia3157487555393578590at_int: ( nat > nat > $o ) > ( int > nat ) > ( int > nat ) > $o ).

thf(sy_c_Pure_Otype_001tf__a,type,
    type_a: itself_a ).

thf(sy_c_Relation_ODomainp_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
    domain8659272630029231332_int_o: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( int > int > $o ) > $o ).

thf(sy_c_Relation_ODomainp_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J,type,
    domain4136455042513400810nt_int: ( ( int > int > int ) > ( int > int > int ) > $o ) > ( int > int > int ) > $o ).

thf(sy_c_Relation_ODomainp_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    domainp_int_o_int_o: ( ( int > $o ) > ( int > $o ) > $o ) > ( int > $o ) > $o ).

thf(sy_c_Relation_ODomainp_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
    domain9219075885666169684nt_int: ( ( int > int ) > ( int > int ) > $o ) > ( int > int ) > $o ).

thf(sy_c_Relation_ODomainp_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
    domain7985844723471903900nt_nat: ( ( int > nat ) > ( int > nat ) > $o ) > ( int > nat ) > $o ).

thf(sy_c_Relation_ODomainp_001_062_It__Matrix__Omat_It__Int__Oint_J_Mt__Matrix__Omat_It__Int__Oint_J_J_001_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_Mt__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    domain6223798533483636846ring_a: ( ( mat_int > mat_int ) > ( mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a ) > $o ) > ( mat_int > mat_int ) > $o ).

thf(sy_c_Relation_ODomainp_001_062_It__Matrix__Omat_It__Int__Oint_J_Mt__Matrix__Ovec_It__Int__Oint_J_J_001_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_Mt__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    domain5159416631507321710ring_a: ( ( mat_int > vec_int ) > ( mat_Fi443519135453058082ring_a > vec_Fi4296597256376197294ring_a ) > $o ) > ( mat_int > vec_int ) > $o ).

thf(sy_c_Relation_ODomainp_001_062_It__Matrix__Ovec_It__Int__Oint_J_Mt__Matrix__Omat_It__Int__Oint_J_J_001_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_Mt__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    domain49596084258168198ring_a: ( ( vec_int > mat_int ) > ( vec_Fi4296597256376197294ring_a > mat_Fi443519135453058082ring_a ) > $o ) > ( vec_int > mat_int ) > $o ).

thf(sy_c_Relation_ODomainp_001_062_It__Matrix__Ovec_It__Int__Oint_J_Mt__Matrix__Ovec_It__Int__Oint_J_J_001_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_Mt__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    domain8208586219136628870ring_a: ( ( vec_int > vec_int ) > ( vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a ) > $o ) > ( vec_int > vec_int ) > $o ).

thf(sy_c_Relation_ODomainp_001_Eo_001_Eo,type,
    domainp_o_o: ( $o > $o > $o ) > $o > $o ).

thf(sy_c_Relation_ODomainp_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    domain6543890336852369843ring_a: ( int > finite_mod_ring_a > $o ) > int > $o ).

thf(sy_c_Relation_ODomainp_001t__Int__Oint_001t__Int__Oint,type,
    domainp_int_int: ( int > int > $o ) > int > $o ).

thf(sy_c_Relation_ODomainp_001t__Int__Oint_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    domain7289196465982206132ring_a: ( int > mat_Fi443519135453058082ring_a > $o ) > int > $o ).

thf(sy_c_Relation_ODomainp_001t__Int__Oint_001t__Matrix__Omat_It__Int__Oint_J,type,
    domainp_int_mat_int: ( int > mat_int > $o ) > int > $o ).

thf(sy_c_Relation_ODomainp_001t__Int__Oint_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    domain1918902550050569536ring_a: ( int > vec_Fi4296597256376197294ring_a > $o ) > int > $o ).

thf(sy_c_Relation_ODomainp_001t__Int__Oint_001t__Matrix__Ovec_It__Int__Oint_J,type,
    domainp_int_vec_int: ( int > vec_int > $o ) > int > $o ).

thf(sy_c_Relation_ODomainp_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    domain1820719717326966442ring_a: ( mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a > $o ) > mat_Fi443519135453058082ring_a > $o ).

thf(sy_c_Relation_ODomainp_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    domain2947197372085612771ring_a: ( mat_int > mat_Fi443519135453058082ring_a > $o ) > mat_int > $o ).

thf(sy_c_Relation_ODomainp_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Int__Oint_J,type,
    domain6199964394958696996at_int: ( mat_int > mat_int > $o ) > mat_int > $o ).

thf(sy_c_Relation_ODomainp_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    domain3984477134522034114ring_a: ( vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a > $o ) > vec_Fi4296597256376197294ring_a > $o ).

thf(sy_c_Relation_ODomainp_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    domain4015354059925764579ring_a: ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > vec_int > $o ).

thf(sy_c_Relation_ODomainp_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Int__Oint_J,type,
    domain4055499821733669156ec_int: ( vec_int > vec_int > $o ) > vec_int > $o ).

thf(sy_c_Relation_ODomainp_001t__Nat__Onat_001t__Nat__Onat,type,
    domainp_nat_nat: ( nat > nat > $o ) > nat > $o ).

thf(sy_c_Relation_Orelcompp_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
    relcom6387603338664227389_int_o: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( ( int > int > $o ) > ( int > int > $o ) > $o ) > ( int > int > $o ) > ( int > int > $o ) > $o ).

thf(sy_c_Relation_Orelcompp_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J,type,
    relcom6240993501255406585nt_int: ( ( int > int > int ) > ( int > int > int ) > $o ) > ( ( int > int > int ) > ( int > int > int ) > $o ) > ( int > int > int ) > ( int > int > int ) > $o ).

thf(sy_c_Relation_Orelcompp_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    relcom989163212620591602_int_o: ( ( int > $o ) > ( int > $o ) > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( int > $o ) > ( int > $o ) > $o ).

thf(sy_c_Relation_Orelcompp_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Finite____Field__Omod____ring_Itf__a_J_Mt__Finite____Field__Omod____ring_Itf__a_J_J,type,
    relcom3368137050767642310ring_a: ( ( int > int ) > ( int > int ) > $o ) > ( ( int > int ) > ( finite_mod_ring_a > finite_mod_ring_a ) > $o ) > ( int > int ) > ( finite_mod_ring_a > finite_mod_ring_a ) > $o ).

thf(sy_c_Relation_Orelcompp_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
    relcom1106299141546538648nt_int: ( ( int > int ) > ( int > int ) > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( int > int ) > ( int > int ) > $o ).

thf(sy_c_Relation_Orelcompp_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
    relcom4622340022947818372nt_nat: ( ( int > nat ) > ( int > nat ) > $o ) > ( ( int > nat ) > ( int > nat ) > $o ) > ( int > nat ) > ( int > nat ) > $o ).

thf(sy_c_Relation_Orelcompp_001_062_It__Matrix__Omat_It__Int__Oint_J_Mt__Matrix__Omat_It__Int__Oint_J_J_001_062_It__Matrix__Omat_It__Int__Oint_J_Mt__Matrix__Omat_It__Int__Oint_J_J_001_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_Mt__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    relcom6302253411340485088ring_a: ( ( mat_int > mat_int ) > ( mat_int > mat_int ) > $o ) > ( ( mat_int > mat_int ) > ( mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a ) > $o ) > ( mat_int > mat_int ) > ( mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a ) > $o ).

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

thf(sy_c_Relation_Orelcompp_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    relcom3932653789432222877ring_a: ( int > finite_mod_ring_a > $o ) > ( finite_mod_ring_a > finite_mod_ring_a > $o ) > int > finite_mod_ring_a > $o ).

thf(sy_c_Relation_Orelcompp_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Int__Oint,type,
    relcom1383171076355693396_a_int: ( int > finite_mod_ring_a > $o ) > ( finite_mod_ring_a > int > $o ) > int > int > $o ).

thf(sy_c_Relation_Orelcompp_001t__Int__Oint_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    relcom2959363069143613434ring_a: ( int > int > $o ) > ( int > finite_mod_ring_a > $o ) > int > finite_mod_ring_a > $o ).

thf(sy_c_Relation_Orelcompp_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
    relcompp_int_int_int: ( int > int > $o ) > ( int > int > $o ) > int > int > $o ).

thf(sy_c_Relation_Orelcompp_001t__Int__Oint_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Int__Oint,type,
    relcom4976855403015346093_a_int: ( int > mat_Fi443519135453058082ring_a > $o ) > ( mat_Fi443519135453058082ring_a > int > $o ) > int > int > $o ).

thf(sy_c_Relation_Orelcompp_001t__Int__Oint_001t__Matrix__Omat_It__Int__Oint_J_001t__Int__Oint,type,
    relcom4445084879353389748nt_int: ( int > mat_int > $o ) > ( mat_int > int > $o ) > int > int > $o ).

thf(sy_c_Relation_Orelcompp_001t__Int__Oint_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Int__Oint,type,
    relcom6250398543212868665_a_int: ( int > vec_Fi4296597256376197294ring_a > $o ) > ( vec_Fi4296597256376197294ring_a > int > $o ) > int > int > $o ).

thf(sy_c_Relation_Orelcompp_001t__Int__Oint_001t__Matrix__Ovec_It__Int__Oint_J_001t__Int__Oint,type,
    relcom3199365128179715880nt_int: ( int > vec_int > $o ) > ( vec_int > int > $o ) > int > int > $o ).

thf(sy_c_Relation_Orelcompp_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    relcom3823866671404279418ring_a: ( mat_int > mat_Fi443519135453058082ring_a > $o ) > ( mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a > $o ) > mat_int > mat_Fi443519135453058082ring_a > $o ).

thf(sy_c_Relation_Orelcompp_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    relcom6459136143736567059ring_a: ( mat_int > mat_int > $o ) > ( mat_int > mat_Fi443519135453058082ring_a > $o ) > mat_int > mat_Fi443519135453058082ring_a > $o ).

thf(sy_c_Relation_Orelcompp_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    relcom6459548400941628422ring_a: ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > ( vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a > $o ) > vec_int > vec_Fi4296597256376197294ring_a > $o ).

thf(sy_c_Relation_Orelcompp_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    relcom5279651581461346463ring_a: ( vec_int > vec_int > $o ) > ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > vec_int > vec_Fi4296597256376197294ring_a > $o ).

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

thf(sy_c_Ring__Hom_Oinj__zero__hom_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    ring_i7582611058579704515ring_a: ( finite_mod_ring_a > finite_mod_ring_a ) > $o ).

thf(sy_c_Ring__Hom_Oinj__zero__hom_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Int__Oint,type,
    ring_i3475985505635201454_a_int: ( finite_mod_ring_a > int ) > $o ).

thf(sy_c_Ring__Hom_Oinj__zero__hom_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    ring_i5052177498423121492ring_a: ( int > finite_mod_ring_a ) > $o ).

thf(sy_c_Ring__Hom_Oinj__zero__hom_001t__Int__Oint_001t__Int__Oint,type,
    ring_i7091729277519141597nt_int: ( int > int ) > $o ).

thf(sy_c_Ring__Hom_Oinj__zero__hom_001t__Int__Oint_001t__Real__Oreal,type,
    ring_i2058719125409607389t_real: ( int > real ) > $o ).

thf(sy_c_Ring__Hom_Oinj__zero__hom_001t__Nat__Onat_001t__Nat__Onat,type,
    ring_i6094866036127137317at_nat: ( nat > nat ) > $o ).

thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Int__Oint,type,
    modulo_modulo_int: int > int > int ).

thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Nat__Onat,type,
    modulo_modulo_nat: nat > nat > nat ).

thf(sy_c_Set_OBex_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    bex_Fi4430655179489311525ring_a: set_Fi2982333969990053029ring_a > ( finite_mod_ring_a > $o ) > $o ).

thf(sy_c_Set_OBex_001t__Int__Oint,type,
    bex_int: set_int > ( int > $o ) > $o ).

thf(sy_c_Set_OBex_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bex_ma3740078314013414594ring_a: set_ma1095064855528551128ring_a > ( mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_Set_OBex_001t__Matrix__Omat_It__Int__Oint_J,type,
    bex_mat_int: set_mat_int > ( mat_int > $o ) > $o ).

thf(sy_c_Set_OBex_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bex_ve7593156434936553806ring_a: set_ve6125835690772642148ring_a > ( vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_Set_OBex_001t__Matrix__Ovec_It__Int__Oint_J,type,
    bex_vec_int: set_vec_int > ( vec_int > $o ) > $o ).

thf(sy_c_Set_OCollect_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    collec4943914941012508720ring_a: ( finite_mod_ring_a > $o ) > set_Fi2982333969990053029ring_a ).

thf(sy_c_Set_OCollect_001t__Int__Oint,type,
    collect_int: ( int > $o ) > set_int ).

thf(sy_c_Set_OCollect_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    collec1508142899102036983ring_a: ( mat_Fi443519135453058082ring_a > $o ) > set_ma1095064855528551128ring_a ).

thf(sy_c_Set_OCollect_001t__Matrix__Omat_It__Int__Oint_J,type,
    collect_mat_int: ( mat_int > $o ) > set_mat_int ).

thf(sy_c_Set_OCollect_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    collec5361221020025176195ring_a: ( vec_Fi4296597256376197294ring_a > $o ) > set_ve6125835690772642148ring_a ).

thf(sy_c_Set_OCollect_001t__Matrix__Ovec_It__Int__Oint_J,type,
    collect_vec_int: ( vec_int > $o ) > set_vec_int ).

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

thf(sy_c_Set_Oimage_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    image_3815122860822722885ring_a: ( finite_mod_ring_a > finite_mod_ring_a ) > set_Fi2982333969990053029ring_a > set_Fi2982333969990053029ring_a ).

thf(sy_c_Set_Oimage_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Int__Oint,type,
    image_4238506139956901036_a_int: ( finite_mod_ring_a > int ) > set_Fi2982333969990053029ring_a > set_int ).

thf(sy_c_Set_Oimage_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    image_3083460890917301922ring_a: ( finite_mod_ring_a > mat_Fi443519135453058082ring_a ) > set_Fi2982333969990053029ring_a > set_ma1095064855528551128ring_a ).

thf(sy_c_Set_Oimage_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    image_6936539011840441134ring_a: ( finite_mod_ring_a > vec_Fi4296597256376197294ring_a ) > set_Fi2982333969990053029ring_a > set_ve6125835690772642148ring_a ).

thf(sy_c_Set_Oimage_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Nat__Onat,type,
    image_4240996610465951312_a_nat: ( finite_mod_ring_a > nat ) > set_Fi2982333969990053029ring_a > set_nat ).

thf(sy_c_Set_Oimage_001t__Int__Oint_001_062_It__Int__Oint_M_Eo_J,type,
    image_int_int_o: ( int > int > $o ) > set_int > set_int_o ).

thf(sy_c_Set_Oimage_001t__Int__Oint_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
    image_int_int_int: ( int > int > int ) > set_int > set_int_int ).

thf(sy_c_Set_Oimage_001t__Int__Oint_001_Eo,type,
    image_int_o: ( int > $o ) > set_int > set_o ).

thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    image_5814698132744821074ring_a: ( int > finite_mod_ring_a ) > set_int > set_Fi2982333969990053029ring_a ).

thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Int__Oint,type,
    image_int_int: ( int > int ) > set_int > set_int ).

thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Nat__Onat,type,
    image_int_nat: ( int > nat ) > set_int > set_nat ).

thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Real__Oreal,type,
    image_int_real: ( int > real ) > set_int > set_real ).

thf(sy_c_Set_Oimage_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    image_4713707003719520592ring_a: ( vec_Fi4296597256376197294ring_a > finite_mod_ring_a ) > set_ve6125835690772642148ring_a > set_Fi2982333969990053029ring_a ).

thf(sy_c_Set_Oimage_001t__Matrix__Ovec_It__Int__Oint_J_001t__Int__Oint,type,
    image_vec_int_int: ( vec_int > int ) > set_vec_int > set_int ).

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

thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Int__Oint,type,
    set_or4662586982721622107an_int: int > int > set_int ).

thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
    arcosh_real: real > real ).

thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
    arsinh_real: real > real ).

thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
    artanh_real: real > real ).

thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
    ln_ln_real: real > real ).

thf(sy_c_Transfer_Obi__total_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
    bi_tot1998502909289846182_int_o: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > $o ).

thf(sy_c_Transfer_Obi__total_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J,type,
    bi_tot1340478029960895404nt_int: ( ( int > int > int ) > ( int > int > int ) > $o ) > $o ).

thf(sy_c_Transfer_Obi__total_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    bi_total_int_o_int_o: ( ( int > $o ) > ( int > $o ) > $o ) > $o ).

thf(sy_c_Transfer_Obi__total_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
    bi_tot5031271806440829206nt_int: ( ( int > int ) > ( int > int ) > $o ) > $o ).

thf(sy_c_Transfer_Obi__total_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
    bi_tot3798040644246563422nt_nat: ( ( int > nat ) > ( int > nat ) > $o ) > $o ).

thf(sy_c_Transfer_Obi__total_001_Eo_001_Eo,type,
    bi_total_o_o: ( $o > $o > $o ) > $o ).

thf(sy_c_Transfer_Obi__total_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    bi_tot8261576339290982118ring_a: ( finite_mod_ring_a > finite_mod_ring_a > $o ) > $o ).

thf(sy_c_Transfer_Obi__total_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    bi_tot623839499179674737ring_a: ( int > finite_mod_ring_a > $o ) > $o ).

thf(sy_c_Transfer_Obi__total_001t__Int__Oint_001t__Int__Oint,type,
    bi_total_int_int: ( int > int > $o ) > $o ).

thf(sy_c_Transfer_Obi__total_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bi_tot2476251792769102444ring_a: ( mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_Transfer_Obi__total_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bi_tot6329329913692241656ring_a: ( mat_Fi443519135453058082ring_a > vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_Transfer_Obi__total_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bi_tot8466079176331800225ring_a: ( mat_int > mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_Transfer_Obi__total_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Int__Oint_J,type,
    bi_tot9202309660982637286at_int: ( mat_int > mat_int > $o ) > $o ).

thf(sy_c_Transfer_Obi__total_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bi_tot786931089041030904ring_a: ( vec_Fi4296597256376197294ring_a > mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_Transfer_Obi__total_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bi_tot4640009209964170116ring_a: ( vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_Transfer_Obi__total_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bi_tot310863827317176225ring_a: ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_Transfer_Obi__total_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Int__Oint_J,type,
    bi_tot7057845087757609446ec_int: ( vec_int > vec_int > $o ) > $o ).

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

thf(sy_c_Transfer_Obi__total_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bi_tot3373772818509728539ring_a: ( set_int > set_Fi2982333969990053029ring_a > $o ) > $o ).

thf(sy_c_Transfer_Obi__total_001t__Set__Oset_It__Matrix__Omat_It__Int__Oint_J_J_001t__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    bi_tot9056204718002498231ring_a: ( set_mat_int > set_ma1095064855528551128ring_a > $o ) > $o ).

thf(sy_c_Transfer_Obi__total_001t__Set__Oset_It__Matrix__Ovec_It__Int__Oint_J_J_001t__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    bi_tot3615525640256922551ring_a: ( set_vec_int > set_ve6125835690772642148ring_a > $o ) > $o ).

thf(sy_c_Transfer_Obi__unique_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
    bi_uni2203252027619187855_int_o: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > $o ).

thf(sy_c_Transfer_Obi__unique_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J,type,
    bi_uni6056933463453604373nt_int: ( ( int > int > int ) > ( int > int > int ) > $o ) > $o ).

thf(sy_c_Transfer_Obi__unique_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    bi_uni6923270185593731663_int_o: ( ( int > $o ) > ( int > $o ) > $o ) > $o ).

thf(sy_c_Transfer_Obi__unique_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
    bi_uni5275641640356057727nt_int: ( ( int > int ) > ( int > int ) > $o ) > $o ).

thf(sy_c_Transfer_Obi__unique_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
    bi_uni4042410478161791943nt_nat: ( ( int > nat ) > ( int > nat ) > $o ) > $o ).

thf(sy_c_Transfer_Obi__unique_001_Eo_001_Eo,type,
    bi_unique_o_o: ( $o > $o > $o ) > $o ).

thf(sy_c_Transfer_Obi__unique_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    bi_uni1022671006909063496ring_a: ( int > finite_mod_ring_a > $o ) > $o ).

thf(sy_c_Transfer_Obi__unique_001t__Int__Oint_001t__Int__Oint,type,
    bi_unique_int_int: ( int > int > $o ) > $o ).

thf(sy_c_Transfer_Obi__unique_001t__Int__Oint_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bi_uni89026028227921119ring_a: ( int > mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_Transfer_Obi__unique_001t__Int__Oint_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bi_uni3942104149151060331ring_a: ( int > vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_Transfer_Obi__unique_001t__Int__Oint_001t__Nat__Onat,type,
    bi_unique_int_nat: ( int > nat > $o ) > $o ).

thf(sy_c_Transfer_Obi__unique_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Int__Oint,type,
    bi_uni4378240033615005919_a_int: ( mat_Fi443519135453058082ring_a > int > $o ) > $o ).

thf(sy_c_Transfer_Obi__unique_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bi_uni8710310146129975544ring_a: ( mat_int > mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_Transfer_Obi__unique_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Int__Oint_J,type,
    bi_uni3915055660617466319at_int: ( mat_int > mat_int > $o ) > $o ).

thf(sy_c_Transfer_Obi__unique_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Int__Oint,type,
    bi_uni5651783173812528491_a_int: ( vec_Fi4296597256376197294ring_a > int > $o ) > $o ).

thf(sy_c_Transfer_Obi__unique_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Nat__Onat,type,
    bi_uni5654273644321578767_a_nat: ( vec_Fi4296597256376197294ring_a > nat > $o ) > $o ).

thf(sy_c_Transfer_Obi__unique_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    bi_uni555094797115351544ring_a: ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_Transfer_Obi__unique_001t__Nat__Onat_001t__Int__Oint,type,
    bi_unique_nat_int: ( nat > int > $o ) > $o ).

thf(sy_c_Transfer_Obi__unique_001t__Nat__Onat_001t__Nat__Onat,type,
    bi_unique_nat_nat: ( nat > nat > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
    left_t5677053946549264806_int_o: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J,type,
    left_t6143790711152109484nt_int: ( ( int > int > int ) > ( int > int > int ) > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    left_t5625308128979377254_int_o: ( ( int > $o ) > ( int > $o ) > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
    left_t6821225679139634454nt_int: ( ( int > int ) > ( int > int ) > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
    left_t5587994516945368670nt_nat: ( ( int > nat ) > ( int > nat ) > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001_Eo_001_Eo,type,
    left_total_o_o: ( $o > $o > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    left_t5999478950615061222ring_a: ( finite_mod_ring_a > finite_mod_ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Int__Oint,type,
    left_t7365413154463734731_a_int: ( finite_mod_ring_a > int > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    left_t3675020542146961857ring_a: ( finite_mod_ring_a > mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    left_t7528098663070101069ring_a: ( finite_mod_ring_a > vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    left_t8941605147251654769ring_a: ( int > finite_mod_ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001t__Int__Oint_001t__Int__Oint,type,
    left_total_int_int: ( int > int > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001t__Int__Oint_001t__Matrix__Omat_It__Int__Oint_J,type,
    left_t1248818525112758481at_int: ( int > mat_int > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001t__Int__Oint_001t__Matrix__Ovec_It__Int__Oint_J,type,
    left_t4735277866268011845ec_int: ( int > vec_int > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    left_t3992335159695895035ring_a: ( mat_Fi443519135453058082ring_a > finite_mod_ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Int__Oint,type,
    left_t1770473636134370422_a_int: ( mat_Fi443519135453058082ring_a > int > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    left_t737000093472603756ring_a: ( mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001t__Matrix__Omat_It__Int__Oint_J_001t__Int__Oint,type,
    left_t525550650202266795nt_int: ( mat_int > int > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    left_t6774590509652353697ring_a: ( mat_int > mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Int__Oint_J,type,
    left_t7186104474549747430at_int: ( mat_int > mat_int > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    left_t5305266654949180527ring_a: ( vec_Fi4296597256376197294ring_a > finite_mod_ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Int__Oint,type,
    left_t3044016776331892994_a_int: ( vec_Fi4296597256376197294ring_a > int > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    left_t2900757510667671428ring_a: ( vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001t__Matrix__Ovec_It__Int__Oint_J_001t__Int__Oint,type,
    left_t8503202935883368735nt_int: ( vec_int > int > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    left_t7842747197492505505ring_a: ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Int__Oint_J,type,
    left_t5041639901324719590ec_int: ( vec_int > vec_int > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001t__Nat__Onat_001t__Nat__Onat,type,
    left_total_nat_nat: ( nat > nat > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    left_t2970111942549241627ring_a: ( set_int > set_Fi2982333969990053029ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001t__Set__Oset_It__Matrix__Omat_It__Int__Oint_J_J_001t__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    left_t5538224795450760887ring_a: ( set_mat_int > set_ma1095064855528551128ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oleft__total_001t__Set__Oset_It__Matrix__Ovec_It__Int__Oint_J_J_001t__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    left_t97545717705185207ring_a: ( set_vec_int > set_ve6125835690772642148ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
    left_u390144976722038927_int_o: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J,type,
    left_u506611856200109589nt_int: ( ( int > int > int ) > ( int > int > int ) > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    left_u4522144268380204623_int_o: ( ( int > $o ) > ( int > $o ) > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
    left_u1710335611130709631nt_int: ( ( int > int ) > ( int > int ) > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
    left_u477104448936443847nt_nat: ( ( int > nat ) > ( int > nat ) > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001_Eo_001_Eo,type,
    left_unique_o_o: ( $o > $o > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    left_u4083587041413029071ring_a: ( finite_mod_ring_a > finite_mod_ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Int__Oint,type,
    left_u312270633112012962_a_int: ( finite_mod_ring_a > int > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    left_u8689944590835972760ring_a: ( finite_mod_ring_a > mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    left_u3319650674904336164ring_a: ( finite_mod_ring_a > vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    left_u1888462625899933000ring_a: ( int > finite_mod_ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001t__Int__Oint_001t__Int__Oint,type,
    left_unique_int_int: ( int > int > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001t__Int__Oint_001t__Matrix__Omat_It__Int__Oint_J,type,
    left_u1167430374829049640at_int: ( int > mat_int > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001t__Int__Oint_001t__Matrix__Ovec_It__Int__Oint_J,type,
    left_u4653889715984303004ec_int: ( int > vec_int > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    left_u9007259208384905938ring_a: ( mat_Fi443519135453058082ring_a > finite_mod_ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Int__Oint,type,
    left_u5090820168553544927_a_int: ( mat_Fi443519135453058082ring_a > int > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001t__Matrix__Omat_It__Int__Oint_J_001t__Int__Oint,type,
    left_u444162499918557954nt_int: ( mat_int > int > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    left_u5910868004070155512ring_a: ( mat_int > mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Int__Oint_J,type,
    left_u6026039346960889295at_int: ( mat_int > mat_int > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    left_u1096818666783415622ring_a: ( vec_Fi4296597256376197294ring_a > finite_mod_ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Int__Oint,type,
    left_u6364363308751067499_a_int: ( vec_Fi4296597256376197294ring_a > int > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    left_u1556899868652710893ring_a: ( vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001t__Matrix__Ovec_It__Int__Oint_J_001t__Int__Oint,type,
    left_u8421814785599659894nt_int: ( vec_int > int > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    left_u6979024691910307320ring_a: ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Int__Oint_J,type,
    left_u3881574773735861455ec_int: ( vec_int > vec_int > $o ) > $o ).

thf(sy_c_Transfer_Oleft__unique_001t__Nat__Onat_001t__Nat__Onat,type,
    left_unique_nat_nat: ( nat > nat > $o ) > $o ).

thf(sy_c_Transfer_Orev__implies,type,
    rev_implies: $o > $o > $o ).

thf(sy_c_Transfer_Oright__total_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
    right_3701678689365064351_int_o: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J,type,
    right_4144311589897252901nt_int: ( ( int > int > int ) > ( int > int > int ) > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    right_3358435141589207135_int_o: ( ( int > $o ) > ( int > $o ) > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
    right_2214481324298164367nt_int: ( ( int > int ) > ( int > int ) > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
    right_981250162103898583nt_nat: ( ( int > nat ) > ( int > nat ) > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001_062_It__Matrix__Omat_It__Int__Oint_J_Mt__Int__Oint_J_001_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_Mt__Finite____Field__Omod____ring_Itf__a_J_J,type,
    right_8513789441842825527ring_a: ( ( mat_int > int ) > ( mat_Fi443519135453058082ring_a > finite_mod_ring_a ) > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001_062_It__Matrix__Omat_It__Int__Oint_J_Mt__Matrix__Ovec_It__Int__Oint_J_J_001_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_Mt__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    right_7147911083355635753ring_a: ( ( mat_int > vec_int ) > ( mat_Fi443519135453058082ring_a > vec_Fi4296597256376197294ring_a ) > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001_062_It__Matrix__Ovec_It__Int__Oint_J_Mt__Int__Oint_J_001_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_Mt__Finite____Field__Omod____ring_Itf__a_J_J,type,
    right_3178293095284162103ring_a: ( ( vec_int > int ) > ( vec_Fi4296597256376197294ring_a > finite_mod_ring_a ) > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001_062_It__Matrix__Ovec_It__Int__Oint_J_Mt__Matrix__Omat_It__Int__Oint_J_J_001_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_Mt__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    right_2038090536106482241ring_a: ( ( vec_int > mat_int ) > ( vec_Fi4296597256376197294ring_a > mat_Fi443519135453058082ring_a ) > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001_062_It__Matrix__Ovec_It__Int__Oint_J_Mt__Matrix__Ovec_It__Int__Oint_J_J_001_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_Mt__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    right_973708634130167105ring_a: ( ( vec_int > vec_int ) > ( vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a ) > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001_Eo_001_Eo,type,
    right_total_o_o: ( $o > $o > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    right_301602178578872031ring_a: ( finite_mod_ring_a > finite_mod_ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Int__Oint,type,
    right_1332816507441248914_a_int: ( finite_mod_ring_a > int > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    right_5872932815158258824ring_a: ( finite_mod_ring_a > mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    right_502638899226622228ring_a: ( finite_mod_ring_a > vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    right_2909008500229168952ring_a: ( int > finite_mod_ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001t__Int__Oint_001t__Int__Oint,type,
    right_total_int_int: ( int > int > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001t__Int__Oint_001t__Matrix__Omat_It__Int__Oint_J,type,
    right_639950172037058840at_int: ( int > mat_int > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001t__Int__Oint_001t__Matrix__Ovec_It__Int__Oint_J,type,
    right_4126409513192312204ec_int: ( int > vec_int > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    right_6190247432707192002ring_a: ( mat_Fi443519135453058082ring_a > finite_mod_ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Int__Oint,type,
    right_8315819795955908335_a_int: ( mat_Fi443519135453058082ring_a > int > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    right_1306295718943872229ring_a: ( mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001t__Matrix__Omat_It__Int__Oint_J_001t__Int__Oint,type,
    right_9140054333981342962nt_int: ( mat_int > int > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    right_6272992325622558440ring_a: ( mat_int > mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Int__Oint_J,type,
    right_3817508881141293023at_int: ( mat_int > mat_int > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    right_7503178927960477494ring_a: ( vec_Fi4296597256376197294ring_a > finite_mod_ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Int__Oint,type,
    right_365990899298655099_a_int: ( vec_Fi4296597256376197294ring_a > int > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    right_3470053136138939901ring_a: ( vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001t__Matrix__Ovec_It__Int__Oint_J_001t__Int__Oint,type,
    right_7894334582807669094nt_int: ( vec_int > int > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    right_7341149013462710248ring_a: ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Int__Oint_J,type,
    right_1673044307916265183ec_int: ( vec_int > vec_int > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001t__Nat__Onat_001t__Nat__Onat,type,
    right_total_nat_nat: ( nat > nat > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    right_8012789954965988834ring_a: ( set_int > set_Fi2982333969990053029ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001t__Set__Oset_It__Matrix__Omat_It__Int__Oint_J_J_001t__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    right_8378705835506627326ring_a: ( set_mat_int > set_ma1095064855528551128ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oright__total_001t__Set__Oset_It__Matrix__Ovec_It__Int__Oint_J_J_001t__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    right_2938026757761051646ring_a: ( set_vec_int > set_ve6125835690772642148ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
    right_6125766759956493782_int_o: ( ( int > int > $o ) > ( int > int > $o ) > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_M_062_It__Int__Oint_Mt__Int__Oint_J_J,type,
    right_2249472770629886940nt_int: ( ( int > int > int ) > ( int > int > int ) > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
    right_8348394670160920726_int_o: ( ( int > $o ) > ( int > $o ) > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
    right_7672189912263821638nt_int: ( ( int > int ) > ( int > int ) > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001_062_It__Int__Oint_Mt__Matrix__Omat_It__Int__Oint_J_J_001_062_It__Finite____Field__Omod____ring_Itf__a_J_Mt__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    right_6181665041646683774ring_a: ( ( int > mat_int ) > ( finite_mod_ring_a > mat_Fi443519135453058082ring_a ) > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001_062_It__Int__Oint_Mt__Matrix__Ovec_It__Int__Oint_J_J_001_062_It__Finite____Field__Omod____ring_Itf__a_J_Mt__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    right_4404654753817203094ring_a: ( ( int > vec_int ) > ( finite_mod_ring_a > vec_Fi4296597256376197294ring_a ) > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001_062_It__Int__Oint_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
    right_6438958750069555854nt_nat: ( ( int > nat ) > ( int > nat ) > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001_062_It__Matrix__Omat_It__Int__Oint_J_Mt__Matrix__Ovec_It__Int__Oint_J_J_001_062_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_Mt__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    right_4915445335281487456ring_a: ( ( mat_int > vec_int ) > ( mat_Fi443519135453058082ring_a > vec_Fi4296597256376197294ring_a ) > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001_062_It__Matrix__Ovec_It__Int__Oint_J_Mt__Matrix__Omat_It__Int__Oint_J_J_001_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_Mt__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    right_9028996824887109752ring_a: ( ( vec_int > mat_int ) > ( vec_Fi4296597256376197294ring_a > mat_Fi443519135453058082ring_a ) > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001_062_It__Matrix__Ovec_It__Int__Oint_J_Mt__Matrix__Ovec_It__Int__Oint_J_J_001_062_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_Mt__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    right_7964614922910794616ring_a: ( ( vec_int > vec_int ) > ( vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a ) > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001_Eo_001_Eo,type,
    right_unique_o_o: ( $o > $o > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    right_6217011779227907862ring_a: ( finite_mod_ring_a > finite_mod_ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Int__Oint,type,
    right_6005435896075721627_a_int: ( finite_mod_ring_a > int > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    right_562089708195504529ring_a: ( finite_mod_ring_a > mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001t__Finite____Field__Omod____ring_Itf__a_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    right_4415167829118643741ring_a: ( finite_mod_ring_a > vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001t__Int__Oint_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    right_7581627888863641665ring_a: ( int > finite_mod_ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001t__Int__Oint_001t__Int__Oint,type,
    right_unique_int_int: ( int > int > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001t__Int__Oint_001t__Matrix__Omat_It__Int__Oint_J,type,
    right_6436628580042324129at_int: ( int > mat_int > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001t__Int__Oint_001t__Matrix__Ovec_It__Int__Oint_J,type,
    right_699715884342801685ec_int: ( int > vec_int > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    right_879404325744437707ring_a: ( mat_Fi443519135453058082ring_a > finite_mod_ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Int__Oint,type,
    right_6838498638095685798_a_int: ( mat_Fi443519135453058082ring_a > int > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    right_8406872553065732764ring_a: ( mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001t__Matrix__Omat_It__Int__Oint_J_001t__Int__Oint,type,
    right_5713360705131832443nt_int: ( mat_int > int > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    right_1339649294516398705ring_a: ( mat_int > mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001t__Matrix__Omat_It__Int__Oint_J_001t__Matrix__Omat_It__Int__Oint_J,type,
    right_3070966312479052566at_int: ( mat_int > mat_int > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    right_2192335820997723199ring_a: ( vec_Fi4296597256376197294ring_a > finite_mod_ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Int__Oint,type,
    right_8112041778293208370_a_int: ( vec_Fi4296597256376197294ring_a > int > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    right_1347257933406024628ring_a: ( vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001t__Matrix__Ovec_It__Int__Oint_J_001t__Int__Oint,type,
    right_4467640953958158575nt_int: ( vec_int > int > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    right_2407805982356550513ring_a: ( vec_int > vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001t__Matrix__Ovec_It__Int__Oint_J_001t__Matrix__Ovec_It__Int__Oint_J,type,
    right_926501739254024726ec_int: ( vec_int > vec_int > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001t__Nat__Onat_001t__Nat__Onat,type,
    right_unique_nat_nat: ( nat > nat > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    right_8649055584691732203ring_a: ( set_int > set_Fi2982333969990053029ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001t__Set__Oset_It__Matrix__Omat_It__Int__Oint_J_J_001t__Set__Oset_It__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    right_1737936343352010375ring_a: ( set_mat_int > set_ma1095064855528551128ring_a > $o ) > $o ).

thf(sy_c_Transfer_Oright__unique_001t__Set__Oset_It__Matrix__Ovec_It__Int__Oint_J_J_001t__Set__Oset_It__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J_J,type,
    right_5520629302461210503ring_a: ( set_vec_int > set_ve6125835690772642148ring_a > $o ) > $o ).

thf(sy_c_Transfer_Otransfer__bforall_001t__Int__Oint,type,
    transfer_bforall_int: ( int > $o ) > ( int > $o ) > $o ).

thf(sy_c_Transfer_Otransfer__bforall_001t__Matrix__Omat_It__Int__Oint_J,type,
    transf2144751673828113484at_int: ( mat_int > $o ) > ( mat_int > $o ) > $o ).

thf(sy_c_Transfer_Otransfer__bforall_001t__Matrix__Ovec_It__Int__Oint_J,type,
    transf5631211014983366848ec_int: ( vec_int > $o ) > ( vec_int > $o ) > $o ).

thf(sy_c_Transfer_Otransfer__forall_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    transf2422954704962549770ring_a: ( finite_mod_ring_a > $o ) > $o ).

thf(sy_c_Transfer_Otransfer__forall_001t__Int__Oint,type,
    transfer_forall_int: ( int > $o ) > $o ).

thf(sy_c_Transfer_Otransfer__forall_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    transf5512653654505236381ring_a: ( mat_Fi443519135453058082ring_a > $o ) > $o ).

thf(sy_c_Transfer_Otransfer__forall_001t__Matrix__Omat_It__Int__Oint_J,type,
    transf2444112438564689642at_int: ( mat_int > $o ) > $o ).

thf(sy_c_Transfer_Otransfer__forall_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    transf142359738573599785ring_a: ( vec_Fi4296597256376197294ring_a > $o ) > $o ).

thf(sy_c_Transfer_Otransfer__forall_001t__Matrix__Ovec_It__Int__Oint_J,type,
    transf5930571779719943006ec_int: ( vec_int > $o ) > $o ).

thf(sy_c_Transitive__Closure_Ortranclp_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    transi6237637440696766096ring_a: ( finite_mod_ring_a > finite_mod_ring_a > $o ) > finite_mod_ring_a > finite_mod_ring_a > $o ).

thf(sy_c_Transitive__Closure_Ortranclp_001t__Int__Oint,type,
    transi5419909967800184737lp_int: ( int > int > $o ) > int > int > $o ).

thf(sy_c_Transitive__Closure_Ortranclp_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    transi7406368010997804439ring_a: ( mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a > $o ) > mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a > $o ).

thf(sy_c_Transitive__Closure_Ortranclp_001t__Matrix__Omat_It__Int__Oint_J,type,
    transi3090561174025329776at_int: ( mat_int > mat_int > $o ) > mat_int > mat_int > $o ).

thf(sy_c_Transitive__Closure_Ortranclp_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    transi2036074095066167843ring_a: ( vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a > $o ) > vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a > $o ).

thf(sy_c_Transitive__Closure_Ortranclp_001t__Matrix__Ovec_It__Int__Oint_J,type,
    transi6577020515180583140ec_int: ( vec_int > vec_int > $o ) > vec_int > vec_int > $o ).

thf(sy_c_Vector__Matrix__Mod_Omat__mod,type,
    vector2311527483241216340at_mod: int > $o ).

thf(sy_c_Vector__Matrix__Mod_Omat__mod_Omat__mod,type,
    vector6118640873655855782at_mod: int > mat_int > mat_int ).

thf(sy_c_Vector__Matrix__Mod_Omat__mod_Ovec__mod,type,
    vector1199560857299316530ec_mod: int > vec_int > vec_int ).

thf(sy_c_Vector__Matrix__Mod_Omat__mod__type_001tf__a,type,
    vector2974885785920725647type_a: itself_a > int > $o ).

thf(sy_c_Vector__Matrix__Mod_Omat__mod__type_OMM__Rel_001tf__a,type,
    vector2798151085771547010_Rel_a: int > mat_int > mat_Fi443519135453058082ring_a > $o ).

thf(sy_c_Vector__Matrix__Mod_Omat__mod__type_OMV__Rel_001tf__a,type,
    vector5230790432342831627_Rel_a: int > vec_int > vec_Fi4296597256376197294ring_a > $o ).

thf(sy_c_Vector__Matrix__Mod_Omod__type_001tf__a,type,
    vector4745807456731380595type_a: itself_a > int > $o ).

thf(sy_c_Vector__Matrix__Mod_Omod__type_OM,type,
    vector_Matrix_mod_M: int > int > int ).

thf(sy_c_Vector__Matrix__Mod_Omod__type_OM__Rel_001tf__a,type,
    vector3024231343486012919_Rel_a: int > int > finite_mod_ring_a > $o ).

thf(sy_c_Vector__Matrix__Mod_Omod__type_Oinv__M,type,
    vector2349909385534816566_inv_M: int > int > int ).

thf(sy_c_member_001_062_It__Int__Oint_M_Eo_J,type,
    member_int_o: ( int > $o ) > set_int_o > $o ).

thf(sy_c_member_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
    member_int_int: ( int > int ) > set_int_int > $o ).

thf(sy_c_member_001t__Finite____Field__Omod____ring_Itf__a_J,type,
    member3034048621153491438ring_a: finite_mod_ring_a > set_Fi2982333969990053029ring_a > $o ).

thf(sy_c_member_001t__Int__Oint,type,
    member_int: int > set_int > $o ).

thf(sy_c_member_001t__Matrix__Omat_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    member6477060778965647545ring_a: mat_Fi443519135453058082ring_a > set_ma1095064855528551128ring_a > $o ).

thf(sy_c_member_001t__Matrix__Omat_It__Int__Oint_J,type,
    member_mat_int: mat_int > set_mat_int > $o ).

thf(sy_c_member_001t__Matrix__Ovec_It__Finite____Field__Omod____ring_Itf__a_J_J,type,
    member1106766863034010949ring_a: vec_Fi4296597256376197294ring_a > set_ve6125835690772642148ring_a > $o ).

thf(sy_c_member_001t__Matrix__Ovec_It__Int__Oint_J,type,
    member_vec_int: vec_int > set_vec_int > $o ).

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

thf(sy_v_m,type,
    m: int ).

% Relevant facts (1274)
thf(fact_0_vec__mod__to__int__vec,axiom,
    ! [V: vec_Fi4296597256376197294ring_a] :
      ( ( vector1199560857299316530ec_mod @ m @ ( map_ve50164598268879916_a_int @ finite1095367895020317408ring_a @ V ) )
      = ( map_ve50164598268879916_a_int @ finite1095367895020317408ring_a @ V ) ) ).

% vec_mod_to_int_vec
thf(fact_1_mat__mod_Ovec__mod_Ocong,axiom,
    vector1199560857299316530ec_mod = vector1199560857299316530ec_mod ).

% mat_mod.vec_mod.cong
thf(fact_2_to__int__mod__ring__hom_Ovec__hom__inj,axiom,
    ! [V: vec_Fi4296597256376197294ring_a,W: vec_Fi4296597256376197294ring_a] :
      ( ( ( map_ve50164598268879916_a_int @ finite1095367895020317408ring_a @ V )
        = ( map_ve50164598268879916_a_int @ finite1095367895020317408ring_a @ W ) )
     => ( V = W ) ) ).

% to_int_mod_ring_hom.vec_hom_inj
thf(fact_3_MV__Rel__def,axiom,
    ! [V: vec_int,V2: vec_Fi4296597256376197294ring_a] :
      ( ( vector5230790432342831627_Rel_a @ m @ V @ V2 )
      = ( ( vector1199560857299316530ec_mod @ m @ V )
        = ( map_ve50164598268879916_a_int @ finite1095367895020317408ring_a @ V2 ) ) ) ).

% MV_Rel_def
thf(fact_4_vec__mod__unit,axiom,
    ! [N: nat,I: nat] :
      ( ( vector1199560857299316530ec_mod @ m @ ( unit_vec_int @ N @ I ) )
      = ( unit_vec_int @ N @ I ) ) ).

% vec_mod_unit
thf(fact_5_to__int__mod__ring__hom_Oeq__iff,axiom,
    ! [X: finite_mod_ring_a,Y: finite_mod_ring_a] :
      ( ( ( finite1095367895020317408ring_a @ X )
        = ( finite1095367895020317408ring_a @ Y ) )
      = ( X = Y ) ) ).

% to_int_mod_ring_hom.eq_iff
thf(fact_6_mod__to__int__mod__ring,axiom,
    ! [X: finite_mod_ring_a] :
      ( ( modulo_modulo_int @ ( finite1095367895020317408ring_a @ X ) @ m )
      = ( finite1095367895020317408ring_a @ X ) ) ).

% mod_to_int_mod_ring
thf(fact_7_M__to__int__mod__ring,axiom,
    ! [X: finite_mod_ring_a] :
      ( ( vector_Matrix_mod_M @ m @ ( finite1095367895020317408ring_a @ X ) )
      = ( finite1095367895020317408ring_a @ X ) ) ).

% M_to_int_mod_ring
thf(fact_8_mat__mod__axioms,axiom,
    vector2311527483241216340at_mod @ m ).

% mat_mod_axioms
thf(fact_9_vec__mod__zero,axiom,
    ! [N: nat] :
      ( ( vector1199560857299316530ec_mod @ m @ ( zero_vec_int @ N ) )
      = ( zero_vec_int @ N ) ) ).

% vec_mod_zero
thf(fact_10_vec__mod__v__representative,axiom,
    ! [V: vec_int] :
      ( ( vector1199560857299316530ec_mod @ m @ V )
      = ( map_ve50164598268879916_a_int @ finite1095367895020317408ring_a @ ( map_ve1626356591056799954ring_a @ ring_18169885480643366966ring_a @ V ) ) ) ).

% vec_mod_v_representative
thf(fact_11_to__int__mod__ring__hom_Oinjectivity,axiom,
    ! [X: finite_mod_ring_a,Y: finite_mod_ring_a] :
      ( ( ( finite1095367895020317408ring_a @ X )
        = ( finite1095367895020317408ring_a @ Y ) )
     => ( X = Y ) ) ).

% to_int_mod_ring_hom.injectivity
thf(fact_12_vec__mod__dim,axiom,
    ! [V: vec_int] :
      ( ( dim_vec_int @ ( vector1199560857299316530ec_mod @ m @ V ) )
      = ( dim_vec_int @ V ) ) ).

% vec_mod_dim
thf(fact_13_inj__zero__hom_Ovec__hom__mset,axiom,
    ! [Hom: int > int,V: vec_int] :
      ( ( ring_i7091729277519141597nt_int @ Hom )
     => ( ( image_mset_int_int @ Hom @ ( matrix7410472831921750563et_int @ V ) )
        = ( matrix7410472831921750563et_int @ ( map_vec_int_int @ Hom @ V ) ) ) ) ).

% inj_zero_hom.vec_hom_mset
thf(fact_14_inj__zero__hom_Ovec__hom__mset,axiom,
    ! [Hom: int > finite_mod_ring_a,V: vec_int] :
      ( ( ring_i5052177498423121492ring_a @ Hom )
     => ( ( image_8934044437988929436ring_a @ Hom @ ( matrix7410472831921750563et_int @ V ) )
        = ( matrix5859482775909362318ring_a @ ( map_ve1626356591056799954ring_a @ Hom @ V ) ) ) ) ).

% inj_zero_hom.vec_hom_mset
thf(fact_15_inj__zero__hom_Ovec__hom__mset,axiom,
    ! [Hom: finite_mod_ring_a > int,V: vec_Fi4296597256376197294ring_a] :
      ( ( ring_i3475985505635201454_a_int @ Hom )
     => ( ( image_7357852445201009398_a_int @ Hom @ ( matrix5859482775909362318ring_a @ V ) )
        = ( matrix7410472831921750563et_int @ ( map_ve50164598268879916_a_int @ Hom @ V ) ) ) ) ).

% inj_zero_hom.vec_hom_mset
thf(fact_16_inj__zero__hom_Ovec__hom__mset,axiom,
    ! [Hom: finite_mod_ring_a > finite_mod_ring_a,V: vec_Fi4296597256376197294ring_a] :
      ( ( ring_i7582611058579704515ring_a @ Hom )
     => ( ( image_1006302053847055227ring_a @ Hom @ ( matrix5859482775909362318ring_a @ V ) )
        = ( matrix5859482775909362318ring_a @ ( map_ve1378714242357356997ring_a @ Hom @ V ) ) ) ) ).

% inj_zero_hom.vec_hom_mset
thf(fact_17_M__Rel__def,axiom,
    ! [X: int,X2: finite_mod_ring_a] :
      ( ( vector3024231343486012919_Rel_a @ m @ X @ X2 )
      = ( ( vector_Matrix_mod_M @ m @ X )
        = ( finite1095367895020317408ring_a @ X2 ) ) ) ).

% M_Rel_def
thf(fact_18_M__def,axiom,
    ! [X: int] :
      ( ( vector_Matrix_mod_M @ m @ X )
      = ( modulo_modulo_int @ X @ m ) ) ).

% M_def
thf(fact_19_Matrix__Vector__Extras_Oof__int__hom_Oeq__iff,axiom,
    ! [X: int,Univ: set_int,Y: int] :
      ( ( member_int @ X @ Univ )
     => ( ( member_int @ Y @ Univ )
       => ( ( ( ring_1_of_int_real @ X )
            = ( ring_1_of_int_real @ Y ) )
          = ( X = Y ) ) ) ) ).

% Matrix_Vector_Extras.of_int_hom.eq_iff
thf(fact_20_to__int__mod__ring__of__int__mod,axiom,
    ! [X: int] :
      ( ( finite1095367895020317408ring_a @ ( ring_18169885480643366966ring_a @ X ) )
      = ( modulo_modulo_int @ X @ m ) ) ).

% to_int_mod_ring_of_int_mod
thf(fact_21_to__int__mod__ring__of__int__M,axiom,
    ! [X: int] :
      ( ( finite1095367895020317408ring_a @ ( ring_18169885480643366966ring_a @ X ) )
      = ( vector_Matrix_mod_M @ m @ X ) ) ).

% to_int_mod_ring_of_int_M
thf(fact_22_M__M,axiom,
    ! [X: int] :
      ( ( vector_Matrix_mod_M @ m @ ( vector_Matrix_mod_M @ m @ X ) )
      = ( vector_Matrix_mod_M @ m @ X ) ) ).

% M_M
thf(fact_23_Matrix__Vector__Extras_Oof__int__hom_Ovec__hom__zero__iff,axiom,
    ! [X: vec_int,N: nat] :
      ( ( ( map_vec_int_int @ ring_1_of_int_int @ X )
        = ( zero_vec_int @ N ) )
      = ( X
        = ( zero_vec_int @ N ) ) ) ).

% Matrix_Vector_Extras.of_int_hom.vec_hom_zero_iff
thf(fact_24_Matrix__Vector__Extras_Oof__int__hom_Ovec__hom__zero__iff,axiom,
    ! [X: vec_int,N: nat] :
      ( ( ( map_vec_int_real @ ring_1_of_int_real @ X )
        = ( zero_vec_real @ N ) )
      = ( X
        = ( zero_vec_int @ N ) ) ) ).

% Matrix_Vector_Extras.of_int_hom.vec_hom_zero_iff
thf(fact_25_mod__type_OM_Ocong,axiom,
    vector_Matrix_mod_M = vector_Matrix_mod_M ).

% mod_type.M.cong
thf(fact_26_mat__mod__type_OMV__Rel_Ocong,axiom,
    vector5230790432342831627_Rel_a = vector5230790432342831627_Rel_a ).

% mat_mod_type.MV_Rel.cong
thf(fact_27_Matrix__Vector__Extras_Oof__int__hom_Ovec__hom__inj,axiom,
    ! [V: vec_int,W: vec_int] :
      ( ( ( map_vec_int_int @ ring_1_of_int_int @ V )
        = ( map_vec_int_int @ ring_1_of_int_int @ W ) )
     => ( V = W ) ) ).

% Matrix_Vector_Extras.of_int_hom.vec_hom_inj
thf(fact_28_Matrix__Vector__Extras_Oof__int__hom_Ovec__hom__inj,axiom,
    ! [V: vec_int,W: vec_int] :
      ( ( ( map_vec_int_real @ ring_1_of_int_real @ V )
        = ( map_vec_int_real @ ring_1_of_int_real @ W ) )
     => ( V = W ) ) ).

% Matrix_Vector_Extras.of_int_hom.vec_hom_inj
thf(fact_29_of__int__hom_Oinjectivity__lim,axiom,
    ! [X: int,Univ: set_int,Y: int] :
      ( ( member_int @ X @ Univ )
     => ( ( member_int @ Y @ Univ )
       => ( ( ( ring_1_of_int_real @ X )
            = ( ring_1_of_int_real @ Y ) )
         => ( X = Y ) ) ) ) ).

% of_int_hom.injectivity_lim
thf(fact_30_Matrix__Vector__Extras_Oinj__zero__hom_Ovec__hom__zero__iff,axiom,
    ! [Hom: int > int,X: vec_int,N: nat] :
      ( ( ring_i7091729277519141597nt_int @ Hom )
     => ( ( ( map_vec_int_int @ Hom @ X )
          = ( zero_vec_int @ N ) )
        = ( X
          = ( zero_vec_int @ N ) ) ) ) ).

% Matrix_Vector_Extras.inj_zero_hom.vec_hom_zero_iff
thf(fact_31_Matrix__Vector__Extras_Oinj__zero__hom_Ovec__hom__zero__iff,axiom,
    ! [Hom: finite_mod_ring_a > int,X: vec_Fi4296597256376197294ring_a,N: nat] :
      ( ( ring_i3475985505635201454_a_int @ Hom )
     => ( ( ( map_ve50164598268879916_a_int @ Hom @ X )
          = ( zero_vec_int @ N ) )
        = ( X
          = ( zero_v1122566495420860901ring_a @ N ) ) ) ) ).

% Matrix_Vector_Extras.inj_zero_hom.vec_hom_zero_iff
thf(fact_32_Matrix__Vector__Extras_Oinj__zero__hom_Ovec__hom__zero__iff,axiom,
    ! [Hom: int > finite_mod_ring_a,X: vec_int,N: nat] :
      ( ( ring_i5052177498423121492ring_a @ Hom )
     => ( ( ( map_ve1626356591056799954ring_a @ Hom @ X )
          = ( zero_v1122566495420860901ring_a @ N ) )
        = ( X
          = ( zero_vec_int @ N ) ) ) ) ).

% Matrix_Vector_Extras.inj_zero_hom.vec_hom_zero_iff
thf(fact_33_Matrix__Vector__Extras_Oinj__zero__hom_Ovec__hom__zero__iff,axiom,
    ! [Hom: finite_mod_ring_a > finite_mod_ring_a,X: vec_Fi4296597256376197294ring_a,N: nat] :
      ( ( ring_i7582611058579704515ring_a @ Hom )
     => ( ( ( map_ve1378714242357356997ring_a @ Hom @ X )
          = ( zero_v1122566495420860901ring_a @ N ) )
        = ( X
          = ( zero_v1122566495420860901ring_a @ N ) ) ) ) ).

% Matrix_Vector_Extras.inj_zero_hom.vec_hom_zero_iff
thf(fact_34_mod__type_OM__Rel_Ocong,axiom,
    vector3024231343486012919_Rel_a = vector3024231343486012919_Rel_a ).

% mod_type.M_Rel.cong
thf(fact_35_of__int__hom_Ovec__hom__mset,axiom,
    ! [V: vec_int] :
      ( ( image_mset_int_real @ ring_1_of_int_real @ ( matrix7410472831921750563et_int @ V ) )
      = ( matrix1887623593855636259t_real @ ( map_vec_int_real @ ring_1_of_int_real @ V ) ) ) ).

% of_int_hom.vec_hom_mset
thf(fact_36_of__int__hom_Ovec__hom__mset,axiom,
    ! [V: vec_int] :
      ( ( image_mset_int_int @ ring_1_of_int_int @ ( matrix7410472831921750563et_int @ V ) )
      = ( matrix7410472831921750563et_int @ ( map_vec_int_int @ ring_1_of_int_int @ V ) ) ) ).

% of_int_hom.vec_hom_mset
thf(fact_37_mat__mod_Ovec__mod__dim,axiom,
    ! [M: int,V: vec_int] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( dim_vec_int @ ( vector1199560857299316530ec_mod @ M @ V ) )
        = ( dim_vec_int @ V ) ) ) ).

% mat_mod.vec_mod_dim
thf(fact_38_mat__mod_Ovec__mod__zero,axiom,
    ! [M: int,N: nat] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( vector1199560857299316530ec_mod @ M @ ( zero_vec_int @ N ) )
        = ( zero_vec_int @ N ) ) ) ).

% mat_mod.vec_mod_zero
thf(fact_39_mat__mod_Ovec__mod__unit,axiom,
    ! [M: int,N: nat,I: nat] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( vector1199560857299316530ec_mod @ M @ ( unit_vec_int @ N @ I ) )
        = ( unit_vec_int @ N @ I ) ) ) ).

% mat_mod.vec_mod_unit
thf(fact_40_Matrix__Vector__Extras_Oinj__zero__hom_Ovec__hom__inj,axiom,
    ! [Hom: finite_mod_ring_a > int,V: vec_Fi4296597256376197294ring_a,W: vec_Fi4296597256376197294ring_a] :
      ( ( ring_i3475985505635201454_a_int @ Hom )
     => ( ( ( map_ve50164598268879916_a_int @ Hom @ V )
          = ( map_ve50164598268879916_a_int @ Hom @ W ) )
       => ( V = W ) ) ) ).

% Matrix_Vector_Extras.inj_zero_hom.vec_hom_inj
thf(fact_41_Matrix__Vector__Extras_Oinj__zero__hom_Ovec__hom__inj,axiom,
    ! [Hom: int > finite_mod_ring_a,V: vec_int,W: vec_int] :
      ( ( ring_i5052177498423121492ring_a @ Hom )
     => ( ( ( map_ve1626356591056799954ring_a @ Hom @ V )
          = ( map_ve1626356591056799954ring_a @ Hom @ W ) )
       => ( V = W ) ) ) ).

% Matrix_Vector_Extras.inj_zero_hom.vec_hom_inj
thf(fact_42_Matrix__Vector__Extras_Oinj__zero__hom_Ovec__hom__inj,axiom,
    ! [Hom: int > int,V: vec_int,W: vec_int] :
      ( ( ring_i7091729277519141597nt_int @ Hom )
     => ( ( ( map_vec_int_int @ Hom @ V )
          = ( map_vec_int_int @ Hom @ W ) )
       => ( V = W ) ) ) ).

% Matrix_Vector_Extras.inj_zero_hom.vec_hom_inj
thf(fact_43_to__int__mod__ring__hom_Oinj__zero__hom__axioms,axiom,
    ring_i3475985505635201454_a_int @ finite1095367895020317408ring_a ).

% to_int_mod_ring_hom.inj_zero_hom_axioms
thf(fact_44_one__MV__Rel,axiom,
    ! [N: nat,I: nat] : ( vector5230790432342831627_Rel_a @ m @ ( unit_vec_int @ N @ I ) @ ( unit_v6648808783362777473ring_a @ N @ I ) ) ).

% one_MV_Rel
thf(fact_45_index__unit__vec_I3_J,axiom,
    ! [N: nat,I: nat] :
      ( ( dim_vec_int @ ( unit_vec_int @ N @ I ) )
      = N ) ).

% index_unit_vec(3)
thf(fact_46_index__unit__vec_I3_J,axiom,
    ! [N: nat,I: nat] :
      ( ( dim_ve9152325144110082507ring_a @ ( unit_v6648808783362777473ring_a @ N @ I ) )
      = N ) ).

% index_unit_vec(3)
thf(fact_47_index__zero__vec_I2_J,axiom,
    ! [N: nat] :
      ( ( dim_vec_int @ ( zero_vec_int @ N ) )
      = N ) ).

% index_zero_vec(2)
thf(fact_48_index__zero__vec_I2_J,axiom,
    ! [N: nat] :
      ( ( dim_ve9152325144110082507ring_a @ ( zero_v1122566495420860901ring_a @ N ) )
      = N ) ).

% index_zero_vec(2)
thf(fact_49_index__map__vec_I2_J,axiom,
    ! [F: finite_mod_ring_a > finite_mod_ring_a,V: vec_Fi4296597256376197294ring_a] :
      ( ( dim_ve9152325144110082507ring_a @ ( map_ve1378714242357356997ring_a @ F @ V ) )
      = ( dim_ve9152325144110082507ring_a @ V ) ) ).

% index_map_vec(2)
thf(fact_50_index__map__vec_I2_J,axiom,
    ! [F: finite_mod_ring_a > int,V: vec_Fi4296597256376197294ring_a] :
      ( ( dim_vec_int @ ( map_ve50164598268879916_a_int @ F @ V ) )
      = ( dim_ve9152325144110082507ring_a @ V ) ) ).

% index_map_vec(2)
thf(fact_51_index__map__vec_I2_J,axiom,
    ! [F: int > finite_mod_ring_a,V: vec_int] :
      ( ( dim_ve9152325144110082507ring_a @ ( map_ve1626356591056799954ring_a @ F @ V ) )
      = ( dim_vec_int @ V ) ) ).

% index_map_vec(2)
thf(fact_52_index__map__vec_I2_J,axiom,
    ! [F: int > int,V: vec_int] :
      ( ( dim_vec_int @ ( map_vec_int_int @ F @ V ) )
      = ( dim_vec_int @ V ) ) ).

% index_map_vec(2)
thf(fact_53_of__int__hom_Ovec__hom__zero,axiom,
    ! [N: nat] :
      ( ( map_vec_int_int @ ring_1_of_int_int @ ( zero_vec_int @ N ) )
      = ( zero_vec_int @ N ) ) ).

% of_int_hom.vec_hom_zero
thf(fact_54_of__int__hom_Ovec__hom__zero,axiom,
    ! [N: nat] :
      ( ( map_ve1626356591056799954ring_a @ ring_18169885480643366966ring_a @ ( zero_vec_int @ N ) )
      = ( zero_v1122566495420860901ring_a @ N ) ) ).

% of_int_hom.vec_hom_zero
thf(fact_55_of__int__hom_Ovec__hom__zero,axiom,
    ! [N: nat] :
      ( ( map_vec_int_real @ ring_1_of_int_real @ ( zero_vec_int @ N ) )
      = ( zero_vec_real @ N ) ) ).

% of_int_hom.vec_hom_zero
thf(fact_56_zero__MV__Rel,axiom,
    ! [N: nat] : ( vector5230790432342831627_Rel_a @ m @ ( zero_vec_int @ N ) @ ( zero_v1122566495420860901ring_a @ N ) ) ).

% zero_MV_Rel
thf(fact_57_left__total__M__Rel,axiom,
    left_t8941605147251654769ring_a @ ( vector3024231343486012919_Rel_a @ m ) ).

% left_total_M_Rel
thf(fact_58_M__inv__M__id,axiom,
    ! [X: int] :
      ( ( vector_Matrix_mod_M @ m @ ( vector2349909385534816566_inv_M @ m @ X ) )
      = ( vector_Matrix_mod_M @ m @ X ) ) ).

% M_inv_M_id
thf(fact_59_left__total__MV__Rel,axiom,
    left_t7842747197492505505ring_a @ ( vector5230790432342831627_Rel_a @ m ) ).

% left_total_MV_Rel
thf(fact_60_mod__mod__trivial,axiom,
    ! [A: int,B: int] :
      ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ B )
      = ( modulo_modulo_int @ A @ B ) ) ).

% mod_mod_trivial
thf(fact_61_mod__mod__trivial,axiom,
    ! [A: nat,B: nat] :
      ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
      = ( modulo_modulo_nat @ A @ B ) ) ).

% mod_mod_trivial
thf(fact_62_Ring__Hom_Oof__int__hom_Oeq__iff,axiom,
    ! [X: int,Y: int] :
      ( ( ( ring_1_of_int_real @ X )
        = ( ring_1_of_int_real @ Y ) )
      = ( X = Y ) ) ).

% Ring_Hom.of_int_hom.eq_iff
thf(fact_63_of__int__eq__iff,axiom,
    ! [W: int,Z: int] :
      ( ( ( ring_1_of_int_real @ W )
        = ( ring_1_of_int_real @ Z ) )
      = ( W = Z ) ) ).

% of_int_eq_iff
thf(fact_64_mem__Collect__eq,axiom,
    ! [A: int,P: int > $o] :
      ( ( member_int @ A @ ( collect_int @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_65_mem__Collect__eq,axiom,
    ! [A: vec_Fi4296597256376197294ring_a,P: vec_Fi4296597256376197294ring_a > $o] :
      ( ( member1106766863034010949ring_a @ A @ ( collec5361221020025176195ring_a @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_66_mem__Collect__eq,axiom,
    ! [A: mat_Fi443519135453058082ring_a,P: mat_Fi443519135453058082ring_a > $o] :
      ( ( member6477060778965647545ring_a @ A @ ( collec1508142899102036983ring_a @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_67_mem__Collect__eq,axiom,
    ! [A: nat,P: nat > $o] :
      ( ( member_nat @ A @ ( collect_nat @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_68_Collect__mem__eq,axiom,
    ! [A2: set_int] :
      ( ( collect_int
        @ ^ [X3: int] : ( member_int @ X3 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_69_Collect__mem__eq,axiom,
    ! [A2: set_ve6125835690772642148ring_a] :
      ( ( collec5361221020025176195ring_a
        @ ^ [X3: vec_Fi4296597256376197294ring_a] : ( member1106766863034010949ring_a @ X3 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_70_Collect__mem__eq,axiom,
    ! [A2: set_ma1095064855528551128ring_a] :
      ( ( collec1508142899102036983ring_a
        @ ^ [X3: mat_Fi443519135453058082ring_a] : ( member6477060778965647545ring_a @ X3 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_71_Collect__mem__eq,axiom,
    ! [A2: set_nat] :
      ( ( collect_nat
        @ ^ [X3: nat] : ( member_nat @ X3 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_72_to__int__mod__ring__hom_Ovec__hom__zero__iff,axiom,
    ! [X: vec_Fi4296597256376197294ring_a,N: nat] :
      ( ( ( map_ve50164598268879916_a_int @ finite1095367895020317408ring_a @ X )
        = ( zero_vec_int @ N ) )
      = ( X
        = ( zero_v1122566495420860901ring_a @ N ) ) ) ).

% to_int_mod_ring_hom.vec_hom_zero_iff
thf(fact_73_mod__type_Oinv__M_Ocong,axiom,
    vector2349909385534816566_inv_M = vector2349909385534816566_inv_M ).

% mod_type.inv_M.cong
thf(fact_74_of__int__hom_Oinj__zero__hom__axioms,axiom,
    ring_i2058719125409607389t_real @ ring_1_of_int_real ).

% of_int_hom.inj_zero_hom_axioms
thf(fact_75_of__int__hom_Oinjectivity,axiom,
    ! [X: int,Y: int] :
      ( ( ( ring_1_of_int_real @ X )
        = ( ring_1_of_int_real @ Y ) )
     => ( X = Y ) ) ).

% of_int_hom.injectivity
thf(fact_76_eq__dim__vec__MV__Rel,axiom,
    ( bNF_re5216812267390093516at_nat @ ( vector5230790432342831627_Rel_a @ m )
    @ ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 )
    @ dim_vec_int
    @ dim_ve9152325144110082507ring_a ) ).

% eq_dim_vec_MV_Rel
thf(fact_77_right__unique__MV__Rel,axiom,
    right_2407805982356550513ring_a @ ( vector5230790432342831627_Rel_a @ m ) ).

% right_unique_MV_Rel
thf(fact_78_bi__total__M__Rel,axiom,
    bi_tot623839499179674737ring_a @ ( vector3024231343486012919_Rel_a @ m ) ).

% bi_total_M_Rel
thf(fact_79_bi__total__MV__Rel,axiom,
    bi_tot310863827317176225ring_a @ ( vector5230790432342831627_Rel_a @ m ) ).

% bi_total_MV_Rel
thf(fact_80_right__total__M__Rel,axiom,
    right_2909008500229168952ring_a @ ( vector3024231343486012919_Rel_a @ m ) ).

% right_total_M_Rel
thf(fact_81_domain__MV__rel,axiom,
    ( ( domain4015354059925764579ring_a @ ( vector5230790432342831627_Rel_a @ m ) )
    = ( ^ [F2: vec_int] : $true ) ) ).

% domain_MV_rel
thf(fact_82_right__total__MV__Rel,axiom,
    right_7341149013462710248ring_a @ ( vector5230790432342831627_Rel_a @ m ) ).

% right_total_MV_Rel
thf(fact_83_dim__update__vec,axiom,
    ! [V: vec_int,I: nat,A: int] :
      ( ( dim_vec_int @ ( update_vec_int @ V @ I @ A ) )
      = ( dim_vec_int @ V ) ) ).

% dim_update_vec
thf(fact_84_dim__update__vec,axiom,
    ! [V: vec_Fi4296597256376197294ring_a,I: nat,A: finite_mod_ring_a] :
      ( ( dim_ve9152325144110082507ring_a @ ( update7295115471411923750ring_a @ V @ I @ A ) )
      = ( dim_ve9152325144110082507ring_a @ V ) ) ).

% dim_update_vec
thf(fact_85_dim__vec__first,axiom,
    ! [V: vec_int,N: nat] :
      ( ( dim_vec_int @ ( vec_first_int @ V @ N ) )
      = N ) ).

% dim_vec_first
thf(fact_86_dim__vec__first,axiom,
    ! [V: vec_Fi4296597256376197294ring_a,N: nat] :
      ( ( dim_ve9152325144110082507ring_a @ ( vec_fi8778413887660436251ring_a @ V @ N ) )
      = N ) ).

% dim_vec_first
thf(fact_87_dim__vec__last,axiom,
    ! [V: vec_int,N: nat] :
      ( ( dim_vec_int @ ( vec_last_int @ V @ N ) )
      = N ) ).

% dim_vec_last
thf(fact_88_dim__vec__last,axiom,
    ! [V: vec_Fi4296597256376197294ring_a,N: nat] :
      ( ( dim_ve9152325144110082507ring_a @ ( vec_la2893097508259760455ring_a @ V @ N ) )
      = N ) ).

% dim_vec_last
thf(fact_89_dim__vec__all__ones,axiom,
    ! [N: nat] :
      ( ( dim_vec_int @ ( matrix2748772424961467270ec_int @ N ) )
      = N ) ).

% dim_vec_all_ones
thf(fact_90_dim__vec__all__ones,axiom,
    ! [N: nat] :
      ( ( dim_ve9152325144110082507ring_a @ ( matrix705363690926585579ring_a @ N ) )
      = N ) ).

% dim_vec_all_ones
thf(fact_91_bi__total__alt__def,axiom,
    ( bi_tot623839499179674737ring_a
    = ( ^ [A3: int > finite_mod_ring_a > $o] :
          ( ( left_t8941605147251654769ring_a @ A3 )
          & ( right_2909008500229168952ring_a @ A3 ) ) ) ) ).

% bi_total_alt_def
thf(fact_92_bi__total__alt__def,axiom,
    ( bi_tot310863827317176225ring_a
    = ( ^ [A3: vec_int > vec_Fi4296597256376197294ring_a > $o] :
          ( ( left_t7842747197492505505ring_a @ A3 )
          & ( right_7341149013462710248ring_a @ A3 ) ) ) ) ).

% bi_total_alt_def
thf(fact_93_bi__total__alt__def,axiom,
    ( bi_tot8466079176331800225ring_a
    = ( ^ [A3: mat_int > mat_Fi443519135453058082ring_a > $o] :
          ( ( left_t6774590509652353697ring_a @ A3 )
          & ( right_6272992325622558440ring_a @ A3 ) ) ) ) ).

% bi_total_alt_def
thf(fact_94_bi__totalI,axiom,
    ! [R: int > finite_mod_ring_a > $o] :
      ( ( left_t8941605147251654769ring_a @ R )
     => ( ( right_2909008500229168952ring_a @ R )
       => ( bi_tot623839499179674737ring_a @ R ) ) ) ).

% bi_totalI
thf(fact_95_bi__totalI,axiom,
    ! [R: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( left_t7842747197492505505ring_a @ R )
     => ( ( right_7341149013462710248ring_a @ R )
       => ( bi_tot310863827317176225ring_a @ R ) ) ) ).

% bi_totalI
thf(fact_96_bi__totalI,axiom,
    ! [R: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( left_t6774590509652353697ring_a @ R )
     => ( ( right_6272992325622558440ring_a @ R )
       => ( bi_tot8466079176331800225ring_a @ R ) ) ) ).

% bi_totalI
thf(fact_97_right__total__fun,axiom,
    ! [A2: int > int > $o,B2: $o > $o > $o] :
      ( ( right_unique_int_int @ A2 )
     => ( ( right_total_o_o @ B2 )
       => ( right_3358435141589207135_int_o @ ( bNF_re5089333283451836215nt_o_o @ A2 @ B2 ) ) ) ) ).

% right_total_fun
thf(fact_98_right__total__fun,axiom,
    ! [A2: int > int > $o,B2: nat > nat > $o] :
      ( ( right_unique_int_int @ A2 )
     => ( ( right_total_nat_nat @ B2 )
       => ( right_981250162103898583nt_nat @ ( bNF_re3715656647883201625at_nat @ A2 @ B2 ) ) ) ) ).

% right_total_fun
thf(fact_99_right__total__fun,axiom,
    ! [A2: int > int > $o,B2: int > int > $o] :
      ( ( right_unique_int_int @ A2 )
     => ( ( right_total_int_int @ B2 )
       => ( right_2214481324298164367nt_int @ ( bNF_re4712519889275205905nt_int @ A2 @ B2 ) ) ) ) ).

% right_total_fun
thf(fact_100_right__total__fun,axiom,
    ! [A2: int > int > $o,B2: ( int > $o ) > ( int > $o ) > $o] :
      ( ( right_unique_int_int @ A2 )
     => ( ( right_3358435141589207135_int_o @ B2 )
       => ( right_3701678689365064351_int_o @ ( bNF_re3403563459893282935_int_o @ A2 @ B2 ) ) ) ) ).

% right_total_fun
thf(fact_101_right__total__fun,axiom,
    ! [A2: int > int > $o,B2: ( int > int ) > ( int > int ) > $o] :
      ( ( right_unique_int_int @ A2 )
     => ( ( right_2214481324298164367nt_int @ B2 )
       => ( right_4144311589897252901nt_int @ ( bNF_re711492959462206631nt_int @ A2 @ B2 ) ) ) ) ).

% right_total_fun
thf(fact_102_right__total__fun,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o,B2: int > finite_mod_ring_a > $o] :
      ( ( right_2407805982356550513ring_a @ A2 )
     => ( ( right_2909008500229168952ring_a @ B2 )
       => ( right_3178293095284162103ring_a @ ( bNF_re5232057317656209005ring_a @ A2 @ B2 ) ) ) ) ).

% right_total_fun
thf(fact_103_right__total__fun,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o,B2: int > finite_mod_ring_a > $o] :
      ( ( right_1339649294516398705ring_a @ A2 )
     => ( ( right_2909008500229168952ring_a @ B2 )
       => ( right_8513789441842825527ring_a @ ( bNF_re2560879581620072301ring_a @ A2 @ B2 ) ) ) ) ).

% right_total_fun
thf(fact_104_right__total__fun,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o,B2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( right_2407805982356550513ring_a @ A2 )
     => ( ( right_7341149013462710248ring_a @ B2 )
       => ( right_973708634130167105ring_a @ ( bNF_re7573024106080040861ring_a @ A2 @ B2 ) ) ) ) ).

% right_total_fun
thf(fact_105_right__total__fun,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o,B2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( right_2407805982356550513ring_a @ A2 )
     => ( ( right_6272992325622558440ring_a @ B2 )
       => ( right_2038090536106482241ring_a @ ( bNF_re6504867418239889053ring_a @ A2 @ B2 ) ) ) ) ).

% right_total_fun
thf(fact_106_right__total__fun,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o,B2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( right_1339649294516398705ring_a @ A2 )
     => ( ( right_7341149013462710248ring_a @ B2 )
       => ( right_7147911083355635753ring_a @ ( bNF_re8335190240456851613ring_a @ A2 @ B2 ) ) ) ) ).

% right_total_fun
thf(fact_107_right__unique__fun,axiom,
    ! [A2: int > int > $o,B2: $o > $o > $o] :
      ( ( right_total_int_int @ A2 )
     => ( ( right_unique_o_o @ B2 )
       => ( right_8348394670160920726_int_o @ ( bNF_re5089333283451836215nt_o_o @ A2 @ B2 ) ) ) ) ).

% right_unique_fun
thf(fact_108_right__unique__fun,axiom,
    ! [A2: int > int > $o,B2: nat > nat > $o] :
      ( ( right_total_int_int @ A2 )
     => ( ( right_unique_nat_nat @ B2 )
       => ( right_6438958750069555854nt_nat @ ( bNF_re3715656647883201625at_nat @ A2 @ B2 ) ) ) ) ).

% right_unique_fun
thf(fact_109_right__unique__fun,axiom,
    ! [A2: int > int > $o,B2: int > int > $o] :
      ( ( right_total_int_int @ A2 )
     => ( ( right_unique_int_int @ B2 )
       => ( right_7672189912263821638nt_int @ ( bNF_re4712519889275205905nt_int @ A2 @ B2 ) ) ) ) ).

% right_unique_fun
thf(fact_110_right__unique__fun,axiom,
    ! [A2: int > int > $o,B2: ( int > $o ) > ( int > $o ) > $o] :
      ( ( right_total_int_int @ A2 )
     => ( ( right_8348394670160920726_int_o @ B2 )
       => ( right_6125766759956493782_int_o @ ( bNF_re3403563459893282935_int_o @ A2 @ B2 ) ) ) ) ).

% right_unique_fun
thf(fact_111_right__unique__fun,axiom,
    ! [A2: int > int > $o,B2: ( int > int ) > ( int > int ) > $o] :
      ( ( right_total_int_int @ A2 )
     => ( ( right_7672189912263821638nt_int @ B2 )
       => ( right_2249472770629886940nt_int @ ( bNF_re711492959462206631nt_int @ A2 @ B2 ) ) ) ) ).

% right_unique_fun
thf(fact_112_right__unique__fun,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( right_2909008500229168952ring_a @ A2 )
     => ( ( right_2407805982356550513ring_a @ B2 )
       => ( right_4404654753817203094ring_a @ ( bNF_re6498750967587248461ring_a @ A2 @ B2 ) ) ) ) ).

% right_unique_fun
thf(fact_113_right__unique__fun,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( right_2909008500229168952ring_a @ A2 )
     => ( ( right_1339649294516398705ring_a @ B2 )
       => ( right_6181665041646683774ring_a @ ( bNF_re5430594279747096653ring_a @ A2 @ B2 ) ) ) ) ).

% right_unique_fun
thf(fact_114_right__unique__fun,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o,B2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( right_7341149013462710248ring_a @ A2 )
     => ( ( right_2407805982356550513ring_a @ B2 )
       => ( right_7964614922910794616ring_a @ ( bNF_re7573024106080040861ring_a @ A2 @ B2 ) ) ) ) ).

% right_unique_fun
thf(fact_115_right__unique__fun,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o,B2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( right_6272992325622558440ring_a @ A2 )
     => ( ( right_2407805982356550513ring_a @ B2 )
       => ( right_4915445335281487456ring_a @ ( bNF_re8335190240456851613ring_a @ A2 @ B2 ) ) ) ) ).

% right_unique_fun
thf(fact_116_right__unique__fun,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o,B2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( right_7341149013462710248ring_a @ A2 )
     => ( ( right_1339649294516398705ring_a @ B2 )
       => ( right_9028996824887109752ring_a @ ( bNF_re6504867418239889053ring_a @ A2 @ B2 ) ) ) ) ).

% right_unique_fun
thf(fact_117_rel__funI,axiom,
    ! [A2: int > int > $o,B2: $o > $o > $o,F: int > $o,G: int > $o] :
      ( ! [X4: int,Y3: int] :
          ( ( A2 @ X4 @ Y3 )
         => ( B2 @ ( F @ X4 ) @ ( G @ Y3 ) ) )
     => ( bNF_re5089333283451836215nt_o_o @ A2 @ B2 @ F @ G ) ) ).

% rel_funI
thf(fact_118_rel__funI,axiom,
    ! [A2: int > int > $o,B2: nat > nat > $o,F: int > nat,G: int > nat] :
      ( ! [X4: int,Y3: int] :
          ( ( A2 @ X4 @ Y3 )
         => ( B2 @ ( F @ X4 ) @ ( G @ Y3 ) ) )
     => ( bNF_re3715656647883201625at_nat @ A2 @ B2 @ F @ G ) ) ).

% rel_funI
thf(fact_119_rel__funI,axiom,
    ! [A2: int > int > $o,B2: int > int > $o,F: int > int,G: int > int] :
      ( ! [X4: int,Y3: int] :
          ( ( A2 @ X4 @ Y3 )
         => ( B2 @ ( F @ X4 ) @ ( G @ Y3 ) ) )
     => ( bNF_re4712519889275205905nt_int @ A2 @ B2 @ F @ G ) ) ).

% rel_funI
thf(fact_120_rel__funI,axiom,
    ! [A2: int > int > $o,B2: ( int > $o ) > ( int > $o ) > $o,F: int > int > $o,G: int > int > $o] :
      ( ! [X4: int,Y3: int] :
          ( ( A2 @ X4 @ Y3 )
         => ( B2 @ ( F @ X4 ) @ ( G @ Y3 ) ) )
     => ( bNF_re3403563459893282935_int_o @ A2 @ B2 @ F @ G ) ) ).

% rel_funI
thf(fact_121_rel__funI,axiom,
    ! [A2: int > int > $o,B2: ( int > int ) > ( int > int ) > $o,F: int > int > int,G: int > int > int] :
      ( ! [X4: int,Y3: int] :
          ( ( A2 @ X4 @ Y3 )
         => ( B2 @ ( F @ X4 ) @ ( G @ Y3 ) ) )
     => ( bNF_re711492959462206631nt_int @ A2 @ B2 @ F @ G ) ) ).

% rel_funI
thf(fact_122_functional__relation,axiom,
    ! [R: int > finite_mod_ring_a > $o] :
      ( ( right_7581627888863641665ring_a @ R )
     => ( ( left_t8941605147251654769ring_a @ R )
       => ! [X5: int] :
          ? [Xa: finite_mod_ring_a] :
            ( ( R @ X5 @ Xa )
            & ! [Y4: finite_mod_ring_a] :
                ( ( R @ X5 @ Y4 )
               => ( Y4 = Xa ) ) ) ) ) ).

% functional_relation
thf(fact_123_functional__relation,axiom,
    ! [R: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( right_2407805982356550513ring_a @ R )
     => ( ( left_t7842747197492505505ring_a @ R )
       => ! [X5: vec_int] :
          ? [Xa: vec_Fi4296597256376197294ring_a] :
            ( ( R @ X5 @ Xa )
            & ! [Y4: vec_Fi4296597256376197294ring_a] :
                ( ( R @ X5 @ Y4 )
               => ( Y4 = Xa ) ) ) ) ) ).

% functional_relation
thf(fact_124_functional__relation,axiom,
    ! [R: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( right_1339649294516398705ring_a @ R )
     => ( ( left_t6774590509652353697ring_a @ R )
       => ! [X5: mat_int] :
          ? [Xa: mat_Fi443519135453058082ring_a] :
            ( ( R @ X5 @ Xa )
            & ! [Y4: mat_Fi443519135453058082ring_a] :
                ( ( R @ X5 @ Y4 )
               => ( Y4 = Xa ) ) ) ) ) ).

% functional_relation
thf(fact_125_lift__01__vec__simp_I1_J,axiom,
    ! [V: vec_int] :
      ( ( dim_vec_int @ ( matrix8301520909418075407nt_int @ V ) )
      = ( dim_vec_int @ V ) ) ).

% lift_01_vec_simp(1)
thf(fact_126_lift__01__vec__simp_I1_J,axiom,
    ! [V: vec_Fi4296597256376197294ring_a] :
      ( ( dim_vec_int @ ( matrix8742746829526049276_a_int @ V ) )
      = ( dim_ve9152325144110082507ring_a @ V ) ) ).

% lift_01_vec_simp(1)
thf(fact_127_lift__01__vec__simp_I1_J,axiom,
    ! [V: vec_int] :
      ( ( dim_ve9152325144110082507ring_a @ ( matrix1095566785459193506ring_a @ V ) )
      = ( dim_vec_int @ V ) ) ).

% lift_01_vec_simp(1)
thf(fact_128_lift__01__vec__simp_I1_J,axiom,
    ! [V: vec_Fi4296597256376197294ring_a] :
      ( ( dim_ve9152325144110082507ring_a @ ( matrix7517040601615355893ring_a @ V ) )
      = ( dim_ve9152325144110082507ring_a @ V ) ) ).

% lift_01_vec_simp(1)
thf(fact_129_of__int__mod__ring__hom__sr_Ovec__hom__zero,axiom,
    ! [N: nat] :
      ( ( map_ve1626356591056799954ring_a @ finite8272632373135393572ring_a @ ( zero_vec_int @ N ) )
      = ( zero_v1122566495420860901ring_a @ N ) ) ).

% of_int_mod_ring_hom_sr.vec_hom_zero
thf(fact_130_M__0,axiom,
    ( ( vector_Matrix_mod_M @ m @ zero_zero_int )
    = zero_zero_int ) ).

% M_0
thf(fact_131_left__totalE,axiom,
    ! [R: int > finite_mod_ring_a > $o] :
      ( ( left_t8941605147251654769ring_a @ R )
     => ! [X5: int] :
        ? [X_1: finite_mod_ring_a] : ( R @ X5 @ X_1 ) ) ).

% left_totalE
thf(fact_132_left__totalE,axiom,
    ! [R: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( left_t7842747197492505505ring_a @ R )
     => ! [X5: vec_int] :
        ? [X_1: vec_Fi4296597256376197294ring_a] : ( R @ X5 @ X_1 ) ) ).

% left_totalE
thf(fact_133_left__totalE,axiom,
    ! [R: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( left_t6774590509652353697ring_a @ R )
     => ! [X5: mat_int] :
        ? [X_1: mat_Fi443519135453058082ring_a] : ( R @ X5 @ X_1 ) ) ).

% left_totalE
thf(fact_134_of__int__mod__ring__to__int__mod__ring,axiom,
    ! [X: finite_mod_ring_a] :
      ( ( finite8272632373135393572ring_a @ ( finite1095367895020317408ring_a @ X ) )
      = X ) ).

% of_int_mod_ring_to_int_mod_ring
thf(fact_135_of__int__hom_Ohom__zero,axiom,
    ( ( ring_1_of_int_int @ zero_zero_int )
    = zero_zero_int ) ).

% of_int_hom.hom_zero
thf(fact_136_of__int__hom_Ohom__zero,axiom,
    ( ( ring_18169885480643366966ring_a @ zero_zero_int )
    = zero_z7902377541816115708ring_a ) ).

% of_int_hom.hom_zero
thf(fact_137_of__int__hom_Ohom__zero,axiom,
    ( ( ring_1_of_int_real @ zero_zero_int )
    = zero_zero_real ) ).

% of_int_hom.hom_zero
thf(fact_138_of__int__hom_Ohom__0__iff,axiom,
    ! [X: int] :
      ( ( ( ring_1_of_int_int @ X )
        = zero_zero_int )
      = ( X = zero_zero_int ) ) ).

% of_int_hom.hom_0_iff
thf(fact_139_of__int__hom_Ohom__0__iff,axiom,
    ! [X: int] :
      ( ( ( ring_1_of_int_real @ X )
        = zero_zero_real )
      = ( X = zero_zero_int ) ) ).

% of_int_hom.hom_0_iff
thf(fact_140_of__int__0__eq__iff,axiom,
    ! [Z: int] :
      ( ( zero_zero_int
        = ( ring_1_of_int_int @ Z ) )
      = ( Z = zero_zero_int ) ) ).

% of_int_0_eq_iff
thf(fact_141_of__int__0__eq__iff,axiom,
    ! [Z: int] :
      ( ( zero_zero_real
        = ( ring_1_of_int_real @ Z ) )
      = ( Z = zero_zero_int ) ) ).

% of_int_0_eq_iff
thf(fact_142_of__int__eq__0__iff,axiom,
    ! [Z: int] :
      ( ( ( ring_1_of_int_int @ Z )
        = zero_zero_int )
      = ( Z = zero_zero_int ) ) ).

% of_int_eq_0_iff
thf(fact_143_of__int__eq__0__iff,axiom,
    ! [Z: int] :
      ( ( ( ring_1_of_int_real @ Z )
        = zero_zero_real )
      = ( Z = zero_zero_int ) ) ).

% of_int_eq_0_iff
thf(fact_144_left__total__parametric,axiom,
    ! [A2: int > int > $o,B2: int > int > $o] :
      ( ( bi_total_int_int @ A2 )
     => ( ( bi_total_int_int @ B2 )
       => ( bNF_re5869992600382051037_o_o_o
          @ ( bNF_re3403563459893282935_int_o @ A2
            @ ( bNF_re5089333283451836215nt_o_o @ B2
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
          @ left_total_int_int
          @ left_total_int_int ) ) ) ).

% left_total_parametric
thf(fact_145_left__total__parametric,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: int > int > $o] :
      ( ( bi_tot623839499179674737ring_a @ A2 )
     => ( ( bi_total_int_int @ B2 )
       => ( bNF_re5891132441370877716_o_o_o
          @ ( bNF_re3873409527727426490_int_o @ A2
            @ ( bNF_re5089333283451836215nt_o_o @ B2
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
          @ left_total_int_int
          @ left_t7365413154463734731_a_int ) ) ) ).

% left_total_parametric
thf(fact_146_left__total__parametric,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: int > finite_mod_ring_a > $o] :
      ( ( bi_tot623839499179674737ring_a @ A2 )
     => ( ( bi_tot623839499179674737ring_a @ B2 )
       => ( bNF_re3287324404599397085_o_o_o
          @ ( bNF_re1743884151495963297ng_a_o @ A2
            @ ( bNF_re8290846538823883642_a_o_o @ B2
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
          @ left_total_int_int
          @ left_t5999478950615061222ring_a ) ) ) ).

% left_total_parametric
thf(fact_147_left__total__parametric,axiom,
    ! [A2: int > int > $o,B2: finite_mod_ring_a > finite_mod_ring_a > $o] :
      ( ( bi_total_int_int @ A2 )
     => ( ( bi_tot8261576339290982118ring_a @ B2 )
       => ( bNF_re3139618654209367653_o_o_o
          @ ( bNF_re6948380915580796713ng_a_o @ A2
            @ ( bNF_re5912972185147205917_a_o_o @ B2
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
          @ left_t8941605147251654769ring_a
          @ left_t8941605147251654769ring_a ) ) ) ).

% left_total_parametric
thf(fact_148_left__total__parametric,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o,B2: int > int > $o] :
      ( ( bi_tot310863827317176225ring_a @ A2 )
     => ( ( bi_total_int_int @ B2 )
       => ( bNF_re3166440945848855070_o_o_o
          @ ( bNF_re7877854262379379050_int_o @ A2
            @ ( bNF_re5089333283451836215nt_o_o @ B2
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
          @ left_t8503202935883368735nt_int
          @ left_t3044016776331892994_a_int ) ) ) ).

% left_total_parametric
thf(fact_149_left__total__parametric,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o,B2: int > int > $o] :
      ( ( bi_tot8466079176331800225ring_a @ A2 )
     => ( ( bi_total_int_int @ B2 )
       => ( bNF_re2185885084462657334_o_o_o
          @ ( bNF_re1270729808710627434_int_o @ A2
            @ ( bNF_re5089333283451836215nt_o_o @ B2
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
          @ left_t525550650202266795nt_int
          @ left_t1770473636134370422_a_int ) ) ) ).

% left_total_parametric
thf(fact_150_left__total__parametric,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( bi_tot623839499179674737ring_a @ A2 )
     => ( ( bi_tot310863827317176225ring_a @ B2 )
       => ( bNF_re8023572202256978639_o_o_o
          @ ( bNF_re4244150877105976961ng_a_o @ A2
            @ ( bNF_re507051067509135658_a_o_o @ B2
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
          @ left_t4735277866268011845ec_int
          @ left_t7528098663070101069ring_a ) ) ) ).

% left_total_parametric
thf(fact_151_left__total__parametric,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( bi_tot623839499179674737ring_a @ A2 )
     => ( ( bi_tot8466079176331800225ring_a @ B2 )
       => ( bNF_re3176011413720292303_o_o_o
          @ ( bNF_re4973150902881326489ng_a_o @ A2
            @ ( bNF_re6153771816476299306_a_o_o @ B2
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
          @ left_t1248818525112758481at_int
          @ left_t3675020542146961857ring_a ) ) ) ).

% left_total_parametric
thf(fact_152_left__total__parametric,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o,B2: int > finite_mod_ring_a > $o] :
      ( ( bi_tot310863827317176225ring_a @ A2 )
     => ( ( bi_tot623839499179674737ring_a @ B2 )
       => ( bNF_re7402094339212515411_o_o_o
          @ ( bNF_re245202343922368753ng_a_o @ A2
            @ ( bNF_re8290846538823883642_a_o_o @ B2
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
          @ left_t8503202935883368735nt_int
          @ left_t5305266654949180527ring_a ) ) ) ).

% left_total_parametric
thf(fact_153_left__total__parametric,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o,B2: int > finite_mod_ring_a > $o] :
      ( ( bi_tot8466079176331800225ring_a @ A2 )
     => ( ( bi_tot623839499179674737ring_a @ B2 )
       => ( bNF_re9174360872848916795_o_o_o
          @ ( bNF_re8055952673531087345ng_a_o @ A2
            @ ( bNF_re8290846538823883642_a_o_o @ B2
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
          @ left_t525550650202266795nt_int
          @ left_t3992335159695895035ring_a ) ) ) ).

% left_total_parametric
thf(fact_154_eq__imp__transfer,axiom,
    ! [A2: int > int > $o] :
      ( ( right_unique_int_int @ A2 )
     => ( bNF_re3403563459893282935_int_o @ A2 @ ( bNF_re5089333283451836215nt_o_o @ A2 @ (=>) )
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) ) ) ).

% eq_imp_transfer
thf(fact_155_eq__imp__transfer,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( right_2407805982356550513ring_a @ A2 )
     => ( bNF_re151890839321169105ng_a_o @ A2 @ ( bNF_re507051067509135658_a_o_o @ A2 @ (=>) )
        @ ^ [Y2: vec_int,Z2: vec_int] : ( Y2 = Z2 )
        @ ^ [Y2: vec_Fi4296597256376197294ring_a,Z2: vec_Fi4296597256376197294ring_a] : ( Y2 = Z2 ) ) ) ).

% eq_imp_transfer
thf(fact_156_eq__imp__transfer,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( right_1339649294516398705ring_a @ A2 )
     => ( bNF_re8187416184292455657ng_a_o @ A2 @ ( bNF_re6153771816476299306_a_o_o @ A2 @ (=>) )
        @ ^ [Y2: mat_int,Z2: mat_int] : ( Y2 = Z2 )
        @ ^ [Y2: mat_Fi443519135453058082ring_a,Z2: mat_Fi443519135453058082ring_a] : ( Y2 = Z2 ) ) ) ).

% eq_imp_transfer
thf(fact_157_Domainp__transfer,axiom,
    ! [B2: int > int > $o,A2: int > int > $o] :
      ( ( bi_total_int_int @ B2 )
     => ( bNF_re2642688597062869533_int_o
        @ ( bNF_re3403563459893282935_int_o @ A2
          @ ( bNF_re5089333283451836215nt_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re5089333283451836215nt_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ domainp_int_int
        @ domainp_int_int ) ) ).

% Domainp_transfer
thf(fact_158_Domainp__transfer,axiom,
    ! [B2: vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a > $o,A2: vec_int > vec_int > $o] :
      ( ( bi_tot4640009209964170116ring_a @ B2 )
     => ( bNF_re7822804841563943683_int_o
        @ ( bNF_re70301032216168413ng_a_o @ A2
          @ ( bNF_re6505802678211463739_a_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re679821270890987293nt_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ domain4015354059925764579ring_a
        @ domain4015354059925764579ring_a ) ) ).

% Domainp_transfer
thf(fact_159_Domainp__transfer,axiom,
    ! [B2: vec_Fi4296597256376197294ring_a > mat_Fi443519135453058082ring_a > $o,A2: vec_int > mat_int > $o] :
      ( ( bi_tot786931089041030904ring_a @ B2 )
     => ( bNF_re2243167975609497975_int_o
        @ ( bNF_re6848855223299790069ng_a_o @ A2
          @ ( bNF_re8041672266701334447_a_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re5326586026928855209nt_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ domain4015354059925764579ring_a
        @ domain2947197372085612771ring_a ) ) ).

% Domainp_transfer
thf(fact_160_Domainp__transfer,axiom,
    ! [B2: mat_Fi443519135453058082ring_a > vec_Fi4296597256376197294ring_a > $o,A2: mat_int > vec_int > $o] :
      ( ( bi_tot6329329913692241656ring_a @ B2 )
     => ( bNF_re6999084953581488503_int_o
        @ ( bNF_re5652364884431686341ng_a_o @ A2
          @ ( bNF_re2162143236097353647_a_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re1257695248469094033nt_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ domain2947197372085612771ring_a
        @ domain4015354059925764579ring_a ) ) ).

% Domainp_transfer
thf(fact_161_Domainp__transfer,axiom,
    ! [B2: mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a > $o,A2: mat_int > mat_int > $o] :
      ( ( bi_tot2476251792769102444ring_a @ B2 )
     => ( bNF_re1419448087627042795_int_o
        @ ( bNF_re3207547038660532189ng_a_o @ A2
          @ ( bNF_re3698012824587224355_a_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re5904460004506961949nt_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ domain2947197372085612771ring_a
        @ domain2947197372085612771ring_a ) ) ).

% Domainp_transfer
thf(fact_162_Domainp__transfer,axiom,
    ! [B2: int > finite_mod_ring_a > $o,A2: int > int > $o] :
      ( ( bi_tot623839499179674737ring_a @ B2 )
     => ( bNF_re2917227035190921876_int_o
        @ ( bNF_re1393113005842329636ng_a_o @ A2
          @ ( bNF_re8290846538823883642_a_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re5089333283451836215nt_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ domainp_int_int
        @ domain6543890336852369843ring_a ) ) ).

% Domainp_transfer
thf(fact_163_Domainp__transfer,axiom,
    ! [B2: vec_int > vec_Fi4296597256376197294ring_a > $o,A2: int > int > $o] :
      ( ( bi_tot310863827317176225ring_a @ B2 )
     => ( bNF_re131580980352085790_int_o
        @ ( bNF_re3675534777603958660ng_a_o @ A2
          @ ( bNF_re507051067509135658_a_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re5089333283451836215nt_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ domainp_int_vec_int
        @ domain1918902550050569536ring_a ) ) ).

% Domainp_transfer
thf(fact_164_Domainp__transfer,axiom,
    ! [B2: mat_int > mat_Fi443519135453058082ring_a > $o,A2: int > int > $o] :
      ( ( bi_tot8466079176331800225ring_a @ B2 )
     => ( bNF_re6408424020554474550_int_o
        @ ( bNF_re4404534803379308188ng_a_o @ A2
          @ ( bNF_re6153771816476299306_a_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re5089333283451836215nt_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ domainp_int_mat_int
        @ domain7289196465982206132ring_a ) ) ).

% Domainp_transfer
thf(fact_165_right__unique__alt__def2,axiom,
    ( right_unique_int_int
    = ( ^ [R2: int > int > $o] :
          ( bNF_re3403563459893282935_int_o @ R2 @ ( bNF_re5089333283451836215nt_o_o @ R2 @ (=>) )
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) ) ) ) ).

% right_unique_alt_def2
thf(fact_166_right__unique__alt__def2,axiom,
    ( right_2407805982356550513ring_a
    = ( ^ [R2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
          ( bNF_re151890839321169105ng_a_o @ R2 @ ( bNF_re507051067509135658_a_o_o @ R2 @ (=>) )
          @ ^ [Y2: vec_int,Z2: vec_int] : ( Y2 = Z2 )
          @ ^ [Y2: vec_Fi4296597256376197294ring_a,Z2: vec_Fi4296597256376197294ring_a] : ( Y2 = Z2 ) ) ) ) ).

% right_unique_alt_def2
thf(fact_167_right__unique__alt__def2,axiom,
    ( right_1339649294516398705ring_a
    = ( ^ [R2: mat_int > mat_Fi443519135453058082ring_a > $o] :
          ( bNF_re8187416184292455657ng_a_o @ R2 @ ( bNF_re6153771816476299306_a_o_o @ R2 @ (=>) )
          @ ^ [Y2: mat_int,Z2: mat_int] : ( Y2 = Z2 )
          @ ^ [Y2: mat_Fi443519135453058082ring_a,Z2: mat_Fi443519135453058082ring_a] : ( Y2 = Z2 ) ) ) ) ).

% right_unique_alt_def2
thf(fact_168_right__total__parametric,axiom,
    ! [A2: int > int > $o,B2: int > int > $o] :
      ( ( bi_total_int_int @ A2 )
     => ( ( bi_total_int_int @ B2 )
       => ( bNF_re5869992600382051037_o_o_o
          @ ( bNF_re3403563459893282935_int_o @ A2
            @ ( bNF_re5089333283451836215nt_o_o @ B2
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
          @ right_total_int_int
          @ right_total_int_int ) ) ) ).

% right_total_parametric
thf(fact_169_right__total__parametric,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: int > int > $o] :
      ( ( bi_tot623839499179674737ring_a @ A2 )
     => ( ( bi_total_int_int @ B2 )
       => ( bNF_re5891132441370877716_o_o_o
          @ ( bNF_re3873409527727426490_int_o @ A2
            @ ( bNF_re5089333283451836215nt_o_o @ B2
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
          @ right_total_int_int
          @ right_1332816507441248914_a_int ) ) ) ).

% right_total_parametric
thf(fact_170_right__total__parametric,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: int > finite_mod_ring_a > $o] :
      ( ( bi_tot623839499179674737ring_a @ A2 )
     => ( ( bi_tot623839499179674737ring_a @ B2 )
       => ( bNF_re3287324404599397085_o_o_o
          @ ( bNF_re1743884151495963297ng_a_o @ A2
            @ ( bNF_re8290846538823883642_a_o_o @ B2
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
          @ right_total_int_int
          @ right_301602178578872031ring_a ) ) ) ).

% right_total_parametric
thf(fact_171_right__total__parametric,axiom,
    ! [A2: int > int > $o,B2: finite_mod_ring_a > finite_mod_ring_a > $o] :
      ( ( bi_total_int_int @ A2 )
     => ( ( bi_tot8261576339290982118ring_a @ B2 )
       => ( bNF_re3139618654209367653_o_o_o
          @ ( bNF_re6948380915580796713ng_a_o @ A2
            @ ( bNF_re5912972185147205917_a_o_o @ B2
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
          @ right_2909008500229168952ring_a
          @ right_2909008500229168952ring_a ) ) ) ).

% right_total_parametric
thf(fact_172_right__total__parametric,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o,B2: int > int > $o] :
      ( ( bi_tot310863827317176225ring_a @ A2 )
     => ( ( bi_total_int_int @ B2 )
       => ( bNF_re3166440945848855070_o_o_o
          @ ( bNF_re7877854262379379050_int_o @ A2
            @ ( bNF_re5089333283451836215nt_o_o @ B2
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
          @ right_7894334582807669094nt_int
          @ right_365990899298655099_a_int ) ) ) ).

% right_total_parametric
thf(fact_173_right__total__parametric,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o,B2: int > int > $o] :
      ( ( bi_tot8466079176331800225ring_a @ A2 )
     => ( ( bi_total_int_int @ B2 )
       => ( bNF_re2185885084462657334_o_o_o
          @ ( bNF_re1270729808710627434_int_o @ A2
            @ ( bNF_re5089333283451836215nt_o_o @ B2
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
          @ right_9140054333981342962nt_int
          @ right_8315819795955908335_a_int ) ) ) ).

% right_total_parametric
thf(fact_174_right__total__parametric,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( bi_tot623839499179674737ring_a @ A2 )
     => ( ( bi_tot310863827317176225ring_a @ B2 )
       => ( bNF_re8023572202256978639_o_o_o
          @ ( bNF_re4244150877105976961ng_a_o @ A2
            @ ( bNF_re507051067509135658_a_o_o @ B2
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
          @ right_4126409513192312204ec_int
          @ right_502638899226622228ring_a ) ) ) ).

% right_total_parametric
thf(fact_175_right__total__parametric,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( bi_tot623839499179674737ring_a @ A2 )
     => ( ( bi_tot8466079176331800225ring_a @ B2 )
       => ( bNF_re3176011413720292303_o_o_o
          @ ( bNF_re4973150902881326489ng_a_o @ A2
            @ ( bNF_re6153771816476299306_a_o_o @ B2
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
          @ right_639950172037058840at_int
          @ right_5872932815158258824ring_a ) ) ) ).

% right_total_parametric
thf(fact_176_right__total__parametric,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o,B2: int > finite_mod_ring_a > $o] :
      ( ( bi_tot310863827317176225ring_a @ A2 )
     => ( ( bi_tot623839499179674737ring_a @ B2 )
       => ( bNF_re7402094339212515411_o_o_o
          @ ( bNF_re245202343922368753ng_a_o @ A2
            @ ( bNF_re8290846538823883642_a_o_o @ B2
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
          @ right_7894334582807669094nt_int
          @ right_7503178927960477494ring_a ) ) ) ).

% right_total_parametric
thf(fact_177_right__total__parametric,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o,B2: int > finite_mod_ring_a > $o] :
      ( ( bi_tot8466079176331800225ring_a @ A2 )
     => ( ( bi_tot623839499179674737ring_a @ B2 )
       => ( bNF_re9174360872848916795_o_o_o
          @ ( bNF_re8055952673531087345ng_a_o @ A2
            @ ( bNF_re8290846538823883642_a_o_o @ B2
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
          @ right_9140054333981342962nt_int
          @ right_6190247432707192002ring_a ) ) ) ).

% right_total_parametric
thf(fact_178_of__int__hom_Ohom__0,axiom,
    ! [X: int] :
      ( ( ( ring_1_of_int_int @ X )
        = zero_zero_int )
     => ( X = zero_zero_int ) ) ).

% of_int_hom.hom_0
thf(fact_179_of__int__hom_Ohom__0,axiom,
    ! [X: int] :
      ( ( ( ring_1_of_int_real @ X )
        = zero_zero_real )
     => ( X = zero_zero_int ) ) ).

% of_int_hom.hom_0
thf(fact_180_of__int__of__int__mod__ring,axiom,
    ring_18169885480643366966ring_a = finite8272632373135393572ring_a ).

% of_int_of_int_mod_ring
thf(fact_181_Let__transfer,axiom,
    ! [A2: int > int > $o,B2: $o > $o > $o] :
      ( bNF_re1280668699144990829nt_o_o @ A2 @ ( bNF_re6378653760509651613_o_o_o @ ( bNF_re5089333283451836215nt_o_o @ A2 @ B2 ) @ B2 )
      @ ^ [S: int,F2: int > $o] : ( F2 @ S )
      @ ^ [S: int,F2: int > $o] : ( F2 @ S ) ) ).

% Let_transfer
thf(fact_182_Let__transfer,axiom,
    ! [A2: int > int > $o,B2: nat > nat > $o] :
      ( bNF_re3451822466932340941at_nat @ A2 @ ( bNF_re1996201511620343607at_nat @ ( bNF_re3715656647883201625at_nat @ A2 @ B2 ) @ B2 )
      @ ^ [S: int,F2: int > nat] : ( F2 @ S )
      @ ^ [S: int,F2: int > nat] : ( F2 @ S ) ) ).

% Let_transfer
thf(fact_183_Let__transfer,axiom,
    ! [A2: int > int > $o,B2: int > int > $o] :
      ( bNF_re8360549327529751101nt_int @ A2 @ ( bNF_re8159601828672395943nt_int @ ( bNF_re4712519889275205905nt_int @ A2 @ B2 ) @ B2 )
      @ ^ [S: int,F2: int > int] : ( F2 @ S )
      @ ^ [S: int,F2: int > int] : ( F2 @ S ) ) ).

% Let_transfer
thf(fact_184_Let__transfer,axiom,
    ! [A2: int > int > $o,B2: ( int > $o ) > ( int > $o ) > $o] :
      ( bNF_re1806261209056574701_int_o @ A2 @ ( bNF_re2642688597062869533_int_o @ ( bNF_re3403563459893282935_int_o @ A2 @ B2 ) @ B2 )
      @ ^ [S: int,F2: int > int > $o] : ( F2 @ S )
      @ ^ [S: int,F2: int > int > $o] : ( F2 @ S ) ) ).

% Let_transfer
thf(fact_185_Let__transfer,axiom,
    ! [A2: int > int > $o,B2: ( int > int ) > ( int > int ) > $o] :
      ( bNF_re776728095411994473nt_int @ A2 @ ( bNF_re3333031753742804947nt_int @ ( bNF_re711492959462206631nt_int @ A2 @ B2 ) @ B2 )
      @ ^ [S: int,F2: int > int > int] : ( F2 @ S )
      @ ^ [S: int,F2: int > int > int] : ( F2 @ S ) ) ).

% Let_transfer
thf(fact_186_rel__fun__mono_H,axiom,
    ! [Y5: int > int > $o,X6: int > int > $o,A2: $o > $o > $o,B2: $o > $o > $o,F: int > $o,G: int > $o] :
      ( ! [X4: int,Y3: int] :
          ( ( Y5 @ X4 @ Y3 )
         => ( X6 @ X4 @ Y3 ) )
     => ( ! [X4: $o,Y3: $o] :
            ( ( A2 @ X4 @ Y3 )
           => ( B2 @ X4 @ Y3 ) )
       => ( ( bNF_re5089333283451836215nt_o_o @ X6 @ A2 @ F @ G )
         => ( bNF_re5089333283451836215nt_o_o @ Y5 @ B2 @ F @ G ) ) ) ) ).

% rel_fun_mono'
thf(fact_187_rel__fun__mono_H,axiom,
    ! [Y5: int > int > $o,X6: int > int > $o,A2: nat > nat > $o,B2: nat > nat > $o,F: int > nat,G: int > nat] :
      ( ! [X4: int,Y3: int] :
          ( ( Y5 @ X4 @ Y3 )
         => ( X6 @ X4 @ Y3 ) )
     => ( ! [X4: nat,Y3: nat] :
            ( ( A2 @ X4 @ Y3 )
           => ( B2 @ X4 @ Y3 ) )
       => ( ( bNF_re3715656647883201625at_nat @ X6 @ A2 @ F @ G )
         => ( bNF_re3715656647883201625at_nat @ Y5 @ B2 @ F @ G ) ) ) ) ).

% rel_fun_mono'
thf(fact_188_rel__fun__mono_H,axiom,
    ! [Y5: int > int > $o,X6: int > int > $o,A2: int > int > $o,B2: int > int > $o,F: int > int,G: int > int] :
      ( ! [X4: int,Y3: int] :
          ( ( Y5 @ X4 @ Y3 )
         => ( X6 @ X4 @ Y3 ) )
     => ( ! [X4: int,Y3: int] :
            ( ( A2 @ X4 @ Y3 )
           => ( B2 @ X4 @ Y3 ) )
       => ( ( bNF_re4712519889275205905nt_int @ X6 @ A2 @ F @ G )
         => ( bNF_re4712519889275205905nt_int @ Y5 @ B2 @ F @ G ) ) ) ) ).

% rel_fun_mono'
thf(fact_189_rel__fun__mono_H,axiom,
    ! [Y5: int > int > $o,X6: int > int > $o,A2: ( int > $o ) > ( int > $o ) > $o,B2: ( int > $o ) > ( int > $o ) > $o,F: int > int > $o,G: int > int > $o] :
      ( ! [X4: int,Y3: int] :
          ( ( Y5 @ X4 @ Y3 )
         => ( X6 @ X4 @ Y3 ) )
     => ( ! [X4: int > $o,Y3: int > $o] :
            ( ( A2 @ X4 @ Y3 )
           => ( B2 @ X4 @ Y3 ) )
       => ( ( bNF_re3403563459893282935_int_o @ X6 @ A2 @ F @ G )
         => ( bNF_re3403563459893282935_int_o @ Y5 @ B2 @ F @ G ) ) ) ) ).

% rel_fun_mono'
thf(fact_190_rel__fun__mono_H,axiom,
    ! [Y5: int > int > $o,X6: int > int > $o,A2: ( int > int ) > ( int > int ) > $o,B2: ( int > int ) > ( int > int ) > $o,F: int > int > int,G: int > int > int] :
      ( ! [X4: int,Y3: int] :
          ( ( Y5 @ X4 @ Y3 )
         => ( X6 @ X4 @ Y3 ) )
     => ( ! [X4: int > int,Y3: int > int] :
            ( ( A2 @ X4 @ Y3 )
           => ( B2 @ X4 @ Y3 ) )
       => ( ( bNF_re711492959462206631nt_int @ X6 @ A2 @ F @ G )
         => ( bNF_re711492959462206631nt_int @ Y5 @ B2 @ F @ G ) ) ) ) ).

% rel_fun_mono'
thf(fact_191_rel__fun__mono,axiom,
    ! [X6: int > int > $o,A2: $o > $o > $o,F: int > $o,G: int > $o,Y5: int > int > $o,B2: $o > $o > $o] :
      ( ( bNF_re5089333283451836215nt_o_o @ X6 @ A2 @ F @ G )
     => ( ! [X4: int,Y3: int] :
            ( ( Y5 @ X4 @ Y3 )
           => ( X6 @ X4 @ Y3 ) )
       => ( ! [X4: $o,Y3: $o] :
              ( ( A2 @ X4 @ Y3 )
             => ( B2 @ X4 @ Y3 ) )
         => ( bNF_re5089333283451836215nt_o_o @ Y5 @ B2 @ F @ G ) ) ) ) ).

% rel_fun_mono
thf(fact_192_rel__fun__mono,axiom,
    ! [X6: int > int > $o,A2: nat > nat > $o,F: int > nat,G: int > nat,Y5: int > int > $o,B2: nat > nat > $o] :
      ( ( bNF_re3715656647883201625at_nat @ X6 @ A2 @ F @ G )
     => ( ! [X4: int,Y3: int] :
            ( ( Y5 @ X4 @ Y3 )
           => ( X6 @ X4 @ Y3 ) )
       => ( ! [X4: nat,Y3: nat] :
              ( ( A2 @ X4 @ Y3 )
             => ( B2 @ X4 @ Y3 ) )
         => ( bNF_re3715656647883201625at_nat @ Y5 @ B2 @ F @ G ) ) ) ) ).

% rel_fun_mono
thf(fact_193_rel__fun__mono,axiom,
    ! [X6: int > int > $o,A2: int > int > $o,F: int > int,G: int > int,Y5: int > int > $o,B2: int > int > $o] :
      ( ( bNF_re4712519889275205905nt_int @ X6 @ A2 @ F @ G )
     => ( ! [X4: int,Y3: int] :
            ( ( Y5 @ X4 @ Y3 )
           => ( X6 @ X4 @ Y3 ) )
       => ( ! [X4: int,Y3: int] :
              ( ( A2 @ X4 @ Y3 )
             => ( B2 @ X4 @ Y3 ) )
         => ( bNF_re4712519889275205905nt_int @ Y5 @ B2 @ F @ G ) ) ) ) ).

% rel_fun_mono
thf(fact_194_rel__fun__mono,axiom,
    ! [X6: int > int > $o,A2: ( int > $o ) > ( int > $o ) > $o,F: int > int > $o,G: int > int > $o,Y5: int > int > $o,B2: ( int > $o ) > ( int > $o ) > $o] :
      ( ( bNF_re3403563459893282935_int_o @ X6 @ A2 @ F @ G )
     => ( ! [X4: int,Y3: int] :
            ( ( Y5 @ X4 @ Y3 )
           => ( X6 @ X4 @ Y3 ) )
       => ( ! [X4: int > $o,Y3: int > $o] :
              ( ( A2 @ X4 @ Y3 )
             => ( B2 @ X4 @ Y3 ) )
         => ( bNF_re3403563459893282935_int_o @ Y5 @ B2 @ F @ G ) ) ) ) ).

% rel_fun_mono
thf(fact_195_rel__fun__mono,axiom,
    ! [X6: int > int > $o,A2: ( int > int ) > ( int > int ) > $o,F: int > int > int,G: int > int > int,Y5: int > int > $o,B2: ( int > int ) > ( int > int ) > $o] :
      ( ( bNF_re711492959462206631nt_int @ X6 @ A2 @ F @ G )
     => ( ! [X4: int,Y3: int] :
            ( ( Y5 @ X4 @ Y3 )
           => ( X6 @ X4 @ Y3 ) )
       => ( ! [X4: int > int,Y3: int > int] :
              ( ( A2 @ X4 @ Y3 )
             => ( B2 @ X4 @ Y3 ) )
         => ( bNF_re711492959462206631nt_int @ Y5 @ B2 @ F @ G ) ) ) ) ).

% rel_fun_mono
thf(fact_196_rel__fun__eq,axiom,
    ( ( bNF_re5089333283451836215nt_o_o
      @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
      @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
    = ( ^ [Y2: int > $o,Z2: int > $o] : ( Y2 = Z2 ) ) ) ).

% rel_fun_eq
thf(fact_197_rel__fun__eq,axiom,
    ( ( bNF_re3715656647883201625at_nat
      @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
      @ ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 ) )
    = ( ^ [Y2: int > nat,Z2: int > nat] : ( Y2 = Z2 ) ) ) ).

% rel_fun_eq
thf(fact_198_rel__fun__eq,axiom,
    ( ( bNF_re4712519889275205905nt_int
      @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
      @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) )
    = ( ^ [Y2: int > int,Z2: int > int] : ( Y2 = Z2 ) ) ) ).

% rel_fun_eq
thf(fact_199_rel__fun__eq,axiom,
    ( ( bNF_re3403563459893282935_int_o
      @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
      @ ^ [Y2: int > $o,Z2: int > $o] : ( Y2 = Z2 ) )
    = ( ^ [Y2: int > int > $o,Z2: int > int > $o] : ( Y2 = Z2 ) ) ) ).

% rel_fun_eq
thf(fact_200_rel__fun__eq,axiom,
    ( ( bNF_re711492959462206631nt_int
      @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
      @ ^ [Y2: int > int,Z2: int > int] : ( Y2 = Z2 ) )
    = ( ^ [Y2: int > int > int,Z2: int > int > int] : ( Y2 = Z2 ) ) ) ).

% rel_fun_eq
thf(fact_201_rel__funD2,axiom,
    ! [A2: int > int > $o,B2: $o > $o > $o,F: int > $o,G: int > $o,X: int] :
      ( ( bNF_re5089333283451836215nt_o_o @ A2 @ B2 @ F @ G )
     => ( ( A2 @ X @ X )
       => ( B2 @ ( F @ X ) @ ( G @ X ) ) ) ) ).

% rel_funD2
thf(fact_202_rel__funD2,axiom,
    ! [A2: int > int > $o,B2: nat > nat > $o,F: int > nat,G: int > nat,X: int] :
      ( ( bNF_re3715656647883201625at_nat @ A2 @ B2 @ F @ G )
     => ( ( A2 @ X @ X )
       => ( B2 @ ( F @ X ) @ ( G @ X ) ) ) ) ).

% rel_funD2
thf(fact_203_rel__funD2,axiom,
    ! [A2: int > int > $o,B2: int > int > $o,F: int > int,G: int > int,X: int] :
      ( ( bNF_re4712519889275205905nt_int @ A2 @ B2 @ F @ G )
     => ( ( A2 @ X @ X )
       => ( B2 @ ( F @ X ) @ ( G @ X ) ) ) ) ).

% rel_funD2
thf(fact_204_rel__funD2,axiom,
    ! [A2: int > int > $o,B2: ( int > $o ) > ( int > $o ) > $o,F: int > int > $o,G: int > int > $o,X: int] :
      ( ( bNF_re3403563459893282935_int_o @ A2 @ B2 @ F @ G )
     => ( ( A2 @ X @ X )
       => ( B2 @ ( F @ X ) @ ( G @ X ) ) ) ) ).

% rel_funD2
thf(fact_205_rel__funD2,axiom,
    ! [A2: int > int > $o,B2: ( int > int ) > ( int > int ) > $o,F: int > int > int,G: int > int > int,X: int] :
      ( ( bNF_re711492959462206631nt_int @ A2 @ B2 @ F @ G )
     => ( ( A2 @ X @ X )
       => ( B2 @ ( F @ X ) @ ( G @ X ) ) ) ) ).

% rel_funD2
thf(fact_206_apply__rsp_H,axiom,
    ! [R1: int > int > $o,R22: $o > $o > $o,F: int > $o,G: int > $o,X: int,Y: int] :
      ( ( bNF_re5089333283451836215nt_o_o @ R1 @ R22 @ F @ G )
     => ( ( R1 @ X @ Y )
       => ( R22 @ ( F @ X ) @ ( G @ Y ) ) ) ) ).

% apply_rsp'
thf(fact_207_apply__rsp_H,axiom,
    ! [R1: int > int > $o,R22: nat > nat > $o,F: int > nat,G: int > nat,X: int,Y: int] :
      ( ( bNF_re3715656647883201625at_nat @ R1 @ R22 @ F @ G )
     => ( ( R1 @ X @ Y )
       => ( R22 @ ( F @ X ) @ ( G @ Y ) ) ) ) ).

% apply_rsp'
thf(fact_208_apply__rsp_H,axiom,
    ! [R1: int > int > $o,R22: int > int > $o,F: int > int,G: int > int,X: int,Y: int] :
      ( ( bNF_re4712519889275205905nt_int @ R1 @ R22 @ F @ G )
     => ( ( R1 @ X @ Y )
       => ( R22 @ ( F @ X ) @ ( G @ Y ) ) ) ) ).

% apply_rsp'
thf(fact_209_apply__rsp_H,axiom,
    ! [R1: int > int > $o,R22: ( int > $o ) > ( int > $o ) > $o,F: int > int > $o,G: int > int > $o,X: int,Y: int] :
      ( ( bNF_re3403563459893282935_int_o @ R1 @ R22 @ F @ G )
     => ( ( R1 @ X @ Y )
       => ( R22 @ ( F @ X ) @ ( G @ Y ) ) ) ) ).

% apply_rsp'
thf(fact_210_apply__rsp_H,axiom,
    ! [R1: int > int > $o,R22: ( int > int ) > ( int > int ) > $o,F: int > int > int,G: int > int > int,X: int,Y: int] :
      ( ( bNF_re711492959462206631nt_int @ R1 @ R22 @ F @ G )
     => ( ( R1 @ X @ Y )
       => ( R22 @ ( F @ X ) @ ( G @ Y ) ) ) ) ).

% apply_rsp'
thf(fact_211_rel__funE,axiom,
    ! [A2: int > int > $o,B2: $o > $o > $o,F: int > $o,G: int > $o,X: int,Y: int] :
      ( ( bNF_re5089333283451836215nt_o_o @ A2 @ B2 @ F @ G )
     => ( ( A2 @ X @ Y )
       => ( B2 @ ( F @ X ) @ ( G @ Y ) ) ) ) ).

% rel_funE
thf(fact_212_rel__funE,axiom,
    ! [A2: int > int > $o,B2: nat > nat > $o,F: int > nat,G: int > nat,X: int,Y: int] :
      ( ( bNF_re3715656647883201625at_nat @ A2 @ B2 @ F @ G )
     => ( ( A2 @ X @ Y )
       => ( B2 @ ( F @ X ) @ ( G @ Y ) ) ) ) ).

% rel_funE
thf(fact_213_rel__funE,axiom,
    ! [A2: int > int > $o,B2: int > int > $o,F: int > int,G: int > int,X: int,Y: int] :
      ( ( bNF_re4712519889275205905nt_int @ A2 @ B2 @ F @ G )
     => ( ( A2 @ X @ Y )
       => ( B2 @ ( F @ X ) @ ( G @ Y ) ) ) ) ).

% rel_funE
thf(fact_214_rel__funE,axiom,
    ! [A2: int > int > $o,B2: ( int > $o ) > ( int > $o ) > $o,F: int > int > $o,G: int > int > $o,X: int,Y: int] :
      ( ( bNF_re3403563459893282935_int_o @ A2 @ B2 @ F @ G )
     => ( ( A2 @ X @ Y )
       => ( B2 @ ( F @ X ) @ ( G @ Y ) ) ) ) ).

% rel_funE
thf(fact_215_rel__funE,axiom,
    ! [A2: int > int > $o,B2: ( int > int ) > ( int > int ) > $o,F: int > int > int,G: int > int > int,X: int,Y: int] :
      ( ( bNF_re711492959462206631nt_int @ A2 @ B2 @ F @ G )
     => ( ( A2 @ X @ Y )
       => ( B2 @ ( F @ X ) @ ( G @ Y ) ) ) ) ).

% rel_funE
thf(fact_216_rel__funD,axiom,
    ! [A2: int > int > $o,B2: $o > $o > $o,F: int > $o,G: int > $o,X: int,Y: int] :
      ( ( bNF_re5089333283451836215nt_o_o @ A2 @ B2 @ F @ G )
     => ( ( A2 @ X @ Y )
       => ( B2 @ ( F @ X ) @ ( G @ Y ) ) ) ) ).

% rel_funD
thf(fact_217_rel__funD,axiom,
    ! [A2: int > int > $o,B2: nat > nat > $o,F: int > nat,G: int > nat,X: int,Y: int] :
      ( ( bNF_re3715656647883201625at_nat @ A2 @ B2 @ F @ G )
     => ( ( A2 @ X @ Y )
       => ( B2 @ ( F @ X ) @ ( G @ Y ) ) ) ) ).

% rel_funD
thf(fact_218_rel__funD,axiom,
    ! [A2: int > int > $o,B2: int > int > $o,F: int > int,G: int > int,X: int,Y: int] :
      ( ( bNF_re4712519889275205905nt_int @ A2 @ B2 @ F @ G )
     => ( ( A2 @ X @ Y )
       => ( B2 @ ( F @ X ) @ ( G @ Y ) ) ) ) ).

% rel_funD
thf(fact_219_rel__funD,axiom,
    ! [A2: int > int > $o,B2: ( int > $o ) > ( int > $o ) > $o,F: int > int > $o,G: int > int > $o,X: int,Y: int] :
      ( ( bNF_re3403563459893282935_int_o @ A2 @ B2 @ F @ G )
     => ( ( A2 @ X @ Y )
       => ( B2 @ ( F @ X ) @ ( G @ Y ) ) ) ) ).

% rel_funD
thf(fact_220_rel__funD,axiom,
    ! [A2: int > int > $o,B2: ( int > int ) > ( int > int ) > $o,F: int > int > int,G: int > int > int,X: int,Y: int] :
      ( ( bNF_re711492959462206631nt_int @ A2 @ B2 @ F @ G )
     => ( ( A2 @ X @ Y )
       => ( B2 @ ( F @ X ) @ ( G @ Y ) ) ) ) ).

% rel_funD
thf(fact_221_Domainp__refl,axiom,
    domain4015354059925764579ring_a = domain4015354059925764579ring_a ).

% Domainp_refl
thf(fact_222_Domainp__refl,axiom,
    domain2947197372085612771ring_a = domain2947197372085612771ring_a ).

% Domainp_refl
thf(fact_223_Domainp__iff,axiom,
    ( domain4015354059925764579ring_a
    = ( ^ [T: vec_int > vec_Fi4296597256376197294ring_a > $o,X3: vec_int] :
        ? [X7: vec_Fi4296597256376197294ring_a] : ( T @ X3 @ X7 ) ) ) ).

% Domainp_iff
thf(fact_224_Domainp__iff,axiom,
    ( domain2947197372085612771ring_a
    = ( ^ [T: mat_int > mat_Fi443519135453058082ring_a > $o,X3: mat_int] :
        ? [X7: mat_Fi443519135453058082ring_a] : ( T @ X3 @ X7 ) ) ) ).

% Domainp_iff
thf(fact_225_right__total__def,axiom,
    ( right_2909008500229168952ring_a
    = ( ^ [R2: int > finite_mod_ring_a > $o] :
        ! [Y6: finite_mod_ring_a] :
        ? [X3: int] : ( R2 @ X3 @ Y6 ) ) ) ).

% right_total_def
thf(fact_226_right__total__def,axiom,
    ( right_7341149013462710248ring_a
    = ( ^ [R2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
        ! [Y6: vec_Fi4296597256376197294ring_a] :
        ? [X3: vec_int] : ( R2 @ X3 @ Y6 ) ) ) ).

% right_total_def
thf(fact_227_right__total__def,axiom,
    ( right_6272992325622558440ring_a
    = ( ^ [R2: mat_int > mat_Fi443519135453058082ring_a > $o] :
        ! [Y6: mat_Fi443519135453058082ring_a] :
        ? [X3: mat_int] : ( R2 @ X3 @ Y6 ) ) ) ).

% right_total_def
thf(fact_228_right__totalI,axiom,
    ! [A2: int > finite_mod_ring_a > $o] :
      ( ! [Y3: finite_mod_ring_a] :
        ? [X5: int] : ( A2 @ X5 @ Y3 )
     => ( right_2909008500229168952ring_a @ A2 ) ) ).

% right_totalI
thf(fact_229_right__totalI,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ! [Y3: vec_Fi4296597256376197294ring_a] :
        ? [X5: vec_int] : ( A2 @ X5 @ Y3 )
     => ( right_7341149013462710248ring_a @ A2 ) ) ).

% right_totalI
thf(fact_230_right__totalI,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ! [Y3: mat_Fi443519135453058082ring_a] :
        ? [X5: mat_int] : ( A2 @ X5 @ Y3 )
     => ( right_6272992325622558440ring_a @ A2 ) ) ).

% right_totalI
thf(fact_231_right__totalE,axiom,
    ! [A2: int > finite_mod_ring_a > $o,Y: finite_mod_ring_a] :
      ( ( right_2909008500229168952ring_a @ A2 )
     => ~ ! [X4: int] :
            ~ ( A2 @ X4 @ Y ) ) ).

% right_totalE
thf(fact_232_right__totalE,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o,Y: vec_Fi4296597256376197294ring_a] :
      ( ( right_7341149013462710248ring_a @ A2 )
     => ~ ! [X4: vec_int] :
            ~ ( A2 @ X4 @ Y ) ) ).

% right_totalE
thf(fact_233_right__totalE,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o,Y: mat_Fi443519135453058082ring_a] :
      ( ( right_6272992325622558440ring_a @ A2 )
     => ~ ! [X4: mat_int] :
            ~ ( A2 @ X4 @ Y ) ) ).

% right_totalE
thf(fact_234_bi__total__def,axiom,
    ( bi_tot623839499179674737ring_a
    = ( ^ [R2: int > finite_mod_ring_a > $o] :
          ( ! [X3: int] :
            ? [X7: finite_mod_ring_a] : ( R2 @ X3 @ X7 )
          & ! [Y6: finite_mod_ring_a] :
            ? [X3: int] : ( R2 @ X3 @ Y6 ) ) ) ) ).

% bi_total_def
thf(fact_235_bi__total__def,axiom,
    ( bi_tot310863827317176225ring_a
    = ( ^ [R2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
          ( ! [X3: vec_int] :
            ? [X7: vec_Fi4296597256376197294ring_a] : ( R2 @ X3 @ X7 )
          & ! [Y6: vec_Fi4296597256376197294ring_a] :
            ? [X3: vec_int] : ( R2 @ X3 @ Y6 ) ) ) ) ).

% bi_total_def
thf(fact_236_bi__total__def,axiom,
    ( bi_tot8466079176331800225ring_a
    = ( ^ [R2: mat_int > mat_Fi443519135453058082ring_a > $o] :
          ( ! [X3: mat_int] :
            ? [X7: mat_Fi443519135453058082ring_a] : ( R2 @ X3 @ X7 )
          & ! [Y6: mat_Fi443519135453058082ring_a] :
            ? [X3: mat_int] : ( R2 @ X3 @ Y6 ) ) ) ) ).

% bi_total_def
thf(fact_237_right__unique__def,axiom,
    ( right_2407805982356550513ring_a
    = ( ^ [R2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
        ! [X3: vec_int,Y6: vec_Fi4296597256376197294ring_a,Z3: vec_Fi4296597256376197294ring_a] :
          ( ( R2 @ X3 @ Y6 )
         => ( ( R2 @ X3 @ Z3 )
           => ( Y6 = Z3 ) ) ) ) ) ).

% right_unique_def
thf(fact_238_right__unique__def,axiom,
    ( right_1339649294516398705ring_a
    = ( ^ [R2: mat_int > mat_Fi443519135453058082ring_a > $o] :
        ! [X3: mat_int,Y6: mat_Fi443519135453058082ring_a,Z3: mat_Fi443519135453058082ring_a] :
          ( ( R2 @ X3 @ Y6 )
         => ( ( R2 @ X3 @ Z3 )
           => ( Y6 = Z3 ) ) ) ) ) ).

% right_unique_def
thf(fact_239_right__uniqueI,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ! [X4: vec_int,Y3: vec_Fi4296597256376197294ring_a,Z4: vec_Fi4296597256376197294ring_a] :
          ( ( A2 @ X4 @ Y3 )
         => ( ( A2 @ X4 @ Z4 )
           => ( Y3 = Z4 ) ) )
     => ( right_2407805982356550513ring_a @ A2 ) ) ).

% right_uniqueI
thf(fact_240_right__uniqueI,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ! [X4: mat_int,Y3: mat_Fi443519135453058082ring_a,Z4: mat_Fi443519135453058082ring_a] :
          ( ( A2 @ X4 @ Y3 )
         => ( ( A2 @ X4 @ Z4 )
           => ( Y3 = Z4 ) ) )
     => ( right_1339649294516398705ring_a @ A2 ) ) ).

% right_uniqueI
thf(fact_241_right__uniqueD,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o,X: vec_int,Y: vec_Fi4296597256376197294ring_a,Z: vec_Fi4296597256376197294ring_a] :
      ( ( right_2407805982356550513ring_a @ A2 )
     => ( ( A2 @ X @ Y )
       => ( ( A2 @ X @ Z )
         => ( Y = Z ) ) ) ) ).

% right_uniqueD
thf(fact_242_right__uniqueD,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o,X: mat_int,Y: mat_Fi443519135453058082ring_a,Z: mat_Fi443519135453058082ring_a] :
      ( ( right_1339649294516398705ring_a @ A2 )
     => ( ( A2 @ X @ Y )
       => ( ( A2 @ X @ Z )
         => ( Y = Z ) ) ) ) ).

% right_uniqueD
thf(fact_243_left__total__def,axiom,
    ( left_t8941605147251654769ring_a
    = ( ^ [R2: int > finite_mod_ring_a > $o] :
        ! [X3: int] :
        ? [X7: finite_mod_ring_a] : ( R2 @ X3 @ X7 ) ) ) ).

% left_total_def
thf(fact_244_left__total__def,axiom,
    ( left_t7842747197492505505ring_a
    = ( ^ [R2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
        ! [X3: vec_int] :
        ? [X7: vec_Fi4296597256376197294ring_a] : ( R2 @ X3 @ X7 ) ) ) ).

% left_total_def
thf(fact_245_left__total__def,axiom,
    ( left_t6774590509652353697ring_a
    = ( ^ [R2: mat_int > mat_Fi443519135453058082ring_a > $o] :
        ! [X3: mat_int] :
        ? [X7: mat_Fi443519135453058082ring_a] : ( R2 @ X3 @ X7 ) ) ) ).

% left_total_def
thf(fact_246_left__totalI,axiom,
    ! [R: int > finite_mod_ring_a > $o] :
      ( ! [X4: int] :
        ? [X_12: finite_mod_ring_a] : ( R @ X4 @ X_12 )
     => ( left_t8941605147251654769ring_a @ R ) ) ).

% left_totalI
thf(fact_247_left__totalI,axiom,
    ! [R: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ! [X4: vec_int] :
        ? [X_12: vec_Fi4296597256376197294ring_a] : ( R @ X4 @ X_12 )
     => ( left_t7842747197492505505ring_a @ R ) ) ).

% left_totalI
thf(fact_248_left__totalI,axiom,
    ! [R: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ! [X4: mat_int] :
        ? [X_12: mat_Fi443519135453058082ring_a] : ( R @ X4 @ X_12 )
     => ( left_t6774590509652353697ring_a @ R ) ) ).

% left_totalI
thf(fact_249_bits__mod__0,axiom,
    ! [A: int] :
      ( ( modulo_modulo_int @ zero_zero_int @ A )
      = zero_zero_int ) ).

% bits_mod_0
thf(fact_250_bits__mod__0,axiom,
    ! [A: nat] :
      ( ( modulo_modulo_nat @ zero_zero_nat @ A )
      = zero_zero_nat ) ).

% bits_mod_0
thf(fact_251_mod__self,axiom,
    ! [A: int] :
      ( ( modulo_modulo_int @ A @ A )
      = zero_zero_int ) ).

% mod_self
thf(fact_252_mod__self,axiom,
    ! [A: nat] :
      ( ( modulo_modulo_nat @ A @ A )
      = zero_zero_nat ) ).

% mod_self
thf(fact_253_mod__by__0,axiom,
    ! [A: int] :
      ( ( modulo_modulo_int @ A @ zero_zero_int )
      = A ) ).

% mod_by_0
thf(fact_254_mod__by__0,axiom,
    ! [A: nat] :
      ( ( modulo_modulo_nat @ A @ zero_zero_nat )
      = A ) ).

% mod_by_0
thf(fact_255_mod__0,axiom,
    ! [A: int] :
      ( ( modulo_modulo_int @ zero_zero_int @ A )
      = zero_zero_int ) ).

% mod_0
thf(fact_256_mod__0,axiom,
    ! [A: nat] :
      ( ( modulo_modulo_nat @ zero_zero_nat @ A )
      = zero_zero_nat ) ).

% mod_0
thf(fact_257_zero__M__Rel,axiom,
    vector3024231343486012919_Rel_a @ m @ zero_zero_int @ zero_z7902377541816115708ring_a ).

% zero_M_Rel
thf(fact_258_eucl__induct,axiom,
    ! [P: int > int > $o,A: int,B: int] :
      ( ! [B3: int] : ( P @ B3 @ zero_zero_int )
     => ( ! [A4: int,B3: int] :
            ( ( B3 != zero_zero_int )
           => ( ( P @ B3 @ ( modulo_modulo_int @ A4 @ B3 ) )
             => ( P @ A4 @ B3 ) ) )
       => ( P @ A @ B ) ) ) ).

% eucl_induct
thf(fact_259_eucl__induct,axiom,
    ! [P: nat > nat > $o,A: nat,B: nat] :
      ( ! [B3: nat] : ( P @ B3 @ zero_zero_nat )
     => ( ! [A4: nat,B3: nat] :
            ( ( B3 != zero_zero_nat )
           => ( ( P @ B3 @ ( modulo_modulo_nat @ A4 @ B3 ) )
             => ( P @ A4 @ B3 ) ) )
       => ( P @ A @ B ) ) ) ).

% eucl_induct
thf(fact_260_right__total__MM__Rel,axiom,
    right_6272992325622558440ring_a @ ( vector2798151085771547010_Rel_a @ m ) ).

% right_total_MM_Rel
thf(fact_261_domain__MM__rel,axiom,
    ( ( domain2947197372085612771ring_a @ ( vector2798151085771547010_Rel_a @ m ) )
    = ( ^ [F2: mat_int] : $true ) ) ).

% domain_MM_rel
thf(fact_262_left__total__MM__Rel,axiom,
    left_t6774590509652353697ring_a @ ( vector2798151085771547010_Rel_a @ m ) ).

% left_total_MM_Rel
thf(fact_263_right__unique__MM__Rel,axiom,
    right_1339649294516398705ring_a @ ( vector2798151085771547010_Rel_a @ m ) ).

% right_unique_MM_Rel
thf(fact_264_bi__total__MM__Rel,axiom,
    bi_tot8466079176331800225ring_a @ ( vector2798151085771547010_Rel_a @ m ) ).

% bi_total_MM_Rel
thf(fact_265_vec__of__dim__0,axiom,
    ! [V: vec_int] :
      ( ( ( dim_vec_int @ V )
        = zero_zero_nat )
      = ( V
        = ( zero_vec_int @ zero_zero_nat ) ) ) ).

% vec_of_dim_0
thf(fact_266_vec__of__dim__0,axiom,
    ! [V: vec_Fi4296597256376197294ring_a] :
      ( ( ( dim_ve9152325144110082507ring_a @ V )
        = zero_zero_nat )
      = ( V
        = ( zero_v1122566495420860901ring_a @ zero_zero_nat ) ) ) ).

% vec_of_dim_0
thf(fact_267_to__int__mod__ring__hom_Ohom__zero,axiom,
    ( ( finite1095367895020317408ring_a @ zero_z7902377541816115708ring_a )
    = zero_zero_int ) ).

% to_int_mod_ring_hom.hom_zero
thf(fact_268_to__int__mod__ring__hom_Ohom__0__iff,axiom,
    ! [X: finite_mod_ring_a] :
      ( ( ( finite1095367895020317408ring_a @ X )
        = zero_zero_int )
      = ( X = zero_z7902377541816115708ring_a ) ) ).

% to_int_mod_ring_hom.hom_0_iff
thf(fact_269_of__int__mod__ring__hom_Ohom__zero,axiom,
    ( ( finite8272632373135393572ring_a @ zero_zero_int )
    = zero_z7902377541816115708ring_a ) ).

% of_int_mod_ring_hom.hom_zero
thf(fact_270_mat__mod__type_OMM__Rel_Ocong,axiom,
    vector2798151085771547010_Rel_a = vector2798151085771547010_Rel_a ).

% mat_mod_type.MM_Rel.cong
thf(fact_271_to__int__mod__ring__hom_Ohom__0,axiom,
    ! [X: finite_mod_ring_a] :
      ( ( ( finite1095367895020317408ring_a @ X )
        = zero_zero_int )
     => ( X = zero_z7902377541816115708ring_a ) ) ).

% to_int_mod_ring_hom.hom_0
thf(fact_272_zero__reorient,axiom,
    ! [X: int] :
      ( ( zero_zero_int = X )
      = ( X = zero_zero_int ) ) ).

% zero_reorient
thf(fact_273_zero__reorient,axiom,
    ! [X: finite_mod_ring_a] :
      ( ( zero_z7902377541816115708ring_a = X )
      = ( X = zero_z7902377541816115708ring_a ) ) ).

% zero_reorient
thf(fact_274_zero__reorient,axiom,
    ! [X: nat] :
      ( ( zero_zero_nat = X )
      = ( X = zero_zero_nat ) ) ).

% zero_reorient
thf(fact_275_zero__reorient,axiom,
    ! [X: real] :
      ( ( zero_zero_real = X )
      = ( X = zero_zero_real ) ) ).

% zero_reorient
thf(fact_276_fun_Orel__transfer,axiom,
    ! [Sa: $o > nat > $o,Sc: $o > nat > $o] :
      ( bNF_re2572702929266883447_nat_o
      @ ( bNF_re7444536988384623437_nat_o @ Sa
        @ ( bNF_re7218653638241686475at_o_o @ Sc
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re1028521115286184183_nat_o
        @ ( bNF_re2497981702703480305_o_nat
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ Sa )
        @ ( bNF_re4654332367156724257at_o_o
          @ ( bNF_re2497981702703480305_o_nat
            @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
            @ Sc )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re5089333283451836215nt_o_o
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) )
      @ ( bNF_re3715656647883201625at_nat
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) ) ) ).

% fun.rel_transfer
thf(fact_277_fun_Orel__transfer,axiom,
    ! [Sa: $o > int > $o,Sc: $o > int > $o] :
      ( bNF_re4473429657033765895_int_o
      @ ( bNF_re5432788727719671445_int_o @ Sa
        @ ( bNF_re5301841019279710247nt_o_o @ Sc
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re4810274416841960511_int_o
        @ ( bNF_re2495491232194430029_o_int
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ Sa )
        @ ( bNF_re5653686079057778813nt_o_o
          @ ( bNF_re2495491232194430029_o_int
            @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
            @ Sc )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re5089333283451836215nt_o_o
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) )
      @ ( bNF_re4712519889275205905nt_int
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) ) ) ).

% fun.rel_transfer
thf(fact_278_fun_Orel__transfer,axiom,
    ! [Sa: nat > $o > $o,Sc: nat > $o > $o] :
      ( bNF_re4194204844150045891nt_o_o
      @ ( bNF_re6709961196992454779_o_o_o @ Sa
        @ ( bNF_re2164719486249941929_o_o_o @ Sc
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re8458729935450468901nt_o_o
        @ ( bNF_re5600653063811665615_nat_o
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ Sa )
        @ ( bNF_re7959771505041706665_o_o_o
          @ ( bNF_re5600653063811665615_nat_o
            @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
            @ Sc )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re3715656647883201625at_nat
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) )
      @ ( bNF_re5089333283451836215nt_o_o
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) ) ) ).

% fun.rel_transfer
thf(fact_279_fun_Orel__transfer,axiom,
    ! [Sa: nat > int > $o,Sc: nat > int > $o] :
      ( bNF_re9024530389434122605_int_o
      @ ( bNF_re3149889684360781247_int_o @ Sa
        @ ( bNF_re2788914913031914203nt_o_o @ Sc
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re3282862283220456469_int_o
        @ ( bNF_re3713166177374151349at_int
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ Sa )
        @ ( bNF_re69706704502853489nt_o_o
          @ ( bNF_re3713166177374151349at_int
            @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
            @ Sc )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re3715656647883201625at_nat
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) )
      @ ( bNF_re4712519889275205905nt_int
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) ) ) ).

% fun.rel_transfer
thf(fact_280_fun_Orel__transfer,axiom,
    ! [Sa: int > $o > $o,Sc: int > $o > $o] :
      ( bNF_re6840425655782752307nt_o_o
      @ ( bNF_re8893569941355005307_o_o_o @ Sa
        @ ( bNF_re4469125395230562381_o_o_o @ Sc
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re6856201910719030053nt_o_o
        @ ( bNF_re3779610718378977651_int_o
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ Sa )
        @ ( bNF_re2570638569070957389_o_o_o
          @ ( bNF_re3779610718378977651_int_o
            @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
            @ Sc )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re4712519889275205905nt_int
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) )
      @ ( bNF_re5089333283451836215nt_o_o
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) ) ) ).

% fun.rel_transfer
thf(fact_281_fun_Orel__transfer,axiom,
    ! [Sa: int > nat > $o,Sc: int > nat > $o] :
      ( bNF_re1378104478368373837_nat_o
      @ ( bNF_re832142806295076215_nat_o @ Sa
        @ ( bNF_re7006145902413812443at_o_o @ Sc
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re6215008164563829709_nat_o
        @ ( bNF_re4715010359784256181nt_nat
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ Sa )
        @ ( bNF_re278470125530178929at_o_o
          @ ( bNF_re4715010359784256181nt_nat
            @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
            @ Sc )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re4712519889275205905nt_int
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) )
      @ ( bNF_re3715656647883201625at_nat
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) ) ) ).

% fun.rel_transfer
thf(fact_282_fun_Orel__transfer,axiom,
    ! [Sa: $o > $o > $o,Sc: $o > $o > $o] :
      ( bNF_re3012816421615927389nt_o_o
      @ ( bNF_re6472675536664000681_o_o_o @ Sa
        @ ( bNF_rel_fun_o_o_o_o @ Sc
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re513079643185015507nt_o_o
        @ ( bNF_re5089333283451836215nt_o_o
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ Sa )
        @ ( bNF_re6378653760509651613_o_o_o
          @ ( bNF_re5089333283451836215nt_o_o
            @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
            @ Sc )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re5089333283451836215nt_o_o
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) )
      @ ( bNF_re5089333283451836215nt_o_o
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) ) ) ).

% fun.rel_transfer
thf(fact_283_fun_Orel__transfer,axiom,
    ! [Sa: $o > $o > $o,Sc: nat > nat > $o] :
      ( bNF_re1168432982574861285_nat_o
      @ ( bNF_re3790380520279025053_nat_o @ Sa
        @ ( bNF_re4705727531993890431at_o_o @ Sc
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re366876804441710237_nat_o
        @ ( bNF_re5089333283451836215nt_o_o
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ Sa )
        @ ( bNF_re8293725029456574741at_o_o
          @ ( bNF_re3715656647883201625at_nat
            @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
            @ Sc )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re2497981702703480305_o_nat
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) )
      @ ( bNF_re2497981702703480305_o_nat
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) ) ) ).

% fun.rel_transfer
thf(fact_284_fun_Orel__transfer,axiom,
    ! [Sa: nat > nat > $o,Sc: $o > $o > $o] :
      ( bNF_re4138666560314401969nt_o_o
      @ ( bNF_re6222992434181357259_o_o_o @ Sa
        @ ( bNF_rel_fun_o_o_o_o @ Sc
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re7816892618387588427nt_o_o
        @ ( bNF_re3715656647883201625at_nat
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ Sa )
        @ ( bNF_re6378653760509651613_o_o_o
          @ ( bNF_re5089333283451836215nt_o_o
            @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
            @ Sc )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re5600653063811665615_nat_o
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) )
      @ ( bNF_re5600653063811665615_nat_o
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) ) ) ).

% fun.rel_transfer
thf(fact_285_fun_Orel__transfer,axiom,
    ! [Sa: nat > nat > $o,Sc: nat > nat > $o] :
      ( bNF_re5912358153685880029_nat_o
      @ ( bNF_re578469030762574527_nat_o @ Sa
        @ ( bNF_re4705727531993890431at_o_o @ Sc
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re8877981933538057493_nat_o
        @ ( bNF_re3715656647883201625at_nat
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ Sa )
        @ ( bNF_re8293725029456574741at_o_o
          @ ( bNF_re3715656647883201625at_nat
            @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
            @ Sc )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re3715656647883201625at_nat
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) )
      @ ( bNF_re3715656647883201625at_nat
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) ) ) ).

% fun.rel_transfer
thf(fact_286_let__rsp,axiom,
    ! [R1: int > int > $o,R22: $o > $o > $o] :
      ( bNF_re1280668699144990829nt_o_o @ R1 @ ( bNF_re6378653760509651613_o_o_o @ ( bNF_re5089333283451836215nt_o_o @ R1 @ R22 ) @ R22 )
      @ ^ [S: int,F2: int > $o] : ( F2 @ S )
      @ ^ [S: int,F2: int > $o] : ( F2 @ S ) ) ).

% let_rsp
thf(fact_287_let__rsp,axiom,
    ! [R1: int > int > $o,R22: nat > nat > $o] :
      ( bNF_re3451822466932340941at_nat @ R1 @ ( bNF_re1996201511620343607at_nat @ ( bNF_re3715656647883201625at_nat @ R1 @ R22 ) @ R22 )
      @ ^ [S: int,F2: int > nat] : ( F2 @ S )
      @ ^ [S: int,F2: int > nat] : ( F2 @ S ) ) ).

% let_rsp
thf(fact_288_let__rsp,axiom,
    ! [R1: int > int > $o,R22: int > int > $o] :
      ( bNF_re8360549327529751101nt_int @ R1 @ ( bNF_re8159601828672395943nt_int @ ( bNF_re4712519889275205905nt_int @ R1 @ R22 ) @ R22 )
      @ ^ [S: int,F2: int > int] : ( F2 @ S )
      @ ^ [S: int,F2: int > int] : ( F2 @ S ) ) ).

% let_rsp
thf(fact_289_let__rsp,axiom,
    ! [R1: int > int > $o,R22: ( int > $o ) > ( int > $o ) > $o] :
      ( bNF_re1806261209056574701_int_o @ R1 @ ( bNF_re2642688597062869533_int_o @ ( bNF_re3403563459893282935_int_o @ R1 @ R22 ) @ R22 )
      @ ^ [S: int,F2: int > int > $o] : ( F2 @ S )
      @ ^ [S: int,F2: int > int > $o] : ( F2 @ S ) ) ).

% let_rsp
thf(fact_290_let__rsp,axiom,
    ! [R1: int > int > $o,R22: ( int > int ) > ( int > int ) > $o] :
      ( bNF_re776728095411994473nt_int @ R1 @ ( bNF_re3333031753742804947nt_int @ ( bNF_re711492959462206631nt_int @ R1 @ R22 ) @ R22 )
      @ ^ [S: int,F2: int > int > int] : ( F2 @ S )
      @ ^ [S: int,F2: int > int > int] : ( F2 @ S ) ) ).

% let_rsp
thf(fact_291_image__mset__is__empty__iff,axiom,
    ! [F: finite_mod_ring_a > int,M2: multis3731679216105815691ring_a] :
      ( ( ( image_7357852445201009398_a_int @ F @ M2 )
        = zero_z3170743180189231877et_int )
      = ( M2 = zero_z6254369252435687234ring_a ) ) ).

% image_mset_is_empty_iff
thf(fact_292_image__mset__empty,axiom,
    ! [F: finite_mod_ring_a > int] :
      ( ( image_7357852445201009398_a_int @ F @ zero_z6254369252435687234ring_a )
      = zero_z3170743180189231877et_int ) ).

% image_mset_empty
thf(fact_293_If__transfer,axiom,
    ! [A2: int > int > $o] :
      ( bNF_re6420062293230768483nt_int
      @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
      @ ( bNF_re711492959462206631nt_int @ A2 @ ( bNF_re4712519889275205905nt_int @ A2 @ A2 ) )
      @ if_int
      @ if_int ) ).

% If_transfer
thf(fact_294_rel__fun__def__butlast,axiom,
    ! [R: int > int > $o,S2: int > int > $o,T2: $o > $o > $o,F: int > int > $o,G: int > int > $o] :
      ( ( bNF_re3403563459893282935_int_o @ R @ ( bNF_re5089333283451836215nt_o_o @ S2 @ T2 ) @ F @ G )
      = ( ! [X3: int,Y6: int] :
            ( ( R @ X3 @ Y6 )
           => ( bNF_re5089333283451836215nt_o_o @ S2 @ T2 @ ( F @ X3 ) @ ( G @ Y6 ) ) ) ) ) ).

% rel_fun_def_butlast
thf(fact_295_rel__fun__def__butlast,axiom,
    ! [R: int > int > $o,S2: int > int > $o,T2: int > int > $o,F: int > int > int,G: int > int > int] :
      ( ( bNF_re711492959462206631nt_int @ R @ ( bNF_re4712519889275205905nt_int @ S2 @ T2 ) @ F @ G )
      = ( ! [X3: int,Y6: int] :
            ( ( R @ X3 @ Y6 )
           => ( bNF_re4712519889275205905nt_int @ S2 @ T2 @ ( F @ X3 ) @ ( G @ Y6 ) ) ) ) ) ).

% rel_fun_def_butlast
thf(fact_296_right__unique__parametric,axiom,
    ! [A2: int > int > $o,B2: int > int > $o] :
      ( ( bi_total_int_int @ A2 )
     => ( ( bi_unique_int_int @ B2 )
       => ( ( bi_total_int_int @ B2 )
         => ( bNF_re5869992600382051037_o_o_o
            @ ( bNF_re3403563459893282935_int_o @ A2
              @ ( bNF_re5089333283451836215nt_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
            @ right_unique_int_int
            @ right_unique_int_int ) ) ) ) ).

% right_unique_parametric
thf(fact_297_right__unique__parametric,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: int > int > $o] :
      ( ( bi_tot623839499179674737ring_a @ A2 )
     => ( ( bi_unique_int_int @ B2 )
       => ( ( bi_total_int_int @ B2 )
         => ( bNF_re5891132441370877716_o_o_o
            @ ( bNF_re3873409527727426490_int_o @ A2
              @ ( bNF_re5089333283451836215nt_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
            @ right_unique_int_int
            @ right_6005435896075721627_a_int ) ) ) ) ).

% right_unique_parametric
thf(fact_298_right__unique__parametric,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: int > finite_mod_ring_a > $o] :
      ( ( bi_tot623839499179674737ring_a @ A2 )
     => ( ( bi_uni1022671006909063496ring_a @ B2 )
       => ( ( bi_tot623839499179674737ring_a @ B2 )
         => ( bNF_re3287324404599397085_o_o_o
            @ ( bNF_re1743884151495963297ng_a_o @ A2
              @ ( bNF_re8290846538823883642_a_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
            @ right_unique_int_int
            @ right_6217011779227907862ring_a ) ) ) ) ).

% right_unique_parametric
thf(fact_299_right__unique__parametric,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o,B2: int > int > $o] :
      ( ( bi_tot310863827317176225ring_a @ A2 )
     => ( ( bi_unique_int_int @ B2 )
       => ( ( bi_total_int_int @ B2 )
         => ( bNF_re3166440945848855070_o_o_o
            @ ( bNF_re7877854262379379050_int_o @ A2
              @ ( bNF_re5089333283451836215nt_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
            @ right_4467640953958158575nt_int
            @ right_8112041778293208370_a_int ) ) ) ) ).

% right_unique_parametric
thf(fact_300_right__unique__parametric,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o,B2: int > int > $o] :
      ( ( bi_tot8466079176331800225ring_a @ A2 )
     => ( ( bi_unique_int_int @ B2 )
       => ( ( bi_total_int_int @ B2 )
         => ( bNF_re2185885084462657334_o_o_o
            @ ( bNF_re1270729808710627434_int_o @ A2
              @ ( bNF_re5089333283451836215nt_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
            @ right_5713360705131832443nt_int
            @ right_6838498638095685798_a_int ) ) ) ) ).

% right_unique_parametric
thf(fact_301_right__unique__parametric,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( bi_tot623839499179674737ring_a @ A2 )
     => ( ( bi_uni555094797115351544ring_a @ B2 )
       => ( ( bi_tot310863827317176225ring_a @ B2 )
         => ( bNF_re8023572202256978639_o_o_o
            @ ( bNF_re4244150877105976961ng_a_o @ A2
              @ ( bNF_re507051067509135658_a_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
            @ right_699715884342801685ec_int
            @ right_4415167829118643741ring_a ) ) ) ) ).

% right_unique_parametric
thf(fact_302_right__unique__parametric,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( bi_tot623839499179674737ring_a @ A2 )
     => ( ( bi_uni8710310146129975544ring_a @ B2 )
       => ( ( bi_tot8466079176331800225ring_a @ B2 )
         => ( bNF_re3176011413720292303_o_o_o
            @ ( bNF_re4973150902881326489ng_a_o @ A2
              @ ( bNF_re6153771816476299306_a_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
            @ right_6436628580042324129at_int
            @ right_562089708195504529ring_a ) ) ) ) ).

% right_unique_parametric
thf(fact_303_right__unique__parametric,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o,B2: int > finite_mod_ring_a > $o] :
      ( ( bi_tot310863827317176225ring_a @ A2 )
     => ( ( bi_uni1022671006909063496ring_a @ B2 )
       => ( ( bi_tot623839499179674737ring_a @ B2 )
         => ( bNF_re7402094339212515411_o_o_o
            @ ( bNF_re245202343922368753ng_a_o @ A2
              @ ( bNF_re8290846538823883642_a_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
            @ right_4467640953958158575nt_int
            @ right_2192335820997723199ring_a ) ) ) ) ).

% right_unique_parametric
thf(fact_304_right__unique__parametric,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o,B2: int > finite_mod_ring_a > $o] :
      ( ( bi_tot8466079176331800225ring_a @ A2 )
     => ( ( bi_uni1022671006909063496ring_a @ B2 )
       => ( ( bi_tot623839499179674737ring_a @ B2 )
         => ( bNF_re9174360872848916795_o_o_o
            @ ( bNF_re8055952673531087345ng_a_o @ A2
              @ ( bNF_re8290846538823883642_a_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
            @ right_5713360705131832443nt_int
            @ right_879404325744437707ring_a ) ) ) ) ).

% right_unique_parametric
thf(fact_305_right__unique__parametric,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o,B2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( bi_tot310863827317176225ring_a @ A2 )
     => ( ( bi_uni555094797115351544ring_a @ B2 )
       => ( ( bi_tot310863827317176225ring_a @ B2 )
         => ( bNF_re1256193828122302425_o_o_o
            @ ( bNF_re151890839321169105ng_a_o @ A2
              @ ( bNF_re507051067509135658_a_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
            @ right_926501739254024726ec_int
            @ right_1347257933406024628ring_a ) ) ) ) ).

% right_unique_parametric
thf(fact_306_right__unique__transfer,axiom,
    ! [A2: int > int > $o,B2: int > int > $o] :
      ( ( right_total_int_int @ A2 )
     => ( ( right_total_int_int @ B2 )
       => ( ( bi_unique_int_int @ B2 )
         => ( bNF_re5869992600382051037_o_o_o
            @ ( bNF_re3403563459893282935_int_o @ A2
              @ ( bNF_re5089333283451836215nt_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ (=>)
            @ right_unique_int_int
            @ right_unique_int_int ) ) ) ) ).

% right_unique_transfer
thf(fact_307_right__unique__transfer,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: int > int > $o] :
      ( ( right_2909008500229168952ring_a @ A2 )
     => ( ( right_total_int_int @ B2 )
       => ( ( bi_unique_int_int @ B2 )
         => ( bNF_re5891132441370877716_o_o_o
            @ ( bNF_re3873409527727426490_int_o @ A2
              @ ( bNF_re5089333283451836215nt_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ (=>)
            @ right_unique_int_int
            @ right_6005435896075721627_a_int ) ) ) ) ).

% right_unique_transfer
thf(fact_308_right__unique__transfer,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: int > finite_mod_ring_a > $o] :
      ( ( right_2909008500229168952ring_a @ A2 )
     => ( ( right_2909008500229168952ring_a @ B2 )
       => ( ( bi_uni1022671006909063496ring_a @ B2 )
         => ( bNF_re3287324404599397085_o_o_o
            @ ( bNF_re1743884151495963297ng_a_o @ A2
              @ ( bNF_re8290846538823883642_a_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ (=>)
            @ right_unique_int_int
            @ right_6217011779227907862ring_a ) ) ) ) ).

% right_unique_transfer
thf(fact_309_right__unique__transfer,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o,B2: int > int > $o] :
      ( ( right_7341149013462710248ring_a @ A2 )
     => ( ( right_total_int_int @ B2 )
       => ( ( bi_unique_int_int @ B2 )
         => ( bNF_re3166440945848855070_o_o_o
            @ ( bNF_re7877854262379379050_int_o @ A2
              @ ( bNF_re5089333283451836215nt_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ (=>)
            @ right_4467640953958158575nt_int
            @ right_8112041778293208370_a_int ) ) ) ) ).

% right_unique_transfer
thf(fact_310_right__unique__transfer,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o,B2: int > int > $o] :
      ( ( right_6272992325622558440ring_a @ A2 )
     => ( ( right_total_int_int @ B2 )
       => ( ( bi_unique_int_int @ B2 )
         => ( bNF_re2185885084462657334_o_o_o
            @ ( bNF_re1270729808710627434_int_o @ A2
              @ ( bNF_re5089333283451836215nt_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ (=>)
            @ right_5713360705131832443nt_int
            @ right_6838498638095685798_a_int ) ) ) ) ).

% right_unique_transfer
thf(fact_311_right__unique__transfer,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( right_2909008500229168952ring_a @ A2 )
     => ( ( right_7341149013462710248ring_a @ B2 )
       => ( ( bi_uni555094797115351544ring_a @ B2 )
         => ( bNF_re8023572202256978639_o_o_o
            @ ( bNF_re4244150877105976961ng_a_o @ A2
              @ ( bNF_re507051067509135658_a_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ (=>)
            @ right_699715884342801685ec_int
            @ right_4415167829118643741ring_a ) ) ) ) ).

% right_unique_transfer
thf(fact_312_right__unique__transfer,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( right_2909008500229168952ring_a @ A2 )
     => ( ( right_6272992325622558440ring_a @ B2 )
       => ( ( bi_uni8710310146129975544ring_a @ B2 )
         => ( bNF_re3176011413720292303_o_o_o
            @ ( bNF_re4973150902881326489ng_a_o @ A2
              @ ( bNF_re6153771816476299306_a_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ (=>)
            @ right_6436628580042324129at_int
            @ right_562089708195504529ring_a ) ) ) ) ).

% right_unique_transfer
thf(fact_313_right__unique__transfer,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o,B2: int > finite_mod_ring_a > $o] :
      ( ( right_7341149013462710248ring_a @ A2 )
     => ( ( right_2909008500229168952ring_a @ B2 )
       => ( ( bi_uni1022671006909063496ring_a @ B2 )
         => ( bNF_re7402094339212515411_o_o_o
            @ ( bNF_re245202343922368753ng_a_o @ A2
              @ ( bNF_re8290846538823883642_a_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ (=>)
            @ right_4467640953958158575nt_int
            @ right_2192335820997723199ring_a ) ) ) ) ).

% right_unique_transfer
thf(fact_314_right__unique__transfer,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o,B2: int > finite_mod_ring_a > $o] :
      ( ( right_6272992325622558440ring_a @ A2 )
     => ( ( right_2909008500229168952ring_a @ B2 )
       => ( ( bi_uni1022671006909063496ring_a @ B2 )
         => ( bNF_re9174360872848916795_o_o_o
            @ ( bNF_re8055952673531087345ng_a_o @ A2
              @ ( bNF_re8290846538823883642_a_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ (=>)
            @ right_5713360705131832443nt_int
            @ right_879404325744437707ring_a ) ) ) ) ).

% right_unique_transfer
thf(fact_315_right__unique__transfer,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o,B2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( right_7341149013462710248ring_a @ A2 )
     => ( ( right_7341149013462710248ring_a @ B2 )
       => ( ( bi_uni555094797115351544ring_a @ B2 )
         => ( bNF_re1256193828122302425_o_o_o
            @ ( bNF_re151890839321169105ng_a_o @ A2
              @ ( bNF_re507051067509135658_a_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ (=>)
            @ right_926501739254024726ec_int
            @ right_1347257933406024628ring_a ) ) ) ) ).

% right_unique_transfer
thf(fact_316_fun__ord__parametric,axiom,
    ! [C: int > int > $o,A2: $o > $o > $o,B2: $o > $o > $o] :
      ( ( bi_total_int_int @ C )
     => ( bNF_re3012816421615927389nt_o_o
        @ ( bNF_re6472675536664000681_o_o_o @ A2
          @ ( bNF_rel_fun_o_o_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re513079643185015507nt_o_o @ ( bNF_re5089333283451836215nt_o_o @ C @ A2 )
          @ ( bNF_re6378653760509651613_o_o_o @ ( bNF_re5089333283451836215nt_o_o @ C @ B2 )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ partia913349131986167100_o_int
        @ partia913349131986167100_o_int ) ) ).

% fun_ord_parametric
thf(fact_317_fun__ord__parametric,axiom,
    ! [C: int > int > $o,A2: $o > $o > $o,B2: nat > nat > $o] :
      ( ( bi_total_int_int @ C )
     => ( bNF_re1168432982574861285_nat_o
        @ ( bNF_re3790380520279025053_nat_o @ A2
          @ ( bNF_re4705727531993890431at_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re366876804441710237_nat_o @ ( bNF_re5089333283451836215nt_o_o @ C @ A2 )
          @ ( bNF_re8293725029456574741at_o_o @ ( bNF_re3715656647883201625at_nat @ C @ B2 )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ partia4541300848039533446at_int
        @ partia4541300848039533446at_int ) ) ).

% fun_ord_parametric
thf(fact_318_fun__ord__parametric,axiom,
    ! [C: int > int > $o,A2: nat > nat > $o,B2: $o > $o > $o] :
      ( ( bi_total_int_int @ C )
     => ( bNF_re4138666560314401969nt_o_o
        @ ( bNF_re6222992434181357259_o_o_o @ A2
          @ ( bNF_rel_fun_o_o_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re7816892618387588427nt_o_o @ ( bNF_re3715656647883201625at_nat @ C @ A2 )
          @ ( bNF_re6378653760509651613_o_o_o @ ( bNF_re5089333283451836215nt_o_o @ C @ B2 )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ partia8197980525518042212_o_int
        @ partia8197980525518042212_o_int ) ) ).

% fun_ord_parametric
thf(fact_319_fun__ord__parametric,axiom,
    ! [C: int > int > $o,A2: nat > nat > $o,B2: nat > nat > $o] :
      ( ( bi_total_int_int @ C )
     => ( bNF_re5912358153685880029_nat_o
        @ ( bNF_re578469030762574527_nat_o @ A2
          @ ( bNF_re4705727531993890431at_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re8877981933538057493_nat_o @ ( bNF_re3715656647883201625at_nat @ C @ A2 )
          @ ( bNF_re8293725029456574741at_o_o @ ( bNF_re3715656647883201625at_nat @ C @ B2 )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ partia3157487555393578590at_int
        @ partia3157487555393578590at_int ) ) ).

% fun_ord_parametric
thf(fact_320_fun__ord__parametric,axiom,
    ! [C: int > int > $o,A2: int > int > $o,B2: $o > $o > $o] :
      ( ( bi_total_int_int @ C )
     => ( bNF_re6130303124124341793nt_o_o
        @ ( bNF_re2126651504659934083_o_o_o @ A2
          @ ( bNF_rel_fun_o_o_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re6961808529855443971nt_o_o @ ( bNF_re4712519889275205905nt_int @ C @ A2 )
          @ ( bNF_re6378653760509651613_o_o_o @ ( bNF_re5089333283451836215nt_o_o @ C @ B2 )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ partia8884556558558592776_o_int
        @ partia8884556558558592776_o_int ) ) ).

% fun_ord_parametric
thf(fact_321_fun__ord__parametric,axiom,
    ! [C: int > int > $o,A2: int > int > $o,B2: nat > nat > $o] :
      ( ( bi_total_int_int @ C )
     => ( bNF_re1274416395763232477_nat_o
        @ ( bNF_re3376528473927230327_nat_o @ A2
          @ ( bNF_re4705727531993890431at_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re3638363003489898445_nat_o @ ( bNF_re4712519889275205905nt_int @ C @ A2 )
          @ ( bNF_re8293725029456574741at_o_o @ ( bNF_re3715656647883201625at_nat @ C @ B2 )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ partia3529141115630423226at_int
        @ partia3529141115630423226at_int ) ) ).

% fun_ord_parametric
thf(fact_322_fun__ord__parametric,axiom,
    ! [C: int > int > $o,A2: $o > $o > $o,B2: int > int > $o] :
      ( ( bi_total_int_int @ C )
     => ( bNF_re9016137329058378357_int_o
        @ ( bNF_re3817415506245077661_int_o @ A2
          @ ( bNF_re5089333283451836215nt_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re6571774352052816285_int_o @ ( bNF_re5089333283451836215nt_o_o @ C @ A2 )
          @ ( bNF_re1277823837431233485nt_o_o @ ( bNF_re4712519889275205905nt_int @ C @ B2 )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ partia5540654559940588002nt_int
        @ partia5540654559940588002nt_int ) ) ).

% fun_ord_parametric
thf(fact_323_fun__ord__parametric,axiom,
    ! [C: int > int > $o,A2: nat > nat > $o,B2: int > int > $o] :
      ( ( bi_total_int_int @ C )
     => ( bNF_re9128218472039263965_int_o
        @ ( bNF_re605504016728627135_int_o @ A2
          @ ( bNF_re5089333283451836215nt_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re5859507444294387733_int_o @ ( bNF_re3715656647883201625at_nat @ C @ A2 )
          @ ( bNF_re1277823837431233485nt_o_o @ ( bNF_re4712519889275205905nt_int @ C @ B2 )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ partia4156841267294633146nt_int
        @ partia4156841267294633146nt_int ) ) ).

% fun_ord_parametric
thf(fact_324_fun__ord__parametric,axiom,
    ! [C: int > int > $o,A2: int > int > $o,B2: int > int > $o] :
      ( ( bi_total_int_int @ C )
     => ( bNF_re4490276714116616413_int_o
        @ ( bNF_re3403563459893282935_int_o @ A2
          @ ( bNF_re5089333283451836215nt_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re619888514246228685_int_o @ ( bNF_re4712519889275205905nt_int @ C @ A2 )
          @ ( bNF_re1277823837431233485nt_o_o @ ( bNF_re4712519889275205905nt_int @ C @ B2 )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ partia4528494827531477782nt_int
        @ partia4528494827531477782nt_int ) ) ).

% fun_ord_parametric
thf(fact_325_fun__ord__parametric,axiom,
    ! [C: int > finite_mod_ring_a > $o,A2: int > int > $o,B2: int > int > $o] :
      ( ( bi_tot623839499179674737ring_a @ C )
     => ( bNF_re7930886852997362739_int_o
        @ ( bNF_re3403563459893282935_int_o @ A2
          @ ( bNF_re5089333283451836215nt_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re7705526925582604071_int_o @ ( bNF_re8614909862389055444nt_int @ C @ A2 )
          @ ( bNF_re8039882297063496332nt_o_o @ ( bNF_re8614909862389055444nt_int @ C @ B2 )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ partia4528494827531477782nt_int
        @ partia1478704387905588059ring_a ) ) ).

% fun_ord_parametric
thf(fact_326_bi__unique__fun,axiom,
    ! [A2: int > int > $o,B2: $o > $o > $o] :
      ( ( bi_total_int_int @ A2 )
     => ( ( bi_unique_o_o @ B2 )
       => ( bi_uni6923270185593731663_int_o @ ( bNF_re5089333283451836215nt_o_o @ A2 @ B2 ) ) ) ) ).

% bi_unique_fun
thf(fact_327_bi__unique__fun,axiom,
    ! [A2: int > int > $o,B2: nat > nat > $o] :
      ( ( bi_total_int_int @ A2 )
     => ( ( bi_unique_nat_nat @ B2 )
       => ( bi_uni4042410478161791943nt_nat @ ( bNF_re3715656647883201625at_nat @ A2 @ B2 ) ) ) ) ).

% bi_unique_fun
thf(fact_328_bi__unique__fun,axiom,
    ! [A2: int > int > $o,B2: int > int > $o] :
      ( ( bi_total_int_int @ A2 )
     => ( ( bi_unique_int_int @ B2 )
       => ( bi_uni5275641640356057727nt_int @ ( bNF_re4712519889275205905nt_int @ A2 @ B2 ) ) ) ) ).

% bi_unique_fun
thf(fact_329_bi__unique__fun,axiom,
    ! [A2: int > int > $o,B2: ( int > $o ) > ( int > $o ) > $o] :
      ( ( bi_total_int_int @ A2 )
     => ( ( bi_uni6923270185593731663_int_o @ B2 )
       => ( bi_uni2203252027619187855_int_o @ ( bNF_re3403563459893282935_int_o @ A2 @ B2 ) ) ) ) ).

% bi_unique_fun
thf(fact_330_bi__unique__fun,axiom,
    ! [A2: int > int > $o,B2: ( int > int ) > ( int > int ) > $o] :
      ( ( bi_total_int_int @ A2 )
     => ( ( bi_uni5275641640356057727nt_int @ B2 )
       => ( bi_uni6056933463453604373nt_int @ ( bNF_re711492959462206631nt_int @ A2 @ B2 ) ) ) ) ).

% bi_unique_fun
thf(fact_331_bi__total__fun,axiom,
    ! [A2: int > int > $o,B2: $o > $o > $o] :
      ( ( bi_unique_int_int @ A2 )
     => ( ( bi_total_o_o @ B2 )
       => ( bi_total_int_o_int_o @ ( bNF_re5089333283451836215nt_o_o @ A2 @ B2 ) ) ) ) ).

% bi_total_fun
thf(fact_332_bi__total__fun,axiom,
    ! [A2: int > int > $o,B2: nat > nat > $o] :
      ( ( bi_unique_int_int @ A2 )
     => ( ( bi_total_nat_nat @ B2 )
       => ( bi_tot3798040644246563422nt_nat @ ( bNF_re3715656647883201625at_nat @ A2 @ B2 ) ) ) ) ).

% bi_total_fun
thf(fact_333_bi__total__fun,axiom,
    ! [A2: int > int > $o,B2: int > int > $o] :
      ( ( bi_unique_int_int @ A2 )
     => ( ( bi_total_int_int @ B2 )
       => ( bi_tot5031271806440829206nt_int @ ( bNF_re4712519889275205905nt_int @ A2 @ B2 ) ) ) ) ).

% bi_total_fun
thf(fact_334_bi__total__fun,axiom,
    ! [A2: int > int > $o,B2: ( int > $o ) > ( int > $o ) > $o] :
      ( ( bi_unique_int_int @ A2 )
     => ( ( bi_total_int_o_int_o @ B2 )
       => ( bi_tot1998502909289846182_int_o @ ( bNF_re3403563459893282935_int_o @ A2 @ B2 ) ) ) ) ).

% bi_total_fun
thf(fact_335_bi__total__fun,axiom,
    ! [A2: int > int > $o,B2: ( int > int ) > ( int > int ) > $o] :
      ( ( bi_unique_int_int @ A2 )
     => ( ( bi_tot5031271806440829206nt_int @ B2 )
       => ( bi_tot1340478029960895404nt_int @ ( bNF_re711492959462206631nt_int @ A2 @ B2 ) ) ) ) ).

% bi_total_fun
thf(fact_336_bi__unique__alt__def2,axiom,
    ( bi_unique_int_int
    = ( ^ [R2: int > int > $o] :
          ( bNF_re3403563459893282935_int_o @ R2
          @ ( bNF_re5089333283451836215nt_o_o @ R2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) ) ) ) ).

% bi_unique_alt_def2
thf(fact_337_eq__transfer,axiom,
    ! [A2: int > int > $o] :
      ( ( bi_unique_int_int @ A2 )
     => ( bNF_re3403563459893282935_int_o @ A2
        @ ( bNF_re5089333283451836215nt_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) ) ) ).

% eq_transfer
thf(fact_338_fun_Orel__refl,axiom,
    ! [Ra: $o > $o > $o,X: int > $o] :
      ( ! [X4: $o] : ( Ra @ X4 @ X4 )
     => ( bNF_re5089333283451836215nt_o_o
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
        @ Ra
        @ X
        @ X ) ) ).

% fun.rel_refl
thf(fact_339_fun_Orel__refl,axiom,
    ! [Ra: nat > nat > $o,X: int > nat] :
      ( ! [X4: nat] : ( Ra @ X4 @ X4 )
     => ( bNF_re3715656647883201625at_nat
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
        @ Ra
        @ X
        @ X ) ) ).

% fun.rel_refl
thf(fact_340_fun_Orel__refl,axiom,
    ! [Ra: int > int > $o,X: int > int] :
      ( ! [X4: int] : ( Ra @ X4 @ X4 )
     => ( bNF_re4712519889275205905nt_int
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
        @ Ra
        @ X
        @ X ) ) ).

% fun.rel_refl
thf(fact_341_fun_Orel__refl,axiom,
    ! [Ra: ( int > $o ) > ( int > $o ) > $o,X: int > int > $o] :
      ( ! [X4: int > $o] : ( Ra @ X4 @ X4 )
     => ( bNF_re3403563459893282935_int_o
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
        @ Ra
        @ X
        @ X ) ) ).

% fun.rel_refl
thf(fact_342_fun_Orel__refl,axiom,
    ! [Ra: ( int > int ) > ( int > int ) > $o,X: int > int > int] :
      ( ! [X4: int > int] : ( Ra @ X4 @ X4 )
     => ( bNF_re711492959462206631nt_int
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
        @ Ra
        @ X
        @ X ) ) ).

% fun.rel_refl
thf(fact_343_left__unique__parametric,axiom,
    ! [A2: int > int > $o,B2: int > int > $o] :
      ( ( bi_unique_int_int @ A2 )
     => ( ( bi_total_int_int @ A2 )
       => ( ( bi_total_int_int @ B2 )
         => ( bNF_re5869992600382051037_o_o_o
            @ ( bNF_re3403563459893282935_int_o @ A2
              @ ( bNF_re5089333283451836215nt_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
            @ left_unique_int_int
            @ left_unique_int_int ) ) ) ) ).

% left_unique_parametric
thf(fact_344_left__unique__parametric,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: int > int > $o] :
      ( ( bi_uni1022671006909063496ring_a @ A2 )
     => ( ( bi_tot623839499179674737ring_a @ A2 )
       => ( ( bi_total_int_int @ B2 )
         => ( bNF_re5891132441370877716_o_o_o
            @ ( bNF_re3873409527727426490_int_o @ A2
              @ ( bNF_re5089333283451836215nt_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
            @ left_unique_int_int
            @ left_u312270633112012962_a_int ) ) ) ) ).

% left_unique_parametric
thf(fact_345_left__unique__parametric,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: int > finite_mod_ring_a > $o] :
      ( ( bi_uni1022671006909063496ring_a @ A2 )
     => ( ( bi_tot623839499179674737ring_a @ A2 )
       => ( ( bi_tot623839499179674737ring_a @ B2 )
         => ( bNF_re3287324404599397085_o_o_o
            @ ( bNF_re1743884151495963297ng_a_o @ A2
              @ ( bNF_re8290846538823883642_a_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
            @ left_unique_int_int
            @ left_u4083587041413029071ring_a ) ) ) ) ).

% left_unique_parametric
thf(fact_346_left__unique__parametric,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o,B2: int > int > $o] :
      ( ( bi_uni555094797115351544ring_a @ A2 )
     => ( ( bi_tot310863827317176225ring_a @ A2 )
       => ( ( bi_total_int_int @ B2 )
         => ( bNF_re3166440945848855070_o_o_o
            @ ( bNF_re7877854262379379050_int_o @ A2
              @ ( bNF_re5089333283451836215nt_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
            @ left_u8421814785599659894nt_int
            @ left_u6364363308751067499_a_int ) ) ) ) ).

% left_unique_parametric
thf(fact_347_left__unique__parametric,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o,B2: int > int > $o] :
      ( ( bi_uni8710310146129975544ring_a @ A2 )
     => ( ( bi_tot8466079176331800225ring_a @ A2 )
       => ( ( bi_total_int_int @ B2 )
         => ( bNF_re2185885084462657334_o_o_o
            @ ( bNF_re1270729808710627434_int_o @ A2
              @ ( bNF_re5089333283451836215nt_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
            @ left_u444162499918557954nt_int
            @ left_u5090820168553544927_a_int ) ) ) ) ).

% left_unique_parametric
thf(fact_348_left__unique__parametric,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( bi_uni1022671006909063496ring_a @ A2 )
     => ( ( bi_tot623839499179674737ring_a @ A2 )
       => ( ( bi_tot310863827317176225ring_a @ B2 )
         => ( bNF_re8023572202256978639_o_o_o
            @ ( bNF_re4244150877105976961ng_a_o @ A2
              @ ( bNF_re507051067509135658_a_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
            @ left_u4653889715984303004ec_int
            @ left_u3319650674904336164ring_a ) ) ) ) ).

% left_unique_parametric
thf(fact_349_left__unique__parametric,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( bi_uni1022671006909063496ring_a @ A2 )
     => ( ( bi_tot623839499179674737ring_a @ A2 )
       => ( ( bi_tot8466079176331800225ring_a @ B2 )
         => ( bNF_re3176011413720292303_o_o_o
            @ ( bNF_re4973150902881326489ng_a_o @ A2
              @ ( bNF_re6153771816476299306_a_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
            @ left_u1167430374829049640at_int
            @ left_u8689944590835972760ring_a ) ) ) ) ).

% left_unique_parametric
thf(fact_350_left__unique__parametric,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o,B2: int > finite_mod_ring_a > $o] :
      ( ( bi_uni555094797115351544ring_a @ A2 )
     => ( ( bi_tot310863827317176225ring_a @ A2 )
       => ( ( bi_tot623839499179674737ring_a @ B2 )
         => ( bNF_re7402094339212515411_o_o_o
            @ ( bNF_re245202343922368753ng_a_o @ A2
              @ ( bNF_re8290846538823883642_a_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
            @ left_u8421814785599659894nt_int
            @ left_u1096818666783415622ring_a ) ) ) ) ).

% left_unique_parametric
thf(fact_351_left__unique__parametric,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o,B2: int > finite_mod_ring_a > $o] :
      ( ( bi_uni8710310146129975544ring_a @ A2 )
     => ( ( bi_tot8466079176331800225ring_a @ A2 )
       => ( ( bi_tot623839499179674737ring_a @ B2 )
         => ( bNF_re9174360872848916795_o_o_o
            @ ( bNF_re8055952673531087345ng_a_o @ A2
              @ ( bNF_re8290846538823883642_a_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
            @ left_u444162499918557954nt_int
            @ left_u9007259208384905938ring_a ) ) ) ) ).

% left_unique_parametric
thf(fact_352_left__unique__parametric,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o,B2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( bi_uni555094797115351544ring_a @ A2 )
     => ( ( bi_tot310863827317176225ring_a @ A2 )
       => ( ( bi_tot310863827317176225ring_a @ B2 )
         => ( bNF_re1256193828122302425_o_o_o
            @ ( bNF_re151890839321169105ng_a_o @ A2
              @ ( bNF_re507051067509135658_a_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
            @ left_u3881574773735861455ec_int
            @ left_u1556899868652710893ring_a ) ) ) ) ).

% left_unique_parametric
thf(fact_353_left__unique__transfer,axiom,
    ! [A2: int > int > $o,B2: int > int > $o] :
      ( ( right_total_int_int @ A2 )
     => ( ( right_total_int_int @ B2 )
       => ( ( bi_unique_int_int @ A2 )
         => ( bNF_re5869992600382051037_o_o_o
            @ ( bNF_re3403563459893282935_int_o @ A2
              @ ( bNF_re5089333283451836215nt_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ (=>)
            @ left_unique_int_int
            @ left_unique_int_int ) ) ) ) ).

% left_unique_transfer
thf(fact_354_left__unique__transfer,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: int > int > $o] :
      ( ( right_2909008500229168952ring_a @ A2 )
     => ( ( right_total_int_int @ B2 )
       => ( ( bi_uni1022671006909063496ring_a @ A2 )
         => ( bNF_re5891132441370877716_o_o_o
            @ ( bNF_re3873409527727426490_int_o @ A2
              @ ( bNF_re5089333283451836215nt_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ (=>)
            @ left_unique_int_int
            @ left_u312270633112012962_a_int ) ) ) ) ).

% left_unique_transfer
thf(fact_355_left__unique__transfer,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: int > finite_mod_ring_a > $o] :
      ( ( right_2909008500229168952ring_a @ A2 )
     => ( ( right_2909008500229168952ring_a @ B2 )
       => ( ( bi_uni1022671006909063496ring_a @ A2 )
         => ( bNF_re3287324404599397085_o_o_o
            @ ( bNF_re1743884151495963297ng_a_o @ A2
              @ ( bNF_re8290846538823883642_a_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ (=>)
            @ left_unique_int_int
            @ left_u4083587041413029071ring_a ) ) ) ) ).

% left_unique_transfer
thf(fact_356_left__unique__transfer,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o,B2: int > int > $o] :
      ( ( right_7341149013462710248ring_a @ A2 )
     => ( ( right_total_int_int @ B2 )
       => ( ( bi_uni555094797115351544ring_a @ A2 )
         => ( bNF_re3166440945848855070_o_o_o
            @ ( bNF_re7877854262379379050_int_o @ A2
              @ ( bNF_re5089333283451836215nt_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ (=>)
            @ left_u8421814785599659894nt_int
            @ left_u6364363308751067499_a_int ) ) ) ) ).

% left_unique_transfer
thf(fact_357_left__unique__transfer,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o,B2: int > int > $o] :
      ( ( right_6272992325622558440ring_a @ A2 )
     => ( ( right_total_int_int @ B2 )
       => ( ( bi_uni8710310146129975544ring_a @ A2 )
         => ( bNF_re2185885084462657334_o_o_o
            @ ( bNF_re1270729808710627434_int_o @ A2
              @ ( bNF_re5089333283451836215nt_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ (=>)
            @ left_u444162499918557954nt_int
            @ left_u5090820168553544927_a_int ) ) ) ) ).

% left_unique_transfer
thf(fact_358_left__unique__transfer,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( right_2909008500229168952ring_a @ A2 )
     => ( ( right_7341149013462710248ring_a @ B2 )
       => ( ( bi_uni1022671006909063496ring_a @ A2 )
         => ( bNF_re8023572202256978639_o_o_o
            @ ( bNF_re4244150877105976961ng_a_o @ A2
              @ ( bNF_re507051067509135658_a_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ (=>)
            @ left_u4653889715984303004ec_int
            @ left_u3319650674904336164ring_a ) ) ) ) ).

% left_unique_transfer
thf(fact_359_left__unique__transfer,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( right_2909008500229168952ring_a @ A2 )
     => ( ( right_6272992325622558440ring_a @ B2 )
       => ( ( bi_uni1022671006909063496ring_a @ A2 )
         => ( bNF_re3176011413720292303_o_o_o
            @ ( bNF_re4973150902881326489ng_a_o @ A2
              @ ( bNF_re6153771816476299306_a_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ (=>)
            @ left_u1167430374829049640at_int
            @ left_u8689944590835972760ring_a ) ) ) ) ).

% left_unique_transfer
thf(fact_360_left__unique__transfer,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o,B2: int > finite_mod_ring_a > $o] :
      ( ( right_7341149013462710248ring_a @ A2 )
     => ( ( right_2909008500229168952ring_a @ B2 )
       => ( ( bi_uni555094797115351544ring_a @ A2 )
         => ( bNF_re7402094339212515411_o_o_o
            @ ( bNF_re245202343922368753ng_a_o @ A2
              @ ( bNF_re8290846538823883642_a_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ (=>)
            @ left_u8421814785599659894nt_int
            @ left_u1096818666783415622ring_a ) ) ) ) ).

% left_unique_transfer
thf(fact_361_left__unique__transfer,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o,B2: int > finite_mod_ring_a > $o] :
      ( ( right_6272992325622558440ring_a @ A2 )
     => ( ( right_2909008500229168952ring_a @ B2 )
       => ( ( bi_uni8710310146129975544ring_a @ A2 )
         => ( bNF_re9174360872848916795_o_o_o
            @ ( bNF_re8055952673531087345ng_a_o @ A2
              @ ( bNF_re8290846538823883642_a_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ (=>)
            @ left_u444162499918557954nt_int
            @ left_u9007259208384905938ring_a ) ) ) ) ).

% left_unique_transfer
thf(fact_362_left__unique__transfer,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o,B2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( right_7341149013462710248ring_a @ A2 )
     => ( ( right_7341149013462710248ring_a @ B2 )
       => ( ( bi_uni555094797115351544ring_a @ A2 )
         => ( bNF_re1256193828122302425_o_o_o
            @ ( bNF_re151890839321169105ng_a_o @ A2
              @ ( bNF_re507051067509135658_a_o_o @ B2
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
            @ (=>)
            @ left_u3881574773735861455ec_int
            @ left_u1556899868652710893ring_a ) ) ) ) ).

% left_unique_transfer
thf(fact_363_rtranclp__parametric,axiom,
    ! [A2: int > int > $o] :
      ( ( bi_unique_int_int @ A2 )
     => ( ( bi_total_int_int @ A2 )
       => ( bNF_re8651060166502312541_int_o
          @ ( bNF_re3403563459893282935_int_o @ A2
            @ ( bNF_re5089333283451836215nt_o_o @ A2
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ( bNF_re3403563459893282935_int_o @ A2
            @ ( bNF_re5089333283451836215nt_o_o @ A2
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ transi5419909967800184737lp_int
          @ transi5419909967800184737lp_int ) ) ) ).

% rtranclp_parametric
thf(fact_364_rtranclp__parametric,axiom,
    ! [A2: int > finite_mod_ring_a > $o] :
      ( ( bi_uni1022671006909063496ring_a @ A2 )
     => ( ( bi_tot623839499179674737ring_a @ A2 )
       => ( bNF_re561345951587129949ng_a_o
          @ ( bNF_re1743884151495963297ng_a_o @ A2
            @ ( bNF_re8290846538823883642_a_o_o @ A2
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ( bNF_re1743884151495963297ng_a_o @ A2
            @ ( bNF_re8290846538823883642_a_o_o @ A2
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ transi5419909967800184737lp_int
          @ transi6237637440696766096ring_a ) ) ) ).

% rtranclp_parametric
thf(fact_365_rtranclp__parametric,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( bi_uni555094797115351544ring_a @ A2 )
     => ( ( bi_tot310863827317176225ring_a @ A2 )
       => ( bNF_re531798068885152853ng_a_o
          @ ( bNF_re151890839321169105ng_a_o @ A2
            @ ( bNF_re507051067509135658_a_o_o @ A2
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ( bNF_re151890839321169105ng_a_o @ A2
            @ ( bNF_re507051067509135658_a_o_o @ A2
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ transi6577020515180583140ec_int
          @ transi2036074095066167843ring_a ) ) ) ).

% rtranclp_parametric
thf(fact_366_rtranclp__parametric,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( bi_uni8710310146129975544ring_a @ A2 )
     => ( ( bi_tot8466079176331800225ring_a @ A2 )
       => ( bNF_re7693591110265091205ng_a_o
          @ ( bNF_re8187416184292455657ng_a_o @ A2
            @ ( bNF_re6153771816476299306_a_o_o @ A2
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ( bNF_re8187416184292455657ng_a_o @ A2
            @ ( bNF_re6153771816476299306_a_o_o @ A2
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ transi3090561174025329776at_int
          @ transi7406368010997804439ring_a ) ) ) ).

% rtranclp_parametric
thf(fact_367_fun__upd__transfer,axiom,
    ! [A2: int > int > $o,B2: $o > $o > $o] :
      ( ( bi_unique_int_int @ A2 )
     => ( bNF_re6967601477061121941_int_o @ ( bNF_re5089333283451836215nt_o_o @ A2 @ B2 ) @ ( bNF_re2682350871644790041_int_o @ A2 @ ( bNF_re3817415506245077661_int_o @ B2 @ ( bNF_re5089333283451836215nt_o_o @ A2 @ B2 ) ) ) @ fun_upd_int_o @ fun_upd_int_o ) ) ).

% fun_upd_transfer
thf(fact_368_fun__upd__transfer,axiom,
    ! [A2: int > int > $o,B2: nat > nat > $o] :
      ( ( bi_unique_int_int @ A2 )
     => ( bNF_re4228487696381020993nt_nat @ ( bNF_re3715656647883201625at_nat @ A2 @ B2 ) @ ( bNF_re5791889273166771917nt_nat @ A2 @ ( bNF_re3552752127234388279nt_nat @ B2 @ ( bNF_re3715656647883201625at_nat @ A2 @ B2 ) ) ) @ fun_upd_int_nat @ fun_upd_int_nat ) ) ).

% fun_upd_transfer
thf(fact_369_fun__upd__transfer,axiom,
    ! [A2: int > int > $o,B2: int > int > $o] :
      ( ( bi_unique_int_int @ A2 )
     => ( bNF_re8280112600883147625nt_int @ ( bNF_re4712519889275205905nt_int @ A2 @ B2 ) @ ( bNF_re6390757846875798589nt_int @ A2 @ ( bNF_re711492959462206631nt_int @ B2 @ ( bNF_re4712519889275205905nt_int @ A2 @ B2 ) ) ) @ fun_upd_int_int @ fun_upd_int_int ) ) ).

% fun_upd_transfer
thf(fact_370_fun__upd__transfer,axiom,
    ! [A2: int > int > $o,B2: ( int > $o ) > ( int > $o ) > $o] :
      ( ( bi_unique_int_int @ A2 )
     => ( bNF_re428690454916900693_int_o @ ( bNF_re3403563459893282935_int_o @ A2 @ B2 ) @ ( bNF_re2903057588882071961_int_o @ A2 @ ( bNF_re8966525682393678365_int_o @ B2 @ ( bNF_re3403563459893282935_int_o @ A2 @ B2 ) ) ) @ fun_upd_int_int_o @ fun_upd_int_int_o ) ) ).

% fun_upd_transfer
thf(fact_371_fun__upd__transfer,axiom,
    ! [A2: int > int > $o,B2: ( int > int ) > ( int > int ) > $o] :
      ( ( bi_unique_int_int @ A2 )
     => ( bNF_re5888381405672822827nt_int @ ( bNF_re711492959462206631nt_int @ A2 @ B2 ) @ ( bNF_re3338030124694030697nt_int @ A2 @ ( bNF_re724639330072410579nt_int @ B2 @ ( bNF_re711492959462206631nt_int @ A2 @ B2 ) ) ) @ fun_upd_int_int_int @ fun_upd_int_int_int ) ) ).

% fun_upd_transfer
thf(fact_372_relcompp__transfer,axiom,
    ! [B2: int > int > $o,A2: int > int > $o,C: int > int > $o] :
      ( ( bi_total_int_int @ B2 )
     => ( bNF_re7404067519983032617_int_o
        @ ( bNF_re3403563459893282935_int_o @ A2
          @ ( bNF_re5089333283451836215nt_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re8651060166502312541_int_o
          @ ( bNF_re3403563459893282935_int_o @ B2
            @ ( bNF_re5089333283451836215nt_o_o @ C
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ( bNF_re3403563459893282935_int_o @ A2
            @ ( bNF_re5089333283451836215nt_o_o @ C
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) ) )
        @ relcompp_int_int_int
        @ relcompp_int_int_int ) ) ).

% relcompp_transfer
thf(fact_373_relcompp__transfer,axiom,
    ! [B2: mat_int > mat_int > $o,A2: mat_int > mat_int > $o,C: mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a > $o] :
      ( ( bi_tot9202309660982637286at_int @ B2 )
     => ( bNF_re849768681852557265ng_a_o
        @ ( bNF_re5814136157216229839_int_o @ A2
          @ ( bNF_re5904460004506961949nt_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re9109869686183513365ng_a_o
          @ ( bNF_re3207547038660532189ng_a_o @ B2
            @ ( bNF_re3698012824587224355_a_o_o @ C
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ( bNF_re3207547038660532189ng_a_o @ A2
            @ ( bNF_re3698012824587224355_a_o_o @ C
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) ) )
        @ relcom6459136143736567059ring_a
        @ relcom6459136143736567059ring_a ) ) ).

% relcompp_transfer
thf(fact_374_relcompp__transfer,axiom,
    ! [B2: int > finite_mod_ring_a > $o,A2: int > int > $o,C: int > int > $o] :
      ( ( bi_tot623839499179674737ring_a @ B2 )
     => ( bNF_re5072219456266741671_int_o
        @ ( bNF_re1393113005842329636ng_a_o @ A2
          @ ( bNF_re8290846538823883642_a_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re1800150913247624340_int_o
          @ ( bNF_re3873409527727426490_int_o @ B2
            @ ( bNF_re5089333283451836215nt_o_o @ C
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ( bNF_re3403563459893282935_int_o @ A2
            @ ( bNF_re5089333283451836215nt_o_o @ C
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) ) )
        @ relcompp_int_int_int
        @ relcom1383171076355693396_a_int ) ) ).

% relcompp_transfer
thf(fact_375_relcompp__transfer,axiom,
    ! [B2: vec_int > vec_Fi4296597256376197294ring_a > $o,A2: int > int > $o,C: int > int > $o] :
      ( ( bi_tot310863827317176225ring_a @ B2 )
     => ( bNF_re8684700889500088319_int_o
        @ ( bNF_re3675534777603958660ng_a_o @ A2
          @ ( bNF_re507051067509135658_a_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re1812577071873895326_int_o
          @ ( bNF_re7877854262379379050_int_o @ B2
            @ ( bNF_re5089333283451836215nt_o_o @ C
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ( bNF_re3403563459893282935_int_o @ A2
            @ ( bNF_re5089333283451836215nt_o_o @ C
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) ) )
        @ relcom3199365128179715880nt_int
        @ relcom6250398543212868665_a_int ) ) ).

% relcompp_transfer
thf(fact_376_relcompp__transfer,axiom,
    ! [B2: mat_int > mat_Fi443519135453058082ring_a > $o,A2: int > int > $o,C: int > int > $o] :
      ( ( bi_tot8466079176331800225ring_a @ B2 )
     => ( bNF_re7916767694611508199_int_o
        @ ( bNF_re4404534803379308188ng_a_o @ A2
          @ ( bNF_re6153771816476299306_a_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re6198949750846496950_int_o
          @ ( bNF_re1270729808710627434_int_o @ B2
            @ ( bNF_re5089333283451836215nt_o_o @ C
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ( bNF_re3403563459893282935_int_o @ A2
            @ ( bNF_re5089333283451836215nt_o_o @ C
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) ) )
        @ relcom4445084879353389748nt_int
        @ relcom4976855403015346093_a_int ) ) ).

% relcompp_transfer
thf(fact_377_map__fun__parametric,axiom,
    ! [A2: int > int > $o,B2: $o > $o > $o,C: int > int > $o,D: $o > $o > $o] : ( bNF_re785544210196170973_int_o @ ( bNF_re5089333283451836215nt_o_o @ A2 @ B2 ) @ ( bNF_re6844020233948794949_int_o @ ( bNF_re5089333283451836215nt_o_o @ C @ D ) @ ( bNF_re443020842677779549_int_o @ ( bNF_re1549289456480014903nt_int @ B2 @ C ) @ ( bNF_re5089333283451836215nt_o_o @ A2 @ D ) ) ) @ map_fun_int_o_int_o @ map_fun_int_o_int_o ) ).

% map_fun_parametric
thf(fact_378_map__fun__parametric,axiom,
    ! [A2: int > int > $o,B2: $o > $o > $o,C: int > int > $o,D: nat > nat > $o] : ( bNF_re8143304301122804317nt_nat @ ( bNF_re5089333283451836215nt_o_o @ A2 @ B2 ) @ ( bNF_re3015352480858811349nt_nat @ ( bNF_re3715656647883201625at_nat @ C @ D ) @ ( bNF_re6096367806326009557nt_nat @ ( bNF_re1549289456480014903nt_int @ B2 @ C ) @ ( bNF_re3715656647883201625at_nat @ A2 @ D ) ) ) @ map_fu4905306330207194066nt_nat @ map_fu4905306330207194066nt_nat ) ).

% map_fun_parametric
thf(fact_379_map__fun__parametric,axiom,
    ! [A2: int > int > $o,B2: $o > $o > $o,C: int > int > $o,D: int > int > $o] : ( bNF_re1144695058418211421nt_int @ ( bNF_re5089333283451836215nt_o_o @ A2 @ B2 ) @ ( bNF_re4856174267440235917nt_int @ ( bNF_re4712519889275205905nt_int @ C @ D ) @ ( bNF_re7329598968520275341nt_int @ ( bNF_re1549289456480014903nt_int @ B2 @ C ) @ ( bNF_re4712519889275205905nt_int @ A2 @ D ) ) ) @ map_fu4902815859698143790nt_int @ map_fu4902815859698143790nt_int ) ).

% map_fun_parametric
thf(fact_380_map__fun__parametric,axiom,
    ! [A2: int > int > $o,B2: nat > nat > $o,C: int > int > $o,D: $o > $o > $o] : ( bNF_re8957533069481939353_int_o @ ( bNF_re3715656647883201625at_nat @ A2 @ B2 ) @ ( bNF_re8874617004901089501_int_o @ ( bNF_re5089333283451836215nt_o_o @ C @ D ) @ ( bNF_re5424208017755137109_int_o @ ( bNF_re6650684261131312217nt_int @ B2 @ C ) @ ( bNF_re5089333283451836215nt_o_o @ A2 @ D ) ) ) @ map_fu8844261311460145622_int_o @ map_fu8844261311460145622_int_o ) ).

% map_fun_parametric
thf(fact_381_map__fun__parametric,axiom,
    ! [A2: int > int > $o,B2: nat > nat > $o,C: int > int > $o,D: nat > nat > $o] : ( bNF_re8516618236367403957nt_nat @ ( bNF_re3715656647883201625at_nat @ A2 @ B2 ) @ ( bNF_re6913270855792892737nt_nat @ ( bNF_re3715656647883201625at_nat @ C @ D ) @ ( bNF_re8092276960064420557nt_nat @ ( bNF_re6650684261131312217nt_int @ B2 @ C ) @ ( bNF_re3715656647883201625at_nat @ A2 @ D ) ) ) @ map_fu8111244225487061266nt_nat @ map_fu8111244225487061266nt_nat ) ).

% map_fun_parametric
thf(fact_382_map__fun__parametric,axiom,
    ! [A2: int > int > $o,B2: nat > nat > $o,C: int > int > $o,D: int > int > $o] : ( bNF_re1675945521237804325nt_int @ ( bNF_re3715656647883201625at_nat @ A2 @ B2 ) @ ( bNF_re421952579363528881nt_int @ ( bNF_re4712519889275205905nt_int @ C @ D ) @ ( bNF_re102136085403910533nt_int @ ( bNF_re6650684261131312217nt_int @ B2 @ C ) @ ( bNF_re4712519889275205905nt_int @ A2 @ D ) ) ) @ map_fu8108753754978010990nt_int @ map_fu8108753754978010990nt_int ) ).

% map_fun_parametric
thf(fact_383_map__fun__parametric,axiom,
    ! [A2: int > int > $o,B2: int > int > $o,C: $o > $o > $o,D: $o > $o > $o] : ( bNF_re2841006154458801825_int_o @ ( bNF_re4712519889275205905nt_int @ A2 @ B2 ) @ ( bNF_re8851674277422367093_int_o @ ( bNF_rel_fun_o_o_o_o @ C @ D ) @ ( bNF_re2562776159637780957_int_o @ ( bNF_re5089333283451836215nt_o_o @ B2 @ C ) @ ( bNF_re5089333283451836215nt_o_o @ A2 @ D ) ) ) @ map_fun_int_int_o_o @ map_fun_int_int_o_o ) ).

% map_fun_parametric
thf(fact_384_map__fun__parametric,axiom,
    ! [A2: int > int > $o,B2: int > int > $o,C: $o > $o > $o,D: nat > nat > $o] : ( bNF_re3201000475353829189nt_nat @ ( bNF_re4712519889275205905nt_int @ A2 @ B2 ) @ ( bNF_re8371370899516666973nt_nat @ ( bNF_re552426215088010623at_nat @ C @ D ) @ ( bNF_re277589241527610453nt_nat @ ( bNF_re5089333283451836215nt_o_o @ B2 @ C ) @ ( bNF_re3715656647883201625at_nat @ A2 @ D ) ) ) @ map_fu8249208328825198840_o_nat @ map_fu8249208328825198840_o_nat ) ).

% map_fun_parametric
thf(fact_385_map__fun__parametric,axiom,
    ! [A2: int > int > $o,B2: int > int > $o,C: $o > $o > $o,D: int > int > $o] : ( bNF_re7994082533931791685nt_int @ ( bNF_re4712519889275205905nt_int @ A2 @ B2 ) @ ( bNF_re3022626809172352605nt_int @ ( bNF_re1549289456480014903nt_int @ C @ D ) @ ( bNF_re1510820403721876237nt_int @ ( bNF_re5089333283451836215nt_o_o @ B2 @ C ) @ ( bNF_re4712519889275205905nt_int @ A2 @ D ) ) ) @ map_fu8246717858316148564_o_int @ map_fu8246717858316148564_o_int ) ).

% map_fun_parametric
thf(fact_386_map__fun__parametric,axiom,
    ! [A2: int > int > $o,B2: int > int > $o,C: nat > nat > $o,D: $o > $o > $o] : ( bNF_re2389797945169007513_int_o @ ( bNF_re4712519889275205905nt_int @ A2 @ B2 ) @ ( bNF_re302001808991886301_int_o @ ( bNF_re4705727531993890431at_o_o @ C @ D ) @ ( bNF_re6080477866362396757_int_o @ ( bNF_re3715656647883201625at_nat @ B2 @ C ) @ ( bNF_re5089333283451836215nt_o_o @ A2 @ D ) ) ) @ map_fu2128507653078608342_nat_o @ map_fu2128507653078608342_nat_o ) ).

% map_fun_parametric
thf(fact_387_fun_Orel__compp,axiom,
    ! [R: $o > $o > $o,S2: $o > $o > $o] :
      ( ( bNF_re5089333283451836215nt_o_o
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
        @ ( relcompp_o_o_o @ R @ S2 ) )
      = ( relcom989163212620591602_int_o
        @ ( bNF_re5089333283451836215nt_o_o
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ R )
        @ ( bNF_re5089333283451836215nt_o_o
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ S2 ) ) ) ).

% fun.rel_compp
thf(fact_388_fun_Orel__compp,axiom,
    ! [R: nat > nat > $o,S2: nat > nat > $o] :
      ( ( bNF_re3715656647883201625at_nat
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
        @ ( relcompp_nat_nat_nat @ R @ S2 ) )
      = ( relcom4622340022947818372nt_nat
        @ ( bNF_re3715656647883201625at_nat
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ R )
        @ ( bNF_re3715656647883201625at_nat
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ S2 ) ) ) ).

% fun.rel_compp
thf(fact_389_fun_Orel__compp,axiom,
    ! [R: int > int > $o,S2: int > int > $o] :
      ( ( bNF_re4712519889275205905nt_int
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
        @ ( relcompp_int_int_int @ R @ S2 ) )
      = ( relcom1106299141546538648nt_int
        @ ( bNF_re4712519889275205905nt_int
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ R )
        @ ( bNF_re4712519889275205905nt_int
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ S2 ) ) ) ).

% fun.rel_compp
thf(fact_390_fun_Orel__compp,axiom,
    ! [R: ( int > $o ) > ( int > $o ) > $o,S2: ( int > $o ) > ( int > $o ) > $o] :
      ( ( bNF_re3403563459893282935_int_o
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
        @ ( relcom989163212620591602_int_o @ R @ S2 ) )
      = ( relcom6387603338664227389_int_o
        @ ( bNF_re3403563459893282935_int_o
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ R )
        @ ( bNF_re3403563459893282935_int_o
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ S2 ) ) ) ).

% fun.rel_compp
thf(fact_391_fun_Orel__compp,axiom,
    ! [R: ( int > int ) > ( int > int ) > $o,S2: ( int > int ) > ( int > int ) > $o] :
      ( ( bNF_re711492959462206631nt_int
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
        @ ( relcom1106299141546538648nt_int @ R @ S2 ) )
      = ( relcom6240993501255406585nt_int
        @ ( bNF_re711492959462206631nt_int
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ R )
        @ ( bNF_re711492959462206631nt_int
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ S2 ) ) ) ).

% fun.rel_compp
thf(fact_392_left__unique__OO,axiom,
    ! [R: mat_int > mat_int > $o,S2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( left_u6026039346960889295at_int @ R )
     => ( ( left_u5910868004070155512ring_a @ S2 )
       => ( left_u5910868004070155512ring_a @ ( relcom6459136143736567059ring_a @ R @ S2 ) ) ) ) ).

% left_unique_OO
thf(fact_393_left__unique__fun,axiom,
    ! [A2: int > int > $o,B2: $o > $o > $o] :
      ( ( left_total_int_int @ A2 )
     => ( ( left_unique_o_o @ B2 )
       => ( left_u4522144268380204623_int_o @ ( bNF_re5089333283451836215nt_o_o @ A2 @ B2 ) ) ) ) ).

% left_unique_fun
thf(fact_394_left__unique__fun,axiom,
    ! [A2: int > int > $o,B2: nat > nat > $o] :
      ( ( left_total_int_int @ A2 )
     => ( ( left_unique_nat_nat @ B2 )
       => ( left_u477104448936443847nt_nat @ ( bNF_re3715656647883201625at_nat @ A2 @ B2 ) ) ) ) ).

% left_unique_fun
thf(fact_395_left__unique__fun,axiom,
    ! [A2: int > int > $o,B2: int > int > $o] :
      ( ( left_total_int_int @ A2 )
     => ( ( left_unique_int_int @ B2 )
       => ( left_u1710335611130709631nt_int @ ( bNF_re4712519889275205905nt_int @ A2 @ B2 ) ) ) ) ).

% left_unique_fun
thf(fact_396_left__unique__fun,axiom,
    ! [A2: int > int > $o,B2: ( int > $o ) > ( int > $o ) > $o] :
      ( ( left_total_int_int @ A2 )
     => ( ( left_u4522144268380204623_int_o @ B2 )
       => ( left_u390144976722038927_int_o @ ( bNF_re3403563459893282935_int_o @ A2 @ B2 ) ) ) ) ).

% left_unique_fun
thf(fact_397_left__unique__fun,axiom,
    ! [A2: int > int > $o,B2: ( int > int ) > ( int > int ) > $o] :
      ( ( left_total_int_int @ A2 )
     => ( ( left_u1710335611130709631nt_int @ B2 )
       => ( left_u506611856200109589nt_int @ ( bNF_re711492959462206631nt_int @ A2 @ B2 ) ) ) ) ).

% left_unique_fun
thf(fact_398_bi__unique__OO,axiom,
    ! [A2: mat_int > mat_int > $o,B2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( bi_uni3915055660617466319at_int @ A2 )
     => ( ( bi_uni8710310146129975544ring_a @ B2 )
       => ( bi_uni8710310146129975544ring_a @ ( relcom6459136143736567059ring_a @ A2 @ B2 ) ) ) ) ).

% bi_unique_OO
thf(fact_399_right__total__OO,axiom,
    ! [A2: int > int > $o,B2: int > finite_mod_ring_a > $o] :
      ( ( right_total_int_int @ A2 )
     => ( ( right_2909008500229168952ring_a @ B2 )
       => ( right_2909008500229168952ring_a @ ( relcom2959363069143613434ring_a @ A2 @ B2 ) ) ) ) ).

% right_total_OO
thf(fact_400_right__total__OO,axiom,
    ! [A2: vec_int > vec_int > $o,B2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( right_1673044307916265183ec_int @ A2 )
     => ( ( right_7341149013462710248ring_a @ B2 )
       => ( right_7341149013462710248ring_a @ ( relcom5279651581461346463ring_a @ A2 @ B2 ) ) ) ) ).

% right_total_OO
thf(fact_401_right__total__OO,axiom,
    ! [A2: mat_int > mat_int > $o,B2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( right_3817508881141293023at_int @ A2 )
     => ( ( right_6272992325622558440ring_a @ B2 )
       => ( right_6272992325622558440ring_a @ ( relcom6459136143736567059ring_a @ A2 @ B2 ) ) ) ) ).

% right_total_OO
thf(fact_402_right__total__OO,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: finite_mod_ring_a > finite_mod_ring_a > $o] :
      ( ( right_2909008500229168952ring_a @ A2 )
     => ( ( right_301602178578872031ring_a @ B2 )
       => ( right_2909008500229168952ring_a @ ( relcom3932653789432222877ring_a @ A2 @ B2 ) ) ) ) ).

% right_total_OO
thf(fact_403_right__total__OO,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o,B2: vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a > $o] :
      ( ( right_7341149013462710248ring_a @ A2 )
     => ( ( right_3470053136138939901ring_a @ B2 )
       => ( right_7341149013462710248ring_a @ ( relcom6459548400941628422ring_a @ A2 @ B2 ) ) ) ) ).

% right_total_OO
thf(fact_404_right__total__OO,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o,B2: mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a > $o] :
      ( ( right_6272992325622558440ring_a @ A2 )
     => ( ( right_1306295718943872229ring_a @ B2 )
       => ( right_6272992325622558440ring_a @ ( relcom3823866671404279418ring_a @ A2 @ B2 ) ) ) ) ).

% right_total_OO
thf(fact_405_bi__total__OO,axiom,
    ! [A2: int > int > $o,B2: int > finite_mod_ring_a > $o] :
      ( ( bi_total_int_int @ A2 )
     => ( ( bi_tot623839499179674737ring_a @ B2 )
       => ( bi_tot623839499179674737ring_a @ ( relcom2959363069143613434ring_a @ A2 @ B2 ) ) ) ) ).

% bi_total_OO
thf(fact_406_bi__total__OO,axiom,
    ! [A2: vec_int > vec_int > $o,B2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( bi_tot7057845087757609446ec_int @ A2 )
     => ( ( bi_tot310863827317176225ring_a @ B2 )
       => ( bi_tot310863827317176225ring_a @ ( relcom5279651581461346463ring_a @ A2 @ B2 ) ) ) ) ).

% bi_total_OO
thf(fact_407_bi__total__OO,axiom,
    ! [A2: mat_int > mat_int > $o,B2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( bi_tot9202309660982637286at_int @ A2 )
     => ( ( bi_tot8466079176331800225ring_a @ B2 )
       => ( bi_tot8466079176331800225ring_a @ ( relcom6459136143736567059ring_a @ A2 @ B2 ) ) ) ) ).

% bi_total_OO
thf(fact_408_bi__total__OO,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: finite_mod_ring_a > finite_mod_ring_a > $o] :
      ( ( bi_tot623839499179674737ring_a @ A2 )
     => ( ( bi_tot8261576339290982118ring_a @ B2 )
       => ( bi_tot623839499179674737ring_a @ ( relcom3932653789432222877ring_a @ A2 @ B2 ) ) ) ) ).

% bi_total_OO
thf(fact_409_bi__total__OO,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o,B2: vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a > $o] :
      ( ( bi_tot310863827317176225ring_a @ A2 )
     => ( ( bi_tot4640009209964170116ring_a @ B2 )
       => ( bi_tot310863827317176225ring_a @ ( relcom6459548400941628422ring_a @ A2 @ B2 ) ) ) ) ).

% bi_total_OO
thf(fact_410_bi__total__OO,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o,B2: mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a > $o] :
      ( ( bi_tot8466079176331800225ring_a @ A2 )
     => ( ( bi_tot2476251792769102444ring_a @ B2 )
       => ( bi_tot8466079176331800225ring_a @ ( relcom3823866671404279418ring_a @ A2 @ B2 ) ) ) ) ).

% bi_total_OO
thf(fact_411_right__unique__OO,axiom,
    ! [A2: vec_int > vec_int > $o,B2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( right_926501739254024726ec_int @ A2 )
     => ( ( right_2407805982356550513ring_a @ B2 )
       => ( right_2407805982356550513ring_a @ ( relcom5279651581461346463ring_a @ A2 @ B2 ) ) ) ) ).

% right_unique_OO
thf(fact_412_right__unique__OO,axiom,
    ! [A2: mat_int > mat_int > $o,B2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( right_3070966312479052566at_int @ A2 )
     => ( ( right_1339649294516398705ring_a @ B2 )
       => ( right_1339649294516398705ring_a @ ( relcom6459136143736567059ring_a @ A2 @ B2 ) ) ) ) ).

% right_unique_OO
thf(fact_413_right__unique__OO,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o,B2: vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a > $o] :
      ( ( right_2407805982356550513ring_a @ A2 )
     => ( ( right_1347257933406024628ring_a @ B2 )
       => ( right_2407805982356550513ring_a @ ( relcom6459548400941628422ring_a @ A2 @ B2 ) ) ) ) ).

% right_unique_OO
thf(fact_414_right__unique__OO,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o,B2: mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a > $o] :
      ( ( right_1339649294516398705ring_a @ A2 )
     => ( ( right_8406872553065732764ring_a @ B2 )
       => ( right_1339649294516398705ring_a @ ( relcom3823866671404279418ring_a @ A2 @ B2 ) ) ) ) ).

% right_unique_OO
thf(fact_415_left__total__OO,axiom,
    ! [R: int > int > $o,S2: int > finite_mod_ring_a > $o] :
      ( ( left_total_int_int @ R )
     => ( ( left_t8941605147251654769ring_a @ S2 )
       => ( left_t8941605147251654769ring_a @ ( relcom2959363069143613434ring_a @ R @ S2 ) ) ) ) ).

% left_total_OO
thf(fact_416_left__total__OO,axiom,
    ! [R: vec_int > vec_int > $o,S2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( left_t5041639901324719590ec_int @ R )
     => ( ( left_t7842747197492505505ring_a @ S2 )
       => ( left_t7842747197492505505ring_a @ ( relcom5279651581461346463ring_a @ R @ S2 ) ) ) ) ).

% left_total_OO
thf(fact_417_left__total__OO,axiom,
    ! [R: mat_int > mat_int > $o,S2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( left_t7186104474549747430at_int @ R )
     => ( ( left_t6774590509652353697ring_a @ S2 )
       => ( left_t6774590509652353697ring_a @ ( relcom6459136143736567059ring_a @ R @ S2 ) ) ) ) ).

% left_total_OO
thf(fact_418_left__total__OO,axiom,
    ! [R: int > finite_mod_ring_a > $o,S2: finite_mod_ring_a > finite_mod_ring_a > $o] :
      ( ( left_t8941605147251654769ring_a @ R )
     => ( ( left_t5999478950615061222ring_a @ S2 )
       => ( left_t8941605147251654769ring_a @ ( relcom3932653789432222877ring_a @ R @ S2 ) ) ) ) ).

% left_total_OO
thf(fact_419_left__total__OO,axiom,
    ! [R: vec_int > vec_Fi4296597256376197294ring_a > $o,S2: vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a > $o] :
      ( ( left_t7842747197492505505ring_a @ R )
     => ( ( left_t2900757510667671428ring_a @ S2 )
       => ( left_t7842747197492505505ring_a @ ( relcom6459548400941628422ring_a @ R @ S2 ) ) ) ) ).

% left_total_OO
thf(fact_420_left__total__OO,axiom,
    ! [R: mat_int > mat_Fi443519135453058082ring_a > $o,S2: mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a > $o] :
      ( ( left_t6774590509652353697ring_a @ R )
     => ( ( left_t737000093472603756ring_a @ S2 )
       => ( left_t6774590509652353697ring_a @ ( relcom3823866671404279418ring_a @ R @ S2 ) ) ) ) ).

% left_total_OO
thf(fact_421_functional__converse__relation,axiom,
    ! [R: int > finite_mod_ring_a > $o] :
      ( ( left_u1888462625899933000ring_a @ R )
     => ( ( right_2909008500229168952ring_a @ R )
       => ! [Y4: finite_mod_ring_a] :
          ? [X4: int] :
            ( ( R @ X4 @ Y4 )
            & ! [Ya: int] :
                ( ( R @ Ya @ Y4 )
               => ( Ya = X4 ) ) ) ) ) ).

% functional_converse_relation
thf(fact_422_functional__converse__relation,axiom,
    ! [R: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( left_u6979024691910307320ring_a @ R )
     => ( ( right_7341149013462710248ring_a @ R )
       => ! [Y4: vec_Fi4296597256376197294ring_a] :
          ? [X4: vec_int] :
            ( ( R @ X4 @ Y4 )
            & ! [Ya: vec_int] :
                ( ( R @ Ya @ Y4 )
               => ( Ya = X4 ) ) ) ) ) ).

% functional_converse_relation
thf(fact_423_functional__converse__relation,axiom,
    ! [R: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( left_u5910868004070155512ring_a @ R )
     => ( ( right_6272992325622558440ring_a @ R )
       => ! [Y4: mat_Fi443519135453058082ring_a] :
          ? [X4: mat_int] :
            ( ( R @ X4 @ Y4 )
            & ! [Ya: mat_int] :
                ( ( R @ Ya @ Y4 )
               => ( Ya = X4 ) ) ) ) ) ).

% functional_converse_relation
thf(fact_424_pcr__Domainp__total,axiom,
    ! [B2: vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a > $o,A2: vec_int > vec_Fi4296597256376197294ring_a > $o,P: vec_int > $o] :
      ( ( left_t2900757510667671428ring_a @ B2 )
     => ( ( ( domain4015354059925764579ring_a @ A2 )
          = P )
       => ( ( domain4015354059925764579ring_a @ ( relcom6459548400941628422ring_a @ A2 @ B2 ) )
          = P ) ) ) ).

% pcr_Domainp_total
thf(fact_425_pcr__Domainp__total,axiom,
    ! [B2: mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a > $o,A2: mat_int > mat_Fi443519135453058082ring_a > $o,P: mat_int > $o] :
      ( ( left_t737000093472603756ring_a @ B2 )
     => ( ( ( domain2947197372085612771ring_a @ A2 )
          = P )
       => ( ( domain2947197372085612771ring_a @ ( relcom3823866671404279418ring_a @ A2 @ B2 ) )
          = P ) ) ) ).

% pcr_Domainp_total
thf(fact_426_pcr__Domainp__total,axiom,
    ! [B2: vec_int > vec_Fi4296597256376197294ring_a > $o,A2: vec_int > vec_int > $o,P: vec_int > $o] :
      ( ( left_t7842747197492505505ring_a @ B2 )
     => ( ( ( domain4055499821733669156ec_int @ A2 )
          = P )
       => ( ( domain4015354059925764579ring_a @ ( relcom5279651581461346463ring_a @ A2 @ B2 ) )
          = P ) ) ) ).

% pcr_Domainp_total
thf(fact_427_pcr__Domainp__total,axiom,
    ! [B2: mat_int > mat_Fi443519135453058082ring_a > $o,A2: mat_int > mat_int > $o,P: mat_int > $o] :
      ( ( left_t6774590509652353697ring_a @ B2 )
     => ( ( ( domain6199964394958696996at_int @ A2 )
          = P )
       => ( ( domain2947197372085612771ring_a @ ( relcom6459136143736567059ring_a @ A2 @ B2 ) )
          = P ) ) ) ).

% pcr_Domainp_total
thf(fact_428_left__total__fun,axiom,
    ! [A2: int > int > $o,B2: $o > $o > $o] :
      ( ( left_unique_int_int @ A2 )
     => ( ( left_total_o_o @ B2 )
       => ( left_t5625308128979377254_int_o @ ( bNF_re5089333283451836215nt_o_o @ A2 @ B2 ) ) ) ) ).

% left_total_fun
thf(fact_429_left__total__fun,axiom,
    ! [A2: int > int > $o,B2: nat > nat > $o] :
      ( ( left_unique_int_int @ A2 )
     => ( ( left_total_nat_nat @ B2 )
       => ( left_t5587994516945368670nt_nat @ ( bNF_re3715656647883201625at_nat @ A2 @ B2 ) ) ) ) ).

% left_total_fun
thf(fact_430_left__total__fun,axiom,
    ! [A2: int > int > $o,B2: int > int > $o] :
      ( ( left_unique_int_int @ A2 )
     => ( ( left_total_int_int @ B2 )
       => ( left_t6821225679139634454nt_int @ ( bNF_re4712519889275205905nt_int @ A2 @ B2 ) ) ) ) ).

% left_total_fun
thf(fact_431_left__total__fun,axiom,
    ! [A2: int > int > $o,B2: ( int > $o ) > ( int > $o ) > $o] :
      ( ( left_unique_int_int @ A2 )
     => ( ( left_t5625308128979377254_int_o @ B2 )
       => ( left_t5677053946549264806_int_o @ ( bNF_re3403563459893282935_int_o @ A2 @ B2 ) ) ) ) ).

% left_total_fun
thf(fact_432_left__total__fun,axiom,
    ! [A2: int > int > $o,B2: ( int > int ) > ( int > int ) > $o] :
      ( ( left_unique_int_int @ A2 )
     => ( ( left_t6821225679139634454nt_int @ B2 )
       => ( left_t6143790711152109484nt_int @ ( bNF_re711492959462206631nt_int @ A2 @ B2 ) ) ) ) ).

% left_total_fun
thf(fact_433_bi__uniqueI,axiom,
    ! [R: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( left_u6979024691910307320ring_a @ R )
     => ( ( right_2407805982356550513ring_a @ R )
       => ( bi_uni555094797115351544ring_a @ R ) ) ) ).

% bi_uniqueI
thf(fact_434_bi__uniqueI,axiom,
    ! [R: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( left_u5910868004070155512ring_a @ R )
     => ( ( right_1339649294516398705ring_a @ R )
       => ( bi_uni8710310146129975544ring_a @ R ) ) ) ).

% bi_uniqueI
thf(fact_435_bi__unique__alt__def,axiom,
    ( bi_uni555094797115351544ring_a
    = ( ^ [A3: vec_int > vec_Fi4296597256376197294ring_a > $o] :
          ( ( left_u6979024691910307320ring_a @ A3 )
          & ( right_2407805982356550513ring_a @ A3 ) ) ) ) ).

% bi_unique_alt_def
thf(fact_436_bi__unique__alt__def,axiom,
    ( bi_uni8710310146129975544ring_a
    = ( ^ [A3: mat_int > mat_Fi443519135453058082ring_a > $o] :
          ( ( left_u5910868004070155512ring_a @ A3 )
          & ( right_1339649294516398705ring_a @ A3 ) ) ) ) ).

% bi_unique_alt_def
thf(fact_437_pcr__Domainp__par__left__total,axiom,
    ! [B2: vec_int > vec_Fi4296597256376197294ring_a > $o,P: vec_int > $o,A2: vec_int > vec_int > $o,P2: vec_int > $o] :
      ( ( ( domain4015354059925764579ring_a @ B2 )
        = P )
     => ( ( left_t5041639901324719590ec_int @ A2 )
       => ( ( bNF_re679821270890987293nt_o_o @ A2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
            @ P2
            @ P )
         => ( ( domain4015354059925764579ring_a @ ( relcom5279651581461346463ring_a @ A2 @ B2 ) )
            = P2 ) ) ) ) ).

% pcr_Domainp_par_left_total
thf(fact_438_pcr__Domainp__par__left__total,axiom,
    ! [B2: mat_int > mat_Fi443519135453058082ring_a > $o,P: mat_int > $o,A2: mat_int > mat_int > $o,P2: mat_int > $o] :
      ( ( ( domain2947197372085612771ring_a @ B2 )
        = P )
     => ( ( left_t7186104474549747430at_int @ A2 )
       => ( ( bNF_re5904460004506961949nt_o_o @ A2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
            @ P2
            @ P )
         => ( ( domain2947197372085612771ring_a @ ( relcom6459136143736567059ring_a @ A2 @ B2 ) )
            = P2 ) ) ) ) ).

% pcr_Domainp_par_left_total
thf(fact_439_pcr__Domainp__par__left__total,axiom,
    ! [B2: vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a > $o,P: vec_Fi4296597256376197294ring_a > $o,A2: vec_int > vec_Fi4296597256376197294ring_a > $o,P2: vec_int > $o] :
      ( ( ( domain3984477134522034114ring_a @ B2 )
        = P )
     => ( ( left_t7842747197492505505ring_a @ A2 )
       => ( ( bNF_re507051067509135658_a_o_o @ A2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
            @ P2
            @ P )
         => ( ( domain4015354059925764579ring_a @ ( relcom6459548400941628422ring_a @ A2 @ B2 ) )
            = P2 ) ) ) ) ).

% pcr_Domainp_par_left_total
thf(fact_440_pcr__Domainp__par__left__total,axiom,
    ! [B2: mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a > $o,P: mat_Fi443519135453058082ring_a > $o,A2: mat_int > mat_Fi443519135453058082ring_a > $o,P2: mat_int > $o] :
      ( ( ( domain1820719717326966442ring_a @ B2 )
        = P )
     => ( ( left_t6774590509652353697ring_a @ A2 )
       => ( ( bNF_re6153771816476299306_a_o_o @ A2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
            @ P2
            @ P )
         => ( ( domain2947197372085612771ring_a @ ( relcom3823866671404279418ring_a @ A2 @ B2 ) )
            = P2 ) ) ) ) ).

% pcr_Domainp_par_left_total
thf(fact_441_neg__fun__distr2,axiom,
    ! [R3: int > int > $o,S3: $o > $o > $o,R: int > int > $o,S2: $o > $o > $o] :
      ( ( right_unique_int_int @ R3 )
     => ( ( left_total_int_int @ R3 )
       => ( ( left_unique_o_o @ S3 )
         => ( ( right_total_o_o @ S3 )
           => ( ord_le9100565418538218190nt_o_o @ ( bNF_re5089333283451836215nt_o_o @ ( relcompp_int_int_int @ R @ R3 ) @ ( relcompp_o_o_o @ S2 @ S3 ) ) @ ( relcom989163212620591602_int_o @ ( bNF_re5089333283451836215nt_o_o @ R @ S2 ) @ ( bNF_re5089333283451836215nt_o_o @ R3 @ S3 ) ) ) ) ) ) ) ).

% neg_fun_distr2
thf(fact_442_neg__fun__distr2,axiom,
    ! [R3: int > int > $o,S3: nat > nat > $o,R: int > int > $o,S2: nat > nat > $o] :
      ( ( right_unique_int_int @ R3 )
     => ( ( left_total_int_int @ R3 )
       => ( ( left_unique_nat_nat @ S3 )
         => ( ( right_total_nat_nat @ S3 )
           => ( ord_le7357923999124086768_nat_o @ ( bNF_re3715656647883201625at_nat @ ( relcompp_int_int_int @ R @ R3 ) @ ( relcompp_nat_nat_nat @ S2 @ S3 ) ) @ ( relcom4622340022947818372nt_nat @ ( bNF_re3715656647883201625at_nat @ R @ S2 ) @ ( bNF_re3715656647883201625at_nat @ R3 @ S3 ) ) ) ) ) ) ) ).

% neg_fun_distr2
thf(fact_443_neg__fun__distr2,axiom,
    ! [R3: int > int > $o,S3: int > int > $o,R: int > int > $o,S2: int > int > $o] :
      ( ( right_unique_int_int @ R3 )
     => ( ( left_total_int_int @ R3 )
       => ( ( left_unique_int_int @ S3 )
         => ( ( right_total_int_int @ S3 )
           => ( ord_le5837993363827774264_int_o @ ( bNF_re4712519889275205905nt_int @ ( relcompp_int_int_int @ R @ R3 ) @ ( relcompp_int_int_int @ S2 @ S3 ) ) @ ( relcom1106299141546538648nt_int @ ( bNF_re4712519889275205905nt_int @ R @ S2 ) @ ( bNF_re4712519889275205905nt_int @ R3 @ S3 ) ) ) ) ) ) ) ).

% neg_fun_distr2
thf(fact_444_neg__fun__distr2,axiom,
    ! [R3: int > int > $o,S3: ( int > $o ) > ( int > $o ) > $o,R: int > int > $o,S2: ( int > $o ) > ( int > $o ) > $o] :
      ( ( right_unique_int_int @ R3 )
     => ( ( left_total_int_int @ R3 )
       => ( ( left_u4522144268380204623_int_o @ S3 )
         => ( ( right_3358435141589207135_int_o @ S3 )
           => ( ord_le8512398041180637710nt_o_o @ ( bNF_re3403563459893282935_int_o @ ( relcompp_int_int_int @ R @ R3 ) @ ( relcom989163212620591602_int_o @ S2 @ S3 ) ) @ ( relcom6387603338664227389_int_o @ ( bNF_re3403563459893282935_int_o @ R @ S2 ) @ ( bNF_re3403563459893282935_int_o @ R3 @ S3 ) ) ) ) ) ) ) ).

% neg_fun_distr2
thf(fact_445_neg__fun__distr2,axiom,
    ! [R3: int > int > $o,S3: ( int > int ) > ( int > int ) > $o,R: int > int > $o,S2: ( int > int ) > ( int > int ) > $o] :
      ( ( right_unique_int_int @ R3 )
     => ( ( left_total_int_int @ R3 )
       => ( ( left_u1710335611130709631nt_int @ S3 )
         => ( ( right_2214481324298164367nt_int @ S3 )
           => ( ord_le25265541537557922_int_o @ ( bNF_re711492959462206631nt_int @ ( relcompp_int_int_int @ R @ R3 ) @ ( relcom1106299141546538648nt_int @ S2 @ S3 ) ) @ ( relcom6240993501255406585nt_int @ ( bNF_re711492959462206631nt_int @ R @ S2 ) @ ( bNF_re711492959462206631nt_int @ R3 @ S3 ) ) ) ) ) ) ) ).

% neg_fun_distr2
thf(fact_446_neg__fun__distr2,axiom,
    ! [R3: int > finite_mod_ring_a > $o,S3: int > finite_mod_ring_a > $o,R: int > int > $o,S2: int > int > $o] :
      ( ( right_7581627888863641665ring_a @ R3 )
     => ( ( left_t8941605147251654769ring_a @ R3 )
       => ( ( left_u1888462625899933000ring_a @ S3 )
         => ( ( right_2909008500229168952ring_a @ S3 )
           => ( ord_le4353216327012020490ng_a_o @ ( bNF_re4694112744541868061ring_a @ ( relcom2959363069143613434ring_a @ R @ R3 ) @ ( relcom2959363069143613434ring_a @ S2 @ S3 ) ) @ ( relcom3368137050767642310ring_a @ ( bNF_re4712519889275205905nt_int @ R @ S2 ) @ ( bNF_re4694112744541868061ring_a @ R3 @ S3 ) ) ) ) ) ) ) ).

% neg_fun_distr2
thf(fact_447_neg__fun__distr2,axiom,
    ! [R3: mat_int > mat_Fi443519135453058082ring_a > $o,S3: mat_int > mat_Fi443519135453058082ring_a > $o,R: mat_int > mat_int > $o,S2: mat_int > mat_int > $o] :
      ( ( right_1339649294516398705ring_a @ R3 )
     => ( ( left_t6774590509652353697ring_a @ R3 )
       => ( ( left_u5910868004070155512ring_a @ S3 )
         => ( ( right_6272992325622558440ring_a @ S3 )
           => ( ord_le3697366711325567390ng_a_o @ ( bNF_re7267033552616699805ring_a @ ( relcom6459136143736567059ring_a @ R @ R3 ) @ ( relcom6459136143736567059ring_a @ S2 @ S3 ) ) @ ( relcom6302253411340485088ring_a @ ( bNF_re3172240519465120989at_int @ R @ S2 ) @ ( bNF_re7267033552616699805ring_a @ R3 @ S3 ) ) ) ) ) ) ) ).

% neg_fun_distr2
thf(fact_448_neg__fun__distr1,axiom,
    ! [R: int > int > $o,R3: int > int > $o,S2: $o > $o > $o,S3: $o > $o > $o] :
      ( ( left_unique_int_int @ R )
     => ( ( right_total_int_int @ R )
       => ( ( right_unique_int_int @ R3 )
         => ( ( left_total_int_int @ R3 )
           => ( ord_le9100565418538218190nt_o_o @ ( bNF_re5089333283451836215nt_o_o @ ( relcompp_int_int_int @ R @ R3 ) @ ( relcompp_o_o_o @ S2 @ S3 ) ) @ ( relcom989163212620591602_int_o @ ( bNF_re5089333283451836215nt_o_o @ R @ S2 ) @ ( bNF_re5089333283451836215nt_o_o @ R3 @ S3 ) ) ) ) ) ) ) ).

% neg_fun_distr1
thf(fact_449_neg__fun__distr1,axiom,
    ! [R: int > int > $o,R3: int > int > $o,S2: nat > nat > $o,S3: nat > nat > $o] :
      ( ( left_unique_int_int @ R )
     => ( ( right_total_int_int @ R )
       => ( ( right_unique_int_int @ R3 )
         => ( ( left_total_int_int @ R3 )
           => ( ord_le7357923999124086768_nat_o @ ( bNF_re3715656647883201625at_nat @ ( relcompp_int_int_int @ R @ R3 ) @ ( relcompp_nat_nat_nat @ S2 @ S3 ) ) @ ( relcom4622340022947818372nt_nat @ ( bNF_re3715656647883201625at_nat @ R @ S2 ) @ ( bNF_re3715656647883201625at_nat @ R3 @ S3 ) ) ) ) ) ) ) ).

% neg_fun_distr1
thf(fact_450_neg__fun__distr1,axiom,
    ! [R: int > int > $o,R3: int > int > $o,S2: int > int > $o,S3: int > int > $o] :
      ( ( left_unique_int_int @ R )
     => ( ( right_total_int_int @ R )
       => ( ( right_unique_int_int @ R3 )
         => ( ( left_total_int_int @ R3 )
           => ( ord_le5837993363827774264_int_o @ ( bNF_re4712519889275205905nt_int @ ( relcompp_int_int_int @ R @ R3 ) @ ( relcompp_int_int_int @ S2 @ S3 ) ) @ ( relcom1106299141546538648nt_int @ ( bNF_re4712519889275205905nt_int @ R @ S2 ) @ ( bNF_re4712519889275205905nt_int @ R3 @ S3 ) ) ) ) ) ) ) ).

% neg_fun_distr1
thf(fact_451_neg__fun__distr1,axiom,
    ! [R: int > int > $o,R3: int > int > $o,S2: ( int > $o ) > ( int > $o ) > $o,S3: ( int > $o ) > ( int > $o ) > $o] :
      ( ( left_unique_int_int @ R )
     => ( ( right_total_int_int @ R )
       => ( ( right_unique_int_int @ R3 )
         => ( ( left_total_int_int @ R3 )
           => ( ord_le8512398041180637710nt_o_o @ ( bNF_re3403563459893282935_int_o @ ( relcompp_int_int_int @ R @ R3 ) @ ( relcom989163212620591602_int_o @ S2 @ S3 ) ) @ ( relcom6387603338664227389_int_o @ ( bNF_re3403563459893282935_int_o @ R @ S2 ) @ ( bNF_re3403563459893282935_int_o @ R3 @ S3 ) ) ) ) ) ) ) ).

% neg_fun_distr1
thf(fact_452_neg__fun__distr1,axiom,
    ! [R: int > int > $o,R3: int > int > $o,S2: ( int > int ) > ( int > int ) > $o,S3: ( int > int ) > ( int > int ) > $o] :
      ( ( left_unique_int_int @ R )
     => ( ( right_total_int_int @ R )
       => ( ( right_unique_int_int @ R3 )
         => ( ( left_total_int_int @ R3 )
           => ( ord_le25265541537557922_int_o @ ( bNF_re711492959462206631nt_int @ ( relcompp_int_int_int @ R @ R3 ) @ ( relcom1106299141546538648nt_int @ S2 @ S3 ) ) @ ( relcom6240993501255406585nt_int @ ( bNF_re711492959462206631nt_int @ R @ S2 ) @ ( bNF_re711492959462206631nt_int @ R3 @ S3 ) ) ) ) ) ) ) ).

% neg_fun_distr1
thf(fact_453_neg__fun__distr1,axiom,
    ! [R: mat_int > mat_int > $o,R3: mat_int > mat_Fi443519135453058082ring_a > $o,S2: mat_int > mat_int > $o,S3: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( left_u6026039346960889295at_int @ R )
     => ( ( right_3817508881141293023at_int @ R )
       => ( ( right_1339649294516398705ring_a @ R3 )
         => ( ( left_t6774590509652353697ring_a @ R3 )
           => ( ord_le3697366711325567390ng_a_o @ ( bNF_re7267033552616699805ring_a @ ( relcom6459136143736567059ring_a @ R @ R3 ) @ ( relcom6459136143736567059ring_a @ S2 @ S3 ) ) @ ( relcom6302253411340485088ring_a @ ( bNF_re3172240519465120989at_int @ R @ S2 ) @ ( bNF_re7267033552616699805ring_a @ R3 @ S3 ) ) ) ) ) ) ) ).

% neg_fun_distr1
thf(fact_454_Domainp__pred__fun__eq,axiom,
    ! [T2: int > int > $o,S2: $o > $o > $o] :
      ( ( left_unique_int_int @ T2 )
     => ( ( domainp_int_o_int_o @ ( bNF_re5089333283451836215nt_o_o @ T2 @ S2 ) )
        = ( basic_pred_fun_int_o @ ( domainp_int_int @ T2 ) @ ( domainp_o_o @ S2 ) ) ) ) ).

% Domainp_pred_fun_eq
thf(fact_455_Domainp__pred__fun__eq,axiom,
    ! [T2: int > int > $o,S2: nat > nat > $o] :
      ( ( left_unique_int_int @ T2 )
     => ( ( domain7985844723471903900nt_nat @ ( bNF_re3715656647883201625at_nat @ T2 @ S2 ) )
        = ( basic_1842754918481324705nt_nat @ ( domainp_int_int @ T2 ) @ ( domainp_nat_nat @ S2 ) ) ) ) ).

% Domainp_pred_fun_eq
thf(fact_456_Domainp__pred__fun__eq,axiom,
    ! [T2: int > int > $o,S2: int > int > $o] :
      ( ( left_unique_int_int @ T2 )
     => ( ( domain9219075885666169684nt_int @ ( bNF_re4712519889275205905nt_int @ T2 @ S2 ) )
        = ( basic_1840264447972274429nt_int @ ( domainp_int_int @ T2 ) @ ( domainp_int_int @ S2 ) ) ) ) ).

% Domainp_pred_fun_eq
thf(fact_457_Domainp__pred__fun__eq,axiom,
    ! [T2: int > int > $o,S2: ( int > $o ) > ( int > $o ) > $o] :
      ( ( left_unique_int_int @ T2 )
     => ( ( domain8659272630029231332_int_o @ ( bNF_re3403563459893282935_int_o @ T2 @ S2 ) )
        = ( basic_1842322873297984402_int_o @ ( domainp_int_int @ T2 ) @ ( domainp_int_o_int_o @ S2 ) ) ) ) ).

% Domainp_pred_fun_eq
thf(fact_458_Domainp__pred__fun__eq,axiom,
    ! [T2: int > int > $o,S2: ( int > int ) > ( int > int ) > $o] :
      ( ( left_unique_int_int @ T2 )
     => ( ( domain4136455042513400810nt_int @ ( bNF_re711492959462206631nt_int @ T2 @ S2 ) )
        = ( basic_1535474925015357768nt_int @ ( domainp_int_int @ T2 ) @ ( domain9219075885666169684nt_int @ S2 ) ) ) ) ).

% Domainp_pred_fun_eq
thf(fact_459_Domainp__pred__fun__eq,axiom,
    ! [T2: vec_int > vec_Fi4296597256376197294ring_a > $o,S2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( left_u6979024691910307320ring_a @ T2 )
     => ( ( domain8208586219136628870ring_a @ ( bNF_re7573024106080040861ring_a @ T2 @ S2 ) )
        = ( basic_8728657254994625763ec_int @ ( domain4015354059925764579ring_a @ T2 ) @ ( domain4015354059925764579ring_a @ S2 ) ) ) ) ).

% Domainp_pred_fun_eq
thf(fact_460_Domainp__pred__fun__eq,axiom,
    ! [T2: vec_int > vec_Fi4296597256376197294ring_a > $o,S2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( left_u6979024691910307320ring_a @ T2 )
     => ( ( domain49596084258168198ring_a @ ( bNF_re6504867418239889053ring_a @ T2 @ S2 ) )
        = ( basic_5242197913839372399at_int @ ( domain4015354059925764579ring_a @ T2 ) @ ( domain2947197372085612771ring_a @ S2 ) ) ) ) ).

% Domainp_pred_fun_eq
thf(fact_461_Domainp__pred__fun__eq,axiom,
    ! [T2: mat_int > mat_Fi443519135453058082ring_a > $o,S2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( left_u5910868004070155512ring_a @ T2 )
     => ( ( domain5159416631507321710ring_a @ ( bNF_re8335190240456851613ring_a @ T2 @ S2 ) )
        = ( basic_5136209132520131159ec_int @ ( domain2947197372085612771ring_a @ T2 ) @ ( domain4015354059925764579ring_a @ S2 ) ) ) ) ).

% Domainp_pred_fun_eq
thf(fact_462_Domainp__pred__fun__eq,axiom,
    ! [T2: mat_int > mat_Fi443519135453058082ring_a > $o,S2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( left_u5910868004070155512ring_a @ T2 )
     => ( ( domain6223798533483636846ring_a @ ( bNF_re7267033552616699805ring_a @ T2 @ S2 ) )
        = ( basic_1649749791364877795at_int @ ( domain2947197372085612771ring_a @ T2 ) @ ( domain2947197372085612771ring_a @ S2 ) ) ) ) ).

% Domainp_pred_fun_eq
thf(fact_463_M__1,axiom,
    ( ( vector_Matrix_mod_M @ m @ one_one_int )
    = one_one_int ) ).

% M_1
thf(fact_464_transfer__forall__transfer_I1_J,axiom,
    ! [A2: int > int > $o] :
      ( ( bi_total_int_int @ A2 )
     => ( bNF_re6378653760509651613_o_o_o
        @ ( bNF_re5089333283451836215nt_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
        @ transfer_forall_int
        @ transfer_forall_int ) ) ).

% transfer_forall_transfer(1)
thf(fact_465_transfer__forall__transfer_I1_J,axiom,
    ! [A2: int > finite_mod_ring_a > $o] :
      ( ( bi_tot623839499179674737ring_a @ A2 )
     => ( bNF_re8869226137141724030_o_o_o
        @ ( bNF_re8290846538823883642_a_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
        @ transfer_forall_int
        @ transf2422954704962549770ring_a ) ) ).

% transfer_forall_transfer(1)
thf(fact_466_transfer__forall__transfer_I1_J,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( bi_tot310863827317176225ring_a @ A2 )
     => ( bNF_re3034707934920152030_o_o_o
        @ ( bNF_re507051067509135658_a_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
        @ transf5930571779719943006ec_int
        @ transf142359738573599785ring_a ) ) ).

% transfer_forall_transfer(1)
thf(fact_467_transfer__forall__transfer_I1_J,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( bi_tot8466079176331800225ring_a @ A2 )
     => ( bNF_re3523364678894640886_o_o_o
        @ ( bNF_re6153771816476299306_a_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
        @ transf2444112438564689642at_int
        @ transf5512653654505236381ring_a ) ) ).

% transfer_forall_transfer(1)
thf(fact_468_transfer__forall__transfer_I2_J,axiom,
    ! [A2: int > int > $o] :
      ( ( right_total_int_int @ A2 )
     => ( bNF_re6378653760509651613_o_o_o
        @ ( bNF_re5089333283451836215nt_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ (=>)
        @ transfer_forall_int
        @ transfer_forall_int ) ) ).

% transfer_forall_transfer(2)
thf(fact_469_transfer__forall__transfer_I2_J,axiom,
    ! [A2: int > finite_mod_ring_a > $o] :
      ( ( right_2909008500229168952ring_a @ A2 )
     => ( bNF_re8869226137141724030_o_o_o
        @ ( bNF_re8290846538823883642_a_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ (=>)
        @ transfer_forall_int
        @ transf2422954704962549770ring_a ) ) ).

% transfer_forall_transfer(2)
thf(fact_470_transfer__forall__transfer_I2_J,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( right_7341149013462710248ring_a @ A2 )
     => ( bNF_re3034707934920152030_o_o_o
        @ ( bNF_re507051067509135658_a_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ (=>)
        @ transf5930571779719943006ec_int
        @ transf142359738573599785ring_a ) ) ).

% transfer_forall_transfer(2)
thf(fact_471_transfer__forall__transfer_I2_J,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( right_6272992325622558440ring_a @ A2 )
     => ( bNF_re3523364678894640886_o_o_o
        @ ( bNF_re6153771816476299306_a_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ (=>)
        @ transf2444112438564689642at_int
        @ transf5512653654505236381ring_a ) ) ).

% transfer_forall_transfer(2)
thf(fact_472_transfer__forall__transfer_I3_J,axiom,
    ! [A2: int > int > $o] :
      ( ( right_total_int_int @ A2 )
     => ( bNF_re6378653760509651613_o_o_o @ ( bNF_re5089333283451836215nt_o_o @ A2 @ (=>) ) @ (=>) @ transfer_forall_int @ transfer_forall_int ) ) ).

% transfer_forall_transfer(3)
thf(fact_473_transfer__forall__transfer_I3_J,axiom,
    ! [A2: int > finite_mod_ring_a > $o] :
      ( ( right_2909008500229168952ring_a @ A2 )
     => ( bNF_re8869226137141724030_o_o_o @ ( bNF_re8290846538823883642_a_o_o @ A2 @ (=>) ) @ (=>) @ transfer_forall_int @ transf2422954704962549770ring_a ) ) ).

% transfer_forall_transfer(3)
thf(fact_474_transfer__forall__transfer_I3_J,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( right_7341149013462710248ring_a @ A2 )
     => ( bNF_re3034707934920152030_o_o_o @ ( bNF_re507051067509135658_a_o_o @ A2 @ (=>) ) @ (=>) @ transf5930571779719943006ec_int @ transf142359738573599785ring_a ) ) ).

% transfer_forall_transfer(3)
thf(fact_475_transfer__forall__transfer_I3_J,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( right_6272992325622558440ring_a @ A2 )
     => ( bNF_re3523364678894640886_o_o_o @ ( bNF_re6153771816476299306_a_o_o @ A2 @ (=>) ) @ (=>) @ transf2444112438564689642at_int @ transf5512653654505236381ring_a ) ) ).

% transfer_forall_transfer(3)
thf(fact_476_Domainp__forall__transfer,axiom,
    ! [A2: int > int > $o] :
      ( ( right_total_int_int @ A2 )
     => ( bNF_re6378653760509651613_o_o_o
        @ ( bNF_re5089333283451836215nt_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
        @ ( transfer_bforall_int @ ( domainp_int_int @ A2 ) )
        @ transfer_forall_int ) ) ).

% Domainp_forall_transfer
thf(fact_477_Domainp__forall__transfer,axiom,
    ! [A2: int > finite_mod_ring_a > $o] :
      ( ( right_2909008500229168952ring_a @ A2 )
     => ( bNF_re8869226137141724030_o_o_o
        @ ( bNF_re8290846538823883642_a_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
        @ ( transfer_bforall_int @ ( domain6543890336852369843ring_a @ A2 ) )
        @ transf2422954704962549770ring_a ) ) ).

% Domainp_forall_transfer
thf(fact_478_Domainp__forall__transfer,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( right_7341149013462710248ring_a @ A2 )
     => ( bNF_re3034707934920152030_o_o_o
        @ ( bNF_re507051067509135658_a_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
        @ ( transf5631211014983366848ec_int @ ( domain4015354059925764579ring_a @ A2 ) )
        @ transf142359738573599785ring_a ) ) ).

% Domainp_forall_transfer
thf(fact_479_Domainp__forall__transfer,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( right_6272992325622558440ring_a @ A2 )
     => ( bNF_re3523364678894640886_o_o_o
        @ ( bNF_re6153771816476299306_a_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
        @ ( transf2144751673828113484at_int @ ( domain2947197372085612771ring_a @ A2 ) )
        @ transf5512653654505236381ring_a ) ) ).

% Domainp_forall_transfer
thf(fact_480_Domainp_Ocases,axiom,
    ! [R4: vec_int > vec_Fi4296597256376197294ring_a > $o,A: vec_int] :
      ( ( domain4015354059925764579ring_a @ R4 @ A )
     => ~ ! [B3: vec_Fi4296597256376197294ring_a] :
            ~ ( R4 @ A @ B3 ) ) ).

% Domainp.cases
thf(fact_481_Domainp_Ocases,axiom,
    ! [R4: mat_int > mat_Fi443519135453058082ring_a > $o,A: mat_int] :
      ( ( domain2947197372085612771ring_a @ R4 @ A )
     => ~ ! [B3: mat_Fi443519135453058082ring_a] :
            ~ ( R4 @ A @ B3 ) ) ).

% Domainp.cases
thf(fact_482_le__zero__eq,axiom,
    ! [N: nat] :
      ( ( ord_less_eq_nat @ N @ zero_zero_nat )
      = ( N = zero_zero_nat ) ) ).

% le_zero_eq
thf(fact_483_of__int__le__iff,axiom,
    ! [W: int,Z: int] :
      ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
      = ( ord_less_eq_int @ W @ Z ) ) ).

% of_int_le_iff
thf(fact_484_of__int__le__iff,axiom,
    ! [W: int,Z: int] :
      ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
      = ( ord_less_eq_int @ W @ Z ) ) ).

% of_int_le_iff
thf(fact_485_bits__mod__by__1,axiom,
    ! [A: int] :
      ( ( modulo_modulo_int @ A @ one_one_int )
      = zero_zero_int ) ).

% bits_mod_by_1
thf(fact_486_bits__mod__by__1,axiom,
    ! [A: nat] :
      ( ( modulo_modulo_nat @ A @ one_one_nat )
      = zero_zero_nat ) ).

% bits_mod_by_1
thf(fact_487_mod__by__1,axiom,
    ! [A: int] :
      ( ( modulo_modulo_int @ A @ one_one_int )
      = zero_zero_int ) ).

% mod_by_1
thf(fact_488_mod__by__1,axiom,
    ! [A: nat] :
      ( ( modulo_modulo_nat @ A @ one_one_nat )
      = zero_zero_nat ) ).

% mod_by_1
thf(fact_489_of__int__eq__1__iff,axiom,
    ! [Z: int] :
      ( ( ( ring_1_of_int_int @ Z )
        = one_one_int )
      = ( Z = one_one_int ) ) ).

% of_int_eq_1_iff
thf(fact_490_of__int__eq__1__iff,axiom,
    ! [Z: int] :
      ( ( ( ring_1_of_int_real @ Z )
        = one_one_real )
      = ( Z = one_one_int ) ) ).

% of_int_eq_1_iff
thf(fact_491_of__int__hom_Ohom__1__iff,axiom,
    ! [X: int] :
      ( ( ( ring_1_of_int_int @ X )
        = one_one_int )
      = ( X = one_one_int ) ) ).

% of_int_hom.hom_1_iff
thf(fact_492_of__int__hom_Ohom__1__iff,axiom,
    ! [X: int] :
      ( ( ( ring_1_of_int_real @ X )
        = one_one_real )
      = ( X = one_one_int ) ) ).

% of_int_hom.hom_1_iff
thf(fact_493_of__int__hom_Ohom__one,axiom,
    ( ( ring_1_of_int_int @ one_one_int )
    = one_one_int ) ).

% of_int_hom.hom_one
thf(fact_494_of__int__hom_Ohom__one,axiom,
    ( ( ring_18169885480643366966ring_a @ one_one_int )
    = one_on2109788427901206336ring_a ) ).

% of_int_hom.hom_one
thf(fact_495_of__int__hom_Ohom__one,axiom,
    ( ( ring_1_of_int_real @ one_one_int )
    = one_one_real ) ).

% of_int_hom.hom_one
thf(fact_496_of__int__le__0__iff,axiom,
    ! [Z: int] :
      ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
      = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).

% of_int_le_0_iff
thf(fact_497_of__int__le__0__iff,axiom,
    ! [Z: int] :
      ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
      = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).

% of_int_le_0_iff
thf(fact_498_of__int__0__le__iff,axiom,
    ! [Z: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
      = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).

% of_int_0_le_iff
thf(fact_499_of__int__0__le__iff,axiom,
    ! [Z: int] :
      ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
      = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).

% of_int_0_le_iff
thf(fact_500_of__int__1__le__iff,axiom,
    ! [Z: int] :
      ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
      = ( ord_less_eq_int @ one_one_int @ Z ) ) ).

% of_int_1_le_iff
thf(fact_501_of__int__1__le__iff,axiom,
    ! [Z: int] :
      ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
      = ( ord_less_eq_int @ one_one_int @ Z ) ) ).

% of_int_1_le_iff
thf(fact_502_of__int__le__1__iff,axiom,
    ! [Z: int] :
      ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
      = ( ord_less_eq_int @ Z @ one_one_int ) ) ).

% of_int_le_1_iff
thf(fact_503_of__int__le__1__iff,axiom,
    ! [Z: int] :
      ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
      = ( ord_less_eq_int @ Z @ one_one_int ) ) ).

% of_int_le_1_iff
thf(fact_504_fun_Orel__mono,axiom,
    ! [R: $o > $o > $o,Ra: $o > $o > $o] :
      ( ( ord_less_eq_o_o_o @ R @ Ra )
     => ( ord_le9100565418538218190nt_o_o
        @ ( bNF_re5089333283451836215nt_o_o
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ R )
        @ ( bNF_re5089333283451836215nt_o_o
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ Ra ) ) ) ).

% fun.rel_mono
thf(fact_505_fun_Orel__mono,axiom,
    ! [R: nat > nat > $o,Ra: nat > nat > $o] :
      ( ( ord_le2646555220125990790_nat_o @ R @ Ra )
     => ( ord_le7357923999124086768_nat_o
        @ ( bNF_re3715656647883201625at_nat
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ R )
        @ ( bNF_re3715656647883201625at_nat
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ Ra ) ) ) ).

% fun.rel_mono
thf(fact_506_fun_Orel__mono,axiom,
    ! [R: int > int > $o,Ra: int > int > $o] :
      ( ( ord_le6741204236512500942_int_o @ R @ Ra )
     => ( ord_le5837993363827774264_int_o
        @ ( bNF_re4712519889275205905nt_int
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ R )
        @ ( bNF_re4712519889275205905nt_int
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ Ra ) ) ) ).

% fun.rel_mono
thf(fact_507_fun_Orel__mono,axiom,
    ! [R: ( int > $o ) > ( int > $o ) > $o,Ra: ( int > $o ) > ( int > $o ) > $o] :
      ( ( ord_le9100565418538218190nt_o_o @ R @ Ra )
     => ( ord_le8512398041180637710nt_o_o
        @ ( bNF_re3403563459893282935_int_o
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ R )
        @ ( bNF_re3403563459893282935_int_o
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ Ra ) ) ) ).

% fun.rel_mono
thf(fact_508_fun_Orel__mono,axiom,
    ! [R: ( int > int ) > ( int > int ) > $o,Ra: ( int > int ) > ( int > int ) > $o] :
      ( ( ord_le5837993363827774264_int_o @ R @ Ra )
     => ( ord_le25265541537557922_int_o
        @ ( bNF_re711492959462206631nt_int
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ R )
        @ ( bNF_re711492959462206631nt_int
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ Ra ) ) ) ).

% fun.rel_mono
thf(fact_509_fun__mono,axiom,
    ! [C: int > int > $o,A2: int > int > $o,B2: $o > $o > $o,D: $o > $o > $o] :
      ( ( ord_le6741204236512500942_int_o @ C @ A2 )
     => ( ( ord_less_eq_o_o_o @ B2 @ D )
       => ( ord_le9100565418538218190nt_o_o @ ( bNF_re5089333283451836215nt_o_o @ A2 @ B2 ) @ ( bNF_re5089333283451836215nt_o_o @ C @ D ) ) ) ) ).

% fun_mono
thf(fact_510_fun__mono,axiom,
    ! [C: int > int > $o,A2: int > int > $o,B2: nat > nat > $o,D: nat > nat > $o] :
      ( ( ord_le6741204236512500942_int_o @ C @ A2 )
     => ( ( ord_le2646555220125990790_nat_o @ B2 @ D )
       => ( ord_le7357923999124086768_nat_o @ ( bNF_re3715656647883201625at_nat @ A2 @ B2 ) @ ( bNF_re3715656647883201625at_nat @ C @ D ) ) ) ) ).

% fun_mono
thf(fact_511_fun__mono,axiom,
    ! [C: int > int > $o,A2: int > int > $o,B2: int > int > $o,D: int > int > $o] :
      ( ( ord_le6741204236512500942_int_o @ C @ A2 )
     => ( ( ord_le6741204236512500942_int_o @ B2 @ D )
       => ( ord_le5837993363827774264_int_o @ ( bNF_re4712519889275205905nt_int @ A2 @ B2 ) @ ( bNF_re4712519889275205905nt_int @ C @ D ) ) ) ) ).

% fun_mono
thf(fact_512_fun__mono,axiom,
    ! [C: int > int > $o,A2: int > int > $o,B2: ( int > $o ) > ( int > $o ) > $o,D: ( int > $o ) > ( int > $o ) > $o] :
      ( ( ord_le6741204236512500942_int_o @ C @ A2 )
     => ( ( ord_le9100565418538218190nt_o_o @ B2 @ D )
       => ( ord_le8512398041180637710nt_o_o @ ( bNF_re3403563459893282935_int_o @ A2 @ B2 ) @ ( bNF_re3403563459893282935_int_o @ C @ D ) ) ) ) ).

% fun_mono
thf(fact_513_fun__mono,axiom,
    ! [C: int > int > $o,A2: int > int > $o,B2: ( int > int ) > ( int > int ) > $o,D: ( int > int ) > ( int > int ) > $o] :
      ( ( ord_le6741204236512500942_int_o @ C @ A2 )
     => ( ( ord_le5837993363827774264_int_o @ B2 @ D )
       => ( ord_le25265541537557922_int_o @ ( bNF_re711492959462206631nt_int @ A2 @ B2 ) @ ( bNF_re711492959462206631nt_int @ C @ D ) ) ) ) ).

% fun_mono
thf(fact_514_one__reorient,axiom,
    ! [X: int] :
      ( ( one_one_int = X )
      = ( X = one_one_int ) ) ).

% one_reorient
thf(fact_515_one__reorient,axiom,
    ! [X: finite_mod_ring_a] :
      ( ( one_on2109788427901206336ring_a = X )
      = ( X = one_on2109788427901206336ring_a ) ) ).

% one_reorient
thf(fact_516_one__reorient,axiom,
    ! [X: nat] :
      ( ( one_one_nat = X )
      = ( X = one_one_nat ) ) ).

% one_reorient
thf(fact_517_one__reorient,axiom,
    ! [X: real] :
      ( ( one_one_real = X )
      = ( X = one_one_real ) ) ).

% one_reorient
thf(fact_518_of__int__hom_Ohom__1,axiom,
    ! [X: int] :
      ( ( ( ring_1_of_int_int @ X )
        = one_one_int )
     => ( X = one_one_int ) ) ).

% of_int_hom.hom_1
thf(fact_519_of__int__hom_Ohom__1,axiom,
    ! [X: int] :
      ( ( ( ring_1_of_int_real @ X )
        = one_one_real )
     => ( X = one_one_int ) ) ).

% of_int_hom.hom_1
thf(fact_520_zero__less__one__class_Ozero__le__one,axiom,
    ord_less_eq_int @ zero_zero_int @ one_one_int ).

% zero_less_one_class.zero_le_one
thf(fact_521_zero__less__one__class_Ozero__le__one,axiom,
    ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).

% zero_less_one_class.zero_le_one
thf(fact_522_zero__less__one__class_Ozero__le__one,axiom,
    ord_less_eq_real @ zero_zero_real @ one_one_real ).

% zero_less_one_class.zero_le_one
thf(fact_523_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
    ord_less_eq_int @ zero_zero_int @ one_one_int ).

% linordered_nonzero_semiring_class.zero_le_one
thf(fact_524_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
    ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).

% linordered_nonzero_semiring_class.zero_le_one
thf(fact_525_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
    ord_less_eq_real @ zero_zero_real @ one_one_real ).

% linordered_nonzero_semiring_class.zero_le_one
thf(fact_526_not__one__le__zero,axiom,
    ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).

% not_one_le_zero
thf(fact_527_not__one__le__zero,axiom,
    ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).

% not_one_le_zero
thf(fact_528_not__one__le__zero,axiom,
    ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).

% not_one_le_zero
thf(fact_529_zero__le,axiom,
    ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).

% zero_le
thf(fact_530_zero__neq__one,axiom,
    zero_zero_int != one_one_int ).

% zero_neq_one
thf(fact_531_zero__neq__one,axiom,
    zero_z7902377541816115708ring_a != one_on2109788427901206336ring_a ).

% zero_neq_one
thf(fact_532_zero__neq__one,axiom,
    zero_zero_nat != one_one_nat ).

% zero_neq_one
thf(fact_533_zero__neq__one,axiom,
    zero_zero_real != one_one_real ).

% zero_neq_one
thf(fact_534_of__int__nonneg,axiom,
    ! [Z: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ Z )
     => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).

% of_int_nonneg
thf(fact_535_of__int__nonneg,axiom,
    ! [Z: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ Z )
     => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).

% of_int_nonneg
thf(fact_536_pos__fun__distr,axiom,
    ! [R: int > int > $o,S2: $o > $o > $o,R3: int > int > $o,S3: $o > $o > $o] : ( ord_le9100565418538218190nt_o_o @ ( relcom989163212620591602_int_o @ ( bNF_re5089333283451836215nt_o_o @ R @ S2 ) @ ( bNF_re5089333283451836215nt_o_o @ R3 @ S3 ) ) @ ( bNF_re5089333283451836215nt_o_o @ ( relcompp_int_int_int @ R @ R3 ) @ ( relcompp_o_o_o @ S2 @ S3 ) ) ) ).

% pos_fun_distr
thf(fact_537_pos__fun__distr,axiom,
    ! [R: int > int > $o,S2: nat > nat > $o,R3: int > int > $o,S3: nat > nat > $o] : ( ord_le7357923999124086768_nat_o @ ( relcom4622340022947818372nt_nat @ ( bNF_re3715656647883201625at_nat @ R @ S2 ) @ ( bNF_re3715656647883201625at_nat @ R3 @ S3 ) ) @ ( bNF_re3715656647883201625at_nat @ ( relcompp_int_int_int @ R @ R3 ) @ ( relcompp_nat_nat_nat @ S2 @ S3 ) ) ) ).

% pos_fun_distr
thf(fact_538_pos__fun__distr,axiom,
    ! [R: int > int > $o,S2: int > int > $o,R3: int > int > $o,S3: int > int > $o] : ( ord_le5837993363827774264_int_o @ ( relcom1106299141546538648nt_int @ ( bNF_re4712519889275205905nt_int @ R @ S2 ) @ ( bNF_re4712519889275205905nt_int @ R3 @ S3 ) ) @ ( bNF_re4712519889275205905nt_int @ ( relcompp_int_int_int @ R @ R3 ) @ ( relcompp_int_int_int @ S2 @ S3 ) ) ) ).

% pos_fun_distr
thf(fact_539_pos__fun__distr,axiom,
    ! [R: int > int > $o,S2: ( int > $o ) > ( int > $o ) > $o,R3: int > int > $o,S3: ( int > $o ) > ( int > $o ) > $o] : ( ord_le8512398041180637710nt_o_o @ ( relcom6387603338664227389_int_o @ ( bNF_re3403563459893282935_int_o @ R @ S2 ) @ ( bNF_re3403563459893282935_int_o @ R3 @ S3 ) ) @ ( bNF_re3403563459893282935_int_o @ ( relcompp_int_int_int @ R @ R3 ) @ ( relcom989163212620591602_int_o @ S2 @ S3 ) ) ) ).

% pos_fun_distr
thf(fact_540_pos__fun__distr,axiom,
    ! [R: int > int > $o,S2: ( int > int ) > ( int > int ) > $o,R3: int > int > $o,S3: ( int > int ) > ( int > int ) > $o] : ( ord_le25265541537557922_int_o @ ( relcom6240993501255406585nt_int @ ( bNF_re711492959462206631nt_int @ R @ S2 ) @ ( bNF_re711492959462206631nt_int @ R3 @ S3 ) ) @ ( bNF_re711492959462206631nt_int @ ( relcompp_int_int_int @ R @ R3 ) @ ( relcom1106299141546538648nt_int @ S2 @ S3 ) ) ) ).

% pos_fun_distr
thf(fact_541_pos__fun__distr,axiom,
    ! [R: mat_int > mat_int > $o,S2: mat_int > mat_int > $o,R3: mat_int > mat_Fi443519135453058082ring_a > $o,S3: mat_int > mat_Fi443519135453058082ring_a > $o] : ( ord_le3697366711325567390ng_a_o @ ( relcom6302253411340485088ring_a @ ( bNF_re3172240519465120989at_int @ R @ S2 ) @ ( bNF_re7267033552616699805ring_a @ R3 @ S3 ) ) @ ( bNF_re7267033552616699805ring_a @ ( relcom6459136143736567059ring_a @ R @ R3 ) @ ( relcom6459136143736567059ring_a @ S2 @ S3 ) ) ) ).

% pos_fun_distr
thf(fact_542_DomainpE,axiom,
    ! [R4: vec_int > vec_Fi4296597256376197294ring_a > $o,A: vec_int] :
      ( ( domain4015354059925764579ring_a @ R4 @ A )
     => ~ ! [B3: vec_Fi4296597256376197294ring_a] :
            ~ ( R4 @ A @ B3 ) ) ).

% DomainpE
thf(fact_543_DomainpE,axiom,
    ! [R4: mat_int > mat_Fi443519135453058082ring_a > $o,A: mat_int] :
      ( ( domain2947197372085612771ring_a @ R4 @ A )
     => ~ ! [B3: mat_Fi443519135453058082ring_a] :
            ~ ( R4 @ A @ B3 ) ) ).

% DomainpE
thf(fact_544_DomainPI,axiom,
    ! [R4: vec_int > vec_Fi4296597256376197294ring_a > $o,A: vec_int,B: vec_Fi4296597256376197294ring_a] :
      ( ( R4 @ A @ B )
     => ( domain4015354059925764579ring_a @ R4 @ A ) ) ).

% DomainPI
thf(fact_545_DomainPI,axiom,
    ! [R4: mat_int > mat_Fi443519135453058082ring_a > $o,A: mat_int,B: mat_Fi443519135453058082ring_a] :
      ( ( R4 @ A @ B )
     => ( domain2947197372085612771ring_a @ R4 @ A ) ) ).

% DomainPI
thf(fact_546_Domainp_Osimps,axiom,
    ( domain4015354059925764579ring_a
    = ( ^ [R5: vec_int > vec_Fi4296597256376197294ring_a > $o,A5: vec_int] :
        ? [B4: vec_int,C2: vec_Fi4296597256376197294ring_a] :
          ( ( A5 = B4 )
          & ( R5 @ B4 @ C2 ) ) ) ) ).

% Domainp.simps
thf(fact_547_Domainp_Osimps,axiom,
    ( domain2947197372085612771ring_a
    = ( ^ [R5: mat_int > mat_Fi443519135453058082ring_a > $o,A5: mat_int] :
        ? [B4: mat_int,C2: mat_Fi443519135453058082ring_a] :
          ( ( A5 = B4 )
          & ( R5 @ B4 @ C2 ) ) ) ) ).

% Domainp.simps
thf(fact_548_one__M__Rel,axiom,
    vector3024231343486012919_Rel_a @ m @ one_one_int @ one_on2109788427901206336ring_a ).

% one_M_Rel
thf(fact_549_non__triv__m,axiom,
    ord_less_int @ one_one_int @ m ).

% non_triv_m
thf(fact_550_transfer__forall__transfer_I5_J,axiom,
    ! [A2: int > int > $o] :
      ( ( bi_total_int_int @ A2 )
     => ( bNF_re6378653760509651613_o_o_o @ ( bNF_re5089333283451836215nt_o_o @ A2 @ rev_implies ) @ rev_implies @ transfer_forall_int @ transfer_forall_int ) ) ).

% transfer_forall_transfer(5)
thf(fact_551_transfer__forall__transfer_I5_J,axiom,
    ! [A2: int > finite_mod_ring_a > $o] :
      ( ( bi_tot623839499179674737ring_a @ A2 )
     => ( bNF_re8869226137141724030_o_o_o @ ( bNF_re8290846538823883642_a_o_o @ A2 @ rev_implies ) @ rev_implies @ transfer_forall_int @ transf2422954704962549770ring_a ) ) ).

% transfer_forall_transfer(5)
thf(fact_552_transfer__forall__transfer_I5_J,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( bi_tot310863827317176225ring_a @ A2 )
     => ( bNF_re3034707934920152030_o_o_o @ ( bNF_re507051067509135658_a_o_o @ A2 @ rev_implies ) @ rev_implies @ transf5930571779719943006ec_int @ transf142359738573599785ring_a ) ) ).

% transfer_forall_transfer(5)
thf(fact_553_transfer__forall__transfer_I5_J,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( bi_tot8466079176331800225ring_a @ A2 )
     => ( bNF_re3523364678894640886_o_o_o @ ( bNF_re6153771816476299306_a_o_o @ A2 @ rev_implies ) @ rev_implies @ transf2444112438564689642at_int @ transf5512653654505236381ring_a ) ) ).

% transfer_forall_transfer(5)
thf(fact_554_transfer__forall__transfer_I4_J,axiom,
    ! [A2: int > int > $o] :
      ( ( bi_total_int_int @ A2 )
     => ( bNF_re6378653760509651613_o_o_o
        @ ( bNF_re5089333283451836215nt_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ rev_implies
        @ transfer_forall_int
        @ transfer_forall_int ) ) ).

% transfer_forall_transfer(4)
thf(fact_555_transfer__forall__transfer_I4_J,axiom,
    ! [A2: int > finite_mod_ring_a > $o] :
      ( ( bi_tot623839499179674737ring_a @ A2 )
     => ( bNF_re8869226137141724030_o_o_o
        @ ( bNF_re8290846538823883642_a_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ rev_implies
        @ transfer_forall_int
        @ transf2422954704962549770ring_a ) ) ).

% transfer_forall_transfer(4)
thf(fact_556_transfer__forall__transfer_I4_J,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( bi_tot310863827317176225ring_a @ A2 )
     => ( bNF_re3034707934920152030_o_o_o
        @ ( bNF_re507051067509135658_a_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ rev_implies
        @ transf5930571779719943006ec_int
        @ transf142359738573599785ring_a ) ) ).

% transfer_forall_transfer(4)
thf(fact_557_transfer__forall__transfer_I4_J,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( bi_tot8466079176331800225ring_a @ A2 )
     => ( bNF_re3523364678894640886_o_o_o
        @ ( bNF_re6153771816476299306_a_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ rev_implies
        @ transf2444112438564689642at_int
        @ transf5512653654505236381ring_a ) ) ).

% transfer_forall_transfer(4)
thf(fact_558_ex__le__of__int,axiom,
    ! [X: real] :
    ? [Z4: int] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z4 ) ) ).

% ex_le_of_int
thf(fact_559_zero__min,axiom,
    ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).

% zero_min
thf(fact_560_le__numeral__extra_I3_J,axiom,
    ord_less_eq_int @ zero_zero_int @ zero_zero_int ).

% le_numeral_extra(3)
thf(fact_561_le__numeral__extra_I3_J,axiom,
    ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).

% le_numeral_extra(3)
thf(fact_562_le__numeral__extra_I3_J,axiom,
    ord_less_eq_real @ zero_zero_real @ zero_zero_real ).

% le_numeral_extra(3)
thf(fact_563_Ex1__parametric,axiom,
    ! [A2: int > int > $o] :
      ( ( bi_unique_int_int @ A2 )
     => ( ( bi_total_int_int @ A2 )
       => ( bNF_re6378653760509651613_o_o_o
          @ ( bNF_re5089333283451836215nt_o_o @ A2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
          @ ex1_int
          @ ex1_int ) ) ) ).

% Ex1_parametric
thf(fact_564_Ex1__parametric,axiom,
    ! [A2: int > finite_mod_ring_a > $o] :
      ( ( bi_uni1022671006909063496ring_a @ A2 )
     => ( ( bi_tot623839499179674737ring_a @ A2 )
       => ( bNF_re8869226137141724030_o_o_o
          @ ( bNF_re8290846538823883642_a_o_o @ A2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
          @ ex1_int
          @ ex1_Fi6469121982000959455ring_a ) ) ) ).

% Ex1_parametric
thf(fact_565_Ex1__parametric,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( bi_uni555094797115351544ring_a @ A2 )
     => ( ( bi_tot310863827317176225ring_a @ A2 )
       => ( bNF_re3034707934920152030_o_o_o
          @ ( bNF_re507051067509135658_a_o_o @ A2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
          @ ex1_vec_int
          @ ex1_ve8867894409661767700ring_a ) ) ) ).

% Ex1_parametric
thf(fact_566_Ex1__parametric,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( bi_uni8710310146129975544ring_a @ A2 )
     => ( ( bi_tot8466079176331800225ring_a @ A2 )
       => ( bNF_re3523364678894640886_o_o_o
          @ ( bNF_re6153771816476299306_a_o_o @ A2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 )
          @ ex1_mat_int
          @ ex1_ma5014816288738628488ring_a ) ) ) ).

% Ex1_parametric
thf(fact_567_not__gr__zero,axiom,
    ! [N: nat] :
      ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
      = ( N = zero_zero_nat ) ) ).

% not_gr_zero
thf(fact_568_of__int__less__iff,axiom,
    ! [W: int,Z: int] :
      ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
      = ( ord_less_int @ W @ Z ) ) ).

% of_int_less_iff
thf(fact_569_of__int__less__iff,axiom,
    ! [W: int,Z: int] :
      ( ( ord_less_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
      = ( ord_less_int @ W @ Z ) ) ).

% of_int_less_iff
thf(fact_570_to__int__mod__ring__hom_Ohom__one,axiom,
    ( ( finite1095367895020317408ring_a @ one_on2109788427901206336ring_a )
    = one_one_int ) ).

% to_int_mod_ring_hom.hom_one
thf(fact_571_to__int__mod__ring__hom_Ohom__1__iff,axiom,
    ! [X: finite_mod_ring_a] :
      ( ( ( finite1095367895020317408ring_a @ X )
        = one_one_int )
      = ( X = one_on2109788427901206336ring_a ) ) ).

% to_int_mod_ring_hom.hom_1_iff
thf(fact_572_of__int__mod__ring__hom__sr_Ohom__one,axiom,
    ( ( finite8272632373135393572ring_a @ one_one_int )
    = one_on2109788427901206336ring_a ) ).

% of_int_mod_ring_hom_sr.hom_one
thf(fact_573_mod__neg__neg__trivial,axiom,
    ! [K: int,L: int] :
      ( ( ord_less_eq_int @ K @ zero_zero_int )
     => ( ( ord_less_int @ L @ K )
       => ( ( modulo_modulo_int @ K @ L )
          = K ) ) ) ).

% mod_neg_neg_trivial
thf(fact_574_mod__pos__pos__trivial,axiom,
    ! [K: int,L: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ K )
     => ( ( ord_less_int @ K @ L )
       => ( ( modulo_modulo_int @ K @ L )
          = K ) ) ) ).

% mod_pos_pos_trivial
thf(fact_575_of__int__0__less__iff,axiom,
    ! [Z: int] :
      ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
      = ( ord_less_int @ zero_zero_int @ Z ) ) ).

% of_int_0_less_iff
thf(fact_576_of__int__0__less__iff,axiom,
    ! [Z: int] :
      ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
      = ( ord_less_int @ zero_zero_int @ Z ) ) ).

% of_int_0_less_iff
thf(fact_577_of__int__less__0__iff,axiom,
    ! [Z: int] :
      ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
      = ( ord_less_int @ Z @ zero_zero_int ) ) ).

% of_int_less_0_iff
thf(fact_578_of__int__less__0__iff,axiom,
    ! [Z: int] :
      ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
      = ( ord_less_int @ Z @ zero_zero_int ) ) ).

% of_int_less_0_iff
thf(fact_579_of__int__less__1__iff,axiom,
    ! [Z: int] :
      ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
      = ( ord_less_int @ Z @ one_one_int ) ) ).

% of_int_less_1_iff
thf(fact_580_of__int__less__1__iff,axiom,
    ! [Z: int] :
      ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
      = ( ord_less_int @ Z @ one_one_int ) ) ).

% of_int_less_1_iff
thf(fact_581_of__int__1__less__iff,axiom,
    ! [Z: int] :
      ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
      = ( ord_less_int @ one_one_int @ Z ) ) ).

% of_int_1_less_iff
thf(fact_582_of__int__1__less__iff,axiom,
    ! [Z: int] :
      ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
      = ( ord_less_int @ one_one_int @ Z ) ) ).

% of_int_1_less_iff
thf(fact_583_less__numeral__extra_I3_J,axiom,
    ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).

% less_numeral_extra(3)
thf(fact_584_less__numeral__extra_I3_J,axiom,
    ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).

% less_numeral_extra(3)
thf(fact_585_less__numeral__extra_I3_J,axiom,
    ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).

% less_numeral_extra(3)
thf(fact_586_ex__of__int__less,axiom,
    ! [X: real] :
    ? [Z4: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z4 ) @ X ) ).

% ex_of_int_less
thf(fact_587_ex__less__of__int,axiom,
    ! [X: real] :
    ? [Z4: int] : ( ord_less_real @ X @ ( ring_1_of_int_real @ Z4 ) ) ).

% ex_less_of_int
thf(fact_588_rev__implies__def,axiom,
    ( rev_implies
    = ( ^ [X3: $o,Y6: $o] :
          ( Y6
         => X3 ) ) ) ).

% rev_implies_def
thf(fact_589_linorder__neqE__linordered__idom,axiom,
    ! [X: int,Y: int] :
      ( ( X != Y )
     => ( ~ ( ord_less_int @ X @ Y )
       => ( ord_less_int @ Y @ X ) ) ) ).

% linorder_neqE_linordered_idom
thf(fact_590_linorder__neqE__linordered__idom,axiom,
    ! [X: real,Y: real] :
      ( ( X != Y )
     => ( ~ ( ord_less_real @ X @ Y )
       => ( ord_less_real @ Y @ X ) ) ) ).

% linorder_neqE_linordered_idom
thf(fact_591_int__one__le__iff__zero__less,axiom,
    ! [Z: int] :
      ( ( ord_less_eq_int @ one_one_int @ Z )
      = ( ord_less_int @ zero_zero_int @ Z ) ) ).

% int_one_le_iff_zero_less
thf(fact_592_neg__mod__sign,axiom,
    ! [L: int,K: int] :
      ( ( ord_less_int @ L @ zero_zero_int )
     => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L ) @ zero_zero_int ) ) ).

% neg_mod_sign
thf(fact_593_Euclidean__Division_Opos__mod__sign,axiom,
    ! [L: int,K: int] :
      ( ( ord_less_int @ zero_zero_int @ L )
     => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) ) ) ).

% Euclidean_Division.pos_mod_sign
thf(fact_594_zmod__trivial__iff,axiom,
    ! [I: int,K: int] :
      ( ( ( modulo_modulo_int @ I @ K )
        = I )
      = ( ( K = zero_zero_int )
        | ( ( ord_less_eq_int @ zero_zero_int @ I )
          & ( ord_less_int @ I @ K ) )
        | ( ( ord_less_eq_int @ I @ zero_zero_int )
          & ( ord_less_int @ K @ I ) ) ) ) ).

% zmod_trivial_iff
thf(fact_595_gr__zeroI,axiom,
    ! [N: nat] :
      ( ( N != zero_zero_nat )
     => ( ord_less_nat @ zero_zero_nat @ N ) ) ).

% gr_zeroI
thf(fact_596_not__less__zero,axiom,
    ! [N: nat] :
      ~ ( ord_less_nat @ N @ zero_zero_nat ) ).

% not_less_zero
thf(fact_597_gr__implies__not__zero,axiom,
    ! [M: nat,N: nat] :
      ( ( ord_less_nat @ M @ N )
     => ( N != zero_zero_nat ) ) ).

% gr_implies_not_zero
thf(fact_598_zero__less__iff__neq__zero,axiom,
    ! [N: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ N )
      = ( N != zero_zero_nat ) ) ).

% zero_less_iff_neq_zero
thf(fact_599_less__int__code_I1_J,axiom,
    ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).

% less_int_code(1)
thf(fact_600_less__eq__int__code_I1_J,axiom,
    ord_less_eq_int @ zero_zero_int @ zero_zero_int ).

% less_eq_int_code(1)
thf(fact_601_less__numeral__extra_I1_J,axiom,
    ord_less_int @ zero_zero_int @ one_one_int ).

% less_numeral_extra(1)
thf(fact_602_less__numeral__extra_I1_J,axiom,
    ord_less_nat @ zero_zero_nat @ one_one_nat ).

% less_numeral_extra(1)
thf(fact_603_less__numeral__extra_I1_J,axiom,
    ord_less_real @ zero_zero_real @ one_one_real ).

% less_numeral_extra(1)
thf(fact_604_of__int__pos,axiom,
    ! [Z: int] :
      ( ( ord_less_int @ zero_zero_int @ Z )
     => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).

% of_int_pos
thf(fact_605_of__int__pos,axiom,
    ! [Z: int] :
      ( ( ord_less_int @ zero_zero_int @ Z )
     => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).

% of_int_pos
thf(fact_606_not__one__less__zero,axiom,
    ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).

% not_one_less_zero
thf(fact_607_not__one__less__zero,axiom,
    ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).

% not_one_less_zero
thf(fact_608_not__one__less__zero,axiom,
    ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).

% not_one_less_zero
thf(fact_609_zero__less__one__class_Ozero__less__one,axiom,
    ord_less_int @ zero_zero_int @ one_one_int ).

% zero_less_one_class.zero_less_one
thf(fact_610_zero__less__one__class_Ozero__less__one,axiom,
    ord_less_nat @ zero_zero_nat @ one_one_nat ).

% zero_less_one_class.zero_less_one
thf(fact_611_zero__less__one__class_Ozero__less__one,axiom,
    ord_less_real @ zero_zero_real @ one_one_real ).

% zero_less_one_class.zero_less_one
thf(fact_612_Euclidean__Division_Opos__mod__bound,axiom,
    ! [L: int,K: int] :
      ( ( ord_less_int @ zero_zero_int @ L )
     => ( ord_less_int @ ( modulo_modulo_int @ K @ L ) @ L ) ) ).

% Euclidean_Division.pos_mod_bound
thf(fact_613_neg__mod__bound,axiom,
    ! [L: int,K: int] :
      ( ( ord_less_int @ L @ zero_zero_int )
     => ( ord_less_int @ L @ ( modulo_modulo_int @ K @ L ) ) ) ).

% neg_mod_bound
thf(fact_614_zmod__le__nonneg__dividend,axiom,
    ! [M: int,K: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ M )
     => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).

% zmod_le_nonneg_dividend
thf(fact_615_Vector__Matrix__Mod_Omat__mod__def,axiom,
    ( vector2311527483241216340at_mod
    = ( ord_less_int @ one_one_int ) ) ).

% Vector_Matrix_Mod.mat_mod_def
thf(fact_616_mat__mod_Onon__triv__m,axiom,
    ! [M: int] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ord_less_int @ one_one_int @ M ) ) ).

% mat_mod.non_triv_m
thf(fact_617_mat__mod_Ointro,axiom,
    ! [M: int] :
      ( ( ord_less_int @ one_one_int @ M )
     => ( vector2311527483241216340at_mod @ M ) ) ).

% mat_mod.intro
thf(fact_618_to__int__mod__ring__hom_Ohom__1,axiom,
    ! [X: finite_mod_ring_a] :
      ( ( ( finite1095367895020317408ring_a @ X )
        = one_one_int )
     => ( X = one_on2109788427901206336ring_a ) ) ).

% to_int_mod_ring_hom.hom_1
thf(fact_619_bot__nat__0_Oextremum,axiom,
    ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).

% bot_nat_0.extremum
thf(fact_620_le0,axiom,
    ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).

% le0
thf(fact_621_imp__le__cong,axiom,
    ! [X: int,X2: int,P: $o,P2: $o] :
      ( ( X = X2 )
     => ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
         => ( P = P2 ) )
       => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
           => P )
          = ( ( ord_less_eq_int @ zero_zero_int @ X2 )
           => P2 ) ) ) ) ).

% imp_le_cong
thf(fact_622_conj__le__cong,axiom,
    ! [X: int,X2: int,P: $o,P2: $o] :
      ( ( X = X2 )
     => ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
         => ( P = P2 ) )
       => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
            & P )
          = ( ( ord_less_eq_int @ zero_zero_int @ X2 )
            & P2 ) ) ) ) ).

% conj_le_cong
thf(fact_623_field__lbound__gt__zero,axiom,
    ! [D1: real,D2: real] :
      ( ( ord_less_real @ zero_zero_real @ D1 )
     => ( ( ord_less_real @ zero_zero_real @ D2 )
       => ? [E: real] :
            ( ( ord_less_real @ zero_zero_real @ E )
            & ( ord_less_real @ E @ D1 )
            & ( ord_less_real @ E @ D2 ) ) ) ) ).

% field_lbound_gt_zero
thf(fact_624_dbl__inc__simps_I2_J,axiom,
    ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
    = one_one_int ) ).

% dbl_inc_simps(2)
thf(fact_625_dbl__inc__simps_I2_J,axiom,
    ( ( neg_nu5901776551076858996ring_a @ zero_z7902377541816115708ring_a )
    = one_on2109788427901206336ring_a ) ).

% dbl_inc_simps(2)
thf(fact_626_dbl__inc__simps_I2_J,axiom,
    ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
    = one_one_real ) ).

% dbl_inc_simps(2)
thf(fact_627_less__one,axiom,
    ! [N: nat] :
      ( ( ord_less_nat @ N @ one_one_nat )
      = ( N = zero_zero_nat ) ) ).

% less_one
thf(fact_628_bot__nat__0_Onot__eq__extremum,axiom,
    ! [A: nat] :
      ( ( A != zero_zero_nat )
      = ( ord_less_nat @ zero_zero_nat @ A ) ) ).

% bot_nat_0.not_eq_extremum
thf(fact_629_neq0__conv,axiom,
    ! [N: nat] :
      ( ( N != zero_zero_nat )
      = ( ord_less_nat @ zero_zero_nat @ N ) ) ).

% neq0_conv
thf(fact_630_less__nat__zero__code,axiom,
    ! [N: nat] :
      ~ ( ord_less_nat @ N @ zero_zero_nat ) ).

% less_nat_zero_code
thf(fact_631_unit__vec__eq,axiom,
    ! [I: nat,N: nat,J: nat] :
      ( ( ord_less_nat @ I @ N )
     => ( ( ( unit_vec_int @ N @ I )
          = ( unit_vec_int @ N @ J ) )
        = ( I = J ) ) ) ).

% unit_vec_eq
thf(fact_632_unit__vec__eq,axiom,
    ! [I: nat,N: nat,J: nat] :
      ( ( ord_less_nat @ I @ N )
     => ( ( ( unit_v6648808783362777473ring_a @ N @ I )
          = ( unit_v6648808783362777473ring_a @ N @ J ) )
        = ( I = J ) ) ) ).

% unit_vec_eq
thf(fact_633_mod__less__eq__dividend,axiom,
    ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ M ) ).

% mod_less_eq_dividend
thf(fact_634_ex__least__nat__le,axiom,
    ! [P: nat > $o,N: nat] :
      ( ( P @ N )
     => ( ~ ( P @ zero_zero_nat )
       => ? [K2: nat] :
            ( ( ord_less_eq_nat @ K2 @ N )
            & ! [I2: nat] :
                ( ( ord_less_nat @ I2 @ K2 )
               => ~ ( P @ I2 ) )
            & ( P @ K2 ) ) ) ) ).

% ex_least_nat_le
thf(fact_635_infinite__descent0,axiom,
    ! [P: nat > $o,N: nat] :
      ( ( P @ zero_zero_nat )
     => ( ! [N2: nat] :
            ( ( ord_less_nat @ zero_zero_nat @ N2 )
           => ( ~ ( P @ N2 )
             => ? [M3: nat] :
                  ( ( ord_less_nat @ M3 @ N2 )
                  & ~ ( P @ M3 ) ) ) )
       => ( P @ N ) ) ) ).

% infinite_descent0
thf(fact_636_gr__implies__not0,axiom,
    ! [M: nat,N: nat] :
      ( ( ord_less_nat @ M @ N )
     => ( N != zero_zero_nat ) ) ).

% gr_implies_not0
thf(fact_637_less__zeroE,axiom,
    ! [N: nat] :
      ~ ( ord_less_nat @ N @ zero_zero_nat ) ).

% less_zeroE
thf(fact_638_not__less0,axiom,
    ! [N: nat] :
      ~ ( ord_less_nat @ N @ zero_zero_nat ) ).

% not_less0
thf(fact_639_not__gr0,axiom,
    ! [N: nat] :
      ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
      = ( N = zero_zero_nat ) ) ).

% not_gr0
thf(fact_640_gr0I,axiom,
    ! [N: nat] :
      ( ( N != zero_zero_nat )
     => ( ord_less_nat @ zero_zero_nat @ N ) ) ).

% gr0I
thf(fact_641_bot__nat__0_Oextremum__strict,axiom,
    ! [A: nat] :
      ~ ( ord_less_nat @ A @ zero_zero_nat ) ).

% bot_nat_0.extremum_strict
thf(fact_642_mod__less__divisor,axiom,
    ! [N: nat,M: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ N )
     => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).

% mod_less_divisor
thf(fact_643_mod__le__divisor,axiom,
    ! [N: nat,M: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ N )
     => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).

% mod_le_divisor
thf(fact_644_unit__vec__nonzero,axiom,
    ! [I: nat,N: nat] :
      ( ( ord_less_nat @ I @ N )
     => ( ( unit_vec_int @ N @ I )
       != ( zero_vec_int @ N ) ) ) ).

% unit_vec_nonzero
thf(fact_645_unit__vec__nonzero,axiom,
    ! [I: nat,N: nat] :
      ( ( ord_less_nat @ I @ N )
     => ( ( unit_v6648808783362777473ring_a @ N @ I )
       != ( zero_v1122566495420860901ring_a @ N ) ) ) ).

% unit_vec_nonzero
thf(fact_646_le__0__eq,axiom,
    ! [N: nat] :
      ( ( ord_less_eq_nat @ N @ zero_zero_nat )
      = ( N = zero_zero_nat ) ) ).

% le_0_eq
thf(fact_647_bot__nat__0_Oextremum__uniqueI,axiom,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ A @ zero_zero_nat )
     => ( A = zero_zero_nat ) ) ).

% bot_nat_0.extremum_uniqueI
thf(fact_648_bot__nat__0_Oextremum__unique,axiom,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ A @ zero_zero_nat )
      = ( A = zero_zero_nat ) ) ).

% bot_nat_0.extremum_unique
thf(fact_649_less__eq__nat_Osimps_I1_J,axiom,
    ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).

% less_eq_nat.simps(1)
thf(fact_650_vec__mod__index__same,axiom,
    ! [I: nat,V: vec_int] :
      ( ( ord_less_nat @ I @ ( dim_vec_int @ V ) )
     => ( ( ord_less_int @ ( vec_index_int @ V @ I ) @ m )
       => ( ( ord_less_eq_int @ zero_zero_int @ ( vec_index_int @ V @ I ) )
         => ( ( vec_index_int @ ( vector1199560857299316530ec_mod @ m @ V ) @ I )
            = ( vec_index_int @ V @ I ) ) ) ) ) ).

% vec_mod_index_same
thf(fact_651_mat__mod_Ovec__mod__index__same,axiom,
    ! [M: int,I: nat,V: vec_int] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( ord_less_nat @ I @ ( dim_vec_int @ V ) )
       => ( ( ord_less_int @ ( vec_index_int @ V @ I ) @ M )
         => ( ( ord_less_eq_int @ zero_zero_int @ ( vec_index_int @ V @ I ) )
           => ( ( vec_index_int @ ( vector1199560857299316530ec_mod @ M @ V ) @ I )
              = ( vec_index_int @ V @ I ) ) ) ) ) ) ).

% mat_mod.vec_mod_index_same
thf(fact_652_vec__mod__index,axiom,
    ! [I: nat,V: vec_int] :
      ( ( ord_less_nat @ I @ ( dim_vec_int @ V ) )
     => ( ( vec_index_int @ ( vector1199560857299316530ec_mod @ m @ V ) @ I )
        = ( modulo_modulo_int @ ( vec_index_int @ V @ I ) @ m ) ) ) ).

% vec_mod_index
thf(fact_653_frac__eq,axiom,
    ! [X: real] :
      ( ( ( archim2898591450579166408c_real @ X )
        = X )
      = ( ( ord_less_eq_real @ zero_zero_real @ X )
        & ( ord_less_real @ X @ one_one_real ) ) ) ).

% frac_eq
thf(fact_654_arcosh__1,axiom,
    ( ( arcosh_real @ one_one_real )
    = zero_zero_real ) ).

% arcosh_1
thf(fact_655_power__int__le__imp__less__exp,axiom,
    ! [X: real,M: int,N: int] :
      ( ( ord_less_real @ one_one_real @ X )
     => ( ( ord_less_real @ ( power_int_real @ X @ M ) @ ( power_int_real @ X @ N ) )
       => ( ( ord_less_eq_int @ zero_zero_int @ N )
         => ( ord_less_int @ M @ N ) ) ) ) ).

% power_int_le_imp_less_exp
thf(fact_656_power__int__le__imp__le__exp,axiom,
    ! [X: real,M: int,N: int] :
      ( ( ord_less_real @ one_one_real @ X )
     => ( ( ord_less_eq_real @ ( power_int_real @ X @ M ) @ ( power_int_real @ X @ N ) )
       => ( ( ord_less_eq_int @ zero_zero_int @ N )
         => ( ord_less_eq_int @ M @ N ) ) ) ) ).

% power_int_le_imp_le_exp
thf(fact_657_power__int__1__left,axiom,
    ! [N: int] :
      ( ( power_int_real @ one_one_real @ N )
      = one_one_real ) ).

% power_int_1_left
thf(fact_658_mod__less,axiom,
    ! [M: nat,N: nat] :
      ( ( ord_less_nat @ M @ N )
     => ( ( modulo_modulo_nat @ M @ N )
        = M ) ) ).

% mod_less
thf(fact_659_index__update__vec2,axiom,
    ! [I3: nat,I: nat,V: vec_int,A: int] :
      ( ( I3 != I )
     => ( ( vec_index_int @ ( update_vec_int @ V @ I @ A ) @ I3 )
        = ( vec_index_int @ V @ I3 ) ) ) ).

% index_update_vec2
thf(fact_660_index__update__vec2,axiom,
    ! [I3: nat,I: nat,V: vec_Fi4296597256376197294ring_a,A: finite_mod_ring_a] :
      ( ( I3 != I )
     => ( ( vec_in8573817152773094745ring_a @ ( update7295115471411923750ring_a @ V @ I @ A ) @ I3 )
        = ( vec_in8573817152773094745ring_a @ V @ I3 ) ) ) ).

% index_update_vec2
thf(fact_661_power__int__eq__0__iff,axiom,
    ! [X: real,N: int] :
      ( ( ( power_int_real @ X @ N )
        = zero_zero_real )
      = ( ( X = zero_zero_real )
        & ( N != zero_zero_int ) ) ) ).

% power_int_eq_0_iff
thf(fact_662_power__int__0__left,axiom,
    ! [M: int] :
      ( ( M != zero_zero_int )
     => ( ( power_int_real @ zero_zero_real @ M )
        = zero_zero_real ) ) ).

% power_int_0_left
thf(fact_663_power__int__0__right,axiom,
    ! [X: real] :
      ( ( power_int_real @ X @ zero_zero_int )
      = one_one_real ) ).

% power_int_0_right
thf(fact_664_frac__1,axiom,
    ( ( archim2898591450579166408c_real @ one_one_real )
    = zero_zero_real ) ).

% frac_1
thf(fact_665_eq__vecI,axiom,
    ! [W: vec_int,V: vec_int] :
      ( ! [I4: nat] :
          ( ( ord_less_nat @ I4 @ ( dim_vec_int @ W ) )
         => ( ( vec_index_int @ V @ I4 )
            = ( vec_index_int @ W @ I4 ) ) )
     => ( ( ( dim_vec_int @ V )
          = ( dim_vec_int @ W ) )
       => ( V = W ) ) ) ).

% eq_vecI
thf(fact_666_eq__vecI,axiom,
    ! [W: vec_Fi4296597256376197294ring_a,V: vec_Fi4296597256376197294ring_a] :
      ( ! [I4: nat] :
          ( ( ord_less_nat @ I4 @ ( dim_ve9152325144110082507ring_a @ W ) )
         => ( ( vec_in8573817152773094745ring_a @ V @ I4 )
            = ( vec_in8573817152773094745ring_a @ W @ I4 ) ) )
     => ( ( ( dim_ve9152325144110082507ring_a @ V )
          = ( dim_ve9152325144110082507ring_a @ W ) )
       => ( V = W ) ) ) ).

% eq_vecI
thf(fact_667_frac__of__int,axiom,
    ! [Z: int] :
      ( ( archim2898591450579166408c_real @ ( ring_1_of_int_real @ Z ) )
      = zero_zero_real ) ).

% frac_of_int
thf(fact_668_index__zero__vec_I1_J,axiom,
    ! [I: nat,N: nat] :
      ( ( ord_less_nat @ I @ N )
     => ( ( vec_index_int @ ( zero_vec_int @ N ) @ I )
        = zero_zero_int ) ) ).

% index_zero_vec(1)
thf(fact_669_index__zero__vec_I1_J,axiom,
    ! [I: nat,N: nat] :
      ( ( ord_less_nat @ I @ N )
     => ( ( vec_in8573817152773094745ring_a @ ( zero_v1122566495420860901ring_a @ N ) @ I )
        = zero_z7902377541816115708ring_a ) ) ).

% index_zero_vec(1)
thf(fact_670_index__zero__vec_I1_J,axiom,
    ! [I: nat,N: nat] :
      ( ( ord_less_nat @ I @ N )
     => ( ( vec_index_nat @ ( zero_vec_nat @ N ) @ I )
        = zero_zero_nat ) ) ).

% index_zero_vec(1)
thf(fact_671_index__zero__vec_I1_J,axiom,
    ! [I: nat,N: nat] :
      ( ( ord_less_nat @ I @ N )
     => ( ( vec_index_real @ ( zero_vec_real @ N ) @ I )
        = zero_zero_real ) ) ).

% index_zero_vec(1)
thf(fact_672_index__map__vec_I1_J,axiom,
    ! [I: nat,V: vec_int,F: int > int] :
      ( ( ord_less_nat @ I @ ( dim_vec_int @ V ) )
     => ( ( vec_index_int @ ( map_vec_int_int @ F @ V ) @ I )
        = ( F @ ( vec_index_int @ V @ I ) ) ) ) ).

% index_map_vec(1)
thf(fact_673_index__map__vec_I1_J,axiom,
    ! [I: nat,V: vec_Fi4296597256376197294ring_a,F: finite_mod_ring_a > int] :
      ( ( ord_less_nat @ I @ ( dim_ve9152325144110082507ring_a @ V ) )
     => ( ( vec_index_int @ ( map_ve50164598268879916_a_int @ F @ V ) @ I )
        = ( F @ ( vec_in8573817152773094745ring_a @ V @ I ) ) ) ) ).

% index_map_vec(1)
thf(fact_674_index__map__vec_I1_J,axiom,
    ! [I: nat,V: vec_int,F: int > finite_mod_ring_a] :
      ( ( ord_less_nat @ I @ ( dim_vec_int @ V ) )
     => ( ( vec_in8573817152773094745ring_a @ ( map_ve1626356591056799954ring_a @ F @ V ) @ I )
        = ( F @ ( vec_index_int @ V @ I ) ) ) ) ).

% index_map_vec(1)
thf(fact_675_index__map__vec_I1_J,axiom,
    ! [I: nat,V: vec_Fi4296597256376197294ring_a,F: finite_mod_ring_a > finite_mod_ring_a] :
      ( ( ord_less_nat @ I @ ( dim_ve9152325144110082507ring_a @ V ) )
     => ( ( vec_in8573817152773094745ring_a @ ( map_ve1378714242357356997ring_a @ F @ V ) @ I )
        = ( F @ ( vec_in8573817152773094745ring_a @ V @ I ) ) ) ) ).

% index_map_vec(1)
thf(fact_676_index__unit__vec_I2_J,axiom,
    ! [I: nat,N: nat] :
      ( ( ord_less_nat @ I @ N )
     => ( ( vec_index_int @ ( unit_vec_int @ N @ I ) @ I )
        = one_one_int ) ) ).

% index_unit_vec(2)
thf(fact_677_index__unit__vec_I2_J,axiom,
    ! [I: nat,N: nat] :
      ( ( ord_less_nat @ I @ N )
     => ( ( vec_in8573817152773094745ring_a @ ( unit_v6648808783362777473ring_a @ N @ I ) @ I )
        = one_on2109788427901206336ring_a ) ) ).

% index_unit_vec(2)
thf(fact_678_index__unit__vec_I2_J,axiom,
    ! [I: nat,N: nat] :
      ( ( ord_less_nat @ I @ N )
     => ( ( vec_index_nat @ ( unit_vec_nat @ N @ I ) @ I )
        = one_one_nat ) ) ).

% index_unit_vec(2)
thf(fact_679_index__unit__vec_I2_J,axiom,
    ! [I: nat,N: nat] :
      ( ( ord_less_nat @ I @ N )
     => ( ( vec_index_real @ ( unit_vec_real @ N @ I ) @ I )
        = one_one_real ) ) ).

% index_unit_vec(2)
thf(fact_680_all__ones__index,axiom,
    ! [I: nat,N: nat] :
      ( ( ord_less_nat @ I @ N )
     => ( ( vec_index_int @ ( matrix2748772424961467270ec_int @ N ) @ I )
        = one_one_int ) ) ).

% all_ones_index
thf(fact_681_all__ones__index,axiom,
    ! [I: nat,N: nat] :
      ( ( ord_less_nat @ I @ N )
     => ( ( vec_in8573817152773094745ring_a @ ( matrix705363690926585579ring_a @ N ) @ I )
        = one_on2109788427901206336ring_a ) ) ).

% all_ones_index
thf(fact_682_all__ones__index,axiom,
    ! [I: nat,N: nat] :
      ( ( ord_less_nat @ I @ N )
     => ( ( vec_index_nat @ ( matrix2751262895470517546ec_nat @ N ) @ I )
        = one_one_nat ) ) ).

% all_ones_index
thf(fact_683_all__ones__index,axiom,
    ! [I: nat,N: nat] :
      ( ( ord_less_nat @ I @ N )
     => ( ( vec_index_real @ ( matrix5166576126360777478c_real @ N ) @ I )
        = one_one_real ) ) ).

% all_ones_index
thf(fact_684_index__update__vec1,axiom,
    ! [I: nat,V: vec_int,A: int] :
      ( ( ord_less_nat @ I @ ( dim_vec_int @ V ) )
     => ( ( vec_index_int @ ( update_vec_int @ V @ I @ A ) @ I )
        = A ) ) ).

% index_update_vec1
thf(fact_685_index__update__vec1,axiom,
    ! [I: nat,V: vec_Fi4296597256376197294ring_a,A: finite_mod_ring_a] :
      ( ( ord_less_nat @ I @ ( dim_ve9152325144110082507ring_a @ V ) )
     => ( ( vec_in8573817152773094745ring_a @ ( update7295115471411923750ring_a @ V @ I @ A ) @ I )
        = A ) ) ).

% index_update_vec1
thf(fact_686_power__int__mono__iff,axiom,
    ! [A: real,B: real,N: int] :
      ( ( ord_less_eq_real @ zero_zero_real @ A )
     => ( ( ord_less_eq_real @ zero_zero_real @ B )
       => ( ( ord_less_int @ zero_zero_int @ N )
         => ( ( ord_less_eq_real @ ( power_int_real @ A @ N ) @ ( power_int_real @ B @ N ) )
            = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).

% power_int_mono_iff
thf(fact_687_index__unit__vec_I1_J,axiom,
    ! [I: nat,N: nat,J: nat] :
      ( ( ord_less_nat @ I @ N )
     => ( ( ord_less_nat @ J @ N )
       => ( ( ( J = I )
           => ( ( vec_index_int @ ( unit_vec_int @ N @ I ) @ J )
              = one_one_int ) )
          & ( ( J != I )
           => ( ( vec_index_int @ ( unit_vec_int @ N @ I ) @ J )
              = zero_zero_int ) ) ) ) ) ).

% index_unit_vec(1)
thf(fact_688_index__unit__vec_I1_J,axiom,
    ! [I: nat,N: nat,J: nat] :
      ( ( ord_less_nat @ I @ N )
     => ( ( ord_less_nat @ J @ N )
       => ( ( ( J = I )
           => ( ( vec_in8573817152773094745ring_a @ ( unit_v6648808783362777473ring_a @ N @ I ) @ J )
              = one_on2109788427901206336ring_a ) )
          & ( ( J != I )
           => ( ( vec_in8573817152773094745ring_a @ ( unit_v6648808783362777473ring_a @ N @ I ) @ J )
              = zero_z7902377541816115708ring_a ) ) ) ) ) ).

% index_unit_vec(1)
thf(fact_689_index__unit__vec_I1_J,axiom,
    ! [I: nat,N: nat,J: nat] :
      ( ( ord_less_nat @ I @ N )
     => ( ( ord_less_nat @ J @ N )
       => ( ( ( J = I )
           => ( ( vec_index_nat @ ( unit_vec_nat @ N @ I ) @ J )
              = one_one_nat ) )
          & ( ( J != I )
           => ( ( vec_index_nat @ ( unit_vec_nat @ N @ I ) @ J )
              = zero_zero_nat ) ) ) ) ) ).

% index_unit_vec(1)
thf(fact_690_index__unit__vec_I1_J,axiom,
    ! [I: nat,N: nat,J: nat] :
      ( ( ord_less_nat @ I @ N )
     => ( ( ord_less_nat @ J @ N )
       => ( ( ( J = I )
           => ( ( vec_index_real @ ( unit_vec_real @ N @ I ) @ J )
              = one_one_real ) )
          & ( ( J != I )
           => ( ( vec_index_real @ ( unit_vec_real @ N @ I ) @ J )
              = zero_zero_real ) ) ) ) ) ).

% index_unit_vec(1)
thf(fact_691_vec__eq__iff,axiom,
    ( ( ^ [Y2: vec_int,Z2: vec_int] : ( Y2 = Z2 ) )
    = ( ^ [X3: vec_int,Y6: vec_int] :
          ( ( ( dim_vec_int @ X3 )
            = ( dim_vec_int @ Y6 ) )
          & ! [I5: nat] :
              ( ( ord_less_nat @ I5 @ ( dim_vec_int @ Y6 ) )
             => ( ( vec_index_int @ X3 @ I5 )
                = ( vec_index_int @ Y6 @ I5 ) ) ) ) ) ) ).

% vec_eq_iff
thf(fact_692_vec__eq__iff,axiom,
    ( ( ^ [Y2: vec_Fi4296597256376197294ring_a,Z2: vec_Fi4296597256376197294ring_a] : ( Y2 = Z2 ) )
    = ( ^ [X3: vec_Fi4296597256376197294ring_a,Y6: vec_Fi4296597256376197294ring_a] :
          ( ( ( dim_ve9152325144110082507ring_a @ X3 )
            = ( dim_ve9152325144110082507ring_a @ Y6 ) )
          & ! [I5: nat] :
              ( ( ord_less_nat @ I5 @ ( dim_ve9152325144110082507ring_a @ Y6 ) )
             => ( ( vec_in8573817152773094745ring_a @ X3 @ I5 )
                = ( vec_in8573817152773094745ring_a @ Y6 @ I5 ) ) ) ) ) ) ).

% vec_eq_iff
thf(fact_693_zero__le__power__int,axiom,
    ! [X: real,N: int] :
      ( ( ord_less_eq_real @ zero_zero_real @ X )
     => ( ord_less_eq_real @ zero_zero_real @ ( power_int_real @ X @ N ) ) ) ).

% zero_le_power_int
thf(fact_694_zero__less__power__int,axiom,
    ! [X: real,N: int] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ord_less_real @ zero_zero_real @ ( power_int_real @ X @ N ) ) ) ).

% zero_less_power_int
thf(fact_695_power__int__not__zero,axiom,
    ! [X: real,N: int] :
      ( ( ( X != zero_zero_real )
        | ( N = zero_zero_int ) )
     => ( ( power_int_real @ X @ N )
       != zero_zero_real ) ) ).

% power_int_not_zero
thf(fact_696_less__eq__vec__def,axiom,
    ( ord_less_eq_vec_int
    = ( ^ [V3: vec_int,W2: vec_int] :
          ( ( ( dim_vec_int @ V3 )
            = ( dim_vec_int @ W2 ) )
          & ! [I5: nat] :
              ( ( ord_less_nat @ I5 @ ( dim_vec_int @ W2 ) )
             => ( ord_less_eq_int @ ( vec_index_int @ V3 @ I5 ) @ ( vec_index_int @ W2 @ I5 ) ) ) ) ) ) ).

% less_eq_vec_def
thf(fact_697_less__eq__vec__def,axiom,
    ( ord_less_eq_vec_nat
    = ( ^ [V3: vec_nat,W2: vec_nat] :
          ( ( ( dim_vec_nat @ V3 )
            = ( dim_vec_nat @ W2 ) )
          & ! [I5: nat] :
              ( ( ord_less_nat @ I5 @ ( dim_vec_nat @ W2 ) )
             => ( ord_less_eq_nat @ ( vec_index_nat @ V3 @ I5 ) @ ( vec_index_nat @ W2 @ I5 ) ) ) ) ) ) ).

% less_eq_vec_def
thf(fact_698_less__eq__vec__def,axiom,
    ( ord_le264858229241918703et_int
    = ( ^ [V3: vec_set_int,W2: vec_set_int] :
          ( ( ( dim_vec_set_int @ V3 )
            = ( dim_vec_set_int @ W2 ) )
          & ! [I5: nat] :
              ( ( ord_less_nat @ I5 @ ( dim_vec_set_int @ W2 ) )
             => ( ord_less_eq_set_int @ ( vec_index_set_int @ V3 @ I5 ) @ ( vec_index_set_int @ W2 @ I5 ) ) ) ) ) ) ).

% less_eq_vec_def
thf(fact_699_less__eq__vec__def,axiom,
    ( ord_less_eq_vec_real
    = ( ^ [V3: vec_real,W2: vec_real] :
          ( ( ( dim_vec_real @ V3 )
            = ( dim_vec_real @ W2 ) )
          & ! [I5: nat] :
              ( ( ord_less_nat @ I5 @ ( dim_vec_real @ W2 ) )
             => ( ord_less_eq_real @ ( vec_index_real @ V3 @ I5 ) @ ( vec_index_real @ W2 @ I5 ) ) ) ) ) ) ).

% less_eq_vec_def
thf(fact_700_frac__ge__0,axiom,
    ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X ) ) ).

% frac_ge_0
thf(fact_701_power__int__0__left__If,axiom,
    ! [M: int] :
      ( ( ( M = zero_zero_int )
       => ( ( power_int_real @ zero_zero_real @ M )
          = one_one_real ) )
      & ( ( M != zero_zero_int )
       => ( ( power_int_real @ zero_zero_real @ M )
          = zero_zero_real ) ) ) ).

% power_int_0_left_If
thf(fact_702_power__int__increasing,axiom,
    ! [N: int,N3: int,A: real] :
      ( ( ord_less_eq_int @ N @ N3 )
     => ( ( ord_less_eq_real @ one_one_real @ A )
       => ( ord_less_eq_real @ ( power_int_real @ A @ N ) @ ( power_int_real @ A @ N3 ) ) ) ) ).

% power_int_increasing
thf(fact_703_power__int__strict__increasing,axiom,
    ! [N: int,N3: int,A: real] :
      ( ( ord_less_int @ N @ N3 )
     => ( ( ord_less_real @ one_one_real @ A )
       => ( ord_less_real @ ( power_int_real @ A @ N ) @ ( power_int_real @ A @ N3 ) ) ) ) ).

% power_int_strict_increasing
thf(fact_704_power__int__strict__decreasing,axiom,
    ! [N: int,N3: int,A: real] :
      ( ( ord_less_int @ N @ N3 )
     => ( ( ord_less_real @ zero_zero_real @ A )
       => ( ( ord_less_real @ A @ one_one_real )
         => ( ord_less_real @ ( power_int_real @ A @ N3 ) @ ( power_int_real @ A @ N ) ) ) ) ) ).

% power_int_strict_decreasing
thf(fact_705_power__int__mono,axiom,
    ! [X: real,Y: real,N: int] :
      ( ( ord_less_eq_real @ X @ Y )
     => ( ( ord_less_eq_int @ zero_zero_int @ N )
       => ( ( ord_less_eq_real @ zero_zero_real @ X )
         => ( ord_less_eq_real @ ( power_int_real @ X @ N ) @ ( power_int_real @ Y @ N ) ) ) ) ) ).

% power_int_mono
thf(fact_706_power__int__strict__antimono,axiom,
    ! [A: real,B: real,N: int] :
      ( ( ord_less_real @ A @ B )
     => ( ( ord_less_real @ zero_zero_real @ A )
       => ( ( ord_less_int @ N @ zero_zero_int )
         => ( ord_less_real @ ( power_int_real @ B @ N ) @ ( power_int_real @ A @ N ) ) ) ) ) ).

% power_int_strict_antimono
thf(fact_707_one__le__power__int,axiom,
    ! [X: real,N: int] :
      ( ( ord_less_eq_real @ one_one_real @ X )
     => ( ( ord_less_eq_int @ zero_zero_int @ N )
       => ( ord_less_eq_real @ one_one_real @ ( power_int_real @ X @ N ) ) ) ) ).

% one_le_power_int
thf(fact_708_one__less__power__int,axiom,
    ! [A: real,N: int] :
      ( ( ord_less_real @ one_one_real @ A )
     => ( ( ord_less_int @ zero_zero_int @ N )
       => ( ord_less_real @ one_one_real @ ( power_int_real @ A @ N ) ) ) ) ).

% one_less_power_int
thf(fact_709_mat__mod_Ovec__mod__index,axiom,
    ! [M: int,I: nat,V: vec_int] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( ord_less_nat @ I @ ( dim_vec_int @ V ) )
       => ( ( vec_index_int @ ( vector1199560857299316530ec_mod @ M @ V ) @ I )
          = ( modulo_modulo_int @ ( vec_index_int @ V @ I ) @ M ) ) ) ) ).

% mat_mod.vec_mod_index
thf(fact_710_power__int__antimono,axiom,
    ! [A: real,B: real,N: int] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ( ord_less_real @ zero_zero_real @ A )
       => ( ( ord_less_int @ N @ zero_zero_int )
         => ( ord_less_eq_real @ ( power_int_real @ B @ N ) @ ( power_int_real @ A @ N ) ) ) ) ) ).

% power_int_antimono
thf(fact_711_power__int__strict__mono,axiom,
    ! [A: real,B: real,N: int] :
      ( ( ord_less_real @ A @ B )
     => ( ( ord_less_eq_real @ zero_zero_real @ A )
       => ( ( ord_less_int @ zero_zero_int @ N )
         => ( ord_less_real @ ( power_int_real @ A @ N ) @ ( power_int_real @ B @ N ) ) ) ) ) ).

% power_int_strict_mono
thf(fact_712_power__int__le__one,axiom,
    ! [X: real,N: int] :
      ( ( ord_less_eq_real @ zero_zero_real @ X )
     => ( ( ord_less_eq_int @ zero_zero_int @ N )
       => ( ( ord_less_eq_real @ X @ one_one_real )
         => ( ord_less_eq_real @ ( power_int_real @ X @ N ) @ one_one_real ) ) ) ) ).

% power_int_le_one
thf(fact_713_power__int__decreasing,axiom,
    ! [N: int,N3: int,A: real] :
      ( ( ord_less_eq_int @ N @ N3 )
     => ( ( ord_less_eq_real @ zero_zero_real @ A )
       => ( ( ord_less_eq_real @ A @ one_one_real )
         => ( ( ( A != zero_zero_real )
              | ( N3 != zero_zero_int )
              | ( N = zero_zero_int ) )
           => ( ord_less_eq_real @ ( power_int_real @ A @ N3 ) @ ( power_int_real @ A @ N ) ) ) ) ) ) ).

% power_int_decreasing
thf(fact_714_arsinh__0,axiom,
    ( ( arsinh_real @ zero_zero_real )
    = zero_zero_real ) ).

% arsinh_0
thf(fact_715_artanh__0,axiom,
    ( ( artanh_real @ zero_zero_real )
    = zero_zero_real ) ).

% artanh_0
thf(fact_716_gcd__nat__induct,axiom,
    ! [P: nat > nat > $o,M: nat,N: nat] :
      ( ! [M4: nat] : ( P @ M4 @ zero_zero_nat )
     => ( ! [M4: nat,N2: nat] :
            ( ( ord_less_nat @ zero_zero_nat @ N2 )
           => ( ( P @ N2 @ ( modulo_modulo_nat @ M4 @ N2 ) )
             => ( P @ M4 @ N2 ) ) )
       => ( P @ M @ N ) ) ) ).

% gcd_nat_induct
thf(fact_717_vec__setI2,axiom,
    ! [I: nat,V: vec_ve5128822793932996635ring_a] :
      ( ( ord_less_nat @ I @ ( dim_ve7352250128364513064ring_a @ V ) )
     => ( member1106766863034010949ring_a @ ( vec_in6730775671236957722ring_a @ V @ I ) @ ( vec_se3276121494910751146ring_a @ V ) ) ) ).

% vec_setI2
thf(fact_718_vec__setI2,axiom,
    ! [I: nat,V: vec_ma98051958688905615ring_a] :
      ( ( ord_less_nat @ I @ ( dim_ve3499172007441373852ring_a @ V ) )
     => ( member6477060778965647545ring_a @ ( vec_in2877697550313818510ring_a @ V @ I ) @ ( vec_se8646415410842387742ring_a @ V ) ) ) ).

% vec_setI2
thf(fact_719_vec__setI2,axiom,
    ! [I: nat,V: vec_nat] :
      ( ( ord_less_nat @ I @ ( dim_vec_nat @ V ) )
     => ( member_nat @ ( vec_index_nat @ V @ I ) @ ( vec_set_nat @ V ) ) ) ).

% vec_setI2
thf(fact_720_vec__setI2,axiom,
    ! [I: nat,V: vec_int] :
      ( ( ord_less_nat @ I @ ( dim_vec_int @ V ) )
     => ( member_int @ ( vec_index_int @ V @ I ) @ ( vec_set_int2 @ V ) ) ) ).

% vec_setI2
thf(fact_721_vec__setI2,axiom,
    ! [I: nat,V: vec_Fi4296597256376197294ring_a] :
      ( ( ord_less_nat @ I @ ( dim_ve9152325144110082507ring_a @ V ) )
     => ( member3034048621153491438ring_a @ ( vec_in8573817152773094745ring_a @ V @ I ) @ ( vec_se7251946917745546697ring_a @ V ) ) ) ).

% vec_setI2
thf(fact_722_ln__one,axiom,
    ( ( ln_ln_real @ one_one_real )
    = zero_zero_real ) ).

% ln_one
thf(fact_723_lift__01__vec__simp_I2_J,axiom,
    ! [I: nat,V: vec_int] :
      ( ( ord_less_nat @ I @ ( dim_vec_int @ V ) )
     => ( ( vec_index_int @ ( matrix8301520909418075407nt_int @ V ) @ I )
        = ( matrix1697308990001484774nt_int @ ( vec_index_int @ V @ I ) ) ) ) ).

% lift_01_vec_simp(2)
thf(fact_724_lift__01__vec__simp_I2_J,axiom,
    ! [I: nat,V: vec_Fi4296597256376197294ring_a] :
      ( ( ord_less_nat @ I @ ( dim_ve9152325144110082507ring_a @ V ) )
     => ( ( vec_index_int @ ( matrix8742746829526049276_a_int @ V ) @ I )
        = ( matrix2011149211968969189_a_int @ ( vec_in8573817152773094745ring_a @ V @ I ) ) ) ) ).

% lift_01_vec_simp(2)
thf(fact_725_lift__01__vec__simp_I2_J,axiom,
    ! [I: nat,V: vec_int] :
      ( ( ord_less_nat @ I @ ( dim_vec_int @ V ) )
     => ( ( vec_in8573817152773094745ring_a @ ( matrix1095566785459193506ring_a @ V ) @ I )
        = ( matrix3587341204756889227ring_a @ ( vec_index_int @ V @ I ) ) ) ) ).

% lift_01_vec_simp(2)
thf(fact_726_lift__01__vec__simp_I2_J,axiom,
    ! [I: nat,V: vec_Fi4296597256376197294ring_a] :
      ( ( ord_less_nat @ I @ ( dim_ve9152325144110082507ring_a @ V ) )
     => ( ( vec_in8573817152773094745ring_a @ ( matrix7517040601615355893ring_a @ V ) @ I )
        = ( matrix6721843712216650060ring_a @ ( vec_in8573817152773094745ring_a @ V @ I ) ) ) ) ).

% lift_01_vec_simp(2)
thf(fact_727_of__zero__hom_Ohom__zero,axiom,
    ( ( matrix1697308990001484774nt_int @ zero_zero_int )
    = zero_zero_int ) ).

% of_zero_hom.hom_zero
thf(fact_728_of__zero__hom_Ohom__zero,axiom,
    ( ( matrix1699799460510535050nt_nat @ zero_zero_int )
    = zero_zero_nat ) ).

% of_zero_hom.hom_zero
thf(fact_729_of__zero__hom_Ohom__zero,axiom,
    ( ( matrix1706393078865277798t_real @ zero_zero_int )
    = zero_zero_real ) ).

% of_zero_hom.hom_zero
thf(fact_730_of__zero__hom_Ohom__zero,axiom,
    ( ( matrix697955278100430218at_int @ zero_zero_nat )
    = zero_zero_int ) ).

% of_zero_hom.hom_zero
thf(fact_731_of__zero__hom_Ohom__zero,axiom,
    ( ( matrix700445748609480494at_nat @ zero_zero_nat )
    = zero_zero_nat ) ).

% of_zero_hom.hom_zero
thf(fact_732_of__zero__hom_Ohom__zero,axiom,
    ( ( matrix8742843541027031818t_real @ zero_zero_nat )
    = zero_zero_real ) ).

% of_zero_hom.hom_zero
thf(fact_733_of__zero__hom_Ohom__zero,axiom,
    ( ( matrix4084289606792104422al_int @ zero_zero_real )
    = zero_zero_int ) ).

% of_zero_hom.hom_zero
thf(fact_734_of__zero__hom_Ohom__zero,axiom,
    ( ( matrix4086780077301154698al_nat @ zero_zero_real )
    = zero_zero_nat ) ).

% of_zero_hom.hom_zero
thf(fact_735_of__zero__hom_Ohom__zero,axiom,
    ( ( matrix3070681271257819494l_real @ zero_zero_real )
    = zero_zero_real ) ).

% of_zero_hom.hom_zero
thf(fact_736_of__zero__hom_Ohom__zero,axiom,
    ( ( matrix3587341204756889227ring_a @ zero_zero_int )
    = zero_z7902377541816115708ring_a ) ).

% of_zero_hom.hom_zero
thf(fact_737_of__zero__hom_Ohom__0__iff,axiom,
    ! [X: int] :
      ( ( ( matrix1697308990001484774nt_int @ X )
        = zero_zero_int )
      = ( X = zero_zero_int ) ) ).

% of_zero_hom.hom_0_iff
thf(fact_738_of__zero__hom_Ohom__0__iff,axiom,
    ! [X: nat] :
      ( ( ( matrix697955278100430218at_int @ X )
        = zero_zero_int )
      = ( X = zero_zero_nat ) ) ).

% of_zero_hom.hom_0_iff
thf(fact_739_of__zero__hom_Ohom__0__iff,axiom,
    ! [X: real] :
      ( ( ( matrix4084289606792104422al_int @ X )
        = zero_zero_int )
      = ( X = zero_zero_real ) ) ).

% of_zero_hom.hom_0_iff
thf(fact_740_of__zero__hom_Ohom__0__iff,axiom,
    ! [X: int] :
      ( ( ( matrix1699799460510535050nt_nat @ X )
        = zero_zero_nat )
      = ( X = zero_zero_int ) ) ).

% of_zero_hom.hom_0_iff
thf(fact_741_of__zero__hom_Ohom__0__iff,axiom,
    ! [X: nat] :
      ( ( ( matrix700445748609480494at_nat @ X )
        = zero_zero_nat )
      = ( X = zero_zero_nat ) ) ).

% of_zero_hom.hom_0_iff
thf(fact_742_of__zero__hom_Ohom__0__iff,axiom,
    ! [X: real] :
      ( ( ( matrix4086780077301154698al_nat @ X )
        = zero_zero_nat )
      = ( X = zero_zero_real ) ) ).

% of_zero_hom.hom_0_iff
thf(fact_743_of__zero__hom_Ohom__0__iff,axiom,
    ! [X: int] :
      ( ( ( matrix1706393078865277798t_real @ X )
        = zero_zero_real )
      = ( X = zero_zero_int ) ) ).

% of_zero_hom.hom_0_iff
thf(fact_744_of__zero__hom_Ohom__0__iff,axiom,
    ! [X: nat] :
      ( ( ( matrix8742843541027031818t_real @ X )
        = zero_zero_real )
      = ( X = zero_zero_nat ) ) ).

% of_zero_hom.hom_0_iff
thf(fact_745_of__zero__hom_Ohom__0__iff,axiom,
    ! [X: real] :
      ( ( ( matrix3070681271257819494l_real @ X )
        = zero_zero_real )
      = ( X = zero_zero_real ) ) ).

% of_zero_hom.hom_0_iff
thf(fact_746_of__zero__hom_Ohom__0__iff,axiom,
    ! [X: finite_mod_ring_a] :
      ( ( ( matrix2011149211968969189_a_int @ X )
        = zero_zero_int )
      = ( X = zero_z7902377541816115708ring_a ) ) ).

% of_zero_hom.hom_0_iff
thf(fact_747_of__zero__neq__one__0,axiom,
    ( ( matrix1697308990001484774nt_int @ zero_zero_int )
    = zero_zero_int ) ).

% of_zero_neq_one_0
thf(fact_748_of__zero__neq__one__0,axiom,
    ( ( matrix1699799460510535050nt_nat @ zero_zero_int )
    = zero_zero_nat ) ).

% of_zero_neq_one_0
thf(fact_749_of__zero__neq__one__0,axiom,
    ( ( matrix1706393078865277798t_real @ zero_zero_int )
    = zero_zero_real ) ).

% of_zero_neq_one_0
thf(fact_750_of__zero__neq__one__0,axiom,
    ( ( matrix697955278100430218at_int @ zero_zero_nat )
    = zero_zero_int ) ).

% of_zero_neq_one_0
thf(fact_751_of__zero__neq__one__0,axiom,
    ( ( matrix700445748609480494at_nat @ zero_zero_nat )
    = zero_zero_nat ) ).

% of_zero_neq_one_0
thf(fact_752_of__zero__neq__one__0,axiom,
    ( ( matrix8742843541027031818t_real @ zero_zero_nat )
    = zero_zero_real ) ).

% of_zero_neq_one_0
thf(fact_753_of__zero__neq__one__0,axiom,
    ( ( matrix4084289606792104422al_int @ zero_zero_real )
    = zero_zero_int ) ).

% of_zero_neq_one_0
thf(fact_754_of__zero__neq__one__0,axiom,
    ( ( matrix4086780077301154698al_nat @ zero_zero_real )
    = zero_zero_nat ) ).

% of_zero_neq_one_0
thf(fact_755_of__zero__neq__one__0,axiom,
    ( ( matrix3070681271257819494l_real @ zero_zero_real )
    = zero_zero_real ) ).

% of_zero_neq_one_0
thf(fact_756_of__zero__neq__one__0,axiom,
    ( ( matrix3587341204756889227ring_a @ zero_zero_int )
    = zero_z7902377541816115708ring_a ) ).

% of_zero_neq_one_0
thf(fact_757_of__zero__neq__one__0__iff,axiom,
    ! [X: int] :
      ( ( ( matrix1697308990001484774nt_int @ X )
        = zero_zero_int )
      = ( X = zero_zero_int ) ) ).

% of_zero_neq_one_0_iff
thf(fact_758_of__zero__neq__one__0__iff,axiom,
    ! [X: nat] :
      ( ( ( matrix697955278100430218at_int @ X )
        = zero_zero_int )
      = ( X = zero_zero_nat ) ) ).

% of_zero_neq_one_0_iff
thf(fact_759_of__zero__neq__one__0__iff,axiom,
    ! [X: real] :
      ( ( ( matrix4084289606792104422al_int @ X )
        = zero_zero_int )
      = ( X = zero_zero_real ) ) ).

% of_zero_neq_one_0_iff
thf(fact_760_of__zero__neq__one__0__iff,axiom,
    ! [X: int] :
      ( ( ( matrix1699799460510535050nt_nat @ X )
        = zero_zero_nat )
      = ( X = zero_zero_int ) ) ).

% of_zero_neq_one_0_iff
thf(fact_761_of__zero__neq__one__0__iff,axiom,
    ! [X: nat] :
      ( ( ( matrix700445748609480494at_nat @ X )
        = zero_zero_nat )
      = ( X = zero_zero_nat ) ) ).

% of_zero_neq_one_0_iff
thf(fact_762_of__zero__neq__one__0__iff,axiom,
    ! [X: real] :
      ( ( ( matrix4086780077301154698al_nat @ X )
        = zero_zero_nat )
      = ( X = zero_zero_real ) ) ).

% of_zero_neq_one_0_iff
thf(fact_763_of__zero__neq__one__0__iff,axiom,
    ! [X: int] :
      ( ( ( matrix1706393078865277798t_real @ X )
        = zero_zero_real )
      = ( X = zero_zero_int ) ) ).

% of_zero_neq_one_0_iff
thf(fact_764_of__zero__neq__one__0__iff,axiom,
    ! [X: nat] :
      ( ( ( matrix8742843541027031818t_real @ X )
        = zero_zero_real )
      = ( X = zero_zero_nat ) ) ).

% of_zero_neq_one_0_iff
thf(fact_765_of__zero__neq__one__0__iff,axiom,
    ! [X: real] :
      ( ( ( matrix3070681271257819494l_real @ X )
        = zero_zero_real )
      = ( X = zero_zero_real ) ) ).

% of_zero_neq_one_0_iff
thf(fact_766_of__zero__neq__one__0__iff,axiom,
    ! [X: finite_mod_ring_a] :
      ( ( ( matrix2011149211968969189_a_int @ X )
        = zero_zero_int )
      = ( X = zero_z7902377541816115708ring_a ) ) ).

% of_zero_neq_one_0_iff
thf(fact_767_of__inj__on__01__hom_Ohom__one,axiom,
    ( ( matrix1697308990001484774nt_int @ one_one_int )
    = one_one_int ) ).

% of_inj_on_01_hom.hom_one
thf(fact_768_of__inj__on__01__hom_Ohom__one,axiom,
    ( ( matrix1699799460510535050nt_nat @ one_one_int )
    = one_one_nat ) ).

% of_inj_on_01_hom.hom_one
thf(fact_769_of__inj__on__01__hom_Ohom__one,axiom,
    ( ( matrix1706393078865277798t_real @ one_one_int )
    = one_one_real ) ).

% of_inj_on_01_hom.hom_one
thf(fact_770_of__inj__on__01__hom_Ohom__one,axiom,
    ( ( matrix697955278100430218at_int @ one_one_nat )
    = one_one_int ) ).

% of_inj_on_01_hom.hom_one
thf(fact_771_of__inj__on__01__hom_Ohom__one,axiom,
    ( ( matrix700445748609480494at_nat @ one_one_nat )
    = one_one_nat ) ).

% of_inj_on_01_hom.hom_one
thf(fact_772_of__inj__on__01__hom_Ohom__one,axiom,
    ( ( matrix8742843541027031818t_real @ one_one_nat )
    = one_one_real ) ).

% of_inj_on_01_hom.hom_one
thf(fact_773_of__inj__on__01__hom_Ohom__one,axiom,
    ( ( matrix4084289606792104422al_int @ one_one_real )
    = one_one_int ) ).

% of_inj_on_01_hom.hom_one
thf(fact_774_of__inj__on__01__hom_Ohom__one,axiom,
    ( ( matrix4086780077301154698al_nat @ one_one_real )
    = one_one_nat ) ).

% of_inj_on_01_hom.hom_one
thf(fact_775_of__inj__on__01__hom_Ohom__one,axiom,
    ( ( matrix3070681271257819494l_real @ one_one_real )
    = one_one_real ) ).

% of_inj_on_01_hom.hom_one
thf(fact_776_of__inj__on__01__hom_Ohom__one,axiom,
    ( ( matrix3587341204756889227ring_a @ one_one_int )
    = one_on2109788427901206336ring_a ) ).

% of_inj_on_01_hom.hom_one
thf(fact_777_of__zero__neq__one__1,axiom,
    ( ( matrix1697308990001484774nt_int @ one_one_int )
    = one_one_int ) ).

% of_zero_neq_one_1
thf(fact_778_of__zero__neq__one__1,axiom,
    ( ( matrix1699799460510535050nt_nat @ one_one_int )
    = one_one_nat ) ).

% of_zero_neq_one_1
thf(fact_779_of__zero__neq__one__1,axiom,
    ( ( matrix1706393078865277798t_real @ one_one_int )
    = one_one_real ) ).

% of_zero_neq_one_1
thf(fact_780_of__zero__neq__one__1,axiom,
    ( ( matrix697955278100430218at_int @ one_one_nat )
    = one_one_int ) ).

% of_zero_neq_one_1
thf(fact_781_of__zero__neq__one__1,axiom,
    ( ( matrix700445748609480494at_nat @ one_one_nat )
    = one_one_nat ) ).

% of_zero_neq_one_1
thf(fact_782_of__zero__neq__one__1,axiom,
    ( ( matrix8742843541027031818t_real @ one_one_nat )
    = one_one_real ) ).

% of_zero_neq_one_1
thf(fact_783_of__zero__neq__one__1,axiom,
    ( ( matrix4084289606792104422al_int @ one_one_real )
    = one_one_int ) ).

% of_zero_neq_one_1
thf(fact_784_of__zero__neq__one__1,axiom,
    ( ( matrix4086780077301154698al_nat @ one_one_real )
    = one_one_nat ) ).

% of_zero_neq_one_1
thf(fact_785_of__zero__neq__one__1,axiom,
    ( ( matrix3070681271257819494l_real @ one_one_real )
    = one_one_real ) ).

% of_zero_neq_one_1
thf(fact_786_of__zero__neq__one__1,axiom,
    ( ( matrix3587341204756889227ring_a @ one_one_int )
    = one_on2109788427901206336ring_a ) ).

% of_zero_neq_one_1
thf(fact_787_to__int__vec__index,axiom,
    ! [I: nat,V: vec_Fi4296597256376197294ring_a] :
      ( ( ord_less_nat @ I @ ( dim_ve9152325144110082507ring_a @ V ) )
     => ( ( vec_index_int @ ( map_ve50164598268879916_a_int @ finite1095367895020317408ring_a @ V ) @ I )
        = ( finite1095367895020317408ring_a @ ( vec_in8573817152773094745ring_a @ V @ I ) ) ) ) ).

% to_int_vec_index
thf(fact_788_of__zero__hom_Ohom__0,axiom,
    ! [X: int] :
      ( ( ( matrix1697308990001484774nt_int @ X )
        = zero_zero_int )
     => ( X = zero_zero_int ) ) ).

% of_zero_hom.hom_0
thf(fact_789_of__zero__hom_Ohom__0,axiom,
    ! [X: nat] :
      ( ( ( matrix697955278100430218at_int @ X )
        = zero_zero_int )
     => ( X = zero_zero_nat ) ) ).

% of_zero_hom.hom_0
thf(fact_790_of__zero__hom_Ohom__0,axiom,
    ! [X: real] :
      ( ( ( matrix4084289606792104422al_int @ X )
        = zero_zero_int )
     => ( X = zero_zero_real ) ) ).

% of_zero_hom.hom_0
thf(fact_791_of__zero__hom_Ohom__0,axiom,
    ! [X: int] :
      ( ( ( matrix1699799460510535050nt_nat @ X )
        = zero_zero_nat )
     => ( X = zero_zero_int ) ) ).

% of_zero_hom.hom_0
thf(fact_792_of__zero__hom_Ohom__0,axiom,
    ! [X: nat] :
      ( ( ( matrix700445748609480494at_nat @ X )
        = zero_zero_nat )
     => ( X = zero_zero_nat ) ) ).

% of_zero_hom.hom_0
thf(fact_793_of__zero__hom_Ohom__0,axiom,
    ! [X: real] :
      ( ( ( matrix4086780077301154698al_nat @ X )
        = zero_zero_nat )
     => ( X = zero_zero_real ) ) ).

% of_zero_hom.hom_0
thf(fact_794_of__zero__hom_Ohom__0,axiom,
    ! [X: int] :
      ( ( ( matrix1706393078865277798t_real @ X )
        = zero_zero_real )
     => ( X = zero_zero_int ) ) ).

% of_zero_hom.hom_0
thf(fact_795_of__zero__hom_Ohom__0,axiom,
    ! [X: nat] :
      ( ( ( matrix8742843541027031818t_real @ X )
        = zero_zero_real )
     => ( X = zero_zero_nat ) ) ).

% of_zero_hom.hom_0
thf(fact_796_of__zero__hom_Ohom__0,axiom,
    ! [X: real] :
      ( ( ( matrix3070681271257819494l_real @ X )
        = zero_zero_real )
     => ( X = zero_zero_real ) ) ).

% of_zero_hom.hom_0
thf(fact_797_of__zero__hom_Ohom__0,axiom,
    ! [X: finite_mod_ring_a] :
      ( ( ( matrix2011149211968969189_a_int @ X )
        = zero_zero_int )
     => ( X = zero_z7902377541816115708ring_a ) ) ).

% of_zero_hom.hom_0
thf(fact_798_vec__contains__img,axiom,
    ! [A: nat,V: vec_nat,F: nat > nat] :
      ( ( member_nat @ A @ ( vec_set_nat @ V ) )
     => ( member_nat @ ( F @ A ) @ ( vec_set_nat @ ( map_vec_nat_nat @ F @ V ) ) ) ) ).

% vec_contains_img
thf(fact_799_vec__contains__img,axiom,
    ! [A: nat,V: vec_nat,F: nat > int] :
      ( ( member_nat @ A @ ( vec_set_nat @ V ) )
     => ( member_int @ ( F @ A ) @ ( vec_set_int2 @ ( map_vec_nat_int @ F @ V ) ) ) ) ).

% vec_contains_img
thf(fact_800_vec__contains__img,axiom,
    ! [A: int,V: vec_int,F: int > nat] :
      ( ( member_int @ A @ ( vec_set_int2 @ V ) )
     => ( member_nat @ ( F @ A ) @ ( vec_set_nat @ ( map_vec_int_nat @ F @ V ) ) ) ) ).

% vec_contains_img
thf(fact_801_vec__contains__img,axiom,
    ! [A: int,V: vec_int,F: int > int] :
      ( ( member_int @ A @ ( vec_set_int2 @ V ) )
     => ( member_int @ ( F @ A ) @ ( vec_set_int2 @ ( map_vec_int_int @ F @ V ) ) ) ) ).

% vec_contains_img
thf(fact_802_vec__contains__img,axiom,
    ! [A: finite_mod_ring_a,V: vec_Fi4296597256376197294ring_a,F: finite_mod_ring_a > int] :
      ( ( member3034048621153491438ring_a @ A @ ( vec_se7251946917745546697ring_a @ V ) )
     => ( member_int @ ( F @ A ) @ ( vec_set_int2 @ ( map_ve50164598268879916_a_int @ F @ V ) ) ) ) ).

% vec_contains_img
thf(fact_803_vec__contains__img,axiom,
    ! [A: int,V: vec_int,F: int > finite_mod_ring_a] :
      ( ( member_int @ A @ ( vec_set_int2 @ V ) )
     => ( member3034048621153491438ring_a @ ( F @ A ) @ ( vec_se7251946917745546697ring_a @ ( map_ve1626356591056799954ring_a @ F @ V ) ) ) ) ).

% vec_contains_img
thf(fact_804_vec__contains__img,axiom,
    ! [A: vec_Fi4296597256376197294ring_a,V: vec_ve5128822793932996635ring_a,F: vec_Fi4296597256376197294ring_a > nat] :
      ( ( member1106766863034010949ring_a @ A @ ( vec_se3276121494910751146ring_a @ V ) )
     => ( member_nat @ ( F @ A ) @ ( vec_set_nat @ ( map_ve8203878701830285061_a_nat @ F @ V ) ) ) ) ).

% vec_contains_img
thf(fact_805_vec__contains__img,axiom,
    ! [A: mat_Fi443519135453058082ring_a,V: vec_ma98051958688905615ring_a,F: mat_Fi443519135453058082ring_a > nat] :
      ( ( member6477060778965647545ring_a @ A @ ( vec_se8646415410842387742ring_a @ V ) )
     => ( member_nat @ ( F @ A ) @ ( vec_set_nat @ ( map_ve6930335561632762489_a_nat @ F @ V ) ) ) ) ).

% vec_contains_img
thf(fact_806_vec__contains__img,axiom,
    ! [A: nat,V: vec_nat,F: nat > vec_Fi4296597256376197294ring_a] :
      ( ( member_nat @ A @ ( vec_set_nat @ V ) )
     => ( member1106766863034010949ring_a @ ( F @ A ) @ ( vec_se3276121494910751146ring_a @ ( map_ve7352989270010254085ring_a @ F @ V ) ) ) ) ).

% vec_contains_img
thf(fact_807_vec__contains__img,axiom,
    ! [A: nat,V: vec_nat,F: nat > mat_Fi443519135453058082ring_a] :
      ( ( member_nat @ A @ ( vec_set_nat @ V ) )
     => ( member6477060778965647545ring_a @ ( F @ A ) @ ( vec_se8646415410842387742ring_a @ ( map_ve3499911149087114873ring_a @ F @ V ) ) ) ) ).

% vec_contains_img
thf(fact_808_of__int__hom_Ovec__hom__inj__lim,axiom,
    ! [V: vec_int,Univ: set_int,W: vec_int] :
      ( ( ord_less_eq_set_int @ ( vec_set_int2 @ V ) @ Univ )
     => ( ( ord_less_eq_set_int @ ( vec_set_int2 @ W ) @ Univ )
       => ( ( ( map_vec_int_int @ ring_1_of_int_int @ V )
            = ( map_vec_int_int @ ring_1_of_int_int @ W ) )
         => ( V = W ) ) ) ) ).

% of_int_hom.vec_hom_inj_lim
thf(fact_809_of__int__hom_Ovec__hom__inj__lim,axiom,
    ! [V: vec_int,Univ: set_int,W: vec_int] :
      ( ( ord_less_eq_set_int @ ( vec_set_int2 @ V ) @ Univ )
     => ( ( ord_less_eq_set_int @ ( vec_set_int2 @ W ) @ Univ )
       => ( ( ( map_vec_int_real @ ring_1_of_int_real @ V )
            = ( map_vec_int_real @ ring_1_of_int_real @ W ) )
         => ( V = W ) ) ) ) ).

% of_int_hom.vec_hom_inj_lim
thf(fact_810_of__zero__neq__one__def,axiom,
    ( matrix1697308990001484774nt_int
    = ( ^ [X3: int] : ( if_int @ ( X3 = zero_zero_int ) @ zero_zero_int @ one_one_int ) ) ) ).

% of_zero_neq_one_def
thf(fact_811_of__zero__neq__one__def,axiom,
    ( matrix1699799460510535050nt_nat
    = ( ^ [X3: int] : ( if_nat @ ( X3 = zero_zero_int ) @ zero_zero_nat @ one_one_nat ) ) ) ).

% of_zero_neq_one_def
thf(fact_812_of__zero__neq__one__def,axiom,
    ( matrix1706393078865277798t_real
    = ( ^ [X3: int] : ( if_real @ ( X3 = zero_zero_int ) @ zero_zero_real @ one_one_real ) ) ) ).

% of_zero_neq_one_def
thf(fact_813_of__zero__neq__one__def,axiom,
    ( matrix697955278100430218at_int
    = ( ^ [X3: nat] : ( if_int @ ( X3 = zero_zero_nat ) @ zero_zero_int @ one_one_int ) ) ) ).

% of_zero_neq_one_def
thf(fact_814_of__zero__neq__one__def,axiom,
    ( matrix700445748609480494at_nat
    = ( ^ [X3: nat] : ( if_nat @ ( X3 = zero_zero_nat ) @ zero_zero_nat @ one_one_nat ) ) ) ).

% of_zero_neq_one_def
thf(fact_815_of__zero__neq__one__def,axiom,
    ( matrix8742843541027031818t_real
    = ( ^ [X3: nat] : ( if_real @ ( X3 = zero_zero_nat ) @ zero_zero_real @ one_one_real ) ) ) ).

% of_zero_neq_one_def
thf(fact_816_of__zero__neq__one__def,axiom,
    ( matrix4084289606792104422al_int
    = ( ^ [X3: real] : ( if_int @ ( X3 = zero_zero_real ) @ zero_zero_int @ one_one_int ) ) ) ).

% of_zero_neq_one_def
thf(fact_817_of__zero__neq__one__def,axiom,
    ( matrix4086780077301154698al_nat
    = ( ^ [X3: real] : ( if_nat @ ( X3 = zero_zero_real ) @ zero_zero_nat @ one_one_nat ) ) ) ).

% of_zero_neq_one_def
thf(fact_818_of__zero__neq__one__def,axiom,
    ( matrix3070681271257819494l_real
    = ( ^ [X3: real] : ( if_real @ ( X3 = zero_zero_real ) @ zero_zero_real @ one_one_real ) ) ) ).

% of_zero_neq_one_def
thf(fact_819_of__zero__neq__one__def,axiom,
    ( matrix3587341204756889227ring_a
    = ( ^ [X3: int] : ( if_Finite_mod_ring_a @ ( X3 = zero_zero_int ) @ zero_z7902377541816115708ring_a @ one_on2109788427901206336ring_a ) ) ) ).

% of_zero_neq_one_def
thf(fact_820_lift__01__vec__def,axiom,
    ( matrix8742746829526049276_a_int
    = ( map_ve50164598268879916_a_int @ matrix2011149211968969189_a_int ) ) ).

% lift_01_vec_def
thf(fact_821_lift__01__vec__def,axiom,
    ( matrix1095566785459193506ring_a
    = ( map_ve1626356591056799954ring_a @ matrix3587341204756889227ring_a ) ) ).

% lift_01_vec_def
thf(fact_822_lift__01__vec__def,axiom,
    ( matrix8301520909418075407nt_int
    = ( map_vec_int_int @ matrix1697308990001484774nt_int ) ) ).

% lift_01_vec_def
thf(fact_823_vec__setE,axiom,
    ! [A: vec_Fi4296597256376197294ring_a,V: vec_ve5128822793932996635ring_a] :
      ( ( member1106766863034010949ring_a @ A @ ( vec_se3276121494910751146ring_a @ V ) )
     => ~ ! [I4: nat] :
            ( ( ( vec_in6730775671236957722ring_a @ V @ I4 )
              = A )
           => ~ ( ord_less_nat @ I4 @ ( dim_ve7352250128364513064ring_a @ V ) ) ) ) ).

% vec_setE
thf(fact_824_vec__setE,axiom,
    ! [A: mat_Fi443519135453058082ring_a,V: vec_ma98051958688905615ring_a] :
      ( ( member6477060778965647545ring_a @ A @ ( vec_se8646415410842387742ring_a @ V ) )
     => ~ ! [I4: nat] :
            ( ( ( vec_in2877697550313818510ring_a @ V @ I4 )
              = A )
           => ~ ( ord_less_nat @ I4 @ ( dim_ve3499172007441373852ring_a @ V ) ) ) ) ).

% vec_setE
thf(fact_825_vec__setE,axiom,
    ! [A: nat,V: vec_nat] :
      ( ( member_nat @ A @ ( vec_set_nat @ V ) )
     => ~ ! [I4: nat] :
            ( ( ( vec_index_nat @ V @ I4 )
              = A )
           => ~ ( ord_less_nat @ I4 @ ( dim_vec_nat @ V ) ) ) ) ).

% vec_setE
thf(fact_826_vec__setE,axiom,
    ! [A: int,V: vec_int] :
      ( ( member_int @ A @ ( vec_set_int2 @ V ) )
     => ~ ! [I4: nat] :
            ( ( ( vec_index_int @ V @ I4 )
              = A )
           => ~ ( ord_less_nat @ I4 @ ( dim_vec_int @ V ) ) ) ) ).

% vec_setE
thf(fact_827_vec__setE,axiom,
    ! [A: finite_mod_ring_a,V: vec_Fi4296597256376197294ring_a] :
      ( ( member3034048621153491438ring_a @ A @ ( vec_se7251946917745546697ring_a @ V ) )
     => ~ ! [I4: nat] :
            ( ( ( vec_in8573817152773094745ring_a @ V @ I4 )
              = A )
           => ~ ( ord_less_nat @ I4 @ ( dim_ve9152325144110082507ring_a @ V ) ) ) ) ).

% vec_setE
thf(fact_828_vec__setI,axiom,
    ! [V: vec_ve5128822793932996635ring_a,I: nat,A: vec_Fi4296597256376197294ring_a] :
      ( ( ( vec_in6730775671236957722ring_a @ V @ I )
        = A )
     => ( ( ord_less_nat @ I @ ( dim_ve7352250128364513064ring_a @ V ) )
       => ( member1106766863034010949ring_a @ A @ ( vec_se3276121494910751146ring_a @ V ) ) ) ) ).

% vec_setI
thf(fact_829_vec__setI,axiom,
    ! [V: vec_ma98051958688905615ring_a,I: nat,A: mat_Fi443519135453058082ring_a] :
      ( ( ( vec_in2877697550313818510ring_a @ V @ I )
        = A )
     => ( ( ord_less_nat @ I @ ( dim_ve3499172007441373852ring_a @ V ) )
       => ( member6477060778965647545ring_a @ A @ ( vec_se8646415410842387742ring_a @ V ) ) ) ) ).

% vec_setI
thf(fact_830_vec__setI,axiom,
    ! [V: vec_nat,I: nat,A: nat] :
      ( ( ( vec_index_nat @ V @ I )
        = A )
     => ( ( ord_less_nat @ I @ ( dim_vec_nat @ V ) )
       => ( member_nat @ A @ ( vec_set_nat @ V ) ) ) ) ).

% vec_setI
thf(fact_831_vec__setI,axiom,
    ! [V: vec_int,I: nat,A: int] :
      ( ( ( vec_index_int @ V @ I )
        = A )
     => ( ( ord_less_nat @ I @ ( dim_vec_int @ V ) )
       => ( member_int @ A @ ( vec_set_int2 @ V ) ) ) ) ).

% vec_setI
thf(fact_832_vec__setI,axiom,
    ! [V: vec_Fi4296597256376197294ring_a,I: nat,A: finite_mod_ring_a] :
      ( ( ( vec_in8573817152773094745ring_a @ V @ I )
        = A )
     => ( ( ord_less_nat @ I @ ( dim_ve9152325144110082507ring_a @ V ) )
       => ( member3034048621153491438ring_a @ A @ ( vec_se7251946917745546697ring_a @ V ) ) ) ) ).

% vec_setI
thf(fact_833_vec__contains__obtains__index,axiom,
    ! [A: vec_Fi4296597256376197294ring_a,V: vec_ve5128822793932996635ring_a] :
      ( ( member1106766863034010949ring_a @ A @ ( vec_se3276121494910751146ring_a @ V ) )
     => ~ ! [I4: nat] :
            ( ( ord_less_nat @ I4 @ ( dim_ve7352250128364513064ring_a @ V ) )
           => ( ( vec_in6730775671236957722ring_a @ V @ I4 )
             != A ) ) ) ).

% vec_contains_obtains_index
thf(fact_834_vec__contains__obtains__index,axiom,
    ! [A: mat_Fi443519135453058082ring_a,V: vec_ma98051958688905615ring_a] :
      ( ( member6477060778965647545ring_a @ A @ ( vec_se8646415410842387742ring_a @ V ) )
     => ~ ! [I4: nat] :
            ( ( ord_less_nat @ I4 @ ( dim_ve3499172007441373852ring_a @ V ) )
           => ( ( vec_in2877697550313818510ring_a @ V @ I4 )
             != A ) ) ) ).

% vec_contains_obtains_index
thf(fact_835_vec__contains__obtains__index,axiom,
    ! [A: nat,V: vec_nat] :
      ( ( member_nat @ A @ ( vec_set_nat @ V ) )
     => ~ ! [I4: nat] :
            ( ( ord_less_nat @ I4 @ ( dim_vec_nat @ V ) )
           => ( ( vec_index_nat @ V @ I4 )
             != A ) ) ) ).

% vec_contains_obtains_index
thf(fact_836_vec__contains__obtains__index,axiom,
    ! [A: int,V: vec_int] :
      ( ( member_int @ A @ ( vec_set_int2 @ V ) )
     => ~ ! [I4: nat] :
            ( ( ord_less_nat @ I4 @ ( dim_vec_int @ V ) )
           => ( ( vec_index_int @ V @ I4 )
             != A ) ) ) ).

% vec_contains_obtains_index
thf(fact_837_vec__contains__obtains__index,axiom,
    ! [A: finite_mod_ring_a,V: vec_Fi4296597256376197294ring_a] :
      ( ( member3034048621153491438ring_a @ A @ ( vec_se7251946917745546697ring_a @ V ) )
     => ~ ! [I4: nat] :
            ( ( ord_less_nat @ I4 @ ( dim_ve9152325144110082507ring_a @ V ) )
           => ( ( vec_in8573817152773094745ring_a @ V @ I4 )
             != A ) ) ) ).

% vec_contains_obtains_index
thf(fact_838_mat__mod_Ovec__setI2,axiom,
    ! [M: int,I: nat,V: vec_ve5128822793932996635ring_a] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( ord_less_nat @ I @ ( dim_ve7352250128364513064ring_a @ V ) )
       => ( member1106766863034010949ring_a @ ( vec_in6730775671236957722ring_a @ V @ I ) @ ( vec_se3276121494910751146ring_a @ V ) ) ) ) ).

% mat_mod.vec_setI2
thf(fact_839_mat__mod_Ovec__setI2,axiom,
    ! [M: int,I: nat,V: vec_ma98051958688905615ring_a] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( ord_less_nat @ I @ ( dim_ve3499172007441373852ring_a @ V ) )
       => ( member6477060778965647545ring_a @ ( vec_in2877697550313818510ring_a @ V @ I ) @ ( vec_se8646415410842387742ring_a @ V ) ) ) ) ).

% mat_mod.vec_setI2
thf(fact_840_mat__mod_Ovec__setI2,axiom,
    ! [M: int,I: nat,V: vec_nat] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( ord_less_nat @ I @ ( dim_vec_nat @ V ) )
       => ( member_nat @ ( vec_index_nat @ V @ I ) @ ( vec_set_nat @ V ) ) ) ) ).

% mat_mod.vec_setI2
thf(fact_841_mat__mod_Ovec__setI2,axiom,
    ! [M: int,I: nat,V: vec_int] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( ord_less_nat @ I @ ( dim_vec_int @ V ) )
       => ( member_int @ ( vec_index_int @ V @ I ) @ ( vec_set_int2 @ V ) ) ) ) ).

% mat_mod.vec_setI2
thf(fact_842_mat__mod_Ovec__setI2,axiom,
    ! [M: int,I: nat,V: vec_Fi4296597256376197294ring_a] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( ord_less_nat @ I @ ( dim_ve9152325144110082507ring_a @ V ) )
       => ( member3034048621153491438ring_a @ ( vec_in8573817152773094745ring_a @ V @ I ) @ ( vec_se7251946917745546697ring_a @ V ) ) ) ) ).

% mat_mod.vec_setI2
thf(fact_843_vec__mod__eq,axiom,
    ! [V: vec_int] :
      ( ( ord_less_eq_set_int @ ( vec_set_int2 @ V ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ m ) )
     => ( ( vector1199560857299316530ec_mod @ m @ V )
        = V ) ) ).

% vec_mod_eq
thf(fact_844_vec__mod__set__vec__same,axiom,
    ! [V: vec_int] :
      ( ( ord_less_eq_set_int @ ( vec_set_int2 @ V ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ m ) )
     => ( ( vec_set_int2 @ ( vector1199560857299316530ec_mod @ m @ V ) )
        = ( vec_set_int2 @ V ) ) ) ).

% vec_mod_set_vec_same
thf(fact_845_index__MV__Rel,axiom,
    ( bNF_re1259227427626606373ring_a @ ( vector5230790432342831627_Rel_a @ m )
    @ ( bNF_re2201348192133994456ring_a
      @ ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 )
      @ ( vector3024231343486012919_Rel_a @ m ) )
    @ ^ [V3: vec_int,I5: nat] : ( if_int @ ( ord_less_nat @ I5 @ ( dim_vec_int @ V3 ) ) @ ( vec_index_int @ V3 @ I5 ) @ zero_zero_int )
    @ ^ [V3: vec_Fi4296597256376197294ring_a,I5: nat] : ( if_Finite_mod_ring_a @ ( ord_less_nat @ I5 @ ( dim_ve9152325144110082507ring_a @ V3 ) ) @ ( vec_in8573817152773094745ring_a @ V3 @ I5 ) @ zero_z7902377541816115708ring_a ) ) ).

% index_MV_Rel
thf(fact_846_all__ones__vec__smult,axiom,
    ! [I: nat,N: nat,K: int] :
      ( ( ord_less_nat @ I @ N )
     => ( ( vec_index_int @ ( smult_vec_int @ K @ ( matrix2748772424961467270ec_int @ N ) ) @ I )
        = K ) ) ).

% all_ones_vec_smult
thf(fact_847_all__ones__vec__smult,axiom,
    ! [I: nat,N: nat,K: finite_mod_ring_a] :
      ( ( ord_less_nat @ I @ N )
     => ( ( vec_in8573817152773094745ring_a @ ( smult_3577053051497313766ring_a @ K @ ( matrix705363690926585579ring_a @ N ) ) @ I )
        = K ) ) ).

% all_ones_vec_smult
thf(fact_848_zero__less__nat__eq,axiom,
    ! [Z: int] :
      ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
      = ( ord_less_int @ zero_zero_int @ Z ) ) ).

% zero_less_nat_eq
thf(fact_849_vec__mod__def,axiom,
    ! [V: vec_int] :
      ( ( vector1199560857299316530ec_mod @ m @ V )
      = ( map_vec_int_int
        @ ^ [X3: int] : ( modulo_modulo_int @ X3 @ m )
        @ V ) ) ).

% vec_mod_def
thf(fact_850_eq__MV__Rel,axiom,
    ( bNF_re151890839321169105ng_a_o @ ( vector5230790432342831627_Rel_a @ m )
    @ ( bNF_re507051067509135658_a_o_o @ ( vector5230790432342831627_Rel_a @ m )
      @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
    @ ^ [V3: vec_int,V4: vec_int] :
        ( ( vector1199560857299316530ec_mod @ m @ V3 )
        = ( vector1199560857299316530ec_mod @ m @ V4 ) )
    @ ^ [Y2: vec_Fi4296597256376197294ring_a,Z2: vec_Fi4296597256376197294ring_a] : ( Y2 = Z2 ) ) ).

% eq_MV_Rel
thf(fact_851_eq__M__Rel,axiom,
    ( bNF_re1743884151495963297ng_a_o @ ( vector3024231343486012919_Rel_a @ m )
    @ ( bNF_re8290846538823883642_a_o_o @ ( vector3024231343486012919_Rel_a @ m )
      @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
    @ ^ [X3: int,Y6: int] :
        ( ( vector_Matrix_mod_M @ m @ X3 )
        = ( vector_Matrix_mod_M @ m @ Y6 ) )
    @ ^ [Y2: finite_mod_ring_a,Z2: finite_mod_ring_a] : ( Y2 = Z2 ) ) ).

% eq_M_Rel
thf(fact_852_lt__dim__vec__MV__Rel,axiom,
    ( bNF_re7850819276413326442_nat_o @ ( vector5230790432342831627_Rel_a @ m )
    @ ( bNF_re4705727531993890431at_o_o
      @ ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 )
      @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
    @ ^ [V3: vec_int,J2: nat] : ( ord_less_nat @ J2 @ ( dim_vec_int @ V3 ) )
    @ ^ [V3: vec_Fi4296597256376197294ring_a,J2: nat] : ( ord_less_nat @ J2 @ ( dim_ve9152325144110082507ring_a @ V3 ) ) ) ).

% lt_dim_vec_MV_Rel
thf(fact_853_scalar__vec__one,axiom,
    ! [V: vec_int] :
      ( ( smult_vec_int @ one_one_int @ V )
      = V ) ).

% scalar_vec_one
thf(fact_854_scalar__vec__one,axiom,
    ! [V: vec_Fi4296597256376197294ring_a] :
      ( ( smult_3577053051497313766ring_a @ one_on2109788427901206336ring_a @ V )
      = V ) ).

% scalar_vec_one
thf(fact_855_scalar__vec__one,axiom,
    ! [V: vec_nat] :
      ( ( smult_vec_nat @ one_one_nat @ V )
      = V ) ).

% scalar_vec_one
thf(fact_856_scalar__vec__one,axiom,
    ! [V: vec_real] :
      ( ( smult_vec_real @ one_one_real @ V )
      = V ) ).

% scalar_vec_one
thf(fact_857_one__smult__vec,axiom,
    ! [V: vec_int] :
      ( ( smult_vec_int @ one_one_int @ V )
      = V ) ).

% one_smult_vec
thf(fact_858_one__smult__vec,axiom,
    ! [V: vec_Fi4296597256376197294ring_a] :
      ( ( smult_3577053051497313766ring_a @ one_on2109788427901206336ring_a @ V )
      = V ) ).

% one_smult_vec
thf(fact_859_one__smult__vec,axiom,
    ! [V: vec_real] :
      ( ( smult_vec_real @ one_one_real @ V )
      = V ) ).

% one_smult_vec
thf(fact_860_index__smult__vec_I2_J,axiom,
    ! [A: int,V: vec_int] :
      ( ( dim_vec_int @ ( smult_vec_int @ A @ V ) )
      = ( dim_vec_int @ V ) ) ).

% index_smult_vec(2)
thf(fact_861_index__smult__vec_I2_J,axiom,
    ! [A: finite_mod_ring_a,V: vec_Fi4296597256376197294ring_a] :
      ( ( dim_ve9152325144110082507ring_a @ ( smult_3577053051497313766ring_a @ A @ V ) )
      = ( dim_ve9152325144110082507ring_a @ V ) ) ).

% index_smult_vec(2)
thf(fact_862_nat__0__iff,axiom,
    ! [I: int] :
      ( ( ( nat2 @ I )
        = zero_zero_nat )
      = ( ord_less_eq_int @ I @ zero_zero_int ) ) ).

% nat_0_iff
thf(fact_863_nat__le__0,axiom,
    ! [Z: int] :
      ( ( ord_less_eq_int @ Z @ zero_zero_int )
     => ( ( nat2 @ Z )
        = zero_zero_nat ) ) ).

% nat_le_0
thf(fact_864_zless__nat__conj,axiom,
    ! [W: int,Z: int] :
      ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
      = ( ( ord_less_int @ zero_zero_int @ Z )
        & ( ord_less_int @ W @ Z ) ) ) ).

% zless_nat_conj
thf(fact_865_of__int__hom_Ovec__hom__smult,axiom,
    ! [Ev: int,V: vec_int] :
      ( ( map_vec_int_int @ ring_1_of_int_int @ ( smult_vec_int @ Ev @ V ) )
      = ( smult_vec_int @ ( ring_1_of_int_int @ Ev ) @ ( map_vec_int_int @ ring_1_of_int_int @ V ) ) ) ).

% of_int_hom.vec_hom_smult
thf(fact_866_of__int__hom_Ovec__hom__smult,axiom,
    ! [Ev: int,V: vec_int] :
      ( ( map_ve1626356591056799954ring_a @ ring_18169885480643366966ring_a @ ( smult_vec_int @ Ev @ V ) )
      = ( smult_3577053051497313766ring_a @ ( ring_18169885480643366966ring_a @ Ev ) @ ( map_ve1626356591056799954ring_a @ ring_18169885480643366966ring_a @ V ) ) ) ).

% of_int_hom.vec_hom_smult
thf(fact_867_of__int__hom_Ovec__hom__smult,axiom,
    ! [Ev: int,V: vec_int] :
      ( ( map_vec_int_real @ ring_1_of_int_real @ ( smult_vec_int @ Ev @ V ) )
      = ( smult_vec_real @ ( ring_1_of_int_real @ Ev ) @ ( map_vec_int_real @ ring_1_of_int_real @ V ) ) ) ).

% of_int_hom.vec_hom_smult
thf(fact_868_of__int__mod__ring__hom__sr_Ovec__hom__smult,axiom,
    ! [Ev: int,V: vec_int] :
      ( ( map_ve1626356591056799954ring_a @ finite8272632373135393572ring_a @ ( smult_vec_int @ Ev @ V ) )
      = ( smult_3577053051497313766ring_a @ ( finite8272632373135393572ring_a @ Ev ) @ ( map_ve1626356591056799954ring_a @ finite8272632373135393572ring_a @ V ) ) ) ).

% of_int_mod_ring_hom_sr.vec_hom_smult
thf(fact_869_mat__mod_Ovec__mod__def,axiom,
    ! [M: int,V: vec_int] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( vector1199560857299316530ec_mod @ M @ V )
        = ( map_vec_int_int
          @ ^ [X3: int] : ( modulo_modulo_int @ X3 @ M )
          @ V ) ) ) ).

% mat_mod.vec_mod_def
thf(fact_870_fun_Opred__transfer,axiom,
    ! [R: $o > $o > $o] :
      ( bNF_re8423317060048895199nt_o_o
      @ ( bNF_rel_fun_o_o_o_o @ R
        @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
      @ ( bNF_re6378653760509651613_o_o_o
        @ ( bNF_re5089333283451836215nt_o_o
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ R )
        @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
      @ ( basic_pred_fun_int_o
        @ ^ [Uu: int] : $true )
      @ ( basic_pred_fun_int_o
        @ ^ [Uu: int] : $true ) ) ).

% fun.pred_transfer
thf(fact_871_fun_Opred__transfer,axiom,
    ! [R: nat > nat > $o] :
      ( bNF_re1475021005839661469_nat_o
      @ ( bNF_re4705727531993890431at_o_o @ R
        @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
      @ ( bNF_re8293725029456574741at_o_o
        @ ( bNF_re3715656647883201625at_nat
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ R )
        @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
      @ ( basic_1842754918481324705nt_nat
        @ ^ [Uu: int] : $true )
      @ ( basic_1842754918481324705nt_nat
        @ ^ [Uu: int] : $true ) ) ).

% fun.pred_transfer
thf(fact_872_fun_Opred__transfer,axiom,
    ! [R: ( int > $o ) > ( int > $o ) > $o] :
      ( bNF_re416558257613726387nt_o_o
      @ ( bNF_re6378653760509651613_o_o_o @ R
        @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
      @ ( bNF_re5869992600382051037_o_o_o
        @ ( bNF_re3403563459893282935_int_o
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ R )
        @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
      @ ( basic_1842322873297984402_int_o
        @ ^ [Uu: int] : $true )
      @ ( basic_1842322873297984402_int_o
        @ ^ [Uu: int] : $true ) ) ).

% fun.pred_transfer
thf(fact_873_fun_Opred__transfer,axiom,
    ! [R: ( int > int ) > ( int > int ) > $o] :
      ( bNF_re5116691816286752797_int_o
      @ ( bNF_re1277823837431233485nt_o_o @ R
        @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
      @ ( bNF_re6987580103263796323nt_o_o
        @ ( bNF_re711492959462206631nt_int
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ R )
        @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
      @ ( basic_1535474925015357768nt_int
        @ ^ [Uu: int] : $true )
      @ ( basic_1535474925015357768nt_int
        @ ^ [Uu: int] : $true ) ) ).

% fun.pred_transfer
thf(fact_874_fun_Opred__transfer,axiom,
    ! [R: int > int > $o] :
      ( bNF_re6571774352052816285_int_o
      @ ( bNF_re5089333283451836215nt_o_o @ R
        @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
      @ ( bNF_re1277823837431233485nt_o_o
        @ ( bNF_re4712519889275205905nt_int
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ R )
        @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
      @ ( basic_1840264447972274429nt_int
        @ ^ [Uu: int] : $true )
      @ ( basic_1840264447972274429nt_int
        @ ^ [Uu: int] : $true ) ) ).

% fun.pred_transfer
thf(fact_875_nat__mono,axiom,
    ! [X: int,Y: int] :
      ( ( ord_less_eq_int @ X @ Y )
     => ( ord_less_eq_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ).

% nat_mono
thf(fact_876_ex__nat,axiom,
    ( ( ^ [P3: nat > $o] :
        ? [X8: nat] : ( P3 @ X8 ) )
    = ( ^ [P4: nat > $o] :
        ? [X3: int] :
          ( ( ord_less_eq_int @ zero_zero_int @ X3 )
          & ( P4 @ ( nat2 @ X3 ) ) ) ) ) ).

% ex_nat
thf(fact_877_all__nat,axiom,
    ( ( ^ [P3: nat > $o] :
        ! [X8: nat] : ( P3 @ X8 ) )
    = ( ^ [P4: nat > $o] :
        ! [X3: int] :
          ( ( ord_less_eq_int @ zero_zero_int @ X3 )
         => ( P4 @ ( nat2 @ X3 ) ) ) ) ) ).

% all_nat
thf(fact_878_eq__nat__nat__iff,axiom,
    ! [Z: int,Z5: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ Z )
     => ( ( ord_less_eq_int @ zero_zero_int @ Z5 )
       => ( ( ( nat2 @ Z )
            = ( nat2 @ Z5 ) )
          = ( Z = Z5 ) ) ) ) ).

% eq_nat_nat_iff
thf(fact_879_fun_ODomainp__rel,axiom,
    ! [R: $o > $o > $o] :
      ( ( domainp_int_o_int_o
        @ ( bNF_re5089333283451836215nt_o_o
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ R ) )
      = ( basic_pred_fun_int_o
        @ ^ [Uu: int] : $true
        @ ( domainp_o_o @ R ) ) ) ).

% fun.Domainp_rel
thf(fact_880_fun_ODomainp__rel,axiom,
    ! [R: nat > nat > $o] :
      ( ( domain7985844723471903900nt_nat
        @ ( bNF_re3715656647883201625at_nat
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ R ) )
      = ( basic_1842754918481324705nt_nat
        @ ^ [Uu: int] : $true
        @ ( domainp_nat_nat @ R ) ) ) ).

% fun.Domainp_rel
thf(fact_881_fun_ODomainp__rel,axiom,
    ! [R: int > int > $o] :
      ( ( domain9219075885666169684nt_int
        @ ( bNF_re4712519889275205905nt_int
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ R ) )
      = ( basic_1840264447972274429nt_int
        @ ^ [Uu: int] : $true
        @ ( domainp_int_int @ R ) ) ) ).

% fun.Domainp_rel
thf(fact_882_fun_ODomainp__rel,axiom,
    ! [R: ( int > $o ) > ( int > $o ) > $o] :
      ( ( domain8659272630029231332_int_o
        @ ( bNF_re3403563459893282935_int_o
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ R ) )
      = ( basic_1842322873297984402_int_o
        @ ^ [Uu: int] : $true
        @ ( domainp_int_o_int_o @ R ) ) ) ).

% fun.Domainp_rel
thf(fact_883_fun_ODomainp__rel,axiom,
    ! [R: ( int > int ) > ( int > int ) > $o] :
      ( ( domain4136455042513400810nt_int
        @ ( bNF_re711492959462206631nt_int
          @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
          @ R ) )
      = ( basic_1535474925015357768nt_int
        @ ^ [Uu: int] : $true
        @ ( domain9219075885666169684nt_int @ R ) ) ) ).

% fun.Domainp_rel
thf(fact_884_nat__mono__iff,axiom,
    ! [Z: int,W: int] :
      ( ( ord_less_int @ zero_zero_int @ Z )
     => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
        = ( ord_less_int @ W @ Z ) ) ) ).

% nat_mono_iff
thf(fact_885_mat__mod_Ovec__mod__eq,axiom,
    ! [M: int,V: vec_int] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( ord_less_eq_set_int @ ( vec_set_int2 @ V ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ M ) )
       => ( ( vector1199560857299316530ec_mod @ M @ V )
          = V ) ) ) ).

% mat_mod.vec_mod_eq
thf(fact_886_mat__mod_Ovec__mod__set__vec__same,axiom,
    ! [M: int,V: vec_int] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( ord_less_eq_set_int @ ( vec_set_int2 @ V ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ M ) )
       => ( ( vec_set_int2 @ ( vector1199560857299316530ec_mod @ M @ V ) )
          = ( vec_set_int2 @ V ) ) ) ) ).

% mat_mod.vec_mod_set_vec_same
thf(fact_887_nat__less__eq__zless,axiom,
    ! [W: int,Z: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ W )
     => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
        = ( ord_less_int @ W @ Z ) ) ) ).

% nat_less_eq_zless
thf(fact_888_nat__le__eq__zle,axiom,
    ! [W: int,Z: int] :
      ( ( ( ord_less_int @ zero_zero_int @ W )
        | ( ord_less_eq_int @ zero_zero_int @ Z ) )
     => ( ( ord_less_eq_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
        = ( ord_less_eq_int @ W @ Z ) ) ) ).

% nat_le_eq_zle
thf(fact_889_nat__mod__distrib,axiom,
    ! [X: int,Y: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ X )
     => ( ( ord_less_eq_int @ zero_zero_int @ Y )
       => ( ( nat2 @ ( modulo_modulo_int @ X @ Y ) )
          = ( modulo_modulo_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).

% nat_mod_distrib
thf(fact_890_count__vec__mod__eq,axiom,
    ! [V: vec_int,X: int] :
      ( ( ord_less_eq_set_int @ ( vec_set_int2 @ V ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ m ) )
     => ( ( count_int @ ( matrix7410472831921750563et_int @ V ) @ X )
        = ( count_int @ ( matrix7410472831921750563et_int @ ( vector1199560857299316530ec_mod @ m @ V ) ) @ X ) ) ) ).

% count_vec_mod_eq
thf(fact_891_nat__zero__as__int,axiom,
    ( zero_zero_nat
    = ( nat2 @ zero_zero_int ) ) ).

% nat_zero_as_int
thf(fact_892_eq__MM__Rel,axiom,
    ( bNF_re8187416184292455657ng_a_o @ ( vector2798151085771547010_Rel_a @ m )
    @ ( bNF_re6153771816476299306_a_o_o @ ( vector2798151085771547010_Rel_a @ m )
      @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
    @ ^ [F2: mat_int,F3: mat_int] :
        ( ( vector6118640873655855782at_mod @ m @ F2 )
        = ( vector6118640873655855782at_mod @ m @ F3 ) )
    @ ^ [Y2: mat_Fi443519135453058082ring_a,Z2: mat_Fi443519135453058082ring_a] : ( Y2 = Z2 ) ) ).

% eq_MM_Rel
thf(fact_893_right__total__relcompp__transfer,axiom,
    ! [B2: int > int > $o,A2: int > int > $o,C: int > int > $o] :
      ( ( right_total_int_int @ B2 )
     => ( bNF_re7404067519983032617_int_o
        @ ( bNF_re3403563459893282935_int_o @ A2
          @ ( bNF_re5089333283451836215nt_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re8651060166502312541_int_o
          @ ( bNF_re3403563459893282935_int_o @ B2
            @ ( bNF_re5089333283451836215nt_o_o @ C
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ( bNF_re3403563459893282935_int_o @ A2
            @ ( bNF_re5089333283451836215nt_o_o @ C
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) ) )
        @ ^ [R2: int > int > $o,S4: int > int > $o,X3: int,Z3: int] :
          ? [Y6: int] :
            ( ( member_int @ Y6 @ ( collect_int @ ( domainp_int_int @ B2 ) ) )
            & ( R2 @ X3 @ Y6 )
            & ( S4 @ Y6 @ Z3 ) )
        @ relcompp_int_int_int ) ) ).

% right_total_relcompp_transfer
thf(fact_894_right__total__relcompp__transfer,axiom,
    ! [B2: int > finite_mod_ring_a > $o,A2: int > int > $o,C: int > int > $o] :
      ( ( right_2909008500229168952ring_a @ B2 )
     => ( bNF_re5072219456266741671_int_o
        @ ( bNF_re1393113005842329636ng_a_o @ A2
          @ ( bNF_re8290846538823883642_a_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re1800150913247624340_int_o
          @ ( bNF_re3873409527727426490_int_o @ B2
            @ ( bNF_re5089333283451836215nt_o_o @ C
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ( bNF_re3403563459893282935_int_o @ A2
            @ ( bNF_re5089333283451836215nt_o_o @ C
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) ) )
        @ ^ [R2: int > int > $o,S4: int > int > $o,X3: int,Z3: int] :
          ? [Y6: int] :
            ( ( member_int @ Y6 @ ( collect_int @ ( domain6543890336852369843ring_a @ B2 ) ) )
            & ( R2 @ X3 @ Y6 )
            & ( S4 @ Y6 @ Z3 ) )
        @ relcom1383171076355693396_a_int ) ) ).

% right_total_relcompp_transfer
thf(fact_895_right__total__relcompp__transfer,axiom,
    ! [B2: vec_int > vec_Fi4296597256376197294ring_a > $o,A2: int > int > $o,C: int > int > $o] :
      ( ( right_7341149013462710248ring_a @ B2 )
     => ( bNF_re8684700889500088319_int_o
        @ ( bNF_re3675534777603958660ng_a_o @ A2
          @ ( bNF_re507051067509135658_a_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re1812577071873895326_int_o
          @ ( bNF_re7877854262379379050_int_o @ B2
            @ ( bNF_re5089333283451836215nt_o_o @ C
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ( bNF_re3403563459893282935_int_o @ A2
            @ ( bNF_re5089333283451836215nt_o_o @ C
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) ) )
        @ ^ [R2: int > vec_int > $o,S4: vec_int > int > $o,X3: int,Z3: int] :
          ? [Y6: vec_int] :
            ( ( member_vec_int @ Y6 @ ( collect_vec_int @ ( domain4015354059925764579ring_a @ B2 ) ) )
            & ( R2 @ X3 @ Y6 )
            & ( S4 @ Y6 @ Z3 ) )
        @ relcom6250398543212868665_a_int ) ) ).

% right_total_relcompp_transfer
thf(fact_896_right__total__relcompp__transfer,axiom,
    ! [B2: mat_int > mat_Fi443519135453058082ring_a > $o,A2: int > int > $o,C: int > int > $o] :
      ( ( right_6272992325622558440ring_a @ B2 )
     => ( bNF_re7916767694611508199_int_o
        @ ( bNF_re4404534803379308188ng_a_o @ A2
          @ ( bNF_re6153771816476299306_a_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re6198949750846496950_int_o
          @ ( bNF_re1270729808710627434_int_o @ B2
            @ ( bNF_re5089333283451836215nt_o_o @ C
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
          @ ( bNF_re3403563459893282935_int_o @ A2
            @ ( bNF_re5089333283451836215nt_o_o @ C
              @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) ) )
        @ ^ [R2: int > mat_int > $o,S4: mat_int > int > $o,X3: int,Z3: int] :
          ? [Y6: mat_int] :
            ( ( member_mat_int @ Y6 @ ( collect_mat_int @ ( domain2947197372085612771ring_a @ B2 ) ) )
            & ( R2 @ X3 @ Y6 )
            & ( S4 @ Y6 @ Z3 ) )
        @ relcom4976855403015346093_a_int ) ) ).

% right_total_relcompp_transfer
thf(fact_897_mat__mod__type_Oindex__MV__Rel,axiom,
    ! [M: int] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( bNF_re1259227427626606373ring_a @ ( vector5230790432342831627_Rel_a @ M )
        @ ( bNF_re2201348192133994456ring_a
          @ ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 )
          @ ( vector3024231343486012919_Rel_a @ M ) )
        @ ^ [V3: vec_int,I5: nat] : ( if_int @ ( ord_less_nat @ I5 @ ( dim_vec_int @ V3 ) ) @ ( vec_index_int @ V3 @ I5 ) @ zero_zero_int )
        @ ^ [V3: vec_Fi4296597256376197294ring_a,I5: nat] : ( if_Finite_mod_ring_a @ ( ord_less_nat @ I5 @ ( dim_ve9152325144110082507ring_a @ V3 ) ) @ ( vec_in8573817152773094745ring_a @ V3 @ I5 ) @ zero_z7902377541816115708ring_a ) ) ) ).

% mat_mod_type.index_MV_Rel
thf(fact_898_mat__mod__type__axioms,axiom,
    vector2974885785920725647type_a @ type_a @ m ).

% mat_mod_type_axioms
thf(fact_899_count__empty,axiom,
    ! [A: int] :
      ( ( count_int @ zero_z3170743180189231877et_int @ A )
      = zero_zero_nat ) ).

% count_empty
thf(fact_900_eq__m__OO__MM__Rel,axiom,
    ( ( relcom6459136143736567059ring_a
      @ ^ [M5: mat_int,M6: mat_int] :
          ( ( vector6118640873655855782at_mod @ m @ M5 )
          = ( vector6118640873655855782at_mod @ m @ M6 ) )
      @ ( vector2798151085771547010_Rel_a @ m ) )
    = ( vector2798151085771547010_Rel_a @ m ) ) ).

% eq_m_OO_MM_Rel
thf(fact_901_mat__mod__type_Oeq__MM__Rel,axiom,
    ! [M: int] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( bNF_re8187416184292455657ng_a_o @ ( vector2798151085771547010_Rel_a @ M )
        @ ( bNF_re6153771816476299306_a_o_o @ ( vector2798151085771547010_Rel_a @ M )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ^ [F2: mat_int,F3: mat_int] :
            ( ( vector6118640873655855782at_mod @ M @ F2 )
            = ( vector6118640873655855782at_mod @ M @ F3 ) )
        @ ^ [Y2: mat_Fi443519135453058082ring_a,Z2: mat_Fi443519135453058082ring_a] : ( Y2 = Z2 ) ) ) ).

% mat_mod_type.eq_MM_Rel
thf(fact_902_mat__mod__type_Oeq__m__OO__MM__Rel,axiom,
    ! [M: int] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( ( relcom6459136143736567059ring_a
          @ ^ [M5: mat_int,M6: mat_int] :
              ( ( vector6118640873655855782at_mod @ M @ M5 )
              = ( vector6118640873655855782at_mod @ M @ M6 ) )
          @ ( vector2798151085771547010_Rel_a @ M ) )
        = ( vector2798151085771547010_Rel_a @ M ) ) ) ).

% mat_mod_type.eq_m_OO_MM_Rel
thf(fact_903_mat__mod__type_Oaxioms_I1_J,axiom,
    ! [M: int] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( vector2311527483241216340at_mod @ M ) ) ).

% mat_mod_type.axioms(1)
thf(fact_904_mat__mod_Omat__mod_Ocong,axiom,
    vector6118640873655855782at_mod = vector6118640873655855782at_mod ).

% mat_mod.mat_mod.cong
thf(fact_905_mat__mod__type_Omod__to__int__mod__ring,axiom,
    ! [M: int,X: finite_mod_ring_a] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( ( modulo_modulo_int @ ( finite1095367895020317408ring_a @ X ) @ M )
        = ( finite1095367895020317408ring_a @ X ) ) ) ).

% mat_mod_type.mod_to_int_mod_ring
thf(fact_906_mat__mod__type_Oeq__MV__Rel,axiom,
    ! [M: int] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( bNF_re151890839321169105ng_a_o @ ( vector5230790432342831627_Rel_a @ M )
        @ ( bNF_re507051067509135658_a_o_o @ ( vector5230790432342831627_Rel_a @ M )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ^ [V3: vec_int,V4: vec_int] :
            ( ( vector1199560857299316530ec_mod @ M @ V3 )
            = ( vector1199560857299316530ec_mod @ M @ V4 ) )
        @ ^ [Y2: vec_Fi4296597256376197294ring_a,Z2: vec_Fi4296597256376197294ring_a] : ( Y2 = Z2 ) ) ) ).

% mat_mod_type.eq_MV_Rel
thf(fact_907_mat__mod__type_Odomain__MM__rel,axiom,
    ! [M: int] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( ( domain2947197372085612771ring_a @ ( vector2798151085771547010_Rel_a @ M ) )
        = ( ^ [F2: mat_int] : $true ) ) ) ).

% mat_mod_type.domain_MM_rel
thf(fact_908_mat__mod__type_Oleft__total__MM__Rel,axiom,
    ! [M: int] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( left_t6774590509652353697ring_a @ ( vector2798151085771547010_Rel_a @ M ) ) ) ).

% mat_mod_type.left_total_MM_Rel
thf(fact_909_mat__mod__type_Oright__unique__MM__Rel,axiom,
    ! [M: int] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( right_1339649294516398705ring_a @ ( vector2798151085771547010_Rel_a @ M ) ) ) ).

% mat_mod_type.right_unique_MM_Rel
thf(fact_910_mat__mod__type_Obi__total__MM__Rel,axiom,
    ! [M: int] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( bi_tot8466079176331800225ring_a @ ( vector2798151085771547010_Rel_a @ M ) ) ) ).

% mat_mod_type.bi_total_MM_Rel
thf(fact_911_mat__mod__type_Oright__total__MM__Rel,axiom,
    ! [M: int] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( right_6272992325622558440ring_a @ ( vector2798151085771547010_Rel_a @ M ) ) ) ).

% mat_mod_type.right_total_MM_Rel
thf(fact_912_mat__mod__type_Oleft__total__MV__Rel,axiom,
    ! [M: int] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( left_t7842747197492505505ring_a @ ( vector5230790432342831627_Rel_a @ M ) ) ) ).

% mat_mod_type.left_total_MV_Rel
thf(fact_913_mat__mod__type_Oright__unique__MV__Rel,axiom,
    ! [M: int] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( right_2407805982356550513ring_a @ ( vector5230790432342831627_Rel_a @ M ) ) ) ).

% mat_mod_type.right_unique_MV_Rel
thf(fact_914_mat__mod__type_Oright__total__MV__Rel,axiom,
    ! [M: int] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( right_7341149013462710248ring_a @ ( vector5230790432342831627_Rel_a @ M ) ) ) ).

% mat_mod_type.right_total_MV_Rel
thf(fact_915_mat__mod__type_Obi__total__MV__Rel,axiom,
    ! [M: int] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( bi_tot310863827317176225ring_a @ ( vector5230790432342831627_Rel_a @ M ) ) ) ).

% mat_mod_type.bi_total_MV_Rel
thf(fact_916_mat__mod__type_Odomain__MV__rel,axiom,
    ! [M: int] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( ( domain4015354059925764579ring_a @ ( vector5230790432342831627_Rel_a @ M ) )
        = ( ^ [F2: vec_int] : $true ) ) ) ).

% mat_mod_type.domain_MV_rel
thf(fact_917_mat__mod__type_Oto__int__mod__ring__of__int__mod,axiom,
    ! [M: int,X: int] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( ( finite1095367895020317408ring_a @ ( ring_18169885480643366966ring_a @ X ) )
        = ( modulo_modulo_int @ X @ M ) ) ) ).

% mat_mod_type.to_int_mod_ring_of_int_mod
thf(fact_918_mat__mod__type_Ovec__mod__to__int__vec,axiom,
    ! [M: int,V: vec_Fi4296597256376197294ring_a] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( ( vector1199560857299316530ec_mod @ M @ ( map_ve50164598268879916_a_int @ finite1095367895020317408ring_a @ V ) )
        = ( map_ve50164598268879916_a_int @ finite1095367895020317408ring_a @ V ) ) ) ).

% mat_mod_type.vec_mod_to_int_vec
thf(fact_919_zero__multiset_Orep__eq,axiom,
    ( ( count_int @ zero_z3170743180189231877et_int )
    = ( ^ [A5: int] : zero_zero_nat ) ) ).

% zero_multiset.rep_eq
thf(fact_920_count__vec__count__mset,axiom,
    ! [V: vec_int,F: finite_mod_ring_a > int,A2: multis3731679216105815691ring_a,A: int] :
      ( ( ( matrix7410472831921750563et_int @ V )
        = ( image_7357852445201009398_a_int @ F @ A2 ) )
     => ( ( count_int @ ( matrix7410472831921750563et_int @ V ) @ A )
        = ( count_int @ ( image_7357852445201009398_a_int @ F @ A2 ) @ A ) ) ) ).

% count_vec_count_mset
thf(fact_921_mat__mod__type_Ozero__MV__Rel,axiom,
    ! [M: int,N: nat] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( vector5230790432342831627_Rel_a @ M @ ( zero_vec_int @ N ) @ ( zero_v1122566495420860901ring_a @ N ) ) ) ).

% mat_mod_type.zero_MV_Rel
thf(fact_922_mat__mod__type_OMV__Rel__def,axiom,
    ! [M: int,V: vec_int,V2: vec_Fi4296597256376197294ring_a] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( ( vector5230790432342831627_Rel_a @ M @ V @ V2 )
        = ( ( vector1199560857299316530ec_mod @ M @ V )
          = ( map_ve50164598268879916_a_int @ finite1095367895020317408ring_a @ V2 ) ) ) ) ).

% mat_mod_type.MV_Rel_def
thf(fact_923_mat__mod__type_Oone__MV__Rel,axiom,
    ! [M: int,N: nat,I: nat] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( vector5230790432342831627_Rel_a @ M @ ( unit_vec_int @ N @ I ) @ ( unit_v6648808783362777473ring_a @ N @ I ) ) ) ).

% mat_mod_type.one_MV_Rel
thf(fact_924_mat__mod__type_Olt__dim__vec__MV__Rel,axiom,
    ! [M: int] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( bNF_re7850819276413326442_nat_o @ ( vector5230790432342831627_Rel_a @ M )
        @ ( bNF_re4705727531993890431at_o_o
          @ ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ^ [V3: vec_int,J2: nat] : ( ord_less_nat @ J2 @ ( dim_vec_int @ V3 ) )
        @ ^ [V3: vec_Fi4296597256376197294ring_a,J2: nat] : ( ord_less_nat @ J2 @ ( dim_ve9152325144110082507ring_a @ V3 ) ) ) ) ).

% mat_mod_type.lt_dim_vec_MV_Rel
thf(fact_925_mat__mod__type_Oeq__dim__vec__MV__Rel,axiom,
    ! [M: int] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( bNF_re5216812267390093516at_nat @ ( vector5230790432342831627_Rel_a @ M )
        @ ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 )
        @ dim_vec_int
        @ dim_ve9152325144110082507ring_a ) ) ).

% mat_mod_type.eq_dim_vec_MV_Rel
thf(fact_926_count__vec__empty,axiom,
    ! [V: vec_int,A: int] :
      ( ( ( dim_vec_int @ V )
        = zero_zero_nat )
     => ( ( count_int @ ( matrix7410472831921750563et_int @ V ) @ A )
        = zero_zero_nat ) ) ).

% count_vec_empty
thf(fact_927_count__vec__empty,axiom,
    ! [V: vec_Fi4296597256376197294ring_a,A: finite_mod_ring_a] :
      ( ( ( dim_ve9152325144110082507ring_a @ V )
        = zero_zero_nat )
     => ( ( count_7654011124160779523ring_a @ ( matrix5859482775909362318ring_a @ V ) @ A )
        = zero_zero_nat ) ) ).

% count_vec_empty
thf(fact_928_vec__count__lt__dim,axiom,
    ! [V: vec_int,A: int] : ( ord_less_eq_nat @ ( count_int @ ( matrix7410472831921750563et_int @ V ) @ A ) @ ( dim_vec_int @ V ) ) ).

% vec_count_lt_dim
thf(fact_929_vec__count__lt__dim,axiom,
    ! [V: vec_Fi4296597256376197294ring_a,A: finite_mod_ring_a] : ( ord_less_eq_nat @ ( count_7654011124160779523ring_a @ ( matrix5859482775909362318ring_a @ V ) @ A ) @ ( dim_ve9152325144110082507ring_a @ V ) ) ).

% vec_count_lt_dim
thf(fact_930_setv__not__in__count0__iff,axiom,
    ! [A: vec_Fi4296597256376197294ring_a,V: vec_ve5128822793932996635ring_a] :
      ( ( ~ ( member1106766863034010949ring_a @ A @ ( vec_se3276121494910751146ring_a @ V ) ) )
      = ( ( count_5653161720919377392ring_a @ ( matrix3196578302645433509ring_a @ V ) @ A )
        = zero_zero_nat ) ) ).

% setv_not_in_count0_iff
thf(fact_931_setv__not__in__count0__iff,axiom,
    ! [A: mat_Fi443519135453058082ring_a,V: vec_ma98051958688905615ring_a] :
      ( ( ~ ( member6477060778965647545ring_a @ A @ ( vec_se8646415410842387742ring_a @ V ) ) )
      = ( ( count_1800083599996238180ring_a @ ( matrix8566872218577070105ring_a @ V ) @ A )
        = zero_zero_nat ) ) ).

% setv_not_in_count0_iff
thf(fact_932_setv__not__in__count0__iff,axiom,
    ! [A: nat,V: vec_nat] :
      ( ( ~ ( member_nat @ A @ ( vec_set_nat @ V ) ) )
      = ( ( count_nat @ ( matrix7412963302430800839et_nat @ V ) @ A )
        = zero_zero_nat ) ) ).

% setv_not_in_count0_iff
thf(fact_933_setv__not__in__count0__iff,axiom,
    ! [A: int,V: vec_int] :
      ( ( ~ ( member_int @ A @ ( vec_set_int2 @ V ) ) )
      = ( ( count_int @ ( matrix7410472831921750563et_int @ V ) @ A )
        = zero_zero_nat ) ) ).

% setv_not_in_count0_iff
thf(fact_934_setv__not__in__count0__iff,axiom,
    ! [A: finite_mod_ring_a,V: vec_Fi4296597256376197294ring_a] :
      ( ( ~ ( member3034048621153491438ring_a @ A @ ( vec_se7251946917745546697ring_a @ V ) ) )
      = ( ( count_7654011124160779523ring_a @ ( matrix5859482775909362318ring_a @ V ) @ A )
        = zero_zero_nat ) ) ).

% setv_not_in_count0_iff
thf(fact_935_of__int__hom_Olim__inj__hom__count__vec,axiom,
    ! [V: vec_int,Univ: set_int,X: int] :
      ( ( ord_less_eq_set_int @ ( vec_set_int2 @ V ) @ Univ )
     => ( ( member_int @ X @ Univ )
       => ( ( count_int @ ( matrix7410472831921750563et_int @ V ) @ X )
          = ( count_real @ ( matrix1887623593855636259t_real @ ( map_vec_int_real @ ring_1_of_int_real @ V ) ) @ ( ring_1_of_int_real @ X ) ) ) ) ) ).

% of_int_hom.lim_inj_hom_count_vec
thf(fact_936_of__int__hom_Olim__inj__hom__count__vec,axiom,
    ! [V: vec_int,Univ: set_int,X: int] :
      ( ( ord_less_eq_set_int @ ( vec_set_int2 @ V ) @ Univ )
     => ( ( member_int @ X @ Univ )
       => ( ( count_int @ ( matrix7410472831921750563et_int @ V ) @ X )
          = ( count_int @ ( matrix7410472831921750563et_int @ ( map_vec_int_int @ ring_1_of_int_int @ V ) ) @ ( ring_1_of_int_int @ X ) ) ) ) ) ).

% of_int_hom.lim_inj_hom_count_vec
thf(fact_937_mat__mod__type_Ovec__mod__v__representative,axiom,
    ! [M: int,V: vec_int] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( ( vector1199560857299316530ec_mod @ M @ V )
        = ( map_ve50164598268879916_a_int @ finite1095367895020317408ring_a @ ( map_ve1626356591056799954ring_a @ ring_18169885480643366966ring_a @ V ) ) ) ) ).

% mat_mod_type.vec_mod_v_representative
thf(fact_938_mat__mod__type_Oto__int__vec__index,axiom,
    ! [M: int,I: nat,V: vec_Fi4296597256376197294ring_a] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( ( ord_less_nat @ I @ ( dim_ve9152325144110082507ring_a @ V ) )
       => ( ( vec_index_int @ ( map_ve50164598268879916_a_int @ finite1095367895020317408ring_a @ V ) @ I )
          = ( finite1095367895020317408ring_a @ ( vec_in8573817152773094745ring_a @ V @ I ) ) ) ) ) ).

% mat_mod_type.to_int_vec_index
thf(fact_939_vec__contains__count__gt1__iff,axiom,
    ! [A: vec_Fi4296597256376197294ring_a,V: vec_ve5128822793932996635ring_a] :
      ( ( member1106766863034010949ring_a @ A @ ( vec_se3276121494910751146ring_a @ V ) )
      = ( ord_less_eq_nat @ one_one_nat @ ( count_5653161720919377392ring_a @ ( matrix3196578302645433509ring_a @ V ) @ A ) ) ) ).

% vec_contains_count_gt1_iff
thf(fact_940_vec__contains__count__gt1__iff,axiom,
    ! [A: mat_Fi443519135453058082ring_a,V: vec_ma98051958688905615ring_a] :
      ( ( member6477060778965647545ring_a @ A @ ( vec_se8646415410842387742ring_a @ V ) )
      = ( ord_less_eq_nat @ one_one_nat @ ( count_1800083599996238180ring_a @ ( matrix8566872218577070105ring_a @ V ) @ A ) ) ) ).

% vec_contains_count_gt1_iff
thf(fact_941_vec__contains__count__gt1__iff,axiom,
    ! [A: nat,V: vec_nat] :
      ( ( member_nat @ A @ ( vec_set_nat @ V ) )
      = ( ord_less_eq_nat @ one_one_nat @ ( count_nat @ ( matrix7412963302430800839et_nat @ V ) @ A ) ) ) ).

% vec_contains_count_gt1_iff
thf(fact_942_vec__contains__count__gt1__iff,axiom,
    ! [A: int,V: vec_int] :
      ( ( member_int @ A @ ( vec_set_int2 @ V ) )
      = ( ord_less_eq_nat @ one_one_nat @ ( count_int @ ( matrix7410472831921750563et_int @ V ) @ A ) ) ) ).

% vec_contains_count_gt1_iff
thf(fact_943_vec__contains__count__gt1__iff,axiom,
    ! [A: finite_mod_ring_a,V: vec_Fi4296597256376197294ring_a] :
      ( ( member3034048621153491438ring_a @ A @ ( vec_se7251946917745546697ring_a @ V ) )
      = ( ord_less_eq_nat @ one_one_nat @ ( count_7654011124160779523ring_a @ ( matrix5859482775909362318ring_a @ V ) @ A ) ) ) ).

% vec_contains_count_gt1_iff
thf(fact_944_right__total__Domainp__transfer,axiom,
    ! [B2: int > int > $o,A2: int > int > $o] :
      ( ( right_total_int_int @ B2 )
     => ( bNF_re2642688597062869533_int_o
        @ ( bNF_re3403563459893282935_int_o @ A2
          @ ( bNF_re5089333283451836215nt_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re5089333283451836215nt_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ^ [T: int > int > $o,X3: int] :
          ? [Y6: int] :
            ( ( member_int @ Y6 @ ( collect_int @ ( domainp_int_int @ B2 ) ) )
            & ( T @ X3 @ Y6 ) )
        @ domainp_int_int ) ) ).

% right_total_Domainp_transfer
thf(fact_945_right__total__Domainp__transfer,axiom,
    ! [B2: int > finite_mod_ring_a > $o,A2: int > int > $o] :
      ( ( right_2909008500229168952ring_a @ B2 )
     => ( bNF_re2917227035190921876_int_o
        @ ( bNF_re1393113005842329636ng_a_o @ A2
          @ ( bNF_re8290846538823883642_a_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re5089333283451836215nt_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ^ [T: int > int > $o,X3: int] :
          ? [Y6: int] :
            ( ( member_int @ Y6 @ ( collect_int @ ( domain6543890336852369843ring_a @ B2 ) ) )
            & ( T @ X3 @ Y6 ) )
        @ domain6543890336852369843ring_a ) ) ).

% right_total_Domainp_transfer
thf(fact_946_right__total__Domainp__transfer,axiom,
    ! [B2: vec_int > vec_Fi4296597256376197294ring_a > $o,A2: int > int > $o] :
      ( ( right_7341149013462710248ring_a @ B2 )
     => ( bNF_re131580980352085790_int_o
        @ ( bNF_re3675534777603958660ng_a_o @ A2
          @ ( bNF_re507051067509135658_a_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re5089333283451836215nt_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ^ [T: int > vec_int > $o,X3: int] :
          ? [Y6: vec_int] :
            ( ( member_vec_int @ Y6 @ ( collect_vec_int @ ( domain4015354059925764579ring_a @ B2 ) ) )
            & ( T @ X3 @ Y6 ) )
        @ domain1918902550050569536ring_a ) ) ).

% right_total_Domainp_transfer
thf(fact_947_right__total__Domainp__transfer,axiom,
    ! [B2: mat_int > mat_Fi443519135453058082ring_a > $o,A2: int > int > $o] :
      ( ( right_6272992325622558440ring_a @ B2 )
     => ( bNF_re6408424020554474550_int_o
        @ ( bNF_re4404534803379308188ng_a_o @ A2
          @ ( bNF_re6153771816476299306_a_o_o @ B2
            @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
        @ ( bNF_re5089333283451836215nt_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ^ [T: int > mat_int > $o,X3: int] :
          ? [Y6: mat_int] :
            ( ( member_mat_int @ Y6 @ ( collect_mat_int @ ( domain2947197372085612771ring_a @ B2 ) ) )
            & ( T @ X3 @ Y6 ) )
        @ domain7289196465982206132ring_a ) ) ).

% right_total_Domainp_transfer
thf(fact_948_mat__mod_Ocount__vec__mod__eq,axiom,
    ! [M: int,V: vec_int,X: int] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( ord_less_eq_set_int @ ( vec_set_int2 @ V ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ M ) )
       => ( ( count_int @ ( matrix7410472831921750563et_int @ V ) @ X )
          = ( count_int @ ( matrix7410472831921750563et_int @ ( vector1199560857299316530ec_mod @ M @ V ) ) @ X ) ) ) ) ).

% mat_mod.count_vec_mod_eq
thf(fact_949_mat__mod__eq__elements__cond,axiom,
    ! [M2: mat_int] :
      ( ( ord_less_eq_set_int @ ( elements_mat_int @ M2 ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ m ) )
     => ( ( elements_mat_int @ ( vector6118640873655855782at_mod @ m @ M2 ) )
        = ( elements_mat_int @ M2 ) ) ) ).

% mat_mod_eq_elements_cond
thf(fact_950_mat__mod__eq__cond,axiom,
    ! [M2: mat_int] :
      ( ( ord_less_eq_set_int @ ( elements_mat_int @ M2 ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ m ) )
     => ( ( vector6118640873655855782at_mod @ m @ M2 )
        = M2 ) ) ).

% mat_mod_eq_cond
thf(fact_951_mat__mod__cond__iff,axiom,
    ! [M2: mat_int,P: mat_int > $o] :
      ( ( ord_less_eq_set_int @ ( elements_mat_int @ M2 ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ m ) )
     => ( ( P @ M2 )
        = ( P @ ( vector6118640873655855782at_mod @ m @ M2 ) ) ) ) ).

% mat_mod_cond_iff
thf(fact_952_MM__Rel__def,axiom,
    ! [F: mat_int,F4: mat_Fi443519135453058082ring_a] :
      ( ( vector2798151085771547010_Rel_a @ m @ F @ F4 )
      = ( ( vector6118640873655855782at_mod @ m @ F )
        = ( map_ma7999993494926133152_a_int @ finite1095367895020317408ring_a @ F4 ) ) ) ).

% MM_Rel_def
thf(fact_953_local_Omat__mod__def,axiom,
    ! [M2: mat_int] :
      ( ( vector6118640873655855782at_mod @ m @ M2 )
      = ( map_mat_int_int
        @ ^ [X3: int] : ( modulo_modulo_int @ X3 @ m )
        @ M2 ) ) ).

% local.mat_mod_def
thf(fact_954_mat__mod__elements__in,axiom,
    ! [X: int,M2: mat_int] :
      ( ( member_int @ X @ ( elements_mat_int @ M2 ) )
     => ( member_int @ ( modulo_modulo_int @ X @ m ) @ ( elements_mat_int @ ( vector6118640873655855782at_mod @ m @ M2 ) ) ) ) ).

% mat_mod_elements_in
thf(fact_955_mat__mod__to__int__mat,axiom,
    ! [N3: mat_Fi443519135453058082ring_a] :
      ( ( vector6118640873655855782at_mod @ m @ ( map_ma7999993494926133152_a_int @ finite1095367895020317408ring_a @ N3 ) )
      = ( map_ma7999993494926133152_a_int @ finite1095367895020317408ring_a @ N3 ) ) ).

% mat_mod_to_int_mat
thf(fact_956_of__int__hom_Omat__hom__inj__lim,axiom,
    ! [M2: mat_int,Univ: set_int,N3: mat_int] :
      ( ( ord_less_eq_set_int @ ( elements_mat_int @ M2 ) @ Univ )
     => ( ( ord_less_eq_set_int @ ( elements_mat_int @ N3 ) @ Univ )
       => ( ( ( map_mat_int_int @ ring_1_of_int_int @ M2 )
            = ( map_mat_int_int @ ring_1_of_int_int @ N3 ) )
         => ( M2 = N3 ) ) ) ) ).

% of_int_hom.mat_hom_inj_lim
thf(fact_957_of__int__hom_Omat__hom__inj__lim,axiom,
    ! [M2: mat_int,Univ: set_int,N3: mat_int] :
      ( ( ord_less_eq_set_int @ ( elements_mat_int @ M2 ) @ Univ )
     => ( ( ord_less_eq_set_int @ ( elements_mat_int @ N3 ) @ Univ )
       => ( ( ( map_mat_int_real @ ring_1_of_int_real @ M2 )
            = ( map_mat_int_real @ ring_1_of_int_real @ N3 ) )
         => ( M2 = N3 ) ) ) ) ).

% of_int_hom.mat_hom_inj_lim
thf(fact_958_Matrix__Vector__Extras_Oof__int__hom_Omat__hom__inj,axiom,
    ! [A2: mat_int,B2: mat_int] :
      ( ( ( map_mat_int_int @ ring_1_of_int_int @ A2 )
        = ( map_mat_int_int @ ring_1_of_int_int @ B2 ) )
     => ( A2 = B2 ) ) ).

% Matrix_Vector_Extras.of_int_hom.mat_hom_inj
thf(fact_959_Matrix__Vector__Extras_Oof__int__hom_Omat__hom__inj,axiom,
    ! [A2: mat_int,B2: mat_int] :
      ( ( ( map_mat_int_real @ ring_1_of_int_real @ A2 )
        = ( map_mat_int_real @ ring_1_of_int_real @ B2 ) )
     => ( A2 = B2 ) ) ).

% Matrix_Vector_Extras.of_int_hom.mat_hom_inj
thf(fact_960_to__int__mod__ring__hom_Omat__hom__inj,axiom,
    ! [A2: mat_Fi443519135453058082ring_a,B2: mat_Fi443519135453058082ring_a] :
      ( ( ( map_ma7999993494926133152_a_int @ finite1095367895020317408ring_a @ A2 )
        = ( map_ma7999993494926133152_a_int @ finite1095367895020317408ring_a @ B2 ) )
     => ( A2 = B2 ) ) ).

% to_int_mod_ring_hom.mat_hom_inj
thf(fact_961_Matrix__Vector__Extras_Oinj__zero__hom_Omat__hom__inj,axiom,
    ! [Hom: finite_mod_ring_a > int,A2: mat_Fi443519135453058082ring_a,B2: mat_Fi443519135453058082ring_a] :
      ( ( ring_i3475985505635201454_a_int @ Hom )
     => ( ( ( map_ma7999993494926133152_a_int @ Hom @ A2 )
          = ( map_ma7999993494926133152_a_int @ Hom @ B2 ) )
       => ( A2 = B2 ) ) ) ).

% Matrix_Vector_Extras.inj_zero_hom.mat_hom_inj
thf(fact_962_Matrix__Vector__Extras_Oinj__zero__hom_Omat__hom__inj,axiom,
    ! [Hom: int > int,A2: mat_int,B2: mat_int] :
      ( ( ring_i7091729277519141597nt_int @ Hom )
     => ( ( ( map_mat_int_int @ Hom @ A2 )
          = ( map_mat_int_int @ Hom @ B2 ) )
       => ( A2 = B2 ) ) ) ).

% Matrix_Vector_Extras.inj_zero_hom.mat_hom_inj
thf(fact_963_Matrix__Vector__Extras_Oinj__zero__hom_Omat__hom__inj,axiom,
    ! [Hom: int > finite_mod_ring_a,A2: mat_int,B2: mat_int] :
      ( ( ring_i5052177498423121492ring_a @ Hom )
     => ( ( ( map_ma352813450859277382ring_a @ Hom @ A2 )
          = ( map_ma352813450859277382ring_a @ Hom @ B2 ) )
       => ( A2 = B2 ) ) ) ).

% Matrix_Vector_Extras.inj_zero_hom.mat_hom_inj
thf(fact_964_mat__mod_Omat__mod__elements__in,axiom,
    ! [M: int,X: int,M2: mat_int] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( member_int @ X @ ( elements_mat_int @ M2 ) )
       => ( member_int @ ( modulo_modulo_int @ X @ M ) @ ( elements_mat_int @ ( vector6118640873655855782at_mod @ M @ M2 ) ) ) ) ) ).

% mat_mod.mat_mod_elements_in
thf(fact_965_mat__mod_Omat__mod__def,axiom,
    ! [M: int,M2: mat_int] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( vector6118640873655855782at_mod @ M @ M2 )
        = ( map_mat_int_int
          @ ^ [X3: int] : ( modulo_modulo_int @ X3 @ M )
          @ M2 ) ) ) ).

% mat_mod.mat_mod_def
thf(fact_966_mat__mod__type_Omat__mod__to__int__mat,axiom,
    ! [M: int,N3: mat_Fi443519135453058082ring_a] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( ( vector6118640873655855782at_mod @ M @ ( map_ma7999993494926133152_a_int @ finite1095367895020317408ring_a @ N3 ) )
        = ( map_ma7999993494926133152_a_int @ finite1095367895020317408ring_a @ N3 ) ) ) ).

% mat_mod_type.mat_mod_to_int_mat
thf(fact_967_mat__mod_Omat__mod__eq__cond,axiom,
    ! [M: int,M2: mat_int] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( ord_less_eq_set_int @ ( elements_mat_int @ M2 ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ M ) )
       => ( ( vector6118640873655855782at_mod @ M @ M2 )
          = M2 ) ) ) ).

% mat_mod.mat_mod_eq_cond
thf(fact_968_mat__mod_Omat__mod__cond__iff,axiom,
    ! [M: int,M2: mat_int,P: mat_int > $o] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( ord_less_eq_set_int @ ( elements_mat_int @ M2 ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ M ) )
       => ( ( P @ M2 )
          = ( P @ ( vector6118640873655855782at_mod @ M @ M2 ) ) ) ) ) ).

% mat_mod.mat_mod_cond_iff
thf(fact_969_mat__mod_Omat__mod__eq__elements__cond,axiom,
    ! [M: int,M2: mat_int] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( ord_less_eq_set_int @ ( elements_mat_int @ M2 ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ M ) )
       => ( ( elements_mat_int @ ( vector6118640873655855782at_mod @ M @ M2 ) )
          = ( elements_mat_int @ M2 ) ) ) ) ).

% mat_mod.mat_mod_eq_elements_cond
thf(fact_970_mat__mod__type_OMM__Rel__def,axiom,
    ! [M: int,F: mat_int,F4: mat_Fi443519135453058082ring_a] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( ( vector2798151085771547010_Rel_a @ M @ F @ F4 )
        = ( ( vector6118640873655855782at_mod @ M @ F )
          = ( map_ma7999993494926133152_a_int @ finite1095367895020317408ring_a @ F4 ) ) ) ) ).

% mat_mod_type.MM_Rel_def
thf(fact_971_mat__mod__N__representative,axiom,
    ! [N3: mat_int] :
      ( ( vector6118640873655855782at_mod @ m @ N3 )
      = ( map_ma7999993494926133152_a_int @ finite1095367895020317408ring_a @ ( map_ma352813450859277382ring_a @ ring_18169885480643366966ring_a @ N3 ) ) ) ).

% mat_mod_N_representative
thf(fact_972_mod__type__axioms,axiom,
    vector4745807456731380595type_a @ type_a @ m ).

% mod_type_axioms
thf(fact_973_mat__mod__elements__map,axiom,
    ! [X: int,M2: mat_int] :
      ( ( member_int @ X @ ( elements_mat_int @ M2 ) )
     => ( ( elements_mat_int @ ( vector6118640873655855782at_mod @ m @ M2 ) )
        = ( image_int_int
          @ ^ [X3: int] : ( modulo_modulo_int @ X3 @ m )
          @ ( elements_mat_int @ M2 ) ) ) ) ).

% mat_mod_elements_map
thf(fact_974_count__image__mset__ge__count,axiom,
    ! [A2: multis3731679216105815691ring_a,B: finite_mod_ring_a,F: finite_mod_ring_a > int] : ( ord_less_eq_nat @ ( count_7654011124160779523ring_a @ A2 @ B ) @ ( count_int @ ( image_7357852445201009398_a_int @ F @ A2 ) @ ( F @ B ) ) ) ).

% count_image_mset_ge_count
thf(fact_975_count__image__mset__ge__count,axiom,
    ! [A2: multiset_int,B: int,F: int > int] : ( ord_less_eq_nat @ ( count_int @ A2 @ B ) @ ( count_int @ ( image_mset_int_int @ F @ A2 ) @ ( F @ B ) ) ) ).

% count_image_mset_ge_count
thf(fact_976_mod__type_Oeq__M__Rel,axiom,
    ! [M: int] :
      ( ( vector4745807456731380595type_a @ type_a @ M )
     => ( bNF_re1743884151495963297ng_a_o @ ( vector3024231343486012919_Rel_a @ M )
        @ ( bNF_re8290846538823883642_a_o_o @ ( vector3024231343486012919_Rel_a @ M )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ^ [X3: int,Y6: int] :
            ( ( vector_Matrix_mod_M @ M @ X3 )
            = ( vector_Matrix_mod_M @ M @ Y6 ) )
        @ ^ [Y2: finite_mod_ring_a,Z2: finite_mod_ring_a] : ( Y2 = Z2 ) ) ) ).

% mod_type.eq_M_Rel
thf(fact_977_vec__set__map,axiom,
    ! [F: nat > nat,V: vec_nat] :
      ( ( vec_set_nat @ ( map_vec_nat_nat @ F @ V ) )
      = ( image_nat_nat @ F @ ( vec_set_nat @ V ) ) ) ).

% vec_set_map
thf(fact_978_vec__set__map,axiom,
    ! [F: int > finite_mod_ring_a,V: vec_int] :
      ( ( vec_se7251946917745546697ring_a @ ( map_ve1626356591056799954ring_a @ F @ V ) )
      = ( image_5814698132744821074ring_a @ F @ ( vec_set_int2 @ V ) ) ) ).

% vec_set_map
thf(fact_979_vec__set__map,axiom,
    ! [F: finite_mod_ring_a > int,V: vec_Fi4296597256376197294ring_a] :
      ( ( vec_set_int2 @ ( map_ve50164598268879916_a_int @ F @ V ) )
      = ( image_4238506139956901036_a_int @ F @ ( vec_se7251946917745546697ring_a @ V ) ) ) ).

% vec_set_map
thf(fact_980_vec__set__map,axiom,
    ! [F: int > int,V: vec_int] :
      ( ( vec_set_int2 @ ( map_vec_int_int @ F @ V ) )
      = ( image_int_int @ F @ ( vec_set_int2 @ V ) ) ) ).

% vec_set_map
thf(fact_981_map__mat__elements,axiom,
    ! [F: nat > nat,A2: mat_nat] :
      ( ( elements_mat_nat @ ( map_mat_nat_nat @ F @ A2 ) )
      = ( image_nat_nat @ F @ ( elements_mat_nat @ A2 ) ) ) ).

% map_mat_elements
thf(fact_982_map__mat__elements,axiom,
    ! [F: int > finite_mod_ring_a,A2: mat_int] :
      ( ( elemen4395573691419627848ring_a @ ( map_ma352813450859277382ring_a @ F @ A2 ) )
      = ( image_5814698132744821074ring_a @ F @ ( elements_mat_int @ A2 ) ) ) ).

% map_mat_elements
thf(fact_983_map__mat__elements,axiom,
    ! [F: finite_mod_ring_a > int,A2: mat_Fi443519135453058082ring_a] :
      ( ( elements_mat_int @ ( map_ma7999993494926133152_a_int @ F @ A2 ) )
      = ( image_4238506139956901036_a_int @ F @ ( elemen4395573691419627848ring_a @ A2 ) ) ) ).

% map_mat_elements
thf(fact_984_map__mat__elements,axiom,
    ! [F: int > int,A2: mat_int] :
      ( ( elements_mat_int @ ( map_mat_int_int @ F @ A2 ) )
      = ( image_int_int @ F @ ( elements_mat_int @ A2 ) ) ) ).

% map_mat_elements
thf(fact_985_mod__type_OM__M,axiom,
    ! [M: int,X: int] :
      ( ( vector4745807456731380595type_a @ type_a @ M )
     => ( ( vector_Matrix_mod_M @ M @ ( vector_Matrix_mod_M @ M @ X ) )
        = ( vector_Matrix_mod_M @ M @ X ) ) ) ).

% mod_type.M_M
thf(fact_986_mat__mod__type_Oaxioms_I2_J,axiom,
    ! [M: int] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( vector4745807456731380595type_a @ type_a @ M ) ) ).

% mat_mod_type.axioms(2)
thf(fact_987_inj__zero__hom_Ovec__hom__set,axiom,
    ! [Hom: nat > nat,V: vec_nat] :
      ( ( ring_i6094866036127137317at_nat @ Hom )
     => ( ( image_nat_nat @ Hom @ ( vec_set_nat @ V ) )
        = ( vec_set_nat @ ( map_vec_nat_nat @ Hom @ V ) ) ) ) ).

% inj_zero_hom.vec_hom_set
thf(fact_988_inj__zero__hom_Ovec__hom__set,axiom,
    ! [Hom: finite_mod_ring_a > int,V: vec_Fi4296597256376197294ring_a] :
      ( ( ring_i3475985505635201454_a_int @ Hom )
     => ( ( image_4238506139956901036_a_int @ Hom @ ( vec_se7251946917745546697ring_a @ V ) )
        = ( vec_set_int2 @ ( map_ve50164598268879916_a_int @ Hom @ V ) ) ) ) ).

% inj_zero_hom.vec_hom_set
thf(fact_989_inj__zero__hom_Ovec__hom__set,axiom,
    ! [Hom: int > finite_mod_ring_a,V: vec_int] :
      ( ( ring_i5052177498423121492ring_a @ Hom )
     => ( ( image_5814698132744821074ring_a @ Hom @ ( vec_set_int2 @ V ) )
        = ( vec_se7251946917745546697ring_a @ ( map_ve1626356591056799954ring_a @ Hom @ V ) ) ) ) ).

% inj_zero_hom.vec_hom_set
thf(fact_990_inj__zero__hom_Ovec__hom__set,axiom,
    ! [Hom: int > int,V: vec_int] :
      ( ( ring_i7091729277519141597nt_int @ Hom )
     => ( ( image_int_int @ Hom @ ( vec_set_int2 @ V ) )
        = ( vec_set_int2 @ ( map_vec_int_int @ Hom @ V ) ) ) ) ).

% inj_zero_hom.vec_hom_set
thf(fact_991_mod__type_Om1,axiom,
    ! [M: int] :
      ( ( vector4745807456731380595type_a @ type_a @ M )
     => ( ord_less_int @ one_one_int @ M ) ) ).

% mod_type.m1
thf(fact_992_mod__type_OM__0,axiom,
    ! [M: int] :
      ( ( vector4745807456731380595type_a @ type_a @ M )
     => ( ( vector_Matrix_mod_M @ M @ zero_zero_int )
        = zero_zero_int ) ) ).

% mod_type.M_0
thf(fact_993_mod__type_OM__1,axiom,
    ! [M: int] :
      ( ( vector4745807456731380595type_a @ type_a @ M )
     => ( ( vector_Matrix_mod_M @ M @ one_one_int )
        = one_one_int ) ) ).

% mod_type.M_1
thf(fact_994_mod__type_OM__def,axiom,
    ! [M: int,X: int] :
      ( ( vector4745807456731380595type_a @ type_a @ M )
     => ( ( vector_Matrix_mod_M @ M @ X )
        = ( modulo_modulo_int @ X @ M ) ) ) ).

% mod_type.M_def
thf(fact_995_mod__type_OM__to__int__mod__ring,axiom,
    ! [M: int,X: finite_mod_ring_a] :
      ( ( vector4745807456731380595type_a @ type_a @ M )
     => ( ( vector_Matrix_mod_M @ M @ ( finite1095367895020317408ring_a @ X ) )
        = ( finite1095367895020317408ring_a @ X ) ) ) ).

% mod_type.M_to_int_mod_ring
thf(fact_996_mat__mod__type_Ointro,axiom,
    ! [M: int] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( vector4745807456731380595type_a @ type_a @ M )
       => ( vector2974885785920725647type_a @ type_a @ M ) ) ) ).

% mat_mod_type.intro
thf(fact_997_mat__mod__type__def,axiom,
    ! [M: int] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
      = ( ( vector2311527483241216340at_mod @ M )
        & ( vector4745807456731380595type_a @ type_a @ M ) ) ) ).

% mat_mod_type_def
thf(fact_998_of__int__hom_Ovec__hom__set,axiom,
    ! [V: vec_int] :
      ( ( image_int_int @ ring_1_of_int_int @ ( vec_set_int2 @ V ) )
      = ( vec_set_int2 @ ( map_vec_int_int @ ring_1_of_int_int @ V ) ) ) ).

% of_int_hom.vec_hom_set
thf(fact_999_of__int__hom_Ovec__hom__set,axiom,
    ! [V: vec_int] :
      ( ( image_int_real @ ring_1_of_int_real @ ( vec_set_int2 @ V ) )
      = ( vec_set_real @ ( map_vec_int_real @ ring_1_of_int_real @ V ) ) ) ).

% of_int_hom.vec_hom_set
thf(fact_1000_mod__type_OM__inv__M__id,axiom,
    ! [M: int,X: int] :
      ( ( vector4745807456731380595type_a @ type_a @ M )
     => ( ( vector_Matrix_mod_M @ M @ ( vector2349909385534816566_inv_M @ M @ X ) )
        = ( vector_Matrix_mod_M @ M @ X ) ) ) ).

% mod_type.M_inv_M_id
thf(fact_1001_mat__mod_Omat__mod__elements__map,axiom,
    ! [M: int,X: int,M2: mat_int] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( member_int @ X @ ( elements_mat_int @ M2 ) )
       => ( ( elements_mat_int @ ( vector6118640873655855782at_mod @ M @ M2 ) )
          = ( image_int_int
            @ ^ [X3: int] : ( modulo_modulo_int @ X3 @ M )
            @ ( elements_mat_int @ M2 ) ) ) ) ) ).

% mat_mod.mat_mod_elements_map
thf(fact_1002_mod__type_Oright__total__M__Rel,axiom,
    ! [M: int] :
      ( ( vector4745807456731380595type_a @ type_a @ M )
     => ( right_2909008500229168952ring_a @ ( vector3024231343486012919_Rel_a @ M ) ) ) ).

% mod_type.right_total_M_Rel
thf(fact_1003_mod__type_Oleft__total__M__Rel,axiom,
    ! [M: int] :
      ( ( vector4745807456731380595type_a @ type_a @ M )
     => ( left_t8941605147251654769ring_a @ ( vector3024231343486012919_Rel_a @ M ) ) ) ).

% mod_type.left_total_M_Rel
thf(fact_1004_mod__type_Obi__total__M__Rel,axiom,
    ! [M: int] :
      ( ( vector4745807456731380595type_a @ type_a @ M )
     => ( bi_tot623839499179674737ring_a @ ( vector3024231343486012919_Rel_a @ M ) ) ) ).

% mod_type.bi_total_M_Rel
thf(fact_1005_mod__type_OM__Rel__def,axiom,
    ! [M: int,X: int,X2: finite_mod_ring_a] :
      ( ( vector4745807456731380595type_a @ type_a @ M )
     => ( ( vector3024231343486012919_Rel_a @ M @ X @ X2 )
        = ( ( vector_Matrix_mod_M @ M @ X )
          = ( finite1095367895020317408ring_a @ X2 ) ) ) ) ).

% mod_type.M_Rel_def
thf(fact_1006_mod__type_Ozero__M__Rel,axiom,
    ! [M: int] :
      ( ( vector4745807456731380595type_a @ type_a @ M )
     => ( vector3024231343486012919_Rel_a @ M @ zero_zero_int @ zero_z7902377541816115708ring_a ) ) ).

% mod_type.zero_M_Rel
thf(fact_1007_mod__type_Oone__M__Rel,axiom,
    ! [M: int] :
      ( ( vector4745807456731380595type_a @ type_a @ M )
     => ( vector3024231343486012919_Rel_a @ M @ one_one_int @ one_on2109788427901206336ring_a ) ) ).

% mod_type.one_M_Rel
thf(fact_1008_mod__type_Oto__int__mod__ring__of__int__M,axiom,
    ! [M: int,X: int] :
      ( ( vector4745807456731380595type_a @ type_a @ M )
     => ( ( finite1095367895020317408ring_a @ ( ring_18169885480643366966ring_a @ X ) )
        = ( vector_Matrix_mod_M @ M @ X ) ) ) ).

% mod_type.to_int_mod_ring_of_int_M
thf(fact_1009_mat__mod__type_Omat__mod__N__representative,axiom,
    ! [M: int,N3: mat_int] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( ( vector6118640873655855782at_mod @ M @ N3 )
        = ( map_ma7999993494926133152_a_int @ finite1095367895020317408ring_a @ ( map_ma352813450859277382ring_a @ ring_18169885480643366966ring_a @ N3 ) ) ) ) ).

% mat_mod_type.mat_mod_N_representative
thf(fact_1010_mem__MV__Rel,axiom,
    ( bNF_re6884500472961882619ng_a_o @ ( vector5230790432342831627_Rel_a @ m )
    @ ( bNF_re6384220461255839808_a_o_o @ ( bNF_re4691038805385103495ring_a @ ( vector5230790432342831627_Rel_a @ m ) )
      @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
    @ ^ [X3: vec_int,Y7: set_vec_int] :
      ? [Y6: vec_int] :
        ( ( member_vec_int @ Y6 @ Y7 )
        & ( ( vector1199560857299316530ec_mod @ m @ X3 )
          = ( vector1199560857299316530ec_mod @ m @ Y6 ) ) )
    @ member1106766863034010949ring_a ) ).

% mem_MV_Rel
thf(fact_1011_less__eq__natural_Orsp,axiom,
    ( bNF_re578469030762574527_nat_o
    @ ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 )
    @ ( bNF_re4705727531993890431at_o_o
      @ ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 )
      @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
    @ ord_less_eq_nat
    @ ord_less_eq_nat ) ).

% less_eq_natural.rsp
thf(fact_1012_less__natural_Orsp,axiom,
    ( bNF_re578469030762574527_nat_o
    @ ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 )
    @ ( bNF_re4705727531993890431at_o_o
      @ ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 )
      @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
    @ ord_less_nat
    @ ord_less_nat ) ).

% less_natural.rsp
thf(fact_1013_mem__MM__Rel,axiom,
    ( bNF_re7855085375772821011ng_a_o @ ( vector2798151085771547010_Rel_a @ m )
    @ ( bNF_re4636312053285623616_a_o_o @ ( bNF_re3622882117544951687ring_a @ ( vector2798151085771547010_Rel_a @ m ) )
      @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
    @ ^ [X3: mat_int,Y7: set_mat_int] :
      ? [Y6: mat_int] :
        ( ( member_mat_int @ Y6 @ Y7 )
        & ( ( vector6118640873655855782at_mod @ m @ X3 )
          = ( vector6118640873655855782at_mod @ m @ Y6 ) ) )
    @ member6477060778965647545ring_a ) ).

% mem_MM_Rel
thf(fact_1014_rel__setI,axiom,
    ! [A2: set_int,B2: set_int,R: int > int > $o] :
      ( ! [X4: int] :
          ( ( member_int @ X4 @ A2 )
         => ? [Xa2: int] :
              ( ( member_int @ Xa2 @ B2 )
              & ( R @ X4 @ Xa2 ) ) )
     => ( ! [Y3: int] :
            ( ( member_int @ Y3 @ B2 )
           => ? [X5: int] :
                ( ( member_int @ X5 @ A2 )
                & ( R @ X5 @ Y3 ) ) )
       => ( bNF_rel_set_int_int @ R @ A2 @ B2 ) ) ) ).

% rel_setI
thf(fact_1015_rel__setI,axiom,
    ! [A2: set_int,B2: set_nat,R: int > nat > $o] :
      ( ! [X4: int] :
          ( ( member_int @ X4 @ A2 )
         => ? [Xa2: nat] :
              ( ( member_nat @ Xa2 @ B2 )
              & ( R @ X4 @ Xa2 ) ) )
     => ( ! [Y3: nat] :
            ( ( member_nat @ Y3 @ B2 )
           => ? [X5: int] :
                ( ( member_int @ X5 @ A2 )
                & ( R @ X5 @ Y3 ) ) )
       => ( bNF_rel_set_int_nat @ R @ A2 @ B2 ) ) ) ).

% rel_setI
thf(fact_1016_rel__setI,axiom,
    ! [A2: set_nat,B2: set_int,R: nat > int > $o] :
      ( ! [X4: nat] :
          ( ( member_nat @ X4 @ A2 )
         => ? [Xa2: int] :
              ( ( member_int @ Xa2 @ B2 )
              & ( R @ X4 @ Xa2 ) ) )
     => ( ! [Y3: int] :
            ( ( member_int @ Y3 @ B2 )
           => ? [X5: nat] :
                ( ( member_nat @ X5 @ A2 )
                & ( R @ X5 @ Y3 ) ) )
       => ( bNF_rel_set_nat_int @ R @ A2 @ B2 ) ) ) ).

% rel_setI
thf(fact_1017_rel__setI,axiom,
    ! [A2: set_nat,B2: set_nat,R: nat > nat > $o] :
      ( ! [X4: nat] :
          ( ( member_nat @ X4 @ A2 )
         => ? [Xa2: nat] :
              ( ( member_nat @ Xa2 @ B2 )
              & ( R @ X4 @ Xa2 ) ) )
     => ( ! [Y3: nat] :
            ( ( member_nat @ Y3 @ B2 )
           => ? [X5: nat] :
                ( ( member_nat @ X5 @ A2 )
                & ( R @ X5 @ Y3 ) ) )
       => ( bNF_rel_set_nat_nat @ R @ A2 @ B2 ) ) ) ).

% rel_setI
thf(fact_1018_rel__setI,axiom,
    ! [A2: set_int,B2: set_Fi2982333969990053029ring_a,R: int > finite_mod_ring_a > $o] :
      ( ! [X4: int] :
          ( ( member_int @ X4 @ A2 )
         => ? [Xa2: finite_mod_ring_a] :
              ( ( member3034048621153491438ring_a @ Xa2 @ B2 )
              & ( R @ X4 @ Xa2 ) ) )
     => ( ! [Y3: finite_mod_ring_a] :
            ( ( member3034048621153491438ring_a @ Y3 @ B2 )
           => ? [X5: int] :
                ( ( member_int @ X5 @ A2 )
                & ( R @ X5 @ Y3 ) ) )
       => ( bNF_re2658327337197749847ring_a @ R @ A2 @ B2 ) ) ) ).

% rel_setI
thf(fact_1019_rel__setI,axiom,
    ! [A2: set_int,B2: set_ve6125835690772642148ring_a,R: int > vec_Fi4296597256376197294ring_a > $o] :
      ( ! [X4: int] :
          ( ( member_int @ X4 @ A2 )
         => ? [Xa2: vec_Fi4296597256376197294ring_a] :
              ( ( member1106766863034010949ring_a @ Xa2 @ B2 )
              & ( R @ X4 @ Xa2 ) ) )
     => ( ! [Y3: vec_Fi4296597256376197294ring_a] :
            ( ( member1106766863034010949ring_a @ Y3 @ B2 )
           => ? [X5: int] :
                ( ( member_int @ X5 @ A2 )
                & ( R @ X5 @ Y3 ) ) )
       => ( bNF_re4209374770798322588ring_a @ R @ A2 @ B2 ) ) ) ).

% rel_setI
thf(fact_1020_rel__setI,axiom,
    ! [A2: set_int,B2: set_ma1095064855528551128ring_a,R: int > mat_Fi443519135453058082ring_a > $o] :
      ( ! [X4: int] :
          ( ( member_int @ X4 @ A2 )
         => ? [Xa2: mat_Fi443519135453058082ring_a] :
              ( ( member6477060778965647545ring_a @ Xa2 @ B2 )
              & ( R @ X4 @ Xa2 ) ) )
     => ( ! [Y3: mat_Fi443519135453058082ring_a] :
            ( ( member6477060778965647545ring_a @ Y3 @ B2 )
           => ? [X5: int] :
                ( ( member_int @ X5 @ A2 )
                & ( R @ X5 @ Y3 ) ) )
       => ( bNF_re356296649875183376ring_a @ R @ A2 @ B2 ) ) ) ).

% rel_setI
thf(fact_1021_rel__setI,axiom,
    ! [A2: set_ve6125835690772642148ring_a,B2: set_int,R: vec_Fi4296597256376197294ring_a > int > $o] :
      ( ! [X4: vec_Fi4296597256376197294ring_a] :
          ( ( member1106766863034010949ring_a @ X4 @ A2 )
         => ? [Xa2: int] :
              ( ( member_int @ Xa2 @ B2 )
              & ( R @ X4 @ Xa2 ) ) )
     => ( ! [Y3: int] :
            ( ( member_int @ Y3 @ B2 )
           => ? [X5: vec_Fi4296597256376197294ring_a] :
                ( ( member1106766863034010949ring_a @ X5 @ A2 )
                & ( R @ X5 @ Y3 ) ) )
       => ( bNF_re5919053795459790748_a_int @ R @ A2 @ B2 ) ) ) ).

% rel_setI
thf(fact_1022_rel__setI,axiom,
    ! [A2: set_ve6125835690772642148ring_a,B2: set_nat,R: vec_Fi4296597256376197294ring_a > nat > $o] :
      ( ! [X4: vec_Fi4296597256376197294ring_a] :
          ( ( member1106766863034010949ring_a @ X4 @ A2 )
         => ? [Xa2: nat] :
              ( ( member_nat @ Xa2 @ B2 )
              & ( R @ X4 @ Xa2 ) ) )
     => ( ! [Y3: nat] :
            ( ( member_nat @ Y3 @ B2 )
           => ? [X5: vec_Fi4296597256376197294ring_a] :
                ( ( member1106766863034010949ring_a @ X5 @ A2 )
                & ( R @ X5 @ Y3 ) ) )
       => ( bNF_re5921544265968841024_a_nat @ R @ A2 @ B2 ) ) ) ).

% rel_setI
thf(fact_1023_rel__setI,axiom,
    ! [A2: set_ma1095064855528551128ring_a,B2: set_int,R: mat_Fi443519135453058082ring_a > int > $o] :
      ( ! [X4: mat_Fi443519135453058082ring_a] :
          ( ( member6477060778965647545ring_a @ X4 @ A2 )
         => ? [Xa2: int] :
              ( ( member_int @ Xa2 @ B2 )
              & ( R @ X4 @ Xa2 ) ) )
     => ( ! [Y3: int] :
            ( ( member_int @ Y3 @ B2 )
           => ? [X5: mat_Fi443519135453058082ring_a] :
                ( ( member6477060778965647545ring_a @ X5 @ A2 )
                & ( R @ X5 @ Y3 ) ) )
       => ( bNF_re4645510655262268176_a_int @ R @ A2 @ B2 ) ) ) ).

% rel_setI
thf(fact_1024_zero__natural_Orsp,axiom,
    zero_zero_nat = zero_zero_nat ).

% zero_natural.rsp
thf(fact_1025_zero__integer_Orsp,axiom,
    zero_zero_int = zero_zero_int ).

% zero_integer.rsp
thf(fact_1026_less__eq__integer_Orsp,axiom,
    ( bNF_re3403563459893282935_int_o
    @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
    @ ( bNF_re5089333283451836215nt_o_o
      @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
      @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
    @ ord_less_eq_int
    @ ord_less_eq_int ) ).

% less_eq_integer.rsp
thf(fact_1027_less__integer_Orsp,axiom,
    ( bNF_re3403563459893282935_int_o
    @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
    @ ( bNF_re5089333283451836215nt_o_o
      @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
      @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
    @ ord_less_int
    @ ord_less_int ) ).

% less_integer.rsp
thf(fact_1028_natural__of__integer_Orsp,axiom,
    ( bNF_re3715656647883201625at_nat
    @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
    @ ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 )
    @ nat2
    @ nat2 ) ).

% natural_of_integer.rsp
thf(fact_1029_modulo__integer_Orsp,axiom,
    ( bNF_re711492959462206631nt_int
    @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
    @ ( bNF_re4712519889275205905nt_int
      @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
      @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) )
    @ modulo_modulo_int
    @ modulo_modulo_int ) ).

% modulo_integer.rsp
thf(fact_1030_modulo__natural_Orsp,axiom,
    ( bNF_re1345281282404953727at_nat
    @ ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 )
    @ ( bNF_re5653821019739307937at_nat
      @ ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 )
      @ ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 ) )
    @ modulo_modulo_nat
    @ modulo_modulo_nat ) ).

% modulo_natural.rsp
thf(fact_1031_mat__mod__type_Omem__MM__Rel,axiom,
    ! [M: int] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( bNF_re7855085375772821011ng_a_o @ ( vector2798151085771547010_Rel_a @ M )
        @ ( bNF_re4636312053285623616_a_o_o @ ( bNF_re3622882117544951687ring_a @ ( vector2798151085771547010_Rel_a @ M ) )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ^ [X3: mat_int,Y7: set_mat_int] :
          ? [Y6: mat_int] :
            ( ( member_mat_int @ Y6 @ Y7 )
            & ( ( vector6118640873655855782at_mod @ M @ X3 )
              = ( vector6118640873655855782at_mod @ M @ Y6 ) ) )
        @ member6477060778965647545ring_a ) ) ).

% mat_mod_type.mem_MM_Rel
thf(fact_1032_mat__mod__type_Omem__MV__Rel,axiom,
    ! [M: int] :
      ( ( vector2974885785920725647type_a @ type_a @ M )
     => ( bNF_re6884500472961882619ng_a_o @ ( vector5230790432342831627_Rel_a @ M )
        @ ( bNF_re6384220461255839808_a_o_o @ ( bNF_re4691038805385103495ring_a @ ( vector5230790432342831627_Rel_a @ M ) )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ^ [X3: vec_int,Y7: set_vec_int] :
          ? [Y6: vec_int] :
            ( ( member_vec_int @ Y6 @ Y7 )
            & ( ( vector1199560857299316530ec_mod @ M @ X3 )
              = ( vector1199560857299316530ec_mod @ M @ Y6 ) ) )
        @ member1106766863034010949ring_a ) ) ).

% mat_mod_type.mem_MV_Rel
thf(fact_1033_right__total__Collect__transfer,axiom,
    ! [A2: int > int > $o] :
      ( ( right_total_int_int @ A2 )
     => ( bNF_re6121003078962415843et_int
        @ ( bNF_re5089333283451836215nt_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ( bNF_rel_set_int_int @ A2 )
        @ ^ [P4: int > $o] :
            ( collect_int
            @ ^ [X3: int] :
                ( ( P4 @ X3 )
                & ( domainp_int_int @ A2 @ X3 ) ) )
        @ collect_int ) ) ).

% right_total_Collect_transfer
thf(fact_1034_right__total__Collect__transfer,axiom,
    ! [A2: int > finite_mod_ring_a > $o] :
      ( ( right_2909008500229168952ring_a @ A2 )
     => ( bNF_re1547907014084023747ring_a
        @ ( bNF_re8290846538823883642_a_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ( bNF_re2658327337197749847ring_a @ A2 )
        @ ^ [P4: int > $o] :
            ( collect_int
            @ ^ [X3: int] :
                ( ( P4 @ X3 )
                & ( domain6543890336852369843ring_a @ A2 @ X3 ) ) )
        @ collec4943914941012508720ring_a ) ) ).

% right_total_Collect_transfer
thf(fact_1035_right__total__Collect__transfer,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( right_7341149013462710248ring_a @ A2 )
     => ( bNF_re8209676071344003583ring_a
        @ ( bNF_re507051067509135658_a_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ( bNF_re4691038805385103495ring_a @ A2 )
        @ ^ [P4: vec_int > $o] :
            ( collect_vec_int
            @ ^ [X3: vec_int] :
                ( ( P4 @ X3 )
                & ( domain4015354059925764579ring_a @ A2 @ X3 ) ) )
        @ collec5361221020025176195ring_a ) ) ).

% right_total_Collect_transfer
thf(fact_1036_right__total__Collect__transfer,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( right_6272992325622558440ring_a @ A2 )
     => ( bNF_re6509371104199398375ring_a
        @ ( bNF_re6153771816476299306_a_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ( bNF_re3622882117544951687ring_a @ A2 )
        @ ^ [P4: mat_int > $o] :
            ( collect_mat_int
            @ ^ [X3: mat_int] :
                ( ( P4 @ X3 )
                & ( domain2947197372085612771ring_a @ A2 @ X3 ) ) )
        @ collec1508142899102036983ring_a ) ) ).

% right_total_Collect_transfer
thf(fact_1037_member__transfer,axiom,
    ! [A2: int > int > $o] :
      ( ( bi_unique_int_int @ A2 )
     => ( bNF_re8356144997044566263_int_o @ A2
        @ ( bNF_re4540111288819221667nt_o_o @ ( bNF_rel_set_int_int @ A2 )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ member_int
        @ member_int ) ) ).

% member_transfer
thf(fact_1038_member__transfer,axiom,
    ! [A2: int > nat > $o] :
      ( ( bi_unique_int_nat @ A2 )
     => ( bNF_re4553266823265959927_nat_o @ A2
        @ ( bNF_re3540757576918167111at_o_o @ ( bNF_rel_set_int_nat @ A2 )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ member_int
        @ member_nat ) ) ).

% member_transfer
thf(fact_1039_member__transfer,axiom,
    ! [A2: nat > int > $o] :
      ( ( bi_unique_nat_int @ A2 )
     => ( bNF_re6703580107126279231_int_o @ A2
        @ ( bNF_re6849929220912172615nt_o_o @ ( bNF_rel_set_nat_int @ A2 )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ member_nat
        @ member_int ) ) ).

% member_transfer
thf(fact_1040_member__transfer,axiom,
    ! [A2: nat > nat > $o] :
      ( ( bi_unique_nat_nat @ A2 )
     => ( bNF_re2900701933347672895_nat_o @ A2
        @ ( bNF_re5850575509011118059at_o_o @ ( bNF_rel_set_nat_nat @ A2 )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ member_nat
        @ member_nat ) ) ).

% member_transfer
thf(fact_1041_member__transfer,axiom,
    ! [A2: int > finite_mod_ring_a > $o] :
      ( ( bi_uni1022671006909063496ring_a @ A2 )
     => ( bNF_re1630919894521622923ng_a_o @ A2
        @ ( bNF_re3268453933031481124_a_o_o @ ( bNF_re2658327337197749847ring_a @ A2 )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ member_int
        @ member3034048621153491438ring_a ) ) ).

% member_transfer
thf(fact_1042_member__transfer,axiom,
    ! [A2: int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( bi_uni3942104149151060331ring_a @ A2 )
     => ( bNF_re3464415642011276407ng_a_o @ A2
        @ ( bNF_re6383911003556803365_a_o_o @ ( bNF_re4209374770798322588ring_a @ A2 )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ member_int
        @ member1106766863034010949ring_a ) ) ).

% member_transfer
thf(fact_1043_member__transfer,axiom,
    ! [A2: int > mat_Fi443519135453058082ring_a > $o] :
      ( ( bi_uni89026028227921119ring_a @ A2 )
     => ( bNF_re3611541376831158135ng_a_o @ A2
        @ ( bNF_re5110367863359280793_a_o_o @ ( bNF_re356296649875183376ring_a @ A2 )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ member_int
        @ member6477060778965647545ring_a ) ) ).

% member_transfer
thf(fact_1044_member__transfer,axiom,
    ! [A2: vec_Fi4296597256376197294ring_a > int > $o] :
      ( ( bi_uni5651783173812528491_a_int @ A2 )
     => ( bNF_re7714729098714725883_int_o @ A2
        @ ( bNF_re6378887138790115109nt_o_o @ ( bNF_re5919053795459790748_a_int @ A2 )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ member1106766863034010949ring_a
        @ member_int ) ) ).

% member_transfer
thf(fact_1045_member__transfer,axiom,
    ! [A2: vec_Fi4296597256376197294ring_a > nat > $o] :
      ( ( bi_uni5654273644321578767_a_nat @ A2 )
     => ( bNF_re4623018748902118651_nat_o @ A2
        @ ( bNF_re5379533426889060553at_o_o @ ( bNF_re5921544265968841024_a_nat @ A2 )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ member1106766863034010949ring_a
        @ member_nat ) ) ).

% member_transfer
thf(fact_1046_member__transfer,axiom,
    ! [A2: mat_Fi443519135453058082ring_a > int > $o] :
      ( ( bi_uni4378240033615005919_a_int @ A2 )
     => ( bNF_re3297285065332102371_int_o @ A2
        @ ( bNF_re8148148883495127705nt_o_o @ ( bNF_re4645510655262268176_a_int @ A2 )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ member6477060778965647545ring_a
        @ member_int ) ) ).

% member_transfer
thf(fact_1047_rel__set__transfer,axiom,
    ! [A2: int > int > $o,B2: int > int > $o] :
      ( bNF_re4478252629936865629_int_o
      @ ( bNF_re3403563459893282935_int_o @ A2
        @ ( bNF_re5089333283451836215nt_o_o @ B2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re4815948244430201443_int_o @ ( bNF_rel_set_int_int @ A2 )
        @ ( bNF_re4540111288819221667nt_o_o @ ( bNF_rel_set_int_int @ B2 )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ bNF_rel_set_int_int
      @ bNF_rel_set_int_int ) ).

% rel_set_transfer
thf(fact_1048_rel__set__transfer,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: int > int > $o] :
      ( bNF_re4468130210263503771_int_o
      @ ( bNF_re3873409527727426490_int_o @ A2
        @ ( bNF_re5089333283451836215nt_o_o @ B2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re414048519855180260_int_o @ ( bNF_re2658327337197749847ring_a @ A2 )
        @ ( bNF_re4540111288819221667nt_o_o @ ( bNF_rel_set_int_int @ B2 )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ bNF_rel_set_int_int
      @ bNF_re1082135344409829809_a_int ) ).

% rel_set_transfer
thf(fact_1049_rel__set__transfer,axiom,
    ! [A2: int > int > $o,B2: finite_mod_ring_a > finite_mod_ring_a > $o] :
      ( bNF_re8072987537887292697ng_a_o
      @ ( bNF_re6948380915580796713ng_a_o @ A2
        @ ( bNF_re5912972185147205917_a_o_o @ B2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re5132486596981259477ng_a_o @ ( bNF_rel_set_int_int @ A2 )
        @ ( bNF_re1992636659909454109_a_o_o @ ( bNF_re3733049804732764288ring_a @ B2 )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ bNF_re2658327337197749847ring_a
      @ bNF_re2658327337197749847ring_a ) ).

% rel_set_transfer
thf(fact_1050_rel__set__transfer,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: int > finite_mod_ring_a > $o] :
      ( bNF_re2336052386105072073ng_a_o
      @ ( bNF_re1743884151495963297ng_a_o @ A2
        @ ( bNF_re8290846538823883642_a_o_o @ B2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re6625280399352257633ng_a_o @ ( bNF_re2658327337197749847ring_a @ A2 )
        @ ( bNF_re3268453933031481124_a_o_o @ ( bNF_re2658327337197749847ring_a @ B2 )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ bNF_rel_set_int_int
      @ bNF_re3733049804732764288ring_a ) ).

% rel_set_transfer
thf(fact_1051_rel__set__transfer,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o,B2: int > int > $o] :
      ( bNF_re5672091554521441735_int_o
      @ ( bNF_re7877854262379379050_int_o @ A2
        @ ( bNF_re5089333283451836215nt_o_o @ B2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re9008368033911170816_int_o @ ( bNF_re4691038805385103495ring_a @ A2 )
        @ ( bNF_re4540111288819221667nt_o_o @ ( bNF_rel_set_int_int @ B2 )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ bNF_re2560616370357726725nt_int
      @ bNF_re5919053795459790748_a_int ) ).

% rel_set_transfer
thf(fact_1052_rel__set__transfer,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o,B2: int > int > $o] :
      ( bNF_re7208957339489685447_int_o
      @ ( bNF_re1270729808710627434_int_o @ A2
        @ ( bNF_re5089333283451836215nt_o_o @ B2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re2751829829268647424_int_o @ ( bNF_re3622882117544951687ring_a @ A2 )
        @ ( bNF_re4540111288819221667nt_o_o @ ( bNF_rel_set_int_int @ B2 )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ bNF_re3806336121531400593nt_int
      @ bNF_re4645510655262268176_a_int ) ).

% rel_set_transfer
thf(fact_1053_rel__set__transfer,axiom,
    ! [A2: vec_int > int > $o,B2: vec_Fi4296597256376197294ring_a > finite_mod_ring_a > $o] :
      ( bNF_re7025310947142835329ng_a_o
      @ ( bNF_re6180959097202804209ng_a_o @ A2
        @ ( bNF_re5329533212257213048_a_o_o @ B2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re8928381418866904901ng_a_o @ ( bNF_re2560616370357726725nt_int @ A2 )
        @ ( bNF_re8560914720294849314_a_o_o @ ( bNF_re4407951392657719893ring_a @ B2 )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ bNF_re4691038805385103495ring_a
      @ bNF_re2658327337197749847ring_a ) ).

% rel_set_transfer
thf(fact_1054_rel__set__transfer,axiom,
    ! [A2: mat_int > int > $o,B2: mat_Fi443519135453058082ring_a > finite_mod_ring_a > $o] :
      ( bNF_re746635091991164545ng_a_o
      @ ( bNF_re5662754106317279473ng_a_o @ A2
        @ ( bNF_re8373915239858509316_a_o_o @ B2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re3414458586112227909ng_a_o @ ( bNF_re3806336121531400593nt_int @ A2 )
        @ ( bNF_re2262145468226031790_a_o_o @ ( bNF_re3095019897404434401ring_a @ B2 )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ bNF_re3622882117544951687ring_a
      @ bNF_re2658327337197749847ring_a ) ).

% rel_set_transfer
thf(fact_1055_rel__set__transfer,axiom,
    ! [A2: int > vec_int > $o,B2: finite_mod_ring_a > vec_Fi4296597256376197294ring_a > $o] :
      ( bNF_re5266488448927231873ng_a_o
      @ ( bNF_re7899986136908408921ng_a_o @ A2
        @ ( bNF_re3816977551999327062_a_o_o @ B2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re3244266564472207961ng_a_o @ ( bNF_re8016063337597145643ec_int @ A2 )
        @ ( bNF_re1568155373528815596_a_o_o @ ( bNF_re6630783400778640435ring_a @ B2 )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ bNF_re2658327337197749847ring_a
      @ bNF_re4691038805385103495ring_a ) ).

% rel_set_transfer
thf(fact_1056_rel__set__transfer,axiom,
    ! [A2: int > mat_int > $o,B2: finite_mod_ring_a > mat_Fi443519135453058082ring_a > $o] :
      ( bNF_re6783927866172000641ng_a_o
      @ ( bNF_re4810065245219074393ng_a_o @ A2
        @ ( bNF_re5352847140489197770_a_o_o @ B2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ ( bNF_re4794200806275638105ng_a_o @ ( bNF_re4529603996441892279at_int @ A2 )
        @ ( bNF_re294612233331293024_a_o_o @ ( bNF_re2777705279855501223ring_a @ B2 )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) )
      @ bNF_re2658327337197749847ring_a
      @ bNF_re3622882117544951687ring_a ) ).

% rel_set_transfer
thf(fact_1057_subset__transfer,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( bi_uni555094797115351544ring_a @ A2 )
     => ( bNF_re8227285363166532965ng_a_o @ ( bNF_re4691038805385103495ring_a @ A2 )
        @ ( bNF_re6384220461255839808_a_o_o @ ( bNF_re4691038805385103495ring_a @ A2 )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ord_le5046699514128596377ec_int
        @ ord_le4912074394114046404ring_a ) ) ).

% subset_transfer
thf(fact_1058_subset__transfer,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( bi_uni8710310146129975544ring_a @ A2 )
     => ( bNF_re2479693389296218493ng_a_o @ ( bNF_re3622882117544951687ring_a @ A2 )
        @ ( bNF_re4636312053285623616_a_o_o @ ( bNF_re3622882117544951687ring_a @ A2 )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ord_le5299038897506728741at_int
        @ ord_le9104675595724731192ring_a ) ) ).

% subset_transfer
thf(fact_1059_subset__transfer,axiom,
    ! [A2: int > finite_mod_ring_a > $o] :
      ( ( bi_uni1022671006909063496ring_a @ A2 )
     => ( bNF_re6625280399352257633ng_a_o @ ( bNF_re2658327337197749847ring_a @ A2 )
        @ ( bNF_re3268453933031481124_a_o_o @ ( bNF_re2658327337197749847ring_a @ A2 )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ord_less_eq_set_int
        @ ord_le3976570047013626949ring_a ) ) ).

% subset_transfer
thf(fact_1060_subset__transfer,axiom,
    ! [A2: int > int > $o] :
      ( ( bi_unique_int_int @ A2 )
     => ( bNF_re4815948244430201443_int_o @ ( bNF_rel_set_int_int @ A2 )
        @ ( bNF_re4540111288819221667nt_o_o @ ( bNF_rel_set_int_int @ A2 )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ord_less_eq_set_int
        @ ord_less_eq_set_int ) ) ).

% subset_transfer
thf(fact_1061_right__total__rel__set,axiom,
    ! [A2: int > finite_mod_ring_a > $o] :
      ( ( right_2909008500229168952ring_a @ A2 )
     => ( right_8012789954965988834ring_a @ ( bNF_re2658327337197749847ring_a @ A2 ) ) ) ).

% right_total_rel_set
thf(fact_1062_right__total__rel__set,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( right_7341149013462710248ring_a @ A2 )
     => ( right_2938026757761051646ring_a @ ( bNF_re4691038805385103495ring_a @ A2 ) ) ) ).

% right_total_rel_set
thf(fact_1063_right__total__rel__set,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( right_6272992325622558440ring_a @ A2 )
     => ( right_8378705835506627326ring_a @ ( bNF_re3622882117544951687ring_a @ A2 ) ) ) ).

% right_total_rel_set
thf(fact_1064_bi__total__rel__set,axiom,
    ! [A2: int > finite_mod_ring_a > $o] :
      ( ( bi_tot623839499179674737ring_a @ A2 )
     => ( bi_tot3373772818509728539ring_a @ ( bNF_re2658327337197749847ring_a @ A2 ) ) ) ).

% bi_total_rel_set
thf(fact_1065_bi__total__rel__set,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( bi_tot310863827317176225ring_a @ A2 )
     => ( bi_tot3615525640256922551ring_a @ ( bNF_re4691038805385103495ring_a @ A2 ) ) ) ).

% bi_total_rel_set
thf(fact_1066_bi__total__rel__set,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( bi_tot8466079176331800225ring_a @ A2 )
     => ( bi_tot9056204718002498231ring_a @ ( bNF_re3622882117544951687ring_a @ A2 ) ) ) ).

% bi_total_rel_set
thf(fact_1067_right__unique__rel__set,axiom,
    ! [A2: int > finite_mod_ring_a > $o] :
      ( ( right_7581627888863641665ring_a @ A2 )
     => ( right_8649055584691732203ring_a @ ( bNF_re2658327337197749847ring_a @ A2 ) ) ) ).

% right_unique_rel_set
thf(fact_1068_right__unique__rel__set,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( right_2407805982356550513ring_a @ A2 )
     => ( right_5520629302461210503ring_a @ ( bNF_re4691038805385103495ring_a @ A2 ) ) ) ).

% right_unique_rel_set
thf(fact_1069_right__unique__rel__set,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( right_1339649294516398705ring_a @ A2 )
     => ( right_1737936343352010375ring_a @ ( bNF_re3622882117544951687ring_a @ A2 ) ) ) ).

% right_unique_rel_set
thf(fact_1070_left__total__rel__set,axiom,
    ! [A2: int > finite_mod_ring_a > $o] :
      ( ( left_t8941605147251654769ring_a @ A2 )
     => ( left_t2970111942549241627ring_a @ ( bNF_re2658327337197749847ring_a @ A2 ) ) ) ).

% left_total_rel_set
thf(fact_1071_left__total__rel__set,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( left_t7842747197492505505ring_a @ A2 )
     => ( left_t97545717705185207ring_a @ ( bNF_re4691038805385103495ring_a @ A2 ) ) ) ).

% left_total_rel_set
thf(fact_1072_left__total__rel__set,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( left_t6774590509652353697ring_a @ A2 )
     => ( left_t5538224795450760887ring_a @ ( bNF_re3622882117544951687ring_a @ A2 ) ) ) ).

% left_total_rel_set
thf(fact_1073_image__transfer,axiom,
    ! [A2: int > nat > $o,B2: int > nat > $o] : ( bNF_re8645648040046385573et_nat @ ( bNF_re4343356799547411545nt_nat @ A2 @ B2 ) @ ( bNF_re1768063143140362033et_nat @ ( bNF_rel_set_int_nat @ A2 ) @ ( bNF_rel_set_int_nat @ B2 ) ) @ image_int_int @ image_nat_nat ) ).

% image_transfer
thf(fact_1074_image__transfer,axiom,
    ! [A2: nat > int > $o,B2: nat > int > $o] : ( bNF_re1078555597002162597et_int @ ( bNF_re6022984109467102297at_int @ A2 @ B2 ) @ ( bNF_re949339946388637489et_int @ ( bNF_rel_set_nat_int @ A2 ) @ ( bNF_rel_set_nat_int @ B2 ) ) @ image_nat_nat @ image_int_int ) ).

% image_transfer
thf(fact_1075_image__transfer,axiom,
    ! [A2: nat > nat > $o,B2: nat > nat > $o] : ( bNF_re5276023518710192181et_nat @ ( bNF_re5653821019739307937at_nat @ A2 @ B2 ) @ ( bNF_re3159760477010384505et_nat @ ( bNF_rel_set_nat_nat @ A2 ) @ ( bNF_rel_set_nat_nat @ B2 ) ) @ image_nat_nat @ image_nat_nat ) ).

% image_transfer
thf(fact_1076_image__transfer,axiom,
    ! [A2: int > int > $o,B2: $o > $o > $o] : ( bNF_re5225647679341271645_set_o @ ( bNF_re5089333283451836215nt_o_o @ A2 @ B2 ) @ ( bNF_re320214293493010595_set_o @ ( bNF_rel_set_int_int @ A2 ) @ ( bNF_rel_set_o_o @ B2 ) ) @ image_int_o @ image_int_o ) ).

% image_transfer
thf(fact_1077_image__transfer,axiom,
    ! [A2: int > int > $o,B2: nat > nat > $o] : ( bNF_re1462970895668484517et_nat @ ( bNF_re3715656647883201625at_nat @ A2 @ B2 ) @ ( bNF_re6950056017887012657et_nat @ ( bNF_rel_set_int_int @ A2 ) @ ( bNF_rel_set_nat_nat @ B2 ) ) @ image_int_nat @ image_int_nat ) ).

% image_transfer
thf(fact_1078_image__transfer,axiom,
    ! [A2: int > int > $o,B2: int > int > $o] : ( bNF_re4448180118338355989et_int @ ( bNF_re4712519889275205905nt_int @ A2 @ B2 ) @ ( bNF_re8781014649373390825et_int @ ( bNF_rel_set_int_int @ A2 ) @ ( bNF_rel_set_int_int @ B2 ) ) @ image_int_int @ image_int_int ) ).

% image_transfer
thf(fact_1079_image__transfer,axiom,
    ! [A2: int > finite_mod_ring_a > $o,B2: int > finite_mod_ring_a > $o] : ( bNF_re5468675425431845637ring_a @ ( bNF_re4694112744541868061ring_a @ A2 @ B2 ) @ ( bNF_re5272088291242829981ring_a @ ( bNF_re2658327337197749847ring_a @ A2 ) @ ( bNF_re2658327337197749847ring_a @ B2 ) ) @ image_int_int @ image_3815122860822722885ring_a ) ).

% image_transfer
thf(fact_1080_image__transfer,axiom,
    ! [A2: int > int > $o,B2: ( int > $o ) > ( int > $o ) > $o] : ( bNF_re497851078371813853_int_o @ ( bNF_re3403563459893282935_int_o @ A2 @ B2 ) @ ( bNF_re286873704650414563_int_o @ ( bNF_rel_set_int_int @ A2 ) @ ( bNF_re8564061778165475840_int_o @ B2 ) ) @ image_int_int_o @ image_int_int_o ) ).

% image_transfer
thf(fact_1081_image__transfer,axiom,
    ! [A2: int > int > $o,B2: ( int > int ) > ( int > int ) > $o] : ( bNF_re4460442335046654529nt_int @ ( bNF_re711492959462206631nt_int @ A2 @ B2 ) @ ( bNF_re6171256825458429567nt_int @ ( bNF_rel_set_int_int @ A2 ) @ ( bNF_re6961201103365092784nt_int @ B2 ) ) @ image_int_int_int @ image_int_int_int ) ).

% image_transfer
thf(fact_1082_image__transfer,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o,B2: int > finite_mod_ring_a > $o] : ( bNF_re7161980590383822241ring_a @ ( bNF_re5232057317656209005ring_a @ A2 @ B2 ) @ ( bNF_re3213975434357579905ring_a @ ( bNF_re4691038805385103495ring_a @ A2 ) @ ( bNF_re2658327337197749847ring_a @ B2 ) ) @ image_vec_int_int @ image_4713707003719520592ring_a ) ).

% image_transfer
thf(fact_1083_Collect__transfer,axiom,
    ! [A2: int > int > $o] :
      ( ( bi_total_int_int @ A2 )
     => ( bNF_re6121003078962415843et_int
        @ ( bNF_re5089333283451836215nt_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ( bNF_rel_set_int_int @ A2 )
        @ collect_int
        @ collect_int ) ) ).

% Collect_transfer
thf(fact_1084_Collect__transfer,axiom,
    ! [A2: int > finite_mod_ring_a > $o] :
      ( ( bi_tot623839499179674737ring_a @ A2 )
     => ( bNF_re1547907014084023747ring_a
        @ ( bNF_re8290846538823883642_a_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ( bNF_re2658327337197749847ring_a @ A2 )
        @ collect_int
        @ collec4943914941012508720ring_a ) ) ).

% Collect_transfer
thf(fact_1085_Collect__transfer,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( bi_tot310863827317176225ring_a @ A2 )
     => ( bNF_re8209676071344003583ring_a
        @ ( bNF_re507051067509135658_a_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ( bNF_re4691038805385103495ring_a @ A2 )
        @ collect_vec_int
        @ collec5361221020025176195ring_a ) ) ).

% Collect_transfer
thf(fact_1086_Collect__transfer,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( bi_tot8466079176331800225ring_a @ A2 )
     => ( bNF_re6509371104199398375ring_a
        @ ( bNF_re6153771816476299306_a_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ( bNF_re3622882117544951687ring_a @ A2 )
        @ collect_mat_int
        @ collec1508142899102036983ring_a ) ) ).

% Collect_transfer
thf(fact_1087_strict__subset__transfer,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( bi_uni555094797115351544ring_a @ A2 )
     => ( bNF_re8227285363166532965ng_a_o @ ( bNF_re4691038805385103495ring_a @ A2 )
        @ ( bNF_re6384220461255839808_a_o_o @ ( bNF_re4691038805385103495ring_a @ A2 )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ord_less_set_vec_int
        @ ord_le4392190172438129592ring_a ) ) ).

% strict_subset_transfer
thf(fact_1088_strict__subset__transfer,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( bi_uni8710310146129975544ring_a @ A2 )
     => ( bNF_re2479693389296218493ng_a_o @ ( bNF_re3622882117544951687ring_a @ A2 )
        @ ( bNF_re4636312053285623616_a_o_o @ ( bNF_re3622882117544951687ring_a @ A2 )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ord_less_set_mat_int
        @ ord_le8584791374048814380ring_a ) ) ).

% strict_subset_transfer
thf(fact_1089_strict__subset__transfer,axiom,
    ! [A2: int > finite_mod_ring_a > $o] :
      ( ( bi_uni1022671006909063496ring_a @ A2 )
     => ( bNF_re6625280399352257633ng_a_o @ ( bNF_re2658327337197749847ring_a @ A2 )
        @ ( bNF_re3268453933031481124_a_o_o @ ( bNF_re2658327337197749847ring_a @ A2 )
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ord_less_set_int
        @ ord_le826492772435143505ring_a ) ) ).

% strict_subset_transfer
thf(fact_1090_Bex__transfer,axiom,
    ! [A2: int > int > $o] :
      ( bNF_re9006250432731904985nt_o_o @ ( bNF_rel_set_int_int @ A2 )
      @ ( bNF_re6378653760509651613_o_o_o
        @ ( bNF_re5089333283451836215nt_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
      @ bex_int
      @ bex_int ) ).

% Bex_transfer
thf(fact_1091_Bex__transfer,axiom,
    ! [A2: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( bNF_re5888346141626434055_a_o_o @ ( bNF_re4691038805385103495ring_a @ A2 )
      @ ( bNF_re3034707934920152030_o_o_o
        @ ( bNF_re507051067509135658_a_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
      @ bex_vec_int
      @ bex_ve7593156434936553806ring_a ) ).

% Bex_transfer
thf(fact_1092_Bex__transfer,axiom,
    ! [A2: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( bNF_re9140219897439888391_a_o_o @ ( bNF_re3622882117544951687ring_a @ A2 )
      @ ( bNF_re3523364678894640886_o_o_o
        @ ( bNF_re6153771816476299306_a_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
      @ bex_mat_int
      @ bex_ma3740078314013414594ring_a ) ).

% Bex_transfer
thf(fact_1093_Bex__transfer,axiom,
    ! [A2: int > finite_mod_ring_a > $o] :
      ( bNF_re3190460641836138519_a_o_o @ ( bNF_re2658327337197749847ring_a @ A2 )
      @ ( bNF_re8869226137141724030_o_o_o
        @ ( bNF_re8290846538823883642_a_o_o @ A2
          @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
        @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
      @ bex_int
      @ bex_Fi4430655179489311525ring_a ) ).

% Bex_transfer
thf(fact_1094_UNIV__M__Rel,axiom,
    bNF_re2658327337197749847ring_a @ ( vector3024231343486012919_Rel_a @ m ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ m ) @ top_to2069866484006881781ring_a ).

% UNIV_M_Rel
thf(fact_1095_fold__graph__transfer,axiom,
    ! [R: int > int > $o] :
      ( ( bi_unique_int_int @ R )
     => ( ( right_total_int_int @ R )
       => ( bNF_re7307145319025026467_int_o
          @ ( bNF_re711492959462206631nt_int @ R
            @ ( bNF_re4712519889275205905nt_int
              @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
              @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) ) )
          @ ( bNF_re2819329681884988983_int_o
            @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
            @ ( bNF_re2448385431412511203_int_o @ ( bNF_rel_set_int_int @ R )
              @ ( bNF_re5089333283451836215nt_o_o
                @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) ) )
          @ finite2438261569651828512nt_int
          @ finite2438261569651828512nt_int ) ) ) ).

% fold_graph_transfer
thf(fact_1096_fold__graph__transfer,axiom,
    ! [R: int > finite_mod_ring_a > $o] :
      ( ( bi_uni1022671006909063496ring_a @ R )
     => ( ( right_2909008500229168952ring_a @ R )
       => ( bNF_re1539142895448806181_int_o
          @ ( bNF_re6585011533847851626nt_int @ R
            @ ( bNF_re4712519889275205905nt_int
              @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
              @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) ) )
          @ ( bNF_re6175638012571284388_int_o
            @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
            @ ( bNF_re7589090870912319844_int_o @ ( bNF_re2658327337197749847ring_a @ R )
              @ ( bNF_re5089333283451836215nt_o_o
                @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) ) )
          @ finite2438261569651828512nt_int
          @ finite3020906298370517803_a_int ) ) ) ).

% fold_graph_transfer
thf(fact_1097_fold__graph__transfer,axiom,
    ! [R: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( bi_uni555094797115351544ring_a @ R )
     => ( ( right_7341149013462710248ring_a @ R )
       => ( bNF_re9120361678303120445_int_o
          @ ( bNF_re6494125082490456090nt_int @ R
            @ ( bNF_re4712519889275205905nt_int
              @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
              @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) ) )
          @ ( bNF_re5257061086073980398_int_o
            @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
            @ ( bNF_re5024843099796160128_int_o @ ( bNF_re4691038805385103495ring_a @ R )
              @ ( bNF_re5089333283451836215nt_o_o
                @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) ) )
          @ finite8948239645023668351nt_int
          @ finite6084671721606877602_a_int ) ) ) ).

% fold_graph_transfer
thf(fact_1098_fold__graph__transfer,axiom,
    ! [R: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( bi_uni8710310146129975544ring_a @ R )
     => ( ( right_6272992325622558440ring_a @ R )
       => ( bNF_re5968936872641161301_int_o
          @ ( bNF_re2807999186244189978nt_int @ R
            @ ( bNF_re4712519889275205905nt_int
              @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
              @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) ) )
          @ ( bNF_re4547852988781568774_int_o
            @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
            @ ( bNF_re6428356065892730240_int_o @ ( bNF_re3622882117544951687ring_a @ R )
              @ ( bNF_re5089333283451836215nt_o_o
                @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
                @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) ) ) )
          @ finite970587359342566411nt_int
          @ finite4811128581409355030_a_int ) ) ) ).

% fold_graph_transfer
thf(fact_1099_Lifting__Set_Ofold__transfer,axiom,
    ! [R: int > int > $o] :
      ( ( bi_unique_int_int @ R )
     => ( ( right_total_int_int @ R )
       => ( bNF_re6640931632208380629nt_int
          @ ( bNF_re711492959462206631nt_int @ R
            @ ( bNF_re4712519889275205905nt_int
              @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
              @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) ) )
          @ ( bNF_re8906821383403939603nt_int
            @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
            @ ( bNF_re2258174677021229181nt_int @ ( bNF_rel_set_int_int @ R )
              @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) ) )
          @ finite_fold_int_int
          @ finite_fold_int_int ) ) ) ).

% Lifting_Set.fold_transfer
thf(fact_1100_Lifting__Set_Ofold__transfer,axiom,
    ! [R: int > finite_mod_ring_a > $o] :
      ( ( bi_uni1022671006909063496ring_a @ R )
     => ( ( right_2909008500229168952ring_a @ R )
       => ( bNF_re8979805298816042759_a_int
          @ ( bNF_re6585011533847851626nt_int @ R
            @ ( bNF_re4712519889275205905nt_int
              @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
              @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) ) )
          @ ( bNF_re8097885208332794076_a_int
            @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
            @ ( bNF_re7749175998128367230nt_int @ ( bNF_re2658327337197749847ring_a @ R )
              @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) ) )
          @ finite_fold_int_int
          @ finite8560253868564812841_a_int ) ) ) ).

% Lifting_Set.fold_transfer
thf(fact_1101_Lifting__Set_Ofold__transfer,axiom,
    ! [R: vec_int > vec_Fi4296597256376197294ring_a > $o] :
      ( ( bi_uni555094797115351544ring_a @ R )
     => ( ( right_7341149013462710248ring_a @ R )
       => ( bNF_re1176066524844287475_a_int
          @ ( bNF_re6494125082490456090nt_int @ R
            @ ( bNF_re4712519889275205905nt_int
              @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
              @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) ) )
          @ ( bNF_re1694616526693603790_a_int
            @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
            @ ( bNF_re1646730027706931610nt_int @ ( bNF_re4691038805385103495ring_a @ R )
              @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) ) )
          @ finite38776084881886333nt_int
          @ finite717485091063693092_a_int ) ) ) ).

% Lifting_Set.fold_transfer
thf(fact_1102_Lifting__Set_Ofold__transfer,axiom,
    ! [R: mat_int > mat_Fi443519135453058082ring_a > $o] :
      ( ( bi_uni8710310146129975544ring_a @ R )
     => ( ( right_6272992325622558440ring_a @ R )
       => ( bNF_re5718981180934321651_a_int
          @ ( bNF_re2807999186244189978nt_int @ R
            @ ( bNF_re4712519889275205905nt_int
              @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
              @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) ) )
          @ ( bNF_re7619386655275720398_a_int
            @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
            @ ( bNF_re3929149045106647194nt_int @ ( bNF_re3622882117544951687ring_a @ R )
              @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) ) )
          @ finite1284495836055560201nt_int
          @ finite8667313987720946328_a_int ) ) ) ).

% Lifting_Set.fold_transfer
thf(fact_1103_injective__lim_Olim__inj__hom__count__vec,axiom,
    ! [A2: set_ve6125835690772642148ring_a,F: vec_Fi4296597256376197294ring_a > int,V: vec_ve5128822793932996635ring_a,X: vec_Fi4296597256376197294ring_a] :
      ( ( matrix5912936110441065912_a_int @ A2 @ F )
     => ( ( ord_le4912074394114046404ring_a @ ( vec_se3276121494910751146ring_a @ V ) @ A2 )
       => ( ( member1106766863034010949ring_a @ X @ A2 )
         => ( ( count_5653161720919377392ring_a @ ( matrix3196578302645433509ring_a @ V ) @ X )
            = ( count_int @ ( matrix7410472831921750563et_int @ ( map_ve8201388231321234785_a_int @ F @ V ) ) @ ( F @ X ) ) ) ) ) ) ).

% injective_lim.lim_inj_hom_count_vec
thf(fact_1104_injective__lim_Olim__inj__hom__count__vec,axiom,
    ! [A2: set_ma1095064855528551128ring_a,F: mat_Fi443519135453058082ring_a > int,V: vec_ma98051958688905615ring_a,X: mat_Fi443519135453058082ring_a] :
      ( ( matrix4639392970243543340_a_int @ A2 @ F )
     => ( ( ord_le9104675595724731192ring_a @ ( vec_se8646415410842387742ring_a @ V ) @ A2 )
       => ( ( member6477060778965647545ring_a @ X @ A2 )
         => ( ( count_1800083599996238180ring_a @ ( matrix8566872218577070105ring_a @ V ) @ X )
            = ( count_int @ ( matrix7410472831921750563et_int @ ( map_ve6927845091123712213_a_int @ F @ V ) ) @ ( F @ X ) ) ) ) ) ) ).

% injective_lim.lim_inj_hom_count_vec
thf(fact_1105_injective__lim_Olim__inj__hom__count__vec,axiom,
    ! [A2: set_nat,F: nat > int,V: vec_nat,X: nat] :
      ( ( matrix8534344249413481690at_int @ A2 @ F )
     => ( ( ord_less_eq_set_nat @ ( vec_set_nat @ V ) @ A2 )
       => ( ( member_nat @ X @ A2 )
         => ( ( count_nat @ ( matrix7412963302430800839et_nat @ V ) @ X )
            = ( count_int @ ( matrix7410472831921750563et_int @ ( map_vec_nat_int @ F @ V ) ) @ ( F @ X ) ) ) ) ) ) ).

% injective_lim.lim_inj_hom_count_vec
thf(fact_1106_injective__lim_Olim__inj__hom__count__vec,axiom,
    ! [A2: set_ve6125835690772642148ring_a,F: vec_Fi4296597256376197294ring_a > finite_mod_ring_a,V: vec_ve5128822793932996635ring_a,X: vec_Fi4296597256376197294ring_a] :
      ( ( matrix1241652128100816697ring_a @ A2 @ F )
     => ( ( ord_le4912074394114046404ring_a @ ( vec_se3276121494910751146ring_a @ V ) @ A2 )
       => ( ( member1106766863034010949ring_a @ X @ A2 )
         => ( ( count_5653161720919377392ring_a @ ( matrix3196578302645433509ring_a @ V ) @ X )
            = ( count_7654011124160779523ring_a @ ( matrix5859482775909362318ring_a @ ( map_ve2232039208261484752ring_a @ F @ V ) ) @ ( F @ X ) ) ) ) ) ) ).

% injective_lim.lim_inj_hom_count_vec
thf(fact_1107_injective__lim_Olim__inj__hom__count__vec,axiom,
    ! [A2: set_ma1095064855528551128ring_a,F: mat_Fi443519135453058082ring_a > finite_mod_ring_a,V: vec_ma98051958688905615ring_a,X: mat_Fi443519135453058082ring_a] :
      ( ( matrix9152092669702307013ring_a @ A2 @ F )
     => ( ( ord_le9104675595724731192ring_a @ ( vec_se8646415410842387742ring_a @ V ) @ A2 )
       => ( ( member6477060778965647545ring_a @ X @ A2 )
         => ( ( count_1800083599996238180ring_a @ ( matrix8566872218577070105ring_a @ V ) @ X )
            = ( count_7654011124160779523ring_a @ ( matrix5859482775909362318ring_a @ ( map_ve919107713008199260ring_a @ F @ V ) ) @ ( F @ X ) ) ) ) ) ) ).

% injective_lim.lim_inj_hom_count_vec
thf(fact_1108_injective__lim_Olim__inj__hom__count__vec,axiom,
    ! [A2: set_nat,F: nat > finite_mod_ring_a,V: vec_nat,X: nat] :
      ( ( matrix8712813245107848855ring_a @ A2 @ F )
     => ( ( ord_less_eq_set_nat @ ( vec_set_nat @ V ) @ A2 )
       => ( ( member_nat @ X @ A2 )
         => ( ( count_nat @ ( matrix7412963302430800839et_nat @ V ) @ X )
            = ( count_7654011124160779523ring_a @ ( matrix5859482775909362318ring_a @ ( map_ve7015489527027549230ring_a @ F @ V ) ) @ ( F @ X ) ) ) ) ) ) ).

% injective_lim.lim_inj_hom_count_vec
thf(fact_1109_injective__lim_Olim__inj__hom__count__vec,axiom,
    ! [A2: set_int,F: int > int,V: vec_int,X: int] :
      ( ( matrix310325924459760438nt_int @ A2 @ F )
     => ( ( ord_less_eq_set_int @ ( vec_set_int2 @ V ) @ A2 )
       => ( ( member_int @ X @ A2 )
         => ( ( count_int @ ( matrix7410472831921750563et_int @ V ) @ X )
            = ( count_int @ ( matrix7410472831921750563et_int @ ( map_vec_int_int @ F @ V ) ) @ ( F @ X ) ) ) ) ) ) ).

% injective_lim.lim_inj_hom_count_vec
thf(fact_1110_injective__lim_Olim__inj__hom__count__vec,axiom,
    ! [A2: set_int,F: int > finite_mod_ring_a,V: vec_int,X: int] :
      ( ( matrix3323680309137099579ring_a @ A2 @ F )
     => ( ( ord_less_eq_set_int @ ( vec_set_int2 @ V ) @ A2 )
       => ( ( member_int @ X @ A2 )
         => ( ( count_int @ ( matrix7410472831921750563et_int @ V ) @ X )
            = ( count_7654011124160779523ring_a @ ( matrix5859482775909362318ring_a @ ( map_ve1626356591056799954ring_a @ F @ V ) ) @ ( F @ X ) ) ) ) ) ) ).

% injective_lim.lim_inj_hom_count_vec
thf(fact_1111_injective__lim_Olim__inj__hom__count__vec,axiom,
    ! [A2: set_Fi2982333969990053029ring_a,F: finite_mod_ring_a > int,V: vec_Fi4296597256376197294ring_a,X: finite_mod_ring_a] :
      ( ( matrix1747488316349179541_a_int @ A2 @ F )
     => ( ( ord_le3976570047013626949ring_a @ ( vec_se7251946917745546697ring_a @ V ) @ A2 )
       => ( ( member3034048621153491438ring_a @ X @ A2 )
         => ( ( count_7654011124160779523ring_a @ ( matrix5859482775909362318ring_a @ V ) @ X )
            = ( count_int @ ( matrix7410472831921750563et_int @ ( map_ve50164598268879916_a_int @ F @ V ) ) @ ( F @ X ) ) ) ) ) ) ).

% injective_lim.lim_inj_hom_count_vec
thf(fact_1112_injective__lim_Olim__inj__hom__count__vec,axiom,
    ! [A2: set_Fi2982333969990053029ring_a,F: finite_mod_ring_a > finite_mod_ring_a,V: vec_Fi4296597256376197294ring_a,X: finite_mod_ring_a] :
      ( ( matrix2095080385522958492ring_a @ A2 @ F )
     => ( ( ord_le3976570047013626949ring_a @ ( vec_se7251946917745546697ring_a @ V ) @ A2 )
       => ( ( member3034048621153491438ring_a @ X @ A2 )
         => ( ( count_7654011124160779523ring_a @ ( matrix5859482775909362318ring_a @ V ) @ X )
            = ( count_7654011124160779523ring_a @ ( matrix5859482775909362318ring_a @ ( map_ve1378714242357356997ring_a @ F @ V ) ) @ ( F @ X ) ) ) ) ) ) ).

% injective_lim.lim_inj_hom_count_vec
thf(fact_1113_of__int__hom_Oinjective__lim__axioms,axiom,
    ! [Univ: set_int] : ( matrix274465127151157942t_real @ Univ @ ring_1_of_int_real ) ).

% of_int_hom.injective_lim_axioms
thf(fact_1114_fun_Orel__refl__strong,axiom,
    ! [X: int > int > $o,Ra: ( int > $o ) > ( int > $o ) > $o] :
      ( ! [Z4: int > $o] :
          ( ( member_int_o @ Z4 @ ( image_int_int_o @ X @ top_top_set_int ) )
         => ( Ra @ Z4 @ Z4 ) )
     => ( bNF_re3403563459893282935_int_o
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
        @ Ra
        @ X
        @ X ) ) ).

% fun.rel_refl_strong
thf(fact_1115_fun_Orel__refl__strong,axiom,
    ! [X: int > int > int,Ra: ( int > int ) > ( int > int ) > $o] :
      ( ! [Z4: int > int] :
          ( ( member_int_int @ Z4 @ ( image_int_int_int @ X @ top_top_set_int ) )
         => ( Ra @ Z4 @ Z4 ) )
     => ( bNF_re711492959462206631nt_int
        @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
        @ Ra
        @ X
        @ X ) ) ).

% fun.rel_refl_strong
thf(fact_1116_fun_Orel__refl__strong,axiom,
    ! [X: finite_mod_ring_a > int,Ra: int > int > $o] :
      ( ! [Z4: int] :
          ( ( member_int @ Z4 @ ( image_4238506139956901036_a_int @ X @ top_to2069866484006881781ring_a ) )
         => ( Ra @ Z4 @ Z4 ) )
     => ( bNF_re1123535563933081591nt_int
        @ ^ [Y2: finite_mod_ring_a,Z2: finite_mod_ring_a] : ( Y2 = Z2 )
        @ Ra
        @ X
        @ X ) ) ).

% fun.rel_refl_strong
thf(fact_1117_fun_Orel__refl__strong,axiom,
    ! [X: finite_mod_ring_a > vec_Fi4296597256376197294ring_a,Ra: vec_Fi4296597256376197294ring_a > vec_Fi4296597256376197294ring_a > $o] :
      ( ! [Z4: vec_Fi4296597256376197294ring_a] :
          ( ( member1106766863034010949ring_a @ Z4 @ ( image_6936539011840441134ring_a @ X @ top_to2069866484006881781ring_a ) )
         => ( Ra @ Z4 @ Z4 ) )
     => ( bNF_re529297735971823867ring_a
        @ ^ [Y2: finite_mod_ring_a,Z2: finite_mod_ring_a] : ( Y2 = Z2 )
        @ Ra
        @ X
        @ X ) ) ).

% fun.rel_refl_strong
thf(fact_1118_fun_Orel__refl__strong,axiom,
    ! [X: finite_mod_ring_a > mat_Fi443519135453058082ring_a,Ra: mat_Fi443519135453058082ring_a > mat_Fi443519135453058082ring_a > $o] :
      ( ! [Z4: mat_Fi443519135453058082ring_a] :
          ( ( member6477060778965647545ring_a @ Z4 @ ( image_3083460890917301922ring_a @ X @ top_to2069866484006881781ring_a ) )
         => ( Ra @ Z4 @ Z4 ) )
     => ( bNF_re7588912355631532003ring_a
        @ ^ [Y2: finite_mod_ring_a,Z2: finite_mod_ring_a] : ( Y2 = Z2 )
        @ Ra
        @ X
        @ X ) ) ).

% fun.rel_refl_strong
thf(fact_1119_fun_Orel__refl__strong,axiom,
    ! [X: finite_mod_ring_a > nat,Ra: nat > nat > $o] :
      ( ! [Z4: nat] :
          ( ( member_nat @ Z4 @ ( image_4240996610465951312_a_nat @ X @ top_to2069866484006881781ring_a ) )
         => ( Ra @ Z4 @ Z4 ) )
     => ( bNF_re126672322541077311at_nat
        @ ^ [Y2: finite_mod_ring_a,Z2: finite_mod_ring_a] : ( Y2 = Z2 )
        @ Ra
        @ X
        @ X ) ) ).

% fun.rel_refl_strong
thf(fact_1120_mat__mod__count__col__eq,axiom,
    ! [J: nat,M2: mat_int,X: int] :
      ( ( ord_less_nat @ J @ ( dim_col_int @ M2 ) )
     => ( ( ord_less_eq_set_int @ ( elements_mat_int @ M2 ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ m ) )
       => ( ( count_int @ ( matrix7410472831921750563et_int @ ( col_int @ ( vector6118640873655855782at_mod @ m @ M2 ) @ J ) ) @ X )
          = ( count_int @ ( matrix7410472831921750563et_int @ ( col_int @ M2 @ J ) ) @ X ) ) ) ) ).

% mat_mod_count_col_eq
thf(fact_1121_mat__mod__vec__mod__col,axiom,
    ! [J: nat,A2: mat_int] :
      ( ( ord_less_nat @ J @ ( dim_col_int @ A2 ) )
     => ( ( col_int @ ( vector6118640873655855782at_mod @ m @ A2 ) @ J )
        = ( vector1199560857299316530ec_mod @ m @ ( col_int @ A2 @ J ) ) ) ) ).

% mat_mod_vec_mod_col
thf(fact_1122_add__is__0,axiom,
    ! [M: nat,N: nat] :
      ( ( ( plus_plus_nat @ M @ N )
        = zero_zero_nat )
      = ( ( M = zero_zero_nat )
        & ( N = zero_zero_nat ) ) ) ).

% add_is_0
thf(fact_1123_Nat_Oadd__0__right,axiom,
    ! [M: nat] :
      ( ( plus_plus_nat @ M @ zero_zero_nat )
      = M ) ).

% Nat.add_0_right
thf(fact_1124_elems__mat__setv__col__0m,axiom,
    ! [J: nat,M2: mat_int] :
      ( ( ord_less_nat @ J @ ( dim_col_int @ M2 ) )
     => ( ( ord_less_eq_set_int @ ( elements_mat_int @ M2 ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ m ) )
       => ( ord_less_eq_set_int @ ( vec_set_int2 @ ( col_int @ M2 @ J ) ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ m ) ) ) ) ).

% elems_mat_setv_col_0m
thf(fact_1125_add__gr__0,axiom,
    ! [M: nat,N: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
      = ( ( ord_less_nat @ zero_zero_nat @ M )
        | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).

% add_gr_0
thf(fact_1126_mat__mod__dim_I2_J,axiom,
    ! [M2: mat_int] :
      ( ( dim_col_int @ ( vector6118640873655855782at_mod @ m @ M2 ) )
      = ( dim_col_int @ M2 ) ) ).

% mat_mod_dim(2)
thf(fact_1127_add__eq__self__zero,axiom,
    ! [M: nat,N: nat] :
      ( ( ( plus_plus_nat @ M @ N )
        = M )
     => ( N = zero_zero_nat ) ) ).

% add_eq_self_zero
thf(fact_1128_plus__nat_Oadd__0,axiom,
    ! [N: nat] :
      ( ( plus_plus_nat @ zero_zero_nat @ N )
      = N ) ).

% plus_nat.add_0
thf(fact_1129_Euclid__induct,axiom,
    ! [P: nat > nat > $o,A: nat,B: nat] :
      ( ! [A4: nat,B3: nat] :
          ( ( P @ A4 @ B3 )
          = ( P @ B3 @ A4 ) )
     => ( ! [A4: nat] : ( P @ A4 @ zero_zero_nat )
       => ( ! [A4: nat,B3: nat] :
              ( ( P @ A4 @ B3 )
             => ( P @ A4 @ ( plus_plus_nat @ A4 @ B3 ) ) )
         => ( P @ A @ B ) ) ) ) ).

% Euclid_induct
thf(fact_1130_mat__mod_Omat__mod__vec__mod__col,axiom,
    ! [M: int,J: nat,A2: mat_int] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( ord_less_nat @ J @ ( dim_col_int @ A2 ) )
       => ( ( col_int @ ( vector6118640873655855782at_mod @ M @ A2 ) @ J )
          = ( vector1199560857299316530ec_mod @ M @ ( col_int @ A2 @ J ) ) ) ) ) ).

% mat_mod.mat_mod_vec_mod_col
thf(fact_1131_less__imp__add__positive,axiom,
    ! [I: nat,J: nat] :
      ( ( ord_less_nat @ I @ J )
     => ? [K2: nat] :
          ( ( ord_less_nat @ zero_zero_nat @ K2 )
          & ( ( plus_plus_nat @ I @ K2 )
            = J ) ) ) ).

% less_imp_add_positive
thf(fact_1132_mat__mod_Omat__mod__dim_I2_J,axiom,
    ! [M: int,M2: mat_int] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( dim_col_int @ ( vector6118640873655855782at_mod @ M @ M2 ) )
        = ( dim_col_int @ M2 ) ) ) ).

% mat_mod.mat_mod_dim(2)
thf(fact_1133_plus__natural_Orsp,axiom,
    ( bNF_re1345281282404953727at_nat
    @ ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 )
    @ ( bNF_re5653821019739307937at_nat
      @ ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 )
      @ ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 ) )
    @ plus_plus_nat
    @ plus_plus_nat ) ).

% plus_natural.rsp
thf(fact_1134_mat__mod_Oelems__mat__setv__col__0m,axiom,
    ! [M: int,J: nat,M2: mat_int] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( ord_less_nat @ J @ ( dim_col_int @ M2 ) )
       => ( ( ord_less_eq_set_int @ ( elements_mat_int @ M2 ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ M ) )
         => ( ord_less_eq_set_int @ ( vec_set_int2 @ ( col_int @ M2 @ J ) ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ M ) ) ) ) ) ).

% mat_mod.elems_mat_setv_col_0m
thf(fact_1135_mat__mod_Omat__mod__count__col__eq,axiom,
    ! [M: int,J: nat,M2: mat_int,X: int] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( ord_less_nat @ J @ ( dim_col_int @ M2 ) )
       => ( ( ord_less_eq_set_int @ ( elements_mat_int @ M2 ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ M ) )
         => ( ( count_int @ ( matrix7410472831921750563et_int @ ( col_int @ ( vector6118640873655855782at_mod @ M @ M2 ) @ J ) ) @ X )
            = ( count_int @ ( matrix7410472831921750563et_int @ ( col_int @ M2 @ J ) ) @ X ) ) ) ) ) ).

% mat_mod.mat_mod_count_col_eq
thf(fact_1136_lt__dim__col__MM__Rel,axiom,
    ( bNF_re1243694822744574826_nat_o @ ( vector2798151085771547010_Rel_a @ m )
    @ ( bNF_re4705727531993890431at_o_o
      @ ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 )
      @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
    @ ^ [M5: mat_int,J2: nat] : ( ord_less_nat @ J2 @ ( dim_col_int @ M5 ) )
    @ ^ [M5: mat_Fi443519135453058082ring_a,J2: nat] : ( ord_less_nat @ J2 @ ( dim_co4406457559947111647ring_a @ M5 ) ) ) ).

% lt_dim_col_MM_Rel
thf(fact_1137_eq__dim__col__MM__Rel,axiom,
    ( bNF_re4847214273728626636at_nat @ ( vector2798151085771547010_Rel_a @ m )
    @ ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 )
    @ dim_col_int
    @ dim_co4406457559947111647ring_a ) ).

% eq_dim_col_MM_Rel
thf(fact_1138_to__int__mod__ring__plus,axiom,
    ! [X: finite_mod_ring_a,Y: finite_mod_ring_a] :
      ( ( finite1095367895020317408ring_a @ ( plus_p6165643967897163644ring_a @ X @ Y ) )
      = ( modulo_modulo_int @ ( plus_plus_int @ ( finite1095367895020317408ring_a @ X ) @ ( finite1095367895020317408ring_a @ Y ) ) @ m ) ) ).

% to_int_mod_ring_plus
thf(fact_1139_M__plus_I1_J,axiom,
    ! [X: int,Y: int] :
      ( ( vector_Matrix_mod_M @ m @ ( plus_plus_int @ ( vector_Matrix_mod_M @ m @ X ) @ Y ) )
      = ( vector_Matrix_mod_M @ m @ ( plus_plus_int @ X @ Y ) ) ) ).

% M_plus(1)
thf(fact_1140_M__plus_I2_J,axiom,
    ! [X: int,Y: int] :
      ( ( vector_Matrix_mod_M @ m @ ( plus_plus_int @ X @ ( vector_Matrix_mod_M @ m @ Y ) ) )
      = ( vector_Matrix_mod_M @ m @ ( plus_plus_int @ X @ Y ) ) ) ).

% M_plus(2)
thf(fact_1141_zle__add1__eq__le,axiom,
    ! [W: int,Z: int] :
      ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
      = ( ord_less_eq_int @ W @ Z ) ) ).

% zle_add1_eq_le
thf(fact_1142_int__le__real__less,axiom,
    ( ord_less_eq_int
    = ( ^ [N4: int,M7: int] : ( ord_less_real @ ( ring_1_of_int_real @ N4 ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M7 ) @ one_one_real ) ) ) ) ).

% int_le_real_less
thf(fact_1143_int__less__real__le,axiom,
    ( ord_less_int
    = ( ^ [N4: int,M7: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N4 ) @ one_one_real ) @ ( ring_1_of_int_real @ M7 ) ) ) ) ).

% int_less_real_le
thf(fact_1144_plus__int__code_I1_J,axiom,
    ! [K: int] :
      ( ( plus_plus_int @ K @ zero_zero_int )
      = K ) ).

% plus_int_code(1)
thf(fact_1145_plus__int__code_I2_J,axiom,
    ! [L: int] :
      ( ( plus_plus_int @ zero_zero_int @ L )
      = L ) ).

% plus_int_code(2)
thf(fact_1146_dup_Orsp,axiom,
    ( bNF_re4712519889275205905nt_int
    @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
    @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
    @ ^ [K3: int] : ( plus_plus_int @ K3 @ K3 )
    @ ^ [K3: int] : ( plus_plus_int @ K3 @ K3 ) ) ).

% dup.rsp
thf(fact_1147_odd__nonzero,axiom,
    ! [Z: int] :
      ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
     != zero_zero_int ) ).

% odd_nonzero
thf(fact_1148_int__ge__induct,axiom,
    ! [K: int,I: int,P: int > $o] :
      ( ( ord_less_eq_int @ K @ I )
     => ( ( P @ K )
       => ( ! [I4: int] :
              ( ( ord_less_eq_int @ K @ I4 )
             => ( ( P @ I4 )
               => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
         => ( P @ I ) ) ) ) ).

% int_ge_induct
thf(fact_1149_int__gr__induct,axiom,
    ! [K: int,I: int,P: int > $o] :
      ( ( ord_less_int @ K @ I )
     => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
       => ( ! [I4: int] :
              ( ( ord_less_int @ K @ I4 )
             => ( ( P @ I4 )
               => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
         => ( P @ I ) ) ) ) ).

% int_gr_induct
thf(fact_1150_zless__add1__eq,axiom,
    ! [W: int,Z: int] :
      ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
      = ( ( ord_less_int @ W @ Z )
        | ( W = Z ) ) ) ).

% zless_add1_eq
thf(fact_1151_plus__integer_Orsp,axiom,
    ( bNF_re711492959462206631nt_int
    @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
    @ ( bNF_re4712519889275205905nt_int
      @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
      @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) )
    @ plus_plus_int
    @ plus_plus_int ) ).

% plus_integer.rsp
thf(fact_1152_odd__less__0__iff,axiom,
    ! [Z: int] :
      ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
      = ( ord_less_int @ Z @ zero_zero_int ) ) ).

% odd_less_0_iff
thf(fact_1153_add1__zle__eq,axiom,
    ! [W: int,Z: int] :
      ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
      = ( ord_less_int @ W @ Z ) ) ).

% add1_zle_eq
thf(fact_1154_zless__imp__add1__zle,axiom,
    ! [W: int,Z: int] :
      ( ( ord_less_int @ W @ Z )
     => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).

% zless_imp_add1_zle
thf(fact_1155_le__imp__0__less,axiom,
    ! [Z: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ Z )
     => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).

% le_imp_0_less
thf(fact_1156_nat__add__distrib,axiom,
    ! [Z: int,Z5: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ Z )
     => ( ( ord_less_eq_int @ zero_zero_int @ Z5 )
       => ( ( nat2 @ ( plus_plus_int @ Z @ Z5 ) )
          = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z5 ) ) ) ) ) ).

% nat_add_distrib
thf(fact_1157_mod__pos__neg__trivial,axiom,
    ! [K: int,L: int] :
      ( ( ord_less_int @ zero_zero_int @ K )
     => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
       => ( ( modulo_modulo_int @ K @ L )
          = ( plus_plus_int @ K @ L ) ) ) ) ).

% mod_pos_neg_trivial
thf(fact_1158_inv__M__def,axiom,
    ! [X: int] :
      ( ( ( ord_less_eq_int @ ( plus_plus_int @ X @ X ) @ m )
       => ( ( vector2349909385534816566_inv_M @ m @ X )
          = X ) )
      & ( ~ ( ord_less_eq_int @ ( plus_plus_int @ X @ X ) @ m )
       => ( ( vector2349909385534816566_inv_M @ m @ X )
          = ( minus_minus_int @ X @ m ) ) ) ) ).

% inv_M_def
thf(fact_1159_ln__inj__iff,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ( ord_less_real @ zero_zero_real @ Y )
       => ( ( ( ln_ln_real @ X )
            = ( ln_ln_real @ Y ) )
          = ( X = Y ) ) ) ) ).

% ln_inj_iff
thf(fact_1160_ln__less__cancel__iff,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ( ord_less_real @ zero_zero_real @ Y )
       => ( ( ord_less_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) )
          = ( ord_less_real @ X @ Y ) ) ) ) ).

% ln_less_cancel_iff
thf(fact_1161_ln__le__cancel__iff,axiom,
    ! [X: real,Y: real] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ( ord_less_real @ zero_zero_real @ Y )
       => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) )
          = ( ord_less_eq_real @ X @ Y ) ) ) ) ).

% ln_le_cancel_iff
thf(fact_1162_ln__less__zero__iff,axiom,
    ! [X: real] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real )
        = ( ord_less_real @ X @ one_one_real ) ) ) ).

% ln_less_zero_iff
thf(fact_1163_ln__gt__zero__iff,axiom,
    ! [X: real] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
        = ( ord_less_real @ one_one_real @ X ) ) ) ).

% ln_gt_zero_iff
thf(fact_1164_ln__eq__zero__iff,axiom,
    ! [X: real] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ( ( ln_ln_real @ X )
          = zero_zero_real )
        = ( X = one_one_real ) ) ) ).

% ln_eq_zero_iff
thf(fact_1165_ln__ge__zero__iff,axiom,
    ! [X: real] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
        = ( ord_less_eq_real @ one_one_real @ X ) ) ) ).

% ln_ge_zero_iff
thf(fact_1166_ln__le__zero__iff,axiom,
    ! [X: real] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ zero_zero_real )
        = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).

% ln_le_zero_iff
thf(fact_1167_M__minus_I2_J,axiom,
    ! [X: int,Y: int] :
      ( ( vector_Matrix_mod_M @ m @ ( minus_minus_int @ X @ ( vector_Matrix_mod_M @ m @ Y ) ) )
      = ( vector_Matrix_mod_M @ m @ ( minus_minus_int @ X @ Y ) ) ) ).

% M_minus(2)
thf(fact_1168_M__minus_I1_J,axiom,
    ! [X: int,Y: int] :
      ( ( vector_Matrix_mod_M @ m @ ( minus_minus_int @ ( vector_Matrix_mod_M @ m @ X ) @ Y ) )
      = ( vector_Matrix_mod_M @ m @ ( minus_minus_int @ X @ Y ) ) ) ).

% M_minus(1)
thf(fact_1169_zle__diff1__eq,axiom,
    ! [W: int,Z: int] :
      ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
      = ( ord_less_int @ W @ Z ) ) ).

% zle_diff1_eq
thf(fact_1170_ln__add__one__self__le__self,axiom,
    ! [X: real] :
      ( ( ord_less_eq_real @ zero_zero_real @ X )
     => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).

% ln_add_one_self_le_self
thf(fact_1171_ln__bound,axiom,
    ! [X: real] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ X ) ) ).

% ln_bound
thf(fact_1172_ln__ge__zero__imp__ge__one,axiom,
    ! [X: real] :
      ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
     => ( ( ord_less_real @ zero_zero_real @ X )
       => ( ord_less_eq_real @ one_one_real @ X ) ) ) ).

% ln_ge_zero_imp_ge_one
thf(fact_1173_ln__less__self,axiom,
    ! [X: real] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ord_less_real @ ( ln_ln_real @ X ) @ X ) ) ).

% ln_less_self
thf(fact_1174_ln__gt__zero__imp__gt__one,axiom,
    ! [X: real] :
      ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
     => ( ( ord_less_real @ zero_zero_real @ X )
       => ( ord_less_real @ one_one_real @ X ) ) ) ).

% ln_gt_zero_imp_gt_one
thf(fact_1175_ln__less__zero,axiom,
    ! [X: real] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ( ord_less_real @ X @ one_one_real )
       => ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real ) ) ) ).

% ln_less_zero
thf(fact_1176_ln__gt__zero,axiom,
    ! [X: real] :
      ( ( ord_less_real @ one_one_real @ X )
     => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).

% ln_gt_zero
thf(fact_1177_minus__int__code_I1_J,axiom,
    ! [K: int] :
      ( ( minus_minus_int @ K @ zero_zero_int )
      = K ) ).

% minus_int_code(1)
thf(fact_1178_ln__ge__zero,axiom,
    ! [X: real] :
      ( ( ord_less_eq_real @ one_one_real @ X )
     => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).

% ln_ge_zero
thf(fact_1179_int__le__induct,axiom,
    ! [I: int,K: int,P: int > $o] :
      ( ( ord_less_eq_int @ I @ K )
     => ( ( P @ K )
       => ( ! [I4: int] :
              ( ( ord_less_eq_int @ I4 @ K )
             => ( ( P @ I4 )
               => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
         => ( P @ I ) ) ) ) ).

% int_le_induct
thf(fact_1180_int__less__induct,axiom,
    ! [I: int,K: int,P: int > $o] :
      ( ( ord_less_int @ I @ K )
     => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
       => ( ! [I4: int] :
              ( ( ord_less_int @ I4 @ K )
             => ( ( P @ I4 )
               => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
         => ( P @ I ) ) ) ) ).

% int_less_induct
thf(fact_1181_minus__integer_Orsp,axiom,
    ( bNF_re711492959462206631nt_int
    @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
    @ ( bNF_re4712519889275205905nt_int
      @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
      @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 ) )
    @ minus_minus_int
    @ minus_minus_int ) ).

% minus_integer.rsp
thf(fact_1182_int__induct,axiom,
    ! [P: int > $o,K: int,I: int] :
      ( ( P @ K )
     => ( ! [I4: int] :
            ( ( ord_less_eq_int @ K @ I4 )
           => ( ( P @ I4 )
             => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
       => ( ! [I4: int] :
              ( ( ord_less_eq_int @ I4 @ K )
             => ( ( P @ I4 )
               => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
         => ( P @ I ) ) ) ) ).

% int_induct
thf(fact_1183_mod__pos__geq,axiom,
    ! [L: int,K: int] :
      ( ( ord_less_int @ zero_zero_int @ L )
     => ( ( ord_less_eq_int @ L @ K )
       => ( ( modulo_modulo_int @ K @ L )
          = ( modulo_modulo_int @ ( minus_minus_int @ K @ L ) @ L ) ) ) ) ).

% mod_pos_geq
thf(fact_1184_image__add__int__atLeastLessThan,axiom,
    ! [L: int,U: int] :
      ( ( image_int_int
        @ ^ [X3: int] : ( plus_plus_int @ X3 @ L )
        @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
      = ( set_or4662586982721622107an_int @ L @ U ) ) ).

% image_add_int_atLeastLessThan
thf(fact_1185_diff__self__eq__0,axiom,
    ! [M: nat] :
      ( ( minus_minus_nat @ M @ M )
      = zero_zero_nat ) ).

% diff_self_eq_0
thf(fact_1186_diff__0__eq__0,axiom,
    ! [N: nat] :
      ( ( minus_minus_nat @ zero_zero_nat @ N )
      = zero_zero_nat ) ).

% diff_0_eq_0
thf(fact_1187_zero__less__diff,axiom,
    ! [N: nat,M: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
      = ( ord_less_nat @ M @ N ) ) ).

% zero_less_diff
thf(fact_1188_diff__is__0__eq_H,axiom,
    ! [M: nat,N: nat] :
      ( ( ord_less_eq_nat @ M @ N )
     => ( ( minus_minus_nat @ M @ N )
        = zero_zero_nat ) ) ).

% diff_is_0_eq'
thf(fact_1189_diff__is__0__eq,axiom,
    ! [M: nat,N: nat] :
      ( ( ( minus_minus_nat @ M @ N )
        = zero_zero_nat )
      = ( ord_less_eq_nat @ M @ N ) ) ).

% diff_is_0_eq
thf(fact_1190_diffs0__imp__equal,axiom,
    ! [M: nat,N: nat] :
      ( ( ( minus_minus_nat @ M @ N )
        = zero_zero_nat )
     => ( ( ( minus_minus_nat @ N @ M )
          = zero_zero_nat )
       => ( M = N ) ) ) ).

% diffs0_imp_equal
thf(fact_1191_minus__nat_Odiff__0,axiom,
    ! [M: nat] :
      ( ( minus_minus_nat @ M @ zero_zero_nat )
      = M ) ).

% minus_nat.diff_0
thf(fact_1192_diff__less,axiom,
    ! [N: nat,M: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ N )
     => ( ( ord_less_nat @ zero_zero_nat @ M )
       => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).

% diff_less
thf(fact_1193_diff__add__0,axiom,
    ! [N: nat,M: nat] :
      ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
      = zero_zero_nat ) ).

% diff_add_0
thf(fact_1194_ln__eq__minus__one,axiom,
    ! [X: real] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ( ( ln_ln_real @ X )
          = ( minus_minus_real @ X @ one_one_real ) )
       => ( X = one_one_real ) ) ) ).

% ln_eq_minus_one
thf(fact_1195_mod__if,axiom,
    ( modulo_modulo_nat
    = ( ^ [M7: nat,N4: nat] : ( if_nat @ ( ord_less_nat @ M7 @ N4 ) @ M7 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M7 @ N4 ) @ N4 ) ) ) ) ).

% mod_if
thf(fact_1196_le__mod__geq,axiom,
    ! [N: nat,M: nat] :
      ( ( ord_less_eq_nat @ N @ M )
     => ( ( modulo_modulo_nat @ M @ N )
        = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).

% le_mod_geq
thf(fact_1197_minus__natural_Orsp,axiom,
    ( bNF_re1345281282404953727at_nat
    @ ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 )
    @ ( bNF_re5653821019739307937at_nat
      @ ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 )
      @ ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 ) )
    @ minus_minus_nat
    @ minus_minus_nat ) ).

% minus_natural.rsp
thf(fact_1198_nat__diff__split,axiom,
    ! [P: nat > $o,A: nat,B: nat] :
      ( ( P @ ( minus_minus_nat @ A @ B ) )
      = ( ( ( ord_less_nat @ A @ B )
         => ( P @ zero_zero_nat ) )
        & ! [D3: nat] :
            ( ( A
              = ( plus_plus_nat @ B @ D3 ) )
           => ( P @ D3 ) ) ) ) ).

% nat_diff_split
thf(fact_1199_nat__diff__split__asm,axiom,
    ! [P: nat > $o,A: nat,B: nat] :
      ( ( P @ ( minus_minus_nat @ A @ B ) )
      = ( ~ ( ( ( ord_less_nat @ A @ B )
              & ~ ( P @ zero_zero_nat ) )
            | ? [D3: nat] :
                ( ( A
                  = ( plus_plus_nat @ B @ D3 ) )
                & ~ ( P @ D3 ) ) ) ) ) ).

% nat_diff_split_asm
thf(fact_1200_ln__le__minus__one,axiom,
    ! [X: real] :
      ( ( ord_less_real @ zero_zero_real @ X )
     => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).

% ln_le_minus_one
thf(fact_1201_nat__diff__distrib_H,axiom,
    ! [X: int,Y: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ X )
     => ( ( ord_less_eq_int @ zero_zero_int @ Y )
       => ( ( nat2 @ ( minus_minus_int @ X @ Y ) )
          = ( minus_minus_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).

% nat_diff_distrib'
thf(fact_1202_nat__diff__distrib,axiom,
    ! [Z5: int,Z: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ Z5 )
     => ( ( ord_less_eq_int @ Z5 @ Z )
       => ( ( nat2 @ ( minus_minus_int @ Z @ Z5 ) )
          = ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z5 ) ) ) ) ) ).

% nat_diff_distrib
thf(fact_1203_diff__nat__eq__if,axiom,
    ! [Z5: int,Z: int] :
      ( ( ( ord_less_int @ Z5 @ zero_zero_int )
       => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z5 ) )
          = ( nat2 @ Z ) ) )
      & ( ~ ( ord_less_int @ Z5 @ zero_zero_int )
       => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z5 ) )
          = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z5 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z5 ) ) ) ) ) ) ).

% diff_nat_eq_if
thf(fact_1204_Bolzano,axiom,
    ! [A: real,B: real,P: real > real > $o] :
      ( ( ord_less_eq_real @ A @ B )
     => ( ! [A4: real,B3: real,C3: real] :
            ( ( P @ A4 @ B3 )
           => ( ( P @ B3 @ C3 )
             => ( ( ord_less_eq_real @ A4 @ B3 )
               => ( ( ord_less_eq_real @ B3 @ C3 )
                 => ( P @ A4 @ C3 ) ) ) ) )
       => ( ! [X4: real] :
              ( ( ord_less_eq_real @ A @ X4 )
             => ( ( ord_less_eq_real @ X4 @ B )
               => ? [D4: real] :
                    ( ( ord_less_real @ zero_zero_real @ D4 )
                    & ! [A4: real,B3: real] :
                        ( ( ( ord_less_eq_real @ A4 @ X4 )
                          & ( ord_less_eq_real @ X4 @ B3 )
                          & ( ord_less_real @ ( minus_minus_real @ B3 @ A4 ) @ D4 ) )
                       => ( P @ A4 @ B3 ) ) ) ) )
         => ( P @ A @ B ) ) ) ) ).

% Bolzano
thf(fact_1205_nat0__intermed__int__val,axiom,
    ! [N: nat,F: nat > int,K: int] :
      ( ! [I4: nat] :
          ( ( ord_less_nat @ I4 @ N )
         => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I4 @ one_one_nat ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
     => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
       => ( ( ord_less_eq_int @ K @ ( F @ N ) )
         => ? [I4: nat] :
              ( ( ord_less_eq_nat @ I4 @ N )
              & ( ( F @ I4 )
                = K ) ) ) ) ) ).

% nat0_intermed_int_val
thf(fact_1206_zabs__less__one__iff,axiom,
    ! [Z: int] :
      ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
      = ( Z = zero_zero_int ) ) ).

% zabs_less_one_iff
thf(fact_1207_abs__integer_Orsp,axiom,
    ( bNF_re4712519889275205905nt_int
    @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
    @ ^ [Y2: int,Z2: int] : ( Y2 = Z2 )
    @ abs_abs_int
    @ abs_abs_int ) ).

% abs_integer.rsp
thf(fact_1208_abs__mod__less,axiom,
    ! [L: int,K: int] :
      ( ( L != zero_zero_int )
     => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L ) ) @ ( abs_abs_int @ L ) ) ) ).

% abs_mod_less
thf(fact_1209_nat__abs__triangle__ineq,axiom,
    ! [K: int,L: int] : ( ord_less_eq_nat @ ( nat2 @ ( abs_abs_int @ ( plus_plus_int @ K @ L ) ) ) @ ( plus_plus_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ).

% nat_abs_triangle_ineq
thf(fact_1210_nat__ivt__aux,axiom,
    ! [N: nat,F: nat > int,K: int] :
      ( ! [I4: nat] :
          ( ( ord_less_nat @ I4 @ N )
         => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
     => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
       => ( ( ord_less_eq_int @ K @ ( F @ N ) )
         => ? [I4: nat] :
              ( ( ord_less_eq_nat @ I4 @ N )
              & ( ( F @ I4 )
                = K ) ) ) ) ) ).

% nat_ivt_aux
thf(fact_1211_mat__mod__count__row__eq,axiom,
    ! [I: nat,M2: mat_int,X: int] :
      ( ( ord_less_nat @ I @ ( dim_row_int @ M2 ) )
     => ( ( ord_less_eq_set_int @ ( elements_mat_int @ M2 ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ m ) )
       => ( ( count_int @ ( matrix7410472831921750563et_int @ ( row_int @ ( vector6118640873655855782at_mod @ m @ M2 ) @ I ) ) @ X )
          = ( count_int @ ( matrix7410472831921750563et_int @ ( row_int @ M2 @ I ) ) @ X ) ) ) ) ).

% mat_mod_count_row_eq
thf(fact_1212_mat__mod__vec__mod__row,axiom,
    ! [I: nat,A2: mat_int] :
      ( ( ord_less_nat @ I @ ( dim_row_int @ A2 ) )
     => ( ( row_int @ ( vector6118640873655855782at_mod @ m @ A2 ) @ I )
        = ( vector1199560857299316530ec_mod @ m @ ( row_int @ A2 @ I ) ) ) ) ).

% mat_mod_vec_mod_row
thf(fact_1213_elems__mat__setv__row__0m,axiom,
    ! [I: nat,M2: mat_int] :
      ( ( ord_less_nat @ I @ ( dim_row_int @ M2 ) )
     => ( ( ord_less_eq_set_int @ ( elements_mat_int @ M2 ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ m ) )
       => ( ord_less_eq_set_int @ ( vec_set_int2 @ ( row_int @ M2 @ I ) ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ m ) ) ) ) ).

% elems_mat_setv_row_0m
thf(fact_1214_zero__less__Suc,axiom,
    ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).

% zero_less_Suc
thf(fact_1215_less__Suc0,axiom,
    ! [N: nat] :
      ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
      = ( N = zero_zero_nat ) ) ).

% less_Suc0
thf(fact_1216_mod__by__Suc__0,axiom,
    ! [M: nat] :
      ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
      = zero_zero_nat ) ).

% mod_by_Suc_0
thf(fact_1217_Suc__pred,axiom,
    ! [N: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ N )
     => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
        = N ) ) ).

% Suc_pred
thf(fact_1218_mat__mod__dim_I1_J,axiom,
    ! [M2: mat_int] :
      ( ( dim_row_int @ ( vector6118640873655855782at_mod @ m @ M2 ) )
      = ( dim_row_int @ M2 ) ) ).

% mat_mod_dim(1)
thf(fact_1219_nat__1,axiom,
    ( ( nat2 @ one_one_int )
    = ( suc @ zero_zero_nat ) ) ).

% nat_1
thf(fact_1220_Suc__diff__1,axiom,
    ! [N: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ N )
     => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
        = N ) ) ).

% Suc_diff_1
thf(fact_1221_one__less__nat__eq,axiom,
    ! [Z: int] :
      ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
      = ( ord_less_int @ one_one_int @ Z ) ) ).

% one_less_nat_eq
thf(fact_1222_nat_Odistinct_I1_J,axiom,
    ! [X22: nat] :
      ( zero_zero_nat
     != ( suc @ X22 ) ) ).

% nat.distinct(1)
thf(fact_1223_old_Onat_Odistinct_I2_J,axiom,
    ! [Nat: nat] :
      ( ( suc @ Nat )
     != zero_zero_nat ) ).

% old.nat.distinct(2)
thf(fact_1224_old_Onat_Odistinct_I1_J,axiom,
    ! [Nat: nat] :
      ( zero_zero_nat
     != ( suc @ Nat ) ) ).

% old.nat.distinct(1)
thf(fact_1225_nat_OdiscI,axiom,
    ! [Nat2: nat,X22: nat] :
      ( ( Nat2
        = ( suc @ X22 ) )
     => ( Nat2 != zero_zero_nat ) ) ).

% nat.discI
thf(fact_1226_old_Onat_Oexhaust,axiom,
    ! [Y: nat] :
      ( ( Y != zero_zero_nat )
     => ~ ! [Nat3: nat] :
            ( Y
           != ( suc @ Nat3 ) ) ) ).

% old.nat.exhaust
thf(fact_1227_nat__induct,axiom,
    ! [P: nat > $o,N: nat] :
      ( ( P @ zero_zero_nat )
     => ( ! [N2: nat] :
            ( ( P @ N2 )
           => ( P @ ( suc @ N2 ) ) )
       => ( P @ N ) ) ) ).

% nat_induct
thf(fact_1228_diff__induct,axiom,
    ! [P: nat > nat > $o,M: nat,N: nat] :
      ( ! [X4: nat] : ( P @ X4 @ zero_zero_nat )
     => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
       => ( ! [X4: nat,Y3: nat] :
              ( ( P @ X4 @ Y3 )
             => ( P @ ( suc @ X4 ) @ ( suc @ Y3 ) ) )
         => ( P @ M @ N ) ) ) ) ).

% diff_induct
thf(fact_1229_zero__induct,axiom,
    ! [P: nat > $o,K: nat] :
      ( ( P @ K )
     => ( ! [N2: nat] :
            ( ( P @ ( suc @ N2 ) )
           => ( P @ N2 ) )
       => ( P @ zero_zero_nat ) ) ) ).

% zero_induct
thf(fact_1230_Suc__neq__Zero,axiom,
    ! [M: nat] :
      ( ( suc @ M )
     != zero_zero_nat ) ).

% Suc_neq_Zero
thf(fact_1231_Zero__neq__Suc,axiom,
    ! [M: nat] :
      ( zero_zero_nat
     != ( suc @ M ) ) ).

% Zero_neq_Suc
thf(fact_1232_Zero__not__Suc,axiom,
    ! [M: nat] :
      ( zero_zero_nat
     != ( suc @ M ) ) ).

% Zero_not_Suc
thf(fact_1233_not0__implies__Suc,axiom,
    ! [N: nat] :
      ( ( N != zero_zero_nat )
     => ? [M4: nat] :
          ( N
          = ( suc @ M4 ) ) ) ).

% not0_implies_Suc
thf(fact_1234_exists__least__lemma,axiom,
    ! [P: nat > $o] :
      ( ~ ( P @ zero_zero_nat )
     => ( ? [X_12: nat] : ( P @ X_12 )
       => ? [N2: nat] :
            ( ~ ( P @ N2 )
            & ( P @ ( suc @ N2 ) ) ) ) ) ).

% exists_least_lemma
thf(fact_1235_zero__notin__Suc__image,axiom,
    ! [A2: set_nat] :
      ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A2 ) ) ).

% zero_notin_Suc_image
thf(fact_1236_mat__mod_Omat__mod__vec__mod__row,axiom,
    ! [M: int,I: nat,A2: mat_int] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( ord_less_nat @ I @ ( dim_row_int @ A2 ) )
       => ( ( row_int @ ( vector6118640873655855782at_mod @ M @ A2 ) @ I )
          = ( vector1199560857299316530ec_mod @ M @ ( row_int @ A2 @ I ) ) ) ) ) ).

% mat_mod.mat_mod_vec_mod_row
thf(fact_1237_gr0__conv__Suc,axiom,
    ! [N: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ N )
      = ( ? [M7: nat] :
            ( N
            = ( suc @ M7 ) ) ) ) ).

% gr0_conv_Suc
thf(fact_1238_gr0__implies__Suc,axiom,
    ! [N: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ N )
     => ? [M4: nat] :
          ( N
          = ( suc @ M4 ) ) ) ).

% gr0_implies_Suc
thf(fact_1239_less__Suc__eq__0__disj,axiom,
    ! [M: nat,N: nat] :
      ( ( ord_less_nat @ M @ ( suc @ N ) )
      = ( ( M = zero_zero_nat )
        | ? [J2: nat] :
            ( ( M
              = ( suc @ J2 ) )
            & ( ord_less_nat @ J2 @ N ) ) ) ) ).

% less_Suc_eq_0_disj
thf(fact_1240_add__is__1,axiom,
    ! [M: nat,N: nat] :
      ( ( ( plus_plus_nat @ M @ N )
        = ( suc @ zero_zero_nat ) )
      = ( ( ( M
            = ( suc @ zero_zero_nat ) )
          & ( N = zero_zero_nat ) )
        | ( ( M = zero_zero_nat )
          & ( N
            = ( suc @ zero_zero_nat ) ) ) ) ) ).

% add_is_1
thf(fact_1241_one__is__add,axiom,
    ! [M: nat,N: nat] :
      ( ( ( suc @ zero_zero_nat )
        = ( plus_plus_nat @ M @ N ) )
      = ( ( ( M
            = ( suc @ zero_zero_nat ) )
          & ( N = zero_zero_nat ) )
        | ( ( M = zero_zero_nat )
          & ( N
            = ( suc @ zero_zero_nat ) ) ) ) ) ).

% one_is_add
thf(fact_1242_One__nat__def,axiom,
    ( one_one_nat
    = ( suc @ zero_zero_nat ) ) ).

% One_nat_def
thf(fact_1243_mod__Suc,axiom,
    ! [M: nat,N: nat] :
      ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
          = N )
       => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
          = zero_zero_nat ) )
      & ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
         != N )
       => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
          = ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ).

% mod_Suc
thf(fact_1244_mod__induct,axiom,
    ! [P: nat > $o,N: nat,P5: nat,M: nat] :
      ( ( P @ N )
     => ( ( ord_less_nat @ N @ P5 )
       => ( ( ord_less_nat @ M @ P5 )
         => ( ! [N2: nat] :
                ( ( ord_less_nat @ N2 @ P5 )
               => ( ( P @ N2 )
                 => ( P @ ( modulo_modulo_nat @ ( suc @ N2 ) @ P5 ) ) ) )
           => ( P @ M ) ) ) ) ) ).

% mod_induct
thf(fact_1245_mod__Suc__le__divisor,axiom,
    ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N ) ) @ N ) ).

% mod_Suc_le_divisor
thf(fact_1246_mat__mod_Omat__mod__dim_I1_J,axiom,
    ! [M: int,M2: mat_int] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( dim_row_int @ ( vector6118640873655855782at_mod @ M @ M2 ) )
        = ( dim_row_int @ M2 ) ) ) ).

% mat_mod.mat_mod_dim(1)
thf(fact_1247_mod__Suc__Suc__eq,axiom,
    ! [M: nat,N: nat] :
      ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) @ N )
      = ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ N ) ) ).

% mod_Suc_Suc_eq
thf(fact_1248_mod__Suc__eq,axiom,
    ! [M: nat,N: nat] :
      ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) @ N )
      = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).

% mod_Suc_eq
thf(fact_1249_Suc_Orsp,axiom,
    ( bNF_re5653821019739307937at_nat
    @ ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 )
    @ ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 )
    @ suc
    @ suc ) ).

% Suc.rsp
thf(fact_1250_ex__least__nat__less,axiom,
    ! [P: nat > $o,N: nat] :
      ( ( P @ N )
     => ( ~ ( P @ zero_zero_nat )
       => ? [K2: nat] :
            ( ( ord_less_nat @ K2 @ N )
            & ! [I2: nat] :
                ( ( ord_less_eq_nat @ I2 @ K2 )
               => ~ ( P @ I2 ) )
            & ( P @ ( suc @ K2 ) ) ) ) ) ).

% ex_least_nat_less
thf(fact_1251_diff__Suc__less,axiom,
    ! [N: nat,I: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ N )
     => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I ) ) @ N ) ) ).

% diff_Suc_less
thf(fact_1252_nat__induct__non__zero,axiom,
    ! [N: nat,P: nat > $o] :
      ( ( ord_less_nat @ zero_zero_nat @ N )
     => ( ( P @ one_one_nat )
       => ( ! [N2: nat] :
              ( ( ord_less_nat @ zero_zero_nat @ N2 )
             => ( ( P @ N2 )
               => ( P @ ( suc @ N2 ) ) ) )
         => ( P @ N ) ) ) ) ).

% nat_induct_non_zero
thf(fact_1253_mat__mod_Oelems__mat__setv__row__0m,axiom,
    ! [M: int,I: nat,M2: mat_int] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( ord_less_nat @ I @ ( dim_row_int @ M2 ) )
       => ( ( ord_less_eq_set_int @ ( elements_mat_int @ M2 ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ M ) )
         => ( ord_less_eq_set_int @ ( vec_set_int2 @ ( row_int @ M2 @ I ) ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ M ) ) ) ) ) ).

% mat_mod.elems_mat_setv_row_0m
thf(fact_1254_Suc__diff__eq__diff__pred,axiom,
    ! [N: nat,M: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ N )
     => ( ( minus_minus_nat @ ( suc @ M ) @ N )
        = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).

% Suc_diff_eq_diff_pred
thf(fact_1255_Suc__pred_H,axiom,
    ! [N: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ N )
     => ( N
        = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).

% Suc_pred'
thf(fact_1256_add__eq__if,axiom,
    ( plus_plus_nat
    = ( ^ [M7: nat,N4: nat] : ( if_nat @ ( M7 = zero_zero_nat ) @ N4 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M7 @ one_one_nat ) @ N4 ) ) ) ) ) ).

% add_eq_if
thf(fact_1257_mat__mod_Omat__mod__count__row__eq,axiom,
    ! [M: int,I: nat,M2: mat_int,X: int] :
      ( ( vector2311527483241216340at_mod @ M )
     => ( ( ord_less_nat @ I @ ( dim_row_int @ M2 ) )
       => ( ( ord_less_eq_set_int @ ( elements_mat_int @ M2 ) @ ( set_or4662586982721622107an_int @ zero_zero_int @ M ) )
         => ( ( count_int @ ( matrix7410472831921750563et_int @ ( row_int @ ( vector6118640873655855782at_mod @ M @ M2 ) @ I ) ) @ X )
            = ( count_int @ ( matrix7410472831921750563et_int @ ( row_int @ M2 @ I ) ) @ X ) ) ) ) ) ).

% mat_mod.mat_mod_count_row_eq
thf(fact_1258_Suc__nat__eq__nat__zadd1,axiom,
    ! [Z: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ Z )
     => ( ( suc @ ( nat2 @ Z ) )
        = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).

% Suc_nat_eq_nat_zadd1
thf(fact_1259_nat__intermed__int__val,axiom,
    ! [M: nat,N: nat,F: nat > int,K: int] :
      ( ! [I4: nat] :
          ( ( ( ord_less_eq_nat @ M @ I4 )
            & ( ord_less_nat @ I4 @ N ) )
         => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
     => ( ( ord_less_eq_nat @ M @ N )
       => ( ( ord_less_eq_int @ ( F @ M ) @ K )
         => ( ( ord_less_eq_int @ K @ ( F @ N ) )
           => ? [I4: nat] :
                ( ( ord_less_eq_nat @ M @ I4 )
                & ( ord_less_eq_nat @ I4 @ N )
                & ( ( F @ I4 )
                  = K ) ) ) ) ) ) ).

% nat_intermed_int_val
thf(fact_1260_lt__dim__row__MM__Rel,axiom,
    ( bNF_re1243694822744574826_nat_o @ ( vector2798151085771547010_Rel_a @ m )
    @ ( bNF_re4705727531993890431at_o_o
      @ ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 )
      @ ^ [Y2: $o,Z2: $o] : ( Y2 = Z2 ) )
    @ ^ [M5: mat_int,I5: nat] : ( ord_less_nat @ I5 @ ( dim_row_int @ M5 ) )
    @ ^ [M5: mat_Fi443519135453058082ring_a,I5: nat] : ( ord_less_nat @ I5 @ ( dim_ro5001971067571046597ring_a @ M5 ) ) ) ).

% lt_dim_row_MM_Rel
thf(fact_1261_eq__dim__row__MM__Rel,axiom,
    ( bNF_re4847214273728626636at_nat @ ( vector2798151085771547010_Rel_a @ m )
    @ ^ [Y2: nat,Z2: nat] : ( Y2 = Z2 )
    @ dim_row_int
    @ dim_ro5001971067571046597ring_a ) ).

% eq_dim_row_MM_Rel
thf(fact_1262_lemma__interval,axiom,
    ! [A: real,X: real,B: real] :
      ( ( ord_less_real @ A @ X )
     => ( ( ord_less_real @ X @ B )
       => ? [D5: real] :
            ( ( ord_less_real @ zero_zero_real @ D5 )
            & ! [Y4: real] :
                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y4 ) ) @ D5 )
               => ( ( ord_less_eq_real @ A @ Y4 )
                  & ( ord_less_eq_real @ Y4 @ B ) ) ) ) ) ) ).

% lemma_interval
thf(fact_1263_lemma__interval__lt,axiom,
    ! [A: real,X: real,B: real] :
      ( ( ord_less_real @ A @ X )
     => ( ( ord_less_real @ X @ B )
       => ? [D5: real] :
            ( ( ord_less_real @ zero_zero_real @ D5 )
            & ! [Y4: real] :
                ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y4 ) ) @ D5 )
               => ( ( ord_less_real @ A @ Y4 )
                  & ( ord_less_real @ Y4 @ B ) ) ) ) ) ) ).

% lemma_interval_lt
thf(fact_1264_ex__leq__Suc,axiom,
    ! [J: nat,P: nat > $o] :
      ( ( ? [I5: nat] :
            ( ( ord_less_eq_nat @ I5 @ ( suc @ J ) )
            & ( P @ I5 ) ) )
      = ( ( P @ zero_zero_nat )
        | ? [I5: nat] :
            ( ( ord_less_eq_nat @ I5 @ J )
            & ( P @ ( suc @ I5 ) ) ) ) ) ).

% ex_leq_Suc
thf(fact_1265_le__Suc__eq_H,axiom,
    ! [X: nat,Y: nat] :
      ( ( ord_less_eq_nat @ X @ ( suc @ Y ) )
      = ( ( X = zero_zero_nat )
        | ? [X9: nat] :
            ( ( X
              = ( suc @ X9 ) )
            & ( ord_less_eq_nat @ X9 @ Y ) ) ) ) ).

% le_Suc_eq'
thf(fact_1266_ex__less__Suc,axiom,
    ! [J: nat,P: nat > $o] :
      ( ( ? [I5: nat] :
            ( ( ord_less_nat @ I5 @ ( suc @ J ) )
            & ( P @ I5 ) ) )
      = ( ( P @ zero_zero_nat )
        | ? [I5: nat] :
            ( ( ord_less_nat @ I5 @ J )
            & ( P @ ( suc @ I5 ) ) ) ) ) ).

% ex_less_Suc
thf(fact_1267_all__less__two,axiom,
    ! [P: nat > $o] :
      ( ( ! [I5: nat] :
            ( ( ord_less_nat @ I5 @ ( suc @ ( suc @ zero_zero_nat ) ) )
           => ( P @ I5 ) ) )
      = ( ( P @ zero_zero_nat )
        & ( P @ ( suc @ zero_zero_nat ) ) ) ) ).

% all_less_two
thf(fact_1268_all__Suc__conv,axiom,
    ! [N: nat,P: nat > $o] :
      ( ( ! [I5: nat] :
            ( ( ord_less_nat @ I5 @ ( suc @ N ) )
           => ( P @ I5 ) ) )
      = ( ( P @ zero_zero_nat )
        & ! [I5: nat] :
            ( ( ord_less_nat @ I5 @ N )
           => ( P @ ( suc @ I5 ) ) ) ) ) ).

% all_Suc_conv
thf(fact_1269_ex__Suc__conv,axiom,
    ! [N: nat,P: nat > $o] :
      ( ( ? [I5: nat] :
            ( ( ord_less_nat @ I5 @ ( suc @ N ) )
            & ( P @ I5 ) ) )
      = ( ( P @ zero_zero_nat )
        | ? [I5: nat] :
            ( ( ord_less_nat @ I5 @ N )
            & ( P @ ( suc @ I5 ) ) ) ) ) ).

% ex_Suc_conv
thf(fact_1270_real__add__minus__iff,axiom,
    ! [X: real,A: real] :
      ( ( ( plus_plus_real @ X @ ( uminus_uminus_real @ A ) )
        = zero_zero_real )
      = ( X = A ) ) ).

% real_add_minus_iff
thf(fact_1271_uminus__int__code_I1_J,axiom,
    ( ( uminus_uminus_int @ zero_zero_int )
    = zero_zero_int ) ).

% uminus_int_code(1)
thf(fact_1272_zmod__zminus2__not__zero,axiom,
    ! [K: int,L: int] :
      ( ( ( modulo_modulo_int @ K @ ( uminus_uminus_int @ L ) )
       != zero_zero_int )
     => ( ( modulo_modulo_int @ K @ L )
       != zero_zero_int ) ) ).

% zmod_zminus2_not_zero
thf(fact_1273_zmod__zminus1__not__zero,axiom,
    ! [K: int,L: int] :
      ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
       != zero_zero_int )
     => ( ( modulo_modulo_int @ K @ L )
       != zero_zero_int ) ) ).

% zmod_zminus1_not_zero

% Helper facts (9)
thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
    ! [X: int,Y: int] :
      ( ( if_int @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
    ! [X: int,Y: int] :
      ( ( if_int @ $true @ X @ Y )
      = X ) ).

thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
    ! [X: nat,Y: nat] :
      ( ( if_nat @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
    ! [X: nat,Y: nat] :
      ( ( if_nat @ $true @ X @ Y )
      = X ) ).

thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
    ! [X: real,Y: real] :
      ( ( if_real @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
    ! [X: real,Y: real] :
      ( ( if_real @ $true @ X @ Y )
      = X ) ).

thf(help_If_3_1_If_001t__Finite____Field__Omod____ring_Itf__a_J_T,axiom,
    ! [P: $o] :
      ( ( P = $true )
      | ( P = $false ) ) ).

thf(help_If_2_1_If_001t__Finite____Field__Omod____ring_Itf__a_J_T,axiom,
    ! [X: finite_mod_ring_a,Y: finite_mod_ring_a] :
      ( ( if_Finite_mod_ring_a @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__Finite____Field__Omod____ring_Itf__a_J_T,axiom,
    ! [X: finite_mod_ring_a,Y: finite_mod_ring_a] :
      ( ( if_Finite_mod_ring_a @ $true @ X @ Y )
      = X ) ).

% Conjectures (1)
thf(conj_0,conjecture,
    ! [X4: vec_int,Y3: vec_Fi4296597256376197294ring_a] :
      ( ( ( vector1199560857299316530ec_mod @ m @ X4 )
       != ( map_ve50164598268879916_a_int @ finite1095367895020317408ring_a @ Y3 ) )
      | ( ( matrix7410472831921750563et_int @ ( vector1199560857299316530ec_mod @ m @ X4 ) )
        = ( image_7357852445201009398_a_int @ finite1095367895020317408ring_a @ ( matrix5859482775909362318ring_a @ Y3 ) ) ) ) ).

%------------------------------------------------------------------------------